TY - JOUR TI - Elliptic curves with full 2-torsion and maximal adelic Galois representations AU - Corwin, David AU - Feng, Tony AU - Li, Zane AU - Trebat-Leder, Sarah T2 - Mathematics of Computation AB - In 1972, Serre showed that the adelic Galois representation associated to a non-CM elliptic curve over a number field has open image in G L 2 ( Z ^ ) \mathrm {GL}_2(\widehat {\mathbb {Z}}) . In (2010), Greicius developed necessary and sufficient criteria for determining when this representation is actually surjective and exhibits such an example. However, verifying these criteria turns out to be difficult in practice; Greicius describes tests for them that apply only to semistable elliptic curves over a specific class of cubic number fields. In this paper, we extend Greicius’s methods in several directions. First, we consider the analogous problem for elliptic curves with full 2-torsion. Following Greicius, we obtain necessary and sufficient conditions for the associated adelic representation to be maximal and also develop a battery of computationally effective tests that can be used to verify these conditions. We are able to use our tests to construct an infinite family of curves over Q ( α ) \mathbb {Q}(\alpha ) with maximal image, where α \alpha is the real root of x 3 + x + 1 x^3 + x + 1 . Next, we extend Greicius’s tests to more general settings, such as non-semistable elliptic curves over arbitrary cubic number fields. Finally, we give a general discussion concerning such problems for arbitrary torsion subgroups. DA - 2014/1/30/ PY - 2014/1/30/ DO - 10.1090/s0025-5718-2014-02804-4 VL - 83 IS - 290 SP - 2925-2951 J2 - Math. Comp. LA - en OP - SN - 0025-5718 1088-6842 UR - http://dx.doi.org/10.1090/s0025-5718-2014-02804-4 DB - Crossref ER - TY - JOUR TI - Quadratic twists of elliptic curves with 3-Selmer rank 1 AU - Li, Zane Kun T2 - International Journal of Number Theory AB - A weaker form of a 1979 conjecture of Goldfeld states that for every elliptic curve E/ℚ, a positive proportion of its quadratic twists E (d) have rank 1. Using tools from Galois cohomology, we give criteria on E and d which force a positive proportion of the quadratic twists of E to have 3-Selmer rank 1 and global root number -1. We then give four nonisomorphic infinite families of elliptic curves E m,n which satisfy these criteria. Conditional on the rank part of the Birch and Swinnerton-Dyer conjecture, this verifies the aforementioned conjecture for infinitely many elliptic curves. Our elliptic curves are easy to give explicitly and we state precisely which quadratic twists d to use. Furthermore, our methods have the potential of being generalized to elliptic curves over other number fields. DA - 2014/7/15/ PY - 2014/7/15/ DO - 10.1142/s1793042114500213 VL - 10 IS - 05 SP - 1191-1217 J2 - Int. J. Number Theory LA - en OP - SN - 1793-0421 1793-7310 UR - http://dx.doi.org/10.1142/s1793042114500213 DB - Crossref ER - TY - JOUR TI - Implied Filtering Densities on the Hidden State of Stochastic Volatility AU - Fuertes, Carlos AU - Papanicolaou, Andrew T2 - Applied Mathematical Finance AB - We formulate and analyse an inverse problem using derivative prices to obtain an implied filtering density on volatility’s hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using Bayesian filtering. However, derivative data can be considered as conditional expectations that are already observed in the market, and which can be used as input to an inverse problem whose solution is an implied conditional density on volatility. Our analysis relies on a specification of the martingale change of measure, which we refer to as separability. This specification has a multiplicative component that behaves like a risk premium on volatility uncertainty in the market. When applied to SPX options data, the estimated model and implied densities produce variance-swap rates that are consistent with the VIX volatility index. The implied densities are relatively stable over time and pick up some of the monthly effects that occur due to the options’ expiration, indicating that the volatility-uncertainty premium could experience cyclic effects due to the maturity date of the options. DA - 2014/4/9/ PY - 2014/4/9/ DO - 10.1080/1350486x.2014.891357 VL - 21 IS - 6 SP - 483-522 J2 - Applied Mathematical Finance LA - en OP - SN - 1350-486X 1466-4313 UR - http://dx.doi.org/10.1080/1350486X.2014.891357 DB - Crossref ER - TY - JOUR TI - Filtering the Maximum Likelihood for Multiscale Problems AU - Papanicolaou, Andrew AU - Spiliopoulos, Konstantinos T2 - Multiscale Modeling & Simulation AB - Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional (on the observations) log-likelihood process has a correction term given by a type of central limit theorem. To achieve this we assume that the operator of the (hidden) fast process has a discrete spectrum and an orthonormal basis of eigenfunctions. Based on these results, we then propose to estimate the unknown parameters of the model based on the limiting log-likelihood, which is an easier function to optimize because it of reduced dimension. We also establish consistency and asymptotic normality of the maximum likelihood estimator based on the reduced log-likelihood. Simulation results illustrate our theoretical findings. DA - 2014/1// PY - 2014/1// DO - 10.1137/140952648 VL - 12 IS - 3 SP - 1193-1229 J2 - Multiscale Model. Simul. LA - en OP - SN - 1540-3459 1540-3467 UR - http://dx.doi.org/10.1137/140952648 DB - Crossref KW - ergodic filtering KW - fast mean reversion KW - homogenization KW - Zakai equation KW - maximum likelihood estimation KW - central limit theory ER - TY - JOUR TI - A regime-switching Heston model for VIX and S&P 500 implied volatilities AU - Papanicolaou, Andrew AU - Sircar, Ronnie T2 - Quantitative Finance AB - Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies have examine whether there is significantly greater risk premium in VIX option prices compared with S&P 500 option prices. We address this issue by proposing and analysing a stochastic volatility model with regime switching. The basic Heston model cannot capture VIX-implied volatilities, as has been documented. We show that the incorporation of sharp regime shifts can bridge this shortcoming. We take advantage of asymptotic and Fourier methods to make the extension tractable, and we present a fit to data, both in times of crisis and relative calm, which shows the effectiveness of the regime switching. DA - 2014/10// PY - 2014/10// DO - 10.1080/14697688.2013.814923 VL - 14 IS - 10 SP - 1811-1827 UR - http://dx.doi.org/10.1080/14697688.2013.814923 KW - Applied mathematical finance KW - Calibration of stochastic volatility KW - VIX options KW - Model calibration ER - TY - JOUR TI - Sparse interpolatory reduced-order models for simulation of light-induced molecular transformations AU - Aoi, M C AU - Kelley, Carl AU - Novak, V AU - Olufsen, M S T2 - Optimization Methods and Software AB - This study presents an analysis of a cerebral autoregulation (CA) model developed by Ursino and Lodi Ursino and Lodi (1997). We have used this model to analyze non-invasive measurements of cerebral blood flow velocity (CBFV) and arterial blood pressure obtained during postural change from sitting to standing for a healthy young subject. This paper includes a sensitivity analysis, ranking model parameters from the most to the least sensitive, and an analysis (using a methodology called subset selection) that allows identification of correlations among model parameters. Finally, we estimated patient specific parameters using the Levenberg-Marquardt optimization method minimizing the least square errors between computed and measured values of CBFV. DA - 2014/// PY - 2014/// DO - 10.3182/20090812-3-DK-2006.0088 VL - 29 IS - 2 SP - 264-273 ER - TY - JOUR TI - A multi-scale method for dynamics simulation in continuum solvent models. I: Finite-difference algorithm for Navier–Stokes equation AU - Xiao, Li AU - Cai, Qin AU - Li, Zhilin AU - Zhao, Hongkai AU - Luo, Ray T2 - Chemical Physics Letters AB - A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design. DA - 2014/11// PY - 2014/11// DO - 10.1016/J.CPLETT.2014.10.033 VL - 616-617 SP - 67-74 J2 - Chemical Physics Letters LA - en OP - SN - 0009-2614 UR - http://dx.doi.org/10.1016/J.CPLETT.2014.10.033 DB - Crossref ER - TY - THES TI - The Geometry of Radial States in Nonlinear Elliptic Problems DA - 2014/// PY - 2014/// ER - TY - JOUR TI - On convergence of the immersed boundary method for elliptic interface problems AU - Li, Zhilin T2 - Mathematics of Computation AB - Peskin’s Immersed Boundary (IB) method has been one of the most popular numerical methods for many years and has been applied to problems in mathematical biology, fluid mechanics, material sciences, and many other areas. Peskin’s IB method is associated with discrete delta functions. It is believed that the IB method is first order accurate in the $L^{\infty }$ norm. But almost no rigorous proof could be found in the literature until recently [Mori, Comm. Pure. Appl. Math: 61:2008] in which the author showed that the velocity is indeed first order accurate for the Stokes equations with a periodic boundary condition. In this paper, we show first order convergence with a $\log h$ factor of the IB method for elliptic interface problems with Dirichlet boundary conditions. DA - 2014/12/16/ PY - 2014/12/16/ DO - 10.1090/s0025-5718-2014-02932-3 VL - 84 IS - 293 SP - 1169-1188 J2 - Math. Comp. LA - en OP - SN - 0025-5718 1088-6842 UR - http://dx.doi.org/10.1090/s0025-5718-2014-02932-3 DB - Crossref ER - TY - JOUR TI - R-Matrix Realization of Two-Parameter Quantum Group Ur,s(gln) AU - Jing, Naihuan AU - Liu, Ming T2 - Communications in Mathematics and Statistics AB - We provide a Faddeev–Reshetikhin–Takhtajan’s RTT approach to the quantum group $$\mathrm{Fun}(\mathrm{GL}_{r,s}(n))$$ and the quantum enveloping algebra $$U_{r,s}(\mathfrak {gl}_n)$$ corresponding to the two-parameter $$R$$ -matrix. We prove that the quantum determinant $${\det }_{r,s}T$$ is a quasi-central element in $$\mathrm{Fun}(\mathrm{GL}_{r,s}(n))$$ generalizing earlier results of Dipper–Donkin and Du–Parshall–Wang. The explicit formulation provides an interpretation of the deforming parameters, and the quantized algebra $$U_{r,s}(R)$$ is identified to $$U_{r,s}(\mathfrak {gl}_n)$$ as the dual algebra. We then construct $$n-1$$ quasi-central elements in $$U_{r,s}(R)$$ which are analogs of higher Casimir elements in $$U_q(\mathfrak {gl}_n)$$ . DA - 2014/12// PY - 2014/12// DO - 10.1007/S40304-014-0037-7 VL - 2 IS - 3-4 SP - 211–230 SN - 2194-6701 2194-671X UR - http://dx.doi.org/10.1007/S40304-014-0037-7 KW - Quantum groups KW - Determinants KW - Casimir elements KW - Yang-Baxter equations ER - TY - CONF TI - A Note on Global Newton Iteration Over Archimedean and Non-Archimedean Fields AU - Hauenstein, Jonathan D. AU - Pan, Victor Y. AU - Szanto, Agnes A2 - Gerdt, Vladimir P. A2 - Koepf, Wolfram A2 - Seiler, Werner M. A2 - Vorozhtsov, Evgenii V. C2 - 2014/// C3 - Computer Algebra in Scientific Computing CY - Cham DA - 2014/// SP - 202-217 PB - Springer International Publishing ER - TY - BOOK TI - Mathematical Software – ICMS 2014: 4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings AU - Hong, Hoon AU - Yap, Chee A3 - Hong, Hoon A3 - Yap, Chee AB - This book constitutes the proceedings of the 4th International Conference on Mathematical Software, ICMS 2014, held in Seoul, South Korea, in August 2014. The 108 papers included in this volume were c DA - 2014/1// PY - 2014/1// DO - 10.1007/978-3-662-44199-2 VL - 8592 PB - Springer SE - UR - https://doi.org/10.1007/978-3-662-44199-2 ER - TY - CONF TI - Synthesis of Optimal Numerical Algorithms Using Real Quantifier Elimination (Case Study: Square Root Computation) AU - Eraşcu, Mădălina AU - Hong, Hoon A2 - Nabeshima, Katsusuke A2 - Nagasaka, Kosaku A2 - Winkler, Franz A2 - Szántó, Ágnes AB - We report on on-going efforts to apply real quantifier elimination to the synthesis of optimal numerical algorithms. In particular, we describe a case study on the square root problem: given a real number x and an error bound ε, find a real interval such that it contains [EQUATION] and its width is less than or equal to ε. C2 - 2014/// C3 - Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation CY - New York, NY, USA DA - 2014/// DO - 10.1145/2608628.2608654 SP - 162–169 PB - Association for Computing Machinery UR - https://doi.org/10.1145/2608628.2608654 ER - TY - CONF TI - Applying Machine Learning Techniques to Baseball Pitch Prediction AU - Hamilton, M. AU - Hoang, P. AU - Layne, L. AU - Murray, J. AU - Padget, D. AU - Stafford, C. AU - Tran, H. T2 - International Conference on Pattern Recognition Applications and Methods A2 - De Marsico, M. A2 - Tabbone, A. A2 - Fred, A. AB - Major League Baseball, a professional baseball league in the US and Canada, is one of the most popular sports leagues in the world. Partially because of its popularity and the wide availability of data from games, baseball has become the subject of significant statistical and mathematical analysis. Pitch analysis is especially useful for helping a team better understand the pitch behavior it may face during a game, allowing the team to develop a corresponding batting strategy to combat the predicted pitch behavior. We apply several common machine learning classification methods to PITCHf/x data to classify pitches by type. We then extend the classification task to prediction by utilizing features only known before a pitch is thrown. By performing significant feature analysis and introducing a novel approach for feature selection, moderate improvement over former results is achieved. C2 - 2014/// C3 - Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods DA - 2014/// DO - 10.5220/0004763905200527 VL - 1 SP - 520–527 PB - SCITEPRESS - Science and and Technology Publications SN - 9789897580185 UR - http://dx.doi.org/10.5220/0004763905200527 ER - TY - JOUR TI - Modern convex analysis AU - Combettes, P.L. AU - Hiriart-Urruty, J.-B. AU - Théra, M. T2 - Mathematical Programming DA - 2014/12// PY - 2014/12// DO - 10.1007/s10107-014-0815-8 VL - 148 SP - 1-4 ER - TY - CONF TI - A forward-backward view of some primal-dual optimization methods in image recovery AU - Combettes, P.L. AU - Condat, L. AU - Pesquet, J.-C. AU - Vũ, B.C. T2 - Proceedings of the IEEE International Conference on Image Processing AB - A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide efficient solutions to large-scale optimization problems. The objective of this paper is to show that a number of existing algorithms can be derived from a general form of the forward-backward algorithm applied in a suitable product space. Our approach also allows us to develop useful extensions of existing algorithms by introducing a variable metric. An illustration to image restoration is provided. C2 - 2014/// C3 - Proceedings of the IEEE International Conference on Image Processing CY - Paris, France DA - 2014/// PY - 2014/10/27/ DO - 10.1109/ICIP.2014.7025841 SP - 4141–4145 ER - TY - JOUR TI - Corrigendum to “Attractors for non-dissipative irrotational von Karman plates with boundary damping” [J. Differential Equations 253 (12) (2012) 3568–3609] AU - Bociu, Lorena AU - Toundykov, Daniel T2 - Journal of Differential Equations DA - 2014/1// PY - 2014/1// DO - 10.1016/J.JDE.2013.10.007 VL - 256 IS - 2 SP - 893 J2 - Journal of Differential Equations LA - en OP - SN - 0022-0396 UR - http://dx.doi.org/10.1016/J.JDE.2013.10.007 DB - Crossref ER - TY - CONF TI - On quantitative compactness estimates for hyperbolic conservation laws C2 - 2014/// C3 - Hyperbolic problems: theory, numerics, applications, 249–257, AIMS Ser. Appl. Math., 8, Am. Inst. Math. Sci. (AIMS), Springfield, MO, DA - 2014/// ER - TY - JOUR TI - Non-Lipschitz points and the SBV regularity of the minimum time function AU - Colombo, G. AU - Nguyen, K.T. AU - Nguyen, L.V. T2 - Calculus of Variations and Partial Differential Equations DA - 2014/// PY - 2014/// DO - 10.1007/s00526-013-0682-9 VL - 51 IS - 1-2 SP - 439-463 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84906306428&partnerID=MN8TOARS ER - TY - CHAP TI - BV Regularity and Differentiability Properties of a Class of Upper Semicontinuous Functions AU - Marigonda, Antonio AU - Nguyen, Khai T. AU - Vittone, Davide T2 - Large-Scale Scientific Computing A2 - Lirkov, I. A2 - Margenov, S. A2 - Waśniewski, J. T3 - Lecture Notes in Computer Science AB - We study a class of upper semicontinuous functions $$f:\mathbb R^d\rightarrow \mathbb R$$ whose hypograph $$\mathrm {hypo}\,f$$ (see Definition 1) satisfies a geometric regularity property, namely: there exist $$c>0$$ , $$\theta \in ]0,1]$$ such that for each $$P$$ on the boundary of $$\mathrm {hypo}\,f$$ there exists a unitary Fréchet (outer) normal $$v\in N^F_{\mathrm {hypo}\,f}(P)\cap \mathbb S^d$$ to $$\mathrm {hypo}\,f$$ with $$\langle v,P-Q\rangle \le c \Vert P-Q\Vert ^{1+\theta }\qquad \mathrm{{for~every}}~Q\in \mathrm {hypo}\,f.$$ PY - 2014/// DO - 10.1007/978-3-662-43880-0_12 VL - 8353 LNCS SP - 116–124 PB - Springer SN - 9783662438794 9783662438800 SV - 8353 UR - http://dx.doi.org/10.1007/978-3-662-43880-0_12 ER - TY - JOUR TI - Weak Convergence of a Seasonally Forced Stochastic Epidemic Model AU - Lloyd, Alun AU - Zhang, Yuan T2 - arXiv preprint arXiv:1412.0964 DA - 2014/// PY - 2014/// ER - TY - JOUR TI - Time-varying, serotype-specific force of infection of dengue virus AU - Reiner, Robert C AU - Stoddard, Steven T AU - Forshey, Brett M AU - King, Aaron A AU - Ellis, Alicia M AU - Lloyd, Alun L AU - Long, Kanya C AU - Rocha, Claudio AU - Vilcarromero, Stalin AU - Astete, Helvio AU - others T2 - Proceedings of the National Academy of Sciences DA - 2014/// PY - 2014/// VL - 111 IS - 26 SP - E2694-E2702 ER - TY - JOUR TI - Recasting the theory of mosquito-borne pathogen transmission dynamics and control T2 - Transactions of the Royal Society of Tropical Medicine and Hygiene DA - 2014/// PY - 2014/// VL - 108 IS - 4 SP - 185-197 ER - TY - JOUR TI - A global assembly of adult female mosquito mark-release-recapture data to inform the control of mosquito-borne pathogens AU - Guerra, Carlos A AU - Reiner, Robert C AU - Perkins, T Alex AU - Lindsay, Steve W AU - Midega, Janet T AU - Brady, Oliver J AU - Barker, Christopher M AU - Reisen, William K AU - Harrington, Laura C AU - Takken, Willem AU - others T2 - Parasit Vectors DA - 2014/// PY - 2014/// VL - 7 IS - 1 SP - 276 ER - TY - JOUR TI - Mathematical methods and models in system biomedicine AU - Pontrelli, Giuseppe AU - Olufsen, Mette S. AU - Ottesen, Johnny T. T2 - Mathematical Biosciences AB - A particular case of the famous quasispecies model — the Crow–Kimura model with a permutation invariant fitness landscape — is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs. DA - 2014/11// PY - 2014/11// DO - 10.1016/J.MBS.2014.09.012 VL - 257 SP - 1 J2 - Mathematical Biosciences LA - en OP - SN - 0025-5564 UR - http://dx.doi.org/10.1016/J.MBS.2014.09.012 DB - Crossref ER - TY - CHAP TI - ImUp: A Maple Package for Uniformity-Improved Reparameterization of Plane Curves AU - Yang, Jing AU - Wang, Dongming AU - Hong, Hoon T2 - Computer Mathematics PY - 2014/// DO - 10.1007/978-3-662-43799-5_29 VL - 10 SP - 437-451 OP - PB - Springer Berlin Heidelberg SN - 9783662437988 9783662437995 UR - http://dx.doi.org/10.1007/978-3-662-43799-5_29 DB - Crossref ER - TY - CHAP TI - Pairing Inversion via Non-degenerate Auxiliary Pairings AU - Chang, Seunghwan AU - Hong, Hoon AU - Lee, Eunjeong AU - Lee, Hyang-Sook T2 - Pairing-Based Cryptography – Pairing 2013 AB - The security of pairing-based cryptosystems is closely related to the difficulty of the pairing inversion problem(PI). In this paper, we discuss the difficulty of pairing inversion on the generalized ate pairings of Vercauteren. First, we provide a simpler approach for PI by generalizing and simplifying Kanayama-Okamoto’s approach; our approach involves modifications of exponentiation inversion(EI) and Miller inversion(MI), via an “auxiliary” pairing. Then we provide a complexity of the modified MI, showing that the complexity depends on the sum-norm of the integer vector defining the auxiliary pairing. Next, we observe that degenerate auxiliary pairings expect to make modified EI harder. We provide a sufficient condition on the integer vector, in terms of its max norm, so that the corresponding auxiliary paring is non-degenerate. Finally, we define an infinite set of curve parameters, which includes those of typical pairing friendly curves, and we show that, within those parameters, PI of arbitrarily given generalized ate pairing can be reduced to modified EI in polynomial time. PY - 2014/// DO - 10.1007/978-3-319-04873-4_5 SP - 77-96 OP - PB - Springer International Publishing SN - 9783319048727 9783319048734 UR - http://dx.doi.org/10.1007/978-3-319-04873-4_5 DB - Crossref ER - TY - CHAP TI - Baseball pitch classification AU - Attarian, A AU - Danis, G AU - Gronsbell, J AU - Iervolino, G AU - Layne, L AU - Padgett, D AU - Tran, H T2 - IAENG Transactions on Engineering Sciences AB - The development of monitoring and inventory system using Radio Frequency Identification (RFID) technology could answer these problems. Thus, this project has been conceived. It aimed to develop a monitoring and inventory system to control access of laboratory rooms. The study was based on a hierarchical structure that used wireless technology. The project would enable the staff to have ready access to all information on the status of the equipment such as previous and current borrowers, condition of the equipment, date of purchase, received date, location of the equipment, etc. In this manner, monitoring and inventory system of all equipment could be improved. PY - 2014/4/7/ DO - 10.1201/b16763-43 SP - 393-399 OP - PB - CRC Press SN - 9781138001367 9781315761817 UR - http://dx.doi.org/10.1201/b16763-43 DB - Crossref ER - TY - JOUR TI - How coherent are the vortices of two-dimensional turbulence? AU - Farazmand, M. AU - Haller, G. T2 - arXiv preprint arXiv:1402.4835 DA - 2014/// PY - 2014/// ER - TY - JOUR TI - The Maxey-Riley Equation: Existence, Uniqueness and Regularity of Solutions AU - Farazmand, M. AU - Haller, G. T2 - J. Nonliner Analysis-B AB - The Maxey–Riley equation describes the motion of an inertial (i.e., finite-size) spherical particle in an ambient fluid flow. The equation is a second-order, implicit integro-differential equation with a singular kernel, and with a forcing term that blows up at the initial time. Despite the widespread use of the equation in applications, the basic properties of its solutions have remained unexplored. Here we fill this gap by proving local existence and uniqueness of mild solutions. For certain initial velocities between the particle and the fluid, the results extend to strong solutions. We also prove continuous differentiability of the mild and strong solutions with respect to their initial conditions. This justifies the search for coherent structures in inertial flows using the Cauchy–Green strain tensor. DA - 2014/// PY - 2014/// DO - 10.1016/j.nonrwa.2014.08.002 N1 - In press RN - In press KW - Inertial particles KW - Fractional-order differential equations KW - Integro-differential equations KW - Maxey-Riley equation ER - TY - JOUR TI - Shearless transport barriers in unsteady two-dimensional flows and maps AU - Farazmand, M. AU - Blazevski, D. AU - Haller, G. T2 - Physica D AB - We develop a variational principle that extends the notion of a shearless transport barrier from steady to general unsteady two-dimensional flows and maps defined over a finite time interval. This principle reveals that hyperbolic Lagrangian Coherent Structures (LCSs) and parabolic LCSs (or jet cores) are the two main types of shearless barriers in unsteady flows. Based on the boundary conditions they satisfy, parabolic barriers are found to be more observable and robust than hyperbolic barriers, confirming widespread numerical observations. Both types of barriers are special null-geodesics of an appropriate Lorentzian metric derived from the Cauchy–Green strain tensor. Using this fact, we devise an algorithm for the automated computation of parabolic barriers. We illustrate our detection method on steady and unsteady non-twist maps and on the aperiodically forced Bickley jet. DA - 2014/// PY - 2014/// DO - 10.1016/j.physd.2014.03.008 VL - 278-279 SP - 44-57 KW - Dynamical systems KW - Shearless transport barriers KW - Invariant tori KW - Lagrangian coherent structures KW - Mixing ER - TY - CONF TI - Detection of Material Dispersion Using SAR AU - Gilman, Mikhail AU - Tsynkov, Semyon C2 - 2014/// C3 - Proceedings of the 10th European Conference on Synthetic Aperture Radar (EUSAR 2014) CY - Berlin-Offenbach, Germany DA - 2014/// SP - 1013-1016 PB - VDE VERLAG GMBH UR - https://stsynkov.math.ncsu.edu/publications/eusar-2014.pdf ER - TY - JOUR TI - An algorithm for splitting parallel sums of linearly composed monotone operators, with applications to signal recovery AU - Becker, S.R. AU - Combettes, P.L. T2 - Journal of Nonlinear and Convex Analysis DA - 2014/1// PY - 2014/1// VL - 15 IS - 1 SP - 137–159 ER - TY - JOUR TI - Estimating Sampling Distributions of Apparent Thermal Diffusivity for Partially Saturated Soils AU - Eslinger, O J AU - Winton, C AU - Ballard, J R AU - Howington, Stacy E AU - Fregosi, Anna AU - Ward, K AU - Kelley, C T T2 - IEEE Trans. Geosci. Remote Sensing DA - 2014/// PY - 2014/// SP - 15 ER - TY - JOUR TI - A-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems with Regularized l_0-Sparsification AU - Alexanderian, Alen AU - Petra, Noemi AU - Stadler, Georg AU - Ghattas, Omar T2 - SIAM Journal on Scientific Computing AB - We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we address the problem of optimizing the location of sensors (at which observational data are collected) to minimize the uncertainty in the parameters estimated by solving the inverse problem, where the uncertainty is expressed by the trace of the posterior covariance. Computing optimal experimental designs (OEDs) is particularly challenging for inverse problems governed by computationally expensive PDE models with infinite-dimensional (or, after discretization, high-dimensional) parameters. To alleviate the computational cost, we exploit the problem structure and build a low-rank approximation of the parameter-to-observable map, preconditioned with the square root of the prior covariance operator. The availability of this low-rank surrogate, relieves our method from expensive PDE solves when evaluating the optimal experimental design objective function, i.e., the trace of the posterior covariance, and its derivatives. Moreover, we employ a randomized trace estimator for efficient evaluation of the OED objective function. We control the sparsity of the sensor configuration by employing a sequence of penalty functions that successively approximate the $\ell_0$-``norm''; this results in binary designs that characterize optimal sensor locations. We present numerical results for inference of the initial condition from spatiotemporal observations in a time-dependent advection-diffusion problem in two and three space dimensions. We find that an optimal design can be computed at a cost, measured in number of forward PDE solves, that is independent of the parameter and sensor dimensions. Moreover, the numerical optimization problem for finding the optimal design can be solved in a number of interior-point quasi-Newton iterations that is insensitive to the parameter and sensor dimensions. We demonstrate numerically that $\ell_0$-sparsified experimental designs obtained via a continuation method outperform $\ell_1$-sparsified designs. DA - 2014/1// PY - 2014/1// DO - 10.1137/130933381 VL - 36 IS - 5 SP - A2122-A2148 SN - 1064-8275 1095-7197 UR - http://dx.doi.org/10.1137/130933381 KW - optimal experimental design KW - A-optimal design KW - Bayesian inference KW - sensor placement KW - ill-posed inverse problems KW - low-rank approximation KW - randomized trace estimator KW - randomized SVD ER - TY - JOUR TI - The q = -1 phenomenon via homology concentration AU - Hersh, P. AU - Shareshian, J. AU - Stanton, D. T2 - Journal of Combinatorics AB - We introduce a homological approach to exhibiting instances of Stembridge's q=-1 phenomenon. This approach is shown to explain two important instances of the phenomenon, namely that of partitions whose Ferrers diagrams fit in a rectangle of fixed size and that of plane partitions fitting in a box of fixed size. A more general framework of invariant and coinvariant complexes with coefficients taken mod 2 is developed, and as a part of this story an analogous homological result for necklaces is conjectured. DA - 2014/// PY - 2014/// DO - 10.4310/joc.2014.v5.n2.a2 VL - 5 IS - 2 SP - 167-194 SN - 2156-3527 2150-959X UR - http://dx.doi.org/10.4310/joc.2014.v5.n2.a2 ER - TY - JOUR TI - Asymptotic behavior of compositions of under-relaxed nonexpansive operators AU - Baillon, Jean-Bernard AU - Combettes, Patrick L. AU - Cominetti, Roberto T2 - Journal of Dynamics and Games AB - In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces. DA - 2014/7// PY - 2014/7// DO - 10.3934/jdg.2014.1.331 VL - 1 IS - 3 SP - 331-346 J2 - JDG LA - en OP - SN - 2164-6066 UR - http://dx.doi.org/10.3934/jdg.2014.1.331 DB - Crossref KW - Cyclic projections KW - De Pierro's conjecture KW - fixed point KW - nonexpansive operator KW - projection operator KW - under-relaxed cycles ER - TY - JOUR TI - Coefficients of a relative of cyclotomic polynomials AU - Liu, Ricky Ini T2 - Acta Arithmetica AB - Let $N=p_1\cdots p_n$ be a product of $n \geq 2$ distinct primes. Define $P_N(x)$ to be the polynomial $$ (1-x^N)\prod_{1\leq i< j\leq n}(1-x^{N/(p_ip_j)})/\prod_{i=1}^n (1-x^{N/p_i}). $$ (When $n=2$, $P_{pq}(x)$ is the $pq$th cyclotomic polynomial $\var DA - 2014/// PY - 2014/// DO - 10.4064/aa165-4-1 VL - 165 IS - 4 SP - 301-325 J2 - Acta Arith. LA - en OP - SN - 0065-1036 1730-6264 UR - http://dx.doi.org/10.4064/aa165-4-1 DB - Crossref KW - cyclotomic polynomial KW - height ER - TY - JOUR TI - Laurent polynomials, Eulerian numbers, and Bernstein's theorem AU - Liu, Ricky Ini T2 - Journal of Combinatorial Theory, Series A AB - Erman, Smith, and Várilly-Alvarado (2011) showed that the expected number of doubly monic Laurent polynomials f(z)=z−m+a−m+1z−m+1+⋯+an−1zn−1+zn whose first m+n−1 powers have vanishing constant term is the Eulerian number 〈m+n−1m−1〉, as well as a more refined result about sparse Laurent polynomials. We give an alternate proof of these results using Bernstein's theorem that clarifies the connection between these objects. In the process, we show that a refinement of Eulerian numbers gives a combinatorial interpretation for volumes of certain rational hyperplane sections of the hypercube. DA - 2014/5// PY - 2014/5// DO - 10.1016/j.jcta.2014.02.003 VL - 124 SP - 244-250 J2 - Journal of Combinatorial Theory, Series A LA - en OP - SN - 0097-3165 UR - http://dx.doi.org/10.1016/j.jcta.2014.02.003 DB - Crossref KW - Eulerian number KW - Bernstein's theorem KW - Hypersimplex ER - TY - CHAP TI - Sparse Polynomial Interpolation by Variable Shift in the Presence of Noise and Outliers in the Evaluations AU - Boyer, Brice AU - Comer, Matthew T. AU - Kaltofen, Erich L. T2 - Computer Mathematics PY - 2014/// DO - 10.1007/978-3-662-43799-5_16 SP - 183-197 OP - PB - Springer Berlin Heidelberg SN - 9783662437988 9783662437995 UR - http://dx.doi.org/10.1007/978-3-662-43799-5_16 DB - Crossref ER - TY - CHAP TI - Symbolic Computation and Complexity Theory Transcript of My Talk AU - Kaltofen, Erich L. T2 - Computer Mathematics PY - 2014/// DO - 10.1007/978-3-662-43799-5_1 SP - 3-7 OP - PB - Springer Berlin Heidelberg SN - 9783662437988 9783662437995 UR - http://dx.doi.org/10.1007/978-3-662-43799-5_1 DB - Crossref ER - TY - CONF TI - Cleaning-up data for sparse model synthesis AU - Kaltofen, Erich L. T2 - the 2014 Symposium AB - The discipline of symbolic computation contributes to mathematical model synthesis in several ways. One is the pioneering creation of interpolation algorithms that can account for sparsity in the resulting multi-dimensional models, for example, by Zippel [12], Ben-Or and Tiwari [1], and in their recent numerical counterparts by Giesbrecht-Labahn-Lee [5] and Kaltofen-Yang-Zhi [9]. C2 - 2014/// C3 - Proceedings of the 2014 Symposium on Symbolic-Numeric Computation - SNC '14 DA - 2014/// DO - 10.1145/2631948.2631949 PB - ACM Press SN - 9781450329637 UR - http://dx.doi.org/10.1145/2631948.2631949 DB - Crossref ER - TY - CONF TI - Numerical linear system solving with parametric entries by error correction AU - Boyer, Brice AU - Kaltofen, Erich L. T2 - the 2014 Symposium AB - We consider the problem of solving a full rank consistent linear system A(u)x = b(u) where the m x n matrix A and the m-dimensional vector b has entries that are polynomials in u over a field. We give an algorithm that computes the unique solution x = f(u)/g(u), which is a vector of rational functions, by evaluating the parameter u at distinct points. Those points ξλ where the matrix A evaluates to a matrix A(ξλ), with entries over the scalar field, of lower rank, or in the numeric setting to an ill-conditioned matrix, are not identified but accounted for by error-correcting code techniques. We also correct true errors where the evaluation at some u = ξλ results in an erroneous, possibly full rank consistent and well-conditioned scalar linear system. Our algorithm generalizes Welch/Berlekamp decoding of Reed/Solomon error correcting codes and their numeric floating point counterparts. C2 - 2014/// C3 - Proceedings of the 2014 Symposium on Symbolic-Numeric Computation - SNC '14 DA - 2014/// DO - 10.1145/2631948.2631956 PB - ACM Press SN - 9781450329637 UR - http://dx.doi.org/10.1145/2631948.2631956 DB - Crossref ER - TY - CONF TI - Essentially optimal interactive certificates in linear algebra AU - Dumas, Jean-Guillaume AU - Kaltofen, Erich T2 - the 39th International Symposium AB - Certificates to a linear algebra computation are additional data structures for each output, which can be used by a---possibly randomized---verification algorithm that proves the correctness of each output. The certificates are essentially optimal if the time (and space) complexity of verification is essentially linear in the input size $N$, meaning $N$ times a factor $N^{o(1)}$, i.e., a factor $N^{\eta(N)}$ with $\lim\_{N\to \infty} \eta(N)$ $=$ $0$. We give algorithms that compute essentially optimal certificates for the positive semidefiniteness, Frobenius form, characteristic and minimal polynomial of an $n\times n$ dense integer matrix $A$. Our certificates can be verified in Monte-Carlo bit complexity $(n^2 \log\|A\|)^{1+o(1)}$, where $\log\|A\|$ is the bit size of the integer entries, solving an open problem in [Kaltofen, Nehring, Saunders, Proc.\ ISSAC 2011] subject to computational hardness assumptions. Second, we give algorithms that compute certificates for the rank of sparse or structured $n\times n$ matrices over an abstract field, whose Monte Carlo verification complexity is $2$ matrix-times-vector products $+$ $n^{1+o(1)}$ arithmetic operations in the field. For example, if the $n\times n$ input matrix is sparse with $n^{1+o(1)}$ non-zero entries, our rank certificate can be verified in $n^{1+o(1)}$ field operations. This extends also to integer matrices with only an extra $\|A\|^{1+o(1)}$ factor. All our certificates are based on interactive verification protocols with the interaction removed by a Fiat-Shamir identification heuristic. The validity of our verification procedure is subject to standard computational hardness assumptions from cryptography. C2 - 2014/// C3 - Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14 DA - 2014/// DO - 10.1145/2608628.2608644 PB - ACM Press SN - 9781450325011 UR - http://dx.doi.org/10.1145/2608628.2608644 DB - Crossref ER - TY - CONF TI - Sparse polynomial interpolation codes and their decoding beyond half the minimum distance AU - Kaltofen, Erich L. AU - Pernet, Clément T2 - the 39th International Symposium AB - We present algorithms performing sparse univariate polynomial interpolation with errors in the evaluations of the polynomial. Based on the initial work by Comer, Kaltofen and Pernet [Proc. ISSAC 2012], we define the sparse polynomial interpolation codes and state that their minimal distance is precisely the length divided by twice the sparsity. At ISSAC 2012, we have given a decoding algorithm for as much as half the minimal distance and a list decoding algorithm up to the minimal distance. Our new polynomial-time list decoding algorithm uses sub-sequences of the received evaluations indexed by a linear progression, allowing the decoding for a larger radius, that is, more errors in the evaluations while returning a list of candidate sparse polynomials. We quantify this improvement for all typically small values of number of terms and number of errors, and provide a worst case asymptotic analysis of this improvement. For instance, for sparsity T = 5 with up to 10 errors we can list decode in polynomial-time from 74 values of the polynomial with unknown terms, whereas our earlier algorithm required 2T (E + 1) = 110 evaluations. We then propose two variations of these codes in characteristic zero, where appropriate choices of values for the variable yield a much larger minimal distance: the length minus twice the sparsity. C2 - 2014/// C3 - Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14 DA - 2014/// DO - 10.1145/2608628.2608660 PB - ACM Press SN - 9781450325011 UR - http://dx.doi.org/10.1145/2608628.2608660 DB - Crossref ER - TY - CONF TI - Sparse multivariate function recovery with a high error rate in the evaluations AU - Kaltofen, Erich L. AU - Yang, Zhengfeng T2 - the 39th International Symposium AB - In [Kaltofen and Yang, Proc. ISSAC 2013] we have generalized algebraic error-correcting decoding to multivariate sparse rational function interpolation from evaluations that can be numerically inaccurate and where several evaluations can have severe errors ("outliers"). Here we present a different algorithm that can interpolate a sparse multivariate rational function from evaluations where the error rate is 1/q for any q > 2, which our ISSAC 2013 algorithm could not handle. When implemented as a numerical algorithm we can, for instance, reconstruct a fraction of trinomials of degree 15 in 50 variables with non-outlier evaluations of relative noise as large as 10-7 and where as much as 1/4 of the 14717 evaluations are outliers with relative error as small as 0.01 (large outliers are easily located by our method). C2 - 2014/// C3 - Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14 DA - 2014/// DO - 10.1145/2608628.2608637 PB - ACM Press SN - 9781450325011 UR - http://dx.doi.org/10.1145/2608628.2608637 DB - Crossref ER - TY - CHAP TI - Linear Differential Algebraic Equations and Observers AU - Bobinyec, Karen S. AU - Campbell, Stephen L. T2 - Surveys in Differential-Algebraic Equations II AB - Observers play an important role in the control of linear systems. Given the importance of DAE models, it is natural that there has been considerable interest in designing and using observers for DAEs. The first part of this paper surveys some aspects of DAEs and observers that lay the foundation for the second part which discusses a recent general approach to observer design for linear DAEs using completions. This approach also holds great promise for nonlinear DAEs. PY - 2014/11/18/ DO - 10.1007/978-3-319-11050-9_1 SP - 1-67 OP - PB - Springer International Publishing SN - 9783319110493 9783319110509 UR - http://dx.doi.org/10.1007/978-3-319-11050-9_1 DB - Crossref ER - TY - JOUR TI - Auxiliary signal design for failure detection in differential-algebraic equations AU - Campbell, Stephen AU - Scott, Jason T2 - Numerical Algebra, Control and Optimization AB - Fault detection and identification (FDI) are important tasks in most modern industrial and mechanical systems and processes. Many of these systems are most naturally modeled by differential-algebraic equations (DAE). This paper addresses active fault detection in DAE. A technique is presented to calculate an auxiliary test signal guaranteeing detection, assuming bounded additive noise. An efficient real time detection algorithm is also provided as are example simulations. The extension to model uncertainty is discussed. DA - 2014/5// PY - 2014/5// DO - 10.3934/naco.2014.4.151 VL - 4 IS - 2 SP - 151-179 J2 - NACO LA - en OP - SN - 2155-3289 UR - http://dx.doi.org/10.3934/naco.2014.4.151 DB - Crossref KW - Active fault detection KW - auxiliary signal design KW - failure detection KW - differential-algebraic equations KW - DAE ER - TY - CONF TI - Auxiliary signal design for failure detection in high index differential-algebraic equations AU - Scott, Jason R. AU - Campbell, Stephen L. T2 - 2014 IEEE 53rd Annual Conference on Decision and Control (CDC) AB - Auxiliary test signals for active fault detection have been studied by several authors but traditionally for systems with discrete time or continuous time nonimpulsive causal models. Recently, a method for designing test signals for systems modeled by higher index differential algebraic equations has been developed. This paper examines more carefully when such a test signal exists and also how to get a useful test signal when the previous algorithm breaks down. C2 - 2014/12// C3 - 53rd IEEE Conference on Decision and Control DA - 2014/12// DO - 10.1109/cdc.2014.7040395 PB - IEEE SN - 9781467360906 9781479977468 9781479977451 UR - http://dx.doi.org/10.1109/cdc.2014.7040395 DB - Crossref ER - TY - CONF TI - Asynchronous auxiliary signal design for failure detection AU - Campbell, Stephen L. AU - Scott, Jason R. T2 - 2014 IEEE International Conference on Systems, Man and Cybernetics - SMC AB - Fault detection and identification (FDI) are important tasks in most modern industrial systems and processes. A variety of approaches both active and passive have been investigated. A test signal or input is used in an active approach. Usually in the active approach the same time window is used for the running of the test and the application of the test signal. However, that is not always the most desirable or practical thing to do. The effect of different signal and observation windows is investigated here for one active approach. C2 - 2014/10// C3 - 2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC) DA - 2014/10// DO - 10.1109/smc.2014.6974340 PB - IEEE SN - 9781479938407 UR - http://dx.doi.org/10.1109/smc.2014.6974340 DB - Crossref ER - TY - JOUR TI - Solving Coupled Composite Monotone Inclusions by Successive Fejér Approximations of their Kuhn--Tucker Set AU - Alotaibi, Abdullah AU - Combettes, Patrick L. AU - Shahzad, Naseer T2 - SIAM Journal on Optimization AB - We propose a new class of primal-dual Fejér monotone algorithms for solving systems of composite monotone inclusions. Our construction is inspired by a framework used by Eckstein and Svaiter for the basic problem of finding a zero of the sum of two monotone operators. At each iteration, points in the graph of the monotone operators present in the model are used to construct a half-space containing the Kuhn--Tucker set associated with the system. The primal-dual update is then obtained via a relaxed projection of the current iterate onto this half-space. An important feature that distinguishes the resulting splitting algorithms from existing ones is that they do not require prior knowledge of bounds on the linear operators involved or the inversion of linear operators. DA - 2014/1// PY - 2014/1// DO - 10.1137/130950616 VL - 24 IS - 4 SP - 2076-2095 J2 - SIAM J. Optim. LA - en OP - SN - 1052-6234 1095-7189 UR - http://dx.doi.org/10.1137/130950616 DB - Crossref KW - duality KW - Fejer monotonicity KW - monotone inclusion KW - monotone operator KW - primal-dual algorithm KW - splitting algorithm ER - TY - JOUR TI - A primal-dual method of partial inverses for composite inclusions AU - Alghamdi, Maryam A. AU - Alotaibi, Abdullah AU - Combettes, Patrick L. AU - Shahzad, Naseer T2 - Optimization Letters AB - Spingarn's method of partial inverses has found many applications in nonlinear analysis and in optimization. We show that it can be employed to solve composite monotone inclusions in duality, thus opening a new range of applications for the partial inverse formalism. The versatility of the resulting primal-dual splitting algorithm is illustrated through applications to structured monotone inclusions and optimization. DA - 2014/3/7/ PY - 2014/3/7/ DO - 10.1007/s11590-014-0734-x VL - 8 IS - 8 SP - 2271-2284 J2 - Optim Lett LA - en OP - SN - 1862-4472 1862-4480 UR - http://dx.doi.org/10.1007/s11590-014-0734-x DB - Crossref KW - Convex optimization KW - Duality KW - Method of partial inverses KW - Monotone operator KW - Splitting algorithm ER - TY - JOUR TI - Modeling Cerebral Blood Flow Velocity During Orthostatic Stress AU - Mader, Greg AU - Olufsen, Mette AU - Mahdi, Adam T2 - Annals of Biomedical Engineering DA - 2014/12/31/ PY - 2014/12/31/ DO - 10.1007/s10439-014-1220-4 VL - 43 IS - 8 SP - 1748-1758 J2 - Ann Biomed Eng LA - en OP - SN - 0090-6964 1573-9686 UR - http://dx.doi.org/10.1007/s10439-014-1220-4 DB - Crossref KW - Cerebral autoregulation KW - Blood pressure KW - Structural identifiability KW - Practical identifiability KW - Viscoelasticity KW - Sensitivity analysis ER - TY - JOUR TI - Evaluation of Diffusive Transport and Cellular Uptake of Nutrients in Tissue Engineered Constructs Using a Hybrid Discrete Mathematical Model AU - Aristotelous, Andreas AU - Haider, Mansoor T2 - Processes AB - Tissue engineering systems for orthopedic tissues, such as articular cartilage, are often based on the use of biomaterial scaffolds that are seeded with cells and supplied with nutrients or growth factors. In such systems, relationships between the functional outcomes of the engineered tissue construct and aspects of the initial system design are not well known, suggesting the use of mathematical models as an additional tool for optimal system design. This study develops a reaction-diffusion model that quantitatively describes the competing effects of nutrient diffusion and the cellular uptake of nutrients in a closed bioreactor system consisting of a cell-seeded scaffold adjacent to a nutrient-rich bath. An off-lattice hybrid discrete modeling framework is employed in which the diffusion equation incorporates a loss term that accounts for absorption due to nutrient uptake by cells that are modeled individually. Numerical solutions are developed based on a discontinuous Galerkin finite element method with high order quadrature to accurately resolve fine-scale cellular effects. The resulting model is applied to demonstrate that the ability of cells to absorb nutrients over time is highly dependent on both the normal distance to the nutrient bath, as well as the nutrient uptake rate for individual cells. DA - 2014/3/28/ PY - 2014/3/28/ DO - 10.3390/pr2020333 VL - 2 IS - 2 SP - 333-344 J2 - Processes LA - en OP - SN - 2227-9717 UR - http://dx.doi.org/10.3390/pr2020333 DB - Crossref KW - reaction-diffusion model KW - hybrid discrete model KW - discontinuous Galerkin ER - TY - JOUR TI - A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization AU - Mehrotra, Sanjay AU - Papp, Dávid T2 - SIAM Journal on Optimization AB - We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date. DA - 2014/1// PY - 2014/1// DO - 10.1137/130925013 VL - 24 IS - 4 SP - 1670-1697 J2 - SIAM J. Optim. LA - en OP - SN - 1052-6234 1095-7189 UR - http://dx.doi.org/10.1137/130925013 DB - Crossref KW - semi-infinite programming KW - robust optimization KW - distributionally robust optimization KW - stochastic programming KW - moment matching KW - column generation KW - cutting surface methods KW - cutting plane methods KW - moment problem ER - TY - JOUR TI - Shared data for intensity modulated radiation therapy (IMRT) optimization research: the CORT dataset AU - Craft, David AU - Bangert, Mark AU - Long, Troy AU - Papp, Dávid AU - Unkelbach, Jan T2 - GigaScience AB - We provide common datasets (which we call the CORT dataset: common optimization for radiation therapy) that researchers can use when developing and contrasting radiation treatment planning optimization algorithms. The datasets allow researchers to make one-to-one comparisons of algorithms in order to solve various instances of the radiation therapy treatment planning problem in intensity modulated radiation therapy (IMRT), including beam angle optimization, volumetric modulated arc therapy and direct aperture optimization. We provide datasets for a prostate case, a liver case, a head and neck case, and a standard IMRT phantom. We provide the dose-influence matrix from a variety of beam/couch angle pairs for each dataset. The dose-influence matrix is the main entity needed to perform optimizations: it contains the dose to each patient voxel from each pencil beam. In addition, the original Digital Imaging and Communications in Medicine (DICOM) computed tomography (CT) scan, as well as the DICOM structure file, are provided for each case. Here we present an open dataset – the first of its kind – to the radiation oncology community, which will allow researchers to compare methods for optimizing radiation dose delivery. DA - 2014/12// PY - 2014/12// DO - 10.1186/2047-217x-3-37 VL - 3 IS - 1 J2 - GigaSci LA - en OP - SN - 2047-217X UR - http://dx.doi.org/10.1186/2047-217x-3-37 DB - Crossref KW - IMRT KW - Optimization KW - Radiation therapy KW - Beam angle optimization KW - VMAT KW - Treatment plan optimization ER - TY - JOUR TI - Exploiting tumor shrinkage through temporal optimization of radiotherapy AU - Unkelbach, Jan AU - Craft, David AU - Hong, Theodore AU - Papp, Dávid AU - Ramakrishnan, Jagdish AU - Salari, Ehsan AU - Wolfgang, John AU - Bortfeld, Thomas T2 - Physics in Medicine and Biology AB - In multi-stage radiotherapy, a patient is treated in several stages separated by weeks or months. This regimen has been motivated mostly by radiobiological considerations, but also provides an approach to reduce normal tissue dose by exploiting tumor shrinkage. The paper considers the optimal design of multi-stage treatments, motivated by the clinical management of large liver tumors for which normal liver dose constraints prohibit the administration of an ablative radiation dose in a single treatment. We introduce a dynamic tumor model that incorporates three factors: radiation induced cell kill, tumor shrinkage, and tumor cell repopulation. The design of multi-stage radiotherapy is formulated as a mathematical optimization problem in which the total dose to the liver is minimized, subject to delivering the prescribed dose to the tumor. Based on the model, we gain insight into the optimal administration of radiation over time, i.e. the optimal treatment gaps and dose levels. We analyze treatments consisting of two stages in detail. The analysis confirms the intuition that the second stage should be delivered just before the tumor size reaches a minimum and repopulation overcompensates shrinking. Furthermore, it was found that, for a large range of model parameters, approximately one third of the dose should be delivered in the first stage. The projected benefit of multi-stage treatments depends on model assumptions. However, the model predicts large liver dose reductions by more than a factor of two for plausible model parameters. The analysis of the tumor model suggests that substantial reduction in normal tissue dose can be achieved by exploiting tumor shrinkage via an optimal design of multi-stage treatments. This suggests taking a fresh look at multi-stage radiotherapy for selected disease sites where substantial tumor regression translates into reduced target volumes. DA - 2014/5/19/ PY - 2014/5/19/ DO - 10.1088/0031-9155/59/12/3059 VL - 59 IS - 12 SP - 3059-3079 J2 - Phys. Med. Biol. OP - SN - 0031-9155 1361-6560 UR - http://dx.doi.org/10.1088/0031-9155/59/12/3059 DB - Crossref KW - temporal optimization KW - split-course radiotherapy KW - tumor shrinkage KW - liver tumors ER - TY - JOUR TI - Plan averaging for multicriteria navigation of sliding window IMRT and VMAT AU - Craft, David AU - Papp, Dávid AU - Unkelbach, Jan T2 - Medical Physics AB - Purpose: To describe a method for combining sliding window plans [intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT)] for use in treatment plan averaging, which is needed for Pareto surface navigation based multicriteria treatment planning. Methods: The authors show that by taking an appropriately defined average of leaf trajectories of sliding window plans, the authors obtain a sliding window plan whose fluence map is the exact average of the fluence maps corresponding to the initial plans. In the case of static‐beam IMRT, this also implies that the dose distribution of the averaged plan is the exact dosimetric average of the initial plans. In VMAT delivery, the dose distribution of the averaged plan is a close approximation of the dosimetric average of the initial plans. Results: The authors demonstrate the method on three Pareto optimal VMAT plans created for a demanding paraspinal case, where the tumor surrounds the spinal cord. The results show that the leaf averaged plans yield dose distributions that approximate the dosimetric averages of the precomputed Pareto optimal plans well. Conclusions: The proposed method enables the navigation of deliverable Pareto optimal plans directly, i.e., interactive multicriteria exploration of deliverable sliding window IMRT and VMAT plans, eliminating the need for a sequencing step after navigation and hence the dose degradation that is caused by such a sequencing step. DA - 2014/1/14/ PY - 2014/1/14/ DO - 10.1118/1.4859295 VL - 41 IS - 2 SP - 021709 J2 - Med. Phys. LA - en OP - SN - 0094-2405 UR - http://dx.doi.org/10.1118/1.4859295 DB - Crossref KW - VMAT KW - sliding window KW - IMRT KW - dynamic KW - dMLC KW - Pareto ER - TY - JOUR TI - Shape-Constrained Estimation Using Nonnegative Splines AU - Papp, Dávid AU - Alizadeh, Farid T2 - Journal of Computational and Graphical Statistics AB - AbstractWe consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online.Key Words: Bernstein polynomialsDensity estimationNonnegative polynomialsRegressionSecond-order programmingSemi-definite programmingSplines SUPPLEMENTARY MATERIALSProofs and some other technical details are provided in the supplementary materials as Appendices.Appendix A: Second-order cone programming (SOCP) and semidefinite programming (SDP): A supplementary section with basic information on SOCP and SDP. (appendices.pdf)Appendix B: An SOCP characterization of nonnegative cubic splines: Theorem 3 and proof. (appendices.pdf)Appendix C: Proof of Theorem 1: Proof. (appendices.pdf)AMPL models of shape-constrained spline estimation problems: The AMPL implementation of the shape-constrained regression and density estimation problems considered in the article. File names indicate the included shape constraint and the degrees of the splines whenever it is different from cubic. (AMPLmodels.zip) DA - 2014/1/2/ PY - 2014/1/2/ DO - 10.1080/10618600.2012.707343 VL - 23 IS - 1 SP - 211-231 J2 - Journal of Computational and Graphical Statistics LA - en OP - SN - 1061-8600 1537-2715 UR - http://dx.doi.org/10.1080/10618600.2012.707343 DB - Crossref KW - Bernstein polynomials KW - Density estimation KW - Nonnegative polynomials KW - Regression KW - Second-order programming KW - Semi-definite programming KW - Splines ER - TY - JOUR TI - A Stochastic Investment Model on Finite Time Horizon AU - Pang, T. T2 - Research on Finance and Management DA - 2014/// PY - 2014/// VL - 2 IS - 1 SP - 1–26 ER - TY - BOOK TI - Uncertainty Quantification: Theory, Implementation and Applications AU - Smith, R.C. DA - 2014/// PY - 2014/// PB - SIAM ER - TY - JOUR TI - HDMR applied to the 1-D, Single Speed Neutron Transport k-Eigenvalue Problem AU - Hu, Z. AU - Smith, R. AU - Willert, J. AU - Kelley, C.T. T2 - Nuclear Science and Engineering DA - 2014/// PY - 2014/// VL - 177 SP - 1–11 ER - TY - JOUR TI - Taut Foliations, Left-Orderability, and Cyclic Branched Covers AU - Gordon, Cameron AU - Lidman, Tye T2 - Acta Mathematica Vietnamica AB - We study the question of when cyclic branched covers of knots admit taut foliations, have left-orderable fundamental groups, and are not L-spaces. DA - 2014/12// PY - 2014/12// DO - 10.1007/s40306-014-0091-y VL - 39 IS - 4 SP - 599-635 J2 - Acta Math Vietnam LA - en OP - SN - 0251-4184 2315-4144 UR - http://dx.doi.org/10.1007/s40306-014-0091-y DB - Crossref KW - Taut foliation KW - Left-orderability KW - Cyclic branched cover ER - TY - JOUR TI - Nonfibered L-space knots AU - Lidman, Tye AU - Watson, Liam T2 - Pacific Journal of Mathematics AB - We construct an infinite family of knots in rational homology spheres with irreducible, non-fibered complements, for which every non-longitudinal filling is an L-space. DA - 2014/5/11/ PY - 2014/5/11/ DO - 10.2140/pjm.2014.267.423 VL - 267 IS - 2 SP - 423-429 J2 - Pacific J. Math. LA - en OP - SN - 0030-8730 0030-8730 UR - http://dx.doi.org/10.2140/pjm.2014.267.423 DB - Crossref KW - Heegaard Floer homology KW - L-space KW - fibration ER - TY - JOUR TI - Berge–Gabai knots and L–space satellite operations AU - Hom, Jennifer AU - Lidman, Tye AU - Vafaee, Faramarz T2 - Algebraic & Geometric Topology AB - Let $P(K)$ be a satellite knot where the pattern, $P$, is a Berge-Gabai knot (i.e., a knot in the solid torus with a non-trivial solid torus Dehn surgery), and the companion, $K$, is a non-trivial knot in $S^3$. We prove that $P(K)$ is an L-space knot if and only if $K$ is an L-space knot and $P$ is sufficiently positively twisted relative to the genus of $K$. This generalizes the result for cables due to Hedden and the first author. DA - 2014/12/31/ PY - 2014/12/31/ DO - 10.2140/agt.2014.14.3745 VL - 14 IS - 6 SP - 3745-3763 J2 - Algebr. Geom. Topol. LA - en OP - SN - 1472-2739 1472-2747 UR - http://dx.doi.org/10.2140/agt.2014.14.3745 DB - Crossref ER - TY - JOUR TI - Rank inequalities for the Heegaard Floer homology of Seifert homology spheres AU - Karakurt, Çağrı AU - Lidman, Tye T2 - Transactions of the American Mathematical Society AB - We establish three rank inequalities for the reduced flavor of Heegaard Floer homology of Seifert fibered integer homology spheres. Combining these inequalities with the known classifications of non-zero degree maps between Seifert fibered spaces, we prove that a map f : Y Y f:Y’ \to Y between Seifert homology spheres yields the inequality | deg f | r a n k H F r e d ( Y ) r a n k H F r e d ( Y ) |\deg f|\mathrm {rank} HF_{\mathrm {red}}(Y) \leq \mathrm {rank} HF_{\mathrm {red}}(Y’) . These inequalities are also applied in conjunction with an algorithm of Némethi to give a method to solve the botany problem for the Heegaard Floer homology of these manifolds. DA - 2014/12/23/ PY - 2014/12/23/ DO - 10.1090/s0002-9947-2014-06451-9 VL - 367 IS - 10 SP - 7291-7322 J2 - Trans. Amer. Math. Soc. LA - en OP - SN - 0002-9947 1088-6850 UR - http://dx.doi.org/10.1090/s0002-9947-2014-06451-9 DB - Crossref ER - TY - JOUR TI - Global Existence of Weak Solutions for the Burgers--Hilbert Equation AU - Bressan, Alberto AU - Nguyen, Khai T. T2 - SIAM Journal on Mathematical Analysis AB - This paper establishes the global existence of weak solutions to the Burgers--Hilbert equation, for general initial data in ${\bf L}^2(\mathbb{R})$. For positive times, the solution lies in ${\bf L}^2\cap{\bf L}^\infty$. A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded. DA - 2014/1// PY - 2014/1// DO - 10.1137/140957536 VL - 46 IS - 4 SP - 2884-2904 J2 - SIAM J. Math. Anal. LA - en OP - SN - 0036-1410 1095-7154 UR - http://dx.doi.org/10.1137/140957536 DB - Crossref KW - Burgers-Hilbert equations KW - weak entropy solutions KW - global existence ER - TY - CONF TI - A fast Kalman filter for time-lapse electrical resistivity tomography AU - Saibaba, A.K. AU - Miller, E.L. AU - Kitandis, P.K. AB - We present a reduced complexity algorithm for time-lapse Electrical Resistivity Tomography (ERT) based on an extended Kalman filter. The key idea of the fast algorithm is an efficient representation of state covariance matrix at each step as a weighted combination of the system noise covariance matrix and a low-rank perturbation term. We propose an efficient algorithm for updating the weights and the basis of the low-rank perturbation. The overall computational cost at each iteration is O(Nn m ) and storage cost O(N), where N is the number of grid points, and n m is the number of measurements. The performance of this algorithm is demonstrated on a challenging application of monitoring the CO 2 plume using synthetic ERT data. C2 - 2014/// C3 - International Geoscience and Remote Sensing Symposium (IGARSS) DA - 2014/// DO - 10.1109/IGARSS.2014.6947146 SP - 3152-3155 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84911398513&partnerID=MN8TOARS KW - Extended Kalman Filter KW - Electrical Resistivity Tomography KW - Fast algorithms ER - TY - JOUR TI - Cigarette smoking and ovarian function AU - Gannon, A. M. AU - Sadeu, J. C. AU - Agarwal, S. K. AU - Hughes, C. L. AU - Foster, W. G. T2 - Ovarian Toxicology, 2nd Edition DA - 2014/// PY - 2014/// SP - 229-248 ER - TY - CONF TI - Uncertainty analysis of a finite deformation viscoelastic model AU - Miles, P. AU - Hays, M. AU - Smith, Ralph AU - Oates, W. S. AB - The viscoelasticity of the dielectric elastomer, VHB 4910, is experimentally characterized, modeled, and analyzed using uncertainty quantification. These materials are known for their large field induced deformation and applications in smart structures, although the rate dependent viscoelastic effects are not well understood. To address this issue, we first quantify hyperelastic and viscoelastic model uncertainty by comparing a finite deformation viscoelastic model to uni-axial rate dependent experiments. The utilization of Bayesian statistics is shown to provide additional insight into different viscoelastic processes within elastomers. This is demonstrated by coupling two hyperelastic models, an Ogden model and a nonaffine model, to different types of viscoelastic models. C2 - 2014/// C3 - Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, 2014, vol 2 DA - 2014/// DO - 10.1115/smasis2014-7440 ER - TY - CONF TI - Tensor product decomposition of (sl)over-cap(n) modules and identities AU - Misra, K. C. AU - Wilson, E. A. C2 - 2014/// C3 - Ramanujan 125 DA - 2014/// VL - 627 SP - 131-144 ER - TY - CONF TI - Model calibration for beam models in the presence of model discrepancy AU - Lewis, A. L. AU - McMahan, J. A. AU - Smith, Ralph AB - Piezoelectric, magnetic and shape memory alloy (SMA) materials offer unique capabilities for energy harvesting and reduced energy requirements in aerospace, aeronautic, automotive, industrial and biomedical applications. However, all of these materials exhibit creep, rate-dependent hysteresis, and constitutive nonlinearities that must be incorporated in models and model-based control designs to achieve their full potential. Furthermore, models and control designs must be constructed in a manner that incorporates parameter and model uncertainties and permits predictions with quantified uncertainties. In this presentation, we compare the Euler-Bernoulli and Timoshenko beam models for a cantilever beam with an applied PZT patch to illustrate parameter estimation in the presence of model discrepancy. C2 - 2014/// C3 - Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, 2014, vol 1 DA - 2014/// DO - 10.1115/smasis2014-7722 ER - TY - BOOK TI - Mathematical software - ICMS 2014: 4th International Congress, Seoul, South Korea, August 5-9, 2014 : Proceedings A3 - Hong, H. A3 - Yap, C. DA - 2014/// PY - 2014/// PB - Heidelberg: Springer ER - TY - BOOK TI - Economic Dynamics of All Members of the United Nations, 2nd Edition AU - Chukwu, EN AB - This book provides an enduring response to modern economic problems and the consequent crises, dealing with the economic modelling of nations and the forecasting of economic growth. The main arguments DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8 VL - 10 SE - 1-196 SN - 978-94-6239-075-1 ER - TY - JOUR TI - On the summability of bivariate rational functions AU - Chen, Shaoshi AU - Singer, Michael F. T2 - JOURNAL OF ALGEBRA AB - We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated, first, in terms of single sums and, finally, in terms of values of special functions. DA - 2014/7/1/ PY - 2014/7/1/ DO - 10.1016/j.jalgebra.2014.03.023 VL - 409 SP - 320-343 SN - 1090-266X KW - Gosper algorithm KW - Summability KW - Double zeta values ER - TY - JOUR TI - On the solvability of nonlinear impulsive boundary value problems AU - Maroncelli, D. AU - Rodriguez, J. T2 - Topological Methods in Nonlinear Analysis AB - In this paper we provide sufficient conditions for the existence of solutions to two-point boundary value problems for nonlinear ordinary differential equations subject to impulses. Our results depend on properties of the nonlinearities as well as on the solution space of the associated linear problem. Our approach is based on topological degree arguments in conjunction with the Lyapunov-Schmidt procedure. DA - 2014/// PY - 2014/// DO - 10.12775/tmna.2014.052 VL - 44 IS - 2 SP - 381-398 ER - TY - JOUR TI - Morse theory for Lagrange multipliers and adiabatic limits AU - Schecter, Stephen AU - Xu, Guangbo T2 - JOURNAL OF DIFFERENTIAL EQUATIONS AB - Given two Morse functions f,μ on a compact manifold M, we study the Morse homology for the Lagrange multiplier function on M×R, which sends (x,η) to f(x)+ημ(x). Take a product metric on M×R, and rescale its R-component by a factor λ2. We show that generically, for large λ, the Morse–Smale–Witten chain complex is isomorphic to the one for f and the metric restricted to μ−1(0), with grading shifted by one. On the other hand, in the limit λ→0, we obtain another chain complex, which is geometrically quite different but has the same homology as the singular homology of μ−1(0). The isomorphism between the chain complexes is provided by the homotopy obtained by varying λ. Our proofs use both the implicit function theorem on Banach manifolds and geometric singular perturbation theory. DA - 2014/12/15/ PY - 2014/12/15/ DO - 10.1016/j.jde.2014.08.018 VL - 257 IS - 12 SP - 4277-4318 SN - 1090-2732 KW - Morse homology KW - Geometric singular perturbation theory KW - Exchange lemma KW - Adiabatic limit ER - TY - CONF TI - ncertainty quantification for robust control design of smart material systems AU - McMahan, J. A. AU - Smith, Ralph AB - The objective in robust control design is to provide mechanisms to achieve tracking or stabilization objectives in the presence of unmodeled dynamics. This is usually achieved by assuming worst case model discrepancies which can significantly degrade control authority if the uncertainty bounds are overly conservative. In this paper, we use uncertainty quantification techniques to construct densities for control outputs that can be used to derive optimal robust control designs. We illustrate the performance of these techniques in the context of systems with smart material actuators and sensors. C2 - 2014/// C3 - Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems - 2013, vol 1 DA - 2014/// DO - 10.1115/smasis2013-3166 ER - TY - JOUR TI - Two by two units AU - Hartwig, R. E. AU - Patricio, P. T2 - Electronic Journal of Linear Algebra AB - In this paper, we will use outer inverses and the Brown-McCoy shift to characterize the existence of the inverse and group inverse of a 2 × 2 block matrix. DA - 2014/// PY - 2014/// DO - 10.13001/1081-3810.1632 VL - 27 SP - 489-503 ER - TY - JOUR TI - Realizations of Affine Lie Algebra A(1)((1)) at Negative Levels AU - Dong, Jilan AU - Jing, Naihuan T2 - ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS (AGMP) AB - A realization of the affine Lie algebra $${A^{(1)}_1}$$ and the relevant $$Z$$ -algebra at negative level $$-k$$ is given in terms of parafermions. This generalizes the recent work on realization of the affine Lie algebra at the critical level. DA - 2014/// PY - 2014/// DO - 10.1007/978-3-642-55361-5_36 VL - 85 SP - 603-616 SN - 2194-1009 ER - TY - JOUR TI - Patient-specific modelling of head-up tilt AU - Williams, Nakeya D. AU - Wind-Willassen, Oistein AU - Wright, Andrew A. AU - Program, Reu AU - Mehlsen, Jesper AU - Ottesen, Johnny T. AU - Olufsen, Mette S. T2 - MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA AB - Short-term cardiovascular responses to head-up tilt (HUT) involve complex cardiovascular regulation in order to maintain blood pressure at homoeostatic levels. This manuscript presents a patient-specific model that uses heart rate as an input to fit the dynamic changes in arterial blood pressure data during HUT. The model contains five compartments representing arteries and veins in the upper and lower body of the systemic circulation, as well as the left ventricle facilitating pumping of the heart. A physiologically based submodel describes gravitational pooling of the blood into the lower extremities during HUT, and a cardiovascular regulation model adjusts cardiac contractility and vascular resistance to the blood pressure changes. Nominal parameter values are computed from patient-specific data and literature estimates. The model is rendered patient specific via the use of parameter estimation techniques. This process involves sensitivity analysis, prediction of a subset of identifiable parameters, and non-linear optimization. The approach proposed here was applied to the analysis of aortic and carotid HUT data from five healthy young subjects. Results showed that it is possible to identify a subset of model parameters that can be estimated allowing the model to fit changes in arterial blood pressure observed at the level of the carotid bifurcation. Moreover, the model estimates physiologically reasonable values for arterial and venous blood pressures, blood volumes and cardiac output for which data are not available. DA - 2014/12// PY - 2014/12// DO - 10.1093/imammb/dqt004 VL - 31 IS - 4 SP - 365-392 SN - 1477-8602 KW - cardiovascular system dynamics KW - head-up tilt KW - sensitivity analysis KW - subset selection KW - parameter estimation ER - TY - CONF TI - Construction of Bayesian prediction intervals for smart systems AU - Wentworth, M. T. AU - Smith, Ralph AB - In this paper, we employ adaptive Metropolis algorithms to construct densities for parameters and quantities of interest for models arising in the analysis of smart material structures. In the first step of the construction, MCMC algorithms are used to quantify the uncertainty in parameters due to measurement errors. We then combine uncertainties from the input parameters and measurement errors, and construct prediction intervals for the quantity of interest by propagating uncertainties through the models. C2 - 2014/// C3 - Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems - 2013, vol 1 DA - 2014/// DO - 10.1115/smasis2013-3168 ER - TY - JOUR TI - Antipathogen genes and the replacement of disease-vectoring mosquito populations: a model-based evaluation AU - Robert, Michael A. AU - Okamoto, Kenichi W. AU - Gould, Fred AU - Lloyd, Alun L. T2 - Evolutionary Applications AB - Recently, genetic strategies aimed at controlling populations of disease-vectoring mosquitoes have received considerable attention as alternatives to traditional measures. Theoretical studies have shown that female-killing (FK), antipathogen (AP), and reduce and replace (R&R) strategies can each decrease the number competent vectors. In this study, we utilize a mathematical model to evaluate impacts on competent Aedes aegypti populations of FK, AP, and R&R releases as well as hybrid strategies that result from combinations of these three approaches. We show that while the ordering of efficacy of these strategies depends upon population life history parameters, sex ratio of releases, and switch time in combination strategies, AP-only and R&R/AP releases typically lead to the greatest long-term reduction in competent vectors. R&R-only releases are often less effective at long-term reduction of competent vectors than AP-only releases or R&R/AP releases. Furthermore, the reduction in competent vectors caused by AP-only releases is easier to maintain than that caused by FK-only or R&R-only releases even when the AP gene confers a fitness cost. We discuss the roles that density dependence and inclusion of females play in the order of efficacy of the strategies. We anticipate that our results will provide added impetus to continue developing AP strategies. DA - 2014/10/10/ PY - 2014/10/10/ DO - 10.1111/eva.12219 VL - 7 IS - 10 SP - 1238-1251 J2 - Evol Appl LA - en OP - SN - 1752-4571 UR - http://dx.doi.org/10.1111/eva.12219 DB - Crossref KW - Aedes aegypti KW - antipathogen genes KW - dengue fever KW - female-killing KW - ordinary differential equation model KW - reduce and replace ER - TY - CONF TI - Uncertainty quantification for a model of HIV-1 patient response to antiretroviral therapy interruptions AU - Baraldi, R. AU - Cross, K. AU - McChesney, C. AU - Poag, L. AU - Thorpe, E. AU - Flores, K. B. AU - Banks, H. T. C2 - 2014/// C3 - 2014 american control conference (acc) DA - 2014/// SP - 2753-2758 ER - TY - JOUR TI - THE EFFECT OF COHERENCE ON SAMPLING FROM MATRICES WITH ORTHONORMAL COLUMNS, AND PRECONDITIONED LEAST SQUARES PROBLEMS AU - Ipsen, Ilse C. F. AU - Wentworth, Thomas T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS AB - Motivated by the least squares solver Blendenpik, we investigate three strategies for uniform sampling of rows from $m\times n$ matrices $Q$ with orthonormal columns. The goal is to determine, with high probability, how many rows are required so that the sampled matrices have full rank and are well-conditioned with respect to inversion. Extensive numerical experiments illustrate that the three sampling strategies (without replacement, with replacement, and Bernoulli sampling) behave almost identically, for small to moderate amounts of sampling. In particular, sampled matrices of full rank tend to have two-norm condition numbers of at most 10. We derive a bound on the condition number of the sampled matrices in terms of the coherence $\mu$ of $Q$. This bound applies to all three different sampling strategies; it implies a, not necessarily tight, lower bound of $\mathcal{O}(m\mu\ln{n})$ for the number of sampled rows; and it is realistic and informative even for matrices of small dimension and the stringent requirement of a 99 percent success probability. For uniform sampling with replacement we derive a potentially tighter condition number bound in terms of the leverage scores of $Q$. To obtain a more easily computable version of this bound, in terms of just the largest leverage scores, we first derive a general bound on the two-norm of diagonally scaled matrices. To facilitate the numerical experiments and test the tightness of the bounds, we present algorithms to generate matrices with user-specified coherence and leverage scores. These algorithms, the three sampling strategies, and a large variety of condition number bounds are implemented in the MATLAB toolbox kappa_SQ. DA - 2014/// PY - 2014/// DO - 10.1137/120870748 VL - 35 IS - 4 SP - 1490-1520 SN - 1095-7162 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84919934241&partnerID=MN8TOARS KW - condition number KW - singular values KW - leverage scores KW - sums of random matrices KW - majorization KW - preconditioning KW - QR factorization ER - TY - CONF TI - Decomposition of permittivity contributions from reflectance using mechanism models AU - Banks, H. T. AU - Catenacci, J. AU - Hu, S. H. AU - Kenz, Z. R. C2 - 2014/// C3 - 2014 american control conference (acc) DA - 2014/// SP - 367-372 ER - TY - JOUR TI - 'Mountain Rouge': A pink-fruited, heirloom-type hybrid tomato and its parent line NC 161L AU - Panthee, D. R. AU - Gardner, R. G. T2 - HortScience DA - 2014/// PY - 2014/// VL - 49 IS - 11 SP - 1463-1464 ER - TY - JOUR TI - 'Mountain Lion': A large-fruited, extended shelf-life hybrid tomato and its parent line, NC 2rinEC AU - Panthee, D. R. AU - Gardner, R. G. T2 - HortScience DA - 2014/// PY - 2014/// VL - 49 IS - 11 SP - 1461-1462 ER - TY - JOUR TI - Special issue on fluid structure interactions preface AU - Li, Z. L. T2 - Numerical Mathematics: Theory, Methods and Applications DA - 2014/// PY - 2014/// VL - 7 IS - 4 SP - I- ER - TY - JOUR TI - Global biogeographic regions in a human-dominated world: the case of human diseases AU - Just, Michael G. AU - Norton, Jacob F. AU - Traud, Amanda L. AU - Antonelli, Tim AU - Poteate, Aaron S. AU - Backus, Gregory A. AU - Snyder-Beattie, Andrew AU - Sanders, R. Wyatt AU - Dunn, Robert R. T2 - ECOSPHERE AB - Since the work of Alfred Russel Wallace, biologists have sought to divide the world into biogeographic regions that reflect the history of continents and evolution. These divisions not only guide conservation efforts, but are also the fundamental reference point for understanding the distribution of life. However, the biogeography of human‐associated species—such as pathogens, crops, or even house guests—has been largely ignored or discounted. As pathogens have the potential for direct consequences on the lives of humans, domestic animals, and wildlife it is prudent to examine their potential biogeographic history. Furthermore, if distinct regions exist for human‐associated pathogens, it would provide possible connections between human wellbeing and pathogen distributions, and, more generally, humans and the deep evolutionary history of the natural world. We tested for the presence of biogeographic regions for diseases of humans due to pathogens using country‐level disease composition data and compared the regions for vectored and non‐vectored diseases. We found discrete biogeographic regions for diseases, with a stronger influence of biogeography on vectored than non‐vectored diseases. We also found significant correlations between these biogeographic regions and environmental or socio‐political factors. While some biogeographic regions reflected those already documented for birds or mammals, others reflected colonial history. From the perspective of diseases caused by pathogens, humans have altered but not evaded the influence of ancient biogeography. This work is the necessary first step in examining the biogeographic relationship between humans and their associates. DA - 2014/11// PY - 2014/11// DO - 10.1890/es14-00201.1 VL - 5 IS - 11 SP - SN - 2150-8925 KW - colonial KW - human associates KW - pathogens ER - TY - JOUR TI - A Robin-Robin Domain Decomposition Method for a Stokes-Darcy Structure Interaction with a Locally Modified Mesh AU - Wang, Zhaohui AU - Li, Zhilin AU - Lubkin, Sharon T2 - Numerical Mathematics-Theory Methods and Applications AB - A new numerical method based on locally modified Cartesian meshes is proposed for solving a coupled system of a fluid flow and a porous media flow. The fluid flow is modeled by the Stokes equations while the porous media flow is modeled by Darcy's law. The method is based on a Robin-Robin domain decomposition method with a Cartesian mesh with local modifications near the interface. Some computational examples are presented and discussed. DA - 2014/// PY - 2014/// DO - 10.4208/nmtma.2014.1305si VL - 7 IS - 4 SP - 435-446 UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000346400800003&KeyUID=WOS:000346400800003 KW - Stokes-Darcy fluid structure interactions KW - Robin-Robin domain decomposition method KW - body fitted mesh KW - locally modified mesh KW - BJS interface condition ER - TY - JOUR TI - Solving Two-Mode Shallow Water Equations Using Finite Volume Methods AU - Castro Diaz, Manuel Jesus AU - Cheng, Yuanzhen AU - Chertock, Alina AU - Kurganov, Alexander T2 - COMMUNICATIONS IN COMPUTATIONAL PHYSICS AB - Abstract In this paper, we develop and study numerical methods for the two-mode shallow water equations recently proposed in [S. STECHMANN, A. MAJDA, and B. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407-432]. Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms. We present several numerical approaches—two operator splitting methods (based on either Roe-type upwind or central-upwind scheme), a central-upwind scheme and a path-conservative central-upwind scheme—and test their performance in a number of numerical experiments. The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method. DA - 2014/11// PY - 2014/11// DO - 10.4208/cicp.180513.230514a VL - 16 IS - 5 SP - 1323-1354 SN - 1991-7120 UR - https://doi-org.prox.lib.ncsu.edu/10.4208/cicp.180513.230514a KW - Two-mode shallow water equations KW - nonconservative products KW - conditional hyperbolicity KW - finite volume methods KW - central-upwind schemes KW - splitting methods KW - upwind schemes ER - TY - JOUR TI - Program Results of Some Nations: Austria and France AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - Just as in Botwana2.m policies can be deduced from the equation for y. It was executed by E. Chukwu. The raw data was taken from International Yearbook publications for 2003 and 2007. DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_10 VL - 10 SP - 155-186 SN - 1875-7642 ER - TY - JOUR TI - ON THE GLOBAL CONVERGENCE OF THE ALTERNATING LEAST SQUARES METHOD FOR RANK-ONE APPROXIMATION TO GENERIC TENSORS AU - Wang, Liqi AU - Chu, Moody T. T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS AB - Tensor decomposition has important applications in various disciplines, but it remains an extremely challenging task even to this date. A slightly more manageable endeavor has been to find a low rank approximation in place of the decomposition. Even for this less stringent undertaking, it is an established fact that tensors beyond matrices can fail to have best low rank approximations, with the notable exception that the best rank-one approximation always exists for tensors of any order. Toward the latter, the most popular approach is the notion of alternating least squares whose specific numerical scheme appears in the form as a variant of the power method. Though the limiting behavior of the objective values is well understood, a proof of global convergence for the iterates themselves has been elusive. This paper partially addresses the missing piece by showing that for almost all tensors, the iterates generated by the alternating least squares method for the rank-one approximation converge globally. The underlying technique employed is an eclectic mix of knowledge from algebraic geometry and dynamical system. DA - 2014/// PY - 2014/// DO - 10.1137/130938207 VL - 35 IS - 3 SP - 1058-1072 SN - 1095-7162 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84907810454&partnerID=MN8TOARS KW - tensor decomposition KW - rank-one tensor approximation KW - alternating least squares KW - global convergence KW - Zariski open set ER - TY - JOUR TI - Impedance boundary conditions for general transient hemodynamics AU - Cousins, Will AU - Gremaud, Pierre A. T2 - INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING AB - We discuss the implementation and calibration of a new generalized structured tree boundary condition for hemodynamics. The main idea is to approximate the impedance corresponding to the vessels downstream from a specific outlet. Unlike previous impedance conditions, the one considered here is applicable to general transient flows as opposed to periodic ones only. The physiological character of the approach significantly simplifies calibration. We also describe a novel way to incorporate autoregulation mechanisms in structured arterial trees at minimal computational cost. The strength of the approach is illustrated and validated on several examples through comparison with clinical data. Copyright © 2014 John Wiley & Sons, Ltd. DA - 2014/11// PY - 2014/11// DO - 10.1002/cnm.2658 VL - 30 IS - 11 SP - 1294-1313 SN - 2040-7947 KW - hemodynamics KW - boundary conditions KW - autoregulation KW - impedance KW - vascular trees ER - TY - JOUR TI - Economic Plans, Programs Policies and Recommendation of 184 Nations AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - In the previous chapter we studied economic growth by modeling through MATLAB regression the growth of gross domestic product, interest rate, employment, value of capital stock, prices, and cumulative balance of payment. It is now a common observation that there is a 30-year gain in the last century of longevity which is related to good health and generation of wealth. Dr. Robert Butler of the International Longevity Center who has studied this for over fifty years affirms this 30-year gain. Furthermore those nations that have a five-year advance in longevity compared to other countries actually have a greater GDP. DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_9 VL - 10 SP - 147-154 SN - 1875-7642 ER - TY - JOUR TI - ERRATA: REGULAR SOLUTIONS OF WAVE EQUATIONS WITH SUPER-CRITICAL SOURCES AND EXPONENTIAL-TO-LOGARITHMIC DAMPING AU - Bociu, Lorena AU - Radu, Petronela AU - Toundykov, Daniel T2 - EVOLUTION EQUATIONS AND CONTROL THEORY AB - This note is an errata for the paper [2] which discusses regular solutions to wave equations with super-critical source terms. The purpose of this note is to address the gap in the proof of uniqueness of such solutions. DA - 2014/6// PY - 2014/6// DO - 10.3934/eect.2014.3.349 VL - 3 IS - 2 SP - 349-354 SN - 2163-2480 KW - Wave equation KW - regular solutions KW - critical exponent KW - super-critical KW - nonlinear damping ER - TY - JOUR TI - Dynamical downscaling of climate change impacts on wind energy resources in the contiguous United States by using a limited-area model with scale-selective data assimilation AU - Liu, B. AU - Costa, K. B. AU - Xie, L. AU - Semazzi, F. H. M. T2 - Advances in Meteorology AB - By using a limited-area model (LAM) in combination with the scale-selective data assimilation (SSDA) approach, wind energy resources in the contiguous United States (CONUS) were downscaled from IPCC CCSM3 global model projections for both current and future climate conditions. An assessment of climate change impacts on wind energy resources in the CONUS region was then conducted. Based on the downscaling results, when projecting into future climate under IPCC’s A1B scenario, the average annual wind speed experiences an overall shift across the CONUS region. From the current climate to the 2040s, the average annual wind speed is expected to increase from 0.1 to 0.2 m s −1 over the Great Plains, Northern Great Lakes Region, and Southwestern United States located southwest of the Rocky Mountains. When projecting into the 2090s from current climate, there is an overall increase in the Great Plains Region and Southwestern United States located southwest of the Rockies with a mean wind speed increase between 0 and 0.1 m s −1 , while, the Northern Great Lakes Region experiences an even greater increase from current climate to 2090s than over the first few decades with an increase of mean wind speed from 0.1 to 0.4 m s −1 . DA - 2014/// PY - 2014/// DO - 10.1155/2014/897246 ER - TY - JOUR TI - Different Modes of Variability over the Tasman Sea: Implications for Regional Climate AU - Liess, Stefan AU - Kumar, Arjun AU - Snyder, Peter K. AU - Kawale, Jaya AU - Steinhaeuser, Karsten AU - Semazzi, Frederick H. M. AU - Ganguly, Auroop R. AU - Samatova, Nagiza F. AU - Kumar, Vipin T2 - JOURNAL OF CLIMATE AB - Abstract A new approach is used to detect atmospheric teleconnections without being bound by orthogonality (such as empirical orthogonal functions). This method employs negative correlations in a global dataset to detect potential teleconnections. One teleconnection occurs between the Tasman Sea and the Southern Ocean. It is related to El Niño–Southern Oscillation (ENSO), the Indian Ocean dipole (IOD), and the southern annular mode (SAM). This teleconnection is significantly correlated with SAM during austral summer, fall, and winter, with IOD during spring, and with ENSO in summer. It can thus be described as a hybrid between these modes. Given previously found relationships between IOD and ENSO, and IOD’s proximity to the teleconnection centers, correlations to IOD are generally stronger than to ENSO. Increasing pressure over the Tasman Sea leads to higher (lower) surface temperature over eastern Australia (the southwestern Pacific) in all seasons and is related to reduced surface temperature over Wilkes Land and Adélie Land in Antarctica during fall and winter. Precipitation responses are generally negative over New Zealand. For one standard deviation of the teleconnection index, precipitation anomalies are positive over Australia in fall, negative over southern Australia in winter and spring, and negative over eastern Australia in summer. When doubling the threshold, the size of the anomalous high-pressure center increases and annual precipitation anomalies are negative over southeastern Australia and northern New Zealand. Eliassen–Palm fluxes quantify the seasonal dependence of SAM, ENSO, and IOD influences. Analysis of the dynamical interactions between these teleconnection patterns can improve prediction of seasonal temperature and precipitation patterns in Australia and New Zealand. DA - 2014/11/15/ PY - 2014/11/15/ DO - 10.1175/jcli-d-13-00713.1 VL - 27 IS - 22 SP - 8466-8486 SN - 1520-0442 KW - Australia KW - Southern Ocean KW - Annular mode KW - ENSO KW - Teleconnections KW - Drought ER - TY - JOUR TI - DYNAMIC MODELING OF BEHAVIOR CHANGE AU - Banks, H. T. AU - Rehm, Keri L. AU - Sutton, Karyn L. AU - Davis, Christine AU - Hail, Lisa AU - Kuerbis, Alexis AU - Morgenstern, Jon T2 - QUARTERLY OF APPLIED MATHEMATICS AB - We consider a conceptual and quantitative modeling approach for investigating dynamic behavior change. While the approach is applicable to behavior change in eating disorders, smoking, substance abuse and other behavioral disorders, here we present our novel dynamical systems modeling approach to understand the processes governing an individual’s behavior in the context of problem drinking. Recent advances in technology have resulted in large intensive longitudinal data sets which are particularly well suited for study within such frameworks. However, the lack of previous work in this area (specifically, on the inter- and intra-personal factors governing the drinking behavior of individuals) renders this a daunting and unique challenge. As a result, issues which are typically routine in mathematical modeling require considerable effort such as the determination of key quantities of interest, and the timescale on which to represent them. We discuss the construction of an initial mathematical model for two starkly distinct individuals and make a case for the potential for such efforts to help in understanding the underlying mechanisms responsible for behavior change in problem drinkers. DA - 2014/// PY - 2014/// DO - 10.1090/s0033-569x-2014-01296-3 VL - 72 IS - 2 SP - 209-251 SN - 1552-4485 KW - Mathematical psychology KW - inverse problems KW - delay differential equations KW - behavior change KW - model comparison ER - TY - JOUR TI - CRITICAL SCALE FOR A CONTINUOUS AIMD MODEL AU - Grigorescu, Ilie AU - Kang, Min T2 - STOCHASTIC MODELS AB - AbstractA scaled version of the general AIMD model of transmission control protocol (TCP) used in Internet traffic congestion management leads to a Markov process x(t) representing the time dependent data flow that moves forward with constant speed on the positive axis and jumps backward to γx(t), 0 < γ < 1 according to a Poisson clock whose rate α(x) depends on the interval swept in between jumps. We give sharp conditions for Harris recurrence and analyze the convergence to equilibrium on multiple scales (polynomial, fractional exponential, exponential) identifying the critical case xα(x) ∼ β. Criticality has different behavior according to whether it occurs at the origin or infinity. In each case, we determine the transient (possibly explosive), null—and positive—recurrent regimes by comparing β to ( − ln γ)− 1.Keywords: AIMDCriticalityGeometric ergodicityHarris recurrenceLocal Doeblin conditionTCPMathematics Subject Classification: Primary 60K30Secondary 60J25, 90B20 DA - 2014/// PY - 2014/// DO - 10.1080/15326349.2014.932697 VL - 30 IS - 3 SP - 319-343 SN - 1532-4214 KW - AIMD KW - Criticality KW - Geometric ergodicity KW - Harris recurrence KW - Local Doeblin condition KW - TCP ER - TY - JOUR TI - Bifurcation analysis of a menstrual cycle model reveals multiple mechanisms linking testosterone and classical PCOS AU - Hendrix, Angelean O. AU - Selgrade, James F. T2 - JOURNAL OF THEORETICAL BIOLOGY AB - A system of 16 differential equations is described which models hormonal regulation of the menstrual cycle focusing on the effects of the androgen testosterone (T) on follicular development and on the synthesis of luteinizing hormone (LH) in the pituitary. Model simulations indicate two stable menstrual cycles - one cycle fitting data in the literature for normal women and the other cycle being anovulatory because of no LH surge. Bifurcations with respect to sensitive model parameters illustrate various characteristics of polycystic ovarian syndrome (PCOS), a leading cause of female infertility. For example, varying one parameter retards the growth of preantral follicles and produces a "stockpiling" of these small follicles as observed in the literature for some PCOS women. Modifying another parameter increases the stimulatory effect of T on LH synthesis resulting in reduced follicular development and anovulation. In addition, the model illustrates how anovulatory and hyperandrogenic cycles which are characteristic of PCOS can be reproduced by perturbing both pituitary sensitivity to T and the follicular production of T. Thus, this model suggests that for some women androgenic activity at the levels of both the pituitary and the ovaries may contribute to the etiology of PCOS. DA - 2014/11/21/ PY - 2014/11/21/ DO - 10.1016/j.jtbi.2014.07.020 VL - 361 SP - 31-40 SN - 1095-8541 KW - Hysteresis KW - Parameters KW - Estradiol KW - Follicle KW - Pituitary ER - TY - JOUR TI - An Eulerian-Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs AU - Chertock, Alina AU - Herty, Michael AU - Kurganov, Alexander T2 - COMPUTATIONAL OPTIMIZATION AND APPLICATIONS DA - 2014/12// PY - 2014/12// DO - 10.1007/s10589-014-9655-y VL - 59 IS - 3 SP - 689-724 SN - 1573-2894 UR - https://doi-org.prox.lib.ncsu.edu/10.1007/s10589-014-9655-y KW - Optimal control KW - Multidimensional hyperbolic partial differential equations KW - Numerical methods ER - TY - JOUR TI - A study of singular spectrum analysis with global optimization techniques AU - Chu, Moody T. AU - Lin, Matthew M. AU - Wang, Liqi T2 - JOURNAL OF GLOBAL OPTIMIZATION DA - 2014/11// PY - 2014/11// DO - 10.1007/s10898-013-0117-3 VL - 60 IS - 3 SP - 551-574 SN - 1573-2916 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84920878763&partnerID=MN8TOARS KW - Singular spectrum analysis KW - Time series KW - Hankel operator KW - Semi-infinite matrix KW - Low rank approximation KW - Vandermonde factorization KW - Global optimization ER - TY - JOUR TI - A direct sampling method for electrical impedance tomography AU - Chow, Yat Tin AU - Ito, Kazufumi AU - Zou, Jun T2 - INVERSE PROBLEMS AB - This work investigates the electrical impedance tomography (EIT) problem in the case when only one or two pairs of Cauchy data is available, which is known to be very difficult in achieving high reconstruction quality owing to its severely ill-posed nature. We propose a simple and efficient direct sampling method (DSM) to locate inhomogeneous inclusions. A new probing function based on the dipole potential is introduced to construct an indicator function for imaging the inclusions. Explicit formulae for the probing and indicator functions are derived in the case when the sampling domain is of spherical geometry in (n = 2, 3). This new method is easy to implement and computationally cheap. Numerical experiments are presented to demonstrate the robustness and effectiveness of the DSM, which provides a new numerical approach for solving the EIT problem. DA - 2014/9// PY - 2014/9// DO - 10.1088/0266-5611/30/9/095003 VL - 30 IS - 9 SP - SN - 1361-6420 KW - electrical impedance tomography KW - limited data KW - inhomogeneous inclusions KW - probing function KW - indicator function KW - reconstruction algorithm ER - TY - CHAP TI - A Note on Global Newton Iteration Over Archimedean and Non-Archimedean Fields AU - Hauenstein, Jonathan D. AU - Pan, Victor Y. AU - Szanto, Agnes T2 - Computer Algebra in Scientific Computing AB - In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called a global Newton iterations. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approximate roots; the second one considers the coefficients in the exact RUR as zeroes of a high dimensional map defined by polynomial reduction and applies Newton iteration on this map. We prove that over fields with a p-adic valuation these two approaches give the same iteration function. However, over fields equipped with the usual Archimedean absolute value they are not equivalent. In the latter case, we give explicitly the iteration function for both approaches. Finally, we analyze the parallel complexity of the different versions of the global Newton iteration, compare them, and demonstrate that they can be efficiently computed. The motivation for this study comes from the certification of approximate roots of overdetermined and singular polynomial systems via the recovery of an exact RUR from approximate numerical data. PY - 2014/// DO - 10.1007/978-3-319-10515-4_15 VL - 8660 SP - 202-217 OP - PB - Springer International Publishing SN - 9783319105147 9783319105154 UR - http://dx.doi.org/10.1007/978-3-319-10515-4_15 DB - Crossref ER - TY - JOUR TI - A Hybrid Deterministic/Monte Carlo Method for Solving the k-Eigenvalue Problem with a Comparison to Analog Monte Carlo Solutions AU - Willert, J. AU - Kelley, C. T. AU - Knoll, D. A. AU - Park, H. T2 - Journal of Computational and Theoretical Transport AB - In this article we present a hybrid deterministic/Monte Carlo algorithm for computing the dominant eigenvalue/eigenvector pair for the neutron transport k-eigenvalue problem in multiple space dimensions. We begin by deriving the Nonlinear Diffusion Acceleration method (Knoll, Park, and Newman, 2011; Park, Knoll, and Newman, 2012 Park, H., Knoll, D.A., Newman, C.K. (2012). Nonlinear acceleration of transport criticality problems. Nuclear Science and Engineering 171:1–14. [Google Scholar]) for the k-eigenvalue problem. We demonstrate that we can adapt the algorithm to utilize a Monte Carlo simulation in place of a deterministic transport sweep. We then show that the new hybrid method can be used to solve a two-group, two dimensional eigenvalue problem. The hybrid method is competitive with analog Monte Carlo in terms of number of particle flights required to compute the eigenvalue; however it produces a much less noisy eigenvector and fission source distribution. Furthermore, we show that we can reduce the error induced by the discretization of the low-order system by appropriate refinement of the mesh. DA - 2014/8/22/ PY - 2014/8/22/ DO - 10.1080/00411450.2014.910225 VL - 43 IS - 1-7 SP - 50-67 SN - 2332-4309 2332-4325 UR - http://dx.doi.org/10.1080/00411450.2014.910225 KW - neutron transport KW - k-eigenvalue problem KW - hybrid methods KW - moment-based acceleration ER - TY - JOUR TI - UNIVERSAL GEOMETRIC CLUSTER ALGEBRAS FROM SURFACES AU - Reading, Nathan T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY AB - A universal geometric cluster algebra over an exchange matrix B B is a universal object in the category of geometric cluster algebras over B B related by coefficient specializations. (Following an earlier paper on universal geometric cluster algebras, we broaden the definition of geometric cluster algebras relative to the definition originally given by Fomin and Zelevinsky.) The universal objects are closely related to a fan F B \mathcal {F}_B called the mutation fan for B B . In this paper, we consider universal geometric cluster algebras and mutation fans for cluster algebras arising from marked surfaces. We identify two crucial properties of marked surfaces: The Curve Separation Property and the Null Tangle Property. The latter property implies the former. We prove the Curve Separation Property for all marked surfaces except once-punctured surfaces without boundary components, and as a result we obtain a construction of the rational part of F B \mathcal {F}_B for these surfaces. We prove the Null Tangle Property for a smaller family of surfaces and use it to construct universal geometric coefficients for these surfaces. DA - 2014/12// PY - 2014/12// DO - 10.1090/s0002-9947-2014-06156-4 VL - 366 IS - 12 SP - 6647-6685 SN - 1088-6850 UR - https://doi.org/10.1090/S0002-9947-2014-06156-4 ER - TY - JOUR TI - Torsion in Khovanov homology of semi-adequate links AU - Przytycki, Jozef H. AU - Sazdanovic, Radmila T2 - FUNDAMENTA MATHEMATICAE AB - The goal of this paper is to address A. Shumakovitch's conjecture about the existence of ${\mathbb {Z}}_2$-torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs, which pr DA - 2014/// PY - 2014/// DO - 10.4064/fm225-1-13 VL - 225 IS - 1 SP - 277-303 SN - 1730-6329 KW - Khovanov homology KW - torsion KW - chromatic graph homology KW - adequate links ER - TY - JOUR TI - Robust Estimates of Covariance Matrices in the Large Dimensional Regime AU - Couillet, Romain AU - Pascal, Frederic AU - Silverstein, Jack W. T2 - IEEE TRANSACTIONS ON INFORMATION THEORY AB - This paper studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using tools from random matrix theory, we prove that, for sample vectors made of independent entries having some moment conditions, the difference between the sample covariance matrix and (a scaled version of) such robust estimator tends to zero in spectral norm, almost surely. This result can be applied to various statistical methods arising from random matrix theory that can be made robust without altering their first order behavior. DA - 2014/11// PY - 2014/11// DO - 10.1109/tit.2014.2354045 VL - 60 IS - 11 SP - 7269-7278 SN - 1557-9654 KW - Robust estimation KW - random matrix theory ER - TY - JOUR TI - Quantum Pfaffians and hyper-Pfaffians AU - Jing, Naihuan AU - Zhang, Jian T2 - ADVANCES IN MATHEMATICS AB - The concept of the quantum Pfaffian is rigorously examined and refurbished using the new method of quantum exterior algebras. We derive a complete family of Plücker relations for the quantum linear transformations, and then use them to give an optimal set of relations required for the quantum Pfaffian. We then give the formula between the quantum determinant and the quantum Pfaffian and prove that any quantum determinant can be expressed as a quantum Pfaffian. Finally the quantum hyper-Pfaffian is introduced, and we prove a similar result of expressing quantum determinants in terms of quantum hyper-Pfaffians at modular cases. DA - 2014/11/10/ PY - 2014/11/10/ DO - 10.1016/j.aim.2014.07.007 VL - 265 SP - 336-361 SN - 1090-2082 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84906491080&partnerID=MN8TOARS KW - Quantum Pfaffians KW - q-Forms KW - Quantum determinants ER - TY - JOUR TI - POSITIVE MARGINS AND PRIMARY DECOMPOSITION AU - Kahle, Thomas AU - Rauh, Johannes AU - Sullivant, Seth T2 - JOURNAL OF COMMUTATIVE ALGEBRA AB - We study random walks on contingency tables with fixed marginals, corresponding to a (log-linear) hierarchical model. If the set of allowed moves is not a Markov basis, then there exist tables with the same marginals that are not connected. We study linear conditions on the values of the marginals that ensure that all tables in a given fiber are connected. We show that many graphical models have the positive margins property, which says that all fibers with strictly positive marginals are connected by the quadratic moves that correspond to conditional independence statements. The property persists under natural operations such as gluing along cliques, but we also construct examples of graphical models not enjoying this property. We also provide a negative answer to a question of Engstr\"om, Kahle, and Sullivant by demonstrating that the global Markov ideal of the complete bipartite graph K_(3,3) is not radical. Our analysis of the positive margins property depends on computing the primary decomposition of the associated conditional independence ideal. The main technical results of the paper are primary decompositions of the conditional independence ideals of graphical models of the $N$-cycle and the complete bipartite graph $K_(2,N-2)$, with various restrictions on the size of the nodes. DA - 2014/// PY - 2014/// DO - 10.1216/jca-2014-6-2-173 VL - 6 IS - 2 SP - 173-208 SN - 1939-2346 KW - Algebraic statistics KW - Markov basis KW - connectivity of fibers KW - binomial primary decomposition ER - TY - JOUR TI - Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation AU - Qureshi, M. Umar AU - Vaughan, Gareth D. A. AU - Sainsbury, Christopher AU - Johnson, Martin AU - Peskin, Charles S. AU - Olufsen, Mette S. AU - Hill, N. A. T2 - BIOMECHANICS AND MODELING IN MECHANOBIOLOGY AB - A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281–1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of ‘large’ arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the ‘smaller’ arteries and veins of radii $$\ge $$ 50 $$\upmu $$ m. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung. DA - 2014/10// PY - 2014/10// DO - 10.1007/s10237-014-0563-y VL - 13 IS - 5 SP - 1137-1154 SN - 1617-7940 KW - Pulmonary circulation KW - Pulmonary hypertension KW - Resistance arteries KW - Structured tree KW - Multiscale mathematical model ER - TY - JOUR TI - Elastocapillary deformations on partially-wetting substrates: rival contact-line models AU - Bostwick, Joshua B. AU - Shearer, Michael AU - Daniels, Karen E. T2 - Soft Matter AB - A partially-wetting liquid can deform the underlying elastic substrate upon which it rests. This situation requires the development of theoretical models to describe the wetting forces imparted by the drop onto the solid substrate, particularly those at the contact-line. We construct a general solution using a displacement potential function for the elastic deformations within a finite elastic substrate associated with these wetting forces, and compare the results for several different contact-line models. Our work incorporates internal contributions to the surface stress from both liquid/solid Σls and Σsg solid/gas solid surface tensions (surface stress), which results in a non-standard boundary-value problem that we solve using a dual integral equation. We compare our results to relevant experiments and conclude that the generalization of solid surface tension Σls ≠ Σsg is an essential feature in any model of partial-wetting. The comparisons also allow us to systematically eliminate some proposed contact-line models. DA - 2014/7/31/ PY - 2014/7/31/ DO - 10.1039/C4SM00891J VL - 10 IS - 37 SP - 7361 J2 - Soft Matter LA - en OP - SN - 1744-683X 1744-6848 UR - http://dx.doi.org/10.1039/C4SM00891J DB - Crossref ER - TY - JOUR TI - UNIPOTENT DIFFERENTIAL ALGEBRAIC GROUPS AS PARAMETERIZED DIFFERENTIAL GALOIS GROUPS AU - Minchenko, Andrey AU - Ovchinnikov, Alexey AU - Singer, Michael F. T2 - JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU AB - We deal with aspects of the direct and inverse problems in parameterized Picard-Vessiot (PPV) theory. It is known that, for certain fields, a linear differential algebraic group (LDAG) G is a PPV Galois group over these fields if and only if G contains a Kolchin-dense finitely generated group. We show that, for a class of LDAGs G, including unipotent groups, G is such a group if and only if it has differential type 0. We give a procedure to determine if a parameterized linear differential equation has a PPV Galois group in this class and show how one can calculate the PPV Galois group of a parameterized linear differential equation if its Galois group has differential type 0. DA - 2014/10// PY - 2014/10// DO - 10.1017/s1474748013000200 VL - 13 IS - 4 SP - 671-700 SN - 1475-3030 KW - differential algebraic groups KW - parameterized differential Galois theory KW - algorithms ER - TY - JOUR TI - The Role of the Dominant Modes of Precipitation Variability over Eastern Africa in Modulating the Hydrology of Lake Victoria AU - Smith, Kara A. AU - Semazzi, Fredrick H. M. T2 - ADVANCES IN METEOROLOGY AB - Previous water budget studies over Lake Victoria basin have shown that there is near balance between rainfall and evaporation and that the variability of Lake Victoria levels is determined virtually entirely by changes in rainfall since evaporation is nearly constant. The variability of rainfall over East Africa is dominated by El Niño-Southern Oscillation (ENSO); however, the second and third most dominant rainfall climate modes also account for significant variability across the region. The relationship between ENSO and other significant modes of precipitation variability with Lake Victoria levels is nonlinear. This relationship should be studied to determine which modes need to be accurately modeled in order to accurately model Lake Victoria levels, which are important to the hydroelectric industry in East Africa. The objective of this analysis is to estimate the relative contributions of the dominant modes of annual precipitation variability to the modulation of Lake Victoria levels for the present day (1950–2012). The first mode of annual rainfall variability accounts for most of the variability in Lake Victoria levels, while the effects of the second and third modes are negligible even though these modes are also significant over the region. DA - 2014/// PY - 2014/// DO - 10.1155/2014/516762 VL - 2014 SP - SN - 1687-9317 ER - TY - JOUR TI - Structural correlation method for model reduction and practical estimation of patient specific parameters illustrated on heart rate regulation AU - Ottesen, Johnny T. AU - Mehlsen, Jesper AU - Olufsen, Mette S. T2 - MATHEMATICAL BIOSCIENCES AB - We consider the inverse and patient specific problem of short term (seconds to minutes) heart rate regulation specified by a system of nonlinear ODEs and corresponding data. We show how a recent method termed the structural correlation method (SCM) can be used for model reduction and for obtaining a set of practically identifiable parameters. The structural correlation method includes two steps: sensitivity and correlation analysis. When combined with an optimization step, it is possible to estimate model parameters, enabling the model to fit dynamics observed in data. This method is illustrated in detail on a model predicting baroreflex regulation of heart rate and applied to analysis of data from a rat and healthy humans. Numerous mathematical models have been proposed for prediction of baroreflex regulation of heart rate, yet most of these have been designed to provide qualitative predictions of the phenomena though some recent models have been developed to fit observed data. In this study we show that the model put forward by Bugenhagen et al. can be simplified without loss of its ability to predict measured data and to be interpreted physiologically. Moreover, we show that with minimal changes in nominal parameter values the simplified model can be adapted to predict observations from both rats and humans. The use of these methods make the model suitable for estimation of parameters from individuals, allowing it to be adopted for diagnostic procedures. DA - 2014/11// PY - 2014/11// DO - 10.1016/j.mbs.2014.07.003 VL - 257 SP - 50-59 SN - 1879-3134 KW - Parameter estimation KW - Inverse problems KW - Model reduction KW - Structural correlation method KW - Nonlinear heart rate model KW - Patient specific modeling ER - TY - JOUR TI - Solving the continuous nonlinear resource allocation problem with an interior point method AU - Wright, Stephen E. AU - Rohal, James J. T2 - OPERATIONS RESEARCH LETTERS AB - Resource allocation problems are usually solved with specialized methods exploiting their general sparsity and problem-specific algebraic structure. We show that the sparsity structure alone yields a closed-form Newton search direction for the generic primal-dual interior point method. Computational tests show that the interior point method consistently outperforms the best specialized methods when no additional algebraic structure is available. DA - 2014/9// PY - 2014/9// DO - 10.1016/j.orl.2014.07.001 VL - 42 IS - 6-7 SP - 404-408 SN - 1872-7468 KW - Convex programming KW - Interior point methods KW - Continuous knapsack ER - TY - JOUR TI - Moisture Variability and Multiscale Interactions during Spring in West Africa AU - Mera, Roberto AU - Laing, Arlene G. AU - Semazzi, Frederick T2 - MONTHLY WEATHER REVIEW AB - Abstract The West African monsoon (WAM) is a vital source of rainfall for the African Sahel. In addition to the agricultural benefit of its rains, it benefits public health because bacterial meningitis outbreaks end with the monsoon onset. Outbreaks occur between December and May, a period of low humidity. Knowledge of the onset of high humidity could aid in predicting where the outbreaks will cease. Therefore, this study investigates the variability of atmospheric moisture during the spring over West Africa, characterizing the sources of moisture, as well as circulation patterns and relative influences of tropical and midlatitude systems. A conceptual model of the evolution of the premonsoon period is presented. The meridional and temporal variability of surface moisture during the spring is modulated by multiscale interactions, as illustrated for the period from mid-April to early May 2009. As westward-propagating, synoptic disturbances move across West Africa, a corresponding peak occurs in the surface relative humidity. With the passage of each disturbance a new and more humid regime is established. Filtered anomalies of outgoing longwave radiation (OLR) indicate that Kelvin waves, equatorial Rossby waves, and possibly the MJO contributed to the initiation and intensification of the synoptic disturbances. During the last of the disturbances, whose passage raised the relative humidity above 40%, a critical threshold for meningitis, an extratropical cyclone also contributed to moisture influx over the Sahel. Analysis of the period 2000–09 shows the relative influences of synoptic and subseasonal circulations on the onset of high relative humidity over the Sahel during the spring. DA - 2014/9// PY - 2014/9// DO - 10.1175/mwr-d-13-00175.1 VL - 142 IS - 9 SP - 3178-3198 SN - 1520-0493 ER - TY - JOUR TI - Modeling endocrine regulation of the menstrual cycle using delay differential equations AU - Harris, Leona A. AU - Selgrade, James F. T2 - MATHEMATICAL BIOSCIENCES AB - This article reviews an effective mathematical procedure for modeling hormonal regulation of the menstrual cycle of adult women. The procedure captures the effects of hormones secreted by several glands over multiple time scales. The specific model described here consists of 13 nonlinear, delay, differential equations with 44 parameters and correctly predicts blood levels of ovarian and pituitary hormones found in the biological literature for normally cycling women. In addition to this normal cycle, the model exhibits another stable cycle which may describe a biologically feasible "abnormal" condition such as polycystic ovarian syndrome. Model simulations illustrate how one cycle can be perturbed to the other cycle. Perturbations due to the exogenous administration of each ovarian hormone are examined. This model may be used to test the effects of hormone therapies on abnormally cycling women as well as the effects of exogenous compounds on normally cycling women. Sensitive parameters are identified and bifurcations in model behavior with respect to parameter changes are discussed. Modeling various aspects of menstrual cycle regulation should be helpful in predicting successful hormone therapies, in studying the phenomenon of cycle synchronization and in understanding many factors affecting the aging of the female reproductive endocrine system. DA - 2014/11// PY - 2014/11// DO - 10.1016/j.mbs.2014.08.011 VL - 257 SP - 11-22 SN - 1879-3134 KW - Bifurcation KW - Estradiol KW - Follicle KW - Parameter KW - Pituitary gland ER - TY - JOUR TI - A Numerical Investigation of the Precipitation over Lake Victoria Basin Using a Coupled Atmosphere-Lake Limited-Area Model AU - Sun, Xia AU - Xie, Lian AU - Semazzi, Fredrick H. M. AU - Liu, Bin T2 - ADVANCES IN METEOROLOGY AB - By using a coupled atmosphere-lake model, which consists of the Weather Research and Forecasting (WRF) model and the Princeton Ocean Model (POM), the present study generated realistic lake surface temperature (LST) over Lake Victoria and revealed the prime importance of LST on the precipitation pattern over the Lake Victoria Basin (LVB). A suite of sensitivity experiments was conducted for the selection of an optimal combination of physics options including cumulus, microphysics, and planetary boundary layer schemes for simulating precipitation over the LVB. The WRF-POM coupled system made a great performance on simulating the expected LST, which is featured with eastward temperature gradient as in the real bathymetry of the lake. Under thorough examination of diagnostic analysis, a distinguished diurnal phenomenon has been unveiled. The precipitation mainly occurs during the nocturnal peak between midnight and early in the morning, which is associated with the strong land breeze circulation, when the lake temperature is warmer than the adjacent land. Further exploration of vertical velocity, surface divergence pattern, and maximum radar reflectivity confirms such conjecture. The time-longitude analysis of maximum radar reflectivity over the entire lake also shows a noticeable pattern of dominating westward propagation. DA - 2014/// PY - 2014/// DO - 10.1155/2014/960924 VL - 2014 SP - SN - 1687-9317 ER - TY - JOUR TI - A Note on the Existence of Nonsmooth Nonconvex Optimization Problems AU - Ito, Kazufumi AU - Kunisch, Karl T2 - JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS AB - Sufficient conditions for the existence of a solution to an abstract optimization problem in Banach spaces are given, which do not rely on convexity, regularity properties or a straightforward coerciveness assumption. Applications to sparsity-constrained optimization and to problems from mechanics are provided. DA - 2014/12// PY - 2014/12// DO - 10.1007/s10957-014-0552-4 VL - 163 IS - 3 SP - 697-706 SN - 1573-2878 KW - Nonsmooth KW - Nonconvex optimization KW - Coerciveness ER - TY - JOUR TI - Use of hybrid discrete cellular models for identification of macroscopic nutrient loss in reaction-diffusion models of tissues AU - Aristotelous, Andreas C. AU - Haider, Mansoor A. T2 - INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING AB - SUMMARY Macroscopic models accounting for cellular effects in natural or engineered tissues may involve unknown constitutive terms that are highly dependent on interactions at the scale of individual cells. Hybrid discrete models, which represent cells individually, were used to develop and apply techniques for modeling diffusive nutrient transport and cellular uptake to identify a nonlinear nutrient loss term in a macroscopic reaction–diffusion model of the system. Flexible and robust numerical methods were used, based on discontinuous Galerkin finite elements in space and a Crank–Nicolson temporal discretization. Scales were bridged via averaging operations over a complete set of subdomains yielding data for identification of a macroscopic nutrient loss term that was accurately captured via a fifth‐order polynomial. Accuracy of the identified macroscopic model was demonstrated by direct, quantitative comparisons of the tissue and cellular scale models in terms of three error norms computed on a mesoscale mesh. Copyright © 2014 John Wiley & Sons, Ltd. DA - 2014/8// PY - 2014/8// DO - 10.1002/cnm.2628 VL - 30 IS - 8 SP - 767-780 SN - 2040-7947 KW - reaction-diffusion model KW - hybrid discrete model KW - discontinuous Galerkin KW - averaging KW - model identification KW - mesoscale model ER - TY - JOUR TI - The geometry and integrability of the Suslov problem AU - Fernandez, Oscar E. AU - Bloch, Anthony M. AU - Zenkov, Dmitry V. T2 - JOURNAL OF MATHEMATICAL PHYSICS AB - In this paper, we discuss the integrability of a nonholonomic mechanical system—a generalized Klebsh–Tisserand case of the Suslov problem. Using the theory of Hamiltonization and the Poincaré–Hopf theorem we analyze the topology of the invariant manifolds and in particular describe their genus. We contrast the results with those for Hamiltonian systems. DA - 2014/11// PY - 2014/11// DO - 10.1063/1.4901754 VL - 55 IS - 11 SP - SN - 1089-7658 ER - TY - JOUR TI - The Hereditary Model of GDP and Employment AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - In this section we derive a hereditary model of gross domestic product, y, and employment L by invoking the “demand and supply principle”, and the “rational expectations hypothesis” which assumes that the expected values of economic variables are functions of the current and past values. DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_8 VL - 10 SP - 117-145 SN - 1875-7642 ER - TY - JOUR TI - STABILITY ANALYSIS OF FLOCK AND MILL RINGS FOR SECOND ORDER MODELS IN SWARMING AU - Albi, G. AU - Balague, D. AU - Carrillo, J. A. AU - Von Brecht, J. T2 - SIAM JOURNAL ON APPLIED MATHEMATICS AB - We study the linear stability of flock and mill ring solutions of two individual based models for biological swarming. The individuals interact via a nonlocal interaction potential that is repulsive in the short range and attractive in the long range. We relate the instability of the flock rings with the instability of the ring solution of the first order model. We observe that repulsive-attractive interactions lead to clustering and fattening instabilities for flock rings that prove analogous to similar instabilities that occur for ring solutions of the first order model. Finally, we numerically explore mill patterns arising from these interactions by varying the asymptotic speed of the system. DA - 2014/// PY - 2014/// DO - 10.1137/13091779x VL - 74 IS - 3 SP - 794-818 SN - 1095-712X KW - swarming KW - interacting particles KW - stability of solutions KW - dynamical systems ER - TY - JOUR TI - Reaction Path Following with Sparse Interpolation AU - Nance, James AU - Jakubikova, Elena AU - Kelley, C. T. T2 - Journal of Chemical Theory and Computation AB - Computing the potential energy of an N-atom molecule is an expensive optimization process of 3N - 6 molecular coordinates, so following reaction pathways as a function of all 3N - 6 coordinates is unfeasible for large molecules. In this paper, we present a method that isolates d < 3N - 6 molecular coordinates and continuously follows reaction paths on d-dimensional potential energy surfaces approximated by a Smolyak's sparse grid interpolation algorithm.1 Compared to dense grids, sparse grids efficiently improve the ratio of invested storage and computing time to approximation accuracy and thus allow one to increase the number of coordinates d in molecular reaction path following simulations. Furthermore, evaluation of the interpolant is much less expensive than the evaluation of the actual energy function, so our technique offers a computationally efficient way to simulate reaction paths on ground and excited state potential energy surfaces. To demonstrate the capabilities of our method, we present simulation results for the isomerization of 2-butene with two, three, and six degrees of freedom. DA - 2014/7/11/ PY - 2014/7/11/ DO - 10.1021/ct5004669 VL - 10 IS - 8 SP - 2942-2949 J2 - J. Chem. Theory Comput. LA - en OP - SN - 1549-9618 1549-9626 UR - http://dx.doi.org/10.1021/ct5004669 DB - Crossref ER - TY - JOUR TI - Program Results: Introduction AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - In Sect. 10, Program Result for Some Nations: Austria and France, we display samples of what can be generated from the data, the programs and their execution from the contents of CD-Rom of the 141 nations. DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_11 VL - 10 SP - 187-188 SN - 1875-7642 ER - TY - JOUR TI - Overview of Each Nations Economic State Dynamics and Control: Equations of GDP, Interest Rate, Employment, Value of Capital Stock, Prices, Cumulative Balance of Payment AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - The economic state is x = [y, R, L, k, p, E). We now recall our earlier equations for interest rate [2, p. 29]—Stability and Time Optimal Control of Hereditary Systems with Applications to Economic Dynamics of the USA. Let M denote money supply (e.g., M1). DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_7 VL - 10 SP - 65-115 SN - 1875-7642 ER - TY - JOUR TI - Numerical Study of Singularity Formation in Relativistic Euler Flows AU - Gremaud, Pierre A. AU - Sun, Yi T2 - COMMUNICATIONS IN COMPUTATIONAL PHYSICS AB - Abstract The formation of singularities in relativistic flows is not well understood. Smooth solutions to the relativistic Euler equations are known to have a finite lifespan; the possible breakdown mechanisms are shock formation, violation of the subluminal conditions and mass concentration. We propose a new hybrid Glimm/central-upwind scheme for relativistic flows. The scheme is used to numerically investigate, for a family of problems, which of the above mechanisms is involved. DA - 2014/8// PY - 2014/8// DO - 10.4208/cicp.221212.300114a VL - 16 IS - 2 SP - 348-364 SN - 1991-7120 KW - Relativistic Euler equations KW - singularity formation KW - Glimm scheme KW - central-upwind scheme KW - hybrid method ER - TY - JOUR TI - Infinite dimensional symmetric spaces and Lax equations compatible with the infinite Toda chain AU - Helminck, G. F. AU - Helminck, A. G. T2 - JOURNAL OF GEOMETRY AND PHYSICS AB - In this paper we present a natural embedding of the infinite Toda chain in a set of Lax equations in the algebra L T consisting of Z × Z -matrices that possess only a finite number of nonzero diagonals above the main central diagonal. This hierarchy of Lax equations describes the evolution of deformations of a set of commuting anti-symmetric matrices and corresponds to splitting this algebra into its anti-symmetric part and the subalgebra of matrices in L T that have no component above the main diagonal. We show that the projections of these deformations satisfy a set of zero curvature relations, which demonstrates the compatibility of the system. Further we introduce a suitable L T -module in which we can distinguish elements, the so-called wave matrices, that will lead you to solutions of the hierarchy. We conclude by showing how wave matrices of the infinite Toda chain hierarchy can be constructed starting from an infinite dimensional symmetric space. DA - 2014/11// PY - 2014/11// DO - 10.1016/j.geomphys.2014.05.023 VL - 85 SP - 60-74 SN - 1879-1662 KW - Lower triangular Z x Z-matrices KW - Lax equations KW - Zero curvature form KW - Linearization KW - Wave matrices ER - TY - JOUR TI - Immersed Interface CIP for One Dimensional Hyperbolic Equations AU - Ito, Kazufumi AU - Takeuchi, Tomoya T2 - COMMUNICATIONS IN COMPUTATIONAL PHYSICS AB - Abstract The immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients. The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities, which is the same order of accuracy of the standard CIP scheme. Some numerical tests are given to verify the accuracy of the proposed method. DA - 2014/7// PY - 2014/7// DO - 10.4208/cicp.070313.221113a VL - 16 IS - 1 SP - 96-114 SN - 1991-7120 KW - CIP method KW - immersed interface method KW - hyperbolic equations in discontinuous media ER - TY - JOUR TI - Gauge-fixing on the lattice via orbifolding AU - Mehta, Dhagash AU - Daleo, Noah S. AU - Hauenstein, Jonathan D. AU - Seaton, Christopher T2 - PHYSICAL REVIEW D AB - When fixing a covariant gauge, most popularly the Landau gauge, on the lattice one encounters the Neuberger 0/0 problem which prevents one from formulating a Becchi--Rouet--Stora--Tyutin symmetry on the lattice. Following the interpretation of this problem in terms of Witten-type topological field theory and using the recently developed Morse theory for orbifolds, we propose a modification of the lattice Landau gauge via orbifolding of the gauge-fixing group manifold and show that this modification circumvents the orbit-dependence issue and hence can be a viable candidate for evading the Neuberger problem. Using algebraic geometry, we also show that though the previously proposed modification of the lattice Landau gauge via stereographic projection relies on delicate departure from the standard Morse theory due to the non-compactness of the underlying manifold, the corresponding gauge-fixing partition function turns out to be orbit independent for all the orbits except in a region of measure zero. DA - 2014/9/9/ PY - 2014/9/9/ DO - 10.1103/physrevd.90.054504 VL - 90 IS - 5 SP - SN - 1550-2368 ER - TY - JOUR TI - Full Hereditary Interacting Model of All Member States of the United Nations AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - Aggregate demand $$ z_{i} $$ is given. DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_3 VL - 10 SP - 15-22 SN - 1875-7642 ER - TY - JOUR TI - Full Employment: Private and Government Policies AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - Employment is currently decaying in the United States of America. Policies of private firms and government to arrest the situation are now hotly debated. This paper is a readable reflection and extraction from Chukwu’s books, Stability and Time-Optimal Control of Hereditary Systems with Application to the Economic Dynamics of the USA,” 2nd Edition, World Scientific 2001 [1], and “The Omega Problem of all Members of the United Nations”, Atlantis Studies in Mathematics for Engineering and Science, Volume 6. Series editor, C. K. Chui, Stanford University, U.S.A. and World Scientific [2]. Reasonable and verifiable economic policies are deduced from Chukwu. DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_1 VL - 10 SP - 1-5 SN - 1875-7642 ER - TY - JOUR TI - Feasible Introgression of an Anti-pathogen Transgene into an Urban Mosquito Population without Using Gene-Drive AU - Okamoto, Kenichi W. AU - Robert, Michael A. AU - Gould, Fred AU - Lloyd, Alun L. T2 - PLOS NEGLECTED TROPICAL DISEASES AB - Background Introgressing anti-pathogen constructs into wild vector populations could reduce disease transmission. It is generally assumed that such introgression would require linking an anti-pathogen gene with a selfish genetic element or similar technologies. Yet none of the proposed transgenic anti-pathogen gene-drive mechanisms are likely to be implemented as public health measures in the near future. Thus, much attention now focuses instead on transgenic strategies aimed at mosquito population suppression, an approach generally perceived to be practical. By contrast, aiming to replace vector competent mosquito populations with vector incompetent populations by releasing mosquitoes carrying a single anti-pathogen gene without a gene-drive mechanism is widely considered impractical. Methodology/Principal Findings Here we use Skeeter Buster, a previously published stochastic, spatially explicit model of Aedes aegypti to investigate whether a number of approaches for releasing mosquitoes with only an anti-pathogen construct would be efficient and effective in the tropical city of Iquitos, Peru. To assess the performance of such releases using realistic release numbers, we compare the transient and long-term effects of this strategy with two other genetic control strategies that have been developed in Ae. aegypti: release of a strain with female-specific lethality, and a strain with both female-specific lethality and an anti-pathogen gene. We find that releasing mosquitoes carrying only an anti-pathogen construct can substantially decrease vector competence of a natural population, even at release ratios well below that required for the two currently feasible alternatives that rely on population reduction. Finally, although current genetic control strategies based on population reduction are compromised by immigration of wild-type mosquitoes, releasing mosquitoes carrying only an anti-pathogen gene is considerably more robust to such immigration. Conclusions/Significance Contrary to the widely held view that transgenic control programs aimed at population replacement require linking an anti-pathogen gene to selfish genetic elements, we find releasing mosquitoes in numbers much smaller than those considered necessary for transgenic population reduction can result in comparatively rapid and robust population replacement. In light of this non-intuitive result, directing efforts to improve rearing capacity and logistical support for implementing releases, and reducing the fitness costs of existing recombinant technologies, may provide a viable, alternative route to introgressing anti-pathogen transgenes under field conditions. DA - 2014/7// PY - 2014/7// DO - 10.1371/journal.pntd.0002827 VL - 8 IS - 7 SP - SN - 1935-2735 ER - TY - JOUR TI - Enumerating copies in the first Gribov region on the lattice in up to four dimensions AU - Mehta, Dhagash AU - Schroeck, Mario T2 - PHYSICAL REVIEW D AB - The covariant gauges are known to suffer from the Gribov problem: even after fixing a gauge non-perturbatively, there may still exist residual copies which are physically equivalent to each other, called Gribov copies. While the influence of Gribov copies in the relevant quantities such as gluon propagators has been heavily debated in recent studies, the significance of the role they play in the Faddeev--Popov procedure is hardly doubted. We concentrate on Gribov copies in the first Gribov region, i.e., the space of Gribov copies at which the Faddeev--Popov operator is strictly positive (semi)definite. We investigate compact U($1$) as the prototypical model of the more complicated standard model group SU($N_{c}$). With our Graphical Processing Unit (GPU) implementation of the relaxation method we collect up to a few million Gribov copies per orbit. We show that the numbers of Gribov copies even in the first Gribov region increase exponentially in two, three and four dimensions. Furthermore, we provide strong indication that the number of Gribov copies is gauge orbit dependent. DA - 2014/5/29/ PY - 2014/5/29/ DO - 10.1103/physrevd.89.094512 VL - 89 IS - 9 SP - SN - 1550-2368 ER - TY - JOUR TI - Employment and Gross Domestic Product Dynamics and Control of Interacting Nations AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - In this chapter models of Gross Domestic Product and Employment of two interacting nations are derived. It is a hereditary differential game of pursuit. It utilizes the principles of supply and demand and of rational expectations. A theory of interaction via net export is postulated. The net export function may include trade, debt repayment, etc. International employments can also be included. The UN and IMF data for two nations are used to validate the theory and test for the degree of cooperation and competition. MATLAB and Maple programs are exploited. The consequences of cooperation and competition are studied, and controllability questions answered. Once the system is proved controllable it can be made sufficiently cooperating, and sustained growth of GDP and employment can be guaranteed. DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_6 VL - 10 SP - 39-64 SN - 1875-7642 ER - TY - CHAP TI - Economic dynamics of all members of the United Nations second edition preface AU - Chukwu, E. N. T2 - Economic dynamics of all members of the united nations, 2nd edition PY - 2014/// VL - 10 SP - V- ER - TY - JOUR TI - Distance-Based Phylogenetic Methods Around a Polytomy AU - Davidson, Ruth AU - Sullivant, Seth T2 - IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS AB - Distance-based phylogenetic algorithms attempt to solve the NP-hard least-squares phylogeny problem by mapping an arbitrary dissimilarity map representing biological data to a tree metric. The set of all dissimilarity maps is a Euclidean space properly containing the space of all tree metrics as a polyhedral fan. Outputs of distance-based tree reconstruction algorithms such as UPGMA and neighbor-joining are points in the maximal cones in the fan. Tree metrics with polytomies lie at the intersections of maximal cones. A phylogenetic algorithm divides the space of all dissimilarity maps into regions based upon which combinatorial tree is reconstructed by the algorithm. Comparison of phylogenetic methods can be done by comparing the geometry of these regions. We use polyhedral geometry to compare the local nature of the subdivisions induced by least-squares phylogeny, UPGMA, and neighbor-joining when the true tree has a single polytomy with exactly four neighbors. Our results suggest that in some circumstances, UPGMA and neighbor-joining poorly match least-squares phylogeny. DA - 2014/// PY - 2014/// DO - 10.1109/tcbb.2014.2309592 VL - 11 IS - 2 SP - 325-335 SN - 1557-9964 KW - Neighbor-joining KW - phylogeny KW - polyhedra KW - polytomy KW - UPGMA ER - TY - JOUR TI - Controllability Theory of the GDP of All Member States of the UN AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - In the earlier chapters we derived the equation DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_5 VL - 10 SP - 31-37 SN - 1875-7642 ER - TY - JOUR TI - Consequences AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - Suppose at time t the coefficients $$ a_{ - 1i} ,a_{oi} ,a_{1i} $$ are fixed, and b ij , the coefficient of competition or cooperation for nation i and nation j is positive. If b ij is positive, the two nations are cooperating. If b ij is increased the net hereditary growth rate of GDP, $$ \frac{{dy_{i} (t)}}{dt} - a_{ - 1i} \frac{{dy_{i} (t - h)}}{dt} $$ is increased, i.e. the production of goods and services grows bigger. Cooperation enhances economic growth. Suppose b ij , the coefficient of competition is negative, decreasing competition will increase the net growth rate. Increasing competition will decrease the net growth rate. DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_4 VL - 10 SP - 23-29 SN - 1875-7642 ER - TY - JOUR TI - Combustion waves and Riemann solutions in light porous foam AU - Chapiro, G. AU - Marchesin, D. AU - Schecter, S. T2 - JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS AB - We prove the existence of traveling waves, and identify the wave sequences appearing in Riemann solutions, for a system of three evolutionary partial differential equations that models combustion of light porous foam under air injection. DA - 2014/6// PY - 2014/6// DO - 10.1142/s021989161450009x VL - 11 IS - 2 SP - 295-328 SN - 1793-6993 KW - Traveling wave KW - Riemann problem KW - filtration combustion KW - combustion in porous media KW - ignition KW - extinction ER - TY - JOUR TI - Cauchy problems related to integrable deformations of pseudo differential operators AU - Helminck, G. F. AU - Helminck, A. G. AU - Panasenko, E. A. T2 - JOURNAL OF GEOMETRY AND PHYSICS AB - In this paper we discuss the solvability of two Cauchy problems in the pseudo differential operators. The first is associated with a set of pseudo differential operators of negative order, the prominent example being the set of strict integral operator parts of the different powers of a solution of the KP hierarchy. We show that it can be solved, provided the setting possesses a compatibility completeness. In such a setting all solutions of the KP hierarchy are obtained by dressing with the solution of the related Cauchy problem. The second Cauchy problem is slightly more general and links up with a set of pseudo differential operators of order zero or less. The key example here is the collection of integral operator parts of the different powers of a solution of the strict KP hierarchy. This system is solvable as soon as exponential and compatibility completeness holds. Also under these circumstances, all solutions of the strict KP hierarchy are obtained by dressing with the solution of the corresponding Cauchy problem. DA - 2014/11// PY - 2014/11// DO - 10.1016/j.geomphys.2014.05.004 VL - 85 SP - 196-205 SN - 1879-1662 KW - Cauchy problem KW - Integrable deformation KW - Pseudo differential operators KW - (Strict) KP hierarchy KW - Zero curvature relations ER - TY - JOUR TI - Are You HIV Invincible? A Probabilistic Study of Discordant Couples in the Context of HIV Transmission AU - Bobashev, Georgiy AU - Norton, Jacob AU - Wechsberg, Wendee AU - Toussova, Olga T2 - PLOS ONE AB - A number of factors have been identified that are related to sexual and injecting HIV transmission. We developed a probabilistic mathematical model to put these factors together and interpret risks in the context of individual behavior among injecting drug-using (IDU) couples in St. Petersburg, Russia. Some HIV-discordant couples have unprotected sex and sometimes inject drugs together but stay discordant for a long time, while some individuals acquire HIV on the first encounter. We considered existing estimates of HIV transmission risks through injecting and sexual contacts to develop a predictive survival model for an individual who is exposed to HIV through intimate relationships. We computed simulated survival curves for a number of behavioral scenarios and discussed sources of simulated uncertainty. We then applied the model to a longitudinal study of HIV-discordant couples and validated the model's forecast. Although individual prediction of seroconversion time appeared impossible, the ability to rank behavioral patterns in terms of HIV risk and to estimate the probability of survival HIV-free will be important to educators and counselors. DA - 2014/5/19/ PY - 2014/5/19/ DO - 10.1371/journal.pone.0094799 VL - 9 IS - 5 SP - SN - 1932-6203 ER - TY - JOUR TI - A Symmetric and Consistent Immersed Finite Element Method for Interface Problems AU - Ji, Haifeng AU - Chen, Jinru AU - Li, Zhilin T2 - JOURNAL OF SCIENTIFIC COMPUTING DA - 2014/12// PY - 2014/12// DO - 10.1007/s10915-014-9837-x VL - 61 IS - 3 SP - 533-557 SN - 1573-7691 KW - Immersed finite element method KW - Interface problems KW - Cartesian mesh KW - Discontinuous coefficient KW - Symmetric and consistent weak form ER - TY - JOUR TI - A Mathematical Solution to Boost the Positive Value of the Cumulative Balance of Payment of the USA AU - Chukwu, Ethelbert Nwakuche AU - Chukwu, EN T2 - ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION AB - Very recently the President of the USA, set up a bipartisan commission to generate strategies to boost the positive value of the Balance of Payment of the USA. A mathematical solution can be deduced from the following research monographs of the author, E. N. Chukwu. (1) E. N. Chukwu, Stability and Time Optimal Control of Hereditary Systems with Application to the Economic Dynamics of the US, 2nd edition, World Scientific, 2001, ISBN 981-02-4674-9. Singapore, New Jersey, London. (2) E. N. Chukwu, Differential Models and Neutral Systems for Controlling the Wealth of Nations, World Scientific, 2001, ISBN 9810243812, Singapore, New Jersey, London. (3) Optimal Control of the Growth of Wealth of Nations, Taylor and Francis, 2003, ISBN 0-415-26966-0, London, New York. (4) E. N. Chukwu, A Mathematical Treatment of Economic Cooperation and Competition Among Nations with Nigeria, USA, UK, China and Middle East Examples, Mathematics in Science and Engineering, v 203, Elsevier, 2005, ISBN-13978-0-444-51859-0, Amsterdam, The Netherlands. (5) E. N. Chukwu, The Omega Problem of all members of the United Nations, Atlantis Studies in Mathematics for Engineering and Science, v 7, World Scientific, pub. Date scheduled Summer 2010. (6) E. N. Chukwu, Stability and Time Optimal Control f Hereditary Systems, Academic Press, Boston, 1992. DA - 2014/// PY - 2014/// DO - 10.2991/978-94-6239-076-8_2 VL - 10 SP - 7-14 SN - 1875-7642 ER - TY - JOUR TI - Time-varying, serotype-specific force of infection of dengue virus AU - Reiner, Robert C., Jr. AU - Stoddard, Steven T. AU - Forshey, Brett M. AU - King, Aaron A. AU - Ellis, Alicia M. AU - Lloyd, Alun L. AU - Long, Kanya C. AU - Rocha, Claudio AU - Vilcarromero, Stalin AU - Astete, Helvio AU - Bazan, Isabel AU - Lenhart, Audrey AU - Vazquez-Prokopec, Gonzalo M. AU - Paz-Soldan, Valerie A. AU - McCall, Philip J. AU - Kitron, Uriel AU - Elder, John P. AU - Halsey, Eric S. AU - Morrison, Amy C. AU - Kochel, Tadeusz J. AU - Scott, Thomas W. T2 - Proceedings of the National Academy of Sciences AB - Significance Using mathematical models to extend knowledge of pathogen transmission and recommend optimized control efforts is dependent on the accuracy of model parameters. The rate at which susceptible individuals become infected [the force of infection (FoI)] is one of the most important parameters, but due to data constraints it is often incorrectly assumed to be constant over time. Using a bespoke method for a 12-y longitudinal dataset of serotype-specific dengue virus (DENV) infections, we estimated time-varying, serotype-specific FoIs for all four DENV serotypes. The FoI varied markedly in time, which implies that DENV transmission dynamics are complex and are best summarized using time-dependent transmission parameters. Our results provide more accurate measures of virus transmission dynamics and a basis for improving selection of control and disease prevention strategies. DA - 2014/5/20/ PY - 2014/5/20/ DO - 10.1073/pnas.1314933111 VL - 111 IS - 26 SP - E2694-E2702 J2 - Proc Natl Acad Sci USA LA - en OP - SN - 0027-8424 1091-6490 UR - http://dx.doi.org/10.1073/pnas.1314933111 DB - Crossref KW - disease ecology KW - emerging infections KW - arthropod-borne virus ER - TY - JOUR TI - TRANSONIC EVAPORATION WAVES IN A SPHERICALLY SYMMETRIC NOZZLE AU - Lin, Xiaobiao AU - Wechselberger, Martin T2 - SIAM JOURNAL ON MATHEMATICAL ANALYSIS AB - This paper studies the liquid-to-vapor phase transition in a cone-shaped nozzle. Using the geometric method presented in [P. Szmolyan and M. Wechselberger, J. Differential Equations, 200 (2004), pp. 69--104], [M. Wechselberger and G. Pettet, Nonlinearity, 23 (2010), pp. 1949--1969], we further develop results on subsonic and supersonic evaporation waves in [H. Fan and X.-B. Lin, SIAM J. Math. Anal., 44 (2012), pp. 405--436] to transonic waves. It is known that transonic waves do not exist if restricted solely to the slow system on the slow manifolds [H. Fan and X.-B. Lin, SIAM J. Math. Anal., 44 (2012), pp. 405--436]. Thus we consider the existence of transonic waves that include layer solutions of the fast system that cross or connect to the sonic surface. In particular, we are able to show the existence and uniqueness of evaporation waves that cross from supersonic to subsonic regions and evaporation waves that connect from the subsonic region to the sonic surface and then continue onto the supersonic branch via the slow flow. DA - 2014/// PY - 2014/// DO - 10.1137/120875363 VL - 46 IS - 2 SP - 1472-1504 SN - 1095-7154 KW - evaporation waves KW - blow-up technique KW - geometric singular perturbation theory ER - TY - JOUR TI - Spin transfer torque generated magnetic droplet solitons (invited) AU - Chung, S. AU - Mohseni, S. M. AU - Sani, S. R. AU - Iacocca, E. AU - Dumas, R. K. AU - Nguyen, T. N. Anh AU - Pogoryelov, Ye AU - Muduli, P. K. AU - Eklund, A. AU - Hoefer, M. AU - Akerman, J. T2 - JOURNAL OF APPLIED PHYSICS AB - We present recent experimental and numerical advancements in the understanding of spin transfer torque generated magnetic droplet solitons. The experimental work focuses on nano-contact spin torque oscillators (NC-STOs) based on orthogonal (pseudo) spin valves where the Co fixed layer has an easy-plane anisotropy, and the [Co/Ni] free layer has a strong perpendicular magnetic anisotropy. The NC-STO resistance and microwave signal generation are measured simultaneously as a function of drive current and applied perpendicular magnetic field. Both exhibit dramatic transitions at a certain current dependent critical field value, where the microwave frequency drops 10 GHz, modulation sidebands appear, and the resistance exhibits a jump, while the magnetoresistance changes sign. We interpret these observations as the nucleation of a magnetic droplet soliton with a large fraction of its magnetization processing with an angle greater than 90°, i.e., around a direction opposite that of the applied field. This interpretation is corroborated by numerical simulations. When the field is further increased, we find that the droplet eventually collapses under the pressure from the Zeeman energy. DA - 2014/5/7/ PY - 2014/5/7/ DO - 10.1063/1.4870696 VL - 115 IS - 17 SP - SN - 1089-7550 ER - TY - JOUR TI - SLOCC invariants for multipartite mixed states AU - Jing, Naihuan AU - Li, Ming AU - Li-Jost, Xianqing AU - Zhang, Tinggui AU - Fei, Shao-Ming T2 - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL AB - We construct a nontrivial set of invariants for any multipartite mixed states under the SLOCC symmetry. These invariants are given by hyperdeterminants and independent from basis change. In particular, a family of d^2 invariants for arbitrary d-dimensional even partite mixed states are explicitly given. DA - 2014/5/30/ PY - 2014/5/30/ DO - 10.1088/1751-8113/47/21/215303 VL - 47 IS - 21 SP - SN - 1751-8121 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84929171716&partnerID=MN8TOARS KW - SLOCC-invariants KW - local unitary equivalent KW - hyperdeterminants ER - TY - JOUR TI - Potential energy landscape of the two-dimensional XY model: Higher-index stationary points AU - Mehta, D. AU - Hughes, C. AU - Kastner, M. AU - Wales, D. J. T2 - JOURNAL OF CHEMICAL PHYSICS AB - The application of numerical techniques to the study of energy landscapes of large systems relies on sufficient sampling of the stationary points. Since the number of stationary points is believed to grow exponentially with system size, we can only sample a small fraction. We investigate the interplay between this restricted sample size and the physical features of the potential energy landscape for the two-dimensional XY model in the absence of disorder with up to N = 100 spins. Using an eigenvector-following technique, we numerically compute stationary points with a given Hessian index I for all possible values of I. We investigate the number of stationary points, their energy and index distributions, and other related quantities, with particular focus on the scaling with N. The results are used to test a number of conjectures and approximate analytic results for the general properties of energy landscapes. DA - 2014/6/14/ PY - 2014/6/14/ DO - 10.1063/1.4880417 VL - 140 IS - 22 SP - SN - 1089-7690 ER - TY - JOUR TI - On the dispersion function for complex values of the parameter c AU - Garcia, R. D. M. AU - Siewert, C. E. T2 - ANNALS OF NUCLEAR ENERGY AB - The dispersion function relevant to one-speed transport theory with isotropic scattering is analyzed for the case of complex values of c, and an explicit expression is given for the discrete eigenvalue ν0. DA - 2014/7// PY - 2014/7// DO - 10.1016/j.anucene.2014.02.015 VL - 69 SP - 203-204 SN - 0306-4549 KW - Transport theory KW - Dispersion function KW - Discrete eigenvalue KW - Complex c ER - TY - JOUR TI - On exact minimization of Higgs potentials AU - Maniatis, Markos AU - Mehta, Dhagash T2 - EUROPEAN PHYSICAL JOURNAL PLUS AB - Minimizing the Higgs potential is an essential task in any model involving Higgs bosons. Exact minimization methods proposed in the literature are based on the polynomial form of the potential. These methods will in general no longer work if loop contributions to the potential are taken into account. We present a method to keep the tree level global minimum unchanged in passing to the effective potential. We illustrate the method for the case of the Minimal Supersymmetric Model (MSSM). DA - 2014/6/3/ PY - 2014/6/3/ DO - 10.1140/epjp/i2014-14109-0 VL - 129 IS - 6 SP - SN - 2190-5444 ER - TY - JOUR TI - Multi-parameter Tikhonov regularization - An augmented approach AU - Ito, Kazufumi AU - Jin, Bangti AU - Takeuchi, Tomoya T2 - CHINESE ANNALS OF MATHEMATICS SERIES B AB - We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle. DA - 2014/5// PY - 2014/5// DO - 10.1007/s11401-014-0835-y VL - 35 IS - 3 SP - 383-398 SN - 1860-6261 KW - Multi-parameter regularization KW - Augmented Tikhonov regularization KW - Balanced discrepancy principle ER - TY - JOUR TI - Local unitary equivalence of multiqubit mixed quantum states AU - Li, Ming AU - Zhang, Tinggui AU - Fei, Shao-Ming AU - Li-Jost, Xianqing AU - Jing, Naihuan T2 - PHYSICAL REVIEW A AB - We present computable criterion for completely classifying multi-qubit quantum states under local unitary operations. The criterion can be used to detect whether two quantum states in multi-qubit systems are local unitary equivalent or not. Once obtaining the positive answer, we are further able to compute the corresponding unitary operators precisely. Since the scheme is based on the mean values of some quantum mechanical observables, it supplies an experimental way to judge the local equivalence of quantum states. DA - 2014/6/23/ PY - 2014/6/23/ DO - 10.1103/physreva.89.062325 VL - 89 IS - 6 SP - SN - 1094-1622 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84903512933&partnerID=MN8TOARS ER - TY - JOUR TI - LIM is not slim AU - Fink, Alex AU - Fraenkel, Aviezri S. AU - Santos, Carlos T2 - INTERNATIONAL JOURNAL OF GAME THEORY DA - 2014/5// PY - 2014/5// DO - 10.1007/s00182-013-0380-z VL - 43 IS - 2 SP - 269-281 SN - 1432-1270 KW - Combinatorial game theory KW - Impartial games KW - NIM KW - Sprague-Grundy theory KW - Ulam-Warburton cellular automaton ER - TY - JOUR TI - Interactions of large amplitude solitary waves in viscous fluid conduits AU - Lowman, Nicholas K. AU - Hoefer, M. A. AU - El, G. A. T2 - JOURNAL OF FLUID MECHANICS AB - Abstract The free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg–de Vries equation and experimentally in the context of shallow water waves, but a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking. The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified. Using a combined numerical and experimental approach, three classes of nonlinear interaction behaviour are identified: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves behave as ‘physical solitons’. Experimental data are shown to be in excellent agreement with numerical simulations of the reduced model. Experimental movies are available with the online version of the paper. DA - 2014/7// PY - 2014/7// DO - 10.1017/jfm.2014.273 VL - 750 SP - 372-384 SN - 1469-7645 KW - pattern formation KW - solitary waves KW - Stokesian dynamics ER - TY - JOUR TI - Infinite Dimensional DeWitt Supergroups and their Bodies AU - Fulp, Ronald T2 - CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES AB - Abstract For Dewitt super groups G modeled via an underlying finitely generated Grassmann algebra it is well known that when there exists a body group BG compatible with the group operation on G , then, generically, the kernel K of the body homomorphism is nilpotent. This is not true when the underlying Grassmann algebra is infinitely generated. We show that it is quasi-nilpotent in the sense that as a Banach Lie group its Lie algebra κ has the property that for each a ∊ κ ad a has a zero spectrum. We also show that the exponential mapping from κ to K is surjective and that K is a quotient manifold of the Banach space κ via a lattice in κ . DA - 2014/6// PY - 2014/6// DO - 10.4153/cmb-2013-025-6 VL - 57 IS - 2 SP - 283-288 SN - 1496-4287 KW - super groups KW - body of super groups KW - Banach Lie groups ER - TY - JOUR TI - Certification and the potential energy landscape AU - Mehta, Dhagash AU - Hauenstein, Jonathan D. AU - Wales, David J. T2 - JOURNAL OF CHEMICAL PHYSICS AB - Typically, there is no guarantee that a numerical approximation obtained using standard nonlinear equation solvers is indeed an actual solution, meaning that it lies in the quadratic convergence basin. Instead, it may lie only in the linear convergence basin, or even in a chaotic region, and hence not converge to the corresponding stationary point when further optimization is attempted. In some cases, these non-solutions could be misleading. Proving that a numerical approximation will quadratically converge to a stationary point is termed certification. In this report, we provide details of how Smale's α-theory can be used to certify numerically obtained stationary points of a potential energy landscape, providing a mathematical proof that the numerical approximation does indeed correspond to an actual stationary point, independent of the precision employed. DA - 2014/6/14/ PY - 2014/6/14/ DO - 10.1063/1.4881638 VL - 140 IS - 22 SP - SN - 1089-7690 ER - TY - JOUR TI - Bruhat order on fixed-point-free involutions in the symmetric group AU - Watson, M. T2 - Electronic Journal of Combinatorics DA - 2014/// PY - 2014/// VL - 21 IS - 2 ER - TY - JOUR TI - Attraction, merger, reflection, and annihilation in magnetic droplet soliton scattering AU - Maiden, M. D. AU - Bookman, L. D. AU - Hoefer, M. A. T2 - PHYSICAL REVIEW B AB - The interaction behaviors of solitons are defining characteristics of these nonlinear, coherent structures. Due to recent experimental observations, thin ferromagnetic films offer a promising medium in which to study the scattering properties of two-dimensional magnetic droplet solitons, particle-like, precessing dipoles. Here, a rich set of two-droplet interaction behaviors are classified through micromagnetic simulations. Repulsive and attractive interaction dynamics are generically determined by the relative phase and speeds of the two droplets and can be classified into four types: (1) merger into a breather bound state, (2) counterpropagation trapped along the axis of symmetry, (3) reflection, and (4) violent droplet annihilation into spin wave radiation and a breather. Utilizing a nonlinear method of images, it is demonstrated that these dynamics describe repulsive/attractive scattering of a single droplet off of a magnetic boundary with pinned/free spin boundary conditions, respectively. These results explain the mechanism by which propagating and stationary droplets can be stabilized in a confined ferromagnet. DA - 2014/5/20/ PY - 2014/5/20/ DO - 10.1103/physrevb.89.180409 VL - 89 IS - 18 SP - SN - 1550-235X ER - TY - JOUR TI - Attaining the Optimal Gaussian Diffusion Acceleration AU - Wu, Sheng-Jhih AU - Hwang, Chii-Ruey AU - Chu, Moody T. T2 - JOURNAL OF STATISTICAL PHYSICS DA - 2014/5// PY - 2014/5// DO - 10.1007/s10955-014-0963-5 VL - 155 IS - 3 SP - 571-590 SN - 1572-9613 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84898545692&partnerID=MN8TOARS KW - Diffusion acceleration KW - Convergence to equilibrium KW - Ornstein-Uhlenbeck process KW - t-Circulant matrices KW - Inverse eigenvalue problem KW - Recursive algorithm KW - MCMC ER - TY - JOUR TI - A note on the CLT of the LSS for sample covariance matrix from a spiked population model AU - Wang, Qinwen AU - Silverstein, Jack W. AU - Yao, Jian-Feng T2 - JOURNAL OF MULTIVARIATE ANALYSIS AB - In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance structure. As an application, we provide an asymptotic power function for the corrected likelihood ratio statistic for testing the presence of spike eigenvalues in the population covariance matrix. This result generalizes an existing formula from the literature where only one simple spike exists. DA - 2014/9// PY - 2014/9// DO - 10.1016/j.jmva.2014.04.021 VL - 130 SP - 194-207 SN - 0047-259X KW - Large-dimensional sample covariance matrices KW - Spiked population model KW - Central limit theorem KW - Centering parameter KW - Factor models ER - TY - JOUR TI - Spin characters of generalized symmetric groups AU - Hu, Xiaoli AU - Jing, Naihuan T2 - MONATSHEFTE FUR MATHEMATIK AB - In 1911 Schur computed the spin character values of the symmetric group using two important ingredients: the first one later became famously known as the Schur Q-functions and the second one was certain creative construction of the projective characters on Clifford algebras. In the context of the McKay correspondence and affine Lie algebras, the first part was generalized to all wreath products by the vertex operator calculus in Frenkel et al. (Duke Math J 111:51–96, 2002) where a large part of the character table was produced. The current paper generalizes the second part and provides the missing projective character values for the wreath product of the symmetric group with a finite abelian group. Our approach relies on Mackey–Wigner’s little groups to construct irreducible modules. In particular, projective modules and spin character values of all classical Weyl groups are obtained. DA - 2014/4// PY - 2014/4// DO - 10.1007/s00605-013-0525-y VL - 173 IS - 4 SP - 495-518 SN - 1436-5081 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84896394195&partnerID=MN8TOARS KW - Wreath products KW - Spin groups KW - Projective characters ER - TY - JOUR TI - Shock Waves in Dispersive Eulerian Fluids AU - Hoefer, M. A. T2 - JOURNAL OF NONLINEAR SCIENCE AB - The long-time behavior of an initial step resulting in a dispersive shock wave (DSW) for the one-dimensional isentropic Euler equations regularized by generic, third-order dispersion is considered by use of Whitham averaging. Under modest assumptions, the jump conditions (DSW locus and speeds) for admissible, weak DSWs are characterized and found to depend only upon the sign of dispersion (convexity or concavity) and a general pressure law. Two mechanisms leading to the breakdown of this simple wave DSW theory for sufficiently large jumps are identified: a change in the sign of dispersion, leading to gradient catastrophe in the modulation equations, and the loss of genuine nonlinearity in the modulation equations. Large amplitude DSWs are constructed for several particular dispersive fluids with differing pressure laws modeled by the generalized nonlinear Schrödinger equation. These include superfluids (Bose–Einstein condensates and ultracold fermions) and “optical fluids.” Estimates of breaking times for smooth initial data and the long-time behavior of the shock tube problem are presented. Detailed numerical simulations compare favorably with the asymptotic results in the weak to moderate amplitude regimes. Deviations in the large amplitude regime are identified with breakdown of the simple wave DSW theory. DA - 2014/6// PY - 2014/6// DO - 10.1007/s00332-014-9199-4 VL - 24 IS - 3 SP - 525-577 SN - 1432-1467 KW - Dispersive shock wave KW - Riemann problem KW - Whitham averaging KW - Dispersive Euler equations KW - Generalized nonlinear Schrodinger equation ER - TY - JOUR TI - Regular cell complexes in total positivity AU - Hersh, Patricia T2 - INVENTIONES MATHEMATICAE AB - Fomin and Shapiro conjectured that the link of the identity in the Bruhat stratification of the totally nonnegative real part of the unipotent radical of a Borel subgroup in a semisimple, simply connected algebraic group defined and split over ${\mathbb{R}}$ is a regular CW complex homeomorphic to a ball. The main result of this paper is a proof of this conjecture. This completes the solution of the question of Bernstein of identifying regular CW complexes arising naturally from representation theory having the (lower) intervals of Bruhat order as their closure posets. A key ingredient is a new criterion for determining whether a finite CW complex is regular with respect to a choice of characteristic maps; it most naturally applies to images of maps from regular CW complexes and is based on an interplay of combinatorics of the closure poset with codimension one topology. DA - 2014/7// PY - 2014/7// DO - 10.1007/s00222-013-0480-1 VL - 197 IS - 1 SP - 57-114 SN - 1432-1297 ER - TY - JOUR TI - Recasting the theory of mosquito-borne pathogen transmission dynamics and control AU - Smith, D. L. AU - Perkins, T. A. AU - Reiner, R. C. AU - Barker, C. M. AU - Niu, T. AU - Chaves, L. F. AU - Ellis, A. M. AU - George, D. B. AU - Le Menach, A. AU - Pulliam, J. R. C. AU - Bisanzio, D. AU - Buckee, C. AU - Chiyaka, C. AU - Cummings, D. A. T. AU - Garcia, A. J. AU - Gatton, M. L. AU - Gething, P. W. AU - Hartley, D. M. AU - Johnston, G. AU - Klein, E. Y. AU - Michael, E. AU - Lloyd, A. L. AU - Pigott, D. M. AU - Reisen, W. K. AU - Ruktanonchai, N. AU - Singh, B. K. AU - Stoller, J. AU - Tatem, A. J. AU - Kitron, U. AU - Godfray, H. C. J. AU - Cohen, J. M. AU - Hay, S. I. AU - Scott, T. W. T2 - Transactions of the Royal Society of Tropical Medicine and Hygiene AB - Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of the world. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonald's formula for R0 and its entomological derivative, vectorial capacity, are now used to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross-Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context for mosquito blood feeding, the movement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control. DA - 2014/3/3/ PY - 2014/3/3/ DO - 10.1093/trstmh/tru026 VL - 108 IS - 4 SP - 185-197 J2 - Transactions of the Royal Society of Tropical Medicine and Hygiene LA - en OP - SN - 0035-9203 1878-3503 UR - http://dx.doi.org/10.1093/trstmh/tru026 DB - Crossref KW - Dengue KW - Filariasis KW - Malaria KW - Mosquito-borne pathogen transmission KW - Vector control KW - West Nile virus ER - TY - JOUR TI - On Multiplicities of Maximal Weights of -Modules AU - Jayne, Rebecca L. AU - Misra, Kailash C. T2 - ALGEBRAS AND REPRESENTATION THEORY DA - 2014/8// PY - 2014/8// DO - 10.1007/s10468-014-9470-2 VL - 17 IS - 4 SP - 1303-1321 SN - 1572-9079 KW - Affine Lie algebras KW - Representations KW - Maximal weights KW - Crystal base KW - Lattice paths KW - Avoiding permutations ER - TY - JOUR TI - Identifiable reparametrizations of linear compartment models AU - Meshkat, Nicolette AU - Sullivant, Seth T2 - JOURNAL OF SYMBOLIC COMPUTATION AB - Structural identifiability concerns finding which unknown parameters of a model can be quantified from given input–output data. Many linear ODE models, used in systems biology and pharmacokinetics, are unidentifiable, which means that parameters can take on an infinite number of values and yet yield the same input–output data. We use commutative algebra and graph theory to study a particular class of unidentifiable models and find conditions to obtain identifiable scaling reparametrizations of these models. Our main result is that the existence of an identifiable scaling reparametrization is equivalent to the existence of a scaling reparametrization by monomial functions. We provide an algorithm for finding these reparametrizations when they exist and partial results beginning to classify graphs which possess an identifiable scaling reparametrization. DA - 2014/5// PY - 2014/5// DO - 10.1016/j.jsc.2013.11.002 VL - 63 SP - 46-67 SN - 0747-7171 KW - Identifiability KW - Compartment models KW - Reparametrization ER - TY - JOUR TI - Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety AU - Bates, Daniel J. AU - Decker, Wolfram AU - Hauenstein, Jonathan D. AU - Peterson, Chris AU - Pfister, Gerhard AU - Schreyer, Frank-Olaf AU - Sommese, Andrew J. AU - Wampler, Charles W. T2 - APPLIED MATHEMATICS AND COMPUTATION AB - Systems of polynomial equations arise throughout mathematics, engineering, and the sciences. It is therefore a fundamental problem both in mathematics and in application areas to find the solution sets of polynomial systems. The focus of this paper is to compare two fundamentally different approaches to computing and representing the solutions of polynomial systems: numerical homotopy continuation and symbolic computation. Several illustrative examples are considered, using the software packages Bertini and Singular. DA - 2014/3/15/ PY - 2014/3/15/ DO - 10.1016/j.amc.2013.12.165 VL - 231 SP - 619-633 SN - 1873-5649 KW - Polynomial system KW - Computational algebraic geometry KW - Numerical computation KW - Homotopy continuation KW - Symbolic computation KW - Primary decomposition ER - TY - JOUR TI - Centralizer of an idempotent in a reductive monoid AU - Putcha, Mohan S. T2 - FORUM MATHEMATICUM AB - Abstract Let DA - 2014/3// PY - 2014/3// DO - 10.1515/form.2011.163 VL - 26 IS - 2 SP - 323-335 SN - 1435-5337 KW - Reductive monoid KW - centralizer KW - idempotent KW - canonical monoid ER - TY - JOUR TI - Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients AU - Chertock, Alina AU - Kurganov, Alexander AU - Liu, Yu T2 - NUMERISCHE MATHEMATIK DA - 2014/8// PY - 2014/8// DO - 10.1007/s00211-013-0597-6 VL - 127 IS - 4 SP - 595-639 SN - 0945-3245 UR - https://doi-org.prox.lib.ncsu.edu/10.1007/s00211-013-0597-6 ER - TY - JOUR TI - A global assembly of adult female mosquito mark-release-recapture data to inform the control of mosquito-borne pathogens AU - Guerra, Carlos A AU - Reiner, Robert C AU - Perkins, T AU - Lindsay, Steve W AU - Midega, Janet T AU - Brady, Oliver J AU - Barker, Christopher M AU - Reisen, William K AU - Harrington, Laura C AU - Takken, Willem AU - Kitron, Uriel AU - Lloyd, Alun L AU - Hay, Simon I AU - Scott, Thomas W AU - Smith, David L T2 - Parasites & Vectors AB - Pathogen transmission by mosquitos is known to be highly sensitive to mosquito bionomic parameters. Mosquito mark-release-recapture (MMRR) experiments are a standard method for estimating such parameters including dispersal, population size and density, survival, blood feeding frequency and blood meal host preferences. We assembled a comprehensive database describing adult female MMRR experiments. Bibliographic searches were used to build a digital library of MMRR studies and selected data describing the reported outcomes were extracted. The resulting database contained 774 unique adult female MMRR experiments involving 58 vector mosquito species from the three main genera of importance to human health: Aedes, Anopheles and Culex. Crude examination of these data revealed patterns associated with geography as well as mosquito genus, consistent with bionomics varying by species-specific life history and ecological context. Recapture success varied considerably and was significantly different amongst genera, with 8, 4 and 1% of adult females recaptured for Aedes, Anopheles and Culex species, respectively. A large proportion of experiments (59%) investigated dispersal and survival and many allowed disaggregation of the release and recapture data. Geographic coverage was limited to just 143 localities around the world. This MMRR database is a substantial contribution to the compilation of global data that can be used to better inform basic research and public health interventions, to identify and fill knowledge gaps and to enrich theory and evidence-based ecological and epidemiological studies of mosquito vectors, pathogen transmission and disease prevention. The database revealed limited geographic coverage and a relative scarcity of information for vector species of substantial public health relevance. It represents, however, a wealth of entomological information not previously compiled and of particular interest for mosquito-borne pathogen transmission models. DA - 2014/// PY - 2014/// DO - 10.1186/1756-3305-7-276 VL - 7 IS - 1 SP - 276 J2 - Parasites & Vectors LA - en OP - SN - 1756-3305 UR - http://dx.doi.org/10.1186/1756-3305-7-276 DB - Crossref KW - Mosquito KW - Vector KW - Mark-release-recapture KW - Database KW - Pathogen transmission models ER - TY - JOUR TI - Special Issue: 2012 ASME Conference on Smart Materials, Adaptive Structures, and Intelligent Systems Preface AU - Smith, Ralph AU - Wereley, Norman M. AU - Myers, Oliver AU - Dragoni, Eugenio AU - Ruggiero, Eric AU - Loh, Kenneth J. T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES DA - 2014/6// PY - 2014/6// DO - 10.1177/1045389x14535539 VL - 25 IS - 9 SP - 1039-1040 SN - 1530-8138 ER - TY - JOUR TI - Single-polarization SAR imaging in the presence of Faraday rotation AU - Gilman, Mikhail AU - Smith, Erick AU - Tsynkov, Semyon T2 - Inverse Problems AB - We discuss the single-polarization SAR imaging with the Faraday rotation (FR) taken into account. The FR leads to a reduction in the intensity of the received radar signal that varies over the signal length. That, in turn, results in a degradation of the image. In particular, the image of a point target may have its intensity peak split in the range direction. To distinguish between the cases of low reflectivity and those where the low antenna signal is due to the FR, we employ the image autocorrelation analysis. This analysis also helps determine the parameters of the FR, which, in turn, allow us to introduce an approach for correcting the single-polarization SAR images distorted by FR. DA - 2014/6/1/ PY - 2014/6/1/ DO - 10.1088/0266-5611/30/7/075002 VL - 30 IS - 7 SP - 075002 J2 - Inverse Problems OP - SN - 0266-5611 1361-6420 UR - http://dx.doi.org/10.1088/0266-5611/30/7/075002 DB - Crossref KW - magnetic field of the Earth KW - anisotropic ionosphere KW - propagation of radio waves through gyrotropic plasma KW - deterioration of radar image KW - image autocorrelation analysis KW - evaluation of Faraday rotation effect KW - correction of the matched filter ER - TY - JOUR TI - REALIZATION OF (sl)over-cap(2)(C) AT THE CRITICAL LEVEL AU - Dunbar, Jonathan AU - Jing, Naihuan AU - Misra, Kailash C. T2 - COMMUNICATIONS IN CONTEMPORARY MATHEMATICS AB - An explicit realization of the affine Lie algebra [Formula: see text] at the critical level is constructed using a mixture of bosons and parafermions. Subsequently, a representation of the associated Lepowsky–Wilson Z-algebra is given on a space of the tensor product of bosonic fields and certain semi-infinite wedge products. DA - 2014/4// PY - 2014/4// DO - 10.1142/s0219199714500060 VL - 16 IS - 2 SP - SN - 1793-6683 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84899490482&partnerID=MN8TOARS KW - Affine Lie algebras KW - critical level KW - bosons KW - parafermions ER - TY - JOUR TI - Isomorphy classes of k-involutions of G(2) AU - Hutchens, J. T2 - Journal of Algebra and its Applications DA - 2014/// PY - 2014/// VL - 13 IS - 7 ER - TY - JOUR TI - High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling AU - Banks, H. T. AU - Birch, Malcolm J. AU - Brewin, Mark P. AU - Greenwald, Stephen E. AU - Hu, Shuhua AU - Kenz, Zackary R. AU - Kruse, Carola AU - Maischak, Matthias AU - Shaw, Simon AU - Whiteman, John R. T2 - INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING AB - SUMMARY We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685–6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension ( r + 1) D and is usually regarded as being too large when r > 1. Werder et al. found that the space‐time coupling matrices are diagonalizable over for r ⩽ 100, and this means that the time‐coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG‐in‐time methodology, for the first time, to second‐order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high‐order (up to degree 7) temporal and spatio‐temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd. DA - 2014/4/13/ PY - 2014/4/13/ DO - 10.1002/nme.4631 VL - 98 IS - 2 SP - 131-156 SN - 1097-0207 KW - viscoelasticity KW - high order methods KW - discontinuous Galerkin finite element method KW - spectral element method KW - space-time finite elements ER - TY - JOUR TI - Classifying Several Classes of Leibniz Algebras AU - Ray, Chelsie Batten AU - Hedges, Allison AU - Stitzinger, Ernest T2 - ALGEBRAS AND REPRESENTATION THEORY AB - We extend results related to maximal subalgebras and ideals from Lie to Leibniz algebras. In particular, we classify minimal non-elementary Leibniz algebras and Leibniz algebras with a unique maximal ideal. In both cases, there are types of these algebras with no Lie algebra analogue. We also give a classification of E-Leibniz algebras which is very similiar to its Lie algebra counterpart. Note that a classification of elementary Leibniz algebras has been shown in Batten Ray et al. (2011). DA - 2014/4// PY - 2014/4// DO - 10.1007/s10468-013-9416-0 VL - 17 IS - 2 SP - 703-712 SN - 1572-9079 KW - Elementary Leibniz algebras KW - E-Leibniz algebras KW - Frattini ideal ER - TY - JOUR TI - CONFINEMENT FOR REPULSIVE-ATTRACTIVE KERNELS AU - Balague, Daniel AU - Carrillo, Jose A. AU - Yao, Yao T2 - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B AB - We investigate the confinement properties of solutions of theaggregation equation with repulsive-attractive potentials. We showthat solutions remain compactly supported in a large fixed balldepending on the initial data and the potential. The argumentsapply to the functional setting of probability measures withmildly singular repulsive-attractive potentials and to thefunctional setting of smooth solutions with a potential being thesum of the Newtonian repulsion at the origin and a smooth suitablygrowing at infinity attractive potential. DA - 2014/7// PY - 2014/7// DO - 10.3934/dcdsb.2014.19.1227 VL - 19 IS - 5 SP - 1227-1248 SN - 1553-524X KW - Aggregation equation KW - particle systems KW - confinement ER - TY - JOUR TI - An inversion-relaxation approach for sampling stationary points of spin model Hamiltonians AU - Hughes, Ciaran AU - Mehta, Dhagash AU - Wales, David J. T2 - JOURNAL OF CHEMICAL PHYSICS AB - Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here, we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate how this approach can find all the stationary points for potentials or Hamiltonians bounded from above, which includes a large class of important spin models, and we show that it is far more efficient than previous methods. For potentials unbounded from above, the relaxation part of the method is still efficient in finding minima and transition states, which are usually the primary focus of attention for atomistic systems. DA - 2014/5/21/ PY - 2014/5/21/ DO - 10.1063/1.4875697 VL - 140 IS - 19 SP - SN - 1089-7690 ER - TY - JOUR TI - A generalization of Newton's identity and Macdonald functions AU - Cai, Tommy Wuxing AU - Jing, Naihuan T2 - JOURNAL OF COMBINATORIAL THEORY SERIES A AB - A generalization of Newton's identity on symmetric functions is given. Using the generalized Newton identity we give a unified method to show the existence of Jack and Macdonald polynomials. We also give a simple proof of the Jing–Józefiak formula for two-row Macdonald functions. DA - 2014/7// PY - 2014/7// DO - 10.1016/j.jcta.2014.04.001 VL - 125 IS - 1 SP - 342-356 SN - 1096-0899 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84906661322&partnerID=MN8TOARS KW - Newton identities KW - Macdonald polynomials KW - Vertex operators ER - TY - JOUR TI - Universal geometric cluster algebras AU - Reading, Nathan T2 - MATHEMATISCHE ZEITSCHRIFT AB - We consider, for each exchange matrix $$B$$ , a category of geometric cluster algebras over $$B$$ and coefficient specializations between the cluster algebras. The category also depends on an underlying ring $$R$$ , usually $$\mathbb {Z},\,\mathbb {Q}$$ , or $$\mathbb {R}$$ . We broaden the definition of geometric cluster algebras slightly over the usual definition and adjust the definition of coefficient specializations accordingly. If the broader category admits a universal object, the universal object is called the cluster algebra over $$B$$ with universal geometric coefficients, or the universal geometric cluster algebra over $$B$$ . Constructing universal geometric coefficients is equivalent to finding an $$R$$ -basis for $$B$$ (a “mutation-linear” analog of the usual linear-algebraic notion of a basis). Polyhedral geometry plays a key role, through the mutation fan $${\mathcal {F}}_B$$ , which we suspect to be an important object beyond its role in constructing universal geometric coefficients. We make the connection between $${\mathcal {F}}_B$$ and $$\mathbf{g}$$ -vectors. We construct universal geometric coefficients in rank $$2$$ and in finite type and discuss the construction in affine type. DA - 2014/6// PY - 2014/6// DO - 10.1007/s00209-013-1264-4 VL - 277 IS - 1-2 SP - 499-547 SN - 1432-1823 UR - https://doi.org/10.1007/s00209-013-1264-4 ER - TY - JOUR TI - Twisted Quantum Toroidal Algebras T-q(-)(g) AU - Jing, Naihuan AU - Liu, Rongjia T2 - LETTERS IN MATHEMATICAL PHYSICS AB - We construct a principally graded quantum loop algebra for the Kac–Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations. DA - 2014/9// PY - 2014/9// DO - 10.1007/s11005-014-0711-4 VL - 104 IS - 9 SP - 1137-1145 SN - 1573-0530 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84904135738&partnerID=MN8TOARS KW - quantum algebras KW - toroidal algebras KW - vertex operators KW - Serre relations ER - TY - JOUR TI - The refined lecture hall theorem via abacus diagrams AU - Bradford, Laura AU - Harris, Meredith AU - Jones, Brant AU - Komarinski, Alex AU - Matson, Carly AU - O'Shea, Edwin T2 - RAMANUJAN JOURNAL AB - Bousquet-Mélou & Eriksson’s lecture hall theorem generalizes Euler’s celebrated distinct-odd partition theorem. We present an elementary and transparent proof of a refined version of the lecture hall theorem using a simple bijection involving abacus diagrams. DA - 2014/6// PY - 2014/6// DO - 10.1007/s11139-013-9525-8 VL - 34 IS - 2 SP - 163-176 SN - 1572-9303 KW - Partitions KW - Lecture hall partitions KW - Bounded partitions KW - Abacus ER - TY - JOUR TI - Optimal two-phase vaccine allocation to geographically different regions under uncertainty AU - Yarmand, Hamed AU - Ivy, Julie S. AU - Denton, Brian AU - Lloyd, Alun L. T2 - EUROPEAN JOURNAL OF OPERATIONAL RESEARCH AB - In this article, we consider a decision process in which vaccination is performed in two phases to contain the outbreak of an infectious disease in a set of geographic regions. In the first phase, a limited number of vaccine doses are allocated to each region; in the second phase, additional doses may be allocated to regions in which the epidemic has not been contained. We develop a simulation model to capture the epidemic dynamics in each region for different vaccination levels. We formulate the vaccine allocation problem as a two-stage stochastic linear program (2-SLP) and use the special problem structure to reduce it to a linear program with a similar size to that of the first stage problem. We also present a Newsvendor model formulation of the problem which provides a closed form solution for the optimal allocation. We construct test cases motivated by vaccine planning for seasonal influenza in the state of North Carolina. Using the 2-SLP formulation, we estimate the value of the stochastic solution and the expected value of perfect information. We also propose and test an easy to implement heuristic for vaccine allocation. We show that our proposed two-phase vaccination policy potentially results in a lower attack rate and a considerable saving in vaccine production and administration cost. DA - 2014/2/16/ PY - 2014/2/16/ DO - 10.1016/j.ejor.2013.08.027 VL - 233 IS - 1 SP - 208-219 SN - 1872-6860 KW - OR in health services KW - Epidemic control KW - Two-phase vaccine allocation KW - Stochastic linear program KW - Newsvendor model KW - Value of stochastic solution ER - TY - JOUR TI - OPTIMAL CONTROL WITH L-p(Omega), p epsilon [0,1), CONTROL COST AU - Ito, Kazufumi AU - Kunisch, Karl T2 - SIAM JOURNAL ON CONTROL AND OPTIMIZATION AB - $L^p$ optimal control with $p\in [0,1)$ is investigated. The difficulty of natural lack of convexity and thus of weak lower semicontinuity is addressed by introducing appropriately chosen regularization terms. Existence results and necessary optimality conditions are obtained, and convergence of a monotone scheme is proved. Special attention is given to the particular case of optimal control problems with quadratic tracking and regularized $L^0$ control costs are given. A maximum principle is derived and existence of controls, in some cases relaxed controls, is proved, and an estimate on the consequences of relaxation are estimated. DA - 2014/// PY - 2014/// DO - 10.1137/120896529 VL - 52 IS - 2 SP - 1251-1275 SN - 1095-7138 KW - L-0 minimization KW - optimal control KW - bang-bang control KW - sparsity optimization KW - maximum principle KW - nonsmooth optimization KW - primal-dual active set method ER - TY - JOUR TI - Multigraded commutative algebra of graph decompositions AU - Engstrom, Alexander AU - Kahle, Thomas AU - Sullivant, Seth T2 - JOURNAL OF ALGEBRAIC COMBINATORICS AB - The toric fiber product is a general procedure for gluing two ideals, homogeneous with respect to the same multigrading, to produce a new homogeneous ideal. Toric fiber products generalize familiar constructions in commutative algebra like adding monomial ideals and the Segre product. We describe how to obtain generating sets of toric fiber products in non-zero codimension and discuss persistence of normality and primary decompositions under toric fiber products. Several applications are discussed, including (a) the construction of Markov bases of hierarchical models in many new cases, (b) a new proof of the quartic generation of binary graph models associated to K 4-minor free graphs, and (c) the recursive computation of primary decompositions of conditional independence ideals. DA - 2014/3// PY - 2014/3// DO - 10.1007/s10801-013-0450-0 VL - 39 IS - 2 SP - 335-372 SN - 1572-9192 KW - Toric fiber product KW - Toric ideal KW - Segre product KW - Markov basis KW - Primary decomposition KW - Algebraic statistics KW - Conditional independence ideal KW - Normality of ideals ER - TY - JOUR TI - High-Dimensional Model Representations for the Neutron Transport Equation AU - Hu, Zhengzheng AU - Smith, Ralph C. AU - Willert, Jeffrey AU - Kelley, C. T. T2 - NUCLEAR SCIENCE AND ENGINEERING AB - AbstractThe Boltzmann transport equation is used to model the neutron flux in a nuclear reactor. The solution of the transport equation is the neutron flux, which depends on a large number of material cross sections that can be on the order of thousands. These cross sections describe various types of possible interactions between neutrons, such as fission, capture, and scattering. The cross sections are measured experimentally and therefore have associated uncertainties. It is thus necessary to quantify how the uncertainty of the cross-section values is propagated through the model for the neutron flux. High-dimensional model representations (HDMRs) can be employed to systematically quantify input-output relations. It can, however, be computationally prohibitive to construct a surrogate model using the HDMR framework for a model that has thousands of parameters. In this paper, we introduce an algorithm that utilizes the New Morris Method to first reduce the parameter space to include only the significant individual and pairwise effects and then construct a surrogate model using a Cut-HDMR expansion within the reduced space. A unified index is introduced to facilitate the comparison of the significance of the model parameters. The accuracy and efficiency of the surrogate model is demonstrated using a one-dimensional neutron transport equation. DA - 2014/7// PY - 2014/7// DO - 10.13182/nse13-52 VL - 177 IS - 3 SP - 350-360 SN - 1943-748X ER - TY - JOUR TI - A lexicographic shellability characterization of geometric lattices AU - Davidson, Ruth AU - Hersh, Patricia T2 - JOURNAL OF COMBINATORIAL THEORY SERIES A AB - Geometric lattices are characterized in this paper as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. Equivalently, geometric lattices are shown to be exactly those finite lattices such that every ordering on the join-irreducibles induces a lexicographic shelling. This new characterization fits into a similar paradigm as McNamaraʼs characterization of supersolvable lattices as those lattices admitting a different type of lexicographic shelling, namely one in which each maximal chain is labeled with a permutation of {1,…,n}. DA - 2014/4// PY - 2014/4// DO - 10.1016/j.jcta.2013.11.001 VL - 123 IS - 1 SP - 8-13 SN - 1096-0899 KW - Geometric lattice KW - Mobius function KW - Shellability KW - Order complex ER - TY - JOUR TI - PEDESTRIAN FLOW MODELS WITH SLOWDOWN INTERACTIONS AU - Chertock, Alina AU - Kurganov, Alexander AU - Polizzi, Anthony AU - Timofeyev, Ilya T2 - MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES AB - In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for pedestrians moving in two opposite directions. Coarse-grained mesoscopic and macroscopic analogs are derived leading to the coupled system of PDEs for the density of the pedestrian traffic. The obtained first-order system of conservation laws is only conditionally hyperbolic. We also derive higher-order nonlinear diffusive corrections resulting in a parabolic macroscopic PDE model. Numerical experiments comparing and contrasting the behavior of the microscopic stochastic model and the resulting coarse-grained PDEs for various parameter settings and initial conditions are performed. These numerical experiments demonstrate that the nonlinear diffusion is essential for reproducing the behavior of the stochastic system in the nonhyperbolic regime. DA - 2014/2// PY - 2014/2// DO - 10.1142/s0218202513400083 VL - 24 IS - 2 SP - SN - 1793-6314 UR - https://doi-org.prox.lib.ncsu.edu/10.1142/S0218202513400083 KW - Pedestrian traffic flow KW - stochastic cellular automata model KW - mesoscopic and macroscopic models KW - exclusion process KW - nonlinear diffusion ER - TY - JOUR TI - Nonnegative rank factorization-a heuristic approach via rank reduction AU - Dong, Bo AU - Lin, Matthew M. AU - Chu, Moody T. T2 - NUMERICAL ALGORITHMS DA - 2014/2// PY - 2014/2// DO - 10.1007/s11075-013-9704-0 VL - 65 IS - 2 SP - 251-274 SN - 1572-9265 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84875296090&partnerID=MN8TOARS KW - Nonnegative matrix KW - Nonnegative rank KW - Nonnegative matrix factorization KW - Nonnegative rank factorization KW - Wedderburn rank reduction formula KW - Completely positive matrix KW - cp-rank ER - TY - JOUR TI - NILPOTENT LIE AND LEIBNIZ ALGEBRAS AU - Ray, Chelsie Batten AU - Combs, Alexander AU - Gin, Nicole AU - Hedges, Allison AU - Hird, J. T. AU - Zack, Laurie T2 - COMMUNICATIONS IN ALGEBRA AB - We extend results on finite dimensional nilpotent Lie algebras to Leibniz algebras and counterexamples to others are found. One generator algebras are used in these examples and are investigated further. DA - 2014/6/3/ PY - 2014/6/3/ DO - 10.1080/00927872.2012.717655 VL - 42 IS - 6 SP - 2404-2410 SN - 1532-4125 ER - TY - JOUR TI - Jack vertex operators and realization of Jack functions AU - Cai, Tommy Wuxing AU - Jing, Naihuan T2 - JOURNAL OF ALGEBRAIC COMBINATORICS AB - We give an iterative method to realize general Jack functions using vertex operators. We first prove some cases of Stanley’s conjecture on positivity of the Littlewood–Richardson coefficients, and then use this method to give a new realization of Jack functions. We also show in general that the images of coefficients of products of Jack vertex operators form a basis of symmetric functions. In particular, this gives a new proof of linear independence for the rectangular and marked rectangular Jack vertex operators. Finally, a generalized Frobenius formula for Jack functions is given and used for evaluation of Dyson integrals and even powers of Vandermonde determinants. DA - 2014/2// PY - 2014/2// DO - 10.1007/s10801-013-0438-9 VL - 39 IS - 1 SP - 53-74 SN - 1572-9192 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84891635006&partnerID=MN8TOARS KW - Symmetric functions KW - Jack polynomials KW - Vertex operators ER - TY - JOUR TI - A variational approach to sparsity optimization based on Lagrange multiplier theory AU - Ito, Kazufumi AU - Kunisch, Karl T2 - INVERSE PROBLEMS AB - Sparsity optimization for linear least squares problems formulated as non-smooth regularization problems are considered in infinite-dimensional sequence spaces ℓp with p ∈ [0, 1]. Necessary optimality conditions in the format of a complementarity system are obtained. A monotonically convergent scheme is developed for the case p ∈ (0, 1]. For the case p = 0 a primal dual active set strategy based on the Lagrange multiplier rule is proposed and analyzed for special cases. DA - 2014/1// PY - 2014/1// DO - 10.1088/0266-5611/30/1/015001 VL - 30 IS - 1 SP - SN - 1361-6420 ER - TY - JOUR TI - A Lotka-Volterra cooperating reaction-diffusion system with degenerate density-dependent diffusion AU - Pao, C. V. T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS AB - In the Lotka–Volterra cooperating reaction–diffusion system if the diffusion coefficients are constants then for a certain set of reaction rates in the reaction function the solution of the system blows up in finite time, and for another set of reaction rates, a unique global solution exists and converges to the trivial solution. However, if the diffusion coefficients are density-dependent then the dynamic behavior of the solution can be quite different. The aim of this paper is to investigate the global existence and the asymptotic behavior of the solution for a class of density-dependent cooperating reaction–diffusion systems where the diffusion coefficients are degenerate. It is shown that the time-dependent problem has a unique bounded global solution, and in addition to the trivial and semi-trivial solutions the corresponding steady-state problem has a positive maximal solution and a positive minimal solution. Moreover, the time-dependent solution converges to the maximal solution for one class of initial functions, and to the minimal solution for another class of initial functions. The above convergence property holds true for any reaction rates in the reaction function. Applications of the above results are given to a porous medium type of reaction–diffusion problem as well as other types of diffusion coefficients, including the finite sum and products of these functions. DA - 2014/1// PY - 2014/1// DO - 10.1016/j.na.2013.09.015 VL - 95 SP - 460-467 SN - 1873-5215 KW - Lotka-Volterra cooperating model KW - Degenerate density-dependent diffusion KW - Positive steady-state solutions KW - Asymptotic behavior KW - Coexistence and stability ER - TY - JOUR TI - A Coupled Immersed Interface and Level Set Method for Three-Dimensional Interfacial Flows with Insoluble Surfactant AU - Xu, Jian-Jun AU - Huang, Yunqing AU - Lai, Ming-Chih AU - Li, Zhilin T2 - COMMUNICATIONS IN COMPUTATIONAL PHYSICS AB - Abstract In this paper, a numerical method is presented for simulating the 3D interfacial flows with insoluble surfactant. The numerical scheme consists of a 3D immersed interface method (IIM) for solving Stokes equations with jumps across the interface and a 3D level-set method for solving the surfactant convection-diffusion equation along a moving and deforming interface. The 3D IIM Poisson solver modifies the one in the literature by assuming that the jump conditions of the solution and the flux are implicitly given at the grid points in a small neighborhood of the interface. This assumption is convenient in conjunction with the level-set techniques. It allows standard Lagrangian interpolation for quantities at the projection points on the interface. The interface jump relations are re-derived accordingly. A novel rotational procedure is given to generate smooth local coordinate systems and make effective interpolation. Numerical examples demonstrate that the IIM Poisson solver and the Stokes solver achieve second-order accuracy. A 3D drop with insoluble surfactant under shear flow is investigated numerically by studying the influences of different physical parameters on the drop deformation. DA - 2014/2// PY - 2014/2// DO - 10.4208/cicp.241012.310513a VL - 15 IS - 2 SP - 451-469 SN - 1991-7120 KW - 3D immersed interface method KW - level-set method KW - insoluble surfactant KW - Stokes interfacial flow KW - drop deformation ER - TY - JOUR TI - Structural Identifiability of Viscoelastic Mechanical Systems AU - Mahdi, Adam AU - Meshkat, Nicolette AU - Sullivant, Seth T2 - PLOS ONE AB - We solve the local and global structural identifiability problems for viscoelastic mechanical models represented by networks of springs and dashpots. We propose a very simple characterization of both local and global structural identifiability based on identifiability tables, with the purpose of providing a guideline for constructing arbitrarily complex, identifiable spring-dashpot networks. We illustrate how to use our results in a number of examples and point to some applications in cardiovascular modeling. DA - 2014/2/11/ PY - 2014/2/11/ DO - 10.1371/journal.pone.0086411 VL - 9 IS - 2 SP - SN - 1932-6203 ER - TY - JOUR TI - Modeling Endocrine Control of the Pituitary-Ovarian Axis: Androgenic Influence and Chaotic Dynamics AU - Hendrix, Angelean O. AU - Hughes, Claude L. AU - Selgrade, James F. T2 - BULLETIN OF MATHEMATICAL BIOLOGY DA - 2014/1// PY - 2014/1// DO - 10.1007/s11538-013-9913-7 VL - 76 IS - 1 SP - 136-156 SN - 1522-9602 KW - Modeling KW - Androgens ER - TY - JOUR TI - MODEL VALIDATION FOR A NONINVASIVE ARTERIAL STENOSIS DETECTION PROBLEM AU - Banks, H. Thomas AU - Hu, Shuhua AU - Kenz, Zackary R. AU - Kruse, Carola AU - Shaw, Simon AU - Whiteman, John AU - Brewin, Mark P. AU - Greenwald, Stephen E. AU - Birch, Malcolm J. T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING AB - A current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use one-dimensional shear wave experimental data from novel acoustic phantoms to validate a corresponding viscoelastic mathematical model. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error. DA - 2014/6// PY - 2014/6// DO - 10.3934/mbe.2014.11.427 VL - 11 IS - 3 SP - 427-448 SN - 1551-0018 KW - Viscoelastic model KW - sensitivity analysis KW - inverse problem KW - asymptotic theory ER - TY - JOUR TI - Diagrammatic description of c-vectors and d-vectors of cluster algebras of finite type AU - Nakanishi, T. AU - Stella, S. T2 - Electronic Journal of Combinatorics DA - 2014/// PY - 2014/// VL - 21 IS - 1 ER - TY - JOUR TI - Sparse interpolatory reduced-order models for simulation of light-induced molecular transformations AU - Mokrauer, D. AU - Kelley, C. T. T2 - Optimization Methods & Software AB - We describe a method for using interpolatory models to accurately and efficiently simulate molecular excitation and relaxation. We use sparse interpolation for efficiency and local error estimation and control for robustness and accuracy. DA - 2014/// PY - 2014/// DO - 10.1080/10556788.2012.693928 VL - 29 IS - 2 SP - 264-273 ER - TY - JOUR TI - Quantification of parameter and model uncertainty for shape memory alloy bending actuators AU - Crews, John H. AU - Smith, Ralph C. T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES AB - In this article, we employ a Bayesian framework to estimate parameter and model uncertainty for shape memory alloy bending actuators. The Bayesian framework provides parameter densities, instead of ordinary least-squares optimal point estimates. Bayes’ rule relates a posterior parameter density to a prior density and likelihood. However, the posterior density is difficult to calculate directly for high-dimensional parameter spaces. Markov chain Monte Carlo methods overcome this difficulty indirectly by creating a Markov chain whose stationary density is the posterior. In this article, we utilize the Delayed Rejection Adaptive Metropolis algorithm for estimating parameter uncertainty. The shape memory alloy bending actuator is modeled using the homogenized energy framework, a computationally efficient and accurate model for various transductive materials. The model is summarized, and techniques for estimating the heat transfer parameters are presented. An algorithmic approach to quantifying uncertainty is useful for numerous reasons. The anticipated use is to quantify uncertainty for robust control algorithms. Robust control is an area of considerable research for smart materials such as shape memory alloy; however, the source of uncertainty is rarely quantified. The methods employed here would greatly aid in the design of robust controllers. DA - 2014/1// PY - 2014/1// DO - 10.1177/1045389x13490842 VL - 25 IS - 2 SP - 229-245 SN - 1530-8138 KW - Shape memory KW - uncertainty quantification KW - Markov chain Monte Carlo ER - TY - JOUR TI - On the solvability of multipoint boundary value problems for discrete systems at resonance AU - Maroncelli, Daniel AU - Rodriguez, Jesus T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS AB - AbstractWe study nonlinear discrete-time boundary value problems at resonance. Criteria for the existence of solutions are established via topological degree theory and the Lyapunov–Schmidt procedure.Keywords:: boundary value problemsBrower's fixed point theoremLyapunov–Schmidt proceduretopological degree theoryresonanceKeywords:: 34B15 Notes1. Email: dmmaronc@ncsu.edu DA - 2014/1/1/ PY - 2014/1/1/ DO - 10.1080/10236198.2013.805216 VL - 20 IS - 1 SP - 24-35 SN - 1563-5120 KW - boundary value problems KW - Brower's fixed point theorem KW - Lyapunov Schmidt procedure KW - topological degree theory KW - resonance ER - TY - JOUR TI - Long-term models of oxidative stress and mitochondrial damage in insulin resistance progression AU - Graham, Erica J. AU - Adler, Frederick R. T2 - JOURNAL OF THEORETICAL BIOLOGY AB - Insulin resistance, characterized by a reduced cellular response to insulin, is a major factor in type 2 diabetes pathogenesis, with a complex etiology consisting of a combination of environmental and genetic factors. Oxidative stress, which develops through an accumulation of toxic reactive oxygen species generated by mitochondria, is believed to contribute to insulin resistance in certain tissues. We develop mathematical models of feedback between reactive oxygen species production and dysfunction in mitochondria to provide insight into the role of oxidative stress in insulin resistance. Our models indicate that oxidative stress generated by glucose overload accelerates irreversible mitochondrial dysfunction. These models provide a foundation for understanding the long-term progression of insulin resistance and type 2 diabetes. DA - 2014/1/7/ PY - 2014/1/7/ DO - 10.1016/j.jtbi.2013.09.028 VL - 340 SP - 238-250 SN - 1095-8541 KW - Type 2 diabetes KW - Superoxide ER - TY - JOUR TI - Confined Dissipative Droplet Solitons in Spin-Valve Nanowires with Perpendicular Magnetic Anisotropy AU - Iacocca, Ezio AU - Dumas, Randy K. AU - Bookman, Lake AU - Mohseni, Majid AU - Chung, Sunjae AU - Hoefer, Mark A. AU - Akerman, Johan T2 - PHYSICAL REVIEW LETTERS AB - Magnetic dissipative droplets are localized, strongly nonlinear dynamical modes excited in nanocontact spin valves with perpendicular magnetic anisotropy. These modes find potential application in nanoscale structures for magnetic storage and computation, but dissipative droplet studies have so far been limited to extended thin films. Here, numerical and asymptotic analyses are used to demonstrate the existence and properties of novel solitons in confined structures. As a nanowire's width is decreased with a nanocontact of fixed size at its center, the observed modes undergo transitions from a fully localized two-dimensional droplet into a two-dimensional droplet edge mode and then a pulsating one-dimensional droplet. These solitons are interpreted as dissipative versions of classical, conservative solitons, allowing for an analytical description of the modes and the mechanisms of bifurcation. The presented results open up new possibilities for the study of low-dimensional solitons and droplet applications in nanostructures. DA - 2014/1/29/ PY - 2014/1/29/ DO - 10.1103/physrevlett.112.047201 VL - 112 IS - 4 SP - SN - 1079-7114 ER - TY - JOUR TI - An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models AU - Harlim, John AU - Mahdi, Adam AU - Majda, Andrew J. T2 - JOURNAL OF COMPUTATIONAL PHYSICS AB - A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model. DA - 2014/1/15/ PY - 2014/1/15/ DO - 10.1016/j.jcp.2013.10.025 VL - 257 SP - 782-812 SN - 1090-2716 KW - Ensemble Kalman filter KW - Nonlinear regression models KW - Parameter estimation of stochastic differential equations KW - Multi-level models ER - TY - JOUR TI - A modeling and uncertainty quantification framework for a flexible structure with macrofiber composite actuators operating in hysteretic regimes AU - Hu, Zhengzheng AU - Smith, Ralph C. AU - Burch, Nathanial AU - Hays, Michael AU - Oates, William S. T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES AB - Macrofiber composites are low cost, durable, and flexible piezoceramic devices that are presently being considered for applications that include shape control of airfoils for improved flight performance, vibration, and noise suppression and energy harvesting. However, macrofiber composites also exhibit hysteresis and constitutive nonlinearities that need to be incorporated in models and model-based control designs to achieve their full capability. In this article, we combine constitutive relations, constructed using the homogenized energy model for ferroelectric hysteresis, with Euler–Bernoulli theory to construct a dynamic macrofiber composite model that quantifies a range of rate-dependent hysteretic behavior of macrofiber composites. Using homogenizing strategies, the macrofiber composite patch is treated as a monolithic material with effective parameters. We initially calibrate the model by estimating parameters through a least squares fit to a subset of the measured data. We find that the estimated parameters yield very accurate fits for quasi-static hysteresis. The estimated parameters also provide reasonably accurate predictions for a range of frequencies that include the first two harmonics. Second, we employ an adaptive Markov chain Monte Carlo algorithm to construct densities and analyze the correlation between parameters. The kernel density estimates derived from the Markov chain Monte Carlo chains imply that most of the model parameters exhibit non-Gaussian distributions. DA - 2014/1// PY - 2014/1// DO - 10.1177/1045389x13489781 VL - 25 IS - 2 SP - 204-228 SN - 1530-8138 KW - Active composites KW - morphing KW - piezoelectric KW - optimization KW - piezoelectric KW - hysteresis ER - TY - JOUR TI - A bootstrapping approach for computing multiple solutions of differential equations AU - Hao, Wenrui AU - Hauenstein, Jonathan D. AU - Hu, Bei AU - Sommese, Andrew J. T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS AB - Discretizing systems of nonlinear algebraic differential equations yields polynomial systems. When using a fine discretization, the resulting polynomial system is often too large to solve using a direct solving approach. Our approach for solving such systems is to utilize a homotopy continuation based method arising from domain decomposition. This method solves polynomial systems arising from subdomains and then uses homotopy continuation to build solutions of the original polynomial system. We illustrate this approach on both one- and two-dimensional problems. DA - 2014/3/1/ PY - 2014/3/1/ DO - 10.1016/j.cam.2013.09.007 VL - 258 SP - 181-190 SN - 1879-1778 KW - Domain decomposition KW - Homotopy continuation KW - Differential equations KW - Multiple solutions KW - Numerical algebraic geometry ER - TY - JOUR TI - LIE SUPERALGEBRAS ARISING FROM BOSONIC REPRESENTATION AU - Jing, Naihuan AU - Xu, Chongbin T2 - COMMUNICATIONS IN ALGEBRA AB - A 2-toroidal Lie superalgebra is constructed using bosonic fields and a ghost field. The superalgebra contains osp(1 | 2n)(1) as a distinguished subalgebra and behaves similarly to the toroidal Lie superalgebra of type B(0, n). Furthermore, this algebra is a central extension of the algebra osp(1 | 2n) ⊗ ℂ[s, s −1, t, t −1]. DA - 2014/1/2/ PY - 2014/1/2/ DO - 10.1080/00927872.2012.713062 VL - 42 IS - 1 SP - 259-270 SN - 1532-4125 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84886393499&partnerID=MN8TOARS KW - Bosonic fields KW - Realization KW - Toroidal Lie superalgebra KW - Primary 17B60 KW - 17B67 KW - 17B69 KW - Secondary 17A45 KW - 81R10 ER -