TY - JOUR TI - A CELL-CENTERED MULTIGRID SOLVER FOR THE FINITE VOLUME DISCRETIZATION OF ANISOTROPIC ELLIPTIC INTERFACE PROBLEMS ON IRREGULAR DOMAINS* AU - Pan, Kejia AU - Wu, Xiaoxin AU - Hu, Hongling AU - Li, Zhilin T2 - JOURNAL OF COMPUTATIONAL MATHEMATICS DA - 2023/12/14/ PY - 2023/12/14/ DO - 10.4208/jcm.2308-m2023-0029 SP - SN - 1991-7139 KW - Elliptic interface problem KW - Discontinuous coefficients KW - Anisotropic coefficients KW - Cascadic multigrid method KW - Richardson extrapolation ER - TY - JOUR TI - Transionospheric Autofocus for Synthetic Aperture Radar AU - Gilman, Mikhail AU - Tsynkov, Semyon V. T2 - SIAM JOURNAL ON IMAGING SCIENCES DA - 2023/// PY - 2023/// DO - 10.1137/22M153570X VL - 16 IS - 4 SP - 2144-2174 SN - 1936-4954 KW - synthetic aperture radar KW - ionosphere KW - autofocus KW - optimization ER - TY - JOUR TI - MULTIPLE SOLUTIONS TO CYLINDRICALLY SYMMETRIC CURL-CURL PROBLEMS AND RELATED SCHRODINGER EQUATIONS WITH SINGULAR POTENTIALS AU - Gaczkowski, Michal AU - Mederski, Jaroslaw AU - Schino, Jacopo T2 - SIAM JOURNAL ON MATHEMATICAL ANALYSIS AB - We look for multiple solutions to the curl-curl problem , , with a nonlinear function which is critical in , i.e., , or has subcritical growth at infinity. If is radial in and below, then we show that the solutions to the problem above are in one-to-one correspondence with the solutions to the following Schrödinger equation: , , where , , and . In the critical case, the multiplicity problem for the latter equation has been studied only in the autonomous case and the available methods seem to be insufficient for the problem involving the singular potential, i.e., , due to the lack of conformal invariance. Therefore we develop methods for the critical curl-curl problem and show the multiplicity of bound states for both equations. In the subcritical case, instead, studying the Schrödinger equation in higher dimensions, we find infinitely many bound states for both problems. DA - 2023/// PY - 2023/// DO - 10.1137/22M1494786 VL - 55 IS - 5 SP - 4425-4444 SN - 1095-7154 KW - cylindrical symmetry KW - curl-curl problems KW - singular potentials KW - multiple solutions ER - TY - JOUR TI - Mixed norm $l^2$ decoupling for paraboloids AU - Dasu, Shival AU - Li, Zane AU - Jung, Hongki AU - Madrid, José AB - Abstract We prove the sharp mixed norm $(l^{2}, L^{q}_{t}L^{r}_{x})$ decoupling estimate for the paraboloid in $d + 1$ dimensions. DA - 2023/9/7/ PY - 2023/9/7/ DO - 10.1093/imrn/rnad226 UR - https://doi.org/10.1093/imrn/rnad226 ER - TY - JOUR TI - Unitary connections on Bratteli diagrams AU - Das, Paramita AU - Ghosh, Mainak AU - Ghosh, Shamindra AU - Jones, Corey T2 - JOURNAL OF TOPOLOGY AND ANALYSIS AB - In this paper, we extend Ocneanu’s theory of connections on graphs to define a 2-category whose 0-cells are tracial Bratteli diagrams, and whose 1-cells are generalizations of unitary connections. We show that this 2-category admits an embedding into the 2-category of hyperfinite von Neumann algebras, generalizing fundamental results from subfactor theory to a 2-categorical setting. DA - 2023/12/28/ PY - 2023/12/28/ DO - 10.1142/S1793525323500589 SP - SN - 1793-7167 KW - Subfactors KW - Bratteli diagram KW - standard invariants KW - C*-2-categories ER - TY - JOUR TI - Efficient algorithms for computing rank‐revealing factorizations on a GPU AU - Heavner, Nathan AU - Chen, Chao AU - Gopal, Abinand AU - Martinsson, Per‐Gunnar T2 - Numerical Linear Algebra with Applications AB - Abstract Standard rank‐revealing factorizations such as the singular value decomposition (SVD) and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms to cast most operations in terms of the Level‐3 BLAS. This article presents two alternative algorithms for computing a rank‐revealing factorization of the form , where and are orthogonal and is trapezoidal (or triangular if is square). Both algorithms use randomized projection techniques to cast most of the flops in terms of matrix‐matrix multiplication, which is exceptionally efficient on the GPU. Numerical experiments illustrate that these algorithms achieve significant acceleration over finely tuned GPU implementations of the SVD while providing low rank approximation errors close to that of the SVD. DA - 2023/6/2/ PY - 2023/6/2/ DO - 10.1002/nla.2515 VL - 30 IS - 6 J2 - Numerical Linear Algebra App LA - en OP - SN - 1070-5325 1099-1506 UR - http://dx.doi.org/10.1002/nla.2515 DB - Crossref ER - TY - JOUR TI - ERROR ESTIMATES OF RESIDUAL MINIMIZATION USING NEURAL NETWORKS FOR LINEAR PDES AU - Shin, Yeonjong AU - Zhang, Zhongqiang AU - Karniadakis, George Em T2 - Journal of Machine Learning for Modeling and Computing AB - We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates for both continuous and discrete formulations of residual minimization in strong and weak forms. The formulations cover recently developed physicsinformed neural networks based on strong and variational formulations. DA - 2023/// PY - 2023/// DO - 10.1615/jmachlearnmodelcomput.2023050411 VL - 4 IS - 4 SP - 73-101 J2 - J Mach Learn Model Comput LA - en OP - SN - 2689-3967 UR - http://dx.doi.org/10.1615/jmachlearnmodelcomput.2023050411 DB - Crossref ER - TY - JOUR TI - Accelerating gradient descent and Adam via fractional gradients AU - Shin, Yeonjong AU - Darbon, Jérôme AU - Karniadakis, George Em T2 - Neural Networks AB - We propose a class of novel fractional-order optimization algorithms. We define a fractional-order gradient via the Caputo fractional derivatives that generalizes integer-order gradient. We refer it to as the Caputo fractional-based gradient, and develop an efficient implementation to compute it. A general class of fractional-order optimization methods is then obtained by replacing integer-order gradients with the Caputo fractional-based gradients. To give concrete algorithms, we consider gradient descent (GD) and Adam, and extend them to the Caputo fractional GD (CfGD) and the Caputo fractional Adam (CfAdam). We demonstrate the superiority of CfGD and CfAdam on several large scale optimization problems that arise from scientific machine learning applications, such as ill-conditioned least squares problem on real-world data and the training of neural networks involving non-convex objective functions. Numerical examples show that both CfGD and CfAdam result in acceleration over GD and Adam, respectively. We also derive error bounds of CfGD for quadratic functions, which further indicate that CfGD could mitigate the dependence on the condition number in the rate of convergence and results in significant acceleration over GD. DA - 2023/4// PY - 2023/4// DO - 10.1016/j.neunet.2023.01.002 VL - 161 SP - 185-201 UR - http://dx.doi.org/10.1016/j.neunet.2023.01.002 ER - TY - JOUR TI - The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients AU - Le, Thuy T. AU - Nguyen, Linh V. AU - Nguyen, Loc H. AU - Park, Hyunha AB - This paper aims to reconstruct the initial condition of a hyperbolic equation with an unknown damping coefficient. Our approach involves approximating the hyperbolic equation's solution by its truncated Fourier expansion in the time domain and using a polynomial-exponential basis. This truncation process facilitates the elimination of the time variable, consequently, yielding a system of quasi-linear elliptic equations. To globally solve the system without needing an accurate initial guess, we employ the Carleman contraction principle. We provide several numerical examples to illustrate the efficacy of our method. The method not only delivers precise solutions but also showcases remarkable computational efficiency. DA - 2023/// PY - 2023/// DO - 10.48550/ARXIV.2308.13152 UR - https://arxiv.org/abs/2308.13152 ER - TY - JOUR TI - The dimensional reduction method for solving a nonlinear inverse heat conduction problem with limited boundary data AU - Dinh-Nho, H`ao AU - Le, Thuy T. AU - Nguyen, Loc H. AB - The objective of this article is to introduce a novel technique for computing numerical solutions to the nonlinear inverse heat conduction problem. This involves solving nonlinear parabolic equations with Cauchy data provided on one side $\Gamma$ of the boundary of the computational domain $\Omega$. The key step of our proposed method is the truncation of the Fourier series of the solution to the governing equation. The truncation technique enables us to derive a system of 1D ordinary differential equations. Then, we employ the well-known Runge-Kutta method to solve this system, which aids in addressing the nonlinearity and the lack of data on $\partial \Omega \setmunus \Gamma$. This new approach is called the dimensional reduction method. By converting the high-dimensional problem into a 1D problem, we achieve exceptional computational speed. Numerical results are provided to support the effectiveness of our approach. DA - 2023/// PY - 2023/// DO - 10.48550/ARXIV.2305.19528 UR - https://arxiv.org/abs/2305.19528 ER - TY - JOUR TI - Numerical verification of the convexification method for a frequency-dependent inverse scattering problem with experimental data AU - Le, Thuy AU - Khoa, Vo Anh AU - Klibanov, Michael Victor AU - Nguyen, Loc Hoang AU - Bidney, Grant AU - Astratov, Vasily AB - The reconstruction of physical properties of a medium from boundary measurements, known as inverse scattering problems, presents significant challenges. The present study aims to validate a newly developed convexification method for a 3D coefficient inverse problem in the case of buried unknown objects in a sandbox, using experimental data collected by a microwave scattering facility at The University of North Carolina at Charlotte. Our study considers the formulation of a coupled quasilinear elliptic system based on multiple frequencies. The system can be solved by minimizing a weighted Tikhonov-like functional, which forms our convexification method. Theoretical results related to the convexification are also revisited in this work. DA - 2023/// PY - 2023/// DO - 10.48550/ARXIV.2306.00761 UR - https://arxiv.org/abs/2306.00761 ER - TY - JOUR TI - Numerical differentiation by the polynomial-exponential basis AU - Nguyen, Phuong M. AU - Le, Thuy T. AU - Nguyen, Loc H. AU - Klibanov, Michael V. AB - Our objective is to calculate the derivatives of data corrupted by noise. This is a challenging task as even small amounts of noise can result in significant errors in the computation. This is mainly due to the randomness of the noise, which can result in high-frequency fluctuations. To overcome this challenge, we suggest an approach that involves approximating the data by eliminating high-frequency terms from the Fourier expansion of the given data with respect to the polynomial-exponential basis. This truncation method helps to regularize the issue, while the use of the polynomial-exponential basis ensures accuracy in the computation. We demonstrate the effectiveness of our approach through numerical examples in one and two dimensions. DA - 2023/// PY - 2023/// DO - 10.48550/ARXIV.2304.05909 UR - https://arxiv.org/abs/2304.05909 ER - TY - JOUR TI - A Carleman-Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data AU - Abney, Ray AU - Le, Thuy T. AU - Nguyen, Loc H. AU - Peters, Cam AB - We propose a globally convergent computational technique for the nonlinear inverse problem of reconstructing the zero-order coefficient in a parabolic equation using partial boundary data. This technique is called the "reduced dimensional method". Initially, we use the polynomial-exponential basis to approximate the inverse problem as a system of 1D nonlinear equations. We then employ a Picard iteration based on the quasi-reversibility method and a Carleman weight function. We will rigorously prove that the sequence derived from this iteration converges to the accurate solution for that 1D system without requesting a good initial guess of the true solution. The key tool for the proof is a Carleman estimate. We will also show some numerical examples. DA - 2023/// PY - 2023/// DO - 10.48550/ARXIV.2309.14599 UR - https://arxiv.org/abs/2309.14599 ER - TY - JOUR TI - Surface Gluing with Signs and Gradings in Decategorified Heegaard Floer Theory AU - Manion, Andrew T2 - INTERNATIONAL MATHEMATICS RESEARCH NOTICES AB - Abstract A previous result about the decategorified bordered (sutured) Heegaard Floer invariants of surfaces glued together along intervals, generalizing the decategorified content of Rouquier and the author’s higher-tensor-product-based gluing theorem in cornered Heegaard Floer homology, was proved only over ${\mathbb{F}}_2$ and without gradings. In this paper we add signs and prove a graded version of the interval gluing theorem over ${\mathbb{Z}}$, enabling a more detailed comparison of these aspects of decategorified Heegaard Floer theory with modern work on non-semisimple 3d TQFTs in mathematics and physics. DA - 2023/10/2/ PY - 2023/10/2/ DO - 10.1093/imrn/rnad238 SP - SN - 1687-0247 ER - TY - JOUR TI - A Perturbation Framework for Convex Minimization and Monotone Inclusion Problems with Nonlinear Compositions AU - Briceno-Arias, Luis M. AU - Combettes, Patrick L. T2 - MATHEMATICS OF OPERATIONS RESEARCH AB - We introduce a framework based on Rockafellar’s perturbation theory to analyze and solve general nonsmooth convex minimization and monotone inclusion problems involving nonlinearly composed functions as well as linear compositions. Such problems have been investigated only from a primal perspective and only for nonlinear compositions of smooth functions in finite-dimensional spaces in the absence of linear compositions. In the context of Banach spaces, the proposed perturbation analysis serves as a foundation for the construction of a dual problem and of a maximally monotone Kuhn–Tucker operator, which is decomposable as the sum of simpler monotone operators. In the Hilbertian setting, this decomposition leads to a block-iterative primal-dual algorithm that fully splits all the components of the problem and appears to be the first proximal splitting algorithm for handling nonlinear composite problems. Various applications are discussed. Funding: The work of L. M. Briceño-Arias was supported by Agencia Nacional de Investigación y Desarrollo-Chile [Grant Fondo Nacional de Desarrollo Científico y Tecnológico 1190871, Grant Centro de Modelamiento Matemático ACE210010, Grant Centro de Modelamiento Matemático FB210005, and basal Funds for Centers of Excellence], and the work of P. L. Combettes was supported by the National Science Foundation [Grant DMS-1818946]. DA - 2023/10/17/ PY - 2023/10/17/ DO - 10.1287/moor.2022.0180 VL - 10 SP - SN - 1526-5471 KW - convex optimization KW - duality KW - monotone operator KW - nonlinear composition KW - perturbation theory KW - proximal method KW - splitting algorithm ER - TY - JOUR TI - A topological data analysis study on murine pulmonary arterial trees with pulmonary hypertension AU - Miller, Megan AU - Johnston, Natalie AU - Livengood, Ian AU - Spinelli, Miya AU - Sazdanovic, Radmila AU - Olufsen, Mette S. T2 - MATHEMATICAL BIOSCIENCES AB - Pulmonary hypertension (PH), defined by a mean pulmonary arterial blood pressure above 20 mmHg in the main pulmonary artery, is a cardiovascular disease impacting the pulmonary vasculature. PH is accompanied by chronic vascular remodeling, wherein vessels become stiffer, large vessels dilate, and smaller vessels constrict. Some types of PH, including hypoxia-induced PH (HPH), also lead to microvascular rarefaction. This study analyzes the change in pulmonary arterial morphometry in the presence of HPH using novel methods from topological data analysis (TDA). We employ persistent homology to quantify arterial morphometry for control and HPH mice characterizing normalized arterial trees extracted from micro-computed tomography (micro-CT) images. We normalize generated trees using three pruning algorithms before comparing the topology of control and HPH trees. This proof-of-concept study shows that the pruning method affects the spatial tree statistics and complexity. We find that HPH trees are stiffer than control trees but have more branches and a higher depth. Relative directional complexities are lower in HPH animals in the right, ventral, and posterior directions. For the radius pruned trees, this difference is more significant at lower perfusion pressures enabling analysis of remodeling of larger vessels. At higher pressures, the arterial networks include more distal vessels. Results show that the right, ventral, and posterior relative directional complexities increase in HPH trees, indicating the remodeling of distal vessels in these directions. Strahler order pruning enables us to generate trees of comparable size, and results, at all pressure, show that HPH trees have lower complexity than the control trees. Our analysis is based on data from 6 animals (3 control and 3 HPH mice), and even though our analysis is performed in a small dataset, this study provides a framework and proof-of-concept for analyzing properties of biological trees using tools from Topological Data Analysis (TDA). Findings derived from this study bring us a step closer to extracting relevant information for quantifying remodeling in HPH. DA - 2023/10// PY - 2023/10// DO - 10.1016/j.mbs.2023.109056 VL - 364 SP - SN - 1879-3134 KW - Pulmonary hypertension KW - Vascular remodeling KW - Image segmentation KW - Tree pruning KW - Strahler order KW - Persistent homology KW - Topological data analysis KW - TDA ER - TY - JOUR TI - Few-Shot Learning Enables Population-Scale Analysis of Leaf Traits in Populus trichocarpa AU - Lagergren, John AU - Pavicic, Mirko AU - Chhetri, Hari B. AU - York, Larry M. AU - Hyatt, Doug AU - Kainer, David AU - Rutter, Erica M. AU - Flores, Kevin AU - Bailey-Bale, Jack AU - Klein, Marie AU - Taylor, Gail AU - Jacobson, Daniel AU - Streich, Jared T2 - PLANT PHENOMICS AB - Plant phenotyping is typically a time-consuming and expensive endeavor, requiring large groups of researchers to meticulously measure biologically relevant plant traits, and is the main bottleneck in understanding plant adaptation and the genetic architecture underlying complex traits at population scale. In this work, we address these challenges by leveraging few-shot learning with convolutional neural networks to segment the leaf body and visible venation of 2,906 Populus trichocarpa leaf images obtained in the field. In contrast to previous methods, our approach (a) does not require experimental or image preprocessing, (b) uses the raw RGB images at full resolution, and (c) requires very few samples for training (e.g., just 8 images for vein segmentation). Traits relating to leaf morphology and vein topology are extracted from the resulting segmentations using traditional open-source image-processing tools, validated using real-world physical measurements, and used to conduct a genome-wide association study to identify genes controlling the traits. In this way, the current work is designed to provide the plant phenotyping community with (a) methods for fast and accurate image-based feature extraction that require minimal training data and (b) a new population-scale dataset, including 68 different leaf phenotypes, for domain scientists and machine learning researchers. All of the few-shot learning code, data, and results are made publicly available. DA - 2023/7/28/ PY - 2023/7/28/ DO - 10.34133/plantphenomics.0072 VL - 5 SP - SN - 2643-6515 ER - TY - JOUR TI - On super quantum discord for high-dimensional bipartite state AU - Zhou, Jianming AU - Hu, Xiaoli AU - Jing, Naihuan T2 - QUANTUM INFORMATION PROCESSING DA - 2023/12/14/ PY - 2023/12/14/ DO - 10.1007/s11128-023-04203-x VL - 22 IS - 12 SP - SN - 1573-1332 UR - https://doi.org/10.1007/s11128-023-04203-x KW - Super quantum discord KW - Quantum correlations KW - Bipartite states KW - Secondary 81Qxx ER - TY - JOUR TI - A Bijection Between K-Kohnert Diagrams and Reverse Set-Valued Tableaux AU - Pan, Jianping AU - Yu, Tianyi T2 - ELECTRONIC JOURNAL OF COMBINATORICS AB - Lascoux polynomials are K-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux (RSVT) rule for Lascoux polynomials and reverse semistandard Young tableaux (RSSYT) rule for key polynomials. Furthermore, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with 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 RSVT and K-Kohnert diagrams. DA - 2023/11/17/ PY - 2023/11/17/ DO - 10.37236/11434 VL - 30 IS - 4 SP - SN - 1077-8926 UR - http://dx.doi.org/10.37236/11434 ER - TY - JOUR TI - Evaluations of Link Polynomials and Recent Constructions in Heegaard Floer Theory AU - Gu, Larry AU - Manion, Andrew T2 - MICHIGAN MATHEMATICAL JOURNAL AB - Using a definition of Euler characteristic for fractionally-graded complexes based on roots of unity, we show that the Euler characteristics of Dowlin's "$\mathfrak{sl}(n)$-like" Heegaard Floer knot invariants $HFK_n$ recover both Alexander polynomial evaluations and $\mathfrak{sl}(n)$ polynomial evaluations at certain roots of unity for links in $S^3$. We show that the equality of these evaluations can be viewed as the decategorified content of the conjectured spectral sequences relating $\mathfrak{sl}(n)$ homology and $HFK_n$. DA - 2023/11// PY - 2023/11// DO - 10.1307/mmj/20216061 VL - 73 IS - 5 SP - 1097-1118 SN - 1945-2365 ER - TY - JOUR TI - Multiplicities of maximal weights of the sℓ (n)-module V (kΛ0) AU - Jayne, Rebecca L. AU - Misra, Kailash C. T2 - JOURNAL OF ALGEBRA AND ITS APPLICATIONS AB - Consider the affine Lie algebra [Formula: see text] with null root [Formula: see text], weight lattice [Formula: see text] and set of dominant weights [Formula: see text]. Let [Formula: see text] [Formula: see text] denote the integrable highest weight [Formula: see text]-module with level [Formula: see text] highest weight [Formula: see text]. Let [Formula: see text] denote the set of weights of [Formula: see text]. A weight [Formula: see text] is a maximal weight if [Formula: see text]. Let [Formula: see text] denote the set of maximal dominant weights which is known to be a finite set. The explicit description of the weights in the set [Formula: see text] is known [R. L. Jayne and K. C. Misra, On multiplicities of maximal dominant weights of [Formula: see text]-modules, Algebr. Represent. Theory 17 (2014) 1303–1321]. In papers [R. L. Jayne and K. C. Misra, Lattice paths, Young tableaux, and weight multiplicities, Ann. Comb. 22 (2018) 147–156; R. L. Jayne and K. C. Misra, Multiplicities of some maximal dominant weights of the [Formula: see text]-modules [Formula: see text], Algebr. Represent. Theory 25 (2022) 477–490], the multiplicities of certain subsets of [Formula: see text] were given in terms of some pattern-avoiding permutations using the associated crystal base theory. In this paper the multiplicity of all the maximal dominant weights of the [Formula: see text]-module [Formula: see text] are given generalizing the results in [R. L. Jayne and K. C. Misra, Lattice paths, Young tableaux, and weight multiplicities, Ann. Comb. 22 (2018) 147–156; R. L. Jayne and K. C. Misra, Multiplicities of some maximal dominant weights of the [Formula: see text]-modules [Formula: see text], Algebr. Represent. Theory 25 (2022) 477–490]. DA - 2023/11/10/ PY - 2023/11/10/ DO - 10.1142/S0219498825500987 SP - SN - 1793-6829 KW - Affine Lie algebra KW - integrable representation KW - crystal base KW - Young tableau KW - avoiding permutation ER - TY - JOUR TI - An optimal control strategy for execution of large stock orders using long short-term memory networks AU - Papanicolaou, A. AU - Fu, H. AU - Krishnamurthy, P. AU - Healy, B. AU - Khorrami, F. T2 - JOURNAL OF COMPUTATIONAL FINANCE AB - We simulate the execution of a large stock order with real data and a general power law in the Almgren and Chriss model. The example we consider is the liquidation of a large position executed over the course of a single trading day in a limit order book. Transaction costs are incurred because large orders walk the order book (that is, they consume order book liquidity beyond the best bid/ask price). We model the order book with a power law that is proportional to trading volume, and thus transaction costs are inversely proportional to a power of the trading volume. We obtain a policy approximation by training a long short-term memory (LSTM) neural network to minimize the transaction costs accumulated when execution is carried out as a sequence of smaller suborders. Using historical Standard & Poor’s 100 price and volume data, we evaluate our LSTM strategy relative to strategies based on the time-weighted average price (TWAP) and volume-weighted average price (VWAP). For execution of a single stock, the input to the LSTM is the cross-section of data on all 100 stocks, including prices, volumes, TWAPs and VWAPs. By using this data cross-section, the LSTM should be able to exploit interstock codependence in volume and price movements, thereby reducing transaction costs for the day. Our tests on Standard & Poor’s 100 data demonstrate that in fact this is so, as our LSTM strategy consistently outperforms TWAP- and VWAP-based strategies. DA - 2023/3// PY - 2023/3// DO - 10.21314/JCF.2023.003 VL - 26 IS - 4 SP - 37-65 SN - 1755-2850 KW - price impact KW - order books KW - optimal execution KW - long short-term memory (LSTM) networks KW - trading volume ER - TY - JOUR TI - RSK tableaux and the weak order on fully commutative permutations AU - Gunawan, Emily AU - Pan, Jianping AU - Russell, Heather M. AU - Tenner, Bridget Eileen T2 - ELECTRONIC JOURNAL OF COMBINATORICS 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. DA - 2023/12/1/ PY - 2023/12/1/ DO - 10.37236/11877 VL - 30 IS - 4 SP - SN - 1077-8926 KW - boolean permutation KW - fully commutative permutation KW - permutation pattern KW - Robinson-Schensted-Knuth correspondence KW - reduced word KW - weak order ER - TY - JOUR TI - Modeling impact of vaccination on COVID-19 dynamics in St. Louis AU - Lacy, Alexanderia AU - Igoe, Morganne AU - Das, Praachi AU - Farthing, Trevor AU - Lloyd, Alun L. AU - Lanzas, Cristina AU - Odoi, Agricola AU - Lenhart, Suzanne T2 - JOURNAL OF BIOLOGICAL DYNAMICS AB - The region of St. Louis, Missouri, has displayed a high level of heterogeneity in COVID-19 cases, hospitalization, and vaccination coverage. We investigate how human mobility, vaccination, and time-varying transmission rates influenced SARS-CoV-2 transmission in five counties in the St. Louis area. A COVID-19 model with a system of ordinary differential equations was developed to illustrate the dynamics with a fully vaccinated class. Using the weekly number of vaccinations, cases, and hospitalization data from five counties in the greater St. Louis area in 2021, parameter estimation for the model was completed. The transmission coefficients for each county changed four times in that year to fit the model and the changing behaviour. We predicted the changes in disease spread under scenarios with increased vaccination coverage. SafeGraph local movement data were used to connect the forces of infection across various counties. DA - 2023/12/31/ PY - 2023/12/31/ DO - 10.1080/17513758.2023.2287084 VL - 17 IS - 1 SP - SN - 1751-3766 KW - Modeling COVID-19 spread KW - St. Louis area KW - SafeGraph movement data KW - vaccination KW - differential equations ER - TY - JOUR TI - The GCD for finite geometric series AU - Hartwig, R. E. AU - Patricio, Pedro T2 - FILOMAT DA - 2023/// PY - 2023/// DO - 10.2298/FIL2329973H VL - 37 IS - 29 SP - 9973-9979 SN - 0354-5180 KW - Finite geometric series KW - Greatest common divisor ER - TY - JOUR TI - Detecting multipartite entanglement via complete orthogonal basis AU - Zhao, Hui AU - Hao, Jia AU - Li, Jing AU - Fei, Shao-Ming AU - Jing, Naihuan AU - Wang, Zhi-Xi T2 - RESULTS IN PHYSICS AB - We study genuine tripartite entanglement and multipartite entanglement in arbitrary n-partite quantum systems based on complete orthogonal basis (COB). While the usual Bloch representation of a density matrix uses three types of generators, the density matrix with COB operators has one uniformed type of generators which may simplify related computations. We take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement and multipartite entanglement. We first convert the general states to simpler forms by using the relationship between general symmetric informationally complete measurements and COB. Then we derive an operational criteria to detect genuine tripartite entanglement. We study multipartite entanglement in arbitrary dimensional multipartite systems. By providing detailed examples, we demonstrate that our criteria can detect more genuine entangled and multipartite entangled states than the previously existing criteria. DA - 2023/11// PY - 2023/11// DO - 10.1016/j.rinp.2023.107060 VL - 54 SP - SN - 2211-3797 KW - Genuine tripartite entanglement KW - Complete orthogonal basis KW - Entanglement ER - TY - JOUR TI - Precision-aware deterministic and probabilistic error bounds for floating point summation AU - Hallman, Eric AU - Ipsen, Ilse C. F. T2 - NUMERISCHE MATHEMATIK DA - 2023/10// PY - 2023/10// DO - 10.1007/s00211-023-01370-y VL - 155 IS - 1-2 SP - 83-119 SN - 0945-3245 ER - TY - JOUR TI - Logarithmic Vertex Algebras and Non-local Poisson Vertex Algebras AU - Bakalov, Bojko AU - Villarreal, Juan J. T2 - COMMUNICATIONS IN MATHEMATICAL PHYSICS DA - 2023/11// PY - 2023/11// DO - 10.1007/s00220-023-04839-x VL - 404 IS - 1 SP - 185-226 SN - 1432-0916 ER - TY - JOUR TI - A COMPUTATIONAL FRAMEWORK FOR EDGE-PRESERVING REGULARIZATION IN DYNAMIC INVERSE PROBLEMS AU - Pasha, Mirjeta AU - Saibaba, Arvind K. AU - Gazzola, Silvia AU - Espanol, Malena I. AU - De Sturler, Eric T2 - ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS AB - We devise efficient methods for dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change in time. Our goal is to solve for all the quantities of interest simultaneously. We consider large-scale ill-posed problems made more challenging by their dynamic nature and, possibly, by the limited amount of available data per measurement step. To alleviate these difficulties, we apply a unified class of regularization methods that enforce simultaneous regularization in space and time (such as edge enhancement at each time instant and proximity at consecutive time instants) and achieve this with low computational cost and enhanced accuracy. More precisely, we develop iterative methods based on a majorization-minimization (MM) strategy with quadratic tangent majorant, which allows the resulting least-squares problem with a total variation regularization term to be solved with a generalized Krylov subspace (GKS) method; the regularization parameter can be determined automatically and efficiently at each iteration. Numerical examples from a wide range of applications, such as limited-angle computerized tomography (CT), space-time image deblurring, and photoacoustic tomography (PAT), illustrate the effectiveness of the described approaches. DA - 2023/// PY - 2023/// DO - 10.1553/etna_vol58s486 VL - 58 SP - 486-516 SN - 1068-9613 KW - dynamic inversion KW - time-dependence KW - edge-preservation KW - majorization-minimization KW - regularization KW - generalized Krylov subspaces KW - image deblurring KW - photoacoustic tomography KW - computerized tomography ER - TY - JOUR TI - Stable high order FD methods for interface and internal layer problems based on non-matching grids AU - Li, Zhilin AU - Pan, Kejia AU - Ruiz-Alvarez, Juan T2 - NUMERICAL ALGORITHMS DA - 2023/11/6/ PY - 2023/11/6/ DO - 10.1007/s11075-023-01680-0 VL - 11 SP - SN - 1572-9265 UR - https://doi.org/10.1007/s11075-023-01680-0 KW - Interface problems KW - Internal layer problems KW - Non-matching grid KW - Discrete maximum principle KW - Hanging nodes ER - TY - JOUR TI - Reconstruction of Vertex Algebras in Even Higher Dimensions AU - Bakalov, Bojko N. AU - Nikolov, Nikolay M. T2 - ANNALES HENRI POINCARE AB - Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any lower dimension and, in particular, to dimension one. In the case when D is even, we find natural conditions under which the converse passage is possible. These conditions include a unitary action of the conformal Lie algebra with a positive energy, which is given by local endomorphisms and obeys certain integrability properties. DA - 2023/11/2/ PY - 2023/11/2/ DO - 10.1007/s00023-023-01384-0 SP - SN - 1424-0661 KW - Primary 17B69 KW - Secondary 81R10 KW - 81T40 ER - TY - JOUR TI - Randomized reduced basis methods for parameterized fractional elliptic PDEs AU - Antil, Harbir AU - Saibaba, Arvind K. T2 - FINITE ELEMENTS IN ANALYSIS AND DESIGN AB - This paper is interested in developing reduced order models (ROMs) for repeated simulation of fractional elliptic partial differential equations (PDEs) for multiple values of the parameters (e.g., diffusion coefficients or fractional exponent) governing these models. These problems arise in many applications including simulating Gaussian processes, geophysical electromagnetics. The approach uses the Kato integral formula to express the solution as an integral involving the solution of a parameterized elliptic PDE, which is discretized using finite elements in space and sinc quadrature for the fractional part. The offline stage of the ROM is accelerated using a solver for shifted linear systems, MPGMRES-Sh, and using a randomized approach for compressing the snapshot matrix. Our approach is both computational and memory efficient. Numerical experiments on a range of model problems, including an application to Gaussian processes, show the benefits of our approach. DA - 2023/12/1/ PY - 2023/12/1/ DO - 10.1016/j.finel.2023.104046 VL - 227 SP - SN - 1872-6925 KW - Fractional elliptic PDEs KW - Reduced order models KW - Iterative methods KW - Randomization KW - Gaussian processes ER - TY - JOUR TI - Separability and classification of multipartite quantum states AU - Ma, Pan-Wen AU - Zhao, Hui AU - Jing, Naihuan T2 - LASER PHYSICS LETTERS AB - Abstract We study separability in arbitrary multipartite quantum systems based on principal base matrices. Necessary conditions are presented for different kinds of separable states. These conditions can give a complete classification of multipartite quantum states. While the usual Bloch representation of a density matrix uses three types of generators, the representation with principal base matrices has one uniform type of generator which simplifies computation. In this paper, we take advantage of this simplicity to derive useful and operational criteria to detect multipartite separability. We first obtain criteria on detecting 1 3 separable, 2 2 separable, 1 1 2 separable and fully separable four-partite quantum states. We then study k -separability for multipartite quantum states in arbitrary dimensions. Detailed examples are given to show that our criteria are able to detect more entanglement states than some existing criteria. DA - 2023/12/1/ PY - 2023/12/1/ DO - 10.1088/1612-202X/ad0537 VL - 20 IS - 12 SP - SN - 1612-202X KW - separability KW - entanglement KW - principal base matrix ER - TY - JOUR TI - Parameter estimation and identifiability analysis for a bivalent analyte model of monoclonal antibody-antigen binding AU - Nguyen, Kyle AU - Li, Kan AU - Flores, Kevin AU - Tomaras, Georgia D. AU - Dennison, S. Moses AU - McCarthy, Janice M. T2 - ANALYTICAL BIOCHEMISTRY AB - Surface plasmon resonance (SPR) is an extensively used technique to characterize antigen-antibody interactions. Affinity measurements by SPR typically involve testing the binding of antigen in solution to monoclonal antibodies (mAbs) immobilized on a chip and fitting the kinetics data using 1:1 Langmuir binding model to derive rate constants. However, when it is necessary to immobilize antigens instead of the mAbs, a bivalent analyte (1:2) binding model is required for kinetics analysis. This model is lacking in data analysis packages associated with high throughput SPR instruments and the packages containing this model do not explore multiple local minima and parameter identifiability issues that are common in non-linear optimization. Therefore, we developed a method to use a system of ordinary differential equations for analyzing 1:2 binding kinetics data. Salient features of this method include a grid search on parameter initialization and a profile likelihood approach to determine parameter identifiability. Using this method we found a non-identifiable parameter in data set collected under the standard experimental design. A simulation-guided improved experimental design led to reliable estimation of all rate constants. The method and approach developed here for analyzing 1:2 binding kinetics data will be valuable for expeditious therapeutic antibody discovery research. DA - 2023/10/15/ PY - 2023/10/15/ DO - 10.1016/j.ab.2023.115263 VL - 679 SP - SN - 1096-0309 KW - Bivalent analyte KW - Binding kinetics KW - Parameter identifiability KW - Surface plasmon resonance ER - TY - JOUR TI - A matrix theory introduction to seaweed algebras and their index AU - Cameron, Alex AU - Coll Jr, Vincent E. AU - Mayers, Nicholas AU - Russoniello, Nicholas T2 - EXPOSITIONES MATHEMATICAE AB - The index of a Lie algebra is an important algebraic invariant, but it is notoriously difficult to compute. However, for the suggestively-named seaweed algebras, the computation of the index can be reduced to a combinatorial formula based on the connected components of a “meander”: a planar graph associated with the algebra. Our index analysis on seaweed algebras requires only basic linear and abstract algebra. Indeed, the main goal of this article is to introduce a broader audience to seaweed algebras with minimal appeal to specialized language and notation from Lie theory. This said, we present several results that do not appear elsewhere and do appeal to more advanced language in the Introduction to provide added context. DA - 2023/12// PY - 2023/12// DO - 10.1016/j.exmath.2023.06.001 VL - 41 IS - 4 SP - SN - 1878-0792 KW - Seaweed Lie algebra KW - Frobenius Lie algebra KW - Index KW - Meander ER - TY - JOUR TI - Statistical properties of BayesCG under the Krylov prior AU - Reid, Tim W. AU - Ipsen, Ilse C. F. AU - Cockayne, Jon AU - Oates, Chris J. T2 - NUMERISCHE MATHEMATIK DA - 2023/10/12/ PY - 2023/10/12/ DO - 10.1007/s00211-023-01375-7 VL - 10 SP - SN - 0945-3245 KW - 15 A10 ER - TY - JOUR TI - Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category AU - Khovanov, Mikhail AU - Sazdanovic, Radmila T2 - FUNDAMENTA MATHEMATICAE AB - The Deligne category of symmetric groups is the additive Karoubi closure of the partition category. It is semisimple for generic values of the parameter $t$ while producing categories of representations of the symmetric group when modded out by the ideal DA - 2023/10/19/ PY - 2023/10/19/ DO - 10.4064/fm283-8-2023 VL - 10 SP - SN - 1730-6329 UR - http://dx.doi.org/10.4064/fm283-8-2023 KW - Deligne category KW - cobordisms KW - partition category ER - TY - JOUR TI - Global Identifiability of Differential Models (vol 73, pg 1831, 2020) AU - Hong, Hoon AU - Ovchinnikov, Alexey AU - Pogudin, Gleb AU - Yap, Chee T2 - COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS AB - We are grateful to Peter Thompson for pointing out an error in [1, Lemma 3.5, p. 1848]. The original proof worked only under the assumption that θ ̂ $\hat{\theta }$ is a vector of constants. However, some of the components of θ ̂ $\hat{\bm{\theta }}$ could be the states of the dynamic under consideration, and the lemma was used in such a setup (i.e., with θ ̂ $\hat{\bm{\theta }}$ involving states) later in [1, Proposition 3.4]. We give a more explicit version of the statement and provide a correct proof. The desired statement will be deduced from the following: Lemma 1.Consider a system of differential equations Proof.Consider the following differential ideal Now we will prove the claim. Consider the ring R : = C [ x , μ ] { u } [ 1 / Q ] $R := \mathbb {C}[\bm{x}, \bm{\mu }]\lbrace \bm{u}\rbrace [1/Q]$ . Let J be the ideal generated by I ∩ C [ x , μ ] { u } $I \cap \mathbb {C}[\bm{x}, \bm{\mu }]\lbrace \bm{u}\rbrace$ in R. The definition of I via the saturation at Q implies that Let R ∼ $\widetilde{R}$ be the localization of R with respect to C { u } $\mathbb {C}\lbrace \bm{u}\rbrace$ and J ∼ $\widetilde{J}$ be the ideal generated by J in this localization. The derivation L $\mathcal {L}$ can be naturally extended to R ∼ $\widetilde{R}$ , and J ∼ $\widetilde{J}$ is also L $\mathcal {L}$ -invariant. It is sufficient to prove that J ∼ ∩ C [ x , μ ] ≠ { 0 } $\widetilde{J}\cap \mathbb {C}[\bm{x}, \bm{\mu }] \ne \lbrace 0\rbrace$ . Consider a nonzero element of J ∼ ∩ C [ x , μ ] { u } $\widetilde{J} \cap \mathbb {C}[\bm{x}, \bm{\mu }]\lbrace \bm{u}\rbrace$ with the smallest number of monomials and, among such elements, an element of the smallest total degree. We will call it S. If S ∈ C [ x , μ ] $S\in \mathbb {C}[\bm{x}, \bm{\mu }]$ , we are done. Otherwise, one of u appears in S, say u1. Let h = ord u 1 S $h = \operatorname{ord}_{u_1}S$ . Since R ∼ $\widetilde{R}$ is a Noetherian ring, there exists N > 0 $N > 0$ such that The following corollary is equivalent to [1, Lemma 3.5, p. 1848] but explicitly highlights that some of the entries of θ ̂ $\hat{\bm{\theta }}$ may be initial conditions, not only system parameters. Corollary 1. (Clarified version of [[1], Lemma 3.5, p. 1848])In the notation of [1, Section 2.2], let P ( μ , x , u , … , u ( N ) ) ∈ C [ μ , x ] { u } $P(\bm{\mu }, \bm{x}, u, \ldots , u^{(N)})\in \mathbb {C}[\bm{\mu }, \bm{x}] \lbrace u \rbrace$ be nonzero. Then there exist nonempty Zariski open subsets Θ ⊂ C s $\Theta {\subset }\mathbb {C}^{s}$ and U ⊂ C ∞ ( 0 ) $U\subset \mathbb {C}^{\infty }(0)$ such that, for every θ ̂ = ( μ ̂ , x ̂ * ) ∈ Θ $\hat{\bm{\theta }} = (\hat{\bm{\mu }}, \hat{\bm{x}}^\ast )\in \Theta$ , u ̂ ∈ U $\hat{u}\in U$ , and the corresponding x ̂ = X ( θ ̂ , u ̂ ) $\hat{\bm{x}} = X(\hat{\bm{\theta }}, \hat{u})$ , the function P ( μ ̂ , x ̂ , u ̂ , … , ( u ̂ ) ( N ) ) $P(\hat{\bm{\mu }}, \hat{\bm{x}}, \hat{u},\ldots ,(\hat{u})^{(N)})$ is a nonzero element of C ∞ ( 0 ) $\mathbb {C}^{\infty }(0)$ . Proof.We apply Lemma 1 to the model Σ and the polynomial P as in the statement, and obtain polynomials P 1 ( x , μ ) $P_1(\bm{x}, \bm{\mu })$ and P2(u). We define Zariski open sets Θ and U by P 1 ≠ 0 $P_1 \ne 0$ and P 2 ( u ) | t = 0 ≠ 0 $P_2(\bm{u})|_{t = 0} \ne 0$ , respectively. Then the lemma implies that, for ( μ ̂ , x ̂ ∗ ) ∈ Θ $(\hat{\bm{\mu }}, \hat{\bm{x}}^*) \in \Theta$ and u ̂ ∈ U $\hat{u} \in U$ , P ( μ ̂ , x ̂ , u ̂ , … , ( u ̂ ) ( N ) ) $P(\hat{\bm{\mu }}, \hat{\bm{x}}, \hat{u},\ldots ,(\hat{u})^{(N)})$ will be a nonzero function. □ $\Box$ DA - 2023/9/22/ PY - 2023/9/22/ DO - 10.1002/cpa.22163 VL - 9 SP - SN - 1097-0312 ER - TY - JOUR TI - Inapparent infections shape the transmission heterogeneity of dengue AU - Vazquez-Prokopec, Gonzalo M. AU - Morrison, Amy C. AU - Paz-Soldan, Valerie AU - Stoddard, Steven T. AU - Koval, William AU - Waller, Lance A. AU - Perkins, T. Alex AU - Lloyd, Alun L. AU - Astete, Helvio AU - Elder, John AU - Scott, Thomas W. AU - Kitron, Uriel T2 - PNAS NEXUS AB - Abstract Transmission heterogeneity, whereby a disproportionate fraction of pathogen transmission events result from a small number of individuals or geographic locations, is an inherent property of many, if not most, infectious disease systems. For vector-borne diseases, transmission heterogeneity is inferred from the distribution of the number of vectors per host, which could lead to significant bias in situations where vector abundance and transmission risk at the household do not correlate, as is the case with dengue virus (DENV). We used data from a contact tracing study to quantify the distribution of DENV acute infections within human activity spaces (AS), the collection of residential locations an individual routinely visits, and quantified measures of virus transmission heterogeneity from two consecutive dengue outbreaks (DENV-4 and DENV-2) that occurred in the city of Iquitos, Peru. Negative-binomial distributions and Pareto fractions showed evidence of strong overdispersion in the number of DENV infections by AS and identified super-spreading units (SSUs): i.e. AS where most infections occurred. Approximately 8% of AS were identified as SSUs, contributing to more than 50% of DENV infections. SSU occurrence was associated more with DENV-2 infection than with DENV-4, a predominance of inapparent infections (74% of all infections), households with high Aedes aegypti mosquito abundance, and high host susceptibility to the circulating DENV serotype. Marked heterogeneity in dengue case distribution, and the role of inapparent infections in defining it, highlight major challenges faced by reactive interventions if those transmission units contributing the most to transmission are not identified, prioritized, and effectively treated. DA - 2023/3// PY - 2023/3// DO - 10.1093/pnasnexus/pgad024 VL - 2 IS - 3 SP - SN - 2752-6542 KW - arbovirus KW - transmission heterogeneity KW - mobility KW - super-spreading ER - TY - JOUR TI - Enhanced quantum channel uncertainty relations by skew information AU - Hu, Xiaoli AU - Hu, Naihong AU - Yu, Bing AU - Jing, Naihuan T2 - QUANTUM INFORMATION PROCESSING AB - By revisiting the mathematical foundation of the uncertainty relation, skew information-based uncertainty sequences are developed for any two quantum channels. A reinforced version of the Cauchy-Schwarz inequality is adopted to improve the uncertainty relation, and a sampling technique of observables' coordinates is used to offset randomness in the inequality. It is shown that the lower bounds of the uncertainty relations are tighter than some previous studies. DA - 2023/10/6/ PY - 2023/10/6/ DO - 10.1007/s11128-023-04113-y VL - 22 IS - 10 SP - SN - 1573-1332 KW - Uncertainty relation KW - Quantum channel KW - Skew information ER - TY - JOUR TI - Two-point functions and constant mean curvature surfaces in R3 AU - Mcgrath, Peter AU - Meekins, Everett T2 - INVOLVE, A JOURNAL OF MATHEMATICS DA - 2023/// PY - 2023/// DO - 10.2140/involve.2023.16.467 VL - 16 IS - 3 SP - 467-482 SN - 1944-4184 KW - constant mean curvature KW - Hopf KW - Alexandrov KW - differential geometry KW - geometric analysis KW - surface ER - TY - JOUR TI - KRYLOV-AWARE STOCHASTIC TRACE ESTIMATION AU - Chen, Tyler AU - Hallman, Eric T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS AB - We introduce an algorithm for estimating the trace of a matrix function using implicit products with a symmetric matrix . Existing methods for implicit trace estimation of a matrix function tend to treat matrix-vector products with as a black box to be computed by a Krylov subspace method. Like other recent algorithms for implicit trace estimation, our approach is based on a combination of deflation and stochastic trace estimation. However, we take a closer look at how products with are integrated into these approaches which enables several efficiencies not present in previously studied methods. In particular, we describe a Krylov subspace method for computing a low-rank approximation of a matrix function by a computationally efficient projection onto Krylov subspace. DA - 2023/// PY - 2023/// DO - 10.1137/22M1494257 VL - 44 IS - 3 SP - 1218-1244 SN - 1095-7162 KW - spectral function KW - Hutchinson's method KW - quadratic trace estimation KW - low-rank approximation KW - block-Lanczos method KW - Krylov subspace method ER - TY - JOUR TI - Asymptotics and criticality for a space-dependent branching process AU - Grigorescu, Ilie AU - Kang, Min T2 - STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES AB - AbstractWe investigate a non-conservative semigroup (St)t≥0 determined by a branching process tracing the evolution of particles moving in a domain in Rd. When a particle is killed at the boundary, a new generation of particles with mean number K¯ is born at a random point in the domain. Between branching, the particles are driven by a diffusion process with Dirichlet boundary conditions. According to the sign of K¯−1, we distinguish super/sub-critical regimes and determine the exact exponential rate for the total number of particles n(t)∼exp⁡(α∗t), with α∗ depending explicitly on K¯. We prove the Yaglom limit St/n(t)→ν, where the quasi-stationary distribution ν is determined by the resolvent of the Dirichlet kernel at the point α∗. The main application is in particle systems, where the normalization of the semigroup by its total mass gives the hydrodynamic limit of the Bak-Sneppen branching diffusions (BSBD). Since ν is the asymptotic profile under equilibrium, and the family of quasi-stationary distributions ν is indexed by K¯, the model provides an explicit example of self-organized criticality.Keywords: SemigroupYaglom limitbranching processessupercriticalqsdBak-SneppenFleming-ViotDirichlet kernelKey Words and Phrases: Primary: 60J3560J80Secondary: 47D0760K35 Disclosure statementNo potential conflict of interest was reported by the author(s). DA - 2023/9/14/ PY - 2023/9/14/ DO - 10.1080/17442508.2023.2256922 SP - SN - 1744-2516 KW - Semigroup KW - Yaglom limit KW - branching processes KW - supercritical KW - qsd KW - Bak-Sneppen KW - Fleming-Viot KW - Dirichlet kernel ER - TY - JOUR TI - Direct mosquito feedings on dengue-2 virus-infected people reveal dynamics of human infectiousness AU - Lambrechts, Louis AU - Reiner, Robert C. AU - Briesemeister, M. Veronica AU - Barrera, Patricia AU - Long, Kanya C. AU - Elson, William H. AU - Vizcarra, Alfonso AU - Astete, Helvio AU - Bazan, Isabel AU - Siles, Crystyan AU - Vilcarromero, Stalin AU - Leguia, Mariana AU - Kawiecki, Anna B. AU - Perkins, T. Alex AU - Lloyd, Alun L. AU - Waller, Lance A. AU - Kitron, Uriel AU - Jenkins, Sarah A. AU - Hontz, Robert D. AU - Campbell, Wesley R. AU - Carrington, Lauren B. AU - Simmons, Cameron P. AU - Ampuero, J. Sonia AU - Vasquez, Gisella AU - Elder, John P. AU - Paz-Soldan, Valerie A. AU - Vazquez-Prokopec, Gonzalo M. AU - Rothman, Alan L. AU - Barker, Christopher M. AU - Scott, Thomas W. AU - Morrison, Amy C. AU - Viennet, Elvina AU - Gilbert, Amy T. T2 - PLOS NEGLECTED TROPICAL DISEASES AB - Dengue virus (DENV) transmission from humans to mosquitoes is a poorly documented, but critical component of DENV epidemiology. Magnitude of viremia is the primary determinant of successful human-to-mosquito DENV transmission. People with the same level of viremia, however, can vary in their infectiousness to mosquitoes as a function of other factors that remain to be elucidated. Here, we report on a field-based study in the city of Iquitos, Peru, where we conducted direct mosquito feedings on people naturally infected with DENV and that experienced mild illness. We also enrolled people naturally infected with Zika virus (ZIKV) after the introduction of ZIKV in Iquitos during the study period. Of the 54 study participants involved in direct mosquito feedings, 43 were infected with DENV-2, two with DENV-3, and nine with ZIKV. Our analysis excluded participants whose viremia was detectable at enrollment but undetectable at the time of mosquito feeding, which was the case for all participants with DENV-3 and ZIKV infections. We analyzed the probability of onward transmission during 50 feeding events involving 27 participants infected with DENV-2 based on the presence of infectious virus in mosquito saliva 7–16 days post blood meal. Transmission probability was positively associated with the level of viremia and duration of extrinsic incubation in the mosquito. In addition, transmission probability was influenced by the day of illness in a non-monotonic fashion; i.e., transmission probability increased until 2 days after symptom onset and decreased thereafter. We conclude that mildly ill DENV-infected humans with similar levels of viremia during the first two days after symptom onset will be most infectious to mosquitoes on the second day of their illness. Quantifying variation within and between people in their contribution to DENV transmission is essential to better understand the biological determinants of human infectiousness, parametrize epidemiological models, and improve disease surveillance and prevention strategies. DA - 2023/9// PY - 2023/9// DO - 10.1371/journal.pntd.0011593 VL - 17 IS - 9 SP - SN - 1935-2735 ER - TY - JOUR TI - Thin liquid films on a slippery vertical cylinder in presence of chemical reaction AU - Chattopadhyay, Souradip T2 - CHEMICAL ENGINEERING SCIENCE AB - In industrial settings, chemical reactions often affect thin liquid films that flow down vertical cylinders. However, the effect of non-isothermal reactions on the dynamics of these films is not fully comprehended. To address this issue, this study investigates the behavior and stability of thin film flows on uniformly heated vertical cylinders that exhibit wall slippage when subjected to a pseudo-zero-order exothermic or endothermic chemical reaction. A reduced model is developed for thin liquid films flowing down vertical cylinders in the presence of exothermic or endothermic chemical reactions, assuming the film thickness is much smaller than the cylinder radius. The heat from the reaction and/or wall heating initiates a thermocapillary Marangoni effect, which is further enhanced by wall slippage, directly affecting the dynamics of the free surface. Linear and weakly nonlinear stability analyses show that wall slip amplifies the instability, while exothermic reactions stabilize the system and endothermic reactions destabilize it. It is also found that chemical reactions significantly influence the supercritical stable, subcritical unstable, unconditional stable, and explosive zones of the thin film. A direct numerical simulation confirms the results of linear and weakly nonlinear analyses. DA - 2023/12/5/ PY - 2023/12/5/ DO - 10.1016/j.ces.2023.119211 VL - 282 SP - SN - 1873-4405 UR - https://doi.org/10.1016/j.ces.2023.119211 ER - TY - RPRT TI - Coarsening of thin films with weak condensation AU - Ji, H. AU - Witelski, T.P. AB - A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A reduced-order dynamical system is derived from the lubrication model based on the nearest-neighbor droplet interactions in the weak condensation limit. Dynamics for periodic arrays of identical drops and pairwise droplet interactions are investigated which provide insights to the coarsening dynamics of a large droplet system. Weak condensation is shown to be a singular perturbation, fundamentally changing the long-time coarsening dynamics for the droplets and the overall mass of the fluid in two additional regimes of long-time dynamics. C6 - 2303.14728 DA - 2023/// PY - 2023/// DO - 10.48550/arXiv.2303.14728 M1 - 2303.14728 M3 - arXiv SN - 2303.14728 ER - TY - JOUR TI - Stochastic Galerkin method for cloud simulation. Part II: A fully random Navier-Stokes-cloud model AU - Chertock, A. AU - Kurganov, A. AU - Lukáčová-Medvid'ová, M. AU - Spichtinger, P. AU - Wiebe, B. T2 - Journal of Computational Physics AB - This paper is a continuation of the work presented in Chertock et al. (2019) [8]. We study uncertainty propagation in warm cloud dynamics of weakly compressible fluids. The mathematical model is governed by a multiscale system of PDEs in which the macroscopic fluid dynamics is described by a weakly compressible Navier-Stokes system and the microscopic cloud dynamics is modeled by a convection-diffusion-reaction system. In order to quantify uncertainties present in the system, we derive and implement a generalized polynomial chaos stochastic Galerkin method. Unlike the first part of this work, where we restricted our consideration to the partially stochastic case in which the uncertainties were only present in the cloud physics equations, we now study a fully random Navier-Stokes-cloud model in which we include randomness in the macroscopic fluid dynamics as well. We conduct a series of numerical experiments illustrating the accuracy and efficiency of the developed approach. DA - 2023/4// PY - 2023/4// DO - 10.1016/j.jcp.2023.111987 VL - 479 SP - 111987 UR - http://dx.doi.org/10.1016/j.jcp.2023.111987 ER - TY - JOUR TI - Denoising convolution algorithms and applications to SAR signal processing AU - Chertock, Alina AU - Mathematics, North Carolina State University AU - Leonard, Chris AU - Tsynkov, Semyon AU - Utyuzhnikov, Sergey AU - Mechanical, Aerospace T2 - Communications on Analysis and Computation AB - Convolutions are one of the most important operations in signal processing. They often involve large arrays and require significant computing time. Moreover, in practice, the signal data to be processed by convolution may be corrupted by noise. In this paper, we introduce a new method for computing the convolutions in the quantized tensor train (QTT) format and removing noise from data using the QTT decomposition. We demonstrate the performance of our method using a common mathematical model for synthetic aperture radar (SAR) processing that involves a sinc kernel and present the entire cost of decomposing the original data array, computing the convolutions, and then reformatting the data back into full arrays. DA - 2023/// PY - 2023/// DO - 10.3934/cac.2023008 VL - 1 IS - 2 SP - 135-156 UR - http://dx.doi.org/10.3934/cac.2023008 ER - TY - JOUR TI - Precision-aware deterministic and probabilistic error bounds for floating point summation AU - Hallman, Eric AU - Ipsen, Ilse C. F. T2 - NUMERISCHE MATHEMATIK DA - 2023/8/30/ PY - 2023/8/30/ DO - 10.1007/s00211-023-01370 VL - 8 SP - SN - 0945-3245 KW - 65G99 KW - 60G42 KW - 60G50 ER - TY - JOUR TI - Logarithmic Vertex Algebras and Non-local Poisson Vertex Algebras AU - Bakalov, Bojko AU - Villarreal, Juan J. T2 - COMMUNICATIONS IN MATHEMATICAL PHYSICS DA - 2023/9/5/ PY - 2023/9/5/ DO - 10.1007/s00220-023-04839 SP - SN - 1432-0916 ER - TY - JOUR TI - A categorical Connes' ?(M) AU - Chen, Quan AU - Jones, Corey AU - Penneys, David T2 - MATHEMATISCHE ANNALEN DA - 2023/8/14/ PY - 2023/8/14/ DO - 10.1007/s00208-023-02695-7 SP - SN - 1432-1807 ER - TY - JOUR TI - Shear imposed falling liquid films on a slippery substrate with Marangoni effects: Effect of odd AU - Desai, Akshay S. AU - Chattopadhyay, Souradip AU - Gaonkar, Amar K. T2 - INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS AB - We investigate the behavior of a thin fluid with disrupted time-reversal symmetry on a uniformly heated inclined surface under external shear stress using modified Navier–Stokes equations, an energy conservation equation, and incorporating a Navier slip condition. Critical conditions for instability onset are determined by a linear stability analysis within the Orr–Sommerfeld framework. We derive a first-order Benney-type evolution equation to study long-wave instabilities. We find slippery substrate, imposed shear stress along the flow direction, and Marangoni number consistently destabilize the flow, while odd viscosity and imposed counter-flow shear stabilize it. A weakly nonlinear analysis using multiple scales reveal distinct zones of instability. Marangoni number, slip length, odd viscosity, and imposed shear direction significantly impact stability and instability regions. Numerical simulations of the free surface evolution equation of a flow system under consideration provide clear evidence of the contributions of thermocapillary, slip length, odd viscosity, and imposed shear direction. Furthermore, our analysis of linear and weakly nonlinear stability, as well as our numerical simulations, exhibit remarkable consistency. DA - 2023/11// PY - 2023/11// DO - 10.1016/j.ijnonlinmec.2023.104507 VL - 156 SP - SN - 1878-5638 UR - https://doi.org/10.1016/j.ijnonlinmec.2023.104507 KW - Slippery inclined plane KW - Odd viscosity KW - Imposed shear KW - Thermocapillarity KW - Interfacial instability ER - TY - RPRT TI - Mixed norm l2 decoupling for paraboloids AU - Dasu, Shival AU - Jung, Hongki AU - Li, Zane Kun AU - Madrid, José AB - We prove the sharp mixed norm $(l^2, L^{q}_{t}L^{r}_{x})$ decoupling estimate for the paraboloid in $d + 1$ dimensions. C6 - 2303.04773 DA - 2023/// PY - 2023/// DO - 10.48550/arXiv.2303.04773 M1 - 2303.04773 M3 - arXiv preprint SN - 2303.04773 ER - TY - JOUR TI - Machine learning from RANS and LES to inform coarse grid simulations AU - Iskhakov, Arsen S. AU - Dinh, Nam T. AU - Leite, Victor Coppo AU - Merzari, Elia T2 - PROGRESS IN NUCLEAR ENERGY AB - Nuclear system thermal hydraulic analysis has historically relied on computationally inexpensive 1D codes. However, such tools are unable to capture multiscale multidimensional effects in large nuclear reactor enclosures. On the other hand, simulations with higher fidelity can be too expensive for such purposes. One of the ways to reduce computational cost is to perform simulations on a coarse grid, which, unfortunately, introduces large discretization errors. In this paper, two high-to-low data-driven approaches are investigated: (1) a coarse grid turbulence model to predict eddy viscosity and (2) correction of errors in coarse grid velocity fields. The approaches aim to reduce grid- and turbulence model-induced errors in coarse grid Reynolds-averaged Navier–Stokes (RANS) simulations. Two sources of high-fidelity data, RANS and large eddy simulations (LES), are explored. To extract the eddy viscosity from the LES data, an inverse optimization problem is solved. However, the LES eddy viscosity is shown to be comparable to the RANS eddy viscosity in terms of error reduction. Therefore, the directly available RANS eddy viscosity was used to develop a coarse grid data-driven turbulence model. Additionally, error correction in velocity is used to reduce the remaining uncertainties and bring the results closer to reality. The performance of the frameworks is demonstrated for a scaled upper plenum of a gas-cooled reactor facility. DA - 2023/9// PY - 2023/9// DO - 10.1016/j.pnucene.2023.104809 VL - 163 SP - SN - 1878-4224 KW - Machine learning KW - Coarse grid RANS KW - Mixing in upper plenum KW - Turbulence modeling KW - Error correction ER - TY - JOUR TI - Variable Yield Responses among Grafted and Nongrafted Late blight-resistant Tomato (Solanum lycopersicum L.) Hybrids in North Carolina AU - Reeves, Ella R. AU - Strayer-Scherer, Amanda AU - Panthee, Dilip R. AU - Gardner, Randolph AU - Meadows, Inga M. T2 - HORTSCIENCE AB - Host resistance is an environmentally and economically sustainable disease management strategy that may be especially beneficial to small-scale and organic growers for whom other management tools such as synthetic pesticides are too costly or not permitted. In western North Carolina, the demand for vine-ripened tomatoes ( Solanum lycopersicum L.) from local and organic farms has led to the development of cultivars bred for resistance to geographically relevant diseases, including late blight of tomato, which causes rapid defoliation and lesions on fruit. Grafting tomato plants has the potential to increase plant vigor and yield; however, this effect is known to be dependent on multiple factors, including scion and geographic location. In this study, we evaluated the yield response of one determinate (‘Mountain Gem’) and four indeterminate (‘Mountain Heritage’, ‘Mountain Girl’, ‘Mountain Rouge’, and ‘NC10291’) late blight–resistant tomato cultivars, grafted on tomato rootstock ‘Maxifort’ or nongrafted, on a commercial farm and at two research facilities in western North Carolina. Yield of marketable fruit from grafted plants was greater than that from nongrafted plants at one location ( P = 0.008); however, yield response of each cultivar, grafted or not grafted, differed by location. Yield was consistently greater from ‘Mountain Gem’ plants than other cultivars, and grafted ‘Mountain Gem’ plants had greater yields later in the season at two locations than nongrafted plants. Because of the late planting date intended to expose cultivars to the late blight pathogen, the full yield potential of the indeterminate cultivars was not realized at all locations. Disease severity caused by Verticillium wilt ( Verticillium dahliae Kleb., Verticillium albo-atrum Reinke & Berthold) was lowest for cultivar Mountain Heritage at two of three locations. Results from this study emphasize the importance of conducting evaluations of grafted tomato plants at multiple locations, including on farm, to optimize the benefits associated with their use. DA - 2023/8// PY - 2023/8// DO - 10.21273/HORTSCI17145-23 VL - 58 IS - 8 SP - 943-948 SN - 2327-9834 KW - cultivar KW - late blight KW - rootstock KW - Verticillium KW - ' Maxifort ' ER - TY - JOUR TI - RANDOMIZED ALGORITHMS FOR ROUNDING IN THE TENSOR-TRAIN FORMAT AU - Al Daas, Hussam AU - Ballard, Grey AU - Cazeaux, Paul AU - Hallman, Eric AU - Miedlar, Agnieszka AU - Pasha, Mirjeta AU - Reid, Tim W. AU - Saibaba, Arvind K. T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING AB - The tensor-train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential equations. For many of these problems, computing the solution explicitly would require an infeasible amount of memory and computational time. While the TT format makes these problems tractable, iterative techniques for solving the PDEs must be adapted to perform arithmetic while maintaining the implicit structure. The fundamental operation used to maintain feasible memory and computational time is called rounding, which truncates the internal ranks of a tensor already in TT format. We propose several randomized algorithms for this task that are generalizations of randomized low-rank matrix approximation algorithms and provide significant reduction in computation compared to deterministic TT-rounding algorithms. Randomization is particularly effective in the case of rounding a sum of TT-tensors (where we observe speedup), which is the bottleneck computation in the adaptation of GMRES to vectors in TT format. We present the randomized algorithms and compare their empirical accuracy and computational time with deterministic alternatives. DA - 2023/// PY - 2023/// DO - 10.1137/21M1451191 VL - 45 IS - 1 SP - A74-A95 SN - 1095-7197 KW - high-dimensional problems KW - randomized algorithms KW - tensor decompositions KW - tensortrain format ER - TY - JOUR TI - Thermocapillary thin film flows on a slippery substrate with odd viscosity effects AU - Chattopadhyay, S. AU - Ji, H. T2 - Physica D: Nonlinear Phenomena AB - This study investigates the behavior of a thin liquid with odd viscosity effects as it flows down a uniformly heated, slippery inclined plane, where the liquid’s time-reversal symmetry is broken. The breaking of symmetry results in interesting effects, as the antisymmetric part of the fluid stress tensor does not vanish. Two models, the Benney-type equation model (BEM) and the weighted residual model (WRM), are constructed to account for the combined effects of slip length, thermocapillarity, and odd viscosity. A detailed stability analysis determines both models’ critical Reynolds numbers Rec. For small slip lengths, the first-order WRM is better at capturing the instability threshold than the first-order BEM. While both models account for the effects of odd viscosity and thermocapillarity, only the Rec of WRM incorporates the wall slip effects. Another significant finding is that the BEM effectively avoids the issue of finite-time blow-up by incorporating odd viscosity. Additionally, employing a weakly nonlinear stability analysis with multiple scales uncovers four flow regions in BEM: supercritical stable, subcritical unstable, unconditional stable, and explosive zones. Two separate bifurcation scenarios emerge for various wave numbers: supercritical within a specific range and subcritical for larger wave numbers. The presence of odd viscosity alleviates the reduction of the unconditional stable zone and the increase in the explosive zone, which are caused by the combined influence of slip and thermal effects. Numerical investigation of traveling wave solutions of WRM shows that wave height is promoted by slip and thermal effects but reduced with increasing odd viscosity coefficient. Further numerical simulations of WRM on a larger domain demonstrate the stabilizing effects of odd viscosity and its interaction with destabilizing slip and thermocapillary effects. DA - 2023/12// PY - 2023/12// DO - 10.1016/j.physd.2023.133883 VL - 455 SP - 133883 SN - 1872-8022 UR - https://doi.org/10.1016/j.physd.2023.133883 KW - Falling films KW - Odd viscosity KW - Slippery substrate KW - Marangoni effect KW - Nonlinear stability ER - TY - JOUR TI - Traveling Wave Solutions of the Kawahara Equation Joining Distinct Periodic Waves AU - Sprenger, Patrick AU - Bridges, Thomas J. AU - Shearer, Michael T2 - JOURNAL OF NONLINEAR SCIENCE DA - 2023/10// PY - 2023/10// DO - 10.1007/s00332-023-09922-0 VL - 33 IS - 5 SP - SN - 1432-1467 ER - TY - JOUR TI - Divisibility of Finite Geometric Series AU - Hartwig, Robert E. AU - Patricio, Pedro T2 - BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY AB - Abstract We give necessary and sufficient conditions for the divisibility of two finite geometric series $$ G_n(x) = 1 + x + x ^ 2 + \cdots + x^{n-1} $$ G n ( x ) = 1 + x + x 2 + + x n - 1 over a field of characteristic zero. DA - 2023/9// PY - 2023/9// DO - 10.1007/s40840-023-01556-5 VL - 46 IS - 5 SP - SN - 2180-4206 KW - Finite geometric series KW - Divisibility KW - Greatest common divisor ER - TY - JOUR TI - CRISPR/Cas9-based split homing gene drive targeting doublesex for population suppression of the global fruit pest Drosophila suzukii AU - Yadav, Amarish K. AU - Butler, Cole AU - Yamamoto, Akihiko AU - Patil, Anandrao A. AU - Lloyd, Alun L. AU - Scott, Maxwell J. T2 - PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA AB - Genetic-based methods offer environmentally friendly species-specific approaches for control of insect pests. One method, CRISPR homing gene drive that target genes essential for development, could provide very efficient and cost-effective control. While significant progress has been made in developing homing gene drives for mosquito disease vectors, little progress has been made with agricultural insect pests. Here, we report the development and evaluation of split homing drives that target the doublesex (dsx) gene in Drosophila suzukii, an invasive pest of soft-skinned fruits. The drive component, consisting of dsx single guide RNA and DsRed genes, was introduced into the female-specific exon of dsx, which is essential for function in females but not males. However, in most strains, hemizygous females were sterile and produced the male dsx transcript. With a modified homing drive that included an optimal splice acceptor site, hemizygous females from each of the four independent lines were fertile. High transmission rates of the DsRed gene (94 to 99%) were observed with a line that expressed Cas9 with two nuclear localization sequences from the D. suzukii nanos promoter. Mutant alleles of dsx with small in-frame deletions near the Cas9 cut site were not functional and thus would not provide resistance to drive. Finally, mathematical modeling showed that the strains could be used for suppression of lab cage populations of D. suzukii with repeated releases at relatively low release ratios (1:4). Our results indicate that the split CRISPR homing gene drive strains could potentially provide an effective means for control of D. suzukii populations. DA - 2023/6/12/ PY - 2023/6/12/ DO - 10.1073/pnas.2301525120 VL - 120 IS - 25 SP - SN - 1091-6490 UR - https://doi.org/10.1073/pnas.2301525120 KW - gene drive KW - CRISPR KW - Drosophila suzukii KW - spotted wing Drosophila KW - doublesex ER - TY - JOUR TI - State constrained stochastic optimal control for continuous and hybrid dynamical systems using DFBSDE AU - Dai, Bolun AU - Krishnamurthy, Prashanth AU - Papanicolaou, Andrew AU - Khorrami, Farshad T2 - AUTOMATICA AB - We develop a computationally efficient learning-based forward–backward stochastic differential equations (FBSDE) controller for both continuous and hybrid dynamical (HD) systems subject to stochastic noise and state constraints. Solutions to stochastic optimal control (SOC) problems satisfy the Hamilton–Jacobi–Bellman (HJB) equation. Using current FBSDE-based solutions, the optimal control can be obtained from the HJB equations using deep neural networks (e.g., long short-term memory (LSTM) networks). To ensure the learned controller respects the constraint boundaries, we enforce the state constraints using a soft penalty function. In addition to previous works, we adapt the deep FBSDE (DFBSDE) control framework to handle HD systems consisting of continuous dynamics and a deterministic discrete state change. We demonstrate our proposed algorithm in simulation on a continuous nonlinear system (cart–pole) and a hybrid nonlinear system (five-link biped). DA - 2023/9// PY - 2023/9// DO - 10.1016/j.automatica.2023.111146 VL - 155 SP - SN - 1873-2836 KW - Stochastic control KW - Optimal control KW - Forward and backward stochastic KW - differential equations ER - TY - JOUR TI - Suppression of Wave Instability in a Liquid Film Flow Down a Non-Uniformly Heated Slippery Inclined Plane Using Odd Viscosity AU - Desai, Akshay S. AU - Chattopadhyay, Souradip AU - Gaonkar, Amar K. AU - Barua, Amlan K. AU - Mukhopadhyay, Anandamoy T2 - JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME AB - Abstract We study the effects of odd viscosity on the stability of a thin Newtonian liquid film flowing down a nonuniformly heated plane under a slip boundary condition. The effect of odd viscosity arises in classical fluids when the time-reversal symmetry breaks down. Due to the odd viscosity, the odd part of the Cauchy stress tensor consists of symmetric and antisymmetric parts and shows several striking effects. We apply the Navier slip boundary condition for the slippery inclined plane at the solid–liquid interface. For our problem, we first derive an evolution equation whose solution describes the film thickness. The equation contains parameters considering the effect of inertia, thermocapillarity, slip length, and odd viscosity. We then perform the linear stability analysis and find that odd viscosity can significantly suppress the combined destabilizing effects of the thermocapillarity and slip length. Next, we analyze the dynamics using the weakly nonlinear approach, which provides details of different subregions of the instability zone. We observe that as the influence of the odd viscosity increases, the supercritical stable and explosive zones shrink while the unconditional stable and subcritical unstable zones expand. We also perform numerical investigation and observe that linear analysis, weakly nonlinear theory, and numerical results are consistent. DA - 2023/9/1/ PY - 2023/9/1/ DO - 10.1115/1.4062471 VL - 145 IS - 9 SP - SN - 1528-901X UR - http://dx.doi.org/10.1115/1.4062471 ER - TY - JOUR TI - Leveraging eco-evolutionary models for gene drive risk assessment AU - Combs, Matthew A. AU - Golnar, Andrew J. AU - Overcash, Justin M. AU - Lloyd, Alun L. AU - Hayes, Keith R. AU - David A. O'Brochta, AU - Pepin, Kim M. T2 - TRENDS IN GENETICS AB - Engineered gene drives create potential for both widespread benefits and irreversible harms to ecosystems. CRISPR-based systems of allelic conversion have rapidly accelerated gene drive research across diverse taxa, putting field trials and their necessary risk assessments on the horizon. Dynamic process-based models provide flexible quantitative platforms to predict gene drive outcomes in the context of system-specific ecological and evolutionary features. Here, we synthesize gene drive dynamic modeling studies to highlight research trends, knowledge gaps, and emergent principles, organized around their genetic, demographic, spatial, environmental, and implementation features. We identify the phenomena that most significantly influence model predictions, discuss limitations of biological complexity and uncertainty, and provide insights to promote responsible development and model-assisted risk assessment of gene drives. DA - 2023/8// PY - 2023/8// DO - 10.1016/j.tig.2023.04.004 VL - 39 IS - 8 SP - 609-623 SN - 1362-4555 ER - TY - JOUR TI - Stable reconstruction of simple Riemannian manifolds from unknown interior sources AU - Hoop, Maarten V AU - Ilmavirta, Joonas AU - Lassas, Matti AU - Saksala, Teemu T2 - INVERSE PROBLEMS AB - Abstract Consider the geometric inverse problem: there is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary? With a finite set of sources we can only hope to get an approximate reconstruction, and we indeed provide a discrete metric approximation to the manifold with explicit data-driven error bounds when the manifold is simple. This is the geometrization of a seismological inverse problem where we measure the arrival times on the surface of waves from an unknown number of unknown interior microseismic events at unknown times. The closeness of two metric spaces with a marked boundary is measured by a labeled Gromov–Hausdorff distance. If measurements are done for infinite time and spatially dense sources, our construction produces the true Riemannian manifold and the finite-time approximations converge to it in the metric sense DA - 2023/9/1/ PY - 2023/9/1/ DO - 10.1088/1361-6420/ace6c9 VL - 39 IS - 9 SP - SN - 1361-6420 KW - inverse problem KW - Riemannian geometry KW - distance function KW - stability KW - discrete approximation ER - TY - JOUR TI - Accurate derivatives approximations and applications to some elliptic PDEs using HOC methods AU - Li, Jin AU - Li, Zhilin AU - Pan, Kejia T2 - APPLIED MATHEMATICS AND COMPUTATION AB - For many application problems that are modeled by partial differential equations (PDEs), not only it is important to obtain accurate approximations to the solutions, but also accurate approximations to the derivatives of the solutions. In this study, some new high order compact (HOC) finite difference schemes are derived to approximate the first and second derivatives of the solution to some elliptic PDEs using the numerical solution obtained from a HOC scheme applied to the same PDE. Convergence analysis for the computed derivatives is also presented to show that the order of the convergence is the same as that of the solution. The new HOC schemes for computing partial derivatives at both interior and boundary grid points take into account of the partial differential equations including the source term and/or the boundary conditions (Dirichlet, Neumann, or Robin). Fourth order accurate compact finite difference formulas with pre-computed coefficients and weights are developed for Poisson/Helmholtz PDEs, and code generated coefficients for diffusion-advection equations with constant coefficients. One important application is a new fourth-order compact scheme for solving incompressible Stokes equations with periodic boundary conditions. DA - 2023/12/15/ PY - 2023/12/15/ DO - 10.1016/j.amc.2023.128265 VL - 459 SP - SN - 1873-5649 UR - https://doi.org/10.1016/j.amc.2023.128265 KW - High order compact derivative computation KW - HOC schemes KW - Poisson/Helmholtz equation KW - Diffusion-advection equation KW - Stokes equations KW - Three Poisson equations approach ER - TY - JOUR TI - Mathematical effects of linear visco-elasticity in quasi-static Biot models ✩ AU - Bociu, Lorena AU - Muha, Boris AU - Webster, Justin T. T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS AB - We investigate and clarify the mathematical properties of linear poro-elastic systems in the presence of classical (linear, Kelvin-Voigt) visco-elasticity. In particular, we quantify the time-regularizing and dissipative effects of visco-elasticity in the context of the quasi-static Biot equations. The full, coupled pressure-displacement presentation of the system is utilized, as well as the framework of implicit, degenerate evolution equations, to demonstrate such effects and characterize linear poro-visco-elastic systems. We consider a simple presentation of the dynamics (with convenient boundary conditions, etc.) for clarity in exposition across several relevant parameter ranges. Clear well-posedness results are provided, with associated a priori estimates on the solutions. In addition, precise statements of admissible initial conditions in each scenario are given. DA - 2023/11/15/ PY - 2023/11/15/ DO - 10.1016/j.jmaa.2023.127462 VL - 527 IS - 2 SP - SN - 1096-0813 KW - Poroelasticity KW - Implicit evolution equations KW - Strong damping KW - Viscoelasticity ER - TY - JOUR TI - Tensor-based flow reconstruction from optimally located sensor measurements AU - Farazmand, Mohammad AU - Saibaba, Arvind K. T2 - JOURNAL OF FLUID MECHANICS AB - Reconstructing high-resolution flow fields from sparse measurements is a major challenge in fluid dynamics. Existing methods often vectorize the flow by stacking different spatial directions on top of each other, hence confounding the information encoded in different dimensions. Here, we introduce a tensor-based sensor placement and flow reconstruction method which retains and exploits the inherent multidimensionality of the flow. We derive estimates for the flow reconstruction error, storage requirements and computational cost of our method. We show, with examples, that our tensor-based method is significantly more accurate than similar vectorized methods. Furthermore, the variance of the error is smaller when using our tensor-based method. While the computational cost of our method is comparable to similar vectorized methods, it reduces the storage cost by several orders of magnitude. The reduced storage cost becomes even more pronounced as the dimension of the flow increases. We demonstrate the efficacy of our method on three examples: a chaotic Kolmogorov flow, in situ and satellite measurements of the global sea surface temperature and three-dimensional unsteady simulated flow around a marine research vessel. DA - 2023/5/4/ PY - 2023/5/4/ DO - 10.1017/jfm.2023.269 VL - 962 SP - SN - 1469-7645 KW - low-dimensional models KW - big data KW - computational methods ER - TY - JOUR TI - Improved tests of genuine entanglement for multiqudits AU - Zhang, Xia AU - Jing, Naihuan AU - Zhao, Hui AU - Liu, Ming AU - Ma, Haitao T2 - Europhysics Letters AB - Abstract We give an improved criterion of genuine multipartite entanglement for an important class of multipartite quantum states using generalized Bloch representations of the density matrices. The practical criterion is designed based on the Weyl operators and can be used for detecting genuine multipartite entanglement in higher-dimensional systems. The test is shown to be significantly stronger than some of the most recent criteria. DA - 2023/8/1/ PY - 2023/8/1/ DO - 10.1209/0295-5075/acec0a UR - https://doi.org/10.1209/0295-5075/acec0a ER - TY - JOUR TI - Analysis of the Limiting Spectral Distribution of Large-dimensional General Information-Plus-Noise-Type Matrices AU - Zhou, Huanchao AU - Hu, Jiang AU - Bai, Zhidong AU - Silverstein, Jack W. T2 - JOURNAL OF THEORETICAL PROBABILITY AB - In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the “general information-plus-noise" type, as studied in Zhou (JTP 36:1203–1226, 2023). Through the equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and we show the determination criterion for its support. We also extend the result in Zhou (JTP 36:1203-1226, 2023) to allow for all possible ratios of row to column of the underlying random matrix. DA - 2023/7/28/ PY - 2023/7/28/ DO - 10.1007/s10959-023-01276-3 VL - 7 SP - SN - 1572-9230 UR - https://doi.org/10.1007/s10959-023-01276-3 KW - Random matrix KW - Limiting spectral distribution KW - Stieltjes transform KW - Information-plus-noise matrix ER - TY - JOUR TI - An Innate Moving Frame on Parametric Surfaces: The Dynamics of Principal Singular Curves AU - Chu, Moody T. AU - Zhang, Zhenyue T2 - Mathematics AB - This article reports an experimental work that unveils some interesting yet unknown phenomena underneath all smooth nonlinear maps. The findings are based on the fact that, generalizing the conventional gradient dynamics, the right singular vectors of the Jacobian matrix of any differentiable map point in directions that are most pertinent to the infinitesimal deformation of the underlying function and that the singular values measure the rate of deformation in the corresponding directions. A continuous adaption of these singular vectors, therefore, constitutes a natural moving frame that carries indwelling information of the variation. This structure exists in any dimensional space, but the development of the fundamental theory and algorithm for surface exploration is an important first step for immediate application and further generalization. In this case, trajectories of these singular vectors, referred to as singular curves, unveil some intriguing patterns per the given function. At points where singular values coalesce, curious and complex behaviors occur, manifesting specific landmarks for the function. Upon analyzing the dynamics, it is discovered that there is a remarkably simple and universal structure underneath all smooth two-parameter maps. This work delineates graphs with this interesting dynamical system and the possible new discovery that, analogous to the double helix with two base parings in DNA, two strands of critical curves and eight base pairings could encode properties of a generic and arbitrary surface. This innate structure suggests that this approach could provide a unifying paradigm in functional genetics, where all smooth surfaces could be genome-sequenced and classified accordingly. Such a concept has sparked curiosity and warrants further investigation. DA - 2023/7/27/ PY - 2023/7/27/ DO - 10.3390/math11153306 VL - 11 IS - 15 SP - 3306 J2 - Mathematics LA - en OP - SN - 2227-7390 UR - http://dx.doi.org/10.3390/math11153306 DB - Crossref KW - moving frame KW - nonlinear variation KW - gradient adaption KW - singular curves KW - critical curves KW - base pairings KW - parametric surfaces KW - geometric genome ER - TY - JOUR TI - COMPATIBILITY IN OZSVaTH-SZAB & Oacute; 'S BORDERED HFK VIA HIGHER REPRESENTATIONS AU - Chang, William AU - Manion, Andrew T2 - PACIFIC JOURNAL OF MATHEMATICS AB - We equip the basic local crossing bimodules in Ozsv\'ath-Szab\'o's theory of bordered knot Floer homology with the structure of 1-morphisms of 2-representations, categorifying the $U_q(\mathfrak{gl}(1|1)^+)$-intertwining property of the corresponding maps between ordinary representations. Besides yielding a new connection between bordered knot Floer homology and higher representation theory in line with work of Rouquier and the second author, this structure gives an algebraic reformulation of a ``compatibility between summands'' property for Ozsv\'ath-Szab\'o's bimodules that is important when building their theory up from local crossings to more global tangles and knots. DA - 2023/4// PY - 2023/4// DO - 10.2140/pjm.2023.323.253 VL - 323 IS - 2 SP - SN - 1945-5844 KW - Heegaard Floer KW - bordered Floer KW - bordered HFK KW - higher representation theory KW - categorification ER - TY - JOUR TI - On the strength of chromatic symmetric homology for graphs AU - Chandler, Alex AU - Sazdanovic, Radmila AU - Stella, Salvatore AU - Yip, Martha T2 - ADVANCES IN APPLIED MATHEMATICS AB - In this paper, we investigate the strength of chromatic symmetric homology as a graph invariant. Chromatic symmetric homology is a lift of the chromatic symmetric function for graphs to a homological setting, and its Frobenius characteristic is a q,t generalization of the chromatic symmetric function. We exhibit three pairs of graphs where each pair has the same chromatic symmetric function but distinct homology over C as Sn-modules. We also show that integral chromatic symmetric homology contains torsion, and based on computations, conjecture that Z2-torsion in bigrading (1,0) detects nonplanarity in the graph. DA - 2023/9// PY - 2023/9// DO - 10.1016/j.aam.2023.102559 VL - 150 SP - SN - 1090-2074 UR - http://dx.doi.org/10.1016/j.aam.2023.102559 KW - Chromatic symmetric function KW - Categorification ER - TY - JOUR TI - Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems AU - Ji, Haifeng AU - Wang, Feng AU - Chen, Jinru AU - Li, Zhilin T2 - ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS AB - In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods without penalties are not guaranteed to converge optimally if the tangential derivative of the exact solution and the jump of the coefficient are not zero on the interface. A nontrivial counter example is also provided to support our theoretical analysis. To recover the optimal convergence rates, we develop a new nonconforming IFE method with additional terms locally on interface edges. The new method is parameter-free which removes the limitation of the conventional partially penalized IFE method. We show the IFE basis functions are unisolvent on arbitrary triangles which is not considered in the literature. Furthermore, different from multipoint Taylor expansions, we derive the optimal approximation capabilities of both the Crouzeix–Raviart and the rotated- Q 1 IFE spaces via a unified approach which can handle the case of variable coefficients easily. Finally, optimal error estimates in both H 1 - and L 2 -norms are proved and confirmed with numerical experiments. DA - 2023/7/3/ PY - 2023/7/3/ DO - 10.1051/m2an/2023047 VL - 57 IS - 4 SP - 2041-2076 SN - 2804-7214 KW - Interface problem KW - Nonconforming KW - Immersed finite element KW - Unfitted mesh ER - TY - JOUR TI - Resolvent and Proximal Compositions AU - Combettes, Patrick L. T2 - SET-VALUED AND VARIATIONAL ANALYSIS AB - We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function. The two operations are linked by the fact that, under mild assumptions, the subdifferential of the proximal composition of a convex function is the resolvent composition of its subdifferential. The resolvent and proximal compositions are shown to encapsulate known concepts, such as the resolvent and proximal averages, as well as new operations pertinent to the analysis of equilibrium problems. A large core of properties of these compositions is established and several instantiations are discussed. Applications to the relaxation of monotone inclusion and convex optimization problems are presented. DA - 2023/9// PY - 2023/9// DO - 10.1007/s11228-023-00678-z VL - 31 IS - 3 SP - SN - 1877-0541 KW - Monotone operator KW - Proximal average KW - Proximal composition KW - Proximal point algorithm KW - Relaxed monotone inclusion KW - Resolvent average KW - Resolvent composition KW - Resolvent mixture ER - TY - JOUR TI - Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator AU - Chertock, Alina AU - Chu, Shaoshuai AU - Kurganov, Alexander T2 - EAST ASIAN JOURNAL ON APPLIED MATHEMATICS DA - 2023/8// PY - 2023/8// DO - 10.4208/eajam.2022-313.160123August2023 VL - 13 IS - 3 SP - 576-609 SN - 2079-7370 KW - Local smoothness indicator KW - scheme adaption KW - strong stability preserving Runge-Kutta methods KW - hyperbolic systems of conservation laws KW - A-WENO schemes ER - TY - JOUR TI - Electrohydrodynamics modeling of droplet actuation on a solid surface by surfactant-mediated electrodewetting AU - Chu, Weiqi AU - Ji, Hangjie AU - Wang, Qining AU - Kim, Chang-Jin C. J. AU - Bertozzi, Andrea 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 - 2023/7/21/ PY - 2023/7/21/ DO - 10.1103/PhysRevFluids.8.073701 VL - 8 IS - 7 SP - SN - 2469-990X UR - https://doi.org/10.1103/PhysRevFluids.8.073701 ER - TY - JOUR TI - Role of odd viscosity on falling films over compliant substrates AU - Chattopadhyay, Souradip AU - Desai, Akshay S. AU - Gaonkar, Amar K. AU - Mukhopadhyay, Anandamoy T2 - PHYSICAL REVIEW FLUIDS AB - We investigate the stability of a thin film flow on a compliant substrate with broken time-reversal symmetry. The broken time-reversal symmetry induces odd viscosity in the liquid. Using coupled equations encompassing the film and substrate, we ascertain that inclusion of a compliant substrate induces instability within the system. Nonetheless, the introduction of odd viscosity notably enhances its stability. Furthermore, under conditions of weak nonlinearity, the incorporation of odd viscosity can effectively mitigate the occurrence of chaotic behavior arising from compliant substrates. Numerical simulations confirm that odd viscosity has a substantial impact on substrate deflection. DA - 2023/6/16/ PY - 2023/6/16/ DO - 10.1103/PhysRevFluids.8.064003 VL - 8 IS - 6 SP - SN - 2469-990X UR - https://doi.org/10.1103/PhysRevFluids.8.064003 ER - TY - JOUR TI - A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces AU - Dong, Baiying AU - Li, Zhilin AU - Ruiz-Alvarez, Juan T2 - COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION DA - 2023/7/10/ PY - 2023/7/10/ DO - 10.1007/s42967-023-00281-x VL - 7 SP - SN - 2661-8893 UR - https://doi.org/10.1007/s42967-023-00281-x KW - Anisotropic parabolic interface problem KW - Hybrid finite element and finite difference (FE-FD) discretization KW - Modified Crank-Nicolson scheme ER - TY - JOUR TI - The smallest mono-unstable convex polyhedron with point masses has 8 faces and 11 vertices AU - Papp, David AU - Regos, Krisztina AU - Domokos, Gabor AU - Bozoki, Sandor T2 - EUROPEAN JOURNAL OF OPERATIONAL RESEARCH AB - In the study of monostatic polyhedra, initiated by John H. Conway in 1966, the main question is to construct such an object with the minimal number of faces and vertices. By distinguishing between various material distributions and stability types, this expands into a small family of related questions. While many upper and lower bounds on the necessary numbers of faces and vertices have been established, none of these questions has been so far resolved. Adapting an algorithm presented in Bozóki et al. (2022), here we offer the first complete answer to a question from this family: by using the toolbox of semidefinite optimization to efficiently generate the hundreds of thousands of infeasibility certificates, we provide the first-ever proof for the existence of a monostatic polyhedron with point masses, having minimal number (V=11) of vertices (Theorem 3) and a minimal number (F=8) of faces. We also show that V=11 is the smallest number of vertices that a mono-unstable polyhedron can have in all dimensions greater than 1 (Corollary 6). DA - 2023/10/16/ PY - 2023/10/16/ DO - 10.1016/j.ejor.2023.04.028 VL - 310 IS - 2 SP - 511-517 SN - 1872-6860 UR - https://doi.org/10.1016/j.ejor.2023.04.028 KW - Semidefinite optimization KW - Static equilibrium KW - Monostatic polyhedron KW - Polynomial inequalities ER - TY - JOUR TI - On toral posets and contact Lie algebras AU - Mayers, Nicholas W. AU - Russoniello, Nicholas T2 - JOURNAL OF GEOMETRY AND PHYSICS AB - A (2k+1)-dimensional Lie algebra is called contact if it admits a one-form φ such that φ∧(dφ)k≠0. Here, we extend recent work to describe a combinatorial procedure for generating contact, type-A Lie poset algebras whose associated posets have chains of arbitrary cardinality, and we conjecture that our construction leads to a complete characterization. DA - 2023/8// PY - 2023/8// DO - 10.1016/j.geomphys.2023.104861 VL - 190 SP - SN - 1879-1662 KW - Contact Lie algebra KW - Lie poset algebra KW - Index KW - Contactization ER - TY - JOUR TI - The h*-polynomial of the order polytope of the zig-zag poset AU - Coons, Jane Ivy AU - Sullivant, Seth T2 - ELECTRONIC JOURNAL OF COMBINATORICS AB - We construct a family of shellings for the canonical triangulation of the order polytope of the zig-zag poset. This gives a new combinatorial interpretation for the coefficients in the numerator of the Ehrhart series of this order polytope in terms of the swap statistic on alternating permutations. We also offer an alternate proof of this result using the techniques of rank selection. Finally, we show that the sequence of coefficients of the numerator of this Ehrhart series is symmetric and unimodal. DA - 2023/6/16/ PY - 2023/6/16/ DO - 10.37236/11526 VL - 30 IS - 2 SP - SN - 1077-8926 ER - TY - JOUR TI - THREE TRAVEL TIME INVERSE PROBLEMS ON SIMPLE RIEMANNIAN MANIFOLDS AU - Ilmavirta, Joonas AU - Liu, Boya AU - Saksala, Teemu T2 - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY AB - We provide new proofs based on the Myers–Steenrod theorem to confirm that travel time data, travel time difference data and the broken scattering relations determine a simple Riemannian metric on a disc up to the natural gauge of a boundary fixing diffeomorphism. Our method of the proof leads to a Lipschitz-type stability estimate for the first two data sets in the class of simple metrics. DA - 2023/6/23/ PY - 2023/6/23/ DO - 10.1090/proc/16453 SP - SN - 1088-6826 KW - Inverse problem KW - Riemannian geometry KW - distance function ER - TY - JOUR TI - Uncertainty relations for metric adjusted skew information and Cauchy-Schwarz inequality AU - Hu, Xiaoli AU - Jing, Naihuan T2 - LASER PHYSICS LETTERS AB - Skew information is a pivotal concept in quantum information, quantum measurement, and quantum metrology. Further studies have lead to the uncertainty relations grounded in metric-adjusted skew information. In this work, we present an in-depth investigation using the methodologies of sampling coordinates of observables and convex functions to refine the uncertainty relations in both the product form of two observables and summation form of multiple observables. DA - 2023/8/1/ PY - 2023/8/1/ DO - 10.1088/1612-202X/accce3 VL - 20 IS - 8 SP - SN - 1612-202X UR - https://doi.org/10.1088/1612-202X/accce3 KW - uncertainty relations KW - skew information KW - Cauchy-Schwarz inequality ER - TY - JOUR TI - Invariants: Computation and Applications AU - Kogan, Irina A. T2 - PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON SYMBOLIC & ALGEBRAIC COMPUTATION, ISSAC 2023 AB - Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of invariants and designing methods and algorithms to compute them remains an active area of ongoing research with an abundance of applications. In this incredibly vast topic, we focus on two particular themes displaying a fruitful interplay between the differential and algebraic invariant theories. First, we show how an algebraic adaptation of the moving frame method from differential geometry leads to a practical algorithm for computing a generating set of rational invariants. Then we discuss the notion of differential invariant signature, its role in solving equivalence problems in geometry and algebra, and some successes and challenges in designing algorithms based on this notion. DA - 2023/// PY - 2023/// DO - 10.1145/3597066.3597149 SP - 40-49 UR - https://doi.org/10.1145/3597066.3597149 KW - group actions KW - algebraic and differential invariants KW - moving frames KW - equivalence KW - signatures ER - TY - JOUR TI - Spatiotemporal fractionation schemes for stereotactic radiosurgery of multiple brain metastases AU - Torelli, Nathan AU - Papp, David AU - Unkelbach, Jan T2 - MEDICAL PHYSICS AB - Stereotactic radiosurgery (SRS) is an established treatment for patients with brain metastases (BMs). However, damage to the healthy brain may limit the tumor dose for patients with multiple lesions.In this study, we investigate the potential of spatiotemporal fractionation schemes to reduce the biological dose received by the healthy brain in SRS of multiple BMs, and also demonstrate a novel concept of spatiotemporal fractionation for polymetastatic cancer patients that faces less hurdles for clinical implementation.Spatiotemporal fractionation (STF) schemes aim at partial hypofractionation in the metastases along with more uniform fractionation in the healthy brain. This is achieved by delivering distinct dose distributions in different fractions, which are designed based on their cumulative biologically effective dose ( BEDα/β${\rm{BED}}_{{{\alpha}}/{{\beta}}}$ ) such that each fraction contributes with high doses to complementary parts of the target volume, while similar dose baths are delivered to the normal tissue. For patients with multiple brain metastases, a novel constrained approach to spatiotemporal fractionation (cSTF) is proposed, which is more robust against setup and biological uncertainties. The approach aims at irradiating entire metastases with possibly different doses, but spatially similar dose distributions in every fraction, where the optimal dose contribution of every fraction to each metastasis is determined using a new planning objective to be added to the BED-based treatment plan optimization problem. The benefits of spatiotemporal fractionation schemes are evaluated for three patients, each with >25 BMs.For the same tumor BED10 and the same brain volume exposed to high doses in all plans, the mean brain BED2 can be reduced compared to uniformly fractionated plans by 9%-12% with the cSTF plans and by 13%-19% with the STF plans. In contrast to the STF plans, the cSTF plans avoid partial irradiation of the individual metastases and are less sensitive to misalignments of the fractional dose distributions when setup errors occur.Spatiotemporal fractionation schemes represent an approach to lower the biological dose to the healthy brain in SRS-based treatments of multiple BMs. Although cSTF cannot achieve the full BED reduction of STF, it improves on uniform fractionation and is more robust against both setup errors and biological uncertainties related to partial tumor irradiation. DA - 2023/6/15/ PY - 2023/6/15/ DO - 10.1002/mp.16457 VL - 6 SP - SN - 2473-4209 KW - fractionation KW - multiple brain metastases KW - stereotactic radiosurgery KW - treatment plan optimization ER - TY - JOUR TI - R-matrix Presentation of Quantum Affine Algebra in Type A2n-1(2) AU - Jing, Naihuan AU - Zhang, Xia AU - Liu, Ming T2 - FRONTIERS OF MATHEMATICS AB - In this paper, we give an RTT presentation of the twisted quantum affine algebra of type A 2−1 (2) and show that it is isomorphic to the Drinfeld new realization via the Gauss decomposition of the L-operators. This provides the first such presentation for twisted quantum affine algebras with nontrivial central elements. DA - 2023/5// PY - 2023/5// DO - 10.1007/s11464-021-0434-7 VL - 18 IS - 3 SP - 513-564 SN - 2731-8656 KW - Quantum affine algebras KW - R-matrix presentations KW - Drinfeld realization ER - TY - JOUR TI - Orbifolds of lattice vertex algebras AU - Bakalov, Bojko AU - Elsinger, Jason AU - Kac, Victor G. AU - Todorov, Ivan T2 - JAPANESE JOURNAL OF MATHEMATICS AB - To a positive-definite even lattice Q, one can associate the lattice vertex algebra VQ, and any automorphism σ of Q lifts to an automorphism of VQ. In this paper, we investigate the orbifold vertex algebra V , which consists of the elements of VQ fixed under σ, in the case when σ has prime order. We describe explicitly the irreducible V -modules, compute their characters, and determine the modular transformations of characters. As an application, we find the asymptotic and quantum dimensions of all irreducible V -modules. We consider in detail the cases when the order of σ is 2 or 3, as well as the case of permutation orbifolds. DA - 2023/6/14/ PY - 2023/6/14/ DO - 10.1007/s11537-023-2249-7 SP - SN - 1861-3624 KW - regular vertex algebra KW - lattice vertex algebra KW - theta function KW - modular transformation KW - orbifold algebra KW - twisted module ER - TY - JOUR TI - Direct Numerical Simulation of Low and Unitary Prandtl Number Fluids in Reactor Downcomer Geometry AU - Tai, Cheng-Kai AU - Nguyen, Tri AU - Iskhakov, Arsen S. AU - Merzari, Elia AU - Dinh, Nam T. AU - Bolotnov, Igor A. T2 - NUCLEAR TECHNOLOGY AB - Mixed convection of low and unitary Prandtl fluids in a vertical passage is fundamental to passive heat removal in liquid metal and gas-cooled advanced reactor designs. Capturing the influence of buoyancy in flow and heat transfer in engineering analysis is hence a cornerstone to the safety of the next-generation reactor. However, accurate prediction of the mixed convection phenomenon has eluded current turbulence and heat transfer modeling approaches, yet further development and validation of modeling methods is limited by a scarcity of high-fidelity data pertaining to reactor heat transfer. In this work, a series of direct numerical simulations was conducted to investigate the influence of buoyancy on descending flow of liquid sodium, lead, and unitary Prandtl fluid in a differentially heated channel that represents the reactor downcomer region. From time-averaged statistics, flow-opposing/aiding buoyant plumes near the heated/cooled wall distort the mean velocity distribution, which gives rise to promotion/suppression of turbulence intensity and modification of turbulent shear stress and heat flux distribution. Frequency analysis of time series also suggests the existence of large-scale convective and thermal structures rising from the heated wall. As a general trend, fluids of lower Prandtl number were found to be more susceptible to the buoyancy effect due to stronger differential buoyancy across the channel. On the other hand, the effectiveness of convective heat transfer of the three studied fluids showed a distinct trend against the influence of buoyancy. Physical reasoning on observation of the Nusselt number trend is also discussed. DA - 2023/6/17/ PY - 2023/6/17/ DO - 10.1080/00295450.2023.2213286 SP - SN - 1943-7471 KW - Direct numerical simulation KW - vertical mixed convection KW - low-Prandtl-number fluids KW - downcomer ER - TY - JOUR TI - Murnaghan-Nakayama Rule and Spin Bitrace for the Hecke-Clifford Algebra AU - Jing, Naihuan AU - Liu, Ning T2 - INTERNATIONAL MATHEMATICS RESEARCH NOTICES AB - Abstract A Pfaffian-type Murnaghan–Nakayama rule is derived for the Hecke–Clifford algebra $\mathcal{H}^{c}_{n}$ based on the Frobenius formula and vertex operators, and this leads to a combinatorial version via the tableaux realization of Schur’s $Q$-functions. As a consequence, a general formula for the irreducible characters $\zeta ^{\lambda }_{\mu }(q)$ using partition-valued functions is derived. Meanwhile, an iterative formula on the indexing partition $\lambda $ via the Pieri rule is also deduced. As applications, some compact formulae of the irreducible characters are given for special partitions and a symmetric property of the irreducible character is found. We also introduce the spin bitrace as the analogue of the bitrace for the Hecke algebra and derive its general combinatorial formula. Tables of irreducible characters are listed for $n\leq 7.$ DA - 2023/7/17/ PY - 2023/7/17/ DO - 10.1093/imrn/rnad158 VL - 7 SP - SN - 1687-0247 UR - https://doi.org/10.1093/imrn/rnad158 ER - TY - JOUR TI - Complex Links and Hilbert-Samuel Multiplicities AU - Helmer, Martin AU - Nanda, Vidit T2 - SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY AB - We describe a framework for estimating Hilbert–Samuel multiplicities for pairs of projective varieties from finite point samples rather than defining equations. The first step involves proving that this multiplicity remains invariant under certain hyperplane sections which reduce to a point and to a curve . Next, we establish that equals the Euler characteristic (and hence the cardinality) of the complex link of in . Finally, we provide explicit bounds on the number of uniform point samples needed (in an annular neighborhood of in ) to determine this Euler characteristic with high confidence. DA - 2023/// PY - 2023/// DO - 10.1137/22M1475533 VL - 7 IS - 1 SP - 29-48 SN - 2470-6566 KW - intersection multiplicity KW - stratified Morse theory KW - complex links KW - Hilbert-Samuel multiplicity ER - TY - JOUR TI - Adapting Cubic Hermite Splines to the Presence of Singularities Through Correction Terms AU - Amat, Sergio AU - Li, Zhilin AU - Ruiz-Alvarez, Juan AU - Solano, Concepcion AU - Trillo, Juan C. T2 - JOURNAL OF SCIENTIFIC COMPUTING AB - Abstract Hermite interpolation is classically used to reconstruct smooth data when the function and its first order derivatives are available at certain nodes. If first order derivatives are not available, it is easy to set a system of equations imposing some regularity conditions at the data nodes in order to obtain them. This process leads to the construction of a Hermite spline. The problem of the described Hermite splines is that the accuracy is lost if the data contains singularities. The consequence is the appearance of oscillations, if there is a jump discontinuity in the function, that globally affects the accuracy of the spline, or the smearing of singularities, if the discontinuities are in the derivatives of the function. This paper is devoted to the construction and analysis of a new technique that allows for the computation of accurate first order derivatives of a function close to singularities using a Hermite spline. The idea is to correct the system of equations of the spline in order to attain the desired accuracy even close to the singularities. Once we have computed the first order derivatives with enough accuracy, a correction term is added to the Hermite spline in the intervals that contain a singularity. The aim is to reconstruct piecewise smooth functions with $$O(h^4)$$ O ( h 4 ) accuracy even close to the singularities. The process of adaption will require some knowledge about the position of the singularity and the jumps of the function and some of its derivatives at the singularity. The whole process can be used as a post-processing, where a correction term is added to the classical cubic Hermite spline. Proofs for the accuracy and regularity of the corrected spline and its derivatives are given. We also analyse the mechanism that eliminates the Gibbs phenomenon close to jump discontinuities in the function. The numerical experiments presented confirm the theoretical results obtained. DA - 2023/6// PY - 2023/6// DO - 10.1007/s10915-023-02191-9 VL - 95 IS - 3 SP - SN - 1573-7691 KW - Splines KW - Adaption to singularities KW - Interpolation KW - Point-values KW - Computer aided design (modeling of curves) ER - TY - JOUR TI - STOCHASTIC EQUILIBRIUM SOLUTION FOR A DEBT MANAGEMENT PROBLEM WITH CURRENCY DEVALUATION AU - Marigonda, Antonio AU - Nguyen, Khai T. T2 - MATHEMATICAL CONTROL AND RELATED FIELDS AB - Consider a model of debt management, where a sovereign state trades some bonds to service the debt with a pool of risk-neutral competitive foreign investors. At each time, the government decides which fraction of the gross domestic product (GDP) should be used to repay the debt, and how much to devaluate its currency. Both these operations have the effect to reduce the actual size of the debt, but have a social cost in terms of welfare sustainability. When the debt-to-GDP ratio reaches a given size $ x^* $, bankruptcy instantly occurs. Moreover, at any time the sovereign state can declare bankruptcy by paying a correspondent bankruptcy cost. To offset the possible loss of part of their investment, the foreign investors buy bonds at a discounted price which is not given a priori. This leads to a nonstandard optimal control problem. For a given bankruptcy threshold $ x^* $, we show that the optimization problem admits an equilibrium solution. The paper also studies properties of optimal feedback strategies, and the asymptotic behaviour of the expected total cost to the borrower as $ x^* $ is pushed to infinity. DA - 2023/5// PY - 2023/5// DO - 10.3934/mcrf.2023014 VL - 5 SP - SN - 2156-8499 KW - Stochastic model KW - infinite time horizon KW - optimal feedback solution KW - debt management KW - currency devaluation ER - TY - JOUR TI - Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data AU - Nguyen, Kyle AU - Rutter, Erica M. AU - Flores, Kevin B. T2 - BULLETIN OF MATHEMATICAL BIOLOGY AB - Reaction-diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates; however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models’ performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k-means clustering to predict the number of subpopulations based on the recovered distributions. DA - 2023/7// PY - 2023/7// DO - 10.1007/s11538-023-01162-3 VL - 85 IS - 7 SP - SN - 1522-9602 KW - Glioblastoma multiforme KW - Random differential equation KW - Parameter estimation KW - k-Means clustering ER - TY - JOUR TI - Mathematical model for filtration and drying in filter membranes AU - Ji, Hangjie AU - Sanaei, Pejman T2 - PHYSICAL REVIEW FLUIDS AB - A filter membrane may be frequently used during its lifetime, with filtration and drying processes occurring in the porous medium for several cycles. As a consequence, the filter performance ultimately deteriorates after several cycles. In this work, we develop a mathematical model that provides insights to the overall porous medium evolution over cycles of filtration and drying processes and predicts the timeline to discard the filter based on its optimum performance. DA - 2023/6/14/ PY - 2023/6/14/ DO - 10.1103/PhysRevFluids.8.064302 VL - 8 IS - 6 SP - SN - 2469-990X UR - https://doi.org/10.1103/PhysRevFluids.8.064302 ER - TY - JOUR TI - Toxicological and pharmacokinetic properties of sucralose-6-acetate and its parent sucralose: in vitro screening assays AU - Schiffman, Susan S. AU - Scholl, Elizabeth H. AU - Furey, Terrence S. AU - Nagle, H. Troy T2 - JOURNAL OF TOXICOLOGY AND ENVIRONMENTAL HEALTH-PART B-CRITICAL REVIEWS AB - The purpose of this study was to determine the toxicological and pharmacokinetic properties of sucralose-6-acetate, a structural analog of the artificial sweetener sucralose. Sucralose-6-acetate is an intermediate and impurity in the manufacture of sucralose, and recent commercial sucralose samples were found to contain up to 0.67% sucralose-6-acetate. Studies in a rodent model found that sucralose-6-acetate is also present in fecal samples with levels up to 10% relative to sucralose which suggest that sucralose is also acetylated in the intestines. A MultiFlow® assay, a high-throughput genotoxicity screening tool, and a micronucleus (MN) test that detects cytogenetic damage both indicated that sucralose-6-acetate is genotoxic. The mechanism of action was classified as clastogenic (produces DNA strand breaks) using the MultiFlow® assay. The amount of sucralose-6-acetate in a single daily sucralose-sweetened drink might far exceed the threshold of toxicological concern for genotoxicity (TTCgenotox) of 0.15 µg/person/day. The RepliGut® System was employed to expose human intestinal epithelium to sucralose-6-acetate and sucralose, and an RNA-seq analysis was performed to determine gene expression induced by these exposures. Sucralose-6-acetate significantly increased the expression of genes associated with inflammation, oxidative stress, and cancer with greatest expression for the metallothionein 1 G gene (MT1G). Measurements of transepithelial electrical resistance (TEER) and permeability in human transverse colon epithelium indicated that sucralose-6-acetate and sucralose both impaired intestinal barrier integrity. Sucralose-6-acetate also inhibited two members of the cytochrome P450 family (CYP1A2 and CYP2C19). Overall, the toxicological and pharmacokinetic findings for sucralose-6-acetate raise significant health concerns regarding the safety and regulatory status of sucralose itself. DA - 2023/5/27/ PY - 2023/5/27/ DO - 10.1080/10937404.2023.2213903 SP - SN - 1521-6950 KW - Sucralose KW - sucralose-6-acetate KW - genotoxicity KW - gene expression KW - intestinal barrier ER - TY - JOUR TI - One-particle loss detection of genuine multipartite entanglement AU - Zhao, Hui AU - Hao, Jia AU - Fei, Shao-Ming AU - Wang, Zhi-Xi AU - Jing, Naihuan T2 - QUANTUM INFORMATION PROCESSING DA - 2023/5/12/ PY - 2023/5/12/ DO - 10.1007/s11128-023-03916-3 VL - 22 IS - 5 SP - SN - 1573-1332 KW - Genuine multipartite entanglement KW - Separability KW - Correlation tensor ER - TY - JOUR TI - Shear imposed falling film with odd viscosity effects AU - Desai, Akshay S. AU - Chattopadhyay, Souradip AU - Gaonkar, Amar K. AU - Mukhopadhyay, Anandamoy T2 - INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS AB - This study examines the behavior of a thin liquid film flowing on an inclined plane subject to imposed shear stress. The liquid’s time-reversal symmetry is broken, and we consider the odd part of the viscosity to describe the Navier–Stokes equation. To investigate the interplay between the imposed shear and odd viscosity on the flow dynamics, we develop a weighted residual model (WRM). We determine the model’s critical Reynolds number (Rec) through linear stability analysis. Our findings indicate that uphill shear tends to stabilize the flow, while downhill shear enhances the instability, albeit reduced by the presence of odd viscosity. We also construct an Orr–Sommerfeld (OS) type eigenvalue problem for normal mode analysis and derive Rec. We discover that in the longwave regime, RecWRM=RecOS. Finally, our numerical simulations of the model align well with our linear stability analysis. DA - 2023/7// PY - 2023/7// DO - 10.1016/j.ijnonlinmec.2023.104422 VL - 153 SP - SN - 1878-5638 UR - https://doi.org/10.1016/j.ijnonlinmec.2023.104422 KW - Thin films KW - Odd viscosity KW - Imposed shear KW - Weighted residual model KW - Interfacial instability ER - TY - JOUR TI - OPTIMAL STRATEGIES FOR GREEN SUPPLY CHAIN CONSIDERING SOCIAL RESPONSIBILITY AND ENVIRONMENTAL RESPONSIBILITY AU - Cong, Jing AU - Pang, Tao AU - Peng, Hongjun T2 - JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION AB - In this paper, we investigate optimal strategies and the effects of Corporate Social Responsibility (CSR) and Corporate Environmental Responsibility (CER) for a green supply chain consisting of a single supplier and a single manufacturer. For two different power structures with four different CSR-CER awareness scenarios, we establish the Stackelberg game models to derive the optimal results on the greenness level, the production quantity, and the social welfare. The first finding is that the degree of CSR awareness or CER awareness of supply chain members has positive effects on the green strategy of the supplier. The second finding is that for any CSR-CER awareness scenario, the greenness level, the production quantity, and the social welfare typically are higher when the party without CSR awareness is the leader. The only exception is that the greenness level of raw materials is higher under the supplier-led than the manufacturer-led when the supplier's CSR awareness is lower under the supplier-led and the manufacturer's CER-aware model. The third finding is that under the supplier-led, the greenness level of raw materials is highest when the manufacturer is CSR-aware; while under the manufacturer-led, the greenness level of raw materials is highest when the supplier is both CSR-aware and CER-aware. DA - 2023/4// PY - 2023/4// DO - 10.3934/jimo.2023048 SP - SN - 1553-166X KW - Green supply chain KW - power structure KW - corporate social responsibility KW - corporate environmental responsibility KW - greenness level ER - TY - JOUR TI - Quantum algebra of multiparameter Manin matrices AU - Jing, Naihuan AU - Liu, Yinlong AU - Zhang, Jian T2 - Journal of Algebra AB - Multiparametric quantum semigroups Mqˆ,pˆ(n) are generalization of the one-parameter general linear semigroups Mq(n), where qˆ=(qij) and pˆ=(pij) are 2n2 parameters satisfying certain conditions. In this paper, we study the algebra of multiparametric Manin matrices using the R-matrix method. The systematic approach enables us to obtain several classical identities such as Muir's identities, Newton's identities, Capelli-type identities, Cauchy-Binet's identity both for determinant and permanent as well as a rigorous proof of the MacMahon master equation for the quantum algebra of multiparametric Manin matrices. Some of the generalized identities are also lifted to multiparameter q-Yangians. DA - 2023/6// PY - 2023/6// DO - 10.1016/j.jalgebra.2023.06.002 UR - https://doi.org/10.1016/j.jalgebra.2023.06.002 ER - TY - JOUR TI - Bulk and mosaic deletions of Egfr reveal regionally defined gliogenesis in the developing mouse forebrain AU - Zhang, Xuying AU - Xiao, Guanxi AU - Johnson, Caroline AU - Cai, Yuheng AU - Horowitz, Zachary K. AU - Mennicke, Christine AU - Coffey, Robert AU - Haider, Mansoor AU - Threadgill, David AU - Eliscu, Rebecca AU - Oldham, Michael C. AU - Greenbaum, Alon AU - Ghashghaei, H. Troy T2 - ISCIENCE AB - The epidermal growth factor receptor (EGFR) plays a role in cell proliferation and differentiation during healthy development and tumor growth; however, its requirement for brain development remains unclear. Here we used a conditional mouse allele for Egfr to examine its contributions to perinatal forebrain development at the tissue level. Subtractive bulk ventral and dorsal forebrain deletions of Egfr uncovered significant and permanent decreases in oligodendrogenesis and myelination in the cortex and corpus callosum. Additionally, an increase in astrogenesis or reactive astrocytes in effected regions was evident in response to cortical scarring. Sparse deletion using mosaic analysis with double markers (MADM) surprisingly revealed a regional requirement for EGFR in rostrodorsal, but not ventrocaudal glial lineages including both astrocytes and oligodendrocytes. The EGFR-independent ventral glial progenitors may compensate for the missing EGFR-dependent dorsal glia in the bulk Egfr-deleted forebrain, potentially exposing a regenerative population of gliogenic progenitors in the mouse forebrain. DA - 2023/3/17/ PY - 2023/3/17/ DO - 10.1016/j.isci.2023.106242 VL - 26 IS - 3 SP - SN - 2589-0042 ER - TY - JOUR TI - NON-LINEAR SINGULARITY FORMATION FOR CIRCULAR VORTEX SHEETS AU - Murray, Ryan AU - Wilcox, Galen T2 - QUARTERLY OF APPLIED MATHEMATICS AB - We study the evolution of vortex sheets according to the Birkhoff-Rott equation, which describe the motion of sharp shear interfaces governed by the incompressible Euler equation in two dimensions. In a recent work, the authors demonstrated within this context a marginal linear stability of circular vortex sheets, standing in sharp contrast with classical instability of the flat vortex sheet, which is known as the Kelvin-Helmholtz instability. This article continues that analysis by investigating how non-linear effects induce singularity formation near the circular vortex sheet. In high-frequency regimes, the singularity formation is primarily driven by a complex-valued, conjugated Burgers equation, which we study by modifying a classical argument from hyperbolic conservation laws. This provides a deeper understanding of the mechanisms driving the breakdown of circular vortex sheets, which are observed both numerically and experimentally. DA - 2023/5/3/ PY - 2023/5/3/ DO - 10.1090/qam/1659 VL - 5 SP - SN - 1552-4485 ER - TY - JOUR TI - Prediction of 3D Velocity Field of Reticulated Foams Using Deep Learning for Transport Analysis AU - Ko, Danny D. AU - Ji, Hangjie AU - Ju, Y. Sungtaek T2 - TRANSPORT IN POROUS MEDIA AB - Abstract Data-driven deep learning models are emerging as a new method to predict the flow and transport through porous media with very little computational power required. Previous deep learning models, however, experience difficulty or require additional computations to predict the 3D velocity field which is essential to characterize porous media at the pore scale. We design a deep learning model and incorporate a physics-informed loss function that enforces the mass conservation for incompressible flows to relate the spatial information of the 3D binary image to the 3D velocity field of porous media. We demonstrate that our model, trained only with synthetic porous media as binary data without additional image processing, can predict the 3D velocity field of real reticulated foams which have microstructures different from porous media that were studied in previous works. Our study provides deep learning framework for predicting the velocity field of porous media and conducting subsequent transport analysis for various engineering applications. As an example, we conduct heat transfer analysis using the predicted velocity fields and demonstrate the accuracy and advantage of our deep learning model. DA - 2023/6/1/ PY - 2023/6/1/ DO - 10.1007/s11242-023-01961-1 VL - 6 SP - SN - 1573-1634 UR - https://doi.org/10.1007/s11242-023-01961-1 KW - Deep learning KW - Convolutional neural network KW - Reticulated foam KW - Fluid flow KW - Heat transfer ER - TY - JOUR TI - Fusing an agent-based model of mosquito population dynamics with a statistical reconstruction of spatio-temporal abundance patterns AU - Cavany, Sean C. AU - Espana, Guido C. AU - Lloyd, Alun AU - Vazquez-Prokopec, Gonzalo AU - Astete, Helvio S. AU - Waller, Lance AU - Kitron, Uriel S. AU - Scott, Thomas AU - Morrison, Amy S. AU - Reiner Jr, Robert AU - Perkins, T. Alex S. T2 - PLOS COMPUTATIONAL BIOLOGY AB - The mosquito Aedes aegypti is the vector of a number of medically-important viruses, including dengue virus, yellow fever virus, chikungunya virus, and Zika virus, and as such vector control is a key approach to managing the diseases they cause. Understanding the impact of vector control on these diseases is aided by first understanding its impact on Ae. aegypti population dynamics. A number of detail-rich models have been developed to couple the dynamics of the immature and adult stages of Ae. aegypti. The numerous assumptions of these models enable them to realistically characterize impacts of mosquito control, but they also constrain the ability of such models to reproduce empirical patterns that do not conform to the models' behavior. In contrast, statistical models afford sufficient flexibility to extract nuanced signals from noisy data, yet they have limited ability to make predictions about impacts of mosquito control on disease caused by pathogens that the mosquitoes transmit without extensive data on mosquitoes and disease. Here, we demonstrate how the differing strengths of mechanistic realism and statistical flexibility can be fused into a single model. Our analysis utilizes data from 176,352 household-level Ae. aegypti aspirator collections conducted during 1999-2011 in Iquitos, Peru. The key step in our approach is to calibrate a single parameter of the model to spatio-temporal abundance patterns predicted by a generalized additive model (GAM). In effect, this calibrated parameter absorbs residual variation in the abundance time-series not captured by other features of the mechanistic model. We then used this calibrated parameter and the literature-derived parameters in the agent-based model to explore Ae. aegypti population dynamics and the impact of insecticide spraying to kill adult mosquitoes. The baseline abundance predicted by the agent-based model closely matched that predicted by the GAM. Following spraying, the agent-based model predicted that mosquito abundance rebounds within about two months, commensurate with recent experimental data from Iquitos. Our approach was able to accurately reproduce abundance patterns in Iquitos and produce a realistic response to adulticide spraying, while retaining sufficient flexibility to be applied across a range of settings. DA - 2023/4// PY - 2023/4// DO - 10.1371/journal.pcbi.1010424 VL - 19 IS - 4 SP - SN - 1553-7358 ER - TY - JOUR TI - New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations AU - Pan, Kejia AU - Fu, Kang AU - Li, Jin AU - Hu, Hongling AU - Li, Zhilin T2 - NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS DA - 2023/5// PY - 2023/5// DO - 10.4208/nmtma.OA-2022-0073 VL - 16 IS - 2 SP - 393-409 SN - 2079-7338 KW - Poisson equation KW - Helmholtz equation KW - sixth-order compact scheme KW - maximum principle KW - staggered grid ER - TY - JOUR TI - Toward an optimal contraception dosing strategy AU - Gavina, Brenda Lyn A. AU - Reyes, V. Aurelio A. AU - Olufsen, Mette AU - Lenhart, Suzanne AU - Ottesen, Johnny T2 - PLOS COMPUTATIONAL BIOLOGY AB - Anovulation refers to a menstrual cycle characterized by the absence of ovulation. Exogenous hormones such as synthetic progesterone and estrogen have been used to attain this state to achieve contraception. However, large doses are associated with adverse effects such as increased risk for thrombosis and myocardial infarction. This study utilizes optimal control theory on a modified menstrual cycle model to determine the minimum total exogenous estrogen/progesterone dose, and timing of administration to induce anovulation. The mathematical model correctly predicts the mean daily levels of pituitary hormones LH and FSH , and ovarian hormones E 2 , P 4 , and Inh throughout a normal menstrual cycle and reflects the reduction in these hormone levels caused by exogenous estrogen and/or progesterone. Results show that it is possible to reduce the total dose by 92% in estrogen monotherapy, 43% in progesterone monotherapy, and that it is most effective to deliver the estrogen contraceptive in the mid follicular phase. Finally, we show that by combining estrogen and progesterone the dose can be lowered even more. These results may give clinicians insights into optimal formulations and schedule of therapy that can suppress ovulation. DA - 2023/4// PY - 2023/4// DO - 10.1371/journal.pcbi.1010073 VL - 19 IS - 4 SP - SN - 1553-7358 ER - TY - JOUR TI - Prediction of pore-scale flow in heterogeneous porous media from periodic structures using deep learning AU - Ko, Danny D. AU - Ji, Hangjie AU - Ju, Y. Sungtaek T2 - AIP Advances AB - Data-driven deep learning models are emerging as a promising method for characterizing pore-scale flow through complex porous media while requiring minimal computational power. However, previous models often require extensive computation to simulate flow through synthetic porous media for use as training data. We propose a convolutional neural network trained solely on periodic unit cells to predict pore-scale velocity fields of complex heterogeneous porous media from binary images without the need for further image processing. Our model is trained using a range of simple and complex unit cells that can be obtained analytically or numerically at a low computational cost. Our results show that the model accurately predicts the permeability and pore-scale flow characteristics of synthetic porous media and real reticulated foams. We significantly improve the convergence of numerical simulations by using the predictions from our model as initial guesses. Our approach addresses the limitations of previous models and improves computational efficiency, enabling the rigorous characterization of large batches of complex heterogeneous porous media for a variety of engineering applications. DA - 2023/4/1/ PY - 2023/4/1/ DO - 10.1063/5.0147472 VL - 13 IS - 4 SP - LA - en OP - SN - 2158-3226 UR - http://dx.doi.org/10.1063/5.0147472 DB - Crossref ER - TY - JOUR TI - Quantifying heterogeneities in arbovirus transmission: Description of the rationale and methodology for a prospective longitudinal study of dengue and Zika virus transmission in Iquitos, Peru (2014-2019) AU - Morrison, Amy C. H. AU - Paz-Soldan, Valerie A. AU - Vazquez-Prokopec, Gonzalo M. AU - Lambrechts, Louis AU - Elson, William H. AU - Barrera, Patricia A. AU - Astete, Helvio C. AU - Briesemeister, Veronica B. AU - Leguia, Mariana C. AU - Jenkins, Sarah A. AU - Long, Kanya C. L. AU - Kawiecki, Anna B. A. AU - Reiner Jr, Robert C. D. AU - Perkins, T. Alex T. AU - Lloyd, Alun L. M. AU - Waller, Lance A. AU - Hontz, Robert D. P. AU - Stoddard, Steven T. L. AU - Barker, Christopher M. W. AU - Kitron, Uriel AU - Elder, John P. AU - Rothman, Alan L. AU - Scott, Thomas W. AU - Grp, Proyecto Dengue T2 - PLOS ONE AB - Current knowledge of dengue virus (DENV) transmission provides only a partial understanding of a complex and dynamic system yielding a public health track record that has more failures than successes. An important part of the problem is that the foundation for contemporary interventions includes a series of longstanding, but untested, assumptions based on a relatively small portion of the human population; i.e., people who are convenient to study because they manifest clinically apparent disease. Approaching dengue from the perspective of people with overt illness has produced an extensive body of useful literature. It has not, however, fully embraced heterogeneities in virus transmission dynamics that are increasingly recognized as key information still missing in the struggle to control the most important insect-transmitted viral infection of humans. Only in the last 20 years have there been significant efforts to carry out comprehensive longitudinal dengue studies. This manuscript provides the rationale and comprehensive, integrated description of the methodology for a five-year longitudinal cohort study based in the tropical city of Iquitos, in the heart of the Peruvian Amazon. Primary data collection for this study was completed in 2019. Although some manuscripts have been published to date, our principal objective here is to support subsequent publications by describing in detail the structure, methodology, and significance of a specific research program. Our project was designed to study people across the entire continuum of disease, with the ultimate goal of quantifying heterogeneities in human variables that affect DENV transmission dynamics and prevention. Because our study design is applicable to other Aedes transmitted viruses, we used it to gain insights into Zika virus (ZIKV) transmission when during the project period ZIKV was introduced and circulated in Iquitos. Our prospective contact cluster investigation design was initiated by detecttion of a person with a symptomatic DENV infection and then followed that person’s immediate contacts. This allowed us to monitor individuals at high risk of DENV infection, including people with clinically inapparent and mild infections that are otherwise difficult to detect. We aimed to fill knowledge gaps by defining the contribution to DENV transmission dynamics of (1) the understudied majority of DENV-infected people with inapparent and mild infections and (2) epidemiological, entomological, and socio-behavioral sources of heterogeneity. By accounting for factors underlying variation in each person’s contribution to transmission we sought to better determine the type and extent of effort needed to better prevent virus transmission and disease. DA - 2023/2/2/ PY - 2023/2/2/ DO - 10.1371/journal.pone.0273798 VL - 18 IS - 2 SP - SN - 1932-6203 ER - TY - JOUR TI - AVIDA: An alternating method for visualizing and integrating data AU - Dover, Kathryn AU - Cang, Zixuan AU - Ma, Anna AU - Nie, Qing AU - Vershynin, Roman T2 - JOURNAL OF COMPUTATIONAL SCIENCE AB - High-dimensional multimodal data arise in many scientific fields. The integration of multimodal data becomes challenging when there is no known correspondence between the samples and the features of different datasets. To tackle this challenge, we introduce AVIDA, a framework for simultaneously performing data alignment and dimension reduction. In the numerical experiments, Gromov–Wasserstein optimal transport and t-distributed stochastic neighbor embedding are used as the alignment and dimension reduction modules respectively. We show that by alternating dimension reduction and alignment, AVIDA aligns the representations of high-dimensional datasets without common features with four synthesized datasets and two real multimodal single-cell datasets. Compared to several existing methods, we demonstrate that AVIDA better preserves structures of individual datasets, especially distinct local structures in the joint low-dimensional representation, while achieving comparable alignment performance. Such a property is important in multimodal single-cell data analysis as some biological processes are uniquely captured by one of the datasets. In general applications, other methods can be used for the alignment and dimension reduction modules. DA - 2023/4// PY - 2023/4// DO - 10.1016/j.jocs.2023.101998 VL - 68 SP - 101998 SN - 1877-7511 KW - Dimension reduction KW - Data integration KW - Multi-omics data ER - TY - JOUR TI - Data-Driven High-to-Low for Coarse Grid System Thermal Hydraulics AU - Iskhakov, Arsen S. AU - Leite, Victor Coppo AU - Merzari, Elia AU - Dinh, Nam T. T2 - NUCLEAR SCIENCE AND ENGINEERING AB - Traditional one-dimensional system thermal-hydraulic analysis has been widely applied in the nuclear industry for licensing purposes because of its numerical efficiency. However, such tools have inherently limited opportunities for modeling multiscale multidimensional flows in large reactor enclosures. Recent interest in three-dimensional coarse grid (CG) simulations has shown their potential in improving the predictive capability of system-level analysis. At the same time, CGs do not allow one to accurately resolve and capture turbulent mixing and stratification, whereas implemented in CG solvers relatively simple turbulence models exhibit large model form uncertainties. Therefore, there is a strong interest in further advances in CG modeling techniques. In this work, two high-to-low data-driven (DD) methodologies (and their combination) are explored to reduce grid and model-induced errors using a case study based on the Texas A&M upper plenum of a high-temperature gas-cooled reactor facility. The first approach relies on the use of a DD turbulence closure [eddy viscosity predicted by a neural network (NN)]. A novel training framework is suggested to consider the influence of grid cell size on closure. The second methodology uses a NN to predict velocity errors to improve low-fidelity results. Both methodologies and their combination have shown the potential to improve CG simulation results by using data with higher fidelity. DA - 2023/4/28/ PY - 2023/4/28/ DO - 10.1080/00295639.2023.2180987 VL - 4 SP - SN - 1943-748X UR - https://publons.com/wos-op/publon/55933581/ KW - Coarse grid computational fluid dynamics KW - data-driven high-to-low KW - machine learning KW - mixing KW - turbulence modeling ER - TY - JOUR TI - Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator AU - Chertock, Alina AU - Chu, Shaoshuai AU - Kurganov, Alexander T2 - EAST ASIAN JOURNAL ON APPLIED MATHEMATICS DA - 2023/4/12/ PY - 2023/4/12/ DO - 10.4208/eajam.2022-313.160123 VL - 4 SP - SN - 2079-7370 KW - Local smoothness indicator KW - scheme adaption KW - strong stability preserving Runge-Kutta methods KW - hyperbolic systems of conservation laws KW - A-WENO schemes ER - TY - JOUR TI - Lax dynamics for Cartan decomposition with applications to Hamiltonian simulation AU - Chu, Moody T T2 - IMA Journal of Numerical Analysis AB - Abstract Simulating the time evolution of a Hamiltonian system on a classical computer is hard—The computational power required to even describe a quantum system scales exponentially with the number of its constituents, let alone integrate its equations of motion. Hamiltonian simulation on a quantum machine is a possible solution to this challenge—Assuming that a quantum system composing of spin-½ particles can be manipulated at will, then it is tenable to engineer the interaction between those particles according to the one that is to be simulated, and thus predict the value of physical quantities by simply performing the appropriate measurements on the system. Establishing a linkage between the unitary operators described mathematically as a logic solution and the unitary operators recognizable as quantum circuits for execution, is therefore essential for algorithm design and circuit implementation. Most current techniques are fallible because of truncation errors or the stagnation at local solutions. This work offers an innovative avenue by tackling the Cartan decomposition with the notion of Lax dynamics. Within the integration errors that is controllable, this approach gives rise to a genuine unitary synthesis that not only is numerically feasible, but also can be utilized to gauge the quality of results produced by other means, and extend the knowledge to a wide range of applications. This paper aims at establishing the theoretic and algorithmic foundations by exploiting the geometric properties of Hamiltonian subalgebras and describing a common mechanism for deriving the Lax dynamics. DA - 2023/4/25/ PY - 2023/4/25/ DO - 10.1093/imanum/drad018 VL - 4 SP - drad018 SN - 0272-4979 1464-3642 UR - http://dx.doi.org/10.1093/imanum/drad018 KW - Hamiltonian simulation KW - Cartan decomposition KW - Lax dynamics KW - exponential map ER - TY - JOUR TI - Triple Linking Numbers and Heegaard Floer Homology AU - Gorsky, Eugene AU - Lidman, Tye AU - Liu, Beibei AU - Moore, Allison H. T2 - INTERNATIONAL MATHEMATICS RESEARCH NOTICES AB - Abstract We establish some new relationships between Milnor invariants and Heegaard Floer homology. This includes a formula for the Milnor triple linking number from the link Floer complex, detection results for the Whitehead link and Borromean rings, and a structural property of the $d$-invariants of surgeries on certain algebraically split links. DA - 2023/3/10/ PY - 2023/3/10/ DO - 10.1093/imrn/rnab368 VL - 2023 IS - 6 SP - 4501-4554 SN - 1687-0247 ER - TY - JOUR TI - Dynamic portfolio choice with uncertain rare-events risk in stock and cryptocurrency markets AU - Lv, Wujun AU - Pang, Tao AU - Xia, Xiaobao AU - Yan, Jingzhou T2 - FINANCIAL INNOVATION AB - Abstract In response to the unprecedented uncertain rare events of the last decade, we derive an optimal portfolio choice problem in a semi-closed form by integrating price diffusion ambiguity, volatility diffusion ambiguity, and jump ambiguity occurring in the traditional stock market and the cryptocurrency market into a single framework. We reach the following conclusions in both markets: first, price diffusion and jump ambiguity mainly determine detection-error probability; second, optimal choice is more significantly affected by price diffusion ambiguity than by jump ambiguity, and trivially affected by volatility diffusion ambiguity. In addition, investors tend to be more aggressive in a stable market than in a volatile one. Next, given a larger volatility jump size, investors tend to increase their portfolio during downward price jumps and decrease it during upward price jumps. Finally, the welfare loss caused by price diffusion ambiguity is more pronounced than that caused by jump ambiguity in an incomplete market. These findings enrich the extant literature on effects of ambiguity on the traditional stock market and the evolving cryptocurrency market. The results have implications for both investors and regulators. DA - 2023/4/5/ PY - 2023/4/5/ DO - 10.1186/s40854-023-00472-8 VL - 9 IS - 1 SP - SN - 2199-4730 KW - Robust portfolio choice KW - Detection error probability KW - Rare events KW - Ambiguity KW - Cryptocurrency KW - Welfare loss ER - TY - JOUR TI - Error estimates of Fourier finite volume element method for parabolic Dirichlet boundary optimal control problems on complex connected domains AU - Liu, Wenju AU - Zhao, Tengjin AU - Ito, Kazufumi AU - Zhang, Zhiyue T2 - APPLIED NUMERICAL MATHEMATICS AB - In this paper, we study the parabolic Dirichlet boundary optimal control on complex connected domains. It is well known that both the complex connected domain and the Dirichlet boundary control bring great difficulties to theoretical analysis and numerical calculation. The complex connected domain is a typical non-convex domain, and it is difficult for the traditional numerical method to obtain the same convergence order as the state and adjoint state for the Dirichlet boundary control. The optimal system of the proposed control problem is first obtained by using Lagrange multiplier method. Then, based on the variational form, the Fourier finite volume element method is used to obtain the fully discrete scheme of the optimality system, that is, using Fourier expansion method in azimuthal direction and applying finite volume element method in radial direction respectively, and the Crank-Nicolson scheme in the time direction. Next, we strictly prove the error estimates of state, adjoint state and Dirichlet boundary control by using the variational discretization concept. Finally, the theoretical analysis results and the feasibility and effectiveness of the proposed method are verified by numerical experiments. DA - 2023/4// PY - 2023/4// DO - 10.1016/j.apnum.2023.01.007 VL - 186 SP - 164-201 SN - 1873-5460 KW - Optimal control KW - Dirichlet boundary control KW - Complex connected domain KW - Polar coordinates KW - Fourier finite volume element method KW - A priori error estimates ER - TY - JOUR TI - HIGH ORDER COMPACT SCHEMES FOR FLUX TYPE BCS AU - Li, Zhilin AU - Pan, Kejia T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING DA - 2023/// PY - 2023/// DO - 10.1137/21M1444771 VL - 45 IS - 2 SP - A646-A674 SN - 1095-7197 UR - https://doi.org/10.1137/21M1444771 KW - Poisson KW - Helmholtz KW - diffusion-advection KW - anisotropic equations KW - high order compact method KW - HOC method for flux BCs KW - discrete maximum principle ER - TY - JOUR TI - Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties AU - Mamis, Konstantinos AU - Farazmand, Mohammad T2 - PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES AB - Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modeling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob's theorem on Gaussian Markov processes, we prove that the correlated Ornstein-Uhlenbeck process is the appropriate tool for modeling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the Ornstein-Uhlenbeck model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the asymptotic distribution of infected individuals. This analytic result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modeling of uncertainties in compartmental models of infectious disease. DA - 2023/1/25/ PY - 2023/1/25/ DO - 10.1098/rspa.2022.0568 VL - 479 IS - 2269 SP - SN - 1471-2946 KW - COVID-19 KW - compartmental models KW - epidemiology KW - uncertainty quantification KW - correlated noise KW - noise-induced transitions ER - TY - JOUR TI - Adaptive basis sets for practical quantum computing AU - Kwon, Hyuk-Yong AU - Curtin, Gregory M. M. AU - Morrow, Zachary AU - Kelley, C. T. AU - Jakubikova, Elena T2 - INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY AB - Abstract Electronic structure calculations on small systems such as H 2 , H 2 O, LiH, and BeH 2 with chemical accuracy are still a challenge for the current generation of noisy intermediate‐scale quantum (NISQ) devices. One of the reasons is that due to the device limitations, only minimal basis sets are commonly applied in quantum chemical calculations, which allows one to keep the number of qubits employed in the calculations at a minimum. However, the use of minimal basis sets leads to very large errors in the computed molecular energies as well as potential energy surface shapes. One way to increase the accuracy of electronic structure calculations is through the development of small basis sets better suited for quantum computing. In this work, we show that the use of adaptive basis sets, in which exponents and contraction coefficients depend on molecular structure, provides an easy way to dramatically improve the accuracy of quantum chemical calculations without the need to increase the basis set size and thus the number of qubits utilized in quantum circuits. As a proof of principle, we optimize an adaptive minimal basis set for quantum computing calculations on an H 2 molecule, in which exponents and contraction coefficients depend on the HH distance, and apply it to the generation of H 2 potential energy surface on IBM‐Q quantum devices. The adaptive minimal basis set reaches the accuracy of the double‐zeta basis sets, thus allowing one to perform double‐zeta quality calculations on quantum devices without the need to utilize twice as many qubits in simulations. This approach can be extended to other molecular systems and larger basis sets in a straightforward manner. DA - 2023/4/5/ PY - 2023/4/5/ DO - 10.1002/qua.27123 VL - 4 SP - SN - 1097-461X UR - https://doi.org/10.1002/qua.27123 KW - adaptive basis set KW - potential energy surface KW - quantum computing ER - TY - JOUR TI - Data-Driven RANS Turbulence Closures for Forced Convection Flow in Reactor Downcomer Geometry AU - Iskhakov, Arsen S. AU - Tai, Cheng-Kai AU - Bolotnov, Igor A. AU - Nguyen, Tri AU - Merzari, Elia AU - Shaver, Dillon R. AU - Dinh, Nam T. T2 - NUCLEAR TECHNOLOGY AB - Recent progress in data-driven turbulence modeling has shown its potential to enhance or replace traditional equation-based Reynolds-averaged Navier-Stokes (RANS) turbulence models. This work utilizes invariant neural network (NN) architectures to model Reynolds stresses and turbulent heat fluxes in forced convection flows (when the models can be decoupled). As the considered flow is statistically one dimensional, the invariant NN architecture for the Reynolds stress model reduces to the linear eddy viscosity model. To develop the data-driven models, direct numerical and RANS simulations in vertical planar channel geometry mimicking a part of the reactor downcomer are performed. Different conditions and fluids relevant to advanced reactors (sodium, lead, unitary-Prandtl number fluid, and molten salt) constitute the training database. The models enabled accurate predictions of velocity and temperature, and compared to the baseline k−τ turbulence model with the simple gradient diffusion hypothesis, do not require tuning of the turbulent Prandtl number. The data-driven framework is implemented in the open-source graphics processing unit–accelerated spectral element solver nekRS and has shown the potential for future developments and consideration of more complex mixed convection flows. DA - 2023/3/16/ PY - 2023/3/16/ DO - 10.1080/00295450.2023.2185056 VL - 3 SP - SN - 1943-7471 UR - https://publons.com/wos-op/publon/58758847/ KW - Machine learning KW - turbulence modeling KW - forced convection KW - low- and high-Prandtl fluids KW - data-driven modeling ER - TY - RPRT TI - Top-degree components of Grothendieck and Lascoux polynomials AU - Pan, J. AU - Yu, T. AB - The Castelnuovo-Mumford polynomial $\widehat{\mathfrak{G}}_w$ with $w \in S_n$ is the highest homogeneous component of the Grothendieck polynomial $\mathfrak{G}_w$. Pechenik, Speyer and Weigandt define a statistic $\mathsf{rajcode}(\cdot)$ on $S_n$ that gives the leading monomial of $\widehat{\mathfrak{G}}_w$. We introduce a statistic $\mathsf{rajcode}(\cdot)$ on any diagram $D$ through a combinatorial construction ``snow diagram'' that augments and decorates $D$. When $D$ is the Rothe diagram of a permutation $w$, $\mathsf{rajcode}(D)$ agrees with the aforementioned $\mathsf{rajcode}(w)$. When $D$ is the key diagram of a weak composition $\alpha$, $\mathsf{rajcode}(D)$ yields the leading monomial of $\widehat{\mathfrak{L}}_\alpha$, the highest homogeneous component of the Lascoux polynomials $\mathfrak{L}_\alpha$. We use $\widehat{\mathfrak{L}}_\alpha$ to construct a basis of $\widehat{V}_n$, the span of $\widehat{\mathfrak{G}}_w$ with $w \in S_n$. Then we show $\widehat{V}_n$ gives a natural algebraic interpretation of a classical $q$-analogue of Bell numbers. C6 - 2302.03643 DA - 2023/// PY - 2023/// DO - 10.48550/arXiv.2302.03643 M1 - 2302.03643 M3 - arXiv preprint SN - 2302.03643 ER - TY - JOUR TI - Numerical integration rules with improved accuracy close to discontinuities AU - Amat, Sergio AU - Li, Zhilin AU - Ruiz-Alvarez, Juan AU - Solano, Concepcion AU - Trillo, Juan C. T2 - MATHEMATICS AND COMPUTERS IN SIMULATION AB - This work is devoted to the construction and analysis of a new nonlinear technique that allows obtaining accurate numerical integrations of any order using data that contains discontinuities, and when the integrand is only known at grid points. The novelty of the technique consists in the inclusion of correction terms with a closed expression that depend on the size of the jumps of the function and its derivatives at the discontinuities, that are supposed to be known. The addition of these terms allows recovering the accuracy of classical numerical integration formulas close to the discontinuities, as these correction terms account for the error that the classical integration formulas commit up to their accuracy at smooth zones. Thus, the correction terms can be added during the integration or as post-processing, which is useful if the main calculation of the integral has been already done using classical formulas. We include several numerical experiments that confirm the theoretical conclusions reached in this article. DA - 2023/8// PY - 2023/8// DO - 10.1016/j.matcom.2023.03.032 VL - 210 SP - 593-614 SN - 1872-7166 UR - https://doi.org/10.1016/j.matcom.2023.03.032 KW - Accurate numerical integration formulas KW - Adaption to discontinuities KW - Definite integration KW - Adapted interpolation ER - TY - JOUR TI - A neural ordinary differential equation model for visualizing deep neural network behaviors in multi-parametric MRI-based glioma segmentation AU - Yang, Zhenyu AU - Hu, Zongsheng AU - Ji, Hangjie AU - Lafata, Kyle AU - Vaios, Eugene AU - Floyd, Scott AU - Yin, Fang-Fang AU - Wang, Chunhao T2 - MEDICAL PHYSICS AB - To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network behavior during multi-parametric MRI-based glioma segmentation as a method to enhance deep learning explainability.By hypothesizing that deep feature extraction can be modeled as a spatiotemporally continuous process, we implemented a novel deep learning model, Neural ODE, in which deep feature extraction was governed by an ODE parameterized by a neural network. The dynamics of (1) MR images after interactions with the deep neural network and (2) segmentation formation can thus be visualized after solving the ODE. An accumulative contribution curve (ACC) was designed to quantitatively evaluate each MR image's utilization by the deep neural network toward the final segmentation results. The proposed Neural ODE model was demonstrated using 369 glioma patients with a 4-modality multi-parametric MRI protocol: T1, contrast-enhanced T1 (T1-Ce), T2, and FLAIR. Three Neural ODE models were trained to segment enhancing tumor (ET), tumor core (TC), and whole tumor (WT), respectively. The key MRI modalities with significant utilization by deep neural networks were identified based on ACC analysis. Segmentation results by deep neural networks using only the key MRI modalities were compared to those using all four MRI modalities in terms of Dice coefficient, accuracy, sensitivity, and specificity.All Neural ODE models successfully illustrated image dynamics as expected. ACC analysis identified T1-Ce as the only key modality in ET and TC segmentations, while both FLAIR and T2 were key modalities in WT segmentation. Compared to the U-Net results using all four MRI modalities, the Dice coefficient of ET (0.784→0.775), TC (0.760→0.758), and WT (0.841→0.837) using the key modalities only had minimal differences without significance. Accuracy, sensitivity, and specificity results demonstrated the same patterns.The Neural ODE model offers a new tool for optimizing the deep learning model inputs with enhanced explainability. The presented methodology can be generalized to other medical image-related deep-learning applications. DA - 2023/3/2/ PY - 2023/3/2/ DO - 10.1002/mp.16286 VL - 3 SP - SN - 2473-4209 KW - deep learning KW - explainability KW - glioma segmentation KW - neural ODE KW - visualization ER - TY - JOUR TI - Vertical autofocus for the phase screen in a turbulent ionosphere AU - Gilman, Mikhail AU - Tsynkov, Semyon T2 - INVERSE PROBLEMS AB - Abstract The performance of spaceborne synthetic aperture radars (SARs) is affected by the Earth’s ionosphere. In particular, the ionospheric turbulence causes phase perturbations of the SAR signals, which may lead to image distortions. A convenient way to model those phase perturbations is by means of a phase screen. The latter is an infinitesimally thin layer positioned at a certain elevation above the Earth’s surface. The radar signal acquires an instant perturbation once its trajectory intersects the screen. The trajectory is a ray between the antenna and the target, and the magnitude of the perturbation is equal to the screen density at the intersection point. The density is a bivariate function of the coordinates along the screen. The coordinates of a specific intersection point are determined by the ray itself, as well as the screen elevation. Thus, the magnitude of the phase perturbation explicitly depends on the screen elevation. Accordingly, to compensate for the resulting image distortions one should be able to determine the elevation of the screen. In the paper, we develop an algorithm of vertical autofocus that derives this elevation from the received SAR data, given a pair of point scatterers in the target area. The proposed algorithm exploits a modification of the coherent interferometric imaging that was previously employed to reduce the effect of phase errors due to the trajectory uncertainty. In our analysis, we highlight the differences between this case and transionospheric propagation. DA - 2023/4/1/ PY - 2023/4/1/ DO - 10.1088/1361-6420/acb8d6 VL - 39 IS - 4 SP - SN - 1361-6420 KW - spaceborne synthetic aperture radar KW - coherent interferometric (CINT) imaging KW - phase screen elevation ER - TY - JOUR TI - Q-Kostka polynomials and spin Green polynomials AU - Jiang, Anguo AU - Jing, Naihuan AU - Liu, Ning T2 - MONATSHEFTE FUR MATHEMATIK AB - We study the Q-Kostka polynomials $$L_{\lambda \mu }(t)$$ by the vertex operator realization of the Q-Hall–Littlewood functions $$G_{\lambda }(x;t)$$ and derive new formulae for $$L_{\lambda \mu }(t)$$ . In particular, we have established stability property for the Q-Kostka polynomials. We also introduce spin Green polynomials $$Y^{\lambda }_{\mu }(t)$$ as both an analogue of the Green polynomials and deformation of the spin irreducible characters of $$\mathfrak S_n$$ . Iterative formulas of the spin Green polynomials are given and some favorable properties parallel to the Green polynomials are obtained. Tables of $$Y^{\lambda }_{\mu }(t)$$ are included for $$n\le 7.$$ DA - 2023/3/20/ PY - 2023/3/20/ DO - 10.1007/s00605-023-01843-0 VL - 3 SP - SN - 1436-5081 UR - https://doi.org/10.1007/s00605-023-01843-0 KW - Kostka polynomials KW - Hall-Littlewood polynomials KW - Schur's Q-polynomials KW - Projective characters ER - TY - JOUR TI - Toroidal integer homology three-spheres have irreducible SU(2)$SU(2)$-representations AU - Lidman, Tye AU - Pinzon-Caicedo, Juanita AU - Zentner, Raphael T2 - JOURNAL OF TOPOLOGY AB - Abstract We prove that if an integer homology three‐sphere contains an embedded incompressible torus, then its fundamental group admits irreducible ‐representations. DA - 2023/3// PY - 2023/3// DO - 10.1112/topo.12275 VL - 16 IS - 1 SP - 344-367 SN - 1753-8424 ER - TY - JOUR TI - Discrete Hamiltonian Variational Mechanics and Hamel's Integrators (vol 33, 26, 2023) AU - Gao, Shan AU - Shi, Donghua AU - Zenkov, Dmitry V. T2 - JOURNAL OF NONLINEAR SCIENCE DA - 2023/4// PY - 2023/4// DO - 10.1007/s00332-023-09890-5 VL - 33 IS - 2 SP - SN - 1432-1467 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. A. AU - Stabell, Adam AU - Ramos, Raul AU - Plikus, Maksim V. V. AU - Atwood, Scott X. X. AU - Nie, Qing T2 - NATURE METHODS AB - Spatial transcriptomic technologies and spatially annotated single-cell RNA sequencing datasets provide unprecedented opportunities to dissect cell-cell communication (CCC). However, incorporation of the spatial information and complex biochemical processes required in the reconstruction of CCC remains a major challenge. Here, we present COMMOT (COMMunication analysis by Optimal Transport) to infer CCC in spatial transcriptomics, which accounts for the competition between different ligand and receptor species as well as spatial distances between cells. A collective optimal transport method is developed to handle complex molecular interactions and spatial constraints. Furthermore, we introduce downstream analysis tools to infer spatial signaling directionality and genes regulated by signaling using machine learning models. We apply COMMOT to simulation data and eight spatial datasets acquired with five different technologies to show its effectiveness and robustness in identifying spatial CCC in data with varying spatial resolutions and gene coverages. Finally, COMMOT identifies new CCCs during skin morphogenesis in a case study of human epidermal development. DA - 2023/1/23/ PY - 2023/1/23/ DO - 10.1038/s41592-022-01728-4 VL - 1 SP - SN - 1548-7105 UR - https://doi.org/10.1038/s41592-022-01728-4 ER - TY - JOUR TI - A diffuse-domain-based numerical method for a chemotaxis-fluid model AU - Wang, Chenxi AU - Chertock, Alina AU - Cui, Shumo AU - Kurganov, Alexander AU - Zhang, Zhen T2 - MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES AB - In this paper, we consider a coupled chemotaxis-fluid system that models self-organized collective behavior of oxytactic bacteria in a sessile drop. This model describes the biological chemotaxis phenomenon in the fluid environment and couples a convective chemotaxis system for the oxygen-consuming and oxytactic bacteria with the incompressible Navier–Stokes equations subject to a gravitational force, which is proportional to the relative surplus of the cell density compared to the water density. We develop a new positivity preserving and high-resolution method for the studied chemotaxis-fluid system. Our method is based on the diffuse-domain approach, which we use to derive a new chemotaxis-fluid diffuse-domain (cf-DD) model for simulating bioconvection in complex geometries. The drop domain is imbedded into a larger rectangular domain, and the original boundary is replaced by a diffuse interface with finite thickness. The original chemotaxis-fluid system is reformulated on the larger domain with additional source terms that approximate the boundary conditions on the physical interface. We show that the cf-DD model converges to the chemotaxis-fluid model asymptotically as the width of the diffuse interface shrinks to zero. We numerically solve the resulting cf-DD system by a second-order hybrid finite-volume finite-difference method and demonstrate the performance of the proposed approach on a number of numerical experiments that showcase several interesting chemotactic phenomena in sessile drops of different shapes, where the bacterial patterns depend on the droplet geometries. DA - 2023/2/23/ PY - 2023/2/23/ DO - 10.1142/S0218202523500094 VL - 2 SP - SN - 1793-6314 KW - Chemotaxis KW - Navier-Stokes equations KW - bioconvection KW - diffuse-domain approach KW - finite-volume method KW - finite-difference method ER - TY - JOUR TI - MONTE CARLO METHODS FOR ESTIMATING THE DIAGONAL OF A REAL SYMMETRIC MATRIX AU - Hallman, Eric AU - Ipsen, Ilse C. F. AU - Saibaba, Arvind K. T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS AB - For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte Carlo estimators based on random Rademacher, sparse Rademacher, and normalized and unnormalized Gaussian vectors and to vectors with bounded fourth moments. The novel use of matrix concentration inequalities in our proofs represents a systematic model for future analyses. Our bounds mostly do not depend explicitly on the matrix dimension, target different error measures than existing work, and imply that the accuracy of the estimators increases with the diagonal dominance of the matrix. Applications to derivative-based global sensitivity metrics and node centrality measures in network science corroborate this, as do numerical experiments on synthetic test matrices. We recommend against the use in practice of sparse Rademacher vectors, which are the basis for many randomized sketching and sampling algorithms, because they tend to deliver barely a digit of accuracy even under large sampling amounts. DA - 2023/// PY - 2023/// DO - 10.1137/22M1476277 VL - 44 IS - 1 SP - 240-269 SN - 1095-7162 UR - https://doi.org/10.1137/22M1476277 KW - concentration inequalities KW - Monte Carlo methods KW - relative error KW - Rademacher random vectors KW - Gaussian random vectors ER - TY - JOUR TI - Radial and non-radial multiple solutions to a general mixed dispersion NLS equation AU - d'Avenia, Pietro AU - Pomponio, Alessio AU - Schino, Jacopo T2 - NONLINEARITY AB - We study the following nonlinear Schr\"odinger equation with a forth order dispersion term \[ \Delta^2u-\beta\Delta u=g(u) \quad \text{in } \mathbb{R}^N \] in the positive and zero mass regimes: in the former, $N\geq 2$ and $\beta > -2\sqrt{m}$, where $m>0$ depends on $g$; in the latter, $N\geq 3$ and $\beta>0$. In either regimes, we find an infinite sequence of solutions under rather generic assumptions about $g$; if $N=2$ in the positive mass case, or $N=4$ in the zero mass case, we need to strengthen such assumptions. Our approach is variational. DA - 2023/3/1/ PY - 2023/3/1/ DO - 10.1088/1361-6544/acb62d VL - 36 IS - 3 SP - 1743-1775 SN - 1361-6544 KW - Bilaplacian KW - mixed-dispersion Schrodinger equation KW - standing wave solutions KW - multiple solutions KW - positive mass case KW - zero mass case KW - radial and non-radial solutions ER - TY - JOUR TI - Conormal Spaces and Whitney Stratifications (Jun, 10.1007/ s10208-022-09574- 8, 2022) AU - Helmer, Martin AU - Nanda, Vidit T2 - FOUNDATIONS OF COMPUTATIONAL MATHEMATICS AB - Abstract This note remedies an error in our paper tilted Conormal Spaces and Whitney Stratifications (Found. Comput. Math., 2022). DA - 2023/2/1/ PY - 2023/2/1/ DO - 10.1007/s10208-022-09602-7 SP - SN - 1615-3383 ER - TY - JOUR TI - A simple model for viral decay dynamics and the distribution of infected cell life spans in SHIV-infected infant rhesus macaques AU - Sass, Julian AU - Awasthi, Achal AU - Obregon-Perko, Veronica AU - McCarthy, Janice AU - Lloyd, Alun L. AU - Chahroudi, Ann AU - Permar, Sallie AU - Chan, Cliburn T2 - MATHEMATICAL BIOSCIENCES AB - The dynamics of HIV viral load following the initiation of antiretroviral therapy is not well-described by simple, single-phase exponential decay. Several mathematical models have been proposed to describe its more complex behavior, the most popular of which is two-phase exponential decay. The underlying assumption in two-phase exponential decay is that there are two classes of infected cells with different lifespans. However, with the exception of CD4+ T cells, there is not a consensus on all of the cell types that can become productively infected, and the fit of the two-phase exponential decay to observed data from SHIV.C.CH505 infected infant rhesus macaques was relatively poor. Therefore, we propose a new model for viral decay, inspired by the Gompertz model where the decay rate itself is a dynamic variable. We modify the Gompertz model to include a linear term that modulates the decay rate. We show that this simple model performs as well as the two-phase exponential decay model on HIV and SIV data sets, and outperforms it for the infant rhesus macaque SHIV.C.CH505 infection data set. We also show that by using a stochastic differential equation formulation, the modified Gompertz model can be interpreted as being driven by a population of infected cells with a continuous distribution of cell lifespans, and estimate this distribution for the SHIV.C.CH505-infected infant rhesus macaques. Thus, we find that the dynamics of viral decay in this model of infant HIV infection and treatment may be explained by a distribution of cell lifespans, rather than two distinct cell types. DA - 2023/2// PY - 2023/2// DO - 10.1016/j.mbs.2022.108958 VL - 356 SP - SN - 1879-3134 KW - Modified Gompertz model KW - HIV viral decay KW - SHIV KW - Stochastic modeling KW - Infected cell lifespan KW - Uncertainty quantification ER - TY - JOUR TI - Evaluation of an open forecasting challenge to assess skill of West Nile virus neuroinvasive disease prediction AU - Holcomb, Karen M. M. AU - Mathis, Sarabeth AU - Staples, J. Erin AU - Fischer, Marc AU - Barker, Christopher M. M. AU - Beard, Charles B. B. AU - Nett, Randall J. J. AU - Keyel, Alexander C. C. AU - Marcantonio, Matteo AU - Childs, Marissa L. L. AU - Gorris, Morgan E. E. AU - Rochlin, Ilia AU - Hamins-Puertolas, Marco AU - Ray, Evan L. L. AU - Uelmen, Johnny A. A. AU - DeFelice, Nicholas AU - Freedman, Andrew S. S. AU - Hollingsworth, Brandon D. D. AU - Das, Praachi AU - Osthus, Dave AU - Humphreys, John M. M. AU - Nova, Nicole AU - Mordecai, Erin A. A. AU - Cohnstaedt, Lee W. W. AU - Kirk, Devin AU - Kramer, Laura D. D. AU - Harris, Mallory J. J. AU - Kain, Morgan P. P. AU - Reed, Emily M. X. AU - Johansson, Michael A. A. T2 - PARASITES & VECTORS AB - West Nile virus (WNV) is the leading cause of mosquito-borne illness in the continental USA. WNV occurrence has high spatiotemporal variation, and current approaches to targeted control of the virus are limited, making forecasting a public health priority. However, little research has been done to compare strengths and weaknesses of WNV disease forecasting approaches on the national scale. We used forecasts submitted to the 2020 WNV Forecasting Challenge, an open challenge organized by the Centers for Disease Control and Prevention, to assess the status of WNV neuroinvasive disease (WNND) prediction and identify avenues for improvement.We performed a multi-model comparative assessment of probabilistic forecasts submitted by 15 teams for annual WNND cases in US counties for 2020 and assessed forecast accuracy, calibration, and discriminatory power. In the evaluation, we included forecasts produced by comparison models of varying complexity as benchmarks of forecast performance. We also used regression analysis to identify modeling approaches and contextual factors that were associated with forecast skill.Simple models based on historical WNND cases generally scored better than more complex models and combined higher discriminatory power with better calibration of uncertainty. Forecast skill improved across updated forecast submissions submitted during the 2020 season. Among models using additional data, inclusion of climate or human demographic data was associated with higher skill, while inclusion of mosquito or land use data was associated with lower skill. We also identified population size, extreme minimum winter temperature, and interannual variation in WNND cases as county-level characteristics associated with variation in forecast skill.Historical WNND cases were strong predictors of future cases with minimal increase in skill achieved by models that included other factors. Although opportunities might exist to specifically improve predictions for areas with large populations and low or high winter temperatures, areas with high case-count variability are intrinsically more difficult to predict. Also, the prediction of outbreaks, which are outliers relative to typical case numbers, remains difficult. Further improvements to prediction could be obtained with improved calibration of forecast uncertainty and access to real-time data streams (e.g. current weather and preliminary human cases). DA - 2023/1/12/ PY - 2023/1/12/ DO - 10.1186/s13071-022-05630-y VL - 16 IS - 1 SP - SN - 1756-3305 KW - Calibration KW - Discriminatory power KW - Forecasting KW - Logarithmic score KW - Multi-model assessment KW - West Nile virus KW - West Nile neuroinvasive disease KW - United States ER - TY - JOUR TI - Physical models of notochord cell packing reveal how tension ratios determine morphometry AU - Curcio, Evan J. AU - Lubkin, Sharon R. T2 - CELLS & DEVELOPMENT AB - The physical and geometric aspects of notochords are investigated using a model of finite-length notochords, with interior vacuolated cells arranged in two common packing configurations, and sheath modeled as homogeneous and thin. The key ratios governing packing patterns and eccentricity are number of cells per unit length λ and cell tension ratio Γ. By analyzing simulations that vary Γ and total number of cells N, we find that eccentricity, λ, and internal pressure approach consistent asymptotic values away from the tapering ends, as N increases. The length of the tapering ends is quantified as a function of Γ and pattern. Formulas are derived for geometric ratios, pressure, and energy as functions of Γ and pattern. These observations on the relationship between mechanics, geometry, and pattern provide a framework for further work which may provide insight into the roles of mechanosensing and pressure-volume regulation in the notochord. DA - 2023/3// PY - 2023/3// DO - 10.1016/j.cdev.2023.203825 VL - 173 SP - SN - 2667-2901 KW - Notochord KW - Foams KW - Biomechanics KW - Cell packing KW - Sheath tension KW - Modeling ER - TY - JOUR TI - Identifiability of linear compartmental tree models and a general formula for input-output equations AU - Bortner, Cashous AU - Gross, Elizabeth AU - Meshkat, Nicolette AU - Shiu, Anne AU - Sullivant, Seth T2 - ADVANCES IN APPLIED MATHEMATICS AB - A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable – that is, whether parameter values can be inferred from noiseless data – directly from the combinatorics of the model. Our main result completely answers this question for models (with one input and one output) in which the underlying graph is a bidirectional tree; moreover, identifiability of such models can be verified visually. Models of this structure include two families of models often appearing in biological applications: catenary and mammillary models. Our analysis of such models is enabled by two supporting results, which are significant in their own right. One result gives the first general formula for the coefficients of input-output equations (certain equations that can be used to determine identifiability) that allows for input and output to be in distinct compartments. In another supporting result, we prove that identifiability is preserved when a model is enlarged and altered in specific ways involving adding a new compartment with a bidirected edge to an existing compartment. DA - 2023/5// PY - 2023/5// DO - 10.1016/j.aam.2023.102490 VL - 146 SP - SN - 1090-2074 ER - TY - JOUR TI - A mathematical method and software for spatially mapping intercellular communication AU - Cang, Zixuan AU - Nie, Qing T2 - NATURE METHODS DA - 2023/1/24/ PY - 2023/1/24/ DO - 10.1038/s41592-022-01729-3 VL - 1 SP - SN - 1548-7105 ER - TY - JOUR TI - On the Canham Problem: Bending Energy Minimizers for any Genus and Isoperimetric Ratio AU - Kusner, Robert AU - McGrath, Peter T2 - ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS AB - Building on work of Mondino–Scharrer, we show that among closed, smoothly embedded surfaces in $${\mathbb {R}}^3$$ of genus g and given isoperimetric ratio v, there exists one with minimum bending energy $${\mathcal {W}}$$ . We do this by gluing $$g+1$$ small catenoidal bridges to the bigraph of a singular solution for the linearized Willmore equation $$\Delta (\Delta +2)\varphi =0$$ on the $$(g+1)$$ -punctured sphere $${\mathbb {S}}^2$$ to construct a comparison surface of genus g with arbitrarily small isoperimetric ratio $$v\in (0, 1)$$ and $${\mathcal {W}}< 8\pi $$ . DA - 2023/2// PY - 2023/2// DO - 10.1007/s00205-022-01833-w VL - 247 IS - 1 SP - SN - 1432-0673 ER - TY - JOUR TI - A new perspective on parameter study of optimization problems AU - Alexanderian, Alen AU - Hart, Joseph AU - Stevens, Mason T2 - APPLIED MATHEMATICS LETTERS AB - We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equations to quantify the uncertainty in the minimizer due to uncertain parameters in the optimization problem. We illustrate the proposed approach with a simple analytic example and an inverse problem governed by an advection diffusion equation. DA - 2023/6// PY - 2023/6// DO - 10.1016/j.aml.2022.108548 VL - 140 SP - SN - 1873-5452 KW - Optimization KW - Post-optimal sensitivity analysis KW - Inverse problems ER - TY - JOUR TI - Certified Hermite matrices from approximate roots AU - Akoglu, Tulay Ayyildiz AU - Szanto, Agnes T2 - JOURNAL OF SYMBOLIC COMPUTATION AB - Let I=〈f1,…,fm〉⊂Q[x1,…,xn] be a zero dimensional radical ideal defined by polynomials given with exact rational coefficients. Assume that we are given approximations {z1,…,zk}⊂Cn for the common roots {ξ1,…,ξk}=V(I)⊆Cn. In this paper we show how to construct and certify the rational entries of Hermite matrices for I from the approximate roots {z1,…,zk}. When I is non-radical, we give methods to construct and certify Hermite matrices for I from the approximate roots. Furthermore, we use signatures of these Hermite matrices to give rational certificates of non-negativity of a given polynomial over a (possibly positive dimensional) real variety, as well as certificates that there is a real root within an ε distance from a given point z∈Qn. DA - 2023/// PY - 2023/// DO - 10.1016/j.jsc.2022.12.001 VL - 117 SP - 101-118 SN - 1095-855X KW - Symbolic-numeric computation KW - Polynomial systems KW - Approximate roots KW - Hermite matrices KW - Certification ER - TY - JOUR TI - A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization with MGARCH and Small Transaction Costs AU - Papanicolaou, Andrew AU - Fu, Hao AU - Krishnamurthy, Prashanth AU - Khorrami, Farshad T2 - IEEE Access AB - We analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on trading. A numerical solution is obtained using a neural network (NN) architecture within a recursive RL loop. A fixed-point theorem proves that NN approximation error has a big-oh bound that we can reduce by increasing the number of NN parameters. The functional form of the trading penalty has a parameter ϵ > 0 that controls the magnitude of transaction costs. When ϵ is small, we can implement an NN algorithm based on the expansion of the solution in powers of ϵ. This expansion has a base term equal to a myopic solution with an explicit form, and a first-order correction term that we compute in the RL loop. Our expansion-based algorithm is stable, allows for fast computation, and outputs a solution that shows positive testing performance. DA - 2023/// PY - 2023/// DO - 10.1109/ACCESS.2023.3245570 SP - 1-1 J2 - IEEE Access OP - SN - 2169-3536 UR - http://dx.doi.org/10.1109/ACCESS.2023.3245570 DB - Crossref ER - TY - JOUR TI - Sharing quantum nonlocality in star network scenarios AU - Zhang, Tinggui AU - Jing, Naihuan AU - Fei, Shao-Ming T2 - FRONTIERS OF PHYSICS AB - The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under bilateral measurements. For the star network scenarios, we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states, for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality. DA - 2023/6// PY - 2023/6// DO - 10.1007/s11467-022-1242-6 VL - 18 IS - 3 SP - SN - 2095-0470 KW - Bell nonlocality KW - quantum network KW - nonlocality sharing KW - POVM measurements ER - TY - JOUR TI - Strands algebras and the affine highest weight property for equivariant hypertoric categories AU - Lauda, Aaron D. AU - Licata, Anthony M. AU - Manion, Andrew T2 - ADVANCES IN MATHEMATICS AB - We show that the equivariant hypertoric convolution algebras introduced by Braden-Licata-Proudfoot-Webster are affine quasi hereditary in the sense of Kleshchev and compute the Ext groups between standard modules. Together with the main result of arXiv:2009.03981, this implies a number of new homological results about the bordered Floer algebras of Ozsvath-Szabo, including the existence of standard modules over these algebras. We prove that the Ext groups between standard modules are isomorphic to the homology of a variant of the Lipshitz-Ozsvath-Thurston bordered strands dg algebras. DA - 2023/1/15/ PY - 2023/1/15/ DO - 10.1016/j.aim.2022.108849 VL - 413 SP - SN - 1090-2082 KW - Hypertoric variety KW - Categorification KW - gl(1 KW - 1) KW - Hyperplane arrangement KW - Bordered Heegaard-Floer homology ER - TY - JOUR TI - Recovering a function from its integrals over conical surfaces through relations with the Radon transform AU - Terzioglu, Fatma T2 - INVERSE PROBLEMS AB - Abstract This paper addresses the overdetermined problem of inverting the n -dimensional cone (or Compton) transform that integrates a function over conical surfaces in R n . The study of the cone transform originates from Compton camera imaging, a nuclear imaging method for the passive detection of gamma-ray sources. We present a new identity relating the n -dimensional cone and Radon transforms through spherical convolutions with arbitrary weight functions. This relationship, which generalizes a previously obtained identity, leads to various inversion formulas in n -dimensions under a mild assumption on the geometry of detectors. We present two such formulas along with the results of their numerical implementation using synthetic phantoms. Compared to our previously discovered inversion techniques, the new formulas are more stable and simpler to implement numerically. DA - 2023/2/1/ PY - 2023/2/1/ DO - 10.1088/1361-6420/acad24 VL - 39 IS - 2 SP - SN - 1361-6420 KW - cone transform KW - inversion KW - exact KW - Compton camera KW - reconstruction ER - TY - JOUR TI - On monogamy and polygamy relations of multipartite systems AU - Zhang, Xia AU - Jing, Naihuan AU - Liu, Ming AU - Ma, Haitao T2 - PHYSICA SCRIPTA AB - Abstract We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy relations for the r -power of the measure. We show in a uniformed manner that the generalized monogamy and polygamy relations are transitive to other powers of the measure in weighted forms We demonstrate that our weighted monogamy and polygamy relations are stronger than recently available relations. Comparisons are given in detailed examples which show that our results are stronger in both situations. DA - 2023/3/1/ PY - 2023/3/1/ DO - 10.1088/1402-4896/acbb37 VL - 98 IS - 3 SP - SN - 1402-4896 UR - https://doi.org/10.1088/1402-4896/acbb37 KW - monogamy KW - polygamy KW - entanglement ER - TY - JOUR TI - Quantum N-toroidal Algebras and Extended Quantized GIM Algebras of N-fold Affinization AU - Gao, Yun AU - Jing, Naihuan AU - Xia, Limeng AU - Zhang, Honglian T2 - COMMUNICATIONS IN MATHEMATICS AND STATISTICS AB - We introduce the notion of quantum N-toroidal algebras as natural generalization of the quantum toroidal algebras as well as extended quantized GIM algebras of N-fold affinization. We show that the quantum N-toroidal algebras are quotients of the extended quantized GIM algebras of N-fold affinization, which generalizes a well-known result of Berman and Moody for Lie algebras. DA - 2023/2/10/ PY - 2023/2/10/ DO - 10.1007/s40304-022-00316-4 VL - 2 SP - SN - 2194-671X UR - https://doi.org/10.1007/s40304-022-00316-4 KW - Generalized intersection matrix KW - Quantized GIM algebra KW - Quantum 2-toroidal algebra KW - Quantum N-toroidal algebra ER - TY - JOUR TI - The geometry of adversarial training in binary classification AU - Bungert, Leon AU - Trillos, Nicolas Garcia AU - Murray, Ryan T2 - INFORMATION AND INFERENCE-A JOURNAL OF THE IMA AB - We establish an equivalence between a family of adversarial training problems for non-parametric binary classification and a family of regularized risk minimization problems where the regularizer is a nonlocal perimeter functional. The resulting regularized risk minimization problems admit exact convex relaxations of the type $L^1+$ (nonlocal) $\operatorname{TV}$, a form frequently studied in image analysis and graph-based learning. A rich geometric structure is revealed by this reformulation which in turn allows us to establish a series of properties of optimal solutions of the original problem, including the existence of minimal and maximal solutions (interpreted in a suitable sense), and the existence of regular solutions (also interpreted in a suitable sense). In addition, we highlight how the connection between adversarial training and perimeter minimization problems provides a novel, directly interpretable, statistical motivation for a family of regularized risk minimization problems involving perimeter/total variation. The majority of our theoretical results are independent of the distance used to define adversarial attacks. DA - 2023/1/13/ PY - 2023/1/13/ DO - 10.1093/imaiai/iaac029 VL - 1 SP - SN - 2049-8772 KW - adversarial training KW - nonlocal perimeter KW - nonlocal total variation KW - existence of solutions KW - regularity ER - TY - JOUR TI - A Quasi-Monte Carlo Method With Krylov Linear Solvers for Multigroup Neutron Transport Simulations AU - Pasmann, Sam AU - Variansyah, Ilham AU - Kelley, C. T. AU - McClarren, Ryan T2 - NUCLEAR SCIENCE AND ENGINEERING AB - In this work we investigate replacing standard quadrature techniques used in deterministic linear solvers with a fixed-seed Quasi–Monte Carlo (QMC) calculation to obtain more accurate and efficient solutions to the neutron transport equation (NTE). QMC is the use of low-discrepancy sequences to sample the phase-space in place of pseudorandom number generators used by traditional Monte Carlo (MC). QMC techniques decrease the variance in the stochastic transport sweep and therefore increase the accuracy of the iterative method. Historically, QMC has largely been ignored by the particle transport community because it breaks the Markovian assumption needed to model scattering in analog MC particle simulations. However, by using iterative methods the NTE can be modeled as a pure-absorption problem. This removes the need to explicitly model particle scattering and provides an application well suited for QMC. To obtain solutions we experimented with three separate iterative solvers: the standard Source Iteration (SI) Solver and two linear Krylov Solvers, i.e., the Generalized Minimal RESidual method (GMRES) and the BiConjugate Gradient STABilized method (BiCGSTAB). The resulting hybrid iterative-QMC solver was assessed on three slab geometry problems of one dimension. In each sample problem the Krylov Solvers achieve convergence with far fewer iterations (up to eight times) than the SI Solver. Regardless of the linear solver used, the hybrid method achieved an approximate convergence rate of O(N−1) as compared to the expected O(N−1/2) of traditional MC simulation across all test problems. DA - 2023/1/13/ PY - 2023/1/13/ DO - 10.1080/00295639.2022.2143704 VL - 1 SP - SN - 1943-748X KW - Neutron transport KW - Monte Carlo methods KW - Quasi-Monte Carlo KW - Krylov linear Solvers ER - TY - JOUR TI - An efficient extrapolation multigrid method based on a HOC scheme on nonuniform rectilinear grids for solving 3D anisotropic convection-diffusion problems AU - Hu, Shuanggui AU - Pan, Kejia AU - Wu, Xiaoxin AU - Ge, Yongbin AU - Li, Zhilin T2 - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING AB - We develop an efficient multigrid method combined with a high-order compact (HOC) finite difference scheme on nonuniform rectilinear grids for solving 3D diagonal anisotropic convection–diffusion problems with boundary/interior layers. Firstly, we derive a fourth-order compact finite difference scheme to discretize the 3D anisotropic convection–diffusion equation on a rectilinear grid. Then, the resulting large-scale asymmetric linear system of equations is solved by a generalized extrapolation cascadic multigrid (gEXCMG) method based on two novel multigrid (MG) prolongation operators. The highlight of this paper is the application of the quintic Lagrange interpolation and the completed Richardson extrapolation in the design of the new MG prolongation operator on nonuniform rectilinear grids, which can produce a good initial guess (sixth-order approximation to the finite difference solution) for the SSOR-preconditioned biconjugate gradient stabilized (BiCGStab) smoother. In the end, numerical experiments show that the gEXCMG method combined with the HOC scheme can achieve fourth-order accuracy for 3D anisotropic convection–diffusion problems with few smoothing steps on the finest grid. Moreover, the proposed gEXCMG method can offer substantially better efficiency than the state-of-the-art algebraic MG solver, namely, aggregation-based algebraic multigrid (AGMG) method, for large linear systems arising from the discretization of second order elliptic PDEs. DA - 2023/1/1/ PY - 2023/1/1/ DO - 10.1016/j.cma.2022.115724 VL - 403 SP - SN - 1879-2138 KW - Convection-diffusion equation KW - Completed Richardson extrapolation KW - Quintic Lagrange interpolation KW - High-order compact scheme KW - Cascadic multigrid ER - TY - JOUR TI - Discrete Hamiltonian Variational Mechanics and Hamel's Integrators AU - Gao, Shan AU - Shi, Donghua AU - Zenkov, Dmitry V. T2 - JOURNAL OF NONLINEAR SCIENCE DA - 2023/4// PY - 2023/4// DO - 10.1007/s00332-022-09875-w VL - 33 IS - 2 SP - SN - 1432-1467 KW - Exact integrators KW - Hamel's equations KW - Nonholonomic systems KW - Momentum KW - Symmetry ER - TY - JOUR TI - O-operators and related structures on Leibniz algebras AU - Sun, Qinxiu AU - Jing, Naihuan T2 - COMMUNICATIONS IN ALGEBRA AB - An $\mathcal{O}$-operator has been used to extend a Leibniz algebra by its representation. In this paper, we investigate several structures related to $\mathcal{O}$-operators on Leibniz algebras and introduce (dual) $\mathcal{O}$N-structures on Leibniz algebras associated to their representations. It is proved that $\mathcal{O}$-operators and dual $\mathcal{O}$N-structures generate each other under certain conditions. It is also shown that a solution of the strong Maurer-Cartan equation on the twilled Leibniz algebra gives rise to a dual $\mathcal{O}$N-structure. Finally, $r-n$ structures, RBN-structures and $\mathcal{B}N$-structures on Leibniz algebras are thoroughly studied and their interdependent relations are also studied. DA - 2023/1/4/ PY - 2023/1/4/ DO - 10.1080/00927872.2022.2154783 VL - 1 SP - SN - 1532-4125 KW - BN-structure KW - (dual) ON-structure KW - Leibniz algebra KW - Maurer-Cartan equation KW - O-operator KW - r - n structure KW - RBN-structure ER - TY - JOUR TI - Generic Properties of First-Order Mean Field Games AU - Bressan, Alberto AU - Nguyen, Khai T. T. T2 - DYNAMIC GAMES AND APPLICATIONS AB - We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. the control. Existence, uniqueness, and stability of solutions are studied from the point of view of generic theory. Within a suitable topological space of dynamics and cost functionals, we prove that, for “nearly all” mean field games (in the Baire category sense) the best reply map is single-valued for a.e. player. As a consequence, the mean field game admits a strong (not randomized) solution. Examples are given of open sets of games admitting a single solution, and other open sets admitting multiple solutions. Further examples show the existence of an open set of MFG having a unique solution which is asymptotically stable w.r.t. the best reply map, and another open set of MFG having a unique solution which is unstable. We conclude with an example of a MFG with terminal constraints which does not have any solution, not even in the mild sense with randomized strategies. DA - 2023/1/2/ PY - 2023/1/2/ DO - 10.1007/s13235-022-00487-3 VL - 1 SP - SN - 2153-0793 ER - TY - JOUR TI - Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems AU - Dong, Baiying AU - Li, Zhilin AU - Ruiz-Álvarez, Juan T2 - Research Reports on Computer Science AB - In this paper, third-order compact and fourth-order finite element methods (FEMs) based on simple modifications of traditional FEMs are proposed for solving one-dimensional Sturm-Liouville boundary value problems (BVPs). The key idea is based on interpolation error estimates. A simple posterior error analysis of the original piecewise linear finite element space leads to a third-order accurate solution in the L2 norm, second-order in the H1, and the energy norm. The novel idea is also applied to obtain a fourth-order FEM based on the quadratic finite element space. The basis functions in the new fourth-order FEM are more compact compared with that of the classic cubic basis functions. Numerical examples presented in this paper have confirmed the convergence order and analysis. A generalization to a class of nonlinear two-point BVPs is also discussed and tested. DA - 2023/1/16/ PY - 2023/1/16/ DO - 10.37256/rrcs.2120232118 UR - https://doi.org/10.37256/rrcs.2120232118 ER - TY - JOUR TI - Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems AU - Dong, Baiying AU - Li, Zhilin AU - Ruiz-Álvarez, Juan T2 - Research Reports on Computer Science DA - 2023/1/16/ PY - 2023/1/16/ DO - 10.37256/rrcs.212023 VL - 2 IS - 1 SP - 15–27 UR - https://ojs.wiserpub.com/index.php/RRCS/article/view/2118 ER - TY - JOUR TI - Controller Design for Distributed Parameter Systems AU - Smith, Ralph C. C. T2 - IEEE CONTROL SYSTEMS MAGAZINE AB - by KIRSTEN A. MORRIS DA - 2023/2// PY - 2023/2// DO - 10.1109/MCS.2022.3216693 VL - 43 IS - 1 SP - 98-100 SN - 1941-000X UR - https://doi.org/10.1109/MCS.2022.3216693 KW - Book reviews KW - Distributed parameter systems KW - Control design KW - State estimation KW - Stability analysis ER - TY - JOUR TI - Well-posedness and ill-posedness of single-phase models for suspensions AU - Barker, T. AU - Gray, J. M. N. T. AU - Schaeffer, D. G. AU - Shearer, M. T2 - JOURNAL OF FLUID MECHANICS AB - Classical theories for suspensions have been formulated by starting from the Navier–Stokes equations describing pure liquid flow and then introducing additional dependencies to account for the presence of suspended particles. These models are often accurate for low particle concentrations but have lacked a convincing description of the frictional interactions of particles, which are important at larger solid volume fractions. The $\mu (J), \varPhi (J)$ rheology, which draws a direct analogy between suspension flow and dry granular flow, is a recent theory that addresses this issue, but is shown here to be dynamically ill-posed for large solid volume fractions. An alternative well-posed theory is introduced that includes additional dependence on the particle-phase dilation and compression. The new theory, denoted vCIDR, is tested numerically to show grid convergence for problems in which the $\mu (J), \varPhi (J)$ rheology instead suffers from catastrophic blow-up. A further well-posed extension provides a framework for handling the transition between viscous and inertial flows. DA - 2023/1/3/ PY - 2023/1/3/ DO - 10.1017/jfm.2022.1004 VL - 954 SP - SN - 1469-7645 UR - https://doi.org/10.1017/jfm.2022.1004 KW - suspensions KW - particle/fluid flow ER - TY - JOUR TI - A Comparison of Mathematical and Statistical Modeling with Longitudinal Data: An Application to Ecological Momentary Assessment of Behavior Change in Individuals with Alcohol Use Disorder AU - Shao, Sijing AU - Canner, Judith E. E. AU - Everett, Rebecca A. AU - Bekele-Maxwell, Kidist AU - Kuerbis, Alexis AU - Stephenson, Lyric AU - Menda, Jennifer AU - Morgenstern, Jon AU - Banks, H. T. T2 - BULLETIN OF MATHEMATICAL BIOLOGY DA - 2023/1// PY - 2023/1// DO - 10.1007/s11538-022-01097-1 VL - 85 IS - 1 SP - SN - 1522-9602 KW - Ecological momentary assessment data KW - Generalized estimating equations KW - Generalized linear mixed models KW - Markov models KW - Generalized linear mixed-effects Markov models KW - Differential equations ER - TY - JOUR TI - Airplane Detection and Classification Based on Mask R-CNN and YOLO with Feature Engineering AU - Attarian, Adam AU - Luo, Minxuan AU - Luo, Yangyang AU - Tran, Hien AU - Xu, Xingfei AU - Yi, Chunxiao AU - Yu, Yahe AU - Zhang, Fa T2 - INTELLIGENT SYSTEMS AND APPLICATIONS, VOL 2 DA - 2023/// PY - 2023/// DO - 10.1007/978-3-031-16078-3_52 VL - 543 SP - 752-768 SN - 2367-3389 KW - Airplane classification KW - Feature engineering KW - Mask R-CNN KW - YOLOv3 ER - TY - JOUR TI - Well-balanced numerical method for atmospheric flow equations with gravity AU - Chertock, Alina AU - Kurganov, Alexander AU - Wu, Tong AU - Yan, Jun T2 - APPLIED MATHEMATICS AND COMPUTATION AB - We are interested in simulating gravitationally stratified atmospheric flows governed by the compressible Euler equations in irregular domains. In such simulations, one of the challenges arises when the computations are conducted on a Cartesian grid. The use of regular rectangular grids that intersect with the irregular boundaries leads to the generation of arbitrarily small and highly distorted computational cells adjacent to the boundaries of the domain. The appearance of such cells may affect both the stability and efficiency of the numerical method and therefore require special attention. In order to overcome this difficulty, we introduce a structured quadrilateral mesh, which is designed for the irregular domain at hand, and solve the studied atmospheric flow equations using a second-order central-upwind scheme. In addition, the resulting numerical method is developed to provide a well-balanced discretization of the underlying system. The latter is achieved by rewriting the governing equations in terms of equilibrium variables representing perturbations of the known background equilibrium state. The proposed method is tested in a number of numerical experiments, including the buoyant bubble rising and interacting with an (zeppelin) obstacle and the Lee wave generation due to topography. The obtained numerical results demonstrate high resolution and robustness of the proposed computational approach. DA - 2023/2/15/ PY - 2023/2/15/ DO - 10.1016/j.amc.2022.127587 VL - 439 SP - SN - 1873-5649 KW - Atmospheric flow equations with gravity KW - Well-balanced central -upwind scheme KW - Equilibrium variables KW - Quadrilateral mesh KW - Irregular domains ER - TY - JOUR TI - Exact solutions in log-concave maximum likelihood estimation AU - Grosdos, Alexandros AU - Heaton, Alexander AU - Kubjas, Kaie AU - Kuznetsova, Olga AU - Scholten, Georgy AU - Sorea, Miruna-Stefana T2 - ADVANCES IN APPLIED MATHEMATICS AB - We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many quantities, namely the function values, or heights, at the data points. We explore in what sense exact solutions to this problem are possible. First, we show that the heights given by the maximum likelihood estimate are generically transcendental. For a cell in one dimension, the maximum likelihood estimator is expressed in closed form using the generalized W-Lambert function. Even more, we show that finding the log-concave maximum likelihood estimate is equivalent to solving a collection of polynomial-exponential systems of a special form. Even in the case of two equations, very little is known about solutions to these systems. As an alternative, we use Smale's α-theory to refine approximate numerical solutions and to certify solutions to log-concave density estimation. DA - 2023/2// PY - 2023/2// DO - 10.1016/j.aam.2022.102448 VL - 143 SP - SN - 1090-2074 KW - Transcendence theory KW - Smale?s ?-theory KW - Lambert functions KW - Polyhedral subdivisions KW - Log-concavity KW - Maximum likelihood estimation KW - Polynomial-exponential systems KW - Certified solutions ER - TY - JOUR TI - Local characteristic decomposition based central-upwind scheme AU - Chertock, Alina AU - Chu, Shaoshuai AU - Herty, Michael AU - Kurganov, Alexander AU - Lukacova-Medvid'ova, Maria T2 - JOURNAL OF COMPUTATIONAL PHYSICS AB - We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the studied systems come from the complicated wave structures, such as shocks, rarefactions and contact discontinuities, arising even for smooth initial conditions. In order to reduce the diffusion in the original central-upwind schemes, we use a local characteristic decomposition procedure to develop a new class of central-upwind schemes. We apply the developed schemes to the one- and two-dimensional Euler equations of gas dynamics to illustrate the performance on a variety of examples. The obtained numerical results clearly demonstrate that the proposed new schemes outperform the original central-upwind schemes. DA - 2023/1/15/ PY - 2023/1/15/ DO - 10.1016/j.jcp.2022.111718 VL - 473 SP - SN - 1090-2716 KW - Local characteristic decomposition KW - Central-upwind schemes KW - Hyperbolic systems of conservative laws KW - Euler equations of gas dynamics ER - TY - JOUR TI - On mixing behavior of a family of random walks determined by a linear recurrence AU - Stanley, Caprice AU - Sullivant, Seth T2 - DISCRETE MATHEMATICS AB - We study random walks on the integers mod Gn that are determined by an integer sequence {Gn}n≥1 generated by a linear recurrence relation. Fourier analysis provides explicit formulas to compute the eigenvalues of the transition matrices and we use this to bound the mixing time of the random walks. DA - 2023/1// PY - 2023/1// DO - 10.1016/j.disc.2022.113166 VL - 346 IS - 1 SP - SN - 1872-681X KW - Random walk KW - Mixing time KW - Linear recurrence ER - TY - JOUR TI - Smooth points on semi-algebraic sets AU - Harris, Katherine AU - Hauenstein, Jonathan D. AU - Szanto, Agnes T2 - JOURNAL OF SYMBOLIC COMPUTATION AB - Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. In this paper, we present a procedure based on computing the critical points of some well-chosen function that guarantees the computation of smooth points in each bounded connected component of a (real) atomic semi-algebraic set. Our technique is intuitive in principal, performs well on previously difficult examples, and is straightforward to implement using existing numerical algebraic geometry software. The practical efficiency of our approach is demonstrated by solving a conjecture on the number of equilibria of the Kuramoto model for the n=4 case. We also apply our method to design an algorithm to compute the real dimension of algebraic sets, the original motivation for this research. We compare the efficiency of our method to existing methods to compute the real dimension on a benchmark family. DA - 2023/// PY - 2023/// DO - 10.1016/j.jsc.2022.09.003 VL - 116 SP - 183-212 SN - 1095-855X KW - Computational real algebraic geometry KW - Real smooth points KW - Real dimension KW - Polar varieties KW - Numerical algebraic geometry KW - Kuramoto model ER - TY - JOUR TI - A certified iterative method for isolated singular roots AU - Mantzaflaris, Angelos AU - Mourrain, Bernard AU - Szanto, Agnes T2 - JOURNAL OF SYMBOLIC COMPUTATION AB - In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root and we compute its multiplicity structure. More precisely, given a polynomial system f=(f1,…,fN)∈C[x1,…,xn]N, we present a Newton iteration on an extended deflated system that locally converges, under regularity conditions, to a small deformation of f such that this deformed system has an exact singular root. The iteration simultaneously converges to the coordinates of the singular root and the coefficients of the so-called inverse system that describes the multiplicity structure at the root. We use α-theory test to certify the quadratic convergence, and to give bounds on the size of the deformation and on the approximation error. The approach relies on an analysis of the punctual Hilbert scheme, for which we provide a new description. We show in particular that some of its strata can be rationally parametrized and exploit these parametrizations in the certification. We show in numerical experimentation how the approximate inverse system can be computed as a starting point of the Newton iterations and the fast numerical convergence to the singular root with its multiplicity structure, certified by our criteria. DA - 2023/// PY - 2023/// DO - 10.1016/j.jsc.2022.08.006 VL - 115 SP - 223-247 SN - 1095-855X KW - Polynomial equations KW - Isolated solution KW - Multiple root KW - Certification KW - Newton iteration KW - Deflation ER - TY - JOUR TI - Numerical analysis of a free boundary problem with non-local obstacles AU - Li, Zhilin AU - Mikayelyan, Hayk T2 - APPLIED MATHEMATICS LETTERS AB - The paper deals with the obstacle-like minimization problem in the cylindrical domain Ω=D×(−l,l) J(u)=∫Ω|∇u|2dx+2∫Dmax{v(x′),0}dx′, where x=(x′,xn), and v(x′)=∫−llu(x′,xn)dxn. The corresponding Euler–Lagrange equation is Δu(x′,xn)=χ{v>0}(x′)+−∂xnu(x′,−l)+∂xnu(x′,l)χ{v=0}(x′). Due to the non-local nature of the obstacle, the comparison principle does not hold for the minimizers u(x), which makes the problem challenging both analytically and numerically. The standard optimization techniques such as Newton or quasi-Newton’s methods require approximations of the Jacobians that are four dimensional tensors and are prohibitively expensive both in storage and computational time due to the nature of the three dimensional problem. In this paper, a new algorithm that can compute the global minimum is introduced. Non-trivial exact solutions have been constructed; and second order accuracy has been confirmed. Another important contribution is the numerical testing of the comparison principle for functions v(x′), as conjectured by M. Chipot and the second author in Chipot and Mikayelyan (2022). DA - 2023/1// PY - 2023/1// DO - 10.1016/j.aml.2022.108414 VL - 135 SP - SN - 1873-5452 UR - https://doi.org/10.1016/j.aml.2022.108414 KW - Obstacle-like minimization problem KW - Free boundary KW - SOR(omega) iteration ER - TY - JOUR TI - Duality of sum of nonnegative circuit polynomials and optimal SONC bounds AU - Papp, David T2 - JOURNAL OF SYMBOLIC COMPUTATION AB - Circuit polynomials are polynomials with properties that make it easy to compute sharp and certifiable global lower bounds for them. Consequently, one may use them to find certifiable lower bounds for any polynomial by writing it as a sum of circuit polynomials with known lower bounds. Recent work has shown that sums of nonnegative circuit polynomials (or SONC polynomials for short) can be used to compute global lower bounds (called SONC bounds) for polynomials in this manner very efficiently both in theory and in practice, if the polynomial is bounded from below and its support satisfies a certain nondegeneracy assumption. The quality of the SONC bound depends on the circuits used in the computation but finding the set of circuits that yield the best attainable SONC bound among the astronomical number of candidate circuits is a non-trivial task that has not been addressed so far. We propose an efficient method to compute the optimal SONC lower bound by iteratively identifying the optimal circuits to use in the SONC bounding process. The method is derived from a new proof of the result that every SONC polynomial decomposes into SONC polynomials on the same support. This proof is based on convex programming duality and motivates a column generation approach that is particularly attractive for sparse polynomials of high degree and with many unknowns. The method is implemented and tested on a large set of sparse polynomial optimization problems with up to 40 unknowns, of degree up to 60, and up to 3000 monomials in the support. The results indicate that the method is efficient in practice and requires only a small number of iterations to identify the optimal circuits. DA - 2023/// PY - 2023/// DO - 10.1016/j.jsc.2022.04.015 VL - 114 SP - 246-266 SN - 1095-855X KW - Polynomial optimization KW - Nonnegativity certificates KW - Circuit polynomials KW - Convex optimization KW - Duality KW - Power cone ER -