TY - CHAP TI - Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules AU - Gasparovic, Ellen AU - Gommel, Maria AU - Purvine, Emilie AU - Sazdanovic, Radmila AU - Wang, Bei AU - Wang, Yusu AU - Ziegelmeier, Lori T2 - Association for Women in Mathematics Series PY - 2022/// DO - 10.1007/978-3-030-95519-9_3 UR - http://dx.doi.org/10.1007/978-3-030-95519-9_3 ER - TY - JOUR TI - GFINNs: GENERIC formalism informed neural networks for deterministic and stochastic dynamical systems AU - Zhang, Zhen AU - Shin, Yeonjong AU - Karniadakis, George Em T2 - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences AB - We propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism. GFINNs comprise two modules, each of which contains two components. We model each component using a neural network whose architecture is designed to satisfy the required conditions. The component-wise architecture design provides flexible ways of leveraging available physics information into neural networks. We prove theoretically that GFINNs are sufficiently expressive to learn the underlying equations, hence establishing the universal approximation theorem. We demonstrate the performance of GFINNs in three simulation problems: gas containers exchanging heat and volume, thermoelastic double pendulum and the Langevin dynamics. In all the examples, GFINNs outperform existing methods, hence demonstrating good accuracy in predictions for both deterministic and stochastic systems. This article is part of the theme issue 'Data-driven prediction in dynamical systems'. DA - 2022/6/20/ PY - 2022/6/20/ DO - 10.1098/rsta.2021.0207 VL - 380 IS - 2229 SN - 1364-503X 1471-2962 UR - http://dx.doi.org/10.1098/rsta.2021.0207 ER - TY - JOUR TI - Effects of depth, width, and initialization: A convergence analysis of layer-wise training for deep linear neural networks AU - Shin, Yeonjong T2 - Analysis and Applications AB - Deep neural networks have been used in various machine learning applications and achieved tremendous empirical successes. However, training deep neural networks is a challenging task. Many alternatives have been proposed in place of end-to-end back-propagation. Layer-wise training is one of them, which trains a single layer at a time, rather than trains the whole layers simultaneously. In this paper, we study a layer-wise training using a block coordinate gradient descent (BCGD) for deep linear networks. We establish a general convergence analysis of BCGD and found the optimal learning rate, which results in the fastest decrease in the loss. We identify the effects of depth, width, and initialization. When the orthogonal-like initialization is employed, we show that the width of intermediate layers plays no role in gradient-based training beyond a certain threshold. Besides, we found that the use of deep networks could drastically accelerate convergence when it is compared to those of a depth 1 network, even when the computational cost is considered. Numerical examples are provided to justify our theoretical findings and demonstrate the performance of layer-wise training by BCGD. DA - 2022/1// PY - 2022/1// DO - 10.1142/s0219530521500263 VL - 20 IS - 01 SP - 73-119 UR - http://dx.doi.org/10.1142/s0219530521500263 ER - TY - JOUR TI - Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions AU - Jagtap, Ameya D. AU - Shin, Yeonjong AU - Kawaguchi, Kenji AU - Karniadakis, George Em T2 - Neurocomputing AB - We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions. KNNs employ the Kronecker product, which provides an efficient way of constructing a very wide network while keeping the number of parameters low. Our theoretical analysis reveals that under suitable conditions, KNNs induce a faster decay of the loss than that by the feed-forward networks. This is also empirically verified through a set of computational examples. Furthermore, under certain technical assumptions, we establish global convergence of gradient descent for KNNs. As a specific case, we propose the Rowdy activation function that is designed to get rid of any saturation region by injecting sinusoidal fluctuations, which include trainable parameters. The proposed Rowdy activation function can be employed in any neural network architecture like feed-forward neural networks, Recurrent neural networks, Convolutional neural networks etc. The effectiveness of KNNs with Rowdy activation is demonstrated through various computational experiments including function approximation using feed-forward neural networks, solution inference of partial differential equations using the physics-informed neural networks, and standard deep learning benchmark problems using convolutional and fully-connected neural networks. DA - 2022/1// PY - 2022/1// DO - 10.1016/j.neucom.2021.10.036 VL - 468 SP - 165-180 UR - http://dx.doi.org/10.1016/j.neucom.2021.10.036 ER - TY - JOUR TI - Approximation rates of DeepONets for learning operators arising from advection–diffusion equations AU - Deng, Beichuan AU - Shin, Yeonjong AU - Lu, Lu AU - zhang, AU - Karniadakis, George T2 - Neural Networks AB - We present the analysis of approximation rates of operator learning in Chen and Chen (1995) and Lu et al. (2021), where continuous operators are approximated by a sum of products of branch and trunk networks. In this work, we consider the rates of learning solution operators from both linear and nonlinear advection-diffusion equations with or without reaction. We find that the approximation rates depend on the architecture of branch networks as well as the smoothness of inputs and outputs of solution operators. DA - 2022/9// PY - 2022/9// DO - 10.1016/j.neunet.2022.06.019 VL - 153 SP - 411-426 UR - http://dx.doi.org/10.1016/j.neunet.2022.06.019 ER - TY - JOUR TI - Active Neuron Least Squares: A training method for multivariate rectified neural networks AU - Ainsworth, Mark AU - Shin, Yeonjong T2 - SIAM Journal on Scientific Computing AB - We propose a novel training method for multivariate two-layer rectified neural networks. The core mechanism is the augmentation of standard gradient descent direction by the inclusion of search vectors which are chosen to explicitly adjust the activation patterns of the neurons. Active neuron least squares (ANLS) proceeds iteratively with each iteration consisting of three steps: (a) generation of search vectors (including ones designed to change activation patterns), (b) identification of the candidate weights, and (c) a decision on which candidate weights are selected for update. We develop stable and efficient procedures for implementing the method. Numerical examples are provided that demonstrate the effectiveness of ANLS compared with existing popular approaches on various learning tasks ranging from function approximation to solving PDEs. DA - 2022/8// PY - 2022/8// DO - 10.1137/21m1460764 VL - 44 IS - 4 SP - A2253-A2275 UR - http://dx.doi.org/10.1137/21m1460764 ER - TY - JOUR TI - The Carleman-Newton method to globally reconstruct a source term for nonlinear parabolic equation AU - Abhishek, Anuj AU - Le, Thuy AU - Nguyen, Loc AU - Khan, Taufiquar AB - We propose to combine the Carleman estimate and the Newton method to solve an inverse source problem for nonlinear parabolic equations from lateral boundary data. The stability of this inverse source problem is conditionally logarithmic. Hence, numerical results due to the conventional least squares optimization might not be reliable. In order to enhance the stability, we approximate this problem by truncating the high frequency terms of the Fourier series that represents the solution to the governing equation. By this, we derive a system of nonlinear elliptic PDEs whose solution consists of Fourier coefficients of the solution to the parabolic governing equation. We solve this system by the Carleman-Newton method. The Carleman-Newton method is a newly developed algorithm to solve nonlinear PDEs. The strength of the Carleman-Newton method includes (1) no good initial guess is required and (2) the computational cost is not expensive. These features are rigorously proved. Having the solutions to this system in hand, we can directly compute the solution to the proposed inverse problem. Some numerical examples are displayed. DA - 2022/// PY - 2022/// DO - 10.48550/ARXIV.2209.08011 UR - https://arxiv.org/abs/2209.08011 ER - TY - JOUR TI - The Gradient Descent Method for the Convexification to Solve Boundary Value Problems of Quasi-Linear PDEs and a Coefficient Inverse Problem AU - Le, Thuy T. AU - Nguyen, Loc T2 - Journal of Scientific Computing AB - We study the global convergence of the gradient descent method of the minimization of strictly convex functionals on an open and bounded set of a Hilbert space. Such results are unknown for this type of sets, unlike the case of the entire Hilbert space. Then, we use our result to establish a general framework to numerically solve boundary value problems for quasi-linear partial differential equations with noisy Cauchy data. The procedure involves the use of Carleman weight functions to convexify a cost functional arising from the given boundary value problem and thus to ensure the convergence of the gradient descent method above. We prove the global convergence of the method as the noise tends to 0. The convergence rate is Lipschitz. Next, we apply this method to solve a highly nonlinear and severely ill-posed coefficient inverse problem, which is the so-called back scattering inverse problem. This problem has many real-world applications. Numerical examples are presented. DA - 2022/// PY - 2022/// DO - 10.1007/s10915-022-01846-3 VL - 91 IS - 3 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85129123569&partnerID=MN8TOARS ER - TY - JOUR TI - The Carleman convexification method for Hamilton-Jacobi equations on the whole space AU - Le, H.P.N. AU - Le, T.T. AU - Nguyen, L.H. T2 - arXiv AB - We propose a new globally convergent numerical method to solve Hamilton-Jacobi equations in $\mathbb{R}^d$, $d \geq 1$. This method is named as the Carleman convexification method. By Carleman convexification, we mean that we use a Carleman weight function to convexify the conventional least squares mismatch functional. We will prove a new version of the convexification theorem guaranteeing that the mismatch functional involving the Carleman weight function is strictly convex and, therefore, has a unique minimizer. Moreover, a consequence of our convexification theorem guarantees that the minimizer of the Carleman weighted mismatch functional is an approximation of the viscosity solution we want to compute. Some numerical results in 1D and 2D will be presented. DA - 2022/// PY - 2022/// DO - 10.48550/arXiv.2206.09824 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85133374996&partnerID=MN8TOARS ER - TY - JOUR TI - Global reconstruction of initial conditions of nonlinear parabolic equations via the Carleman-contraction method AU - Le, T.T. T2 - arXiv AB - We propose a global convergent numerical method to reconstruct the initial condition of a nonlinear parabolic equation from the measurement of both Dirichlet and Neumann data on the boundary of a bounded domain. The first step in our method is to derive, from the nonlinear governing parabolic equation, a nonlinear systems of elliptic partial differential equations (PDEs) whose solution yields directly the solution of the inverse source problem. We then establish a contraction mapping-like iterative scheme to solve this system. The convergence of this iterative scheme is rigorously proved by employing a Carleman estimate and the argument in the proof of the traditional contraction mapping principle. This convergence is fast in both theoretical and numerical senses. Moreover, our method, unlike the methods based on optimization, does not require a good initial guess of the true solution. Numerical examples are presented to verify these results. DA - 2022/// PY - 2022/// DO - 10.48550/arXiv.2205.10648 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85131640139&partnerID=MN8TOARS ER - TY - JOUR TI - Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data AU - Le, T.T. AU - Klibanov, M.V. AU - Nguyen, L.H. AU - Sullivan, A. AU - Nguyen, L. T2 - Inverse Problems AB - Abstract It is demonstrated that the contraction mapping principle with the involvement of a Carleman weight function works for a coefficient inverse problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the corresponding numerical method is established. Numerical studies for both computationally simulated and experimentally collected data are presented. The experimental part is concerned with the problem of computing dielectric constants of explosive-like targets in the standoff mode using severely underdetermined data. DA - 2022/// PY - 2022/// DO - 10.1088/1361-6420/ac50b8 VL - 38 IS - 4 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85126525729&partnerID=MN8TOARS ER - TY - JOUR TI - A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data AU - Le, T.T.T. AU - Nguyen, L.H. T2 - Journal of Inverse and Ill-Posed Problems AB - Abstract We propose a new numerical method for the solution of the problem of the reconstruction of the initial condition of a quasilinear parabolic equation from the measurements of both Dirichlet and Neumann data on the boundary of a bounded domain. Although this problem is highly nonlinear, we do not require an initial guess of the true solution. The key in our method is the derivation of a boundary value problem for a system of coupled quasilinear elliptic equations whose solution is the vector function of the spatially dependent Fourier coefficients of the solution to the governing parabolic equation. We solve this problem by an iterative method. The global convergence of the system is rigorously established using a Carleman estimate. Numerical examples are presented. DA - 2022/// PY - 2022/// DO - 10.1515/jiip-2020-0028 VL - 30 IS - 2 SP - 265-286 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85085658625&partnerID=MN8TOARS ER - TY - JOUR TI - A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications AU - Le, Thuy T. AU - Nguyen, Loc H. AU - Tran, Hung V. T2 - Computers & Mathematics with Applications AB - We propose a new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic PDE. The main idea is to repeatedly solve its linearization by using the quasi-reversibility method with a suitable Carleman weight function. The presence of the Carleman weight function allows us to employ a Carleman estimate to prove the convergence of the sequence generated by the iterative scheme above to the desired solution. The convergence of the iteration is fast at an exponential rate without the need of an initial good guess. We apply this method to compute solutions to some general quasilinear elliptic equations and a large class of first-order Hamilton-Jacobi equations. Numerical results are presented. DA - 2022/11// PY - 2022/11// DO - 10.1016/j.camwa.2022.08.032 VL - 125 SP - 13-24 UR - https://doi.org/10.1016/j.camwa.2022.08.032 ER - TY - BOOK TI - Integration in Finite Terms: Fundamental Sources T2 - Texts & Monographs in Symbolic Computation A3 - Raab, Clemens G. A3 - Singer, Michael F. DA - 2022/// PY - 2022/// DO - 10.1007/978-3-030-98767-1 PB - Springer International Publishing SN - 9783030987664 9783030987671 UR - http://dx.doi.org/10.1007/978-3-030-98767-1 ER - TY - CONF TI - Solving Linear Systems on a GPU with Hierarchically Off-Diagonal Low-Rank Approximations AU - Chen, Chao AU - Martinsson, Per-Gunnar T2 - SC22: International Conference for High Performance Computing, Networking, Storage and Analysis AB - We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the factorization of many large sparse matrices. The coefficient matrices are often data-sparse in the sense that their off-diagonal blocks have low numerical ranks; specifically, we focus on “hierarchically off-diagonal low-rank (HODLR)” matrices. We introduce algorithms for factorizing HODLR matrices and for applying the factorizations on a GPU. The algorithms leverage the efficiency of batched dense linear algebra, and they scale nearly linearly with the matrix size when the numerical ranks are fixed. The accuracy of the HODLR-matrix approximation is a tunable parameter, so we can construct high-accuracy fast direct solvers or low-accuracy robust preconditioners. Numerical results show that we can solve problems with several millions of unknowns in a couple of seconds on a single GPU. C2 - 2022/11// C3 - SC22: International Conference for High Performance Computing, Networking, Storage and Analysis DA - 2022/11// DO - 10.1109/sc41404.2022.00089 SP - 1-15 PB - IEEE UR - http://dx.doi.org/10.1109/sc41404.2022.00089 ER - TY - JOUR TI - Overlapping Domain Decomposition Preconditioner for Integral Equations AU - Chen, Chao AU - Biros, George T2 - SIAM Journal on Scientific Computing AB - The discretization of certain integral equations, e.g., the first-kind Fredholm equation of Laplace's equation, leads to symmetric positive-definite linear systems, where the coefficient matrix is dense and often ill-conditioned. We introduce a new preconditioner based on a novel overlapping domain decomposition that can be combined efficiently with fast direct solvers. Empirically, we observe that the condition number of the preconditioned system is $O(1)$, independent of the problem size. Our domain decomposition is designed so that we can construct approximate factorizations of the subproblems efficiently. In particular, we apply the recursive skeletonization algorithm to subproblems associated with every subdomain. We present numerical results on problem sizes up to $16\,384^2$ in two dimensions (2D) and $256^3$ in three dimensions (3D), which were solved in less than 16 hours and three hours, respectively, on an Intel Xeon Platinum 8280M. DA - 2022/11/14/ PY - 2022/11/14/ DO - 10.1137/21m1442917 VL - 44 IS - 6 SP - A3617-A3644 J2 - SIAM J. Sci. Comput. LA - en OP - SN - 1064-8275 1095-7197 UR - http://dx.doi.org/10.1137/21m1442917 DB - Crossref ER - TY - JOUR TI - Weakly viscoelastic film flowing down a rotating inclined plane AU - Chattopadhyay, Souradip AU - Mukhopadhyay, Anandamoy T2 - Physics of Fluids AB - We investigate the nonlinear stability of a thin viscoelastic film flowing under the effects of gravity and Coriolis and centrifugal forces. We assume that the viscoelastic liquid satisfies the rheological property of Walters' liquid B″. We may consider this case as a viscoelastic flow down a rotating cone and far from the apex. Using the classical long wave expansion technique, we derive a nonlinear evolution equation describing the shape of the liquid interface as a function of space and time and also derive its stability characteristics. We solve the physical system in a two-step procedure. In the first step, we use the normal mode method to characterize the linear nature. The linear study reveals that the linear growth rate is invariant with the Coriolis effect but is significantly affected by the viscoelastic parameter Γ as well as the Taylor number Ta. It is found that both Γ and Ta destabilize the flow. In the second step, we solve an elaborated nonlinear film flow model based on the method of multiple scales and demarcate different instability zones. The weakly nonlinear study shows that with an increase in Γ and Ta, the supercritical stable region and the explosion area increase whereas the unconditional stable and the subcritical unstable region shrink. Finally, on validating our analytical predictions by performing a direct numerical simulation, a good agreement between the results of the linear stability analysis, weakly nonlinear stability analysis, and the numerical simulations is found. DA - 2022/1// PY - 2022/1// DO - 10.1063/5.0077366 VL - 34 IS - 1 UR - https://doi.org/10.1063/5.0077366 ER - TY - JOUR TI - Falling liquid films on a slippery substrate with variable fluid properties AU - Chattopadhyay, Souradip AU - Boragunde, Pavanvasudev AU - Gaonkar, Amar K. AU - Barua, Amlan K. AU - Mukhopadhyay, Anandamoy T2 - International Journal of Non-Linear Mechanics AB - We investigate the stability of a gravity-driven, thin, Newtonian liquid flowing on a uniformly heated slippery inclined plane. We construct a mathematical model of the flow that comprises the Navier–Stokes equation coupled with the equation of energy. While the rest of the boundary conditions are standard for thin-film problems, we apply a Navier slip boundary condition at the solid–liquid interface. We assume that the fluid thermophysical properties — density, dynamical viscosity, surface tension, and thermal diffusivity vary linearly with temperature as long as the change in temperature is small. In the analysis part, we follow the standard long-wave theory and construct a nonlinear evolution equation for the film thickness. This is followed by a linear and weakly nonlinear stability analysis. The linear analysis allows us to compute the critical Reynolds number of our problem and from this study, we conclude that the slippery substrate destabilizes the film flow. The weakly nonlinear stability analysis finds a finer description of various stable/unstable zones. Finally, we perform a numerical simulation of the evolution equation in a periodic domain using spectral methods. Our numerical results support the analytical predictions of the instability threshold using the linear and weakly nonlinear theories. The influence of the small Biot number is also investigated in presence of the slip length together with the variable fluid properties. DA - 2022/12// PY - 2022/12// DO - 10.1016/j.ijnonlinmec.2022.104200 VL - 147 UR - https://doi.org/10.1016/j.ijnonlinmec.2022.104200 ER - TY - CHAP TI - Effects of Strong Viscosity with Variable Fluid Properties on Falling Film Instability AU - Mukhopadhyay, Anandamoy AU - Chattopadhyay, Souradip AU - Barua, Amlan K. T2 - NODYCON Conference Proceedings Series AB - The stability and dynamics of a gravity-driven, viscous, incompressible, Newtonian thin liquid film draining down a uniformly heated inclined plane are examined. We assume the thermophysical properties of the film such as density, surface tension, and thermal diffusivity vary linearly, whereas the viscosity varies exponentially with the small variation of temperature. Employing the classical long-wave expansion technique, a nonlinear evolution equation of Benney type, is derived in terms of film thickness h(x, t). The linear stability analysis is performed using the normal mode approach and a critical Reynolds number is obtained. The linear study reveals that the flow is more stable when the variation of viscosity is exponential as compared to a linear variation. The variation of density also affects the linear stability criteria. The method of multiple scales is used to investigate the weakly nonlinear stability of the flow, and we observe that for the variation of Kμ, Kρ, Kσ both the supercritical stable and subcritical unstable zones are possible together with the unconditional stable and explosive zones. Finally, we perform the numerical simulation in a periodic domain and confirm the results obtained by linear and weakly nonlinear studies. PY - 2022/// DO - 10.1007/978-3-030-81162-4_7 SP - 75-85 PB - Springer International Publishing UR - http://dx.doi.org/10.1007/978-3-030-81162-4_7 ER - TY - JOUR TI - Effect of odd-viscosity on the dynamics and stability of a thin liquid film flowing down on a vertical moving plate AU - Chattopadhyay, Souradip AU - Subedar, Gowri Y. AU - Gaonkar, Amar K. AU - Barua, Amlan K. AU - Mukhopadhyay, Anandamoy T2 - International Journal of Non-Linear Mechanics AB - In this study, we focus on the problem of hydrodynamic instability of a thin, viscous, Newtonian liquid film with broken time-reversal-symmetry flowing down along the surface of a vertical moving plate. The presence of odd viscosity gives rise to new terms in the pressure gradient of the flow. Utilizing the classical long-wave perturbation method, we obtain the analytical solutions as well as derive the nonlinear evolution equation of Benney-type in terms of film thickness h(x,t) which is significantly modified due to the presence of odd viscosity in the liquid. We solve the linear model by using the normal mode approach and for three different conditions, namely, the quiescent, up-moving and down-moving plate velocity. The linear study shows that the effect of the down-moving motion of the vertical plate is to enhance the stability of the film flow whereas the up-moving motion of the vertical plate tends to reduce it. Further, the study shows that odd viscosity always has a stabilizing effect on the flow field. In addition, the Orr–Sommerfeld equation is also derived and solved analytically to obtain the critical Reynolds number. Finally, we show the numerical solution of the evolution equation in a periodic domain which clearly demonstrates the role of odd-viscosity on the dynamics of the plate motions of thin film flows coating in isothermal environments. Our study clearly shows how odd viscosity influences the stability of the flow. DA - 2022/4// PY - 2022/4// DO - 10.1016/j.ijnonlinmec.2022.103905 VL - 140 UR - https://doi.org/10.1016/j.ijnonlinmec.2022.103905 ER - TY - JOUR TI - Dynamics and stability of weakly viscoelastic film flowing down a uniformly heated slippery incline AU - Chattopadhyay, Souradip AU - Desai, Akshay S. T2 - Physical Review Fluids AB - A theoretical model is presented to investigate the stability of a thin viscoelastic fluid draining down a uniformly heated slippery inclined plane. The instability is enhanced as the slippery length and viscoelasticity increase. When the wall is heated, the instability is reinforced. DA - 2022/6/30/ PY - 2022/6/30/ DO - 10.1103/PhysRevFluids.7.064007 VL - 7 IS - 6 UR - https://doi.org/10.1103/PhysRevFluids.7.064007 ER - TY - JOUR TI - Electrohydrodynamics modeling of droplet actuation on a solid surface by surfactant-mediated electrodewetting AU - Chu, W. AU - Ji, H. AU - Wang, Q. AU - Kim, C.-J. AU - Bertozzi, A.L. T2 - Physical Review Fluids AB - Developed to address the drawbacks of electro-wetting, electro-dewetting is a digital microfluidic technique that makes a liquid dewet on a substrate using an electric potential. In this paper, we propose an electrohydrodynamic model to describe the dynamic evolution of a charged slender drop under the influence of an external electric field. We introduce lubrication theory to simplify the model and reproduce fundamental microfluidic operations, including dewetting, rewetting, and droplet shifting. DA - 2022/7// PY - 2022/7// DO - 10.1103/PhysRevFluids.8.073701 VL - 8 IS - 7 SP - 073701 ER - TY - RPRT TI - On travelling waves of a control-volume model for liquid films flowing down a fibre AU - Taranets, R. AU - Ji, H. AU - Chugunova, M. AB - This paper analytically investigates the solutions to a control-volume model for liquid films flowing down a vertical fibre. The dynamic evolution of the free surface is governed by a coupled degenerate nonlinear PDE system for the fluid film radius and the axial velocity. We prove the existence of weak solutions to the coupled system based on the application of a priori estimates derived for energy-entropy functionals. Existence of travelling wave solutions to the system is also established. Numerical studies are presented to illustrate the derived analytical results for both the dynamic PDE solutions and the travelling wave structures. C6 - 2301.02720 DA - 2022/// PY - 2022/// DO - 10.48550/arXiv.2301.02720 M1 - 2301.02720 M3 - arXiv SN - 2301.02720 ER - TY - JOUR TI - On a hybrid continuum-kinetic model for complex fluids AU - Chertock, A. AU - Degond, P. AU - Dimarco, G. AU - Lukáčová-Medvid’ová, M. AU - Ruhi, A. T2 - Partial Differential Equations and Applications AB - Abstract In the present work, we first introduce a general framework for modelling complex multiscale fluids and then focus on the derivation and analysis of a new hybrid continuum-kinetic model. In particular, we combine conservation of mass and momentum for an isentropic macroscopic model with a kinetic representation of the microscopic behavior. After introducing a small scale of interest, we compute the complex stress tensor by means of the Irving-Kirkwood formula. The latter requires an expansion of the kinetic distribution around an equilibrium state and a successive homogenization over the fast in time and small in space scale dynamics. For a new hybrid continuum-kinetic model the results of linear stability analysis indicate a conditional stability in the relevant low speed regimes and linear instability for high speed regimes for higher modes. Extensive numerical experiments confirm that the proposed multiscale model can reflect new phenomena of complex fluids not being present in standard Newtonian fluids. Consequently, the proposed general technique can be successfully used to derive new interesting systems combining the macro and micro structure of a given physical problem. DA - 2022/10// PY - 2022/10// DO - 10.1007/s42985-022-00198-9 VL - 3 IS - 5 UR - http://dx.doi.org/10.1007/s42985-022-00198-9 ER - TY - JOUR TI - The GKR Protocol Revisited: Nearly Optimal Prover-Complexity For Polynomial-Time Wiring Algorithms and For Primality Testing in n(1/2+o(1)) Rounds AU - Kaltofen, Erich L. T2 - PROCEEDINGS OF THE 2022 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2022 AB - The proof-of-work interactive protocol by Shafi Goldwasser, Yael T. Kalai and Guy N. Rothblum (GKR) [STOC 2008, JACM 2015] certifies the execution of an algorithm via the evaluation of a corresponding boolean or arithmetic circuit whose structure is known to the verifier by circuit wiring algorithms that define the uniformity of the circuit. Here we study protocols whose prover time- and space-complexities are within a poly-logarithmic factor of the time- and space-complexity of the algorithm; we call those protocols 'prover-nearly-optimal.' We show that the uniformity assumptions can be relaxed from LOGSPACE to polynomial-time in the bit-lengths of the labels which enumerate the nodes in the circuit. Our protocol applies GKR recursively to the arising sumcheck problems on each level of the circuit whose values are verified, and deploys any of the prover-nearly-optimal versions of GKR on the constructed sorting/prefix circuits with log-depth wiring functions. DA - 2022/// PY - 2022/// DO - 10.1145/3476446.3536183 SP - 177-186 KW - cloud computing KW - primality testing KW - proof-of-work certificate ER - TY - JOUR TI - Sparse Polynomial Hermite Interpolation AU - Kaltofen, Erich L. T2 - PROCEEDINGS OF THE 2022 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2022 AB - We present Hermite polynomial interpolation algorithms that for a sparse univariate polynomial f with coefficients from a field compute the polynomial from fewer points than the classical algorithms. If the interpolating polynomial f has t terms, our algorithms, which use randomization, require argument/value triples (wi,f(wi),f'(wi)) for i=0, ..., t + ↾(t+1)/2↿ - 1, where w is randomly sampled and the probability of a correct output is determined from a degree bound for f. With f' we denote the derivative of f. Our algorithms generalize to multivariate polynomials, higher derivatives and sparsity with respect to Chebyshev polynomial bases. We have algorithms that can correct errors in the points by oversampling at a limited number of good values. If an upper bound B ≥ t for the number of terms is given, our algorithms use a randomly selected w and, with high probability, t/2 + B triples, but then never return an incorrect output. DA - 2022/// PY - 2022/// DO - 10.1145/3476446.3535501 SP - 469-478 KW - model fitting KW - gradient data KW - measurement minimization ER - TY - RPRT TI - Challenge Problem 1: Preliminary Model Development and Assessment of Flexible Heat Transfer Modeling Approaches AU - Wiser, Ralph; AU - Baglietto, Emilio; AU - Iskhakov, Arsen; AU - Dinh, Nam T.; AU - Tai, Cheng-Kai; AU - Bolotnov, Igor; AU - Nguyen, Tri; AU - Merzari, Elia; AU - Shaver, Dillon AB - plenum of Texas A&M University’s 1/16th scaled very-high-temperature gas-cooled reactor (VHTR), and (2) development of wall heat-transfer correlation for laminar flow in a wall-heated pipe. The CFD tool validation exercises can be helpful to choose the models and CFD tools to simulate and design specific components of the HTRGs such as upper plenum where jet mixing is a complex phenomenon. In a loss of forced circulation event, the laminar flow can be observed during the development of natural circulation flow. This work includes the development and validation of heat transfer correlations for laminar flow using the Nek5000 CFD code due to limited available experimental data for laminar flow conditions to guide low-order models (1D). In this report, the flow characteristics of a single isothermal jet discharging into the upper plenum was investigated using the Nek5000 Large-Eddy Simulation (LES) CFD tool. Several numerical simulations were performed for various jet-discharged Reynolds numbers ranging from 3,413 to 12,819. A grid-independent study was performed. The numerical results of mean velocity, root-mean-square fluctuating velocity, and Reynolds stress were compared against the benchmark data. Good agreement was obtained between simulated and measured data for axial mean velocities, except near the upper plenum hemisphere. The maximum predicted errors for axial mean velocities at various normalized coolant channel diameter heights of 1, 5, and 10 are 1.56%, 1.88%, and 3.82%, respectively. In addition, the predicted root-mean-square fluctuating velocity and Reynolds stress are qualitatively in agreement with the experimental data. The Nek5000 code was used to develop wall-heat transfer correlation for laminar flow in a cylindrical tube. Several simulations were performed for various Reynolds flow and wall-heat fluxes. A new heat transfer correlation was developed using data from Nek5000 simulation results and regression functions in Matlab. The developed heat transfer correlation is valid for various Reynolds flows from 200 to 2000. The predicted R² value for model fit was 0.875, which ensures that 87.5% of the model data lies on the Nek5000 data. Moreover, a machine learning (ML) tool was used to train and test the Nek5000 data. A good fit of the ML-based model was observed with the test data. DA - 2022/6// PY - 2022/6// DO - 10.2172/1881860 UR - https://www.osti.gov/biblio/1881860 ER - TY - RPRT TI - A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem AU - Cook, Brian AU - Hughes, Kevin AU - Li, Zane Kun AU - Mudgal, Akshat AU - Robert, Olivier AU - Yung, Po-Lam AB - We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely does solution counting in older partial progress on Vinogradov's mean value theorem correspond to in Fourier decoupling theory. C6 - 2207.01097 DA - 2022/// PY - 2022/// DO - 10.48550/arXiv.2207.01097 M1 - 2207.01097 M3 - arXiv preprint SN - 2207.01097 ER - TY - RPRT TI - An introduction to decoupling and harmonic analysis over Qp AU - Li, Zane Kun AB - The goal of this expository paper is to provide an introduction to decoupling by working in the simpler setting of decoupling for the parabola over $\mathbb{Q}_p$. Over $\mathbb{Q}_p$, commonly used heuristics in decoupling are significantly easier to make rigorous over $\mathbb{Q}_p$ than over $\mathbb{R}$ and such decoupling theorems over $\mathbb{Q}_p$ are still strong enough to derive interesting number theoretic conclusions. C6 - 2209.01644 DA - 2022/// PY - 2022/// DO - 10.48550/arXiv.2209.01644 M1 - 2209.01644 M3 - arXiv preprint SN - 2209.01644 ER - TY - JOUR TI - Decoupling for fractal subsets of the parabola AU - Chang, Alan AU - Dios Pont, Jaume de AU - Greenfeld, Rachel AU - Jamneshan, Asgar AU - Li, Zane Kun AU - Madrid, José T2 - Mathematische Zeitschrift AB - We consider decoupling for a fractal subset of the parabola. We reduce studying $$l^{2}L^{p}$$ decoupling for a fractal subset on the parabola $$\{(t, t^2) : 0 \le t \le 1\}$$ to studying $$l^{2}L^{p/3}$$ decoupling for the projection of this subset to the interval [0, 1]. This generalizes the decoupling theorem of Bourgain-Demeter in the case of the parabola. Due to the sparsity and fractal like structure, this allows us to improve upon Bourgain–Demeter’s decoupling theorem for the parabola. In the case when p/3 is an even integer we derive theoretical and computational tools to explicitly compute the associated decoupling constant for this projection to [0, 1]. Our ideas are inspired by the recent work on ellipsephic sets by Biggs ( arXiv:1912.04351 , 2019 and Acta Arith. 200(4):331–348, 2021) using nested efficient congruencing. DA - 2022/2/3/ PY - 2022/2/3/ DO - 10.1007/s00209-021-02950-0 VL - 301 IS - 2 SP - 1851-1879 J2 - Math. Z. LA - en OP - SN - 0025-5874 1432-1823 UR - http://dx.doi.org/10.1007/s00209-021-02950-0 DB - Crossref ER - TY - JOUR TI - On travelling wave solutions of a model of a liquid film flowing down a fibre AU - HANGJIE, JI AU - TARANETS, ROMAN AU - CHUGUNOVA, MARINA T2 - European Journal of Applied Mathematics AB - Abstract Existence of non-negative weak solutions is shown for a full curvature thin-film model of a liquid thin film flowing down a vertical fibre. The proof is based on the application of a priori estimates derived for energy-entropy functionals. Long-time behaviour of these weak solutions is analysed and, under some additional constraints for the model parameters and initial values, convergence towards a travelling wave solution is obtained. Numerical studies of energy minimisers and travelling waves are presented to illustrate analytical results. DA - 2022/10// PY - 2022/10// DO - 10.1017/S0956792521000255 VL - 33 IS - 5 SP - 864-893 UR - https://doi.org/10.1017/S0956792521000255 ER - TY - JOUR TI - Screening cell-cell communication in spatial transcriptomics via collective optimal transport AU - Cang, Zixuan AU - Zhao, Yanxiang AU - Almet, Axel A. AU - Stabell, Adam AU - Ramos, Raul AU - Plikus, Maksim AU - Atwood, Scott X. AU - Nie, Qing AB - Abstract Spatial transcriptomic technologies and spatially annotated single cell RNA-sequencing (scRNA-seq) datasets provide unprecedented opportunities to dissect cell-cell communication (CCC). How to incorporate the spatial information and complex biochemical processes in reconstructing CCC remains a major challenge. Here we present COMMOT to infer CCC in spatial transcriptomics, which accounts for the competition among different ligand and receptor species as well as spatial distances between cells. A novel collective optimal transport method is developed to handle complex molecular interactions and spatial constraints. We introduce downstream analysis tools on spatial directionality of signalings and genes regulated by such signalings using machine learning models. We apply COMMOT to simulation data and eight spatial datasets acquired with five different technologies, showing its effectiveness and robustness in identifying spatial CCC in data with varying spatial resolutions and gene coverages. Finally, COMMOT reveals new CCCs during skin morphogenesis in a case study of human epidermal development. Both the method and the computational package have broad applications in inferring cell-cell interactions within spatial genomics datasets. DA - 2022/8/26/ PY - 2022/8/26/ DO - 10.1101/2022.08.24.505185 UR - https://doi.org/10.1101/2022.08.24.505185 ER - TY - JOUR TI - On Smith normal forms of q-Varchenko matrices AU - Boulware, N. AU - Jing, N. AU - Misra, K. C. T2 - ALGEBRA AND DISCRETE MATHEMATICS AB - In this paper, we investigate q-Varchenko matrices for some hyperplane arrangements with symmetry in two andthree dimensions, and prove that they have a Smith normal formover Z[q]. In particular, we examine the hyperplane arrangement forthe regular n-gon in the plane and the dihedral model in the spaceand Platonic polyhedra. In each case, we prove that the q-Varchenko matrix associated with the hyperplane arrangement has a Smith normal form over Z[q] and realize their congruent transformation matrices over Z[q] as well. DA - 2022/// PY - 2022/// DO - 10.12958/adm2006 VL - 34 IS - 2 SP - 187-222 SN - 2415-721X KW - Smith normal forms KW - hyperplane arrangements KW - Platonic solids KW - Varchenko matrices ER - TY - JOUR TI - Geographic disparities and determinants of COVID-19 incidence risk in the greater St. Louis Area, Missouri (United States) AU - Das, Praachi AU - Igoe, Morganne AU - Lenhart, Suzanne AU - Luong, Lan AU - Lanzas, Cristina AU - Lloyd, Alun L. AU - Odoi, Agricola T2 - PLOS ONE AB - Background Evidence seems to suggest that the risk of Coronavirus Disease 2019 (COVID-19) might vary across communities due to differences in population characteristics and movement patterns. However, little is known about these differences in the greater St Louis Area of Missouri and yet this information is useful for targeting control efforts. Therefore, the objectives of this study were to investigate (a) geographic disparities of COVID-19 risk and (b) associations between COVID-19 risk and socioeconomic, demographic, movement and chronic disease factors in the Greater St. Louis Area of Missouri, USA. Methods Data on COVID-19 incidence and chronic disease hospitalizations were obtained from the Department of Health and Missouri Hospital Association, respectively. Socioeconomic and demographic data were obtained from the 2018 American Community Survey while population mobility data were obtained from the SafeGraph website. Choropleth maps were used to identify geographic disparities of COVID-19 risk and several sociodemographic and chronic disease factors at the ZIP Code Tabulation Area (ZCTA) spatial scale. Global negative binomial and local geographically weighted negative binomial models were used to investigate associations between ZCTA-level COVID-19 risk and socioeconomic, demographic and chronic disease factors. Results There were geographic disparities found in COVID-19 risk. Risks tended to be higher in ZCTAs with high percentages of the population with a bachelor’s degree (p<0.0001) and obesity hospitalizations (p<0.0001). Conversely, risks tended to be lower in ZCTAs with high percentages of the population working in agriculture (p<0.0001). However, the association between agricultural occupation and COVID-19 risk was modified by per capita between ZCTA visits. Areas that had both high per capita between ZCTA visits and high percentages of the population employed in agriculture had high COVID-19 risks. The strength of association between agricultural occupation and COVID-19 risk varied by geographic location. Conclusions Geographic disparities of COVID-19 risk exist in the St. Louis area and are associated with sociodemographic factors, population movements, and obesity hospitalization risks. The latter is particularly concerning due to the growing prevalence of obesity and the known immunological impairments among obese individuals. Therefore, future studies need to focus on improving our understanding of the relationships between COVID-19 vaccination efficacy, obesity and waning of immunity among obese individuals so as to better guide vaccination regimens and reduce disparities. DA - 2022/9/28/ PY - 2022/9/28/ DO - 10.1371/journal.pone.0274899 VL - 17 IS - 9 SP - SN - 1932-6203 ER - TY - RPRT TI - RSK tableaux and the weak order on fully commutative permutations AU - Gunawan, E. AU - Pan, J. AU - Russell, H.M. AU - Tenner, B.E. AB - For each fully commutative permutation, we construct a "boolean core," which is the maximal boolean permutation in its principal order ideal under the right weak order. We partition the set of fully commutative permutations into the recently defined crowded and uncrowded elements, distinguished by whether or not their RSK insertion tableaux satisfy a sparsity condition. We show that a fully commutative element is uncrowded exactly when it shares the RSK insertion tableau with its boolean core. We present the dynamics of the right weak order on fully commutative permutations, with particular interest in when they change from uncrowded to crowded. In particular, we use consecutive permutation patterns and descents to characterize the minimal crowded elements under the right weak order. C6 - 2212.05002 DA - 2022/// PY - 2022/// DO - 10.48550/arXiv.2212.05002 M1 - 2212.05002 M3 - ArXiv preprint SN - 2212.05002 UR - arXiv:2212.05002 ER - TY - RPRT TI - Runs and RSK tableaux of boolean permutations AU - Gunawan, E. AU - Pan, J. AU - Russell, H.M. AU - Tenner, B.E. A3 - arXiv AB - We define and construct the "canonical reduced word" of a boolean permutation, and show that the RSK tableaux for that permutation can be read off directly from this reduced word. We also describe those tableaux that can correspond to boolean permutations, and enumerate them. In addition, we generalize a result of Mazorchuk and Tenner, showing that the "run" statistic influences the shape of the RSK tableau of arbitrary permutations, not just of those that are boolean. C6 - 2207.05119 DA - 2022/// PY - 2022/// DO - 10.48550/arXiv.2207.05119 M1 - 2207.05119 M3 - arXiv preprint PB - arXiv SN - 2207.05119 UR - https://arxiv.org/abs/2207.05119 ER - TY - RPRT TI - A Bijection between K-Kohnert Diagrams and Reverse Set-Valued Tableaux AU - Pan, J. AU - Yu, T. AB - Lascoux polynomials are $K$-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux ($\mathsf{RSVT}$) rule for Lascoux polynomials and reverse semistandard Young tableaux ($\mathsf{RSSYT}$) rule for key polynomials. Furthermore, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with $\mathsf{RSSYT}$. Ross and Yong introduced $K$-Kohnert diagrams, which are analogues of Kohnert diagrams. They conjectured a $K$-Kohnert diagram rule for Lascoux polynomials. We establish this conjecture by constructing a weight-preserving bijection between $\mathsf{RSVT}$ and $K$-Kohnert diagrams. C6 - 2206.08993 DA - 2022/// PY - 2022/// DO - 10.48550/arXiv.2206.08993 M1 - 2206.08993 M3 - arXiv preprint SN - 2206.08993 ER - TY - JOUR TI - KNOT CONCORDANCE IN HOMOLOGY COBORDISMS AU - Hom, Jenniffer AU - Levine, Adam Simon AU - Lidman, Tye T2 - DUKE MATHEMATICAL JOURNAL AB - Let CˆZ denote the group of knots in homology spheres that bound homology balls, modulo smooth concordance in homology cobordisms. Answering a question of Matsumoto, the second author previously showed that the natural map from the smooth knot concordance group C to CˆZ is not surjective. Using tools from Heegaard Floer homology, we show that the cokernel of this map, which can be understood as the non-locally-flat piecewise-linear concordance group, is infinitely generated and contains elements of infinite order. In the appendix, we provide a careful proof that any piecewise-linear surface in a smooth 4-manifold can be isotoped to be smooth away from cone points. DA - 2022/10/15/ PY - 2022/10/15/ DO - 10.1215/00127094-2021-0110 VL - 171 IS - 15 SP - 3089-3131 SN - 1547-7398 ER - TY - JOUR TI - Beyond body size-new traits for new heights in trait-based modelling of predator-prey dynamics AU - Wootton, Kate L. AU - Curtsdotter, Alva AU - Jonsson, Tomas AU - Banks, H. T. AU - Bommarco, Riccardo AU - Roslin, Tomas AU - Laubmeier, Amanda N. T2 - PLOS ONE AB - Food webs map feeding interactions among species, providing a valuable tool for understanding and predicting community dynamics. Using species' body sizes is a promising avenue for parameterizing food-web models, but such approaches have not yet been able to fully recover observed community dynamics. Such discrepancies suggest that traits other than body size also play important roles. For example, differences in species' use of microhabitat or non-consumptive effects of intraguild predators may affect dynamics in ways not captured by body size. In Laubmeier et al. (2018), we developed a dynamic food-web model incorporating microhabitat and non-consumptive predator effects in addition to body size, and used simulations to suggest an optimal sampling design of a mesocosm experiment to test the model. Here, we perform the mesocosm experiment to generate empirical time-series of insect herbivore and predator abundance dynamics. We minimize least squares error between the model and time-series to determine parameter values of four alternative models, which differ in terms of including vs excluding microhabitat use and non-consumptive predator-predator effects. We use both statistical and expert-knowledge criteria to compare the models and find including both microhabitat use and non-consumptive predator-predator effects best explains observed aphid and predator population dynamics, followed by the model including microhabitat alone. This ranking suggests that microhabitat plays a larger role in driving population dynamics than non-consumptive predator-predator effects, although both are clearly important. Our results illustrate the importance of additional traits alongside body size in driving trophic interactions. They also point to the need to consider trophic interactions and population dynamics in a wider community context, where non-trophic impacts can dramatically modify the interplay between multiple predators and prey. Overall, we demonstrate the potential for utilizing traits beyond body size to improve trait-based models and the value of iterative cycling between theory, data and experiment to hone current insights into how traits affect food-web dynamics. DA - 2022/7/21/ PY - 2022/7/21/ DO - 10.1371/journal.pone.0251896 VL - 17 IS - 7 SP - SN - 1932-6203 ER - TY - JOUR TI - Connections between vector-valued and highest weight Jack and Macdonald polynomials AU - Colmenarejo, Laura AU - Dunkl, Charles F. AU - Luque, Jean-Gabriel T2 - ANNALES DE L INSTITUT HENRI POINCARE D AB - We analyze conditions under which a projection from the vector-valued Jack orMacdonald polynomials to scalar polynomials has useful properties, specially commuting with the actions of the symmetric group or Hecke algebra, respectively, and with the Cherednik operators for which these polynomials are eigenfunctions. In the framework of representation theory of the symmetric group and the Hecke algebra, we study the relation between singular nonsymmetric Jack and Macdonald polynomials and highest weight symmetric Jack and Macdonald polynomials. Moreover, we study the quasistaircase partition as a continuation of our study on the conjectures of Bernevig and Haldane on clustering properties of symmetric Jack polynomials. DA - 2022/// PY - 2022/// DO - 10.4171/AIHPD/119 VL - 9 IS - 2 SP - 297-348 SN - 2308-5835 KW - Macdonald and Jack Polynomials KW - singular polynomials KW - highest weight polynomials KW - vector-valued polynomials KW - representation theory of symmetric group and Hecke algebra ER - TY - JOUR TI - STRUCTURED MATRIX APPROXIMATIONS VIA TENSOR DECOMPOSITIONS AU - Kilmer, Misha E. AU - Saibaba, Arvind K. T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS AB - We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block banded), or be more highly structured (e.g., symmetric block Toeplitz). The goal is to uncover additional latent structure that will in turn lead to computationally efficient algorithms when the new structured matrix approximations are employed in place of the original operator. Our approach has three steps: map the structured matrix to tensors, use tensor compression algorithms, and map the compressed tensors back to obtain two different matrix representations—sum of Kronecker products and block low-rank format. The use of tensor decompositions enables us to uncover latent structure in the problem and leads to compressed representations of the original matrix that can be used efficiently in applications. The resulting matrix approximations are memory efficient, easy to compute with, and preserve the error that is due to the tensor compression in the Frobenius norm. Our framework is quite general. We illustrate the ability of our method to uncover block-low-rank format on structured matrices from two applications: system identification and space-time covariance matrices. In addition, we demonstrate that our approach can uncover the sum of structured Kronecker products structure on several matrices from the SuiteSparse collection. Finally, we show that our framework is broad enough to encompass and improve on other related results from the literature, as we illustrate with the approximation of a three-dimensional blurring operator. DA - 2022/// PY - 2022/// DO - 10.1137/21M1418290 VL - 43 IS - 4 SP - 1599-1626 SN - 1095-7162 KW - structured matrices KW - tensor decompositions KW - Kronecker products KW - system identifica-tion KW - image deblurring KW - covariance matrices ER - TY - JOUR TI - A BLOCK BIDIAGONALIZATION METHOD FOR FIXED-ACCURACY LOW-RANK MATRIX APPROXIMATION AU - Hallman, Eric T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS AB - We present randUBV, a randomized algorithm for matrix sketching based on the block Lanzcos bidiagonalization process. Given a matrix $\mathbb{A}$, it produces a low-rank approximation of the form $\mathbb{UBV}^T$, where $\mathbb{U}$ and $\mathbb{V}$ have orthonormal columns in exact arithmetic and $\mathbb{B}$ is block bidiagonal. In finite precision, the columns of both $\mathbb{U}$ and $\mathbb{V}$ will be close to orthonormal. Our algorithm is closely related to the randQB algorithms of Yu, Gu, and Li [SIAM J. Matrix Anal. Appl., 39 (2018), pp. 1339--1359]. in that the entries of $\mathbb{B}$ are incrementally generated and the Frobenius norm approximation error may be efficiently estimated. It is therefore suitable for the fixed-accuracy problem and so is designed to terminate as soon as a user input error tolerance is reached. Numerical experiments suggest that the block Lanczos method is generally competitive with or superior to algorithms that use power iteration, even when $\mathbb{A}$ has significant clusters of singular values. DA - 2022/// PY - 2022/// DO - 10.1137/21M1397866 VL - 43 IS - 2 SP - 661-680 SN - 1095-7162 KW - block Lanczos KW - randomized algorithm KW - low-rank matrix approximation KW - fixed-accuracy problem ER - TY - JOUR TI - Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States AU - Chang, Jingmei AU - Jing, Naihuan AU - Zhang, Tinggui T2 - INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS AB - In this paper, we study the stochastic local operation and classical communication (SLOCC) and local unitary (LU) equivalence for multi-qudit states by mode-n matricization of the coefficient tensors. We establish a new scheme of using the CANDECOMP/PARAFAC (CP) decomposition of tensors to find necessary and sufficient conditions between the mode-n unfolding and SLOCC&LU equivalence for pure multi-qudit states. For multipartite mixed states, we present a necessary and sufficient condition for LU equivalence and necessary condition for SLOCC equivalence. DA - 2022/12/23/ PY - 2022/12/23/ DO - 10.1007/s10773-022-05267-8 VL - 62 IS - 1 SP - SN - 1572-9575 KW - SLOCC KW - Local unitary equivalence KW - CP decomposition ER - TY - JOUR TI - Trading Signals in VIX Futures AU - Avellaneda, Marco AU - Li, Thomas Nanfeng AU - Papanicolaou, Andrew AU - Wang, Gaozhan T2 - Applied Mathematical Finance AB - We propose a new approach for trading VIX futures. We assume that the term structure of VIX futures follows a Markov model. Our trading strategy selects a position in VIX futures by maximizing the expected utility for a day-ahead horizon given the current shape and level of the term structure. Computationally, we model the functional dependence between the VIX futures curve, the VIX futures positions, and the expected utility as a deep neural network with five hidden layers. Out-of-sample backtests of the VIX futures trading strategy suggest that this approach gives rise to reasonable portfolio performance, and to positions in which the investor will be either long or short VIX futures contracts depending on the market environment. DA - 2022/1/20/ PY - 2022/1/20/ DO - 10.1080/1350486x.2021.2010584 VL - 1 SP - 1-24 UR - http://dx.doi.org/10.1080/1350486x.2021.2010584 ER - TY - JOUR TI - SIGNAL RECOVERY FROM INCONSISTENT NONLINEAR OBSERVATIONS AU - Combettes, Patrick L. AU - Woodstock, Zev C. T2 - 2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP) AB - We show that many nonlinear observation models in signal recovery can be represented using firmly nonexpansive operators. To address problems with inaccurate measurements, we propose solving a variational inequality relaxation which is guaranteed to possess solutions under mild conditions and which coincides with the original problem if it happens to be consistent. We then present an efficient algorithm for its solution, as well as numerical applications in signal and image recovery, including an experimental operator-theoretic method of promoting sparsity. DA - 2022/// PY - 2022/// DO - 10.1109/ICASSP43922.2022.9746145 SP - 5872-5876 SN - 1520-6149 KW - Firmly nonexpansive operator KW - inconsistent nonlinear observations KW - signal recovery KW - variational inequality ER - TY - JOUR TI - BLOCK-ACTIVATED ALGORITHMS FOR MULTICOMPONENT FULLY NONSMOOTH MINIMIZATION AU - Bui, Minh N. AU - Combettes, Patrick L. AU - Woodstock, Zev C. T2 - 2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP) AB - Under consideration are multicomponent minimization problems involving a separable nonsmooth convex function penalizing the components individually, and nonsmooth convex coupling terms penalizing linear mixtures of the components. We investigate the application of block-activated proximal algorithms for solving such problems, i.e., algorithms which, at each iteration, need to use only a block of the underlying functions, as opposed to all of them as in standard methods. For smooth coupling functions, several block-activated algorithms exist and they are well understood. By contrast, in the fully nonsmooth case, few block-activated methods are available and little effort has been devoted to assessing them. Our goal is to shed more light on the implementation, the features, and the behavior of these algorithms, compare their merits, and provide machine learning and image recovery experiments illustrating their performance. DA - 2022/// PY - 2022/// DO - 10.1109/ICASSP43922.2022.9747479 SP - 5428-5432 SN - 1520-6149 KW - Block-activated algorithm KW - image recovery KW - machine learning KW - nonsmooth convex minimization KW - proximal splitting ER - TY - JOUR TI - A critical assessment of the detailed Aedes aegypti simulation model Skeeter Buster 2 using field experiments of indoor insecticidal control in Iquitos, Peru AU - Gunning, Christian E. AU - Morrison, Amy C. AU - Okamoto, Kenichi W. AU - Scott, Thomas W. AU - Astete, Helvio AU - Vásquez, Gissella M. AU - Gould, Fred AU - Lloyd, Alun L. T2 - PLOS Neglected Tropical Diseases AB - The importance of mosquitoes in human pathogen transmission has motivated major research efforts into mosquito biology in pursuit of more effective vector control measures. Aedes aegypti is a particular concern in tropical urban areas, where it is the primary vector of numerous flaviviruses, including the yellow fever, Zika, and dengue viruses. With an anthropophilic habit, Ae. aegypti prefers houses, human blood meals, and ovipositioning in water-filled containers. We hypothesized that this relatively simple ecological niche should allow us to predict the impacts of insecticidal control measures on mosquito populations. To do this, we use Skeeter Buster 2 (SB2), a stochastic, spatially explicit, mechanistic model of Ae. aegypti population biology. SB2 builds on Skeeter Buster, which reproduced equilibrium dynamics of Ae. aegypti in Iquitos, Peru. Our goal was to validate SB2 by predicting the response of mosquito populations to perturbations by indoor insecticidal spraying and widespread destructive insect surveys. To evaluate SB2, we conducted two field experiments in Iquitos, Peru: a smaller pilot study in 2013 (S-2013) followed by a larger experiment in 2014 (L-2014). Here, we compare model predictions with (previously reported) empirical results from these experiments. In both simulated and empirical populations, repeated spraying yielded substantial yet temporary reductions in adult densities. The proportional effects of spraying were broadly comparable between simulated and empirical results, but we found noteworthy differences. In particular, SB2 consistently over-estimated the proportion of nulliparous females and the proportion of containers holding immature mosquitoes. We also observed less temporal variation in simulated surveys of adult abundance relative to corresponding empirical observations. Our results indicate the presence of ecological heterogeneities or sampling processes not effectively represented by SB2. Although additional empirical research could further improve the accuracy and precision of SB2, our results underscore the importance of non-linear dynamics in the response of Ae. aegypti populations to perturbations, and suggest general limits to the fine-grained predictability of its population dynamics over space and time. DA - 2022/12/22/ PY - 2022/12/22/ DO - 10.1371/journal.pntd.0010863 UR - https://doi.org/10.1371/journal.pntd.0010863 ER - TY - JOUR TI - Big data approaches to knot theory: Understanding the structure of the Jones polynomial AU - Levitt, Jesse S. F. AU - Hajij, Mustafa AU - Sazdanovic, Radmila T2 - JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS AB - In this paper, we examine the properties of the Jones polynomial using dimensionality reduction learning techniques combined with ideas from topological data analysis. Our data set consists of more than 10 million knots up to 17 crossings and two other special families up to 2001 crossings. We introduce and describe a method for using filtrations to analyze infinite data sets where representative sampling is impossible or impractical, an essential requirement for working with knots and the data from knot invariants. In particular, this method provides a new approach for analyzing knot invariants using Principal Component Analysis. Using this approach on the Jones polynomial data, we find that it can be viewed as an approximately three-dimensional subspace, that this description is surprisingly stable with respect to the filtration by the crossing number, and that the results suggest further structures to be examined and understood. DA - 2022/11/28/ PY - 2022/11/28/ DO - 10.1142/S021821652250095X VL - 11 SP - SN - 1793-6527 UR - http://dx.doi.org/10.1142/s021821652250095x KW - Knot invariants KW - knot polynomials KW - Jones polynomial KW - signature KW - topological data analysis KW - PCA KW - filtered PCA KW - data analysis ER - TY - JOUR TI - Criteria of Genuine Multipartite Entanglement Based on Correlation Tensors AU - Jing, Naihuan AU - Zhang, Meiming T2 - INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS AB - We revisit the genuine multipartite entanglement by a simplified method, which only involves the Schmidt decomposition and local unitary transformation. We construct a local unitary equivalent class of the tri-qubit quantum state, then use the trace norm of the whole correlation tensor as a measurement to detect genuine multipartite entanglement. By detailed examples, we show our result can detect more genuinely entangled states. Furthermore, we generalize the genuine multipartite entanglement criterion to tripartite higher-dimensional systems. DA - 2022/12/6/ PY - 2022/12/6/ DO - 10.1007/s10773-022-05253-0 VL - 61 IS - 12 SP - SN - 1572-9575 KW - Genuine multipartite entanglement KW - Correlation tensor ER - TY - JOUR TI - Extensions of mean-field approximations for environmentally-transmitted pathogen networks AU - Davies, Kale AU - Lenhart, Suzanne AU - Day, Judy AU - Lloyd, Alun L. AU - Lanzas, Cristina T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING AB - Many pathogens spread via environmental transmission, without requiring host-to-host direct contact. While models for environmental transmission exist, many are simply constructed intuitively with structures analogous to standard models for direct transmission. As model insights are generally sensitive to the underlying model assumptions, it is important that we are able understand the details and consequences of these assumptions. We construct a simple network model for an environmentally-transmitted pathogen and rigorously derive systems of ordinary differential equations (ODEs) based on different assumptions. We explore two key assumptions, namely homogeneity and independence, and demonstrate that relaxing these assumptions can lead to more accurate ODE approximations. We compare these ODE models to a stochastic implementation of the network model over a variety of parameters and network structures, demonstrating that with fewer restrictive assumptions we are able to achieve higher accuracy in our approximations and highlighting more precisely the errors produced by each assumption. We show that less restrictive assumptions lead to more complicated systems of ODEs and the potential for unstable solutions. Due to the rigour of our derivation, we are able to identify the reason behind these errors and propose potential resolutions. DA - 2022/// PY - 2022/// DO - 10.3934/mbe.2023075 VL - 20 IS - 2 SP - 1637-1673 SN - 1551-0018 KW - environmental transmission KW - moment closure approximations KW - mean-field models KW - network models KW - individual-based models KW - infectious disease ER - TY - JOUR TI - AN L-8 SECOND ORDER CARTESIAN METHOD FOR 3D ANISOTROPIC INTERFACE PROBLEMS AU - Dong, Baiying AU - Feng, Xiufeng AU - Li, Zhilin T2 - JOURNAL OF COMPUTATIONAL MATHEMATICS DA - 2022/// PY - 2022/// DO - 10.4208/jcm.2103-m2020-0107 VL - 40 IS - 6 SP - 882-912 SN - 1991-7139 KW - Key veords KW - 3D anisotropic PDE KW - Cartesian meshes KW - Finite element method KW - Finite differ KW - ence method KW - Maximum preserving IIM KW - Convergence analysis ER - TY - JOUR TI - TWISTED QUANTUM AFFINIZATIONS AND QUANTIZATION OF EXTENDED AFFINE LIE ALGEBRAS AU - Chen, Fulin AU - Jing, Naihuan AU - Kong, Fei AU - Tan, Shaobin T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY AB - In this paper, for an arbitrary Kac-Moody Lie algebra g {\mathfrak g} and a diagram automorphism μ \mu of g {\mathfrak g} satisfying certain natural linking conditions, we introduce and study a μ \mu -twisted quantum affinization algebra U ( g ^ μ ) {\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right ) of g {\mathfrak g} . When g {\mathfrak g} is of finite type, U ( g ^ μ ) {\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right ) is Drinfeld’s current algebra realization of the twisted quantum affine algebra. When μ = i d \mu =\mathrm {id} and g {\mathfrak g} in affine type, U ( g ^ μ ) {\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right ) is the quantum toroidal algebra introduced by Ginzburg, Kapranov and Vasserot. As the main results of this paper, we first prove a triangular decomposition for U ( g ^ μ ) {\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right ) . Second, we give a simple characterization of the affine quantum Serre relations on restricted U ( g ^ μ ) {\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right ) -modules in terms of “normal order products”. Third, we prove that the category of restricted U ( g ^ μ ) {\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right ) -modules is a monoidal category and hence obtain a topological Hopf algebra structure on the “restricted completion” of U ( g ^ μ ) {\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right ) . Last, we study the classical limit of U ( g ^ μ ) {\mathcal U}_\hbar \left (\hat {\mathfrak g}_\mu \right ) and abridge it to the quantization theory of extended affine Lie algebras. In particular, based on a classification result of Allison-Berman-Pianzola, we obtain the \hbar -deformation of all nullity 2 2 extended affine Lie algebras. DA - 2022/10/28/ PY - 2022/10/28/ DO - 10.1090/tran/8706 VL - 10 SP - SN - 1088-6850 KW -   KW - Twisted quantum affinization KW - extended affine Lie algebra KW - quantum Kac-Moody algebra KW - triangular decomposition KW - Hopf algebra ER - TY - JOUR TI - High-order accurate numerical simulation of monochromatic waves in photonic crystal ring resonators with the help of a non-iterative domain decomposition AU - North, Evan AU - Tsynkov, Semyon AU - Turkel, Eli T2 - JOURNAL OF COMPUTATIONAL ELECTRONICS DA - 2022/11/20/ PY - 2022/11/20/ DO - 10.1007/s10825-022-01973-y VL - 11 SP - SN - 1572-8137 KW - Scattering rods KW - Periodic lattice KW - Helmholtz equation KW - Method of difference potentials KW - Exact coupling between non-overlapping subdomains KW - High-order accurate compact finite difference schemes ER - TY - JOUR TI - Deforming vertex algebras by vertex bialgebras AU - Jing, Naihuan AU - Kong, Fei AU - Li, Haisheng AU - Tan, Shaobin T2 - COMMUNICATIONS IN CONTEMPORARY MATHEMATICS AB - This is a continuation of a previous study initiated by the third author on nonlocal vertex bialgebras and smash product nonlocal vertex algebras. In this paper, we study a notion of right [Formula: see text]-comodule nonlocal vertex algebra for a nonlocal vertex bialgebra [Formula: see text] and give a construction of deformations of vertex algebras with a right [Formula: see text]-comodule nonlocal vertex algebra structure and a compatible [Formula: see text]-module nonlocal vertex algebra structure. We also give a construction of [Formula: see text]-coordinated quasi modules for smash product nonlocal vertex algebras. As an example, we give a family of quantum vertex algebras by deforming the vertex algebras associated to non-degenerate even lattices. DA - 2022/11/11/ PY - 2022/11/11/ DO - 10.1142/S0219199722500675 VL - 11 SP - SN - 1793-6683 KW - Vertex algebra KW - smash product KW - quantum vertex algebra KW - phi-coordinated quasi module KW - lattice vertex operator algebra ER - TY - JOUR TI - DOMINANCE PHENOMENA: MUTATION, SCATTERING AND CLUSTER ALGEBRAS AU - Reading, Nathan T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY AB - An exchange matrix B B dominates an exchange matrix B B’ if the signs of corresponding entries weakly agree, with the entry of B B always having weakly greater absolute value. When B B dominates B B’ , interesting things happen in many cases (but not always): the identity map between the associated mutation-linear structures is often mutation-linear; the mutation fan for B B often refines the mutation fan for B B’ ; the scattering (diagram) fan for B B often refines the scattering fan for B B’ ; and there is often an injective homomorphism from the principal-coefficients cluster algebra for B B’ to the principal-coefficients cluster algebra for B B , preserving g \mathbf {g} -vectors and sending the set of cluster variables for B B’ (or an analogous larger set) into the set of cluster variables for B B (or an analogous larger set). The scope of the description “often” is not the same in all four contexts and is not settled in any of them. In this paper, we prove theorems that provide examples of these dominance phenomena. DA - 2022/10/28/ PY - 2022/10/28/ DO - 10.1090/tran/7888 VL - 10 SP - SN - 1088-6850 ER - TY - JOUR TI - Quantum Supergroup U-r,U-s(osp(1,2)), Scasimir operators and Dickson polynomials AU - Liu, Fu AU - Hu, Naihong AU - Jing, Naihuan T2 - JOURNAL OF ALGEBRA AND ITS APPLICATIONS AB - We study the center of two-parameter quantum supergroup [Formula: see text] using the Dickson polynomial. We show that the Scasimir operator is completely determined by the [Formula: see text]-deformed Chebychev polynomial, generalizing an earlier work of Arnaudon and Bauer. DA - 2022/10/26/ PY - 2022/10/26/ DO - 10.1142/S0219498824500038 VL - 10 SP - SN - 1793-6829 KW - Two-parameter quantum supergroup KW - center KW - Dickson polynomial KW - Scasimir operator ER - TY - JOUR TI - Extremal Khovanov homology and the girth of a knot AU - Sazdanovic, Radmila AU - Scofield, Daniel T2 - JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS AB - We show that Khovanov link homology is trivial in a range of gradings and utilize relations between Khovanov and chromatic graph homology to determine extreme Khovanov groups and corresponding coefficients of the Jones polynomial. The extent to which chromatic homology and the chromatic polynomial can be used to compute integral Khovanov homology of a link depends on the maximal girth of its all-positive graphs. In this paper, we define the girth of a link, discuss relations to other knot invariants, and describe possible values for girth. Analyzing girth leads to a description of possible all-A state graphs of any given link; e.g., if a link has a diagram such that the girth of the corresponding all-A graph is equal to [Formula: see text], then the girth of the link is equal to [Formula: see text] DA - 2022/10/31/ PY - 2022/10/31/ DO - 10.1142/S0218216522500833 VL - 10 SP - SN - 1793-6527 UR - http://dx.doi.org/10.1142/s0218216522500833 KW - Categorification KW - chromatic graph homology KW - Jones polynomial KW - Khovanov homology ER - TY - JOUR TI - Principal Eigenportfolios for U.S. Equities AU - Avellaneda, Marco AU - Healy, Brian AU - Papanicolaou, Andrew AU - Papanicolaou, George T2 - SIAM Journal on Financial Mathematics AB - We analyze portfolios constructed from the principal eigenvector of the equity returns' correlation matrix and compare these portfolios with the capitalization weighted market portfolio. It is well known empirically that principal eigenportfolios are a good proxy for the market portfolio. We quantify this property through the large-dimensional asymptotic analysis of a spike model with diverging top eigenvalue, comprising a rank-one matrix and a random matrix. We show that, in this limit, the top eigenvector of the correlation matrix is close to the vector of market betas divided componentwise by returns standard deviation. Historical returns data are generally consistent with this analysis of the correspondence between the top eigenportfolio and the market portfolio. We further examine this correspondence using eigenvectors obtained from hierarchically constructed tensors where stocks are separated into their respective industry sectors. This hierarchical approach results in a principal factor whose portfolio weights are all positive for a greater percentage of time compared to the weights of the vanilla eigenportfolio computed from the correlation matrix. Returns from hierarchical construction are also more robust with respect to the duration of the time window used for estimation. All principal eigenportfolios that we observe have returns that exceed those of the market portfolio between 1994 and 2020. We attribute these excess returns to the brief periods where short holdings are more than a small percentage of portfolio weight. DA - 2022/7/18/ PY - 2022/7/18/ DO - 10.1137/20M1383501 VL - 13 IS - 3 SP - 702-744 J2 - SIAM J. Finan. Math. LA - en OP - SN - 1945-497X UR - http://dx.doi.org/10.1137/20M1383501 DB - Crossref KW - eigenportfolios KW - principal component analysis KW - tensor decompositions ER - TY - JOUR TI - A 3-categorical perspective on G$G$-crossed braided categories AU - Jones, Corey AU - Penneys, David AU - Reutter, David T2 - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES AB - A braided monoidal category may be considered a 3-category with one object and one 1-morphism. In this paper, we show that, more generally, 3-categories with one object and 1-morphisms given by elements of a group G $G$ correspond to G $G$ -crossed braided categories, certain mathematical structures which have emerged as important invariants of low-dimensional quantum field theories. More precisely, we show that the 4-category of 3-categories C $\mathcal {C}$ equipped with a 3-functor B G → C $\mathrm{B}G \rightarrow \mathcal {C}$ which is essentially surjective on objects and 1-morphisms is equivalent to the 2-category of G $G$ -crossed braided categories. This provides a uniform approach to various constructions of G $G$ -crossed braided categories. DA - 2022/11/3/ PY - 2022/11/3/ DO - 10.1112/jlms.12687 SP - SN - 1469-7750 ER - TY - JOUR TI - Adversarial classification: Necessary conditions and geometric flows T2 - Journal of Machine Learning Research DA - 2022/// PY - 2022/// VL - 23 IS - 187 SP - 1-38 ER - TY - JOUR TI - Least-squares method for recovering multiple medium parameters AU - Ito, Kazufumi AU - Liang, Ying AU - Zou, Jun T2 - INVERSE PROBLEMS AB - Abstract We present a two-stage least-squares method for inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the first stage, while a total least-squares method with a mixed regularization is used to recover the medium profile in the second stage. The total least-squares method is designed to minimize the residual of the model equation and the data fitting, along with an appropriate regularization, in an attempt to significantly improve the accuracy of the approximation obtained from the first stage. We shall also present an analysis on the well-posedness and convergence of this algorithm. Numerical experiments are carried out to verify the accuracies and robustness of this novel two-stage least-squares algorithm, with high tolerance of noise in the data. DA - 2022/12/1/ PY - 2022/12/1/ DO - 10.1088/1361-6420/ac999a VL - 38 IS - 12 SP - SN - 1361-6420 KW - inverse medium problem KW - multiple parameters KW - least-squares method KW - mixed regularization ER - TY - JOUR TI - 3D time-dependent scattering about complex shapes using high order difference potentials AU - Petropavlovsky, Sergey AU - Tsynkov, Semyon AU - Turkel, Eli T2 - JOURNAL OF COMPUTATIONAL PHYSICS AB - We compute the scattering of unsteady acoustic waves about complex three-dimensional bodies with high order accuracy. The geometry of a scattering body is defined with the help of CAD. Its surface is represented as a collection of non-overlapping patches, each parameterized independently by means of high order splines (NURBS). As a specific example, we consider a submarine-like scatterer constructed using five different patches. The acoustic wave equation on the region exterior to the scatterer is solved by first reducing it to a system of Calderon's boundary operator equations. The latter are obtained using the method of difference potentials coupled with a compact fourth order accurate finite difference scheme. When solving the boundary operator equations, we employ Huygens' principle. It allows us to work on a sliding time window of non-increasing duration rather than keep the entire temporal history of the solution at the boundary. The proposed methodology demonstrates grid-independent computational complexity at the boundary and sub-linear complexity with respect to the grid dimension. It efficiently handles complex non-conforming geometries on Cartesian grids with no penalty for either accuracy or stability due to the cut cells. Its performance does not deteriorate over arbitrarily long simulation times. The exact treatment of artificial outer boundaries is inherently built in. Finally, multiple similar problems can be solved efficiently at a low individual cost per problem. This is important when, for example, the boundary condition on the surface changes but the scattering body stays the same. DA - 2022/12/15/ PY - 2022/12/15/ DO - 10.1016/j.jcp.2022.111632 VL - 471 SP - SN - 1090-2716 KW - Unsteady acoustic waves KW - CAD surface with patched parameterization KW - High order splines (NURBS) KW - Calderon?s boundary equations KW - Huygens? principle KW - High-order compact schemes on Cartesian grids ER - TY - JOUR TI - A computational study of aortic reconstruction in single ventricle patients AU - Taylor-LaPole, Alyssa M. AU - Colebank, Mitchel J. AU - Weigand, Justin D. AU - Olufsen, Mette S. AU - Puelz, Charles T2 - BIOMECHANICS AND MODELING IN MECHANOBIOLOGY DA - 2022/11/5/ PY - 2022/11/5/ DO - 10.1007/s10237-022-01650-w VL - 11 SP - SN - 1617-7940 UR - https://doi.org/10.1007/s10237-022-01650-w KW - Hypoplastic left heart syndrome KW - Fontan circulation KW - Double outlet right ventricle KW - Perfusion KW - Fluid mechanics KW - Simulation KW - Systemic circulation ER - TY - JOUR TI - Ribbon homology cobordisms AU - Daemi, Aliakbar AU - Lidman, Tye AU - Vela-Vick, David Shea AU - Wong, C. -M. Michael T2 - ADVANCES IN MATHEMATICS AB - We study 4-dimensional homology cobordisms without 3-handles, showing that they interact nicely with Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. Using these, we derive obstructions to such cobordisms. As one example of these obstructions, we generalize other recent results on the behavior of knot Floer homology under ribbon concordances. Finally, we provide topological applications, including to Dehn surgery problems. DA - 2022/10/29/ PY - 2022/10/29/ DO - 10.1016/j.aim.2022.108580 VL - 408 SP - SN - 1090-2082 KW - Homology cobordism KW - Ribbon concordance KW - Thurston geometries KW - Character varieties KW - Floer homology KW - Dehn surgery ER - TY - JOUR TI - An immersed C R-P-0 element for Stokes interface problems and the optimal convergence analysis AU - Ji, Haifeng AU - Wang, Feng AU - Chen, Jinru AU - Li, Zhilin T2 - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING AB - This paper presents and analyzes an immersed finite element (IFE) method for solving Stokes interface problems with a piecewise constant viscosity coefficient that has a jump across the interface. In the method, the triangulation does not need to fit the interface and the IFE spaces are constructed from the traditional $CR$-$P_0$ element with modifications near the interface according to the interface jump conditions. We prove that the IFE basis functions are unisolvent on arbitrary interface elements and the IFE spaces have the optimal approximation capabilities, although the proof is challenging due to the coupling of the velocity and the pressure. The stability and the optimal error estimates of the proposed IFE method are also derived rigorously. The constants in the error estimates are shown to be independent of the interface location relative to the triangulation. Numerical examples are provided to verify the theoretical results. DA - 2022/9/1/ PY - 2022/9/1/ DO - 10.1016/j.cma.2022.115306 VL - 399 SP - SN - 1879-2138 KW - Stokes equations KW - Interface KW - Immersed finite element KW - Unfitted mesh KW - Two-phase flow KW - Error estimates ER - TY - JOUR TI - Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions AU - Saibaba, Arvind K. AU - Minster, Rachel AU - Kilmer, Misha E. T2 - ADVANCES IN COMPUTATIONAL MATHEMATICS AB - In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to accomplish the tensor compression, provide a detailed analysis of the computational costs, provide insight into the error of the resulting approximations, and discuss the benefits of the proposed approaches. We also apply the tensor-based function approximation to develop low-rank matrix approximations to kernel matrices that describe pairwise interactions between two sets of points; the resulting low-rank approximations are efficient to compute and store (the complexity is linear in the number of points). We present an adaptive version of the function and kernel approximation that determines an approximation that satisfies a user-specified relative error over a set of random points. We extend our approach to the case where the kernel requires repeated evaluations for many values of (hyper)parameters that govern the kernel. We give detailed numerical experiments on example problems involving multivariate function approximation, low-rank matrix approximations of kernel matrices involving well-separated clusters of sources and target points, and a global low-rank approximation of kernel matrices with an application to Gaussian processes. We observe speedups up to 18X over standard matrix-based approaches. DA - 2022/10// PY - 2022/10// DO - 10.1007/s10444-022-09979-7 VL - 48 IS - 5 SP - SN - 1572-9044 KW - Multivariate function approximation KW - Tucker format KW - Randomized algorithms KW - Low-rank approximations KW - Kernel methods ER - TY - JOUR TI - On Hopf algebraic structures of quantum toroidal algebras AU - Jing, Naihuan AU - Zhang, Honglian T2 - COMMUNICATIONS IN ALGEBRA AB - We define an algebra U0 using a simplified set of generators for the quantum toroidal algebra Uq(sln+1,tor) and show that there exists an epimorphism from U0 to Uq(sln+1,tor). We derive a closed formula of the comultiplication on the generators of U0 that extends that of the quantum affine algebra Uq(sl̂n+1). As a consequence, we show that U0 is a Hopf algebra for n = 1, 2 and give conjectural formulas in the general case. We further show that U0 is isomorphic to a double algebra. DA - 2022/10/1/ PY - 2022/10/1/ DO - 10.1080/00927872.2022.2127604 VL - 10 SP - SN - 1532-4125 KW - Drinfeld realization KW - comultiplication KW - Drinfeld generator KW - Hopf algebra KW - quantum toroidal algebra ER - TY - JOUR TI - Direct Numerical Simulation of Low and Unitary Prandtl Number Fluids in Reactor Downcomer Geometry AU - Tai, C.-K. AU - Nguyen, T. AU - Iskhakov, A.S. AU - Merzari, E. AU - Dinh, N. AU - Bolotnov, I.A. T2 - arXiv DA - 2022/// PY - 2022/// UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85128839982&partnerID=MN8TOARS ER - TY - JOUR TI - Data-driven Hi2Lo for Coarse-grid System Thermal Hydraulic Modeling AU - Iskhakov, A.S. AU - Dinh, N.T. AU - Leite, V.C. AU - Merzari, E. T2 - arXiv DA - 2022/// PY - 2022/// UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85126815096&partnerID=MN8TOARS ER - TY - JOUR TI - Two Quantum Proxy Blind Signature Schemes Based on Controlled Quantum Teleportation AU - Luo, Qiming AU - Zhang, Tinggui AU - Huang, Xiaofen AU - Jing, Naihuan T2 - ENTROPY AB - We present a scheme for teleporting an unknown, two-particle entangled state with a message from a sender (Alice) to a receiver (Bob) via a six-particle entangled channel. We also present another scheme for teleporting an unknown one-particle entangled state with a message transmitted in a two-way form between the same sender and receiver via a five-qubit cluster state. One-way hash functions, Bell-state measurements, and unitary operations are adopted in these two schemes. Our schemes use the physical characteristics of quantum mechanics to implement delegation, signature, and verification processes. Moreover, a quantum key distribution protocol and a one-time pad are adopted in these schemes. DA - 2022/10// PY - 2022/10// DO - 10.3390/e24101421 VL - 24 IS - 10 SP - SN - 1099-4300 UR - https://doi.org/10.3390/e24101421 KW - quantum teleportation KW - quantum signature KW - proxy signature KW - blind signature ER - TY - JOUR TI - DUAL CERTIFICATES AND EFFICIENT RATIONAL SUM-OF-SQUARES DECOMPOSITIONS FOR POLYNOMIAL OPTIMIZATION OVER COMPACT SETS AU - Davis, Maria M. AU - Papp, David T2 - SIAM JOURNAL ON OPTIMIZATION AB - We study the problem of computing weighted sum-of-squares (WSOS) certificates for positive polynomials over a compact semialgebraic set. Building on the theory of interior-point methods for convex optimization, we introduce the concept of dual certificates, which allows us to interpret vectors from the dual of the sum-of-squares cone as rigorous nonnegativity certificates of a WSOS polynomial. Whereas conventional WSOS certificates are alternative representations of the polynomials they certify, dual certificates are distinct from the certified polynomials; moreover, each dual certificate certifies a full-dimensional convex cone of WSOS polynomials. For a theoretical application, we give a short new proof of Powers's theorems on the existence of rational WSOS certificates of positive polynomials. For a computational application, we show that exact WSOS certificates can be constructed from numerically computed dual certificates at little additional cost, without any rounding or projection steps applied to the numerical certificates. We also present an algorithm for computing the optimal WSOS lower bound of a given polynomial along with a rational dual certificate, with a polynomial-time computational cost per iteration and linear rate of convergence. DA - 2022/// PY - 2022/// DO - 10.1137/21M1422574 VL - 32 IS - 4 SP - 2461-2492 SN - 1095-7189 UR - https://doi.org/10.1137/21M1422574 KW - Key words KW - polynomial optimization KW - nonnegativity certificates KW - sum-of-squares KW - nonsymmetric conic optimization ER - TY - JOUR TI - Hyper-differential sensitivity analysis for inverse problems governed by ODEs with application to COVID-19 modeling AU - Stevens, Mason AU - Sunseri, Isaac AU - Alexanderian, Alen T2 - MATHEMATICAL BIOSCIENCES AB - We consider inverse problems governed by systems of ordinary differential equations (ODEs) that contain uncertain parameters in addition to the parameters being estimated. In such problems, which are common in applications, it is important to understand the sensitivity of the solution of the inverse problem to the uncertain model parameters. It is also of interest to understand the sensitivity of the inverse problem solution to different types of measurements or parameters describing the experimental setup. Hyper-differential sensitivity analysis (HDSA) is a sensitivity analysis approach that provides tools for such tasks. We extend existing HDSA methods by developing methods for quantifying the uncertainty in the estimated parameters. Specifically, we propose a linear approximation to the solution of the inverse problem that allows efficiently approximating the statistical properties of the estimated parameters. We also explore the use of this linear model for approximate global sensitivity analysis. As a driving application, we consider an inverse problem governed by a COVID-19 model. We present comprehensive computational studies that examine the sensitivity of this inverse problem to several uncertain model parameters and different types of measurement data. Our results also demonstrate the effectiveness of the linear approximation model for uncertainty quantification in inverse problems and for parameter screening. DA - 2022/9// PY - 2022/9// DO - 10.1016/j.mbs.2022.108887 VL - 351 SP - SN - 1879-3134 KW - Inverse problems KW - Sensitivity analysis KW - Uncertainty quantification KW - Design of experiments KW - Computational epidemiology ER - TY - JOUR TI - Detection of genuine entanglement for multipartite quantum states AU - Zhao, Hui AU - Liu, Yu-Qiu AU - Jing, Naihuan AU - Wang, Zhi-Xi T2 - QUANTUM INFORMATION PROCESSING AB - We study genuine tripartite entanglement and multipartite entanglement of arbitrary $n$-partite quantum states by using the representations with generalized Pauli operators of a density matrices. While the usual Bloch representation of a density matrix uses three types of generators in the special unitary Lie algebra $\mathfrak{su}(d)$, the representation with generalized Pauli operators has one uniformed type of generators and it simplifies computation. In this paper, we take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement. We also obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions. The new method can detect more entangled states than previous methods as backed by detailed examples. DA - 2022/9/17/ PY - 2022/9/17/ DO - 10.1007/s11128-022-03659-7 VL - 21 IS - 9 SP - SN - 1573-1332 KW - Genuine entanglement KW - Correlation tensor KW - Generalized Pauli operators ER - TY - JOUR TI - An in-silico analysis of experimental designs to study ventricular function: A focus on the right ventricle AU - Colebank, Mitchel J. AU - Chesler, Naomi C. T2 - PLOS Computational Biology AB - In-vivo studies of pulmonary vascular disease and pulmonary hypertension (PH) have provided key insight into the progression of right ventricular (RV) dysfunction. Additional in-silico experiments using multiscale computational models have provided further details into biventricular mechanics and hemodynamic function in the presence of PH, yet few have assessed whether model parameters are practically identifiable prior to data collection. Moreover, none have used modeling to devise synergistic experimental designs. To address this knowledge gap, we conduct a practical identifiability analysis of a multiscale cardiovascular model across four simulated experimental designs. We determine a set of parameters using a combination of Morris screening and local sensitivity analysis, and test for practical identifiability using profile likelihood-based confidence intervals. We employ Markov chain Monte Carlo (MCMC) techniques to quantify parameter and model forecast uncertainty in the presence of noise corrupted data. Our results show that model calibration to only RV pressure suffers from practical identifiability issues and suffers from large forecast uncertainty in output space. In contrast, parameter and model forecast uncertainty is substantially reduced once additional left ventricular (LV) pressure and volume data is included. A comparison between single point systolic and diastolic LV data and continuous, time-dependent LV pressure-volume data reveals that at least some quantitative data from both ventricles should be included for future experimental studies. DA - 2022/9/20/ PY - 2022/9/20/ DO - 10.1371/journal.pcbi.1010017 UR - https://doi.org/10.1371/journal.pcbi.1010017 ER - TY - JOUR TI - Limiting eigenvalue behavior of a class of large dimensional random matrices formed from a Hadamard product AU - Silverstein, Jack W. T2 - RANDOM MATRICES-THEORY AND APPLICATIONS AB - This paper investigates the strong limiting behavior of the eigenvalues of the class of matrices [Formula: see text], studied in [V. L. Girko, Theory of Stochastic Canonical Equations: Vol. [Formula: see text] (Kluwer Academic Publishers, Dordrecht, 2001)]. Here, [Formula: see text] is an [Formula: see text] random matrix consisting of independent complex standardized random variables, [Formula: see text], [Formula: see text], has nonnegative entries, and ∘ denotes Hadamard (componentwise) product. Results are obtained under assumptions on the entries of [Formula: see text] and [Formula: see text] which are different from those in [V. L. Girko, Theory of Stochastic Canonical Equations: Vol. 1 (Kluwer Academic Publishers, Dordrecht, 2001)], which include a Lindeberg condition on the entries of [Formula: see text], as well as a bound on the average of the rows and columns of [Formula: see text]. The present paper separates the assumptions needed on [Formula: see text] and [Formula: see text]. It assumes a Lindeberg condition on the entries of [Formula: see text], along with a tightness-like condition on the entries of [Formula: see text]. DA - 2022/7/28/ PY - 2022/7/28/ DO - 10.1142/S2010326322500502 VL - 7 SP - SN - 2010-3271 KW - Eigenvalues of random matrices KW - Hadamard product KW - deterministic equivalent ER - TY - JOUR TI - Logarithmic Vertex Algebras AU - Bakalov, Bojko N. AU - Villarreal, Juan J. T2 - TRANSFORMATION GROUPS AB - We introduce and study the notion of a logarithmic vertex algebra, which is a vertex algebra with logarithmic singularities in the operator product expansion of quantum fields; thus providing a rigorous formulation of the algebraic properties of quantum fields in logarithmic conformal field theory. We develop a framework that allows many results about vertex algebras to be extended to logarithmic vertex algebras, including in particular the Borcherds identity and Kac Existence Theorem. Several examples are investigated in detail, and they exhibit some unexpected new features that are peculiar to the logarithmic case. DA - 2022/9/9/ PY - 2022/9/9/ DO - 10.1007/s00031-022-09759-z SP - SN - 1531-586X KW - Logarithmic conformal field theory KW - Vertex algebra KW - Virasoro algebra ER - TY - JOUR TI - A novel stochastic optimization method for handling misalignments of proton and photon doses in combined treatments AU - Fabiano, Silvia AU - Torelli, Nathan AU - Papp, David AU - Unkelbach, Jan T2 - PHYSICS IN MEDICINE AND BIOLOGY AB - Abstract Objective. Combined proton–photon treatments, where most fractions are delivered with photons and only a few are delivered with protons, may represent a practical approach to optimally use limited proton resources. It has been shown that, when organs at risk (OARs) are located within or near the tumor, the optimal multi-modality treatment uses protons to hypofractionate parts of the target volume and photons to achieve near-uniform fractionation in dose-limiting healthy tissues, thus exploiting the fractionation effect. These plans may be sensitive to range and setup errors, especially misalignments between proton and photon doses. Thus, we developed a novel stochastic optimization method to directly incorporate these uncertainties into the biologically effective dose (BED)-based simultaneous optimization of proton and photon plans. Approach. The method considers the expected value E b and standard deviation σ b of the cumulative BED b in every voxel of a structure. For the target, a piecewise quadratic penalty function of the form b min E b 2 σ b + 2 is minimized, aiming for plans in which the expected BED minus two times the standard deviation exceeds the prescribed BED b min . Analogously, E b + 2 σ b b max + 2 is considered for OARs. Main results. Using a spinal metastasis case and a liver cancer patient, it is demonstrated that the novel stochastic optimization method yields robust combined treatment plans. Tumor coverage and a good sparing of the main OARs are maintained despite range and setup errors, and especially misalignments between proton and photon doses. This is achieved without explicitly considering all combinations of proton and photon error scenarios. Significance. Concerns about range and setup errors for safe clinical implementation of optimized proton–photon radiotherapy can be addressed through an appropriate stochastic planning method. DA - 2022/9/21/ PY - 2022/9/21/ DO - 10.1088/1361-6560/ac858f VL - 67 IS - 18 SP - SN - 1361-6560 KW - combined proton-photon radiotherapy KW - IMRT KW - IMPT KW - stochastic optimization ER - TY - JOUR TI - A Perspective on Data-Driven Coarse Grid Modeling for System Level Thermal Hydraulics AU - Iskhakov, Arsen S. AU - Tai, Cheng-Kai AU - Bolotnov, Igor A. AU - Dinh, Nam T. T2 - NUCLEAR SCIENCE AND ENGINEERING DA - 2022/9/10/ PY - 2022/9/10/ DO - 10.1080/00295639.2022.2107864 VL - 9 SP - SN - 1943-748X UR - http://dx.doi.org/10.1080/00295639.2022.2107864 KW - Data-driven methods KW - coarse grid modeling KW - system thermal hydraulics KW - machine learning KW - multiscale bridging ER - TY - JOUR TI - Kryging: geostatistical analysis of large-scale datasets using Krylov subspace methods AU - Majumder, Suman AU - Guan, Yawen AU - Reich, Brian J. AU - Saibaba, Arvind K. T2 - STATISTICS AND COMPUTING AB - Analyzing massive spatial datasets using a Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental health. We present a novel approximate inference methodology that uses profile likelihood and Krylov subspace methods to estimate the spatial covariance parameters and makes spatial predictions with uncertainty quantification for point-referenced spatial data. “Kryging” combines Kriging and Krylov subspace methods and applies for both observations on regular grid and irregularly spaced observations, and for any Gaussian process with a stationary isotropic (and certain geometrically anisotropic) covariance function, including the popular Matérn covariance family. We make use of the block Toeplitz structure with Toeplitz blocks of the covariance matrix and use fast Fourier transform methods to bypass the computational and memory bottlenecks of approximating log-determinant and matrix-vector products. We perform extensive simulation studies to show the effectiveness of our model by varying sample sizes, spatial parameter values and sampling designs. A real data application is also performed on a dataset consisting of land surface temperature readings taken by the MODIS satellite. Compared to existing methods, the proposed method performs satisfactorily with much less computation time and better scalability. DA - 2022/10// PY - 2022/10// DO - 10.1007/s11222-022-10104-3 VL - 32 IS - 5 SP - SN - 1573-1375 KW - Approximate inference KW - Profile likelihood KW - Block Toeplitz matrix KW - Fast Fourier transform KW - Krylov subspace methods KW - Golub-Kahan bidiagonalization ER - TY - JOUR TI - A resource for integrated genomic analysis of the human liver AU - Zhou, Yi-Hui AU - Gallins, Paul J. AU - Etheridge, Amy S. AU - Jima, Dereje AU - Scholl, Elizabeth AU - Wright, Fred A. AU - Innocenti, Federico T2 - SCIENTIFIC REPORTS AB - In this study, we generated whole-transcriptome RNA-Seq from n = 192 genotyped liver samples and used these data with existing data from the GTEx Project (RNA-Seq) and previous liver eQTL (microarray) studies to create an enhanced transcriptomic sequence resource in the human liver. Analyses of genotype-expression associations show pronounced enrichment of associations with genes of drug response. The associations are primarily consistent across the two RNA-Seq datasets, with some modest variation, indicating the importance of obtaining multiple datasets to produce a robust resource. We further used an empirical Bayesian model to compare eQTL patterns in liver and an additional 20 GTEx tissues, finding that MHC genes, and especially class II genes, are enriched for liver-specific eQTL patterns. To illustrate the utility of the resource to augment GWAS analysis with small sample sizes, we developed a novel meta-analysis technique to combine several liver eQTL data sources. We also illustrate its application using a transcriptome-enhanced re-analysis of a study of neutropenia in pancreatic cancer patients. The associations of genotype with liver expression, including splice variation and its genetic associations, are made available in a searchable genome browser. DA - 2022/9/7/ PY - 2022/9/7/ DO - 10.1038/s41598-022-18506-z VL - 12 IS - 1 SP - SN - 2045-2322 ER - TY - JOUR TI - Postural orthostatic tachycardia syndrome explained using a baroreflex response model AU - Geddes, Justen R. AU - Ottesen, Johnny T. AU - Mehlsen, Jesper AU - Olufsen, Mette S. T2 - JOURNAL OF THE ROYAL SOCIETY INTERFACE AB - Patients with postural orthostatic tachycardia syndrome (POTS) experience an excessive increase in heart rate (HR) and low-frequency (∼0.1 Hz) blood pressure (BP) and HR oscillations upon head-up tilt (HUT). These responses are attributed to increased baroreflex (BR) responses modulating sympathetic and parasympathetic signalling. This study uses a closed-loop cardiovascular compartment model controlled by the BR to predict BP and HR dynamics in response to HUT. The cardiovascular model predicts these quantities in the left ventricle, upper and lower body arteries and veins. HUT is simulated by letting gravity shift blood volume (BV) from the upper to the lower body compartments, and the BR control is modelled using set-point functions modulating peripheral vascular resistance, compliance, and cardiac contractility in response to changes in mean carotid BP. We demonstrate that modulation of parameters characterizing BR sensitivity allows us to predict the persistent increase in HR and the low-frequency BP and HR oscillations observed in POTS patients. Moreover, by increasing BR sensitivity, inhibiting BR control of the lower body vasculature, and decreasing central BV, we demonstrate that it is possible to simulate patients with neuropathic and hyperadrenergic POTS. DA - 2022/8/24/ PY - 2022/8/24/ DO - 10.1098/rsif.2022.0220 VL - 19 IS - 193 SP - SN - 1742-5662 KW - POTS KW - baroreflex KW - autonomic dysfunction KW - head-up tilt KW - mathematical modelling ER - TY - JOUR TI - Optimal Strategies for A Dual-Channel Farming Supply Chain with Horizontal Competition and Cooperation AU - Peng, Hongjun AU - Sun, Wenting AU - Pang, Tao T2 - ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH AB - In this paper, we consider a dual-channel farming supply chain with two farmers and one distributor, where agriculture products produced by farmers have different quality levels. Farmers sell high-quality products to supermarkets and normal-quality products to small retail markets, respectively. Three scenarios are investigated: decentralized selling through the distributor to supermarkets (the DD mode); centralized selling through the distributor to supermarkets (the CD mode); centralized selling directly to supermarkets (the CS mode). Under the CS mode, farmers need to bear some extra sale cost such as inventory and transportation cost. We derive farmers’ optimal strategies of production effort and quality investment. It turns out that as farming scale expands, farmers’ production effort decreases, while quality investment increases. Moreover, two farmers’ quality investments are the highest under the CS mode and the least under the DD mode. black Further analysis indicates that farmers’ total profits are generally the highest under the CS mode, but farmers obtain the highest profits under the CD mode if farmers’ extra sale cost under the CS mode exceeds a certain level. Therefore, to improve farmers’ welfare and agriculture products’ quality simultaneously, the CS mode may be the best choice in most cases, and it leads to a “win–win” situation for farmers and consumers. DA - 2022/4/26/ PY - 2022/4/26/ DO - 10.1142/S0217595922500154 SP - SN - 1793-7019 KW - Dual-channel farming supply chain KW - quality levels KW - horizontal cooperation and competition KW - production effort KW - quality investment ER - TY - JOUR TI - Effects of problem complexity reduction on parameter sensitivity and classification in charring ablator scenarios AU - Rostkowski, Przemyslaw AU - Meurisse, Jeremie B. E. AU - Thornton, John M. AU - Smith, Ralph C. AU - Panesi, Marco T2 - AEROSPACE SCIENCE AND TECHNOLOGY AB - We investigate here effects of adaptations like dimension reduction, omission of parameter correlation, and grid refinement on parameter influence over material temperature response and total recession. The task is accomplished by applying Morris screening and method of Sobol' sensitivity studies applied to a range of 3-D, 1-D, and 1-D TC1-driver cases for the MSL entry through the Martian atmosphere, where the material response of the MSL heat shield is simulated with NASA's PATO toolbox. Results of the investigation show that lower-dimensional approaches can, in some cases, be utilized for initial parameter screening prior to execution of a fully-detailed simulation, but in general, obtained sensitivities differ. Moreover, coarse computational grids do not impose significantly distinct input-output mechanics and can be utilized for accurate screening and quantitative sensitivity analysis exercises even with non-negligible residual values. The investigation also discusses the implications of an unknown correlation structure on parameter sensitivities while finding little evidence of significant correlation effects on parameter classification given input uncertainty bounds defined in this work. DA - 2022/5// PY - 2022/5// DO - 10.1016/j.ast.2022.107522 VL - 124 SP - SN - 1626-3219 KW - Mars Science Laboratory KW - Ablator KW - Material response KW - Sensitivity analysis KW - Sobol indices KW - Morris screening ER - TY - JOUR TI - Global sensitivity analysis: A novel generation of mighty estimators based on rank statistics AU - Gamboa, Fabrice AU - Gremaud, Pierre AU - Klein, Thierry AU - Lagnoux, Agnes T2 - BERNOULLI AB - We propose a new statistical estimation framework for a large family of global sensitivity analysis indices. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Chatterjee (Calcutta Statist. Assoc. Bull. 33 (1984) 1–2). We show how to apply this approach to compute not only the Cramér-von-Mises indices, directly related to Chatterjee’s notion of correlation, but also first-order Sobol’ indices, general metric space indices and higher-order moment indices. We establish consistency of the resulting estimators and demonstrate their numerical efficiency, especially for small sample sizes. In addition, we prove a central limit theorem for the estimators of the first-order Sobol’ indices. DA - 2022/11// PY - 2022/11// DO - 10.3150/21-BEJ1421 VL - 28 IS - 4 SP - 2345-2374 SN - 1573-9759 KW - Global sensitivity analysis KW - Cram?r-von-Mises distance KW - Pick-Freeze method KW - Chatterjee?s coefficient of correlation KW - Sobol? indices estimation ER - TY - JOUR TI - Quantum separability criteria based on realignment moments AU - Zhang, Tinggui AU - Jing, Naihuan AU - Fei, Shao-Ming T2 - QUANTUM INFORMATION PROCESSING AB - Quantum entanglement is the core resource in quantum information processing and quantum computing. It is an significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is presented in [Phys. Rev. Lett. 125, 200501 (2020)] by Elben et al. based on the first three partially transposed (PT) moments of density matrices. Then in [Phys. Rev. Lett. 127, 060504 (2021)] Yu \emph{et al.} proposed two general powerful criteria based on the PT moments. In this paper, based on the realignment operations of matrices we propose entanglement detection criteria in terms of such realignment moments. We show by detailed example that the realignment moments can also be used to identify quantum entanglement. DA - 2022/8/13/ PY - 2022/8/13/ DO - 10.1007/s11128-022-03630-6 VL - 21 IS - 8 SP - SN - 1573-1332 KW - Quantum entanglement KW - Separability criteria KW - Partially transposed (PT) moments KW - Realignment moments ER - TY - JOUR TI - Modeling a Pandemic: Predicting the Future AU - Lloyd, Alun AB - One of the simplest mathematical models for transmission of an infectious disease is the so-called SIR (Susceptible/Infected/Recovered) model. After explaining the setup of the model, we explore what it tells us about the spread of an infection such as COVID-19. The reproduction number (R) quantifies the average number of infections caused by an infected individual. If R is greater than one, the infection can spread. R depends on features such as the duration of infection, the number of contacts people make, the probability of transmission when an infected person meets a susceptible person, and the fraction of the population that is susceptible. Thinking about R lets us figure out how effective control measures need to be in order to dampen transmission. It also explains herd immunity: infection can no longer increase if there are not enough susceptible people in the population to maintain transmission. Finally, we explore the consequences of prematurely relaxing control measures. DA - 2022/6/22/ PY - 2022/6/22/ DO - 10.52750/915817 UR - https://doi.org/10.52750/915817 ER - TY - JOUR TI - Models: What Are They and Should We Believe Them? AU - Lloyd, Alun AB - During the COVID-19 outbreak we have often seen predictions of the epidemic created using models. These influence important decisions about disease control measures. But we hear that predictions made by models change, so how much can we trust them? In this talk, I discuss what models are, their limitations, and why their predictions have uncertainty. Having a better understanding of models will help us be better consumers of the information they provide. DA - 2022/6/22/ PY - 2022/6/22/ DO - 10.52750/905485 UR - https://doi.org/10.52750/905485 ER - TY - JOUR TI - Directed Gaussian graphical models with toric vanishing ideals AU - Misra, Pratik AU - Sullivant, Seth T2 - ADVANCES IN APPLIED MATHEMATICS AB - Directed Gaussian graphical models are statistical models that use a directed acyclic graph (DAG) to represent the conditional independence structures between a set of jointly normal random variables. The DAG specifies the model through recursive factorization of the parametrization, via restricted conditional distributions. In this paper, we make an attempt to characterize the DAGs whose vanishing ideals are toric ideals. In particular, we give some combinatorial criteria to construct such DAGs from smaller DAGs which have toric vanishing ideals. An associated monomial map called the shortest trek map plays an important role in our description of toric Gaussian DAG models. For DAGs whose vanishing ideal is toric, we prove results about the generating sets of those toric ideals. DA - 2022/7// PY - 2022/7// DO - 10.1016/j.aam.2022.102345 VL - 138 SP - SN - 1090-2074 KW - Clique sum KW - d-Separation KW - t-Separation KW - Shortest trek map KW - Safe gluing ER - TY - JOUR TI - Separability Criteria Based on the Weyl Operators AU - Huang, Xiaofen AU - Zhang, Tinggui AU - Zhao, Ming-Jing AU - Jing, Naihuan T2 - ENTROPY AB - Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We show that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation. DA - 2022/8// PY - 2022/8// DO - 10.3390/e24081064 VL - 24 IS - 8 SP - SN - 1099-4300 UR - https://doi.org/10.3390/e24081064 KW - separability KW - Weyl operators KW - Bloch representation KW - correlation matrix KW - quantum teleportation ER - TY - JOUR TI - Computationally efficient methods for large-scale atmospheric inverse modeling AU - Cho, Taewon AU - Chung, Julianne AU - Miller, Scot M. AU - Saibaba, Arvind K. T2 - GEOSCIENTIFIC MODEL DEVELOPMENT AB - Abstract. Atmospheric inverse modeling describes the process of estimating greenhouse gas fluxes or air pollution emissions at the Earth's surface using observations of these gases collected in the atmosphere. The launch of new satellites, the expansion of surface observation networks, and a desire for more detailed maps of surface fluxes have yielded numerous computational and statistical challenges for standard inverse modeling frameworks that were often originally designed with much smaller data sets in mind. In this article, we discuss computationally efficient methods for large-scale atmospheric inverse modeling and focus on addressing some of the main computational and practical challenges. We develop generalized hybrid projection methods, which are iterative methods for solving large-scale inverse problems, and specifically we focus on the case of estimating surface fluxes. These algorithms confer several advantages. They are efficient, in part because they converge quickly, they exploit efficient matrix–vector multiplications, and they do not require inversion of any matrices. These methods are also robust because they can accurately reconstruct surface fluxes, they are automatic since regularization or covariance matrix parameters and stopping criteria can be determined as part of the iterative algorithm, and they are flexible because they can be paired with many different types of atmospheric models. We demonstrate the benefits of generalized hybrid methods with a case study from NASA's Orbiting Carbon Observatory 2 (OCO-2) satellite. We then address the more challenging problem of solving the inverse model when the mean of the surface fluxes is not known a priori; we do so by reformulating the problem, thereby extending the applicability of hybrid projection methods to include hierarchical priors. We further show that by exploiting mathematical relations provided by the generalized hybrid method, we can efficiently calculate an approximate posterior variance, thereby providing uncertainty information. DA - 2022/7/20/ PY - 2022/7/20/ DO - 10.5194/gmd-15-5547-2022 VL - 15 IS - 14 SP - 5547-5565 SN - 1991-9603 ER - TY - JOUR TI - Distributed Gradient Flow: Nonsmoothness, Nonconvexity, and Saddle Point Evasion AU - Swenson, Brian AU - Murray, Ryan AU - Poor, H. Vincent AU - Kar, Soummya T2 - IEEE TRANSACTIONS ON AUTOMATIC CONTROL AB - The article considers distributed gradient flow (DGF) for multiagent nonconvex optimization. DGF is a continuous-time approximation of distributed gradient descent that is often easier to study than its discrete-time counterpart. The article has two main contributions. First, the article considers optimization of nonsmooth, nonconvex objective functions. It is shown that DGF converges to critical points in this setting. The article then considers the problem of avoiding saddle points. It is shown that if agents’ objective functions are assumed to be smooth and nonconvex, then DGF can only converge to a saddle point from a zero-measure set of initial conditions. To establish this result, the article proves a stable manifold theorem for DGF, which is a fundamental contribution of independent interest. In a companion article, analogous results are derived for discrete-time algorithms. DA - 2022/8// PY - 2022/8// DO - 10.1109/TAC.2021.3111853 VL - 67 IS - 8 SP - 3949-3964 SN - 1558-2523 UR - https://doi.org/10.1109/TAC.2021.3111853 KW - Optimization KW - Convergence KW - Linear programming KW - Manifolds KW - Standards KW - Heuristic algorithms KW - Trajectory KW - Distributed optimization KW - gradient descent KW - gradient flow KW - nonconvex optimization KW - nonsmooth optimization KW - saddle point KW - stable manifold ER - TY - JOUR TI - Lagrangian Cobordisms and Legendrian Invariants in Knot Floer Homology AU - Baldwin, John A. AU - Lidman, Tye AU - Wong, C-M Michael T2 - MICHIGAN MATHEMATICAL JOURNAL AB - We prove that the LOSS and GRID invariants of Legendrian links in knot Floer homology behave in certain functorial ways with respect to decomposable Lagrangian cobordisms in the symplectization of the standard contact structure on R3. Our results give new, computable, and effective obstructions to the existence of such cobordisms. DA - 2022/3// PY - 2022/3// DO - 10.1307/mmj/20195786 VL - 71 IS - 1 SP - 145-175 SN - 1945-2365 ER - TY - JOUR TI - Identifying multicellular spatiotemporal organization of cells with SpaceFlow AU - Ren, Honglei AU - Walker, Benjamin L. AU - Cang, Zixuan AU - Nie, Qing T2 - NATURE COMMUNICATIONS AB - Abstract One major challenge in analyzing spatial transcriptomic datasets is to simultaneously incorporate the cell transcriptome similarity and their spatial locations. Here, we introduce SpaceFlow, which generates spatially-consistent low-dimensional embeddings by incorporating both expression similarity and spatial information using spatially regularized deep graph networks. Based on the embedding, we introduce a pseudo-Spatiotemporal Map that integrates the pseudotime concept with spatial locations of the cells to unravel spatiotemporal patterns of cells. By comparing with multiple existing methods on several spatial transcriptomic datasets at both spot and single-cell resolutions, SpaceFlow is shown to produce a robust domain segmentation and identify biologically meaningful spatiotemporal patterns. Applications of SpaceFlow reveal evolving lineage in heart developmental data and tumor-immune interactions in human breast cancer data. Our study provides a flexible deep learning framework to incorporate spatiotemporal information in analyzing spatial transcriptomic data. DA - 2022/7/14/ PY - 2022/7/14/ DO - 10.1038/s41467-022-31739-w VL - 13 IS - 1 SP - SN - 2041-1723 UR - https://doi.org/10.1038/s41467-022-31739-w ER - TY - JOUR TI - Quantifying rare events in spotting: How far do wildfires spread? AU - Mendez, Alexander AU - Farazmand, Mohammad T2 - FIRE SAFETY JOURNAL AB - Spotting refers to the transport of burning pieces of firebrand by wind which, at the time of landing, may ignite new fires beyond the direct ignition zone of the main fire. Spot fires that occur far from the original burn unit are rare but have consequential ramifications since their prediction and control remains challenging. To facilitate their prediction, we examine three methods for quantifying the landing distribution of firebrands: crude Monte Carlo simulations, importance sampling, and large deviation theory (LDT). In particular, we propose an LDT method that accurately and parsimoniously quantifies the low probability events at the tail of the landing distribution. In contrast, Monte Carlo and importance sampling methods are most efficient in quantifying the high probability landing distances near the mode of the distribution. However, they become computationally intractable for quantifying the tail of the distribution due to the large sample size required. We also show that the most probable landing distance grows linearly with the mean characteristic velocity of the wind field. Furthermore, defining the relative landed mass as the proportion of mass landed at a given distance from the main fire, we derive an explicit formula which allows computing this quantity as a function of the landing distribution at a negligible computational cost. We numerically demonstrate our findings on two prescribed wind fields. DA - 2022/9// PY - 2022/9// DO - 10.1016/j.firesaf.2022.103630 VL - 132 SP - SN - 1873-7226 UR - https://doi.org/10.1016/j.firesaf.2022.103630 KW - Firebrand transport KW - Spotting KW - Monte Carlo method KW - Rare event simulation KW - Large deviation theory ER - TY - JOUR TI - Optimal technology adoption for power generation AU - Detemple, Jerome AU - Kitapbayev, Yerkin T2 - ENERGY ECONOMICS AB - We examine the decision problem of a power producer contemplating an upgrade of its current generation capacity based on a fossil fuel technology (gas plant), when price processes have affine drift and differentiable volatility functions. The operator can choose the best of four mutually exclusive alternatives, continue operating the current technology, replace it by a more efficient fossil fuel technology (gas plant), replace it by a renewable technology (wind plant), and divest (liquidate). There are four corresponding decision regions with three boundaries. Optimal boundaries of regions are characterized through a trivariate system of coupled Fredholm equations and valuation formulas derived. Investing in a more efficient gas plant is optimal if the gas price falls below some threshold and the electricity price exceeds an associated (gas) boundary. For some parameters, the gas price must also exceed a lower threshold. Investing in a wind plant is optimal if the gas price becomes sufficiently high and the electricity price exceeds an associated (wind) boundary. Liquidation is optimal if the electricity price falls below a (liquidation) boundary. The continuation region lies in between these boundaries. The possibility of investing in wind displaces new gas investment and postpones liquidation of the existing gas plant. We study the value of the firm and the Green Energy premium, and assess the impact of model parameters. • Four alternatives: Continue as is, switch to efficient gas technology, switch to wind, or liquidate. • Electricity and gas price processes with affine drifts and differentiable volatility functions. • Waiting is always optimal when two of the three alternatives have equal value, even if infinite. • The value of Green Energy (wind premium) does not necessarily increase when the gas price increases. DA - 2022/7// PY - 2022/7// DO - 10.1016/j.eneco.2022.106085 VL - 111 SP - SN - 1873-6181 KW - Investment KW - Power generation KW - Replacement KW - Wind plant KW - Gas Plant KW - Liquidation KW - Exclusive alternatives KW - Optimal boundaries KW - Firm value KW - Value of Green Energy ER - TY - JOUR TI - Tighter monogamy relations of entanglement measures based on fidelity AU - Zhang, Meiming AU - Jing, Naihuan T2 - LASER PHYSICS LETTERS AB - Abstract We study the Bures measure of entanglement and the geometric measure of entanglement as special cases of entanglement measures based on fidelity, and find their tighter monogamy inequalities over tri-qubit systems as well as multi-qubit systems. Furthermore, we derive the monogamy inequality of concurrence for qudit quantum systems by projecting higher-dimensional states to qubit substates. DA - 2022/8/1/ PY - 2022/8/1/ DO - 10.1088/1612-202X/ac772e VL - 19 IS - 8 SP - SN - 1612-202X KW - monogamy KW - Bures measure of entanglement KW - geometric measure of entanglement KW - concurrence ER - TY - JOUR TI - Bubble packing, eccentricity, and notochord development AU - Sorrell, Emma L. AU - Lubkin, Sharon R. T2 - CELLS & DEVELOPMENT AB - This paper develops a theoretical basis for the observed relationship between cell arrangements in notochords and analog physical models, and the eccentricity of their cross sections. Three models are developed and analyzed, of the mechanics of cell packing in sheaths. The key ratios governing the packing patterns and eccentricity are cells per unit length λ, tension ratio Γ, and eccentricity e. For flexible and semi-flexible sheaths, the optimal packing pattern shifts from "bamboo", with a symmetric cross section, to "staircase", with an eccentric cross section, at a critical value λ = 1.13. In rigid tubes, this threshold is lowered as imposed eccentricity is increased. Patterns can be observed which are not optimal; pattern transitions may occur below or above the critical λ values. The eccentricity of staircase patterns in flexible and semi-flexible tubes is found to be dependent on the tension ratio Γ, increasing as sheath tension decreases relative to interior cell tension. A novel "serpentine" packing pattern appears for low Γ near the critical λ. The developmental utility of enforcing notochord eccentricity is discussed, as well as potential mechanisms for such control. DA - 2022/3// PY - 2022/3// DO - 10.1016/j.cdev.2021.203753 VL - 169 SP - SN - 2667-2901 KW - Notochord KW - Foam KW - Biomechanics KW - Packing pattern KW - Tissue mechanics ER - TY - JOUR TI - Non-iterative domain decomposition for the Helmholtz equation with strong material discontinuities AU - North, Evan AU - Tsynkov, Semyon AU - Turkel, Eli T2 - APPLIED NUMERICAL MATHEMATICS AB - Many wave propagation problems involve discontinuous material properties. We propose to solve such problems by non-overlapping domain decomposition combined with the method of difference potentials (MDP). The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with projection on the boundary. The unknowns for the Calderon's equation are the Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered by applying their respective Calderon's equations to the same data at the common interface. Solutions on individual subdomains are computed concurrently using a direct solver. Our method proves to be insensitive to large jumps in the wavenumber for transmission problems, as well as interior cross-points and mixed boundary conditions, which may be a challenge to many other domain decomposition methods. DA - 2022/3// PY - 2022/3// DO - 10.1016/j.apnum.2021.10.024 VL - 173 SP - 51-78 SN - 1873-5460 KW - Time-harmonic waves KW - Non-overlapping domain decomposition KW - Calderon's operators KW - Difference potentials KW - Exact coupling between subdomains KW - High-order accuracy KW - Spectral representation at the boundary KW - Compact finite difference schemes KW - Direct solution KW - Complexity bounds KW - Discontinuous coefficients KW - Interior cross-points ER - TY - JOUR TI - Shock interactions for the Burgers-Hilbert equation AU - Bressan, Alberto AU - Galtung, Sondre T. AU - Grunert, Katrin AU - Nguyen, Khai T. T2 - COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS AB - This paper provides an asymptotic description of a solution to the Burgers-Hilbert equation in a neighborhood of a point where two shocks interact. The solution is obtained as the sum of a function with H2 regularity away from the shocks plus a corrector term having an asymptotic behavior like |x| ln |x| close to each shock. A key step in the analysis is the construction of piecewise smooth solutions with a single shock for a general class of initial data. DA - 2022/6/24/ PY - 2022/6/24/ DO - 10.1080/03605302.2022.2084628 VL - 6 SP - SN - 1532-4133 KW - Burgers-Hilbert equation KW - weak solution KW - piecewise regular solution KW - shock interaction ER - TY - JOUR TI - Technical note: Optimal allocation of limited proton therapy resources using model-based patient selection AU - Papp, David AU - Unkelbach, Jan T2 - MEDICAL PHYSICS AB - We consider the following scenario: A radiotherapy clinic has a limited number of proton therapy slots available each day to treat cancer patients of a given tumor site. The clinic's goal is to minimize the expected number of complications in the cohort of all patients of that tumor site treated at the clinic, and thereby maximize the benefit of its limited proton resources.To address this problem, we extend the normal tissue complication probability (NTCP) model-based approach to proton therapy patient selection to the situation of limited resources at a given institution. We assume that, on each day, a newly diagnosed patient is scheduled for treatment at the clinic with some probability and with some benefit ΔNTCP$\Delta NTCP$ from protons over photons, which is drawn from a probability distribution. When a new patient is scheduled for treatment, a decision for protons or photons must be made, and a patient may wait only for a limited amount of time for a proton slot becoming available. The goal is to determine the ΔNTCP$\Delta NTCP$ thresholds for selecting a patient for proton therapy, which optimally balance the competing goals of making use of all available slots while not blocking slots with patients with low benefit. This problem can be formulated as a Markov decision process (MDP) and the optimal thresholds can be determined via a value-policy iteration method.The optimal ΔNTCP$\Delta NTCP$ thresholds depend on the number of available proton slots, the average number of patients under treatment, and the distribution of ΔNTCP$\Delta NTCP$ values. In addition, the optimal thresholds depend on the current utilization of the facility. For example, if one proton slot is available and a second frees up shortly, the optimal ΔNTCP$\Delta NTCP$ threshold is lower compared to a situation where all but one slot remain blocked for longer.MDP methodology can be used to augment current NTCP model-based patient selection methods to the situation that, on any given day, the number of proton slots is limited. The optimal ΔNTCP$\Delta NTCP$ threshold then depends on the current utilization of the proton facility. Although, the optimal policy yields only a small nominal benefit over a constant threshold, it is more robust against variations in patient load. DA - 2022/6/26/ PY - 2022/6/26/ DO - 10.1002/mp.15812 VL - 6 SP - SN - 2473-4209 KW - Markov decision process KW - patient selection KW - proton therapy ER - TY - JOUR TI - MONTE CARLO ESTIMATORS FOR THE SCHATTEN p-NORM OF SYMMETRIC POSITIVE SEMIDEFINITE MATRICES AU - DUDLEY, E. T. H. A. N. AU - SAIBABA, A. R. V. I. N. D. K. AU - ALEXANDERIAN, A. L. E. N. T2 - ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS AB - We present numerical methods for computing the Schatten p-norm of positive semi-definite matrices. Our motivation stems from uncertainty quantification and optimal experimental design for inverse problems, where the Schatten p-norm defines a measure of uncertainty. Computing the Schatten p-norm of high-dimensional matrices is computationally expensive. We propose a matrix-free method to estimate the Schatten p-norm using a Monte Carlo estimator and derive convergence results and error estimates for the estimator. To efficiently compute the Schatten p-norm for non-integer and large values of p, we use an estimator using Chebyshev polynomial approximations and extend our convergence and error analysis to this setting as well. We demonstrate the performance of our proposed estimators on several test matrices and in an application to optimal experimental design for a model inverse problem. DA - 2022/// PY - 2022/// DO - 10.1553/etna_vol55s213 VL - 55 SP - 213-241 SN - 1068-9613 KW - Schatten p-norm KW - Monte Carlo estimator KW - optimal experimental design KW - Chebyshev polynomials ER - TY - JOUR TI - TAaCGH Suite for Detecting Cancer-Specific Copy Number Changes Using Topological Signatures AU - Aslam, Jai AU - Ardanza-Trevijano, Sergio AU - Xiong, Jingwei AU - Arsuaga, Javier AU - Sazdanovic, Radmila T2 - ENTROPY AB - Copy number changes play an important role in the development of cancer and are commonly associated with changes in gene expression. Persistence curves, such as Betti curves, have been used to detect copy number changes; however, it is known these curves are unstable with respect to small perturbations in the data. We address the stability of lifespan and Betti curves by providing bounds on the distance between persistence curves of Vietoris–Rips filtrations built on data and slightly perturbed data in terms of the bottleneck distance. Next, we perform simulations to compare the predictive ability of Betti curves, lifespan curves (conditionally stable) and stable persistent landscapes to detect copy number aberrations. We use these methods to identify significant chromosome regions associated with the four major molecular subtypes of breast cancer: Luminal A, Luminal B, Basal and HER2 positive. Identified segments are then used as predictor variables to build machine learning models which classify patients as one of the four subtypes. We find that no single persistence curve outperforms the others and instead suggest a complementary approach using a suite of persistence curves. In this study, we identified new cytobands associated with three of the subtypes: 1q21.1-q25.2, 2p23.2-p16.3, 23q26.2-q28 with the Basal subtype, 8p22-p11.1 with Luminal B and 2q12.1-q21.1 and 5p14.3-p12 with Luminal A. These segments are validated by the TCGA BRCA cohort dataset except for those found for Luminal A. DA - 2022/7// PY - 2022/7// DO - 10.3390/e24070896 VL - 24 IS - 7 SP - SN - 1099-4300 UR - https://www.mdpi.com/1099-4300/24/7/896 KW - breast cancer molecular subtypes KW - genomics KW - topological data analysis KW - CNA copy number aberrations KW - lifespan curves KW - Betti curves KW - persistence landscapes ER - TY - JOUR TI - Using ultrasonic attenuation in cortical bone to infer distributions on pore size AU - White, R. D. AU - Alexanderian, A. AU - Yousefian, O. AU - Karbalaeisadegh, Y. AU - Bekele-Maxwell, K. AU - Kasali, A. AU - Banks, H. T. AU - Talmant, M. AU - Grimal, Q. AU - Muller, M. T2 - APPLIED MATHEMATICAL MODELLING AB - In this work we infer the underlying distribution on pore radius in human cortical bone samples using ultrasonic attenuation data. We first discuss how to formulate polydisperse attenuation models using a probabilistic approach and the Waterman Truell model for scattering attenuation. We then compare the Independent Scattering Approximation and the higher-order Waterman Truell models’ forward predictions for total attenuation in polydisperse samples. Following this, we formulate an inverse problem under the Prohorov Metric Framework coupled with variational regularization to stabilize this inverse problem. We then use experimental attenuation data taken from human cadaver samples and solve inverse problems resulting in nonparametric estimates of the probability density function on pore radius. We compare these estimates to the “true” microstructure of the bone samples determined via microCT imaging. We find that our methodology allows us to reliably estimate the underlying microstructure of the bone from attenuation data. DA - 2022/9// PY - 2022/9// DO - 10.1016/j.apm.2022.05.024 VL - 109 SP - 819-832 SN - 1872-8480 KW - Ultrasound KW - Cortical bone KW - Polydisperse KW - Waterman truell KW - Inverse problems KW - Variational regularization ER - TY - JOUR TI - Conormal Spaces and Whitney Stratifications AU - Helmer, Martin AU - Nanda, Vidit T2 - FOUNDATIONS OF COMPUTATIONAL MATHEMATICS AB - We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal spaces and maps, and (b) a new interpretation of this conormal criterion via primary decomposition, which can be practically implemented on a computer. We show that this algorithm improves upon the existing state of the art by several orders of magnitude, even for relatively small input varieties. En route, we introduce related algorithms for efficiently stratifying affine varieties, flags on a given variety, and algebraic maps. DA - 2022/6/14/ PY - 2022/6/14/ DO - 10.1007/s10208-022-09574-8 SP - SN - 1615-3383 KW - Whitney stratification KW - Conormal variety KW - Ideal saturation ER - TY - JOUR TI - Unsupervised learning methods for efficient geographic clustering and identification of disease disparities with applications to county-level colorectal cancer incidence in California AU - McMahon, Mallory E. AU - Doroshenko, Lyubov AU - Roostaei, Javad AU - Cho, Hyunsoon AU - Haider, Mansoor A. T2 - HEALTH CARE MANAGEMENT SCIENCE DA - 2022/6/23/ PY - 2022/6/23/ DO - 10.1007/s10729-022-09604-5 VL - 6 SP - SN - 1572-9389 UR - https://doi.org/10.1007/s10729-022-09604-5 KW - Spatial clustering KW - Self-organizing map KW - K-Means clustering KW - Optimization KW - Colorectal cancer ER - TY - JOUR TI - UNIQUENESS OF THE PARTIAL TRAVEL TIME REPRESENTATION OF A COMPACT RIEMANNIAN MANIFOLD WITH STRICTLY CONVEX BOUNDARY AU - Pavlechko, Ella AU - Saksala, Teemu T2 - INVERSE PROBLEMS AND IMAGING AB - <p style='text-indent:20px;'>In this paper a compact Riemannian manifold with strictly convex boundary is reconstructed from its partial travel time data. This data assumes that an open measurement region on the boundary is given, and that for every point in the manifold, the respective distance function to the points on the measurement region is known. This geometric inverse problem has many connections to seismology, in particular to microseismicity. The reconstruction is based on embedding the manifold in a function space. This requires the differentiation of the distance functions. Therefore this paper also studies some global regularity properties of the distance function on a compact Riemannian manifold with strictly convex boundary.</p> DA - 2022/5// PY - 2022/5// DO - 10.3934/ipi.2022028 SP - SN - 1930-8345 KW -   KW - Inverse problem KW - Riemannian geometry KW - distance function KW - geodesics ER - TY - JOUR TI - Statistical Arbitrage for Multiple Co-integrated Stocks AU - Li, Thomas Nanfeng AU - Papanicolaou, Andrew T2 - Applied Mathematics & Optimization AB - In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a Hamilton–Jacobi–Bellman (HJB) partial differential equation, which we solve for both an unconstrained portfolio and a portfolio constrained to be market neutral. Our analyses demonstrate sufficient conditions on the model parameters to ensure long-term stability of the HJB solutions and stable growth rates for the optimal portfolios. To gauge how these optimal portfolios behave in practice, we perform backtests on historical stock prices of the S&P 500 constituents from year 2000 through year 2021. These backtests suggest three key conclusions: that the proposed co-integrated model with eigenportfolios being factors can generate a large number of co-integrated stocks over a long time horizon, that the optimal portfolios are sensitive to parameter estimation, and that the statistical arbitrage strategies are more profitable in periods when overall market volatilities are high. DA - 2022/6/7/ PY - 2022/6/7/ DO - 10.1007/s00245-022-09838-3 VL - 86 IS - 1 SP - J2 - Appl Math Optim LA - en OP - SN - 0095-4616 1432-0606 UR - http://dx.doi.org/10.1007/s00245-022-09838-3 DB - Crossref KW - Co-integrated stocks KW - Eigenportfolio KW - Factor model KW - Market-neutral portfolio KW - Matrix Riccati equation KW - Optimisation KW - Statistical arbitrage KW - Stochastic control ER - TY - JOUR TI - Post-Radiotherapy PET Image Outcome Prediction by Deep Learning Under Biological Model Guidance: A Feasibility Study of Oropharyngeal Cancer Application AU - Ji, Hangjie AU - Lafata, Kyle AU - Mowery, Yvonne AU - Brizel, David AU - Bertozzi, Andrea L. AU - Yin, Fang-Fang AU - Wang, Chunhao T2 - FRONTIERS IN ONCOLOGY AB - To develop a method of biologically guided deep learning for post-radiation 18FDG-PET image outcome prediction based on pre-radiation images and radiotherapy dose information.Based on the classic reaction-diffusion mechanism, a novel biological model was proposed using a partial differential equation that incorporates spatial radiation dose distribution as a patient-specific treatment information variable. A 7-layer encoder-decoder-based convolutional neural network (CNN) was designed and trained to learn the proposed biological model. As such, the model could generate post-radiation 18FDG-PET image outcome predictions with breakdown biological components for enhanced explainability. The proposed method was developed using 64 oropharyngeal patients with paired 18FDG-PET studies before and after 20-Gy delivery (2 Gy/day fraction) by intensity-modulated radiotherapy (IMRT). In a two-branch deep learning execution, the proposed CNN learns specific terms in the biological model from paired 18FDG-PET images and spatial dose distribution in one branch, and the biological model generates post-20-Gy 18FDG-PET image prediction in the other branch. As in 2D execution, 718/233/230 axial slices from 38/13/13 patients were used for training/validation/independent test. The prediction image results in test cases were compared with the ground-truth results quantitatively.The proposed method successfully generated post-20-Gy 18FDG-PET image outcome prediction with breakdown illustrations of biological model components. Standardized uptake value (SUV) mean values in 18FDG high-uptake regions of predicted images (2.45 ± 0.25) were similar to ground-truth results (2.51 ± 0.33). In 2D-based Gamma analysis, the median/mean Gamma Index (<1) passing rate of test images was 96.5%/92.8% using the 5%/5 mm criterion; such result was improved to 99.9%/99.6% when 10%/10 mm was adopted.The developed biologically guided deep learning method achieved post-20-Gy 18FDG-PET image outcome predictions in good agreement with ground-truth results. With the breakdown biological modeling components, the outcome image predictions could be used in adaptive radiotherapy decision-making to optimize personalized plans for the best outcome in the future. DA - 2022/5/13/ PY - 2022/5/13/ DO - 10.3389/fonc.2022.895544 VL - 12 SP - SN - 2234-943X KW - biological modeling KW - deep learning KW - image outcome prediction KW - radiotherapy KW - (18)FDG-PET ER - TY - JOUR TI - An XGBoost-Based Fitted Q Iteration for Finding the Optimal STI Strategies for HIV Patients AU - Yu, Yahe AU - Tran, Hien T2 - IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS AB - The computational algorithm proposed in this article is an important step toward the development of computational tools that could help guide clinicians to personalize the management of human immunodeficiency virus (HIV) infection. In this article, an XGBoost-based fitted Q iteration algorithm is proposed for finding the optimal structured treatment interruption (STI) strategies for HIV patients. Using the XGBoost-based fitted Q iteration algorithm, we can obtain acceptable and optimal STI strategies with fewer training data, when compared with the extra-tree-based fitted Q iteration algorithm, deep Q-networks (DQNs), and proximal policy optimization (PPO) algorithm. In addition, the XGBoost-based fitted Q iteration algorithm is computationally more efficient than the extra-tree-based fitted Q iteration algorithm. DA - 2022/6/2/ PY - 2022/6/2/ DO - 10.1109/TNNLS.2022.3176204 VL - 6 SP - SN - 2162-2388 KW - Viruses (medical) KW - Immune system KW - Drugs KW - Numerical models KW - Subspace constraints KW - Mathematical models KW - Load modeling KW - Fitted Q iteration algorithm KW - human immunodeficiency virus (HIV) KW - reinforcement learning KW - structured treatment interruption (STI) strategy KW - XGBoost regression ER - TY - JOUR TI - Numerical simulation and analysis of multiscale interface coupling between a poroelastic medium and a lumped hydraulic circuit: Comparison between functional iteration and operator splitting methods AU - Bociu, Lorena AU - Guidoboni, Giovanna AU - Sacco, Riccardo AU - Prada, Daniele T2 - JOURNAL OF COMPUTATIONAL PHYSICS AB - We consider a multiscale problem modeling the flow of a fluid through a deformable porous medium, described by a system of partial differential equations (PDEs), connected with a lumped hydraulic circuit, described by a system of ordinary differential equations (ODEs). This PDE/ODE coupled problem includes interface conditions enforcing the continuity of mass and the balance of stresses across models at different scales. In the present article, we address questions related to the solution methods of the PDE/ODE coupled problem via staggered algorithms, focusing on a detailed comparison between functional iterations and an energy-based operator splitting method and how they handle the interface conditions. We provide sufficient conditions for the convergence of functional iterations and prove that the energy-based operator splitting method is unconditionally stable with respect to the size of the time discretization step. DA - 2022/10/1/ PY - 2022/10/1/ DO - 10.1016/j.jcp.2022.111379 VL - 466 SP - SN - 1090-2716 UR - https://doi.org/10.1016/j.jcp.2022.111379 KW - Multiscale interface coupling KW - Poroelasticity KW - Lumped hydraulic circuit KW - Operator splitting KW - Functional iterations ER - TY - JOUR TI - Torsion in thin regions of Khovanov homology AU - Chandler, Alex AU - Lowrance, Adam M. AU - Sazdanovic, Radmila AU - Summers, Victor T2 - CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES AB - Abstract In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is, links whose Khovanov homology is supported on two adjacent diagonals, are known to contain only $\mathbb {Z}_2$ torsion. In this paper, we prove a local version of this result. If the Khovanov homology of a link is supported on two adjacent diagonals over a range of homological gradings and the Khovanov homology satisfies some other mild restrictions, then the Khovanov homology of that link has only $\mathbb {Z}_2$ torsion over that range of homological gradings. These conditions are then shown to be met by an infinite family of three-braids, strictly containing all three-strand torus links, thus giving a partial answer to Sazdanović and Przytycki’s conjecture that three-braids have only $\mathbb {Z}_2$ torsion in Khovanov homology. We use these computations and our main theorem to obtain the integral Khovanov homology for all links in this family. DA - 2022/6// PY - 2022/6// DO - 10.4153/S0008414X21000043 VL - 74 IS - 3 SP - 630-654 SN - 1496-4279 KW - Knot KW - Khovanov homology KW - homologically thin ER - TY - JOUR TI -

A broken circuit model for chromatic homology theories

AU - Chandler, Alex AU - Sazdanovic, Radmila T2 - EUROPEAN JOURNAL OF COMBINATORICS AB - Using the tools of algebraic Morse theory, and the thin poset approach to constructing homology theories, we give the categorification of Whitney’s broken circuit theorem for the chromatic polynomial, and for Stanley’s chromatic symmetric function. DA - 2022/8// PY - 2022/8// DO - 10.1016/j.ejc.2022.103538 VL - 104 SP - SN - 1095-9971 UR - http://dx.doi.org/10.1016/j.ejc.2022.103538 ER - TY - JOUR TI - A high order compact time/space finite difference scheme for the 2D and 3D wave equation with a damping layer AU - Kahana, Adar AU - Smith, Fouche AU - Turkel, Eli AU - Tsynkov, Semyon T2 - JOURNAL OF COMPUTATIONAL PHYSICS AB - We consider fourth order accurate compact schemes, in both space and time, for the second order wave equation with a variable speed of sound. For unbounded domains we add a fourth order accurate sponge layer to damp the outgoing waves. We demonstrate that usually this is more efficient than lower order schemes despite being implicit and conditionally stable. Fast time marching of the implicit scheme is accomplished by iterative methods such as multi-grid. Computations confirm the design convergence rate for the in-homogeneous, variable wave speed equation. DA - 2022/7/1/ PY - 2022/7/1/ DO - 10.1016/j.jcp.2022.111161 VL - 460 SP - SN - 1090-2716 KW - Compact finite differences KW - Absorbing boundary layer KW - Unbounded domain KW - High-order accuracy KW - Wave equation ER - TY - JOUR TI - Influence of water table dynamics on spatial and temporal patterns of hydroclimate extremes over Lake Victoria Basin, East Africa: Comparison of wet and dry years AU - Anyah, Richard AU - Xia, Sun AU - Semazzi, Fredrick T2 - INTERNATIONAL JOURNAL OF CLIMATOLOGY AB - Abstract WRF model coupled to water table dynamics has been adapted to investigate the spatial and temporal evolution of wet and dry conditions over Lake Victoria Basin. Two 2‐year long simulations were conducted using coupled model with water table and the uncoupled (without water table) for wet and dry periods. Influence of water table on land–atmosphere coupling and interconnections among precipitation, soil moisture, evapotranspiration, and surface energy fluxes were examined. Overall, the coupled model simulated significantly higher monthly rainfall amounts during both the short (March‐May) and long (October‐December) rains of the wet year, which was more consistent with observations particularly over the lake surface and immediate hinterlands. Simulated monthly rainfall differences between coupled and uncoupled were pronounced during the peak of long rains, exceeding 100mm over the lake surface. Toward the end of the rainfall season (May) the difference was minimal. During the short rains significant differences occurred mostly in November, especially over the eastern shores. But during the relatively dry year minimal differences were generally witnessed throughout the year except in May, east of Lake Victoria. The coupled model simulated stronger matching among rainfall, soil moisture, and evapotranspiration over areas with shallow water table, for example in Kisumu to the east and Bukoba to the west. In these areas coupled model simulated higher soil moisture corresponding to higher evapotranspiration and precipitation. These interconnections were more pronounced during short and long rains in 1997 (wet) compared to 2010 (dry). Wet conditions over the gulf of Kisumu corresponded with rise in water table especially during October–December 1997 consistent with ENSO‐related flooding over the area. Hence, our study demonstrated that incorporating water table resulted in realistic interconnections between precipitation, soil moisture, ET, and surface energy fluxes, and could improve simulation and prediction of spatial‐temporal evolution of wet and dry conditions over Lake Victoria Basin. DA - 2022/5/16/ PY - 2022/5/16/ DO - 10.1002/joc.7682 SP - SN - 1097-0088 KW - Lake Victoria Basin KW - water table dynamics KW - wet and dry conditions ER - TY - JOUR TI - Weak solutions in nonlinear poroelasticity with incompressible constituents AU - Bociu, Lorena AU - Muha, Boris AU - Webster, Justin T. T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS AB - We consider quasi-static nonlinear poroelastic systems with applications in biomechanics and, in particular, tissue perfusion. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid pressure are considered. The system under consideration represents a nonlinear, implicit, degenerate evolution problem, which falls outside of the well-known implicit semigroup monotone theory. Previous literature related to proving existence of weak solutions for these systems is based on constructing solutions as limits of approximations, and energy estimates are obtained only for the constructed solutions. In comparison, in this treatment we provide for the first time a direct, fixed point strategy for proving the existence of weak solutions, which is made possible by a novel result on the uniqueness of weak solutions of the associated linear system (where the permeability is given as a function of space and time). The uniqueness proof for the associated linear problem is based on novel energy estimates for arbitrary weak solutions, rather than just for constructed solutions. The results of this work provide a foundation for addressing strong solutions, as well as uniqueness of weak solutions for nonlinear poroelastic systems. DA - 2022/10// PY - 2022/10// DO - 10.1016/j.nonrwa.2022.103563 VL - 67 SP - SN - 1878-5719 KW - Nonlinear poroelasticity KW - Implicit evolution equations KW - Quasilinear parabolic KW - Weak solutions KW - Energy methods KW - Incompressible constituents ER - TY - JOUR TI - Local Unitary Equivalence of Generic Multi-qubits Based on the CP Decomposition AU - Chang, Jingmei AU - Jing, Naihuan T2 - INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS AB - The CANDECOMP/PARAFAC (CP) decomposition is a generalization of the spectral decomposition of matrices to higher-order tensors. In this paper we use the CP decomposition to study unitary equivalence of higher order tensors and construct several invariants of local unitary equivalence for general higher order tensors. Based on this new method, we study the coefficient tensors of 3-qubit states and obtain a necessary and sufficient criterion for local unitary equivalence of general tripartite states in terms of the CP decomposition. We also generalize this method to obtain some invariants of local unitary equivalence for general multi-partite qudits. DA - 2022/5/12/ PY - 2022/5/12/ DO - 10.1007/s10773-022-05106-w VL - 61 IS - 5 SP - SN - 1572-9575 KW - Local unitary equivalence KW - Tensors KW - CP decomposition ER - TY - JOUR TI - Consistent time‐homogeneous modeling of SPX and VIX derivatives AU - Papanicolaou, Andrew T2 - Mathematical Finance AB - Abstract This paper shows how to recover a stochastic volatility model (SVM) from a market model of the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore are better suited for pricing VIX futures and VIX derivatives. But the VIX itself is a derivative of the S&P500 (SPX) and it is common practice to price SPX derivatives using an SVM. Therefore, consistent modeling for both SPX and VIX should involve an SVM that can be obtained by inverting the market model. This paper's main result is a method for the recovery of a stochastic volatility function by solving an inverse problem where the input is the VIX function given by a market model. Analysis will show conditions necessary for there to be a unique solution to this inverse problem. The models are consistent if the recovered volatility function is non‐negative. Examples are presented to illustrate the theory, to highlight the issue of negativity in solutions, and to show the potential for inconsistency in non‐Markov settings. DA - 2022/5/14/ PY - 2022/5/14/ DO - 10.1111/mafi.12348 VL - 32 IS - 3 SP - 907-940 J2 - Mathematical Finance LA - en OP - SN - 0960-1627 1467-9965 UR - http://dx.doi.org/10.1111/mafi.12348 DB - Crossref KW - consistent pricing KW - market models KW - stochastic volatility KW - VIX futures ER - TY - JOUR TI - A new patch up technique for elliptic partial differential equation with irregularities AU - Singh, Swarn AU - Singh, Suruchi AU - Li, Zhilin T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS AB - This paper presents a new technique based on a collocation method using cubic splines for second order elliptic equation with irregularities in one dimension and two dimensions. The differential equation is first collocated at the two smooth sub domains divided by the interface. We extend the sub domains from the interior of the domain and then the scheme at the interface is developed by patching them up. The scheme obtained gives the second order accurate solution at the interface as well as at the regular points. Second order accuracy for the approximations of the first order and the second order derivative of the solution can also be seen from the experiments performed. Numerical experiments for 2D problems also demonstrate the second order accuracy of the present scheme for the solution u and the derivatives ux,uxx and the mixed derivative uxy. The approach to derive the interface relations, established in this paper for elliptic interface problems, can be helpful to derive high order accurate numerical methods. Numerical tests exhibit the super convergent properties of the scheme. DA - 2022/6// PY - 2022/6// DO - 10.1016/j.cam.2021.113975 VL - 407 SP - SN - 1879-1778 KW - Elliptic partial differential equation KW - Interface KW - Jump conditions KW - Cubic spline collocation KW - Irregularities KW - Patch up technique ER - TY - JOUR TI - Model-assisted deep learning of rare extreme events from partial observations AU - Asch, Anna AU - J. Brady, Ethan AU - Gallardo, Hugo AU - Hood, John AU - Chu, Bryan AU - Farazmand, Mohammad T2 - CHAOS AB - To predict rare extreme events using deep neural networks, one encounters the so-called small data problem because even long-term observations often contain few extreme events. Here, we investigate a model-assisted framework where the training data are obtained from numerical simulations, as opposed to observations, with adequate samples from extreme events. However, to ensure the trained networks are applicable in practice, the training is not performed on the full simulation data; instead, we only use a small subset of observable quantities, which can be measured in practice. We investigate the feasibility of this model-assisted framework on three different dynamical systems (Rössler attractor, FitzHugh-Nagumo model, and a turbulent fluid flow) and three different deep neural network architectures (feedforward, long short-term memory, and reservoir computing). In each case, we study the prediction accuracy, robustness to noise, reproducibility under repeated training, and sensitivity to the type of input data. In particular, we find long short-term memory networks to be most robust to noise and to yield relatively accurate predictions, while requiring minimal fine-tuning of the hyperparameters. DA - 2022/4// PY - 2022/4// DO - 10.1063/5.0077646 VL - 32 IS - 4 SP - SN - 1089-7682 UR - https://doi.org/10.1063/5.0077646 ER - TY - JOUR TI - Near-Optimal Variance-Based Uncertainty Relations AU - Xiao, Yunlong AU - Jing, Naihuan AU - Yu, Bing AU - Fei, Shao-Ming AU - Li-Jost, Xianqing T2 - FRONTIERS IN PHYSICS AB - Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg’s uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum theory. Aside from its fundamental significance, the mathematical characterization of this restriction, known as ‘uncertainty relation’, plays important roles in a wide range of applications, stimulating the formation of tighter uncertainty relations. In this work, we investigate the fundamental limitations of variance-based uncertainty relations, and introduce several ‘near optimal’ bounds for incompatible observables. Our results consist of two morphologically distinct phases: lower bounds that illustrate the uncertainties about measurement outcomes, and the upper bound that indicates the potential knowledge we can gain. Combining them together leads to an uncertainty interval , which captures the essence of uncertainties in quantum theory. Finally, we have detailed how to formulate lower bounds for product-form variance-based uncertainty relations by employing entropic uncertainty relations, and hence built a link between different forms of uncertainty relations. DA - 2022/4/1/ PY - 2022/4/1/ DO - 10.3389/fphy.2022.846330 VL - 10 SP - SN - 2296-424X KW -

numbers:& nbsp;03.65.ta,& nbsp;& nbsp;03.67.a,& nbsp;& nbsp;42.50.lc

KW - uncertainty relation KW - variance-based KW - uncertainty interval ER - TY - JOUR TI - Detection of Multipartite Entanglement Based on Heisenberg-Weyl Representation of Density Matrices AU - Zhao, Hui AU - Yang, Yu AU - Jing, Naihuan AU - Wang, Zhi-Xi AU - Fei, Shao-Ming T2 - INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS AB - We study entanglement and genuine entanglement of tripartite and four-partite quantum states by using Heisenberg-Weyl (HW) representation of density matrices. Based on the correlation tensors in HW representation, we present criteria to detect entanglement and genuine tripartite and four-partite entanglement. Detailed examples show that our method can detect more entangled states than previous criteria. DA - 2022/5/10/ PY - 2022/5/10/ DO - 10.1007/s10773-022-05123-9 VL - 61 IS - 5 SP - SN - 1572-9575 KW - Heisenberg-Weyl representation KW - Genuine entanglement KW - Correlation tensor ER - TY - JOUR TI - Tukey Depths and Hamilton-Jacobi Differential Equations AU - Molina-Fructuoso, Martin AU - Murray, Ryan T2 - SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE AB - Widespread application of modern machine learning has increased the need for robust statistical algorithms. This work studies one such fundamental statistical concept known as the Tukey depth. We study the problem in the continuum (population) limit. In particular, we formally derive the associated necessary conditions, which take the form of a first-order partial differential equation which is necessarily satisfied at points where the Tukey depth is smooth. We discuss the interpretation of this formal necessary condition in terms of the viscosity solution of a Hamilton--Jacobi equation, but with a nonclassical Hamiltonian with discontinuous dependence on the gradient at zero. We prove that this equation possesses a unique viscosity solution and that this solution always bounds the Tukey depth from below. In certain cases we prove that the Tukey depth is equal to the viscosity solution, and we give some illustrations of standard numerical methods from the optimal control community which deal directly with the partial differential equation. We conclude by outlining several promising research directions both in terms of new numerical algorithms and theoretical challenges. DA - 2022/// PY - 2022/// DO - 10.1137/21M1411998 VL - 4 IS - 2 SP - 604-633 SN - 2577-0187 UR - https://doi.org/10.1137/21M1411998 KW - statistical depths KW - robust statistics KW - Hamilton-Jacobi equations KW - viscosity solutions ER - TY - JOUR TI - Shape-morphing reduced-order models for nonlinear Schrodinger equations AU - Anderson, William AU - Farazmand, Mohammad T2 - NONLINEAR DYNAMICS AB - We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrodinger (NLS) equations. We compare two nonlinear reduced-order modeling methods: (i) The reduced Lagrangian approach which relies on the variational formulation of NLS and (ii) The recently developed method of reduced-order nonlinear solutions (RONS). First, we prove the surprising result that, although the two methods are seemingly quite different, they can be obtained from the real and imaginary parts of a single complex-valued master equation. Furthermore, for the NLS equation in a stationary frame, we show that the reduced Lagrangian method fails to predict the correct group velocity of the waves whereas RONS predicts the correct group velocity. Finally, for the modified NLS equation, where the reduced Lagrangian approach is inapplicable, the RONS reduced-order model accurately approximates the true solutions. DA - 2022/4/25/ PY - 2022/4/25/ DO - 10.1007/s11071-022-07448-w VL - 4 IS - 4 SP - SN - 1573-269X UR - https://doi.org/10.1007/s11071-022-07448-w KW - Model order reduction KW - Partial differential equations KW - Nonlinear Schrodinger equation KW - Variational methods ER - TY - JOUR TI - A multilevel approach to stochastic trace estimation AU - Hallman, Eric AU - Troester, Devon T2 - LINEAR ALGEBRA AND ITS APPLICATIONS AB - This article presents a randomized matrix-free method for approximating the trace of f(A), where A is a large symmetric matrix and f is a function analytic in a closed interval containing the eigenvalues of A. Our method uses a combination of stochastic trace estimation (i.e., Hutchinson's method), Chebyshev approximation, and multilevel Monte Carlo techniques. We establish general bounds on the approximation error of this method by extending an existing error bound for Hutchinson's method to multilevel trace estimators. Numerical experiments are conducted for common applications such as estimating the log-determinant, nuclear norm, and Estrada index. We find that using multilevel techniques can substantially reduce the variance of existing single-level estimators. DA - 2022/4/1/ PY - 2022/4/1/ DO - 10.1016/j.laa.2021.12.010 VL - 638 SP - 125-149 SN - 1873-1856 KW - Spectral function KW - Trace estimation KW - Chebyshev approximation KW - Hutchinson's trace estimator KW - Multilevel Monte Carlo ER - TY - JOUR TI - On Weissler's Conjecture on the Hamming Cube I AU - Ivanisvili, P. AU - Nazarov, F. T2 - INTERNATIONAL MATHEMATICS RESEARCH NOTICES AB - Abstract Let $1\leq p \leq q &lt;\infty $ and let $w \in \mathbb{C}$. Weissler conjectured that the Hermite operator $e^{w\Delta }$ is bounded as an operator from $L^{p}$ to $L^{q}$ on the Hamming cube $\{-1,1\}^{n}$ with the norm bound independent of $n$ if and only if $$\begin{align*} |p-2-e^{2w}(q-2)|\leq p-|e^{2w}|q. \end{align*}$$It was proved in [ 1], [ 2], and [ 17] in all cases except $2&lt;p\leq q &lt;3$ and $3/2&lt;p\leq q &lt;2$, which stood open until now. The goal of this paper is to give a full proof of Weissler’s conjecture in the case $p=q$. Several applications will be presented. DA - 2022/4/25/ PY - 2022/4/25/ DO - 10.1093/imrn/rnaa363 VL - 2022 IS - 9 SP - 6991-7020 SN - 1687-0247 ER - TY - JOUR TI - The Green polynomials via vertex operators AU - Jing, Naihuan AU - Liu, Ning T2 - JOURNAL OF PURE AND APPLIED ALGEBRA AB - An iterative formula for the Green polynomial is given using the vertex operator realization of the Hall-Littlewood function. Based on this, (1) a general combinatorial formula of the Green polynomial is given; (2) several compact formulas are given for Green's polynomials associated with upper partitions of length $\leq 3$ and the diagonal lengths $\leq 3$; (3) a Murnaghan-Nakayama type formula for the Green polynomial is obtained; and (4) an iterative formula is derived for the bitrace of the finite general linear group $G$ and the Iwahori-Hecke algebra of type $A$ on the permutation module of $G$ by its Borel subgroup. DA - 2022/8// PY - 2022/8// DO - 10.1016/j.jpaa.2022.107032 VL - 226 IS - 8 SP - SN - 1873-1376 KW - Green's polynomials KW - Vertex operators KW - Hall-Littlewood functions KW - Hecke algebra ER - TY - JOUR TI - A new parameter free partially penalized immersed finite element and the optimal convergence analysis AU - Ji, Haifeng AU - Wang, Feng AU - Chen, Jinru AU - Li, Zhilin T2 - NUMERISCHE MATHEMATIK AB - This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the coercivity of the method without requiring an ad-hoc stabilization parameter. The optimal approximation capabilities of the immersed finite element space is proved via a novel new approach that is much simpler than that in the literature. A new trace inequality which is necessary to prove the optimal convergence of immersed finite element methods is established on interface elements. Optimal error estimates are derived rigorously with the constant independent of the interface location relative to the mesh. The new method and analysis have also been extended to variable coefficients and three-dimensional problems. Numerical examples are also provided to confirm the theoretical analysis and efficiency of the new method. DA - 2022/4// PY - 2022/4// DO - 10.1007/s00211-022-01276-1 VL - 150 IS - 4 SP - 1035-1086 SN - 0945-3245 KW - 65N15 KW - 65N30 KW - 35R05 ER - TY - JOUR TI - From Graph Cuts to Isoperimetric Inequalities: Convergence Rates of Cheeger Cuts on Data Clouds AU - Trillos, Nicolas Garcia AU - Murray, Ryan AU - Thorpe, Matthew T2 - ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS AB - Abstract In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of Cheeger cuts. We consider proximity graphs built from data sampled from an underlying distribution supported on a generic smooth compact manifold $${\mathcal {M}}$$ M . In this setting, we obtain high probability convergence rates for both the Cheeger constant and the associated Cheeger cuts towards their continuum counterparts. The key technical tools are careful estimates of interpolation operators which lift empirical Cheeger cuts to the continuum, as well as continuum stability estimates for isoperimetric problems. To the best of our knowledge the quantitative estimates obtained here are the first of their kind. DA - 2022/4/8/ PY - 2022/4/8/ DO - 10.1007/s00205-022-01770-8 VL - 4 SP - SN - 1432-0673 ER - TY - JOUR TI - Quantum discords of tripartite quantum systems AU - Zhou, Jianming AU - Hu, Xiaoli AU - Jing, Naihuan T2 - QUANTUM INFORMATION PROCESSING AB - The quantum discord of bipartite systems is one of the best-known measures of non-classical correlations and an important quantum resource. In the recent work appeared in [Phys. Rev. Lett 2020, 124:110401], the quantum discord has been generalized to multipartite systems. In this paper, we give analytic solutions of the quantum discord for tripartite states with fourteen parameters. DA - 2022/4/5/ PY - 2022/4/5/ DO - 10.1007/s11128-022-03490-0 VL - 21 IS - 4 SP - SN - 1573-1332 UR - https://doi.org/10.1007/s11128-022-03490-0 KW - Quantum discord KW - Quantum correlations KW - Tripartite quantum states KW - Optimization on manifolds ER - TY - JOUR TI - Low-rank approximation to entangled multipartite quantum systems AU - Lin, Matthew M. AU - Chu, Moody T. T2 - QUANTUM INFORMATION PROCESSING DA - 2022/3/30/ PY - 2022/3/30/ DO - 10.1007/s11128-022-03467-z VL - 21 IS - 4 SP - SN - 1573-1332 UR - https://doi.org/10.1007/s11128-022-03467-z KW - Entanglement KW - Separability KW - Multipartite system KW - Low-rank approximation KW - Gradient dynamics KW - Wirtinger calculus ER - TY - JOUR TI - The Genome of the Poecilogonous Annelid Streblospio benedicti AU - Zakas, Christina AU - Harry, Nathan D. AU - Scholl, Elizabeth H. AU - Rockman, Matthew V T2 - GENOME BIOLOGY AND EVOLUTION AB - Abstract Streblospio benedicti is a common marine annelid that has become an important model for developmental evolution. It is the only known example of poecilogony (where two distinct developmental modes occur within a single species) that is due to a heritable difference in egg size. The dimorphic developmental programs and life-histories exhibited in this species depend on differences within the genome, making it an optimal model for understanding the genomic basis of developmental divergence. Studies using S. benedicti have begun to uncover the genetic and genomic principles that underlie developmental uncoupling, but until now they have been limited by the lack of availability of genomic tools. Here, we present an annotated chromosomal-level genome assembly of S. benedicti generated from a combination of Illumina reads, Nanopore long reads, Chicago and Hi-C chromatin interaction sequencing, and a genetic map from experimental crosses. At 701.4 Mb, the S. benedicti genome is the largest annelid genome to date that has been assembled to chromosomal scaffolds. The complete genome of S. benedicti is valuable for functional genomic analyses of development and evolution, as well as phylogenetic comparison within the annelida and the Lophotrochozoa. Despite having two developmental modes, there is no evidence of genome duplication or substantial gene number expansions. Instead, lineage-specific repeats account for much of the expansion of this genome compared with other annelids. DA - 2022/2/4/ PY - 2022/2/4/ DO - 10.1093/gbe/evac008 VL - 14 IS - 2 SP - SN - 1759-6653 KW - poecilogony KW - life-history evolution KW - developmental genomics KW - Lophotrochozoa ER - TY - JOUR TI - On genuine entanglement for tripartite systems AU - Zhao, Hui AU - Liu, Lin AU - Wang, Zhi-Xi AU - Jing, Naihuan AU - Li, Jing T2 - INTERNATIONAL JOURNAL OF QUANTUM INFORMATION AB - In this paper, we investigate the genuine entanglement in tripartite systems based on partial transposition and the norm of correlation tensors of the density matrices. We first derive an analytical sufficient criterion to detect genuine entanglement of tripartite qubit states combining with the partial transposition of the density matrices. Then, we use the norm of correlation tensors to study genuine entanglement for tripartite qudit quantum states and obtain a genuine entanglement criterion by constructing certain matrices. With detailed examples, our results are seen to be able to detect more genuine tripartite entangled states than previous studies. DA - 2022/3// PY - 2022/3// DO - 10.1142/S0219749921500386 VL - 20 IS - 02 SP - SN - 1793-6918 KW - Genuine entanglement KW - partial transposition KW - correlation tensor KW - Frobenius norm ER - TY - JOUR TI - Identifiable Paths and Cycles in Linear Compartmental Models AU - Bortner, Cashous AU - Meshkat, Nicolette T2 - BULLETIN OF MATHEMATICAL BIOLOGY AB - We introduce a class of linear compartmental models called identifiable path/cycle models which have the property that all of the monomial functions of parameters associated to the directed cycles and paths from input compartments to output compartments are identifiable and give sufficient conditions to obtain an identifiable path/cycle model. Removing leaks, we then show how one can obtain a locally identifiable model from an identifiable path/cycle model. These identifiable path/cycle models yield the only identifiable models with certain conditions on their graph structure and thus we provide necessary and sufficient conditions for identifiable models with certain graph properties. A sufficient condition based on the graph structure of the model is also provided so that one can test if a model is an identifiable path/cycle model by examining the graph itself. We also provide some necessary conditions for identifiability based on graph structure. Our proofs use algebraic and combinatorial techniques. DA - 2022/5// PY - 2022/5// DO - 10.1007/s11538-022-01007-5 VL - 84 IS - 5 SP - SN - 1522-9602 KW - Structural identifiability KW - Linear compartmental model KW - Identifiable functions of parameters KW - Identifiable combinations ER - TY - JOUR TI - Static replication of European standard dispersion options AU - Bossu, Sébastien AU - Carr, Peter AU - Papanicolaou, Andrew T2 - Quantitative Finance DA - 2022/3/23/ PY - 2022/3/23/ DO - 10.1080/14697688.2022.2040743 VL - 22 IS - 5 SP - 799-811 J2 - Quantitative Finance LA - en OP - SN - 1469-7688 1469-7696 UR - http://dx.doi.org/10.1080/14697688.2022.2040743 DB - Crossref ER - TY - JOUR TI - Tightening monogamy and polygamy relations of unified entanglement in multipartite systems AU - Zhang, Mei-Ming AU - Jing, Naihuan AU - Zhao, Hui T2 - QUANTUM INFORMATION PROCESSING AB - We study the monogamy and polygamy inequalities of unified entanglement in multipartite quantum systems. We first derive the monogamy inequality of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition, and then obtain the monogamy inequalities of the $\alpha$th ($0\leq\alpha\leq\frac{r}{2}, r\geq\sqrt{2}$) power of entanglement of formation for tripartite states and their generalizations in multi-qubit quantum states. We also generalize the polygamy inequalities of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition. Moreover, we investigate polygamy inequalities of the $\beta$th ($\beta\geq \max\{1, s\}, 0\leq s\leq s_0, 0\leq s_0\leq\sqrt{2}$) power of the entanglement of formation for $2\otimes2\otimes2$ and $n$-qubit quantum systems. Finally, using detailed examples, we show that the results are tighter than previous studies. DA - 2022/3/31/ PY - 2022/3/31/ DO - 10.1007/s11128-022-03479-9 VL - 21 IS - 4 SP - SN - 1573-1332 UR - https://doi.org/10.1007/s11128-022-03479-9 KW - Monogamy KW - Polygamy KW - Unified-(q, s) entanglement KW - Entanglement of formation ER - TY - JOUR TI - An in-silico analysis of experimental designs to study right ventricular function and pulmonary hypertension AU - Colebank, M. J. AU - Chesler, N.C. AB - Abstract In-vivo studies of pulmonary hypertension (PH) have provided key insight into the progression of the disease and right ventricular (RV) dysfunction. Additional in-silico experiments using multiscale computational models have provided further details into biventricular mechanics and hemodynamic function in the presence of PH, yet few have assessed whether model parameters are identifiable prior to data collection. Moreover, none have used modeling to devise synergistic experimental designs. To address this knowledge gap, we conduct an identifiability analysis of a multiscale cardiovascular model across four simulated experimental designs. We determine a set of parameters using a combination of Morris screening and local sensitivity analysis, and test for identifiability using profile likelihood based confidence intervals. We employ Markov chain Monte Carlo (MCMC) techniques to quantify parameter and model forecast uncertainty in the presence of noise corrupted data. Our results show that model calibration to only RV pressure suffers from identifiability issues and suffers from large forecast uncertainty in output space. In contrast, parameter and model forecast uncertainty is substantially reduced once additional left ventricular (LV) pressure and volume data is included. A comparison between single point systolic and diastolic LV data and continuous, time-dependent LV pressure volume data reveals that even basic, functional data from the LV remedies identifiability issues and provides substantial insight into biventricular interactions. Author Summary Computational models of cardiac dynamics are becoming increasingly useful in understanding the underlying mechanisms of disease. In-silico analyses are especially insightful in understanding PH and eventual RV dysfunction, as these conditions are diagnosed months to years after disease onset. Many researchers couple computational models with in-vivo experimental models of PH, yet few ever assess what data might be necessary or sufficient for parameter inference prior to designing their experiments. Here, we considered a multiscale computational model including sarcomere dynamics, biventricular interactions, and vascular hemodynamics, and assessed whether parameters could be inferred accurately given limited cardiac data. We utilized sensitivity analyses, profile likelihood confidence intervals, and MCMC to quantify parameter influence and uncertainty. We observed that RV pressure alone is not sufficient to infer the influential parameters in the model, whereas combined pressure and volume data in both the RV and LV reduced uncertainty in model parameters and in model forecasts. We conclude that synergistic PH studies utilizing computational modeling include these data to reduce issues with parameter identifiability and minimize uncertainty. DA - 2022/3/25/ PY - 2022/3/25/ DO - 10.1101/2022.03.22.485347 VL - 3 UR - https://doi.org/10.1101/2022.03.22.485347 ER - TY - JOUR TI - Rank-1 Approximation for Entangled Multipartite Real Systems AU - Lin, Matthew M. AU - Chu, Moody T. T2 - JOURNAL OF SCIENTIFIC COMPUTING DA - 2022/4// PY - 2022/4// DO - 10.1007/s10915-022-01805-y VL - 91 IS - 1 SP - SN - 1573-7691 UR - http://dx.doi.org/10.1007/s10915-022-01805-y KW - Entanglement KW - Separability KW - Multipartite system KW - Low-rank approximation KW - Nonlinear eigenvalue problem KW - Nonlinear singular value problem ER - TY - JOUR TI - Detection of genuine tripartite entanglement based on Bloch representation of density matrices AU - Zhao, Hui AU - Liu, Yu-Qiu AU - Jing, Naihuan AU - Wang, Zhi-Xi AU - Fei, Shao-Ming T2 - QUANTUM INFORMATION PROCESSING AB - We study the genuine multipartite entanglement in tripartite quantum systems. By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms and consider certain matrices from correlation tensors in the Bloch representation of the simplified density matrices. Using these special matrices, we obtain new criteria for genuine multipartite entanglement. Detail examples show that our criteria are able to detect more tripartite entangled and genuine tripartite entangled states than some existing criteria. DA - 2022/3// PY - 2022/3// DO - 10.1007/s11128-022-03456-2 VL - 21 IS - 3 SP - SN - 1573-1332 KW - Genuine multipartite entanglement KW - Separability KW - Correlation tensor ER - TY - JOUR TI - Polarimetric radar interferometry in the presence of differential Faraday rotation AU - Gilman, Mikhail AU - Tsynkov, Semyon T2 - INVERSE PROBLEMS AB - Abstract Faraday rotation (FR) affects the low-frequency transionospheric radar by creating cross-talk between polarizations. The baseline part of FR can be compensated for by applying an appropriate linear transformation—rotation with a known FR angle. Yet the differential Faraday rotation (dFR), which is a frequency-dependent part of FR, persists and introduces distortions into the observations. We build a simplified model with two polarimetric scattering channels that allows us to evaluate the effect of dFR on the accuracy of PolInSAR reconstruction. We also assess the severity of distortions due to dFR for the future BIOMASS mission and several other spaceborne radar systems. DA - 2022/4/1/ PY - 2022/4/1/ DO - 10.1088/1361-6420/ac5525 VL - 38 IS - 4 SP - SN - 1361-6420 KW - synthetic aperture radar KW - ionosphere KW - differential Faraday rotation KW - polarimetric radar interferometry ER - TY - JOUR TI - A Variational Inequality Model for the Construction of Signals from Inconsistent Nonlinear Equations\ast AU - Combettes, Patrick L. AU - Woodstock, Zev C. T2 - SIAM JOURNAL ON IMAGING SCIENCES AB - Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 17 May 2021Accepted: 03 September 2021Published online: 04 January 2022Keywordsimage recovery, signal synthesis, monotone operator, nonlinear observation, firmly nonexpansive operator, variational inequalityAMS Subject Headings46N10, 90C25, 68U10, 49J40Publication DataISSN (online): 1936-4954Publisher: Society for Industrial and Applied MathematicsCODEN: sjisbi DA - 2022/// PY - 2022/// DO - 10.1137/21M1420368 VL - 15 IS - 1 SP - 84-109 SN - 1936-4954 KW - image recovery KW - signal synthesis KW - monotone operator KW - nonlinear observation KW - firmly nonexpansive operator KW - variational inequality ER - TY - JOUR TI - Structural identifiability of series-parallel LCR systems AU - Bortner, Cashous AU - Sullivant, Seth T2 - JOURNAL OF SYMBOLIC COMPUTATION AB - We consider the identifiability problem for the parameters of series-parallel LCR circuit networks. We prove that for networks with only two classes of components (inductor-capacitor (LC), inductor-resistor (LR), and capacitor-resistor (RC)), the parameters are identifiable if and only if the number of non-monic coefficients of the constitutive equations equals the number of parameters. The notion of the “type” of the constitutive equations plays a key role in the identifiability of LC, LR, and RC networks. We also investigate the general series-parallel LCR circuits (with all three classes of components), and classify the types of constitutive equations that can arise, showing that there are 22 different types. However, we produce an example that shows that the basic notion of type that works to classify identifiability of two class networks is not sufficient to classify the identifiability of general series-parallel LCR circuits. DA - 2022/// PY - 2022/// DO - 10.1016/j.jsc.2022.01.002 VL - 112 SP - 79-104 SN - 1095-855X KW - Identifiability KW - Structural identifiability KW - LCR circuit KW - Resultant KW - Algebraic geometry KW - Algebraic statistics ER - TY - JOUR TI - Production and green technology investment strategy for contract-farming supply chain under yield insurance AU - Shi, Ligang AU - Pang, Tao AU - Peng, Hongjun T2 - JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY AB - We consider a contract-farming supply chain with multiple farmers and an agro-dealer, where farmers are risk-averse and they invest in green technologies. To hedge the risk of yield uncertainty, farmers can purchase agricultural yield insurance. We build a Stackelberg game model to investigate the optimal decisions of farmers and the agro-dealer. The results show that agricultural competition, yield uncertainty, and farmers’ risk aversion have negative impacts on the farm size and the agrochemical reduction technology input, while the yield insurance has positive impacts. We also show that, for farmers with low initial agrochemical input, yield insurance can reduce the agrochemical inputs per acre, and the total agrochemical inputs despite that the farm size increases. Therefore, yield insurance can reduce agricultural pollution emissions. Despite the result of higher social welfare, more agricultural competition generates higher agricultural pollution emissions because farmers would have no incentive to invest more in green technologies. Furthermore, yield insurance enhances the social welfare if the environmental damage of agrochemicals is low. However, when the environmental damage of agrochemicals is high, the social welfare decreases under the yield insurance. DA - 2022/2/4/ PY - 2022/2/4/ DO - 10.1080/01605682.2022.2033141 SP - SN - 1476-9360 KW - Contract-farming KW - yield insurance KW - green technology KW - risk-averse ER - TY - JOUR TI - Deciphering tissue structure and function using spatial transcriptomics AU - Walker, Benjamin L. AU - Cang, Zixuan AU - Ren, Honglei AU - Bourgain-Chang, Eric AU - Nie, Qing T2 - Communications Biology AB - Abstract The rapid development of spatial transcriptomics (ST) techniques has allowed the measurement of transcriptional levels across many genes together with the spatial positions of cells. This has led to an explosion of interest in computational methods and techniques for harnessing both spatial and transcriptional information in analysis of ST datasets. The wide diversity of approaches in aim, methodology and technology for ST provides great challenges in dissecting cellular functions in spatial contexts. Here, we synthesize and review the key problems in analysis of ST data and methods that are currently applied, while also expanding on open questions and areas of future development. DA - 2022/3/10/ PY - 2022/3/10/ DO - 10.1038/s42003-022-03175-5 UR - https://doi.org/10.1038/s42003-022-03175-5 ER - TY - JOUR TI - A complex-valued gradient flow for the entangled bipartite low rank approximation AU - Chu, Moody T. AU - Lin, Matthew M. T2 - COMPUTER PHYSICS COMMUNICATIONS AB - Entanglement of quantum states in a composite system is of profound importance in many applications. With respect to some suitably selected basis, the entanglement can be mathematically characterized via the Kronecker product of complex-valued density matrices. An approximation to a mixed state can be thought of as calculating its nearest separable state. Such a task encounters several challenges in computation. First, the added twist by the entanglement via the Kronecker product destroys the multi-linearity. The popular alternating least squares techniques for tensor approximation can hardly be applied. Second, there is no clear strategy for selecting a priori a proper low rank for the approximation. Third, the conventional calculus is not enough to address the optimization of real-valued functions over complex variables. This paper proposes a dynamical system approach to tackle low rank approximation of entangled bipartite systems, which has several advantages, including 1) A gradient dynamics in the complex space can be described in a fairly concise way; 2) The global convergence from any starting point to a local solution is guaranteed; 3) The requirement that the combination coefficients of pure states must be a probability distribution can be ensured; 4) The rank can be dynamically adjusted. This paper discusses the theory, algorithms, and presents some numerical experiments. DA - 2022/2// PY - 2022/2// DO - 10.1016/j.cpc.2021.108185 VL - 271 SP - SN - 1879-2944 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85116536880&partnerID=MN8TOARS KW - Quantum states KW - Entanglement KW - Separability KW - Bipartite system KW - Low-rank approximation KW - Gradient dynamics KW - Wirtinger calculus ER - TY - JOUR TI - A Variant Modified Skew-Normal Splitting Iterative Method for Non-Hermitian Positive Definite Linear Systems AU - Li, Rui AU - Yin, Jun-Feng AU - Li, Zhi-Lin T2 - NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS DA - 2022/2/16/ PY - 2022/2/16/ DO - 10.4208/nmtma.OA-2021-0038 VL - 2 SP - SN - 2079-7338 KW - Non-Hermitian matrix KW - skew-normal splitting KW - precondition KW - complex linear system ER - TY - JOUR TI - Geographic disparities and predictors of COVID-19 hospitalization risks in the St. Louis Area, Missouri (USA) AU - Igoe, Morganne AU - Das, Praachi AU - Lenhart, Suzanne AU - Lloyd, Alun L. AU - Luong, Lan AU - Tian, Dajun AU - Lanzas, Cristina AU - Odoi, Agricola T2 - BMC PUBLIC HEALTH AB - There is evidence of geographic disparities in COVID-19 hospitalization risks that, if identified, could guide control efforts. Therefore, the objective of this study was to investigate Zip Code Tabulation Area (ZCTA)-level geographic disparities and identify predictors of COVID-19 hospitalization risks in the St. Louis area.Hospitalization data for COVID-19 and several chronic diseases were obtained from the Missouri Hospital Association. ZCTA-level data on socioeconomic and demographic factors were obtained from the American Community Survey. Geographic disparities in distribution of COVID-19 age-adjusted hospitalization risks, socioeconomic and demographic factors as well as chronic disease risks were investigated using choropleth maps. Predictors of ZCTA-level COVID-19 hospitalization risks were investigated using global negative binomial and local geographically weighted negative binomial models.COVID-19 hospitalization risks were significantly higher in ZCTAs with high diabetes hospitalization risks (p < 0.0001), COVID-19 risks (p < 0.0001), black population (p = 0.0416), and populations with some college education (p = 0.0005). The associations between COVID-19 hospitalization risks and the first three predictors varied by geographic location.There is evidence of geographic disparities in COVID-19 hospitalization risks that are driven by differences in socioeconomic, demographic and health-related factors. The impacts of these factors vary by geographical location implying that a 'one-size-fits-all' approach may not be appropriate for management and control. Using both global and local models leads to a better understanding of geographic disparities. These findings are useful for informing health planning to identify geographic areas likely to have high numbers of individuals needing hospitalization as well as guiding vaccination efforts. DA - 2022/2/15/ PY - 2022/2/15/ DO - 10.1186/s12889-022-12716-w VL - 22 IS - 1 SP - SN - 1471-2458 KW - Severe Acute Respiratory Syndrome Coronavirus 2 KW - SARS-CoV-2 KW - Coronavirus Disease 2019 KW - COVID-19 KW - Disparities KW - Hospitalization Risks KW - Predictors KW - Negative Binomial Models KW - Geographically Weighted Regression Models KW - Epidemiology KW - Missouri ER - TY - JOUR TI - Detection of genuine multipartite entanglement based on principal basis matrix representations AU - Zhao, Hui AU - Liu, Yu-Qiu AU - Fei, Shao-Ming AU - Wang, Zhi-Xi AU - Jing, Naihuan T2 - LASER PHYSICS LETTERS AB - Abstract We study the genuine multipartite entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to simpler forms and then construct some special matrices from the correlation tensors of the simplified density matrices. Based on the different linear combinations of these matrices, necessary conditions are presented to detect genuine multipartite entanglement of tripartite states. Detailed examples show that our method can detect more entangled states than previous ones. DA - 2022/3/1/ PY - 2022/3/1/ DO - 10.1088/1612-202X/ac50af VL - 19 IS - 3 SP - SN - 1612-202X KW - genuine multipartite entanglement KW - principal basis KW - correlation tensor ER - TY - JOUR TI - 'Mountain Bebe': Hybrid Grape Tomato and Its Parents NC 7 Grape and NC 8 Grape AU - Panthee, Dilip R. AU - Gardner, Randy G. T2 - HORTSCIENCE AB - ‘Mountain Bebe’ is the F1 hybrid of NC 7 Grape × NC 8 Grape. It is resistant to late blight (Ph-2 and Ph-3 genes), tomato spotted wilt virus (Sw-5 gene), and fusarium wilt races 2 and 3 (I-2 and I-3 genes). The hybrid has a compact, indeterminate growth habit with short internodes (br gene). It has total soluble solids equal to ‘Mountain Honey’ with dark red fruits of ≈11.7 g per fruit.Origin‘Mountain Bebe’ (tested as NC10259) is the F1 hybrid of NC DA - 2022/3// PY - 2022/3// DO - 10.21273/HORTSCI16366-21 VL - 57 IS - 3 SP - 444-446 SN - 2327-9834 KW - brachytic (br) gene KW - crimson KW - grape tomato KW - I-3 gene KW - og(c) gene KW - Ph-2 ene KW - Ph-3-gene KW - Solanum lycopersicum KW - Sw-5 gene ER - TY - JOUR TI - Weak convergence of a collection of random functions defined by the eigenvectors of large dimensional random matrices AU - Silverstein, Jack W. T2 - RANDOM MATRICES-THEORY AND APPLICATIONS AB - For each n, let [Formula: see text] be Haar distributed on the group of [Formula: see text] unitary matrices. Let [Formula: see text] denote orthogonal nonrandom unit vectors in [Formula: see text] and let [Formula: see text], [Formula: see text]. Define the following functions on [Formula: see text]: [Formula: see text], [Formula: see text], [Formula: see text]. Then it is proven that [Formula: see text], [Formula: see text], considered as random processes in [Formula: see text], converge weakly, as [Formula: see text], to [Formula: see text] independent copies of Brownian bridge. The same result holds for the [Formula: see text] processes in the real case, where [Formula: see text] is real orthogonal Haar distributed and [Formula: see text], with [Formula: see text] in [Formula: see text] and [Formula: see text] in [Formula: see text] replaced with [Formula: see text] and [Formula: see text], respectively. This latter result will be shown to hold for the matrix of eigenvectors of [Formula: see text] where [Formula: see text] is [Formula: see text] consisting of the entries of [Formula: see text], i.i.d. standardized and symmetrically distributed, with each [Formula: see text] and [Formula: see text] as [Formula: see text]. This result extends the result in [J. W. Silverstein, Ann. Probab. 18 (1990) 1174–1194]. These results are applied to the detection problem in sampling random vectors mostly made of noise and detecting whether the sample includes a nonrandom vector. The matrix [Formula: see text] is studied where [Formula: see text] is Hermitian or symmetric and nonnegative definite with either its matrix of eigenvectors being Haar distributed, or [Formula: see text], [Formula: see text] nonrandom and [Formula: see text] is a nonrandom unit vector. Results are derived on the distributional behavior of the inner product of vectors orthogonal to [Formula: see text] with the eigenvector associated with the largest eigenvalue of [Formula: see text] DA - 2022/10// PY - 2022/10// DO - 10.1142/S2010326322500332 VL - 11 IS - 04 SP - SN - 2010-3271 UR - https://doi.org/10.1142/S2010326322500332 KW - Weak convergence on D[0,1] KW - eigenvectors of random matrices KW - Brownian bridge KW - Haar measure ER - TY - JOUR TI - Aggregate Alpha in the Hedge Fund Industry: A Further Look at Best Ideas AU - Amir-Ghassemi, F. AU - Papanicolaou, A. AU - Perlow, M. T2 - JOURNAL OF PORTFOLIO MANAGEMENT AB - 1. F. Amir-Ghassemi 1. is a partner at Epsilon Asset Management in New York, NY. (research{at}epsilonmgmt.com) 2. A. Papanicolaou 1. is an assistant professor in the Department of Mathematics at North Carolina State University in Raleigh, NC. (apapani{at}ncsu.edu) 3. M. Perlow 1. is a partner at Epsilon Asset Management in New York, NY. (research{at}epsilonmgmt.com) This article is an examination of the stock-picking behavior of nearly 1,500 hedge funds using regulatory mandated position-level data from the SEC (Form 13F). Using data from June 1999 to December 2018, abnormal excess alpha is found on both a gross and dollar basis. Breaking the 20-year sample into two periods, the authors note a significant decline in gross alpha after the 2008 global financial crisis. In contrast, dollar alphas remain economically and statistically significant. This finding coincides with an increase in aggregate assets in the post-crisis period, suggesting asset growth may be impeding gross alphas. To test this hypothesis, the authors analyze the Best Ideas within manager portfolios. They find no significant difference between the alphas generated by managers’ Best Ideas and the rest of their portfolios, suggesting asset growth is not a significant determinant of alpha deterioration. These findings broadly contrast with prior studies conducted on mutual funds, suggesting differences in portfolio construction and incentive effects. DA - 2022/2// PY - 2022/2// DO - 10.3905/jpm.2021.1.313 VL - 48 IS - 3 SP - 220-239 SN - 2168-8656 ER - TY - JOUR TI - EVOLUTION OF NONLINEAR REDUCED-ORDER SOLUTIONS FOR PDEs WITH CONSERVED QUANTITIES AU - Anderson, William AU - Farazmand, Mohammad T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING AB - Reduced-order models of time-dependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a well-developed theory. However, more general models where the reduced solutions depend nonlinearly on time varying parameters have thus far been derived in an ad hoc manner. Here, we introduce reduced-order nonlinear solutions (RONS): a unified framework for deriving reduced-order models that depend nonlinearly on a set of time-dependent parameters. The set of all possible reduced-order solutions are viewed as a manifold immersed in the function space of the PDE. The parameters are evolved such that the instantaneous discrepancy between reduced dynamics and the full PDE dynamics is minimized. This results in a set of explicit ordinary differential equations on the tangent bundle of the manifold. In the special case of linear parameter dependence, our reduced equations coincide with the standard Galerkin projection. Furthermore, any number of conserved quantities of the PDE can readily be enforced in our framework. Since RONS does not assume an underlying variational formulation for the PDE, it is applicable to a broad class of problems. We demonstrate the efficacy of RONS on three examples: an advection-diffusion equation, the nonlinear Schrödinger equation, and Euler's equation for ideal fluids. DA - 2022/// PY - 2022/// DO - 10.1137/21M1415972 VL - 44 IS - 1 SP - A176-A197 SN - 1095-7197 UR - https://doi.org/10.1137/21M1415972 KW - model order reduction KW - partial differential equations KW - conservation laws KW - Galerkin projection ER - TY - JOUR TI - Uncrowding Algorithm for Hook-Valued Tableaux AU - Pan, Jianping AU - Pappe, Joseph AU - Poh, Wencin AU - Schilling, Anne T2 - Annals of Combinatorics AB - Whereas set-valued tableaux are the combinatorial objects associated to stable Grothendieck polynomials, hook-valued tableaux are associated to stable canonical Grothendieck polynomials. In this paper, we define a novel uncrowding algorithm for hook-valued tableaux. The algorithm "uncrowds" the entries in the arm of the hooks and yields a set-valued tableau and a column-flagged increasing tableau. We prove that our uncrowding algorithm intertwines with crystal operators. An alternative uncrowding algorithm that "uncrowds" the entries in the leg instead of the arm of the hooks is also given. As an application of uncrowding, we obtain various expansions of the canonical Grothendieck polynomials. DA - 2022/1/30/ PY - 2022/1/30/ DO - 10.1007/s00026-022-00567-6 VL - 26 IS - 1 SP - 261-301 J2 - Ann. Comb. LA - en OP - SN - 0218-0006 0219-3094 UR - http://dx.doi.org/10.1007/s00026-022-00567-6 DB - Crossref KW - Stable (canonical) Grothendieck polynomials KW - Hook-valued tableaux KW - crystal bases KW - uncrowding algorithm ER - TY - JOUR TI - On irreducible characters of the Iwahori-Hecke algebra in type A AU - Jing, Naihuan AU - Liu, Ning T2 - JOURNAL OF ALGEBRA AB - In this paper, we use vertex operators to compute irreducible characters of the Iwahori-Hecke algebra of type A. Two general formulas are given for the irreducible characters in terms of those of the symmetric groups or the Iwahori-Hecke algebras in lower degrees. Explicit formulas are derived for the irreducible characters labeled by hooks and two-row partitions. We also formulate a determinant type Murnaghan-Nakayama formula and give another proof of the combinatorial Murnaghan-Nakayama rule. As applications, we study super-characters of the Iwahori-Hecke algebra as well as the bitrace of the regular representation and provide a simple proof of the Halverson-Leduc-Ram formula. DA - 2022/5/15/ PY - 2022/5/15/ DO - 10.1016/j.jalgebra.2022.01.020 VL - 598 SP - 24-47 SN - 1090-266X UR - https://doi.org/10.1016/j.jalgebra.2022.01.020 KW - Hecke algebras KW - Jing operators KW - Schur polynomials KW - Murnaghan-Nakayama rule ER - TY - JOUR TI - Monogamy and Polygamy Relations of Quantum Correlations for Multipartite Systems AU - Zhang, Mei-Ming AU - Jing, Naihuan AU - Zhao, Hui T2 - INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS AB - We study the monogamy and polygamy inequalities of quantum correlations in arbitrary dimensional multipartite quantum systems. We first derive the monogamy inequality of the α th $\left (0\leq \alpha \leq \frac {r}{2}, r\geq 2\right )$ power of concurrence for any 2 ⊗ 2 ⊗ 2n− 2 tripartite states and generalize it to the n-qubit quantum states. In addition to concurrence, we show that the monogamy relations are satisfied by other quantum correlation measures such as entanglement of formation. Moreover, the polygamy inequality of the β th (β ≤ 0) power of concurrence and the β th (β ≥ s, 0 ≤ s ≤ 1) power of the negativity are presented for 2 ⊗ 2 ⊗ 2n− 2. We then obtain the polygamy inequalities of quantum correlations for multipartite states. Finally, our results are shown to be tighter than previous studies using detailed examples. DA - 2022/1// PY - 2022/1// DO - 10.1007/s10773-022-04971-9 VL - 61 IS - 1 SP - SN - 1572-9575 UR - https://doi.org/10.1007/s10773-022-04971-9 KW - Monogamy KW - Polygamy KW - Concurrence KW - Negativity ER - TY - JOUR TI - Newton's Method in Mixed Precision AU - Kelley, C. T. T2 - SIAM REVIEW AB - We investigate the use of reduced precision arithmetic to solve the linear equation for the Newton step. If one neglects the backward error in the linear solve, then well-known convergence theory implies that using single precision in the linear solve has very little negative effect on the nonlinear convergence rate. However, if one considers the effects of backward error, then the usual textbook estimates are very pessimistic and even the state-of-the-art estimates using probabilistic rounding analysis do not fully conform to experiments. We report on experiments with a specific example. We store and factor Jacobians in double, single, and half precision. In the single precision case we observe that the convergence rates for the nonlinear iteration do not degrade as the dimension increases and that the nonlinear iteration statistics are essentially identical to the double precision computation. In half precision we see that the nonlinear convergence rates, while poor, do not degrade as the dimension increases. DA - 2022/3// PY - 2022/3// DO - 10.1137/20M1342902 VL - 64 IS - 1 SP - 191-211 SN - 1095-7200 UR - https://doi.org/10.1137/20M1342902 KW - Newton's method KW - mixed precision arithmetic KW - backward error KW - probabilistic rounding analysis ER - TY - JOUR TI - Level-1/2 Realization of Quantum N-Toroidal Algebra in Type C-n AU - Jing, Naihuan AU - Wang, Qianbao AU - Zhang, Honglian T2 - ALGEBRA COLLOQUIUM AB - We construct a level -1/2 vertex representation of the quantum [Formula: see text]-toroidal algebra of type [Formula: see text], which is a natural generalization of the usual quantum toroidal algebra. The construction also provides a vertex representation of the quantum toroidal algebra for type [Formula: see text] as a by-product. DA - 2022/3// PY - 2022/3// DO - 10.1142/S1005386722000074 VL - 29 IS - 01 SP - 79-98 SN - 0219-1733 KW - vertex representation KW - quantum N-toroidal algebra KW - vertex operator KW - toroidal Lie algebra ER - TY - JOUR TI - Exchangeable and sampling-consistent distributions on rooted binary trees AU - Hollering, Benjamin AU - Sullivant, Seth T2 - JOURNAL OF APPLIED PROBABILITY AB - Abstract We introduce a notion of finite sampling consistency for phylogenetic trees and show that the set of finitely sampling-consistent and exchangeable distributions on n -leaf phylogenetic trees is a polytope. We use this polytope to show that the set of all exchangeable and sampling-consistent distributions on four-leaf phylogenetic trees is exactly Aldous’ beta-splitting model, and give a description of some of the vertices for the polytope of distributions on five leaves. We also introduce a new semialgebraic set of exchangeable and sampling consistent models we call the multinomial model and use it to characterize the set of exchangeable and sampling-consistent distributions. Using this new model, we obtain a finite de Finetti-type theorem for rooted binary trees in the style of Diaconis’ theorem on finite exchangeable sequences. DA - 2022/1/14/ PY - 2022/1/14/ DO - 10.1017/jpr.2021.28 SP - SN - 1475-6072 KW - Beta-splitting model KW - multinomial model KW - random trees ER - TY - JOUR TI - Improved unitary uncertainty relations AU - Hu, Xiaoli AU - Jing, Naihuan T2 - QUANTUM INFORMATION PROCESSING AB - We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy–Schwarz inequality using a method of brackets and convex functions. The unitary uncertainty relations outperform several strong unitary uncertainty relations, notably better than some recent best lower bounds such as [Phys. Rev. Lett. 120, 230402 (2018)] and [Phys. Rev. A. 100, 022116 (2019)]. DA - 2022/2// PY - 2022/2// DO - 10.1007/s11128-021-03396-3 VL - 21 IS - 2 SP - SN - 1573-1332 UR - https://doi.org/10.1007/s11128-021-03396-3 KW - Uncertainty relations KW - Cauchy-Schwarz inequality KW - Unitary operators ER - TY - JOUR TI - Racial and ethnic disparities in pregnancy complications and the protective role of greenspace: A retrospective birth cohort study AU - Runkle, Jennifer D. AU - Matthews, Jessica L. AU - Sparks, Laurel AU - McNicholas, Leo AU - Sugg, Margaret M. T2 - SCIENCE OF THE TOTAL ENVIRONMENT AB - Greenspace may positively impact pregnancy health for racially and economically minoritized populations; few studies have examined local availability and accessibility of green/park space in reducing maternal morbidity. The objective of this retrospective birth cohort study was to examine the association between residential exposure to greenspace and adverse pregnancy health outcomes in a Southern US state characterized by high poverty and racial disparities in maternal health (2013-2017). National data from the Protected Area database - United States (PAD-US) and ParkServe estimated three publicly available and accessible residential greenspace measures-a more direct proxy than using remotely-sensed greenness indicators (e.g., normalized difference vegetation index (NDVI))-(a) percent area of greenspace (M1), (b) area of available greenspace per person (M2), (c) total population within a 10-minute walk (M3). Generalized Estimating Equations with logistic regression were used to examine the association between individual greenspace metrics and South Carolina hospital deliveries (n = 238,922 deliveries) for women with correlated maternal health outcomes for gestational hypertension (GHTN), gestational diabetes (GD), severe maternal morbidity (SMM), preeclampsia (PRE), mental disorders (MD), depressive disorders (DD), and preterm birth (PTB). Lowest compared to highest tertiles of all three metrics were associated with increased risk for MD, DD, and a monotonic increase in GD, particularly for black women. Women with the lowest access to M2 and M3 were more at risk for PRE, PTB, and MD. We observed that women in low-income, majority-black communities in the lowest versus highest tertile of M2 were more likely to experience a DD, MD, SMM, or PTB compared to primarily high-income majority-white communities. Available and accessible green/park space may present as an effective nature-based intervention to reduce maternal complications, particularly for gestational diabetes and other pregnancy health risks for which there are currently few known evidence-based primary prevention strategies. DA - 2022/2/20/ PY - 2022/2/20/ DO - 10.1016/j.scitotenv.2021.152145 VL - 808 SP - SN - 1879-1026 KW - Greenspace KW - Pregnancy KW - Gestational diabetes KW - Maternal morbidity KW - Structural racism KW - Index of Concentration at the Extremes (ICE) ER - TY - JOUR TI - Numerical predictions of shear stress and cyclic stretch in pulmonary hypertension due to left heart failure AU - Bartolo, Michelle A. AU - Qureshi, M. Umar AU - Colebank, Mitchel J. AU - Chesler, Naomi C. AU - Olufsen, Mette S. T2 - BIOMECHANICS AND MODELING IN MECHANOBIOLOGY AB - Isolated post-capillary pulmonary hypertension (Ipc-PH) occurs due to left heart failure, which contributes to 1 out of every 9 deaths in the United States. In some patients, through unknown mechanisms, Ipc-PH transitions to combined pre-/post-capillary PH (Cpc-PH) and is associated with a dramatic increase in mortality. Altered mechanical forces and subsequent biological signaling in the pulmonary vascular bed likely contribute to the transition from Ipc-PH to Cpc-PH. However, even in a healthy pulmonary circulation, the mechanical forces in the smallest vessels (the arterioles, capillary bed, and venules) have not been quantitatively defined. This study is the first to examine this question via a computational fluid dynamics model of the human pulmonary arteries, arterioles, venules, and veins. Using this model, we predict temporal and spatial dynamics of cyclic stretch and wall shear stress with healthy and diseased hemodynamics. In the normotensive case for large vessels, numerical simulations show that large arteries have higher pressure and flow than large veins, as well as more pronounced changes in area throughout the cardiac cycle. In the microvasculature, shear stress increases and cyclic stretch decreases as vessel radius decreases. When we impose an increase in left atrial pressure to simulate Ipc-PH, shear stress decreases and cyclic stretch increases as compared to the healthy case. Overall, this model predicts pressure, flow, shear stress, and cyclic stretch that providing a way to analyze and investigate hypotheses related to disease progression in the pulmonary circulation. DA - 2022/1/17/ PY - 2022/1/17/ DO - 10.1007/s10237-021-01538-1 VL - 1 SP - SN - 1617-7940 UR - https://doi.org/10.1007/s10237-021-01538-1 KW - Pulmonary hypertension KW - Micro-circulation KW - Wall shear stress KW - Cyclic stretch KW - Left heart disease KW - Computational modeling KW - Pulse wave propagation ER - TY - JOUR TI - Computing fusion rules for spherical G-extensions of fusion categories AU - Bischoff, Marcel AU - Jones, Corey T2 - SELECTA MATHEMATICA-NEW SERIES AB - A G-extension of a fusion category $${\mathcal {C}}$$ yields a categorical action of G on the center $$Z({{\mathcal {C}}})$$ . If the extension admits a spherical structure, we provide a method for recovering its fusion rules in terms of the action. We then apply this to find closed formulas for the fusion rules of extensions of some group theoretical categories and of cyclic permutation crossed extensions of modular categories. DA - 2022/5// PY - 2022/5// DO - 10.1007/s00029-021-00725-3 VL - 28 IS - 2 SP - SN - 1420-9020 ER - TY - JOUR TI - Multitask neural networks for predicting bladder pressure with time series data AU - Warrier, Sangeeta AU - Rutter, Erica M. AU - Flores, Kevin B. T2 - BIOMEDICAL SIGNAL PROCESSING AND CONTROL AB - Multitask learning (MTL) can improve accuracy over vanilla neural networks in modeling population level time series data. This can be accomplished by assigning the prediction for each individual in the population as a separate task, thereby leveraging the heterogeneity of population level data. Here, we investigate a novel approach by training recurrent neural networks (RNNs) in a multitask setting. We apply this new methodology to experimental data for predicting bladder pressure, and then bladder contractions, from an external urethral sphincter electromyograph (EUS EMG) signal. We found that the multitask models make more accurate individual level predictions than their single tasking counterparts. We observed that, for bladder pressure prediction, either incorporating multitask learning or RNN structure generalized best to out of sample test data and multitasking RNNs had high out of sample correlation coefficients. These results suggest that MTL models could be used to leverage heterogeneous population time series data for making individualized predictions. From these bladder pressure predictions, we predicted the onset of bladder contractions. Our results indicate that the MTL RNN model was superior in both intra- and inter-individual bladder contraction predictions as measured by sensitivity (85.7%), specificity (98.7%) and precision (73.5%). DA - 2022/2// PY - 2022/2// DO - 10.1016/j.bspc.2021.103298 VL - 72 SP - SN - 1746-8108 KW - Multitask neural networks KW - Recurrent neural networks KW - Time series data KW - Bladder dysfunction KW - Bladder contraction KW - Spectrogram ER - TY - JOUR TI - Well-Balancing via Flux Globalization: Applications to Shallow Water Equations with Wet/Dry Fronts AU - Chertock, Alina AU - Kurganov, Alexander AU - Liu, Xin AU - Liu, Yongle AU - Wu, Tong T2 - JOURNAL OF SCIENTIFIC COMPUTING DA - 2022/1// PY - 2022/1// DO - 10.1007/s10915-021-01680-z VL - 90 IS - 1 SP - SN - 1573-7691 KW - Flux globalization KW - Central-upwind schemes KW - Well-balanced schemes KW - "Lake-at-rest" steady states KW - "Dry lake" steady states ER - TY - JOUR TI - Symmetry and isoperimetry for Riemannian surfaces AU - Hoisington, Joseph Ansel AU - McGrath, Peter T2 - CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS AB - For a domain $$\Omega $$ in a geodesically convex surface, we introduce a scattering energy $$\mathcal {E}(\Omega )$$ , which measures the asymmetry of $$\Omega $$ by quantifying its incompatibility with an isometric circle action. We prove several sharp quantitative isoperimetric inequalities involving $$\mathcal {E}(\Omega )$$ and characterize the domains with vanishing scattering energy by their convexity and rotational symmetry. We also give a new of the sharp Sobolev inequality for Riemannian surfaces. DA - 2022/2// PY - 2022/2// DO - 10.1007/s00526-021-02117-z VL - 61 IS - 1 SP - SN - 1432-0835 ER - TY - JOUR TI - Alfonso: Matlab Package for Nonsymmetric Conic Optimization AU - Papp, Dávid AU - Yıldız, Sercan T2 - INFORMS Journal on Computing AB - We present alfonso, an open-source Matlab package for solving conic optimization problems over nonsymmetric convex cones. The implementation is based on the authors’ corrected analysis of a method of Skajaa and Ye. It enables optimization over any convex cone as long as a logarithmically homogeneous self-concordant barrier is available for the cone or its dual. This includes many nonsymmetric cones, for example, hyperbolicity cones and their duals (such as sum-of-squares cones), semidefinite and second-order cone representable cones, power cones, and the exponential cone. Besides enabling the solution of problems that cannot be cast as optimization problems over a symmetric cone, algorithms for nonsymmetric conic optimization also offer performance advantages for problems whose symmetric cone programming representation requires a large number of auxiliary variables or has a special structure that can be exploited in the barrier computation. The worst-case iteration complexity of alfonso is the best known for nonsymmetric cone optimization: [Formula: see text] iterations to reach an ε-optimal solution, where ν is the barrier parameter of the barrier function used in the optimization. Alfonso can be interfaced with a Matlab function (supplied by the user) that computes the Hessian of a barrier function for the cone. A simplified interface is also available to optimize over the direct product of cones for which a barrier function has already been built into the software. This interface can be easily extended to include new cones. Both interfaces are illustrated by solving linear programs. The oracle interface and the efficiency of alfonso are also demonstrated using an optimal design of experiments problem in which the tailored barrier computation greatly decreases the solution time compared with using state-of-the-art, off-the-shelf conic optimization software. Summary of Contribution: The paper describes an open-source Matlab package for optimization over nonsymmetric cones. A particularly important feature of this software is that, unlike other conic optimization software, it enables optimization over any convex cone as long as a suitable barrier function is available for the cone or its dual, not limiting the user to a small number of specific cones. Nonsymmetric cones for which such barriers are already known include, for example, hyperbolicity cones and their duals (such as sum-of-squares cones), semidefinite and second-order cone representable cones, power cones, and the exponential cone. Thus, the scope of this software is far larger than most current conic optimization software. This does not come at the price of efficiency, as the worst-case iteration complexity of our algorithm matches the iteration complexity of the most successful interior-point methods for symmetric cones. Besides enabling the solution of problems that cannot be cast as optimization problems over a symmetric cone, our software can also offer performance advantages for problems whose symmetric cone programming representation requires a large number of auxiliary variables or has a special structure that can be exploited in the barrier computation. This is also demonstrated in this paper via an example in which our code significantly outperforms Mosek 9 and SCS 2. DA - 2022/1// PY - 2022/1// DO - 10.1287/ijoc.2021.1058 VL - 34 IS - 1 SP - 11-19 UR - https://doi.org/10.1287/ijoc.2021.1058 KW - conic optimization KW - interior-point method KW - self-concordant barrier KW - nonsymmetric cone KW - software ER - TY - JOUR TI - Lattice structure of modular vertex algebras AU - Huang, Haihua AU - Jing, Naihuan T2 - JOURNAL OF ALGEBRA AB - In this paper we study the integral form of the lattice vertex algebra VL. We show that divided powers of general vertex operators preserve the integral lattice spanned by Schur functions indexed by partition-valued functions. We also show that the Garland operators, counterparts of divided powers of Heisenberg elements in affine Lie algebras, also preserve the integral form. These construe analogs of the Kostant Z-forms for the enveloping algebras of simple Lie algebras and the algebraic affine Lie groups in the situation of the lattice vertex algebras. DA - 2022/2/15/ PY - 2022/2/15/ DO - 10.1016/j.jalgebra.2021.10.030 VL - 592 SP - 1-17 SN - 1090-266X UR - https://doi.org/10.1016/j.jalgebra.2021.10.030 KW - Vertex algebras KW - Integral forms KW - Modular vertex algebras KW - Automorphism groups ER - TY - JOUR TI - A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients AU - Pan, Kejia AU - Wu, Xiaoxin AU - Hu, Hongling AU - Yu, Yunlong AU - Li, Zhilin T2 - JOURNAL OF COMPUTATIONAL PHYSICS AB - In this paper, an efficient cell-centered extrapolation cascadic multigrid (CEXCMG) method is proposed for solving large linear system of equations resulting from finite volume (FV) discretizations of three dimensional (3D) anisotropic diffusion equations with discontinuous coefficients. For cell-centered FV schemes, the values at vertex need to be approximated often by a linear combination of neighboring cell-centered values. In the literature, the weighted coefficients are obtained by solving local linear system of equations which is costly in 3D. One of the novelties of this paper is a new approach for obtaining vertex values by interpolating the cell-centered ones, which avoids solving local linear system of equations even with arbitrary diffusion tensors. Another main novelty of this paper is a new cascadic multigrid solver based on a prolongation operator, the newly developed explicit gradient transfer method, and a splitting extrapolation operator for solving 3D anisotropic diffusion equations with discontinuous coefficients. Numerical experiments are presented to demonstrate the efficiency and robustness of the CEXCMG method in terms of the mesh size and the contrast in the coefficients of the anisotropic diffusion tensor. DA - 2022/1/15/ PY - 2022/1/15/ DO - 10.1016/j.jcp.2021.110794 VL - 449 SP - SN - 1090-2716 UR - https://doi.org/10.1016/j.jcp.2021.110794 KW - Diffusion equation KW - Discontinuous coefficients KW - Anisotropic coefficients KW - Richardson extrapolation KW - Finite volume method KW - Cell-centered multigrid method ER - TY - JOUR TI - The maximum entropy method for data fusion and uncertainty quantification in multifunctional materials and structures AU - Gao, Wei AU - Miles, Paul R AU - Smith, Ralph C AU - Oates, William S T2 - Journal of Intelligent Material Systems and Structures AB - The quantification of uncertainty in intelligent material systems and structures requires methods to objectively compare complex models to measurements, where the majority of cases include multiple model outputs and quantities of interests given multiphysics coupling. This creates questions about constructing appropriate measures of uncertainty during fusion of data and comparisons between data and models. Novel materials with complex or poorly understood coupling can benefit from advanced statistical analysis to judge models in light of multiphysics data. Here, we apply the Maximum Entropy (ME) method to more complicated ferroelectric single crystals containing domain structures and soft electrostrictive membranes under both mechanical and electrical loading. Multiple quantities of interest are considered, which requires fusing heterogeneous information together when quantifying the uncertainty of lower fidelity models. We find that parameters, which were initially unidentifiable using a single quantity of interest, become identifiable using multiple quantities of interest. We also show that posterior densities may broaden or narrow when multiple data sets are fused together. This is likely due to conflict or agreement, respectively, between the different quantities of interest and the multiple model outputs. Such information is important to advance our predictions of intelligent materials and structures from multi-model inputs and heterogeneous data. DA - 2022/5// PY - 2022/5// DO - 10.1177/1045389X211048220 VL - 10 SP - 1045389X2110482 UR - https://doi.org/10.1177/1045389X211048220 KW - Maximum entropy KW - data fusion KW - uncertainty quantification KW - dielectric elastomer membrane KW - ferroelectric domain wall ER - TY - JOUR TI - A tribute to PR Krishnaiah AU - Bai, Zhidong AU - Silverstein, Jack W. T2 - JOURNAL OF MULTIVARIATE ANALYSIS AB - The authors reminisce on their association with P.R. Krishnaiah, renowned professor of statistics at the University of Pittsburgh and founding editor of the Journal of Multivariate Analysis. They recount their individual associations with him, mainly involving the behavior of eigenvalues of random matrices, and outline two areas of applied work he performed with one of the authors. DA - 2022/3// PY - 2022/3// DO - 10.1016/j.jmva.2021.104828 VL - 188 SP - SN - 0047-259X UR - https://doi.org/10.1016/j.jmva.2021.104828 KW - GIC of model selection KW - Image reconstruction KW - Prof. Krishnaiah KW - Random matrices ER - TY - JOUR TI - On quantum toroidal algebra of type A(1) AU - Chen, Fulin AU - Jing, Naihuan AU - Kong, Fei AU - Tan, Shaobin T2 - JOURNAL OF PURE AND APPLIED ALGEBRA AB - In this paper we introduce a new quantum algebra which specializes to the 2-toroidal Lie algebra of type A1. We prove that this quantum toroidal algebra has a natural triangular decomposition, a (topological) Hopf algebra structure and a vertex operator realization. DA - 2022/1// PY - 2022/1// DO - 10.1016/j.jpaa.2021.106814 VL - 226 IS - 1 SP - SN - 1873-1376 KW - Quantum toroidal algebra KW - Triangular decomposition KW - Hopf algebra ER - TY - JOUR TI - Least squares formulation for ill-posed inverse problems and applications AU - Chung, Eric AU - Ito, Kazufumi AU - Yamamoto, Masahiro T2 - APPLICABLE ANALYSIS AB - In this paper we propose a least squares formulation for ill-posed inverse problems. For example, ill-posed inverse problems in partial differential equations are those such that a solution of inverse problem exists for a smooth data but it does not depend continuously on data, or there is no solution for inverse problem, e.g. the Cauchy problem for elliptic equations and backward solution of parabolic equations. We develop the least squares formulation in which the sum of equations error over domain and data fitting criterion and Tikhonov regularization terms is minimized over entire solutions. In this way we can establish the existence and uniqueness of an inverse solution and establish the continuity of the inverse solution for noisy data in L2. The method can be applied to a general class of non-linear inverse problems and an operator theoretic stability analysis is developed. We describe how one can apply the method for various PDE inverse problems. Numerical tests using backward heat equation and Cauchy problem for elliptic equations are presented to demonstrate the applicability and performance of the proposed method. DA - 2022/10/13/ PY - 2022/10/13/ DO - 10.1080/00036811.2021.1884228 VL - 101 IS - 15 SP - 5247-5261 SN - 1563-504X KW - Ill-posed inverse problem KW - least squares formulation KW - continuous dependency on data ER - TY - JOUR TI - Multiplicities of Some Maximal Dominant Weights of the (sl)over-cap(n)-Modules V (k Lambda(0)) AU - Jayne, Rebecca L. AU - Misra, Kailash C. T2 - ALGEBRAS AND REPRESENTATION THEORY DA - 2022/4// PY - 2022/4// DO - 10.1007/s10468-021-10031-3 VL - 25 IS - 2 SP - 477-490 SN - 1572-9079 KW - Affine Lie algebra KW - Crystal base KW - Lattice path KW - Young tableau KW - Pattern-avoiding permutation ER -