TY - JOUR
TI - PAIRS TRADING OF TWO ASSETS WITH UNCERTAINTY IN CO-INTEGRATION'S LEVEL OF MEAN REVERSION
AU - Lee, Sangmin
AU - Papanicolaou, Andrew
T2 - International Journal of Theoretical and Applied Finance
AB - This paper considers a stochastic control problem derived from a model for pairs trading under incomplete information. We decompose an individual asset's drift into two parts: an industry drift plus some additional stochasticity. The extra stochasticity may be unobserved, which means the investor has only partial information. We solve the control problem under both full and partial informations for utility function [Formula: see text], and we make comparisons. We show the existence of stable solution to the associated matrix Riccati equations in both cases for [Formula: see text], but for [Formula: see text] there remains potential for infinite value functions in finite time. Also, we quantify the expected loss in utility due to partial information, and present a numerical study to illustrate the contribution of this paper.
DA - 2016/12//
PY - 2016/12//
DO - 10.1142/s0219024916500540
VL - 19
IS - 08
SP - 1650054
J2 - Int. J. Theor. Appl. Finan.
LA - en
OP -
SN - 0219-0249 1793-6322
UR - http://dx.doi.org/10.1142/S0219024916500540
DB - Crossref
KW - Pairs trading
KW - co-integration
KW - Kalman filter
KW - partial information
KW - stochastic control
ER -
TY - JOUR
TI - Analysis of VIX Markets with a Time-Spread Portfolio
AU - Papanicolaou, A.
T2 - Applied Mathematical Finance
AB - This paper explores the relationship between option markets for the S&P500 (SPX) and Chicago Board Options Exchange’s CBOE’s Volatility Index (VIX). Results are obtained by using the so-called time-spread portfolio to replicate a future contract on the squared VIX. The time-spread portfolio is interesting because it provides a model-free link between derivative prices for SPX and VIX. Time spreads can be computed from SPX put options with different maturities, which results in a term structure for squared volatility. This term structure can be compared to the VIX-squared term structure that is backed-out from VIX call options. The time-spread portfolio is also used to measure volatility-of-volatility (vol-of-vol) and the volatility leverage effect. There may emerge small differences in these measurements, depending on whether time spreads are computed with options on SPX or options on VIX. A study of 2012 daily options data shows that vol-of-vol estimates utilizing SPX data will reflect the volatility leverage effect, whereas estimates that exclusively utilize VIX options will predominantly reflect the premia in the VIX-future term structure.
DA - 2016/9/2/
PY - 2016/9/2/
DO - 10.1080/1350486x.2017.1290534
VL - 23
IS - 5
SP - 374-408
J2 - Applied Mathematical Finance
LA - en
OP -
SN - 1350-486X 1466-4313
UR - http://dx.doi.org/10.1080/1350486X.2017.1290534
DB - Crossref
ER -
TY - CONF
TI - Real-Time Stabilization of a Single Inverted Pendulum Using a Power Series Based Controller
AU - Tran, H.
AU - Kennedy, Emese A.
T2 - International MultiConference of Engineers and Computer Scientists
A2 - Yang, Gi-Chul
A2 - Ao, Sio-Iong
A2 - Huang, Xu
A2 - Castillo, Oscar
C2 - 2016///
C3 - Transactions on engineering technologies : International MultiConference of Engineers and Computer Scientists 2015
CY - Hong Kong
DA - 2016///
PY - 2015/3/18/
SP - 1–14
PB - Springer
SN - 978-981-10-0550-3
ER -
TY - CONF
TI - Swing-up of an Inverted Pendulum on a Cart Using a Modified Energy Based Approach
AU - Tran, H.
AU - Kennedy, Emese
T2 - International MultiConference of Engineers and Computer Scientists : IMECS 2016
C2 - 2016///
C3 - International MultiConference of Engineers and Computer Scientists : IMECS 2016 : 16-18 March, 2016, the Royal Garden Hotel, Kowloon, Hong Kong
CY - Royal Garden Hotel, Kowloon, Hong Kong
DA - 2016///
PY - 2016/3/16/
VL - I
SP - 185–190
PB - Newswood Limited, International Association of Engineers
SN - 978-988-19253-8-1 978-988-14047-6-3
ER -
TY - JOUR
TI - Free Boundary Fluid-Elasticity Interactions: Adjoint Sensitivity Analysis
T2 - New Trends in Differential Equations, Control Theory and Optimization
DA - 2016///
PY - 2016///
ER -
TY - CONF
TI - Stochastic forward-backward and primal-dual approximation algorithms with application to online image restoration
AU - Combettes, P.L.
AU - Pesquet, J.-C.
T2 - Proceedings of the European Signal Processing Conference
AB - Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily smooth. Our framework can handle stochastic approximations of the gradient of the smooth function and allows for stochastic errors in the evaluation of the proximity operator of the nonsmooth function. The almost sure convergence of the iterates generated by the algorithm to a minimizer is established under relatively mild assumptions. We also propose a stochastic version of a popular primal-dual proximal splitting algorithm, establish its convergence, and apply it to an online image restoration problem.
C2 - 2016///
C3 - Proceedings of the European Signal Processing Conference
CY - Budapest, Hungary
DA - 2016///
PY - 2016/8/29/
DO - 10.1109/EUSIPCO.2016.7760561
ER -
TY - JOUR
TI - On the Burgers–Poisson equation
AU - Grunert, K.
AU - Nguyen, Khai T.
T2 - Journal of Differential Equations
AB - In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L^1(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.
DA - 2016/9//
PY - 2016/9//
DO - 10.1016/j.jde.2016.05.028
VL - 261
IS - 6
SP - 3220-3246
J2 - Journal of Differential Equations
LA - en
OP -
SN - 0022-0396
UR - http://dx.doi.org/10.1016/J.JDE.2016.05.028
DB - Crossref
KW - Burgers-Poisson equation
KW - Existence
KW - Uniqueness
KW - Blow-up
ER -
TY - JOUR
TI - Quantitative Compactness Estimates for Hamilton–Jacobi Equations
AU - Ancona, F.
AU - Cannarsa, P.
AU - Nguyen, K.T.
T2 - Archive for Rational Mechanics and Analysis
AB - We study quantitative compactness estimates in $\mathbf{W}^{1,1}_{loc}$ for the map $S_t$, $t>0$ that associates to every given initial data $u_0\in Lip(\mathbb{R}^N)$ the corresponding solution $S_t u_0$ of a Hamilton-Jacobi equation $$ u_t+H\big(\nabla_{/!x} u\big)=0\,, \qquad t\geq 0,\quad x\in \mathbb{R}^N, $$ with a uniformly convex Hamiltonian $H=H(p)$. We provide upper and lower estimates of order $1/\varepsilon^N$ on the the Kolmogorov $\varepsilon$-entropy in $\mathbf{W}^{1,1}$ of the image through the map $S_t$ of sets of bounded, compactly supported initial data. Estimates of this type are inspired by a question posed by P.D. Lax within the context of conservation laws, andcould provide a measure of the order of "resolution" of a numerical method implemented for this equation.
DA - 2016///
PY - 2016///
DO - 10.1007/s00205-015-0907-5
VL - 219
IS - 2
SP - 793-828
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84952631180&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Coupled heterogeneities and their impact on parasite transmission and control
T2 - Trends in parasitology
DA - 2016///
PY - 2016///
VL - 32
IS - 5
SP - 356-367
ER -
TY - CHAP
TI - Modelling Pesticide Treatment Effects on Lygus hesperus in Cotton Fields
AU - Banks, H. T.
AU - Banks, J. E.
AU - Murad, Neha
AU - Rosenheim, J. A.
AU - Tillman, K.
T2 - IFIP Advances in Information and Communication Technology
AB - We continue our efforts on modeling of the population dynamics of herbivorous insects in order to develop and implement effective pest control protocols. In the context of inverse problems, we explore the dynamic effects of pesticide treatments on Lygus hesperus, a common pest of cotton in the western United States. Fitting models to field data, we consider model selection for an appropriate mathematical model and corresponding statistical models, and use techniques to compare models. We address the question of whether data, as it is currently collected, can support time-dependent (as opposed to constant) parameter estimates.
PY - 2016///
DO - 10.1007/978-3-319-55795-3_8
SP - 95-106
OP -
PB - Springer International Publishing
SN - 9783319557946 9783319557953
UR - http://dx.doi.org/10.1007/978-3-319-55795-3_8
DB - Crossref
ER -
TY - CHAP
TI - Causality-Guided Feature Selection
AU - Chaudhary, Mandar S.
AU - Gonzalez, Doel L.
AU - Bello, Gonzalo A.
AU - Angus, Michael P.
AU - Desai, Dhara
AU - Harenberg, Steve
AU - Doraiswamy, P. Murali
AU - Semazzi, Fredrick H. M.
AU - Kumar, Vipin
AU - Samatova, Nagiza F.
T2 - Advanced Data Mining and Applications
AB - Identifying meaningful features that drive a phenomenon (response) of interest in complex systems of interconnected factors is a challenging problem. Causal discovery methods have been previously applied to estimate bounds on causal strengths of factors on a response or to identify meaningful interactions between factors in complex systems, but these approaches have been used only for inferential purposes. In contrast, we posit that interactions between factors with a potential causal association on a given response could be viable candidates not only for hypothesis generation but also for predictive modeling. In this work, we propose a causality-guided feature selection methodology that identifies factors having a potential cause-effect relationship in complex systems, and selects features by clustering them based on their causal strength with respect to the response. To this end, we estimate statistically significant causal effects on the response of factors taking part in potential causal relationships, while addressing associated technical challenges, such as multicollinearity in the data. We validate the proposed methodology for predicting response in five real-world datasets from the domain of climate science and biology. The selected features show predictive skill and consistent performance across different domains.
PY - 2016///
DO - 10.1007/978-3-319-49586-6_26
SP - 391-405
OP -
PB - Springer International Publishing
SN - 9783319495859 9783319495866
UR - http://dx.doi.org/10.1007/978-3-319-49586-6_26
DB - Crossref
ER -
TY - JOUR
TI - Kinematics of fluid particles on the sea surface: Hamiltonian theory
AU - Fedele, F.
AU - Chandre, C.
AU - Farazmand, M.
T2 - Journal of Fluid Mechanics
AB - We derive the John-Sclavounos equations describing the motion of a fluid particle on the sea surface from first principles using Lagrangian and Hamiltonian formalisms applied to the motion of a frictionless particle constrained on an unsteady surface. The main result is that vorticity generated on a stress-free surface vanishes at a wave crest when the horizontal particle velocity equals the crest propagation speed, which is the kinematic criterion for wave breaking. If this holds for the largest crest, then the symplectic two-form associated with the Hamiltonian dynamics reduces instantaneously to that associated with the motion of a particle in free flight, as if the surface did not exist. Further, exploiting the conservation of the Hamiltonian function for steady surfaces and traveling waves we show that particle velocities remain bounded at all times, ruling out the possibility of the finite-time blowup of solutions.
DA - 2016/7/21/
PY - 2016/7/21/
DO - 10.1017/jfm.2016.453
VL - 801
SP - 260-288
J2 - J. Fluid Mech.
LA - en
OP -
SN - 0022-1120 1469-7645
UR - http://dx.doi.org/10.1017/jfm.2016.453
DB - Crossref
KW - general fluid mechanics
KW - Hamiltonian theory
KW - waves/free-surface flows
ER -
TY - JOUR
TI - Polar rotation angle identifies elliptic islands in unsteady dynamical systems
AU - Farazmand, Mohammad
AU - Haller, George
T2 - Physica D: Nonlinear Phenomena
AB - We propose rotation inferred from the polar decomposition of the flow gradient as a diagnostic for elliptic (or vortex-type) invariant regions in non-autonomous dynamical systems. We consider here two- and three-dimensional systems, in which polar rotation can be characterized by a single angle. For this polar rotation angle (PRA), we derive explicit formulas using the singular values and vectors of the flow gradient. We find that closed level sets of the PRA reveal elliptic islands in great detail, and singular level sets of the PRA uncover centers of such islands. Both features turn out to be objective (frame-invariant) for two-dimensional systems. We illustrate the diagnostic power of PRA for elliptic structures on several examples.
DA - 2016/2//
PY - 2016/2//
DO - 10.1016/j.physd.2015.09.007
VL - 315
SP - 1-12
J2 - Physica D: Nonlinear Phenomena
LA - en
OP -
SN - 0167-2789
UR - http://dx.doi.org/10.1016/j.physd.2015.09.007
DB - Crossref
KW - Non-autonomous dynamical systems
KW - Invariant tori
KW - Coherent structures
KW - Turbulence
KW - Polar decomposition
ER -
TY - JOUR
TI - Defining coherent vortices objectively from the vorticity
AU - Haller, G.
AU - Hadjighasem, A.
AU - Farazmand, M.
AU - Huhn, F.
T2 - Journal of Fluid Mechanics
AB - Rotationally coherent Lagrangian vortices are formed by tubes of deforming fluid elements that complete equal bulk material rotation relative to the mean rotation of the deforming fluid volume. We show that the initial positions of such tubes coincide with tubular level surfaces of the Lagrangian-averaged vorticity deviation (LAVD), the trajectory integral of the normed difference of the vorticity from its spatial mean. The LAVD-based vortices are objective, i.e. remain unchanged under time-dependent rotations and translations of the coordinate frame. In the limit of vanishing Rossby numbers in geostrophic flows, cyclonic LAVD vortex centres are precisely the observed attractors for light particles. A similar result holds for heavy particles in anticyclonic LAVD vortices. We also establish a relationship between rotationally coherent Lagrangian vortices and their instantaneous Eulerian counterparts. The latter are formed by tubular surfaces of equal material rotation rate, objectively measured by the instantaneous vorticity deviation (IVD). We illustrate the use of the LAVD and the IVD to detect rotationally coherent Lagrangian and Eulerian vortices objectively in several two- and three-dimensional flows.
DA - 2016/4/13/
PY - 2016/4/13/
DO - 10.1017/jfm.2016.151
VL - 795
SP - 136-173
J2 - J. Fluid Mech.
LA - en
OP -
SN - 0022-1120 1469-7645
UR - http://dx.doi.org/10.1017/jfm.2016.151
DB - Crossref
KW - nonlinear dynamical systems
KW - topological fluid dynamics
KW - vortex dynamics
ER -
TY - JOUR
TI - Algebraic Decay to Equilibrium for the Becker--Döring Equations
AU - Murray, Ryan W.
AU - Pego, Robert L.
T2 - SIAM Journal on Mathematical Analysis
AB - This paper studies rates of decay to equilibrium for the Becker--Doring equations with subcritical initial data. In particular, algebraic rates of decay are established when initial perturbations of equilibrium have polynomial moments. This is proved by using new dissipation estimates in polynomially weighted $\ell^1$ spaces, operator decomposition techniques from kinetic theory, and interpolation estimates from the study of traveling waves.
DA - 2016/1//
PY - 2016/1//
DO - 10.1137/15m1038578
VL - 48
IS - 4
SP - 2819-2842
KW - coagulation-fragmentation equations
KW - rate of decay to equilibrium
KW - interpolation inequalities
ER -
TY - JOUR
TI - Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems
T2 - Physical Review E
AB - Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals defined in terms of Optimally Time Dependent (OTD) modes. One such functional has the form of the largest eigenvalue of the symmetric part of the linearized dynamics reduced to these modes. In contrast to other choices of subspaces, the proposed modes are flow invariant and therefore a projection onto them is dynamically meaningful. We illustrate the application of these indicators on three examples: a prototype low-dimensional model, a body forced turbulent fluid flow, and a unidirectional model of nonlinear water waves. We use Bayesian statistics to quantify the predictive power of the proposed indicators.
DA - 2016/9/14/
PY - 2016/9/14/
DO - 10.1103/physreve.94.032212
UR - http://dx.doi.org/10.1103/physreve.94.032212
ER -
TY - JOUR
TI - An adjoint-based approach for finding invariant solutions of Navier–Stokes equations
T2 - Journal of Fluid Mechanics
AB - We consider the incompressible Navier–Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and travelling-wave solutions of the Navier–Stokes equations. Using the adjoint equations, arbitrary initial conditions evolve to the vicinity of a (relative) equilibrium at which point a few Newton-type iterations yield the desired (relative) equilibrium solution. We apply this adjoint-based method to a chaotic two-dimensional Kolmogorov flow. A convergence rate of $100\,\%$ is observed, leading to the discovery of $21$ new steady-state and travelling-wave solutions at Reynolds number $Re=40$ . Some of the new invariant solutions have spatially localized structures that were previously believed to exist only on domains with large aspect ratios. We show that one of the newly found steady-state solutions underpins the temporal intermittencies, i.e. high energy dissipation episodes of the flow. More precisely, it is shown that each intermittent episode of a generic turbulent trajectory corresponds to its close passage to this equilibrium solution.
DA - 2016/5/25/
PY - 2016/5/25/
DO - 10.1017/jfm.2016.203
UR - http://dx.doi.org/10.1017/jfm.2016.203
KW - chaos
KW - intermittency
KW - transition to turbulence
ER -
TY - JOUR
TI - An Empirical Analysis of the Impact of the Internet Finance on Money Market
AU - Wu, P.
AU - Yao, Y.
AU - Pang, T.
T2 - Contemporary Economic Management
DA - 2016///
PY - 2016///
VL - 38
IS - 7
SP - 84–93
ER -
TY - CHAP
TI - Active Fault Detection in Nonlinear Differential Algebraic Equations II: Using Linearizations
AU - Campbell, S.L.
AU - Scott, J.R.
T2 - Fault Detection: Methods, Applications and Technology
A2 - Martin, Daniel
PY - 2016///
SP - 29–51
PB - Nova Publishers
ER -
TY - CHAP
TI - Active Fault Detection in Nonlinear Differential Algebraic Equations I: General Systems
AU - Campbell, S.L.
T2 - Fault Detection: Methods, Applications and Technology
A2 - Martin, Daniel
PY - 2016///
SP - 1–27
PB - Nova Publishers
SN - 978-1-53610-359-5
ER -
TY - CHAP
TI - Difference Potentials Methods for Hyperbolic Problems Using High Order Finite Difference Schemes
AU - Britt, Steven
AU - Petropavlovsky, Sergei
AU - Tsynkov, Semyon
AU - Turkel, Eli
T2 - Book of Abstracts, International Conference on Spectral and High Order Methods, ICOSAHOM 2016,
Rio De Janeiro, Brazil, June 2016
PY - 2016///
UR - https://stsynkov.math.ncsu.edu/publications/icosahomAbstract2016.pdf
ER -
TY - JOUR
TI - Solving composite monotone inclusions in reflexive Banach spaces by constructing best Bregman approximations from their Kuhn-Tucker set
AU - Combettes, P.L.
AU - Nguyen, Q.V.
T2 - Journal of Convex Analysis
DA - 2016/5//
PY - 2016/5//
VL - 23
IS - 2
SP - 481–510
ER -
TY - JOUR
TI - Wave propagation in a 1D fluid dynamics model using pressure-area measurements from ovine arteries
AU - Battista, Christina
AU - Bia, Daniel
AU - Germán, Yanina Zócalo
AU - Armentano, Ricardo L.
AU - Haider, Mansoor A.
AU - Olufsen, Mette S.
T2 - Journal of Mechanics in Medicine and Biology
AB - This study considers a 1D fluid dynamics arterial network model with 14 vessels developed to assimilate ex vivo 0D temporal data for pressure-area dynamics in individual vessel segments from 11 male Merino sheep. A 0D model was used to estimate vessel wall parameters in a two-parameter elastic model and a four-parameter Kelvin viscoelastic model. This was done using nonlinear optimization minimizing the least squares error between model predictions and measured cross-sectional areas. Subsequently, estimated values for elastic stiffness and unstressed area were related to construct a nonlinear relationship. This relation was used in the network model. A 1D single vessel model of the aorta was then developed and used to estimate the inflow profile and parameters for total resistance and compliance for the downstream network and to demonstrate effects of incorporating viscoelasticity in the arterial wall. Lastly, the extent to which vessel wall parameters estimated from ex vivo data can be used to realistically simulate pressure and area in a vessel network was evaluated. Elastic wall parameters in the network simulations were found to yield pressure-area relationships across all vessel locations and sheep that were in ranges comparable to those in the ex vivo data.
DA - 2016/3//
PY - 2016/3//
DO - 10.1142/S021951941650007X
VL - 16
IS - 02
SP - 1650007
SN - 0219-5194 1793-6810
UR - http://dx.doi.org/10.1142/S021951941650007X
KW - Fluid mechanics
KW - cardiovascular model
KW - viscoelastic
KW - arterial wall
KW - arterial network
ER -
TY - JOUR
TI - On the Seasonal Occurrence and Abundance of the Zika Virus Vector Mosquito Aedes Aegypti in the Contiguous United States
AU - Monaghan, Andrew J.
AU - Morin, Cory W.
AU - Steinhoff, Daniel F.
AU - Wilhelmi, Olga
AU - Hayden, Mary
AU - Quattrochi, Dale A.
AU - Reiskind, Michael
AU - Lloyd, Alun L.
AU - Smith, Kirk
AU - Schmidt, Chris A.
AU - Scalf, Paige E.
AU - Ernst, Kacey
T2 - PLoS Currents
AB - Introduction: An ongoing Zika virus pandemic in Latin America and the Caribbean has raised concerns that travel-related introduction of Zika virus could initiate local transmission in the United States (U.S.) by its primary vector, the mosquito Aedes aegypti.
Methods: We employed meteorologically driven models for 2006-2015 to simulate the potential seasonal abundance of adult Aedes aegypti for fifty cities within or near the margins of its known U.S. range. Mosquito abundance results were analyzed alongside travel and socioeconomic factors that are proxies of viral introduction and vulnerability to human-vector contact.
Results: Meteorological conditions are largely unsuitable for Aedes aegypti over the U.S. during winter months (December-March), except in southern Florida and south Texas where comparatively warm conditions can sustain low-to-moderate potential mosquito abundance. Meteorological conditions are suitable for Aedes aegypti across all fifty cities during peak summer months (July-September), though the mosquito has not been documented in all cities. Simulations indicate the highest mosquito abundance occurs in the Southeast and south Texas where locally acquired cases of Aedes-transmitted viruses have been reported previously. Cities in southern Florida and south Texas are at the nexus of high seasonal suitability for Aedes aegypti and strong potential for travel-related virus introduction. Higher poverty rates in cities along the U.S.-Mexico border may correlate with factors that increase human exposure to Aedes aegypti.
Discussion: Our results can inform baseline risk for local Zika virus transmission in the U.S. and the optimal timing of vector control activities, and underscore the need for enhanced surveillance for Aedes mosquitoes and Aedes-transmitted viruses.
DA - 2016///
PY - 2016///
DO - 10.1371/currents.outbreaks.50dfc7f46798675fc63e7d7da563da76
J2 - PLoS Curr
LA - en
OP -
SN - 2157-3999
UR - http://dx.doi.org/10.1371/currents.outbreaks.50dfc7f46798675fc63e7d7da563da76
DB - Crossref
ER -
TY - JOUR
TI - Comparison of two detailed models of Aedes aegypti
population dynamics
AU - Legros, Mathieu
AU - Otero, Marcelo
AU - Romeo Aznar, Victoria
AU - Solari, Hernan
AU - Gould, Fred
AU - Lloyd, Alun L.
T2 - Ecosphere
AB - The success of control programs for mosquito borne diseases can be enhanced by crucial information provided by models of the mosquito populations. Models, however, can differ in their structure, complexity and biological assumptions, and these differences impact their predictions. Unfortunately, it is typically difficult to determine why two complex models make different predictions because we lack structured side-by-side comparisons of models using comparable parameterization. Here we present a detailed comparison of two complex, spatially-explicit, stochastic models of the population dynamics of Aedes aegypti, the main vector of dengue, yellow fever, chikungunya and Zika viruses. Both models describe the mosquito's biological and ecological characteristics, but differ in complexity and specific assumptions. We compare the predictions of these models in two selected climatic settings, a tropical and weakly seasonal climate in Iquitos, Peru, and a temperate and strongly seasonal climate in Buenos Aires, Argentina. Both models were calibrated to operate at identical average densities in unperturbed conditions in both settings, by adjusting parameters regulating densities in each model (number of larval development sites and amount of nutritional resources). We show that the models differ in their sensitivity to environmental conditions (temperature and rainfall), and trace differences to specific model assumptions. Temporal dynamics of the Ae. aegypti populations predicted by the two models differ more markedly under strongly seasonal Buenos Aires conditions. We use both models to simulate killing of larvae and/or adults with insecticides in selected areas. We show that predictions of population recovery by the models differ substantially, an effect likely related to model assumptions regarding larval development and (direct or delayed) density dependence. Our methodical comparison provides important guidance for model improvement by identifying key areas of Ae. aegypti ecology that substantially affect model predictions, and revealing the impact of model assumptions on population dynamics predictions in unperturbed and perturbed conditions.
DA - 2016/10//
PY - 2016/10//
DO - 10.1002/ecs2.1515
VL - 7
IS - 10
SP - e01515
J2 - Ecosphere
LA - en
OP -
SN - 2150-8925
UR - http://dx.doi.org/10.1002/ecs2.1515
DB - Crossref
KW - Aedes aegypti
KW - model comparison
KW - mosquito-borne diseases
KW - population dynamics
KW - spatial model
KW - vector control
ER -
TY - JOUR
TI - RandNLA, Pythons, and the CUR for your data problems: Reporting from G2S3 in Delphi
AU - Gallopoulos, S.
AU - Drineas, P.
AU - Ipsen, I.C.F.
AU - Mahoney, M.W.
T2 - SIAM News
DA - 2016/1//
PY - 2016/1//
VL - 49
IS - 1
SP - 7-8
ER -
TY - JOUR
TI - Hyperbolic Equations with Mixed Boundary Conditions: Shape Differentiability Analysis
AU - Bociu, Lorena
AU - Zolésio, Jean-Paul
T2 - Applied Mathematics & Optimization
DA - 2016/4/18/
PY - 2016/4/18/
DO - 10.1007/s00245-016-9354-4
VL - 76
IS - 2
SP - 375-398
J2 - Appl Math Optim
LA - en
OP -
SN - 0095-4616 1432-0606
UR - http://dx.doi.org/10.1007/s00245-016-9354-4
DB - Crossref
ER -
TY - JOUR
TI - An efficient grid lattice algorithm for pricing American-style options
AU - Liu, Zhongkai
AU - Pang, Tao
T2 - International Journal of Financial Markets and Derivatives
AB - Option pricing is an important area of research in the finance community. In this paper, we develop a computationally feasible and efficient lattice algorithm in pricing American-style options. The key idea is to build a time adjusted grid lattice model and afterwards implement backward induction to price options. The time adjusted grid lattice guarantees high accuracy in relatively few discrete finite nodes. To illustrate the performance of the lattice algorithm, European and American options are priced separately, and results are compared to other popular methods in terms of both accuracy and efficiency. All suggest that the proposed lattice algorithm does a better job. Moreover, the fast convergence behaviours of the lattice algorithm as well as the relationship between the converged option price and the number of determination dates are studied as well.
DA - 2016///
PY - 2016///
DO - 10.1504/ijfmd.2016.076978
VL - 5
IS - 1
SP - 36
J2 - IJFMD
LA - en
OP -
SN - 1756-7130 1756-7149
UR - http://dx.doi.org/10.1504/ijfmd.2016.076978
DB - Crossref
ER -
TY - CONF
TI - Numerical Sparsity Determination and Early Termination
AU - Hao, Zhiwei
AU - Kaltofen, Erich L.
AU - Zhi, Lihong
T2 - the ACM
AB - Ankur Moitra in his paper at STOC 2015 has given an in-depth analysis of how oversampling improves the conditioning of the arising Prony systems for sparse interpolation and signal recovery from numeric data. Moitra assumes that oversampling is done for a number of samples beyond the actual sparsity of the polynomial/signal. We give an algorithm that can be used to compute the sparsity and estimate the minimal number of samples needed in numerical sparse interpolation. The early termination strategy of polynomial interpolation has been incorporated in the algorithm: by oversampling at a small number of extra sample points we can diagnose that the sparsity has not been reached.
C2 - 2016///
C3 - Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16
DA - 2016///
DO - 10.1145/2930889.2930924
PB - ACM Press
SN - 9781450343800
UR - http://dx.doi.org/10.1145/2930889.2930924
DB - Crossref
KW - Hankel matrix
KW - Vandermonde matrix
KW - sparse polynomial interpolation
KW - condition number
KW - early termination
KW - sparse signal processing
ER -
TY - JOUR
TI - Solving higher index DAE optimal control problems
AU - Campbell, Stephen
AU - Kunkel, Peter
T2 - Numerical Algebra, Control and Optimization
AB - A number of methods have been proposed for solving optimal control problems where the process being optimized
is described by a differential algebraic equation (DAE). However, many of these methods require special circumstances
to hold or the user to have special software. In this paper we go over many of these options and discuss
what is usually necessary for them to be successful. We use a nonlinear index three control problem
to illustrate many of our observations..
DA - 2016/12//
PY - 2016/12//
DO - 10.3934/naco.2016020
VL - 6
IS - 4
SP - 447-472
J2 - NACO
LA - en
OP -
SN - 2155-3289
UR - http://dx.doi.org/10.3934/naco.2016020
DB - Crossref
KW - Optimal control
KW - differential algebraic equations
KW - higher index
KW - numerical methods
KW - direct transcription
ER -
TY - JOUR
TI - Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions
AU - Combettes, Patrick L.
AU - Eckstein, Jonathan
T2 - Mathematical Programming
AB - We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone operators needs to be processed, as opposed to all operators as in established methods. Flexible strategies are used to select the blocks of operators activated at each iteration. In addition, we allow lags in operator processing, permitting asynchronous implementation. The decomposition phase of each iteration of our methods is to generate points in the graphs of the selected monotone operators, in order to construct a half-space containing the Kuhn–Tucker set associated with the system. The coordination phase of each iteration involves a projection onto this half-space. We present two related methods: the first method provides weakly convergent primal and dual sequences under general conditions, while the second is a variant in which strong convergence is guaranteed without additional assumptions. Neither algorithm requires prior knowledge of bounds on the linear operators involved or the inversion of linear operators. Our algorithmic framework unifies and significantly extends the approaches taken in earlier work on primal-dual projective splitting methods.
DA - 2016/7/5/
PY - 2016/7/5/
DO - 10.1007/s10107-016-1044-0
VL - 168
IS - 1-2
SP - 645-672
J2 - Math. Program.
LA - en
OP -
SN - 0025-5610 1436-4646
UR - http://dx.doi.org/10.1007/s10107-016-1044-0
DB - Crossref
KW - Asynchronous algorithm
KW - Block-iterative algorithm
KW - Duality
KW - Monotone inclusion
KW - Monotone operator
KW - Primal-dual algorithm
KW - Splitting algorithm
ER -
TY - CONF
TI - Free boundary fluid-elasticity interactions: Adjoint sensitivity analysis
AU - Bociu, Lorena
AU - Martin, Kristina
T2 - 8th Congress of Romanian Mathematicians
C2 - 2016/6/16/
C3 - New Trends in Differential Equations, Control Theory and Optimization
DA - 2016/6/16/
DO - 10.1142/9789813142862_0002
PB - WORLD SCIENTIFIC
SN - 9789813142855 9789813142862
UR - http://dx.doi.org/10.1142/9789813142862_0002
DB - Crossref
ER -
TY - JOUR
TI - Build to understand: synthetic approaches to biology
AU - Wang, Le-Zhi
AU - Wu, Fuqing
AU - Flores, Kevin
AU - Lai, Ying-Cheng
AU - Wang, Xiao
T2 - Integrative Biology
AB - In this review we discuss how synthetic biology facilitates the task of investigating genetic circuits that are observed in naturally occurring biological systems.
DA - 2016///
PY - 2016///
DO - 10.1039/c5ib00252d
VL - 8
IS - 4
SP - 394-408
J2 - Integr. Biol.
LA - en
OP -
SN - 1757-9694 1757-9708
UR - http://dx.doi.org/10.1039/c5ib00252d
DB - Crossref
ER -
TY - JOUR
TI - Stochastic approximations and perturbations in forward-backward splitting for monotone operators
AU - Combettes, P.L.
AU - Pesquet, J.-C.
T2 - Pure and Applied Functional Analysis
DA - 2016/1//
PY - 2016/1//
VL - 1
IS - 1
SP - 13–37
ER -
TY - CHAP
TI - Lattice Theory of the Poset of Regions
AU - Reading, N.
T2 - Lattice Theory: Special Topics and Applications
PY - 2016///
DO - 10.1007/978-3-319-44236-5_9
VL - 2
SP - 399-487
OP -
PB - Springer International Publishing
SN - 9783319442358 9783319442365
UR - http://dx.doi.org/10.1007/978-3-319-44236-5_9
DB - Crossref
ER -
TY - CHAP
TI - Finite Coxeter Groups and the Weak Order
AU - Reading, N.
T2 - Lattice Theory: Special Topics and Applications
PY - 2016///
DO - 10.1007/978-3-319-44236-5_10
VL - 2
SP - 489-561
OP -
PB - Springer International Publishing
SN - 9783319442358 9783319442365
UR - http://dx.doi.org/10.1007/978-3-319-44236-5_10
DB - Crossref
ER -
TY - JOUR
TI - Coxeter arrangements in three dimensions
AU - Ehrenborg, Richard
AU - Klivans, Caroline
AU - Reading, Nathan
T2 - Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
AB - Let $$\mathcal {A}$$
be a finite real linear hyperplane arrangement in three dimensions. Suppose further that all the regions of $$\mathcal {A}$$
are isometric. We prove that $$\mathcal {A}$$
is necessarily a Coxeter arrangement. As it is well known that the regions of a Coxeter arrangement are isometric, this characterizes three-dimensional Coxeter arrangements precisely as those arrangements with isometric regions. It is an open question whether this suffices to characterize Coxeter arrangements in higher dimensions. We also present the three families of affine arrangements in the plane which are not reflection arrangements, but in which all the regions are isometric.
DA - 2016/2/22/
PY - 2016/2/22/
DO - 10.1007/s13366-016-0286-6
VL - 57
IS - 4
SP - 891-897
J2 - Beitr Algebra Geom
LA - en
OP -
SN - 0138-4821 2191-0383
UR - http://dx.doi.org/10.1007/s13366-016-0286-6
DB - Crossref
KW - Hyperplane arrangements
KW - Finite Coxeter systems
KW - Spherical geometry
ER -
TY - JOUR
TI - Lifting Markov bases and higher codimension toric fiber products
AU - Rauh, Johannes
AU - Sullivant, Seth
T2 - Journal of Symbolic Computation
AB - We study how to lift Markov bases and Gröbner bases along linear maps of lattices. We give a lifting algorithm that allows to compute such bases iteratively provided a certain associated semigroup is normal. Our main application is the toric fiber product of toric ideals, where lifting gives Markov bases of the factor ideals that satisfy the compatible projection property. We illustrate the technique by computing Markov bases of various infinite families of hierarchical models. The methodology also implies new finiteness results for iterated toric fiber products.
DA - 2016/5//
PY - 2016/5//
DO - 10.1016/j.jsc.2015.07.003
VL - 74
SP - 276-307
J2 - Journal of Symbolic Computation
LA - en
OP -
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2015.07.003
DB - Crossref
KW - Markov bases
KW - Toric fiber product
KW - Lifting
KW - Grobner bases
ER -
TY - JOUR
TI - Pretzel knots with L-space surgeries
AU - Lidman, Tye
AU - Moore, Allison H.
T2 - The Michigan Mathematical Journal
AB - A rational homology sphere whose Heegaard Floer homology is the same as that of a lens space is called an L-space. We classify pretzel knots with any number of tangles which admit L-space surgeries. This rests on Gabai's classification of fibered pretzel links.
DA - 2016/3//
PY - 2016/3//
DO - 10.1307/mmj/1457101813
VL - 65
IS - 1
SP - 105-130
J2 - Michigan Math. J.
LA - en
OP -
SN - 0026-2285
UR - http://dx.doi.org/10.1307/mmj/1457101813
DB - Crossref
ER -
TY - JOUR
TI - Global existence of weak solutions for Burgers-Poisson equation
AU - Nguyen, Tien Khai
AU - Grunert, K.
T2 - Journal of Differential Equations
DA - 2016///
PY - 2016///
VL - 23
IS - 4
SP - 23–46
ER -
TY - JOUR
TI - The compactness estimates for Hamilton Jacobi Equations depending on space
AU - Nguyen, Tien Khai
AU - Ancona, F.
AU - Cannarsa, P.
T2 - Bulletin of the Institute of Mathematics, Academia Sinica
DA - 2016///
PY - 2016///
VL - 11
SP - 63–113
ER -
TY - JOUR
TI - The bang–bang theorem via Baire category: a dual approach
AU - Bressan, Alberto
AU - Mazzola, Marco
AU - Nguyen, Khai T.
T2 - Nonlinear Differential Equations and Applications NoDEA
AB - The paper develops a new approach to the classical bang–bang theorem in linear control theory, based on Baire category. Among all controls which steer the system from the origin to a given point $${\bar x}$$
, we consider those which minimize an auxiliary linear functional $${\phi}$$
. For all $${\phi}$$
in a residual set, we show that the minimizing control is unique and takes values within a set of extreme points.
DA - 2016/7/30/
PY - 2016/7/30/
DO - 10.1007/s00030-016-0400-3
VL - 23
IS - 4
J2 - Nonlinear Differ. Equ. Appl.
LA - en
OP -
SN - 1021-9722 1420-9004
UR - http://dx.doi.org/10.1007/s00030-016-0400-3
DB - Crossref
ER -
TY - JOUR
TI - An equilibrium model of debt and bankruptcy
AU - Bressan, Alberto
AU - Nguyen, Khai T.
T2 - ESAIM: Control, Optimisation and Calculus of Variations
AB - We study optimal strategies for a borrower, who services a debt in an infinite time horizon, taking into account the risk of possible bankruptcy. In a first model, the interest rate as well as the instantaneous bankruptcy risk are given, increasing functions of the total amount of debt. In a second model only the bankruptcy risk is given, while the interest rate is determined from a Nash equilibrium, in a game between the borrower and a pool of risk-neutral lenders. This yields a non-standard optimal control problem for the borrower, where the dynamics involves all future values of the control. For this model, optimal repayment strategies are constructed, in open-loop form. In addition, for optimal strategies in feedback form, our analysis shows that the value function should satisfy a new kind of nonlinear, degenerate elliptic equation.
DA - 2016/9/9/
PY - 2016/9/9/
DO - 10.1051/cocv/2016030
VL - 22
IS - 4
SP - 953-982
J2 - ESAIM: COCV
OP -
SN - 1292-8119 1262-3377
UR - http://dx.doi.org/10.1051/cocv/2016030
DB - Crossref
KW - Optimal control
KW - differential game
KW - optimal debt management
KW - bankruptcy risk
ER -
TY - JOUR
TI - Parameter Selection and Verification Techniques Based on Global Sens Analysis Illustrated for an HIV Model
AU - Wentworth, Mami T.
AU - Smith, Ralph C.
AU - Banks, H. T.
T2 - SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
AB - We consider parameter selection and verification techniques for models having one or more parameters that are noninfluential in the sense that they minimally impact model outputs. We illustrate these techniques for a dynamic HIV model but note that the parameter selection and verification framework is applicable to a wide range of biological and physical models. To accommodate the nonlinear input to output relations, which are typical for such models, we focus on global sensitivity analysis techniques, including those based on the Pearson correlation coefficient, Sobol indices based on second-order model representations, and Morris indices, as well as a parameter selection technique based on standard errors. A significant objective is to provide verification strategies to assess the accuracy of those techniques, which we illustrate in the context of the HIV model.
DA - 2016///
PY - 2016///
DO - 10.1137/15m1008245
VL - 4
IS - 1
SP - 266-297
SN - 2166-2525
KW - global sensitivity analysis
KW - parameter selection
KW - verificatio
ER -
TY - JOUR
TI - Approximately continuous functions have approximate extrema, a new proof
AU - Freiling, C.
AU - Humke, P. D.
AU - O'Malley, R. J.
T2 - Real Analysis Exchange
DA - 2016///
PY - 2016///
DO - 10.14321/realanalexch.41.2.0409
VL - 41
IS - 2
SP - 409-414
ER -
TY - JOUR
TI - An alternate solution to Scottish book 157
AU - Freiling, C.
AU - Humke, P. D.
AU - O'Malley, R. J.
T2 - Real Analysis Exchange
DA - 2016///
PY - 2016///
DO - 10.14321/realanalexch.41.2.0403
VL - 41
IS - 2
SP - 403-408
ER -
TY - CONF
TI - Bayesian metropolis methods applied to sensor networks for radiation source localization
AU - Hite, J. M.
AU - Mattingly, J. K.
AU - Schmidt, K. L.
AU - Stelanescu, R.
AU - Smith, Ralph
AB - We present an application of statistical techniques to the localization of an unknown gamma source in an urban environment. By formulating the problem as a task of Bayesian parameter estimation, we are able to apply Markov Chain Monte Carlo (MCMC) to generate a full posterior probability density estimating the source location and intensity based on counts reported from a distributed detector network. To facilitate the calibration procedure, we employ a simplified photon transport model with low computational cost and test the proposed methodology in a simulated urban environment, with calibration data generated using the radiation transport code MCNP. The Bayesian methodology is able to identify the source location and intensity along with providing a full posterior density.
C2 - 2016///
C3 - 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)
DA - 2016///
DO - 10.1109/mfi.2016.7849519
SP - 389–393
ER -
TY - JOUR
TI - Genetic engineering to eradicate invasive mice on islands: Modeling the efficiency and ecological impacts
AU - Backus, G. A.
AU - Gross, K.
T2 - Ecosphere
DA - 2016///
PY - 2016///
VL - 7
IS - 12
ER -
TY - JOUR
TI - Reduced Order Gaussian Smoothing for Nonlinear Data Assimilation
AU - King, Sarah A.
AU - Kang, Wei
AU - Ito, Kaztifurni
T2 - IFAC PAPERSONLINE
AB - Abstract: We investigate Gaussian filtering for data assimilation in numerical weather prediction (NWP). Data assimilation is the process of combining prior forecasts and observations to produce a system estimate. The prevailing data assimilation method in operational NWP centers is variational data assimilation. This method involves solving a cost function over a time window forming a maximum likelihood estimate. This method, however, requires the use of linearized models which in practice are difficult to produce and maintain. As an alternative we propose Gaussian smoothing for derivative-free, nonlinear data assimilation. Gaussian filters and their corresponding smoothers use numerical integration to evaluate the recursive Bayesian formulas for optimal filtering under Gaussian assumptions. This numerical integration typically requires many model evaluations making conventional Gaussian filtering/smoothing impractical for use in NWP. We will present a reduced order method for forming a Rauch-Tung-Striebel (RTS) type smoother. To do so we review the Bayesian filtering and smoothing equations and discuss an efficient numerical method for evaluating them. We will then discuss a numerical example using the Korteweg-de Vries equation to compare our technique to the standard variational approach.
DA - 2016///
PY - 2016///
DO - 10.1016/j.ifacol.2016.10.163
VL - 49
IS - 18
SP - 199-204
SN - 2405-8963
KW - State Estimation
KW - Large-Scale Systems
KW - Order Reduction
KW - Smoothing
KW - Filtering
ER -
TY - JOUR
TI - Parameter Estimation for Predictive Simulation of Oscillatory Systems with Model Discrepancy
AU - McMahan, Jerry A., Jr.
AU - Smith, Ralph C.
T2 - IFAC PAPERSONLINE
AB - Abstract: A Bayesian framework provides a methodology in which inferences from measurement data can be used to bound the uncertainties in the predictive simulation of a physical system. The accuracy of these bounds relies on the satisfaction of statistical assumptions on the measurement error. Discrepancies between the model and the true physics can invalidate these assumptions. We examine the effect of such model discrepancies in the context of an oscillating cantilever beam. First we illustrate the influence of discrepancies in a simplified model of purely periodic signals and then we observe how discrepancies affect the accuracy of prediction uncertainty bounds using Bayesian parameter inference on a Euler-Bernoulli beam model. Our study shows small changes in the inference setup can result in significant differences in prediction accuracy and calls attention to important considerations for the practical application of Bayesian parameter estimation.
DA - 2016///
PY - 2016///
DO - 10.1016/j.ifacol.2016.10.203
VL - 49
IS - 18
SP - 428-433
SN - 2405-8963
KW - parameter estimation
KW - Bayesian inversion
KW - modeling errors
KW - oscillation
KW - prediction intervals
ER -
TY - JOUR
TI - Frequentist and Bayesian Lasso Techniques for Parameter Selection in Nonlinearly Parameterized Models
AU - Coleman, Kayla D.
AU - Schmidt, Kathleen
AU - Smith, Ralph C.
T2 - IFAC PAPERSONLINE
AB - Abstract: In this paper, we discuss the use of frequentist and Bayesian lasso (least absolute shrinkage and selection operator) techniques for parameter selection in nonlinearly parameterized models employed for control design. This is necessary to isolate the subset of identifiable or influential parameters, which can be uniquely calibrated from experimental data. We survey the performance of existing algorithms and present a new Bayesian lasso implementation based on the Delayed Rejection Adaptive Metropolis (DRAM) algorithm.
DA - 2016///
PY - 2016///
DO - 10.1016/j.ifacol.2016.10.201
VL - 49
IS - 18
SP - 416-421
SN - 2405-8963
KW - DRAM
KW - parameter selection
KW - regularization
KW - regression
KW - identifiability
ER -
TY - JOUR
TI - Fourth-order compact schemes for Helmholtz equations with piecewise wave numbers in the polar coordinates
AU - Su, X. L.
AU - Feng, X. F.
AU - Li, Z. L.
T2 - Journal of Computational Mathematics
DA - 2016///
PY - 2016///
VL - 34
IS - 5
SP - 499-510
ER -
TY - CONF
TI - Pansharpening via coupled triple factorization dictionary learning
AU - Skau, E.
AU - Wohlberg, B.
AU - Krim, H.
AU - Dai, L. Y.
AB - Data fusion is the operation of integrating data from different modalities to construct a single consistent representation. This paper proposes variations of coupled dictionary learning through an additional factorization. One variation of this model is applicable to the pansharpening data fusion problem. Real world pansharpening data was applied to train and test our proposed formulation. The results demonstrate that the data fusion model can successfully be applied to the pan-sharpening problem.
C2 - 2016///
C3 - International conference on acoustics speech and signal processing
DA - 2016///
DO - 10.1109/icassp.2016.7471873
SP - 1234-1237
ER -
TY - JOUR
TI - ON HAMEL'S EQUATIONS
AU - Zenkov, Dmitry V.
T2 - THEORETICAL AND APPLIED MECHANICS
AB - This paper reviews recent results on the extension of Hame?s formalism to infinite-dimensional mechanical systems and to variational integrators. Of a particular interest are applications to the dynamics and numerical integration of systems with velocity constraints.
DA - 2016///
PY - 2016///
DO - 10.2298/tam160612011z
VL - 43
IS - 2
SP - 191-220
SN - 1450-5584
KW - infinite-dimensional mechanics
KW - nonholonomic constraints
KW - variational integrators
ER -
TY - CONF
TI - A universal framework for non-deteriorating time-domain numerical algorithms in Maxwell’s electrodynamics
AU - Fedoseyev, A.
AU - Kansa, E. J.
AU - Tsynkov, S.
AU - Petropavlovskiy, S.
AU - Osintcev, M.
AU - Shumlak, U.
AU - Henshaw, W. D.
T2 - APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’16
A2 - Todorov, Michail D.
AB - We present the implementation of the Lacuna method, that removes a key diffculty that currently hampers many existing methods for computing unsteady electromagnetic waves on unbounded regions. Numerical accuracy and/or stability may deterio-rate over long times due to the treatment of artificial outer boundaries. We describe a developed universal algorithm and software that correct this problem by employing the Huygens’ principle and lacunae of Maxwell’s equations.The algorithm provides a temporally uniform guaranteed error bound (no deterioration at all), and the software will enable robust electromagnetic simulations in a high-performance computing environment. The methodology applies to any geometry, any scheme, and any boundary condition. It eliminates the long-time deterioration regardless of its origin and how it manifests itself. In retrospect, the lacunae method was first proposed by V. Ryaben’kii and subsequently developed by S. Tsynkov.We have completed development of an innovative numerical methodology for high fidelity error-controlled modeling of a broad variety of electromagnetic and other wave phenomena. Proof-of-concept 3D computations have been conducted that con-vincingly demonstrate the feasibility and effciency of the proposed approach. Our algorithms are being implemented as robust commercial software tools in a standalone module to be combined with existing numerical schemes in several widely used computational electromagnetic codes.
C2 - 2016///
C3 -
DA - 2016///
DO - 10.1063/1.4964955
VL - 1773
SP -
PB - Author(s)
UR - http://dx.doi.org/10.1063/1.4964955
DB - Crossref
ER -
TY - JOUR
TI - Parameter Estimation Using Unidentified Individual Data in Individual Based Models
AU - Banks, H. T.
AU - Baraldi, R.
AU - Catenacci, J.
AU - Myers, N.
T2 - MATHEMATICAL MODELLING OF NATURAL PHENOMENA
AB - In physiological experiments, it is common for measurements to be collected from multiple subjects. Often it is the case that a subject cannot be measured or identified at multiple time points (referred to as unidentified individual data in this work but often referred to as aggregate population data [5, Chapter 5]). Due to a lack of alternative methods, this form of data is typically treated as if it is collected from a single individual. This assumption leads to an overconfidence in model parameter values and model based predictions. We propose a novel method which accounts for inter-individual variability in experiments where only unidentified individual data is available. Both parametric and nonparametric methods for estimating the distribution of parameters which vary among individuals are developed. These methods are illustrated using both simulated data, and data taken from a physiological experiment. Taking the approach outlined in this paper results in more accurate quantification of the uncertainty attributed to inter-individual variability.
DA - 2016///
PY - 2016///
DO - 10.1051/mmnp/201611602
VL - 11
IS - 6
SP - 9-27
SN - 1760-6101
KW - pharmacokinetics
KW - pharmacodynamics
KW - physiological based pharmacokinetic modeling
KW - inter-individual parameter variability
KW - uncertainty quantification
KW - random differential equations
KW - distribution estimation
KW - Prohorov metric framework
KW - aggregate population data
ER -
TY - JOUR
TI - LINEARIZED HYDRO-ELASTICITY: A NUMERICAL STUDY
AU - Bociu, Lorena
AU - Derochers, Steven
AU - Toundykov, Daniel
T2 - EVOLUTION EQUATIONS AND CONTROL THEORY
AB - In view of control and stability theory, a recently obtained linearization around a steady state of a fluid-structure interaction is considered. The linearization was performed with respect to an external forcing term and was derived in an earlier paper via shape optimization techniques. In contrast to other approaches, like transporting to a fixed reference configuration, or using transpiration techniques, the shape optimization route is most suited to incorporating the geometry of the problem into the analysis. This refined description brings up new terms---missing in the classical coupling of linear Stokes flow and linear elasticity---in the matching of the normal stresses and the velocities on the interface.
Later, it was demonstrated that this linear PDE system generates a $C_0$ semigroup, however, unlike in the standard Stokes-elasticity coupling, the wellposedness result depended on the fluid's viscosity and the new boundary terms which, among other things, involve the curvature of the interface.
Here, we implement a finite element scheme for approximating solutions of this fluid-elasticity dynamics and numerically investigate the dependence of the discretized model on the ``new terms present therein, in contrast with the classical Stokes-linear elasticity system.
DA - 2016/12//
PY - 2016/12//
DO - 10.3934/eect.2016018
VL - 5
IS - 4
SP - 533-559
SN - 2163-2480
KW - Fluid-structure
KW - hydro-elasticity
KW - Stokes
KW - elasticity
KW - free boundary
KW - moving boundary
KW - linearization
KW - finite elements
KW - sensitivity
ER -
TY - JOUR
TI - A PARAMETER SUBSET SELECTION ALGORITHM FORMIXED-EFFECTS MODELS
AU - Schmidt, Kathleen L.
AU - Smith, Ralph C.
T2 - INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION
DA - 2016///
PY - 2016///
DO - 10.1615/int.j.uncertaintyquantification.2016016469
VL - 6
IS - 5
SP - 405-416
SN - 2152-5099
KW - mixed-effects models
KW - sensitivity analysis
KW - model selection
KW - parameter subset selection
ER -
TY - JOUR
TI - Transcranial Doppler-Based Surrogates for Cerebral Blood Flow: A Statistical Study
AU - Hart, Joseph
AU - Novak, Vera
AU - Saunders, Charles
AU - Gremaud, Pierre A.
T2 - PLOS ONE
AB - It is commonly assumed that perfusion in a given cerebral territory can be inferred from Blood Flow Velocity (BFV) measurements in the corresponding stem artery. In order to test this hypothesis, we construct a cerebral blood flow (CBF) estimator based on transcranial Doppler (TCD) blood flow velocity and ten other easily available patient characteristics and clinical parameters. A total of 261 measurements were collected from 88 older patients. The estimator is based on local regression (Random Forest). Its performance is analyzed against baseline CBF from 3-D pseudocontinuous arterial spin labeling (pCASL) magnetic resonance imaging (MRI). Patient specific CBF predictions are of poor quality (r = 0.41 and p-value = 4.5 × 10-12); the hypothesis is thus not clearly supported by evidence.
DA - 2016/11/23/
PY - 2016/11/23/
DO - 10.1371/journal.pone.0165536
VL - 11
IS - 11
SP -
SN - 1932-6203
ER -
TY - JOUR
TI - The CARD Act and Young Borrowers: The Effects and the Affected
AU - Debbaut, Peter
AU - Ghent, Andra
AU - Kudlyak, Marianna
T2 - JOURNAL OF MONEY CREDIT AND BANKING
AB - We study a new law that restricts credit to individuals under age 21. We first use a difference-in-difference approach to estimate the effect of the law on credit card availability. Following the passage of the law, individuals under age 21 are 8 percentage points (15%) less likely to have a credit card, have fewer cards, and, conditional on having a card at all, are 35% more likely to have a cosigned card. We then use data from before the passage of the law to identify the characteristics of those individuals most likely to be affected by the Act.
DA - 2016/10//
PY - 2016/10//
DO - 10.1111/jmcb.12340
VL - 48
IS - 7
SP - 1495-1513
SN - 1538-4616
KW - young borrowers
KW - life cycle borrowing
KW - consumer protection
ER -
TY - CONF
TI - Non-parametric bounds on the nearest neighbor classification accuracy based on the Henze-Penrose metric
AU - Ghanem, S.
AU - Skau, E.
AU - Krim, H.
AU - Clouse, H. S.
AU - Sakla, W.
AB - Analysis procedures for higher-dimensional data are generally computationally costly; thereby justifying the high research interest in the area. Entropy-based divergence measures have proven their effectiveness in many areas of computer vision and pattern recognition. However, the complexity of their implementation might be prohibitive in resource-limited applications, as they require estimates of probability densities which are very difficult to compute directly for high-dimensional data. In this paper, we investigate the usage of a non-parametric distribution-free metric, known as the Henze-Penrose test statistic, to estimate the divergence between different classes of vehicles. In this regard, we apply some common feature extraction techniques to further characterize the distributional separation relative to the original data. Moreover, we employ the Henze-Penrose metric to obtain bounds for the Nearest Neighbor (NN) classification accuracy. Simulation results demonstrate the effectiveness and the reliability of this metric in estimating the inter-class separability. In addition, the proposed bounds are exploited for selecting the least number of features that would retain sufficient discriminative information.
C2 - 2016///
C3 - 2016 ieee international conference on image processing (icip)
DA - 2016///
DO - 10.1109/icip.2016.7532581
SP - 1364-1368
ER -
TY - JOUR
TI - Improved uncertainty relation in the presence of quantum memory
AU - Xiao, Yunlong
AU - Jing, Naihuan
AU - Fei, Shao-Ming
AU - Li-Jost, Xianqing
T2 - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
AB - In Coles-Piani's recent remarkable version of the entropic uncertainty principle, the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty relation in the presence of quantum memory and find the exact dependence on all $d$ largest overlaps between two measurements on any $d$-dimensional Hilbert space. The corresponding entropic uncertainty principle in the absence of quantum memory is also derived. Our bounds are strictly tighter than previous entropic bounds in the presence of quantum memory, which have potential applications to quantum cryptography with entanglement witnesses and quantum key distributions.
DA - 2016/12/9/
PY - 2016/12/9/
DO - 10.1088/1751-8113/49/49/49lt01
VL - 49
IS - 49
SP -
SN - 1751-8121
KW - uncertainty relations
KW - entropy
KW - quantum memory
ER -
TY - JOUR
TI - Aggregate data and the Prohorov Metric Framework: Efficient gradient computation
AU - Banks, H. T.
AU - Catenacci, Jared
T2 - APPLIED MATHEMATICS LETTERS
AB - We discuss efficient methods for computing gradients in inverse problems for estimation of distributions for individual parameters in models where only aggregate or population level data is available. The ideas are illustrated with two examples arising in applications.
DA - 2016/6//
PY - 2016/6//
DO - 10.1016/j.aml.2015.12.004
VL - 56
SP - 1-9
SN - 0893-9659
KW - Inverse problems
KW - Least squares estimation
KW - Estimation of probability distributions
KW - Splines
KW - Prohorov metric
ER -
TY - JOUR
TI - Statistical parameter estimation of dielectric materials using MCMC for nonlinear hierarchical models
AU - Kojima, Fumio
AU - Banks, H. Thomas
T2 - INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS
DA - 2016///
PY - 2016///
DO - 10.3233/jae-162207
VL - 52
IS - 1-2
SP - 49-54
SN - 1875-8800
KW - Inverse problem
KW - nondestructive evaluation
KW - electromagnetic interrogation
KW - polarization
ER -
TY - JOUR
TI - Quantifying the degradation in thermally treated ceramic matrix composites
AU - Banks, H. T.
AU - Catenacci, Jared
AU - Criner, Amanda
T2 - INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS
DA - 2016///
PY - 2016///
DO - 10.3233/jae-162168
VL - 52
IS - 1-2
SP - 3-24
SN - 1875-8800
KW - Ceramic matrix composites
KW - prohorov metric
KW - reflectance spectroscopy
KW - uncertainty quantification
ER -
TY - JOUR
TI - Heterogeneous mechanics of the mouse pulmonary arterial network
AU - Lee, Pilhwa
AU - Carlson, Brian E.
AU - Chesler, Naomi
AU - Olufsen, Mette S.
AU - Qureshi, M. Umar
AU - Smith, Nicolas P.
AU - Sochi, Taha
AU - Beard, Daniel A.
T2 - BIOMECHANICS AND MODELING IN MECHANOBIOLOGY
AB - Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure-radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.
DA - 2016/10//
PY - 2016/10//
DO - 10.1007/s10237-015-0757-y
VL - 15
IS - 5
SP - 1245-1261
SN - 1617-7940
KW - Arterial blood flow
KW - Vessel mechanics
KW - Heterogeneity
KW - Pulmonary arterial network
KW - Pressure-radius relationship
KW - Wave intensity analysis
ER -
TY - JOUR
TI - Unknotting and maximum unknotting numbers
AU - Zekovic, Ana
AU - Jablan, Slavik
AU - Kauffman, Louis
AU - Sazdanovic, Radmila
AU - Stosic, Marko
T2 - JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
AB - We introduce concepts of the maximum unknotting number and the mixed unknotting number, taking into consideration the Bernhard–Jablan Conjecture about computing the unknotting number based only on minimal knot diagrams. The existence of Kauffman knots (alternating knots, such that a crossing change does not change their minimal crossing number) was first suggested by Kauffman. We extend the concept and offer three related classes of knots named: Kauffman knots, Zeković knots and Taniyama knots.
DA - 2016/8//
PY - 2016/8//
DO - 10.1142/s0218216516410108
VL - 25
IS - 9
SP -
SN - 1793-6527
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84979240749&partnerID=MN8TOARS
KW - Unknotting number
KW - unlinking number
KW - Conway notation
KW - maximum unknotting number
ER -
TY - JOUR
TI - Surgery obstructions and Heegaard Floer homology
AU - Hom, Jennifer
AU - Karakurt, Cagri
AU - Lidman, Tye
T2 - GEOMETRY & TOPOLOGY
AB - Using Taubes' periodic ends theorem, Auckly gave examples of toroidal and hyperbolic irreducible integer homology spheres which are not surgery on a knot in the three-sphere. We give an obstruction to a homology sphere being surgery on a knot coming from Heegaard Floer homology. This is used to construct infinitely many small Seifert fibered examples.
DA - 2016///
PY - 2016///
DO - 10.2140/gt.2016.20.2219
VL - 20
IS - 4
SP - 2219-2251
SN - 1364-0380
ER -
TY - JOUR
TI - Stability of Concatenated Traveling Waves
AU - Lin, Xiao-Biao
AU - Schecter, Stephen
T2 - JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
DA - 2016/9//
PY - 2016/9//
DO - 10.1007/s10884-015-9428-z
VL - 28
IS - 3-4
SP - 867-896
SN - 1572-9222
KW - Interaction of waves
KW - Reaction-diffusion equation
KW - Spatial dynamics
KW - Laplace transform
KW - Exponential dichotomy in trace space
ER -
TY - JOUR
TI - Remembrance Slavik Jablan (1952-2015)
AU - Sazdanovic, Radmila
AU - Kauffman, Louis H.
AU - Radovic, Ljiljana
T2 - JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
DA - 2016/8//
PY - 2016/8//
DO - 10.1142/s021821651602003x
VL - 25
IS - 9
SP -
SN - 1793-6527
ER -
TY - JOUR
TI - Remembering Slavik Jablan
AU - Kauffman, Louis H.
AU - Lambropoulou, Sofia
AU - Sazdanovic, Radmila
T2 - JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
DA - 2016/8//
PY - 2016/8//
DO - 10.1142/s0218216516020028
VL - 25
IS - 9
SP -
SN - 1793-6527
ER -
TY - CONF
TI - RFI modeling and prediction approach for SATOP applications: RFI prediction models
AU - Nguyen, Tien M.
AU - Tran, Hien T.
AU - Wang, Zhonghai
AU - Coons, Amanda
AU - Nguyen, Charles C.
AU - Lane, Steven A.
AU - Pham, Khanh D.
AU - Chen, Genshe
AU - Wang, Gang
T2 - SPIE Defense + Security
A2 - Pham, Khanh D.
A2 - Chen, Genshe
AB - This paper describes a technical approach for the development of RFI prediction models using carrier synchronization loop when calculating Bit or Carrier SNR degradation due to interferences for (i) detecting narrow-band and wideband RFI signals, and (ii) estimating and predicting the behavior of the RFI signals. The paper presents analytical and simulation models and provides both analytical and simulation results on the performance of USB (Unified S-Band) waveforms in the presence of narrow-band and wideband RFI signals. The models presented in this paper will allow the future USB command systems to detect the RFI presence, estimate the RFI characteristics and predict the RFI behavior in real-time for accurate assessment of the impacts of RFI on the command Bit Error Rate (BER) performance. The command BER degradation model presented in this paper also allows the ground system operator to estimate the optimum transmitted SNR to maintain a required command BER level in the presence of both friendly and un-friendly RFI sources.
C2 - 2016/5/13/
C3 - Sensors and Systems for Space Applications IX
DA - 2016/5/13/
DO - 10.1117/12.2223518
VL - 9838
SP -
PB - SPIE
UR - http://dx.doi.org/10.1117/12.2223518
DB - Crossref
KW - RFI modeling and prediction
KW - RFI prediction
KW - Carrier synchronization loop
KW - Signal-to-Noise Ratio (SNR)
KW - Unified S-Band
KW - RFI estimating and predicting
KW - Command
KW - Bit Error Rate (BER)
ER -
TY - JOUR
TI - Quantifying cellular and subcellular stretches in embryonic lung epithelia under peristalsis: where to look for mechanosensing
AU - Bokka, Kishore K.
AU - Jesudason, Edwin C.
AU - Warburton, David
AU - Lubkin, Sharon R.
T2 - INTERFACE FOCUS
AB - Peristalsis begins in the lung as soon as the smooth muscle (SM) forms, and persists until birth. As the prenatal lung is filled with liquid, SM action can, through lumen pressure, deform tissues far from the immediately adjacent tissues. Stretching of embryonic tissues has been shown to have potent morphogenetic effects. We hypothesize that these effects are at work in lung morphogenesis. In order to refine that broad hypothesis in a quantitative framework, we geometrically analyse cell shapes in an epithelial tissue, and individual cell deformations resulting from peristaltic waves that completely occlude the airway. Typical distortions can be very large, with opposite orientations in the stalk and tip regions. Apical distortions are always greater than basal distortions. We give a quantitative estimate of the relationship between length of occluded airway and the resulting tissue stretch in the distal tip. We refine our analysis of cell stresses and strains from peristalsis with a simple mechanical model of deformation of cells within an epithelium, which accounts for basic subcellular geometry and material properties. The model identifies likely stress concentrations near the nucleus and at the apical cell-cell junction. The surprisingly large strains of airway peristalsis may serve to rearrange cells and stimulate other mechanosensitive processes by repeatedly aligning cytoskeletal components and/or breaking and reforming lateral cell-cell adhesions. Stress concentrations between nuclei of adjacent cells may serve as a mechanical control mechanism guiding the alignment of nuclei as an epithelium matures.
DA - 2016/10/6/
PY - 2016/10/6/
DO - 10.1098/rsfs.2016.0031
VL - 6
IS - 5
SP -
SN - 2042-8901
UR - https://doi.org/10.1098/rsfs.2016.0031
KW - lung
KW - airway
KW - peristalsis
KW - deformation
KW - stenosis
KW - morphogenesis
ER -
TY - JOUR
TI - Prioritization of pesticides based on daily dietary exposure potential as determined from the SHEDS model
AU - Melnyk, Lisa Jo
AU - Wang, Zhaohui
AU - Li, Zhilin
AU - Xue, Jianping
T2 - FOOD AND CHEMICAL TOXICOLOGY
AB - A major pathway for exposure to many pesticides is through diet. The objectives were to rank pesticides by comparing their calculated daily dietary exposure as determined by EPA's Stochastic Human Exposure and Dose Simulation (SHEDS) to single pesticides for different age groups to acceptable daily intakes (ADI), characterize pesticide trends in exposures over different time periods, and determine commodities contributing to pesticide exposures. SHEDS was applied, using Pesticide Data Program (PDP) (1991-2011) and pesticide usage data on crops from USDA combined with NHANES dietary consumption data, to generate exposure estimates by age group. ADI data collected from EPA, WHO, and other sources were used to rank pesticides based on relativeness of the dietary exposure potential to ADI by age groups. Sensitivity analysis provided trends in pesticide exposures. Within SHEDS, commodities contributing the majority of pesticides with greatest exposure potential were determined. The results indicated that the highest ranking pesticides were methamidophos and diazinon which exceeded 100% of the ADI. Sensitivity analysis indicated that exposure to methamidophos, diazinon, malathion, ethion and formetanate hydrochloride had a marked decrease from 1991-1999 to 2000-2011. Contributions analysis indicated that apples, mushroom, carrots, and lettuce contributed to diazinon exposure. Beans and pepper contributed to methamidophos exposure.
DA - 2016/10//
PY - 2016/10//
DO - 10.1016/j.fct.2016.07.025
VL - 96
SP - 167-173
SN - 1873-6351
KW - Risk ranking
KW - Pesticides
KW - Dietary exposure
KW - ADI
ER -
TY - JOUR
TI - Plaited polyhedra: A knot theory point of view
AU - Radovic, Ljiljana
AU - Gerdes, Paulus
AU - Jablan, Slavik
AU - Sazdanovic, Radmila
T2 - JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
AB - Plaited polyhedra, discovered by P. Gerdes in African dance rattle capsules are analyzed from the knot-theory point of view. Every plaited polyhedron can be derived from a knot or link diagram as its dual. In the attempt to classify obtained plaited polyhedra, we propose different methods based on families of knots and links in Conway notation or their corresponding braid families, both leading to the notion of families of plaited polyhedra.
DA - 2016/8//
PY - 2016/8//
DO - 10.1142/s0218216516410066
VL - 25
IS - 9
SP -
SN - 1793-6527
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84980383623&partnerID=MN8TOARS
KW - Plaited polyhedra
KW - schlegel diagram
KW - basic polyhedra
KW - knots
KW - links
KW - conway notation
ER -
TY - JOUR
TI - On Bayesian A- and D-Optimal Experimental Designs in Infinite Dimensions
AU - Alexanderian, Alen
AU - Gloor, Philip J.
AU - Ghattas, Omar
T2 - BAYESIAN ANALYSIS
AB - We consider Bayesian linear inverse problems in infinite-dimensional separable Hilbert spaces, with a Gaussian prior measure and additive Gaussian noise model, and provide an extension of the concept of Bayesian D-optimality to the infinite-dimensional case. To this end, we derive the infinite-dimensional version of the expression for the Kullback–Leibler divergence from the posterior measure to the prior measure, which is subsequently used to derive the expression for the expected information gain. We also study the notion of Bayesian A-optimality in the infinite-dimensional setting, and extend the well known (in the finite-dimensional case) equivalence of the Bayes risk of the MAP estimator with the trace of the posterior covariance, for the Gaussian linear case, to the infinite-dimensional Hilbert space case.
DA - 2016/9//
PY - 2016/9//
DO - 10.1214/15-ba969
VL - 11
IS - 3
SP - 671-695
SN - 1936-0975
KW - Bayesian inference in Hilbert space
KW - Gaussian measure
KW - Kullback-Leibler divergence
KW - Bayesian optimal experimental design
KW - expected information gain
KW - Bayes risk
ER -
TY - JOUR
TI - ON THE COMPLEXITY OF LOCAL SEARCH IN UNCONSTRAINED QUADRATIC BINARY OPTIMIZATION
AU - Papp, David
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - We consider the problem of finding a local minimum of a binary quadratic function and show by an elementary construction that every descending local search algorithm takes exponential time in the worst case.
DA - 2016///
PY - 2016///
DO - 10.1137/15m1047775
VL - 26
IS - 2
SP - 1257-1261
SN - 1095-7189
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84976872183&partnerID=MN8TOARS
KW - local optimization
KW - binary quadratic optimization
KW - exponential complexity
ER -
TY - JOUR
TI - Linear Time Interactive Certificates for the Minimal Polynomial and the Determinant of a Sparse Matrix
AU - Dumas, Jean -Guillaume
AU - Kaltofen, Erich
AU - Thome, Emmanuel
AU - Villard, Gilles
T2 - PROCEEDINGS OF THE 2016 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION (ISSAC 2016)
AB - Computational problem certificates are additional data structures for each output, which can be used by a---possibly randomized---verification algorithm that proves the correctness of each output. In this paper, we give an algorithm that computes a certificate for the minimal polynomial of sparse or structured matrices over an abstract field, of sufficiently large cardinality, whose Monte Carlo verification complexity requires a single matrix-vector multiplication and a linear number of extra field operations. We also propose a novel preconditioner that ensures irreducibility of the characteristic polynomial of the generically preconditioned matrix. This preconditioner takes linear time to be applied and uses only two random entries. We then combine these two techniques to give algorithms that compute certificates for the determinant, and thus for the characteristic polynomial, whose Monte Carlo verification complexity is therefore also linear.
DA - 2016///
PY - 2016///
DO - 10.1145/2930889.2930908
SP - 199-206
ER -
TY - JOUR
TI - HOID: HIGHER ORDER INTERPOLATORY DECOMPOSITION FOR TENSORS BASED ON TUCKER REPRESENTATION
AU - Saibaba, Arvind K.
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - We derive a CUR-type factorization for tensors in the Tucker format based on interpolatory decomposition, which we will denote as higher order interpolatory Decomposition (HOID). Given a tensor $\mathbf{\mathcal{X}}$, the algorithm provides a set of column vectors $\{ \mathbf{C}_n\}_{n=1}^d$ which are columns extracted from the mode-$n$ tensor unfolding, along with a core tensor $\mathbf{\mathcal{G}}$ and, together, they satisfy some error bounds. Compared to the higher order SVD algorithm, the HOID provides a decomposition that preserves certain important features of the original tensor such as sparsity, non-negativity, integer values, etc. Error bounds along with detailed estimates of computational costs are provided. The algorithms proposed in this paper have been validated against carefully chosen numerical examples which highlight the favorable properties of the algorithms. Related methods for subset selection proposed for matrix CUR decomposition, such as the discrete empirical interpolation method ...
DA - 2016///
PY - 2016///
DO - 10.1137/15m1048628
VL - 37
IS - 3
SP - 1223-1249
SN - 1095-7162
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84990853624&partnerID=MN8TOARS
KW - tensors
KW - interpolatory decomposition
KW - CUR decomposition
KW - Tucker decomposition
ER -
TY - BOOK
TI - Applied Abstract Algebra
AU - Klima, R.
AU - Sigman, N.
AU - Stitzinger, E.
DA - 2016///
PY - 2016///
PB - Boca Raton: CRC Press
SN - 9781482248234
ER -
TY - JOUR
TI - Analysis of Nonlinear Poro-Elastic and Poro-Visco-Elastic Models
AU - Bociu, Lorena
AU - Guidoboni, Giovanna
AU - Sacco, Riccardo
AU - Webster, Justin T.
T2 - Archive for Rational Mechanics and Analysis
AB - We consider the initial and boundary value problem for a system of partial differential equations describing the motion of a fluid–solid mixture under the assumption of full saturation. The ability of the fluid phase to flow within the solid skeleton is described by the permeability tensor, which is assumed here to be a multiple of the identity and to depend nonlinearly on the volumetric solid strain. In particular, we study the problem of the existence of weak solutions in bounded domains, accounting for non-zero volumetric and boundary forcing terms. We investigate the influence of viscoelasticity on the solution functional setting and on the regularity requirements for the forcing terms. The theoretical analysis shows that different time regularity requirements are needed for the volumetric source of linear momentum and the boundary source of traction depending on whether or not viscoelasticity is present. The theoretical results are further investigated via numerical simulations based on a novel dual mixed hybridized finite element discretization. When the data are sufficiently regular, the simulations show that the solutions satisfy the energy estimates predicted by the theoretical analysis. Interestingly, the simulations also show that, in the purely elastic case, the Darcy velocity and the related fluid energy might become unbounded if indeed the data do not enjoy the time regularity required by the theory.
DA - 2016/7/14/
PY - 2016/7/14/
DO - 10.1007/s00205-016-1024-9
VL - 222
IS - 3
SP - 1445-1519
J2 - Arch Rational Mech Anal
LA - en
OP -
SN - 0003-9527 1432-0673
UR - http://dx.doi.org/10.1007/s00205-016-1024-9
DB - Crossref
ER -
TY - JOUR
TI - Adaptive and active materials: selected papers from the ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems (SMASIS 15) (Colorado Springs, CO, USA, 21-23 September 2015)
AU - Smith, Ralph C.
AU - Anderson, Iain
AU - Hartl, Darren
AU - Atulasimha, Jayasimha
AU - Sarles, Stephen A.
AU - Wissa, Aimy
AU - Shafer, Michael
T2 - SMART MATERIALS AND STRUCTURES
DA - 2016/10//
PY - 2016/10//
DO - 10.1088/0964-1726/25/10/100201
VL - 25
IS - 10
SP -
SN - 1361-665X
ER -
TY - CONF
TI - A topological collapse for document summarization
AU - Guan, Hui
AU - Tang, Wen
AU - Krim, Hamid
AU - Keiser, James
AU - Rindos, Andrew
AU - Sazdanovic, Radmila
AB - As a useful tool to summarize documents, keyphrase extraction extracts a set of single or multiple words, called keyphrases, that capture the primary topics discussed in a document. In this paper we propose DoCollapse, a topological collapse-based unsupervised keyphrase extraction method that relies on networking document by semantic relatedness of candidate keyphrases. A semantic graph is built with candidates keyphrases as vertices and then reduced to its core using topological collapse algorithm to facilitate final keyphrase selection. Iteratively collapsing dominated vertices aids in removing noisy candidates and revealing important points. We conducted experiments on two standard evaluation datasets composed of scientific papers and found that DoCollapse outperforms state-of-the-art methods. Results show that simplifying a document graph by homology-preserving topological collapse benefits keyphrase extraction.
C2 - 2016/7//
C3 - 2016 IEEE 17th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)
DA - 2016/7//
DO - 10.1109/spawc.2016.7536867
VL - 2016-August
PB - IEEE
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84984653594&partnerID=MN8TOARS
ER -
TY - JOUR
TI - A note on how to develop interdisciplinary collaborations between experimentalists and theoreticians
AU - Madzvamuse, Anotida
AU - Lubkin, Sharon R.
T2 - INTERFACE FOCUS
AB - This special issue is inspired by and based on the six-month research programme held at the Isaac Newton Institute (INI) for Mathematical Sciences, Cambridge, UK between 13 July and 18 December 2015 entitled ‘Coupling geometric partial differential equations with physics for cell morphology, motility and pattern formation’. The research programme was the first of its kind to bring together at the INI world-leading theoreticians, experimentalists, biomedical practitioners and statisticians. This diverse and large group came together to share paired goals: understanding how current mathematical techniques, including mathematical modelling and numerical and statistical analysis, can be used to formulate and analyse topical problems in cell motility and pattern formation, and conversely, how diverse experimental results can be translated into predictive mathematical and computational models across several spatio-temporal scales. Recent advances in cell motility and pattern formation, including high-resolution imaging techniques in three dimensions, necessitate new mathematical and computational theories to help guide, suggest, refine and sharpen further experimental hypotheses. The research programme laid down premises for topical research that mandated coupling molecular, cellular, tissue and fluid dynamics in a multi-scale interdisciplinary environment thereby enabling the generation of new scientific knowledge across several disciplines.
The six-month research programme included three workshops and an Open for Business event at the INI, a satellite meeting at the University of Sussex, and a unique hands-on experimental workshop in Germany on cell migration and advanced microscopy, hosted jointly by RWTH Aachen University and Forschungszentrum Julich. Hence, with the goal of breaking barriers between these disciplines, the programme was tailored in a way that best harnessed expertise and knowledge between experimental and theoretical sciences.
DA - 2016/10/6/
PY - 2016/10/6/
DO - 10.1098/rsfs.2016.0069
VL - 6
IS - 5
SP -
SN - 2042-8901
UR - https://doi.org/10.1098/rsfs.2016.0069
KW - experimental biology
KW - theoretical biology
KW - biophysics
KW - cell biology
ER -
TY - JOUR
TI - A SEQUENTIAL METHOD FOR A CLASS OF STABLE MATHEMATICAL PROGRAMMING PROBLEMS
AU - Ito, Kazufumi
AU - Kunisch, Karl
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - A sequential programming method of first order for constrained optimization in infinite dimensional spaces is presented. It is referred to as the SP method. It relies on Lipschitz stability of the minimizers with respect to perturbations in an essential way, and is motivated by optimal control problems with partial differential equations as constraints. Convergence and convergence rate are analyzed based on solutions of first order optimality conditions and on Lagrange multiplier theory. The first order SP method does not rely on an approximation of the Hessian of the Lagrange functional and consequently it avoids instabilities due to possible indefiniteness far from a local minimum. It is especially well suited for bilinear control problems and can be extended to certain classes of nonsmooth and convex problems. It can efficiently be implemented by the use of saddle point solvers, with complexity which is between that of gradient and SQP methods. For the important class of bilinear control problems the m...
DA - 2016///
PY - 2016///
DO - 10.1137/140985597
VL - 26
IS - 2
SP - 1262-1292
SN - 1095-7189
KW - sequential linearization
KW - optimal bilinear control
KW - mathematical programming
KW - nonsmooth optimization
ER -
TY - JOUR
TI - Solving optimal control problems with control delays using direct transcription
AU - Betts, John T.
AU - Campbell, Stephen L.
AU - Thompson, Karmethia C.
T2 - APPLIED NUMERICAL MATHEMATICS
AB - The numerical treatment of optimal control problems with state and control delays is important in a wide variety of scientific and technical applications. Solutions to these types of problems are difficult to obtain via analytic techniques since the system may be nonlinear and subjected to complicated inputs and constraints. There are several numerical methods available to compute the solutions of optimal control problems without delays. One such popular method is direct transcription. Although the numerical solutions of optimal control delay problems are important, less literature and software exists in this area. A general purpose industrial grade direct transcription code that can handle optimal control problems with both state and control constraints and delays is under development. Control delays pose a special challenge. A new technique for treating control delays when using a direct transcription approach is investigated in this paper.
DA - 2016/10//
PY - 2016/10//
DO - 10.1016/j.apnum.2015.12.008
VL - 108
SP - 185-203
SN - 1873-5460
KW - Delay
KW - Optimal control
KW - Direct transcription
KW - Numerical methods
ER -
TY - JOUR
TI - Rota-Baxter operators on Witt and Virasoro algebras
AU - Gao, Xu
AU - Liu, Ming
AU - Bai, Chengming
AU - Jing, Naihuan
T2 - JOURNAL OF GEOMETRY AND PHYSICS
AB - The homogeneous Rota–Baxter operators on the Witt and Virasoro algebras are classified. As applications, the induced solutions of the classical Yang–Baxter equation and the induced pre-Lie and PostLie algebra structures are obtained.
DA - 2016/10//
PY - 2016/10//
DO - 10.1016/j.geomphys.2016.06.007
VL - 108
SP - 1-20
SN - 1879-1662
UR - https://doi.org/10.1016/j.geomphys.2016.06.007
KW - Rota-Baxter operator
KW - Witt algebra
KW - Virasoro algebra
KW - Pre-Lie algebra
KW - PostLie algebra
ER -
TY - JOUR
TI - Quantum discord of X-states as optimization of a one variable function
AU - Jing, Naihuan
AU - Yu, Bing
T2 - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
AB - We solve the quantum discord completely as an optimization of certain one variable function for arbitrary two qubit X state. Exact solutions of the quantum discord are obtained for several nontrivial regions of the five parametric space for the quantum state. Exceptional solutions are determined via an iterative algorithm.
DA - 2016/9/23/
PY - 2016/9/23/
DO - 10.1088/1751-8113/49/38/385302
VL - 49
IS - 38
SP -
SN - 1751-8121
KW - quantum discord
KW - quantum correlation
KW - optimization
KW - von Neumann measures
ER -
TY - JOUR
TI - Numerical methods for coupled systems of quasilinear elliptic equations with nonlinear boundary conditions
AU - Pao, C. V.
AU - He, T. P.
T2 - Journal of Applied Analysis and Computation
DA - 2016///
PY - 2016///
VL - 6
IS - 2
SP - 543-581
ER -
TY - JOUR
TI - Homotopy derivations
AU - Doubek, Martin
AU - Lada, Tom
T2 - JOURNAL OF HOMOTOPY AND RELATED STRUCTURES
AB - We define a strong homotopy derivation of (cohomological) degree k of a strong homotopy algebra over an operad $$\mathcal {P}$$ . This involves resolving the operad obtained from $$\mathcal {P}$$ by adding a generator with “derivation relations”. For a wide class of Koszul operads $$\mathcal {P}$$ , in particular $$\mathcal {A}{ss}$$ and $$\mathcal {L}{ie}$$ , we describe the strong homotopy derivations by coderivations and show that they are closed under the Lie bracket. We show that symmetrization of a strong homotopy derivation of an $$A_\infty $$ algebra yields a strong homotopy derivation of the symmetrized $$L_\infty $$ algebra. We give examples of strong homotopy derivations generalizing inner derivations.
DA - 2016/9//
PY - 2016/9//
DO - 10.1007/s40062-015-0118-7
VL - 11
IS - 3
SP - 599-630
SN - 1512-2891
ER -
TY - JOUR
TI - Gradient free active subspace construction using Morris screening elementary effects
AU - Lewis, Allison
AU - Smith, Ralph
AU - Williams, Brian
T2 - COMPUTERS & MATHEMATICS WITH APPLICATIONS
AB - Among multivariate functions with high-dimensional input spaces, it is common for functions to vary more strongly in a few dominant directions related to a small number of highly influential parameters. In such cases, the input dimension may be greatly reduced by constructing a low-dimensional response space that is aligned with the directions of strongest dominance; this is the basis behind active subspace methods. Until recently, gradient-based methods have been employed to construct the active subspace. We introduce a gradient-free active subspace construction method that avoids the need to sample from the gradient, which may not be available, via construction of a coarse approximation to the gradient matrix by employing the concept of “elementary effects” from Morris screening procedures. In addition, we introduce the use of adaptive step sizes and directions, when constructing these elementary effects, to allow for more accuracy in locally sensitive regions while still covering a substantial amount of the input space. This increases algorithmic efficiency by avoiding function evaluations in directions in which the gradient is relatively flat. To demonstrate the method, we use an elliptic PDE example with two correlation lengths to illustrate the effects of differing rates of singular value decay. The gradient-free active subspace method is compared to a local sensitivity analysis using coordinate reduction. This problem is then modified to contain a clearly defined 10-dimensional active subspace for verification of our method on a more complex example.
DA - 2016/9//
PY - 2016/9//
DO - 10.1016/j.camwa.2016.07.022
VL - 72
IS - 6
SP - 1603-1615
SN - 1873-7668
KW - Active subspace construction
KW - Reduced-order modeling
KW - Morris screening
ER -
TY - JOUR
TI - Drinfeld Realization of Quantum Twisted Affine Algebras via Braid Group
AU - Jing, Naihuan
AU - Zhang, Honglian
T2 - ADVANCES IN MATHEMATICAL PHYSICS
AB - The Drinfeld realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization for the twisted quantum affine algebras using Lusztig’s braid group action.
DA - 2016///
PY - 2016///
DO - 10.1155/2016/4843075
VL - 2016
SP -
SN - 1687-9139
ER -
TY - JOUR
TI - Analysis of a domain decomposition method for linear transport problems on networks
AU - Collins, J. B.
AU - Gremaud, P. A.
T2 - APPLIED NUMERICAL MATHEMATICS
AB - In this paper we analyze the convergence of the domain decomposition method applied to transport problems on networks. In particular, we derive estimates for the number of required iterations for linear problems. These estimates can be used to determine when the implementation of domain decomposition methods would be beneficial for this type of problems.
DA - 2016/11//
PY - 2016/11//
DO - 10.1016/j.apnum.2016.06.004
VL - 109
SP - 61-72
SN - 1873-5460
KW - Transport
KW - Network
KW - Domain decomposition
ER -
TY - JOUR
TI - An information theoretic approach to use high-fidelity codes to calibrate low-fidelity codes
AU - Lewis, Allison
AU - Smith, Ralph
AU - Williams, Brian
AU - Figueroa, Victor
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - For many simulation models, it can be prohibitively expensive or physically infeasible to obtain a complete set of experimental data to calibrate model parameters. In such cases, one can alternatively employ validated higher-fidelity codes to generate simulated data, which can be used to calibrate the lower-fidelity code. In this paper, we employ an information-theoretic framework to determine the reduction in parameter uncertainty that is obtained by evaluating the high-fidelity code at a specific set of design conditions. These conditions are chosen sequentially, based on the amount of information that they contribute to the low-fidelity model parameters. The goal is to employ Bayesian experimental design techniques to minimize the number of high-fidelity code evaluations required to accurately calibrate the low-fidelity model. We illustrate the performance of this framework using heat and diffusion examples, a 1-D kinetic neutron diffusion equation, and a particle transport model, and include initial results from the integration of the high-fidelity thermal-hydraulics code Hydra-TH with a low-fidelity exponential model for the friction correlation factor.
DA - 2016/11/1/
PY - 2016/11/1/
DO - 10.1016/j.jcp.2016.08.001
VL - 324
SP - 24-43
SN - 1090-2716
KW - Model calibration
KW - Bayesian experimental design
KW - Optimal evaluation
KW - Mutual information
ER -
TY - JOUR
TI - A General, Synthetic Model for Predicting Biodiversity Gradients from Environmental Geometry
AU - Gross, Kevin
AU - Snyder-Beattie, Andrew
T2 - AMERICAN NATURALIST
AB - Latitudinal and elevational biodiversity gradients fascinate ecologists, and have inspired dozens of explanations. The geometry of the abiotic environment is sometimes thought to contribute to these gradients, yet evaluations of geometric explanations are limited by a fragmented understanding of the diversity patterns they predict. This article presents a mathematical model that synthesizes multiple pathways by which environmental geometry can drive diversity gradients. The model characterizes species ranges by their environmental niches and limits on range sizes and places those ranges onto the simplified geometries of a sphere or cone. The model predicts nuanced and realistic species-richness gradients, including latitudinal diversity gradients with tropical plateaus and mid-latitude inflection points and elevational diversity gradients with low-elevation diversity maxima. The model also illustrates the importance of a mid-environment effect that augments species richness at locations with intermediate environments. Model predictions match multiple empirical biodiversity gradients, depend on ecological traits in a testable fashion, and formally synthesize elements of several geometric models. Together, these results suggest that previous assessments of geometric hypotheses should be reconsidered and that environmental geometry may play a deeper role in driving biodiversity gradients than is currently appreciated.
DA - 2016/10//
PY - 2016/10//
DO - 10.1086/688171
VL - 188
IS - 4
SP - E85-E97
SN - 1537-5323
KW - biological diversity
KW - environmental geometry
KW - mathematical model
KW - niche
KW - species range
KW - species richness
ER -
TY - JOUR
TI - Vertex Operators Arising from Jacobi-Trudi Identities
AU - Jing, Naihuan
AU - Rozhkovskaya, Natasha
T2 - COMMUNICATIONS IN MATHEMATICAL PHYSICS
AB - We give an interpretation of the boson-fermion correspondence as a direct consequence of the Jacobi–Trudi identity. This viewpoint enables us to construct from a generalized version of the Jacobi–Trudi identity the action of a Clifford algebra on the polynomial algebras that arrive as analogues of the algebra of symmetric functions. A generalized Giambelli identity is also proved to follow from that identity. As applications, we obtain explicit formulas for vertex operators corresponding to characters of the classical Lie algebras, shifted Schur functions, and generalized Schur symmetric functions associated to linear recurrence relations.
DA - 2016/9//
PY - 2016/9//
DO - 10.1007/s00220-015-2564-9
VL - 346
IS - 2
SP - 679-701
SN - 1432-0916
ER -
TY - JOUR
TI - Two-parameter twisted quantum affine algebras
AU - Jing, Naihuan
AU - Zhang, Honglian
T2 - JOURNAL OF MATHEMATICAL PHYSICS
AB - We establish Drinfeld realization for the two-parameter twisted quantum affine algebras using a new method. The Hopf algebra structure for Drinfeld generators is given for both untwisted and twisted two-parameter quantum affine algebras, which include the quantum affine algebras as special cases.
DA - 2016/9//
PY - 2016/9//
DO - 10.1063/1.4962722
VL - 57
IS - 9
SP -
SN - 1089-7658
ER -
TY - JOUR
TI - Subalgebras of the Fomin-Kirillov algebra
AU - Blasiak, Jonah
AU - Liu, Ricky Ini
AU - Meszaros, Karola
T2 - JOURNAL OF ALGEBRAIC COMBINATORICS
AB - The Fomin–Kirillov algebra $${\mathcal {E}}_n$$ is a noncommutative quadratic algebra with a generator for every edge of the complete graph on n vertices. For any graph G on n vertices, we define $${{\mathcal {E}}_G}$$ to be the subalgebra of $${\mathcal {E}}_n$$ generated by the edges of G. We show that these algebras have many parallels with Coxeter groups and their nil-Coxeter algebras: for instance, $${\mathcal {E}}_G$$ is a free $${\mathcal {E}}_H$$ -module for any $$H\subseteq G$$ , and if $${\mathcal {E}}_G$$ is finite-dimensional, then its Hilbert series has symmetric coefficients. We determine explicit monomial bases and Hilbert series for $${\mathcal {E}}_G$$ when G is a simply laced finite Dynkin diagram or a cycle, in particular showing that $${\mathcal {E}}_G$$ is finite-dimensional in these cases. We also present conjectures for the Hilbert series of $${\mathcal {E}}_{\tilde{D}_n}$$ , $${\mathcal {E}}_{\tilde{E}_6}$$ , and $${\mathcal {E}}_{\tilde{E}_7}$$ , as well as the graphs G on six vertices for which $$\mathcal {E}_G$$ is finite-dimensional.
DA - 2016/11//
PY - 2016/11//
DO - 10.1007/s10801-016-0688-4
VL - 44
IS - 3
SP - 785-829
SN - 1572-9192
KW - Fomin-Kirillov algebra
KW - Coxeter group
KW - nil-Coxeter algebra
KW - Nichols algebra
ER -
TY - JOUR
TI - Quantum Permanents and Hafnians via Pfaffians
AU - Jing, Naihuan
AU - Zhang, Jian
T2 - LETTERS IN MATHEMATICAL PHYSICS
AB - Quantum determinants and Pfaffians or permanents and Hafnians are introduced on the two parameter quantum general linear group. Fundamental identities among quantum Pf, Hf, and det are proved in the general setting. We show that there are two special quantum algebras among the quantum groups, where the quantum Pfaffians have integral Laurent polynomials as coefficients. As a consequence, the quantum Hafnian is computed by a closely related quantum permanent and identical to the quantum Pfaffian on this special quantum algebra.
DA - 2016/10//
PY - 2016/10//
DO - 10.1007/s11005-016-0881-3
VL - 106
IS - 10
SP - 1451-1464
SN - 1573-0530
KW - q-determinant
KW - q-permanent
KW - q-Pfaffian
KW - q-Hafnian
KW - Hopf algebras
ER -
TY - JOUR
TI - Optimal Universal Uncertainty Relations
AU - Li, Tao
AU - Xiao, Yunlong
AU - Ma, Teng
AU - Fei, Shao-Ming
AU - Jing, Naihuan
AU - Li-Jost, Xianqing
AU - Wang, Zhi-Xi
T2 - SCIENTIFIC REPORTS
AB - Abstract We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111 , 230401 (2013)] and [J. Phys. A. 46 , 272002 (2013)]. The results give rise to state independent uncertainty relations satisfied by any nonnegative Schur-concave functions. On the other hand, a remarkable recent result of entropic uncertainty relation is the direct-sum majorization relation. In this paper, we illustrate our bounds by showing how they provide a complement to that in [Phys. Rev. A. 89 , 052115 (2014)].
DA - 2016/10/24/
PY - 2016/10/24/
DO - 10.1038/srep35735
VL - 6
SP -
SN - 2045-2322
ER -
TY - JOUR
TI - Mutually Exclusive Uncertainty Relations
AU - Xiao, Yunlong
AU - Jing, Naihuan
T2 - SCIENTIFIC REPORTS
AB - The uncertainty principle is one of the characteristic properties of quantum theory based on incompatibility. Apart from the incompatible relation of quantum states, mutually exclusiveness is another remarkable phenomenon in the information- theoretic foundation of quantum theory. We investigate the role of mutual exclusive physical states in the recent work of stronger uncertainty relations for all incompatible observables by Mccone and Pati and generalize the weighted uncertainty relation to the product form as well as their multi-observable analogues. The new bounds capture both incompatibility and mutually exclusiveness, and are tighter compared with the existing bounds.
DA - 2016/11/8/
PY - 2016/11/8/
DO - 10.1038/srep36616
VL - 6
SP -
SN - 2045-2322
ER -
TY - JOUR
TI - Mitochondrial Genome Sequences and Structures Aid in the Resolution of Piroplasmida phylogeny
AU - Schreeg, Megan E.
AU - Marr, Henry S.
AU - Tarigo, Jaime L.
AU - Cohn, Leah A.
AU - Bird, David M.
AU - Scholl, Elizabeth H.
AU - Levy, Michael G.
AU - Wiegmann, Brian M.
AU - Birkenheuer, Adam J.
T2 - PLOS ONE
AB - The taxonomy of the order Piroplasmida, which includes a number of clinically and economically relevant organisms, is a hotly debated topic amongst parasitologists. Three genera (Babesia, Theileria, and Cytauxzoon) are recognized based on parasite life cycle characteristics, but molecular phylogenetic analyses of 18S sequences have suggested the presence of five or more distinct Piroplasmida lineages. Despite these important advancements, a few studies have been unable to define the taxonomic relationships of some organisms (e.g. C. felis and T. equi) with respect to other Piroplasmida. Additional evidence from mitochondrial genome sequences and synteny should aid in the inference of Piroplasmida phylogeny and resolution of taxonomic uncertainties. In this study, we have amplified, sequenced, and annotated seven previously uncharacterized mitochondrial genomes (Babesia canis, Babesia vogeli, Babesia rossi, Babesia sp. Coco, Babesia conradae, Babesia microti-like sp., and Cytauxzoon felis) and identified additional ribosomal fragments in ten previously characterized mitochondrial genomes. Phylogenetic analysis of concatenated mitochondrial and 18S sequences as well as cox1 amino acid sequence identified five distinct Piroplasmida groups, each of which possesses a unique mitochondrial genome structure. Specifically, our results confirm the existence of four previously identified clades (B. microti group, Babesia sensu stricto, Theileria equi, and a Babesia sensu latu group that includes B. conradae) while supporting the integration of Theileria and Cytauxzoon species into a single fifth taxon. Although known biological characteristics of Piroplasmida corroborate the proposed phylogeny, more investigation into parasite life cycles is warranted to further understand the evolution of the Piroplasmida. Our results provide an evolutionary framework for comparative biology of these important animal and human pathogens and help focus renewed efforts toward understanding the phylogenetic relationships within the group.
DA - 2016/11/10/
PY - 2016/11/10/
DO - 10.1371/journal.pone.0165702
VL - 11
IS - 11
SP -
SN - 1932-6203
ER -
TY - JOUR
TI - Matrix Schubert varieties and Gaussian conditional independence models
AU - Fink, Alex
AU - Rajchgot, Jenna
AU - Sullivant, Seth
T2 - JOURNAL OF ALGEBRAIC COMBINATORICS
AB - Matrix Schubert varieties are certain varieties in the affine space of square matrices which are determined by specifying rank conditions on submatrices. We study these varieties for generic matrices, symmetric matrices, and upper triangular matrices in view of two applications to algebraic statistics: We observe that special conditional independence models for Gaussian random variables are intersections of matrix Schubert varieties in the symmetric case. Consequently, we obtain a combinatorial primary decomposition algorithm for some conditional independence ideals. We also characterize the vanishing ideals of Gaussian graphical models for generalized Markov chains. In the course of this investigation, we are led to consider three related stratifications, which come from the Schubert stratification of a flag variety. We provide some combinatorial results, including describing the stratifications using the language of rank arrays and enumerating the strata in each case.
DA - 2016/12//
PY - 2016/12//
DO - 10.1007/s10801-016-0698-2
VL - 44
IS - 4
SP - 1009-1046
SN - 1572-9192
KW - Gaussian random variables
KW - Conditional independence
KW - Gaussian graphical models
KW - Matrix Schubert varieties
KW - Kazhdan-Lusztig varieties
ER -
TY - JOUR
TI - From Conway Notation to LinKnot
AU - Jablan, Slavik V.
AU - Sazdanovic, Radmila
T2 - KNOT THEORY AND ITS APPLICATIONS
DA - 2016///
PY - 2016///
DO - 10.1090/conm/670/13445
VL - 670
SP - 63-92
SN - 1098-3627
ER -
TY - JOUR
TI - Comments on direct transcription solution of DAE constrained optimal control problems with two discretization approaches
AU - Campbell, Stephen L.
AU - Betts, John T.
T2 - NUMERICAL ALGORITHMS
DA - 2016/11//
PY - 2016/11//
DO - 10.1007/s11075-016-0119-6
VL - 73
IS - 3
SP - 807-838
SN - 1572-9265
KW - Optimal control
KW - Direct transcription
KW - Pseudospectral
KW - Differential algebraic equation
ER -
TY - CONF
TI - Auxiliary signal design for failure detection with initial prior information
AU - Campbell, Stephen L.
AU - Scott, Jason R.
T2 - SoutheastCon 2016
AB - Fault detection and the related problem of identification (FDI) play an important role in many modern technological systems and processes. A variety of active and passive approaches have been investigated. Previous work on auxiliary signal design for one active approach used a bound on total uncertainty which included the state at the start of the test as part of a cost function. However, in some applications that may not be the most natural thing to do if there is some information about prior behavior. Using this prior information in a different way leads to several changes in algorithms and software. This paper investigates these changes and their consequences.
C2 - 2016/3//
C3 - SoutheastCon 2016
DA - 2016/3//
DO - 10.1109/secon.2016.7506738
PB - IEEE
SN - 9781509022465
UR - http://dx.doi.org/10.1109/SECON.2016.7506738
DB - Crossref
ER -
TY - CONF
TI - Actuator effects on auxiliary signal design for failure detection
AU - Campbell, Stephen L.
AU - Owen, Hailey
T2 - SoutheastCon 2016
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. In much of the active work the focus was on designing an optimal test signal. However, much less attention was given to actually generating that test signal. Here the effect of including actuator effects in generating an optimal test signal for active fault detection is investigated.
C2 - 2016/3//
C3 - SoutheastCon 2016
DA - 2016/3//
DO - 10.1109/secon.2016.7506748
PB - IEEE
SN - 9781509022465
UR - http://dx.doi.org/10.1109/SECON.2016.7506748
DB - Crossref
ER -
TY - JOUR
TI - ANALYSIS ON A NONNEGATIVE MATRIX FACTORIZATION AND ITS APPLICATIONS
AU - Chow, Yat Tin
AU - Ito, Kazufumi
AU - Zou, Jun
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - In this work we perform some mathematical analysis on a special nonnegative matrix trifactorization (NMF) and apply this NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of positive data and images in terms of tensor products of positive vectors and investigate its effectiveness in terms of the number of tensor products to be used in the approximation. A new multilevel analysis (MLA) framework is suggested to extract major components in the matrix representing structures of different resolutions but still preserve the positivity of the basis and sparsity of the approximation. We will also propose and formulate a semismooth Newton method based on primal-dual active sets for the nonnegative factorization. Numerical results are given to demonstrate the effectiveness of the proposed method at capturing features in images and structures of inverse problems under no a priori assumption on the underlying structure in the data as well as to provide a sparse low-rank representation of the data.
DA - 2016///
PY - 2016///
DO - 10.1137/15m1020824
VL - 38
IS - 5
SP - B645-B684
SN - 1095-7197
KW - nonnegative matrix factorization
KW - clustering
KW - feature extraction
KW - multilevel analysis
KW - inverse problems
ER -
TY - JOUR
TI - Uncertainty analysis of continuum scale ferroelectric energy landscapes using density functional theory
AU - Oates, William S.
AU - Miles, Paul
AU - Leon, Lider
AU - Smith, Ralph
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2016
AB - Density functional theory (DFT) provides exceptional predictions of material properties of ideal crystal structures such as elastic modulus and dielectric constants. This includes ferroelectric crystals where excellent predictions of spontaneous polarization, lattice strain, and elastic moduli have been predicted using DFT. Less analysis has focused on quantifying uncertainty of the energy landscape over a broad range of polarization states in ferroelectric materials. This is non-trivial because the degrees of freedom contained within a unit cell are reduced to a single vector order parameter which is normally polarization. For example, lead titanate contains five atoms and 15 degrees of freedom of atomic nuclei motion which contribute to the overall unit cell polarization. Bayesian statistics is used to identify the uncertainty and propagation of error of a continuum scale, Landau energy function for lead titanate. Uncertainty in different parameters is quantified and this uncertainty is propagated through the model to illustrate error propagation over the energy surface. Such results are shown to have an impact in integration of quantum simulations within a ferroelectric phase field continuum modeling framework.
DA - 2016///
PY - 2016///
DO - 10.1117/12.2219273
VL - 9800
SP -
SN - 1996-756X
ER -
TY - JOUR
TI - Technical Note: Improving the VMERGE treatment planning algorithm for rotational radiotherapy
AU - Gaddy, Melissa R.
AU - Papp, David
T2 - MEDICAL PHYSICS
AB - The authors revisit the VMERGE treatment planning algorithm by Craft et al. ["Multicriteria VMAT optimization," Med. Phys. 39, 686-696 (2012)] for arc therapy planning and propose two changes to the method that are aimed at improving the achieved trade-off between treatment time and plan quality at little additional planning time cost, while retaining other desirable properties of the original algorithm.The original VMERGE algorithm first computes an "ideal," high quality but also highly time consuming treatment plan that irradiates the patient from all possible angles in a fine angular grid with a highly modulated beam and then makes this plan deliverable within practical treatment time by an iterative fluence map merging and sequencing algorithm. We propose two changes to this method. First, we regularize the ideal plan obtained in the first step by adding an explicit constraint on treatment time. Second, we propose a different merging criterion that comprises of identifying and merging adjacent maps whose merging results in the least degradation of radiation dose.The effect of both suggested modifications is evaluated individually and jointly on clinical prostate and paraspinal cases. Details of the two cases are reported.In the authors' computational study they found that both proposed modifications, especially the regularization, yield noticeably improved treatment plans for the same treatment times than what can be obtained using the original VMERGE method. The resulting plans match the quality of 20-beam step-and-shoot IMRT plans with a delivery time of approximately 2 min.
DA - 2016/7//
PY - 2016/7//
DO - 10.1118/1.4953193
VL - 43
IS - 7
SP - 4093-4097
SN - 2473-4209
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84975226392&partnerID=MN8TOARS
KW - arc therapy
KW - treatment planning
KW - optimization
KW - rotational therapy
ER -
TY - JOUR
TI - THE NONNEGATIVE MATRIX FACTORIZATION: REGULARIZATION AND COMPLEXITY
AU - Ito, K.
AU - Landi, A. K.
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - Data continues to grow, and it has become ever important to find effective big data analysis techniques. Computational tools, such as singular value decomposition, have been employed in the interpretation of big data. Another tool has recently gained popularity and comparative success: the nonnegative matrix factorization (NMF). The NMF method is a feature selection, dimension reduction algorithm which takes a data matrix and finds a simpler representation. In this paper, we discuss the choice of regularization parameters for a regularized NMF problem, and we develop a primal-dual active set method which enhances the representation. In addition, we examine rank determination for the case of the NMF problem. We develop a method to choose the proper complexity based on the concept of NMF-singular values.
DA - 2016///
PY - 2016///
DO - 10.1137/14099841x
VL - 38
IS - 2
SP - B327-B346
SN - 1095-7197
KW - nonnegative matrix factorization
KW - primal-dual active set
KW - regularization
KW - complexity
ER -
TY - JOUR
TI - Coupled Heterogeneities and Their Impact on Parasite Transmission and Control
AU - Vazquez-Prokopec, Gonzalo M.
AU - Perkins, T. Alex
AU - Waller, Lance A.
AU - Lloyd, Alun L.
AU - Reiner, Robert C., Jr
AU - Scott, Thomas W.
AU - Kitron, Uriel
T2 - Trends in Parasitology
AB - Most host-parasite systems exhibit remarkable heterogeneity in the contribution to transmission of certain individuals, locations, host infectious states, or parasite strains. While significant advancements have been made in the understanding of the impact of transmission heterogeneity in epidemic dynamics and parasite persistence and evolution, the knowledge base of the factors contributing to transmission heterogeneity is limited. We argue that research efforts should move beyond considering the impact of single sources of heterogeneity and account for complex couplings between conditions with potential synergistic impacts on parasite transmission. Using theoretical approaches and empirical evidence from various host-parasite systems, we investigate the ecological and epidemiological significance of couplings between heterogeneities and discuss their potential role in transmission dynamics and the impact of control.
DA - 2016/5//
PY - 2016/5//
DO - 10.1016/j.pt.2016.01.001
VL - 32
IS - 5
SP - 356-367
J2 - Trends in Parasitology
LA - en
OP -
SN - 1471-4922
UR - http://dx.doi.org/10.1016/j.pt.2016.01.001
DB - Crossref
ER -
TY - JOUR
TI - Construction of bound entangled states based on permutation operators
AU - Zhao, Hui
AU - Guo, Sha
AU - Jing, Naihuan
AU - Fei, Shaoming
T2 - QUANTUM INFORMATION PROCESSING
AB - We present a construction of new bound entangled states from given bound entangled states for arbitrary dimensional bipartite systems. One way to construct bound entangled states is to show that these states are positive partial transpose (PPT) and violate the range criterion at the same time. By applying certain operators to given bound entangled states or to one of the subsystems of the given bound entangled states, we obtain a set of new states which are both PPT and violate the range criterion. We show that the derived bound entangled states are not local unitary equivalent to the original bound entangled states by detail examples.
DA - 2016/4//
PY - 2016/4//
DO - 10.1007/s11128-015-1218-3
VL - 15
IS - 4
SP - 1529-1538
SN - 1573-1332
KW - Bound entanglement
KW - Positive partial transpose
KW - Range criterion
KW - Local unitary equivalent
ER -
TY - JOUR
TI - AN INFINITE TIME HORIZON PORTFOLIO OPTIMIZATION MODEL WITH DELAYS
AU - Pang, Tao
AU - Hussain, Azmat
T2 - MATHEMATICAL CONTROL AND RELATED FIELDS
AB - In this paper we consider a portfolio optimization problem of the Merton's type over an infinite time horizon. Unlike the classical Markov model, we consider a system with delays. The problem is formulated as a stochastic control problem on an infinite time horizon and the state evolves according to a process governed by a stochastic process with delay. The goal is to choose investment and consumption controls such that the total expected discounted utility is maximized. Under certain conditions, we derive the explicit solutions for the associated Hamilton-Jacobi-Bellman (HJB) equations in a finite dimensional space for logarithmic and power utility functions. For those utility functions, verification results are established to ensure that the solutions are equal to the value functions, and the optimal controls are derived, too.
DA - 2016/12//
PY - 2016/12//
DO - 10.3934/mcrf.2016018
VL - 6
IS - 4
SP - 629-651
SN - 2156-8499
KW - Portfolio optimization
KW - Hamilton-Jacobi-Bellman equation
KW - dynamic programming
KW - stochastic control
KW - stochastic delay equation
ER -
TY - JOUR
TI - Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems
AU - Banks, H. T.
AU - Catenacci, J.
AU - Hu, S. H.
T2 - Journal of Inverse and Ill-Posed Problems
DA - 2016///
PY - 2016///
VL - 24
IS - 4
SP - 413-433
ER -
TY - JOUR
TI - Twisted logarithmic modules of free field algebras
AU - Bakalov, Bojko
AU - Sullivan, McKay
T2 - JOURNAL OF MATHEMATICAL PHYSICS
AB - Given a non-semisimple automorphism $\varphi$ of a vertex algebra $V$, the fields in a $\varphi$-twisted $V$-module involve the logarithm of the formal variable, and the action of the Virasoro operator $L_0$ on such module is not semisimple. We construct examples of such modules and realize them explicitly as Fock spaces when $V$ is generated by free fields. Specifically, we consider the cases of symplectic fermions (odd superbosons), free fermions, and $\beta\gamma$-system (even superfermions). In each case, we determine the action of the Virasoro algebra.
DA - 2016/6//
PY - 2016/6//
DO - 10.1063/1.4953249
VL - 57
IS - 6
SP -
SN - 1089-7658
ER -
TY - JOUR
TI - Twisted Logarithmic Modules of Vertex Algebras
AU - Bakalov, Bojko
T2 - COMMUNICATIONS IN MATHEMATICAL PHYSICS
AB - Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted fields involve the logarithm of the formal variable. We develop the theory of such twisted modules and, in particular, derive a Borcherds identity and commutator formula for them. We investigate in detail the examples of affine and Heisenberg vertex algebras.
DA - 2016/7//
PY - 2016/7//
DO - 10.1007/s00220-015-2503-9
VL - 345
IS - 1
SP - 355-383
SN - 1432-0916
ER -
TY - JOUR
TI - The Opportunity to Translate Developmental Toxicology into a Therapeutic Discipline
AU - Hughes, Claude L.
AU - Waters, Michael D.
AU - Allen, David
AU - Obasanjo, Iyabo
T2 - TRANSLATIONAL TOXICOLOGY: DEFINING A NEW THERAPEUTIC DISCIPLINE
AB - Since presentation of our view of translational developmental toxicology in 2013, numerous investigations from a wide range of approaches have added to the evidence underlying our core premise; namely that as the potential adverse developmental effects from a range of exposures are progressively defined, preventative or mitigative therapies can be conceived, assessed and ethically implemented. The spectrum of studies reported in recent years span a wide range of exposure categories and various developmental outcomes ranging from molecular and cellular to the organismal level up to and including human behavior. Since human exposures to chemicals, physical agents and social factors are inevitable, the human fetus is subject to effects that can have lifelong consequences. In order to apply the translational concept to developmental toxicology, established or potential therapeutic obstetrical, neonatal, childhood and adolescent interventions will be required. Those that undergo testing during developmentally sensitive intervals will likely derive from generally-regarded-as-safe (GRAS) or well-established/repurposed pharmaceutical options. Ultimately if we are to translate environmental health discoveries into safe and effective interventions, we must assert and characterize valid, applicable therapies such as GRAS treatments and eventually “ethical pharmaceuticals” for the protective care of these highly vulnerable young people. We can create a safe and efficacious environmental health portfolio of interventional options to improve human health that include both reduction/avoidance of exposure and specific preventative/mitigative/restorative therapeutics. In this chapter we will broadly update new insights that have been gained over the last 2 years regarding the progress of translational developmental toxicology toward becoming a therapeutic discipline.
DA - 2016///
PY - 2016///
DO - 10.1007/978-3-319-27449-2_1
SP - 3-44
SN - 2168-4219
KW - Translational toxicology developmental exposures
KW - Obstetrical, neonatal, childhood and adolescent therapies
ER -
TY - JOUR
TI - Strong entropic uncertainty relations for multiple measurements
AU - Xiao, Yunlong
AU - Jing, Naihuan
AU - Fei, Shao-Ming
AU - Li, Tao
AU - Li-Jost, Xianqing
AU - Ma, Teng
AU - Wang, Zhi-Xi
T2 - PHYSICAL REVIEW A
AB - In this paper, we study entropic uncertainty relations on a finite-dimensional Hilbert space and provide several tighter bounds for multi-measurements, with some of them also valid for R\'{e}nyi and Tsallis entropies besides the Shannon entropy. We employ majorization theory and actions of the symmetric group to obtain an {\it admixture bound} for entropic uncertainty relations for multi-measurements. Comparisons among all bounds for multi-measurements are shown in figures in our favor.
DA - 2016/4/29/
PY - 2016/4/29/
DO - 10.1103/physreva.93.042125
VL - 93
IS - 4
SP -
SN - 2469-9934
ER -
TY - JOUR
TI - Local unitary equivalence of quantum states and simultaneous orthogonal equivalence
AU - Jing, Naihuan
AU - Yang, Min
AU - Zhao, Hui
T2 - JOURNAL OF MATHEMATICAL PHYSICS
AB - The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through simultaneous similarity under projective orthogonal transformations, and four parametrization independent algorithms are proposed to judge when two density matrices on $\mathbb C^{d_1}\otimes \mathbb C^{d_2}$ are locally unitary equivalent in connection with trace identities, Weierstrass pencils, Albert determinants and Smith normal forms.
DA - 2016/6//
PY - 2016/6//
DO - 10.1063/1.4954230
VL - 57
IS - 6
SP -
SN - 1089-7658
ER -
TY - JOUR
TI - Ligand-Mediated Toxicology: Characterization and Translational Prospects
AU - Ansari, Rais
AU - Hughes, Claude L.
AU - Husain, Kazim
T2 - TRANSLATIONAL TOXICOLOGY: DEFINING A NEW THERAPEUTIC DISCIPLINE
DA - 2016///
PY - 2016///
DO - 10.1007/978-3-319-27449-2_4
SP - 113-137
SN - 2168-4219
KW - Translational toxicology
KW - Endocrine disruption
KW - Epigenetics
KW - Ligand
KW - Receptor mediated toxicity
KW - Xenosensors
ER -
TY - JOUR
TI - Laser Measurements of the H Atom plus Ozone Rate Constant at Mesospheric Temperatures
AU - Liu, Yingdi
AU - Peng, Jian
AU - Reppert, Kelsey
AU - Callahan, Sara
AU - Smith, Gregory P.
T2 - JOURNAL OF PHYSICAL CHEMISTRY A
AB - The exothermic H + O3 reaction produces OH(v) Meinel band emissions, used to derive mesospheric H concentrations and chemical heating rates. We remeasured its rate constant to reduce its uncertainty and extended the measurements to lower mesospheric temperatures using modern laser-induced fluorescence (LIF) techniques. H atoms were produced by pulsed ultraviolet laser trace photolysis of O3, followed by reaction of O(1D) with added H2. A second, delayed, frequency-mixed dye laser measured the reaction decay rate with the remaining ozone using LIF. We monitored either the H atom decay by two photon excitation at 205 nm and detection of red fluorescence, or the OH (v = 9) product time evolution with excitation of the B2Σ+–X2Π (0,9) band at 237 nm and emission in the blue B2Σ+–A2Σ+ (0,7) band. By cooling the enclosed low pressure flow cell we obtained measurements from 140 to 305 K at 20 to 200 Torr in Ar. Small kinetic modeling corrections were made for secondary regeneration of H atoms. The results are consistent with the current NASA JPL recommendation for this rate constant and establish its extrapolation down to the lower temperatures of the mesosphere.
DA - 2016/6/9/
PY - 2016/6/9/
DO - 10.1021/acs.jpca.6b02986
VL - 120
IS - 22
SP - 3855-3860
SN - 1089-5639
ER -
TY - JOUR
TI - Isomorphy classes of involutions of SO(n, k, beta), n > 2
AU - Benim, R. W.
AU - Dometrius, C. E.
AU - Helminck, A. G.
AU - Wu, L.
T2 - Journal of Lie Theory
DA - 2016///
PY - 2016///
VL - 26
IS - 2
SP - 383-438
ER -
TY - JOUR
TI - Higher Sugawara Operators for the Quantum Affine Algebras of Type A
AU - Frappat, Luc
AU - Jing, Naihuan
AU - Molev, Alexander
AU - Ragoucy, Eric
T2 - COMMUNICATIONS IN MATHEMATICAL PHYSICS
AB - We give explicit formulas for the elements of the center of the completed quantum affine algebra in type $A$ at the critical level which are associated with the fundamental representations. We calculate the images of these elements under a Harish-Chandra-type homomorphism. These images coincide with those in the free field realization of the quantum affine algebra and reproduce generators of the $q$-deformed classical $W$-algebra of Frenkel and Reshetikhin.
DA - 2016/7//
PY - 2016/7//
DO - 10.1007/s00220-015-2566-7
VL - 345
IS - 2
SP - 631-657
SN - 1432-0916
ER -
TY - JOUR
TI - Heresthetics and choice from tournaments
AU - Moser, Scott
AU - Fenn, Molly
AU - Ji, Ran
AU - Maiden, Michelle
AU - Panosian, Melanie
T2 - JOURNAL OF THEORETICAL POLITICS
AB - Moser et al. provide a formalization of heresthetics, the “art of political strategy”, in collective choice settings. In doing so they introduce the heresthetically stable set as the set of outcomes least susceptible to manipulation of issue dimension. In this note we correct a small error in the original paper, and close several open questions asked there in. We examine the heresthetically stable set as a tournament solution, establishing some basic properties it possesses, and many it does not posses. In addition, we relate the heresthetically stable set to other tournament solutions, notably the weak uncovered and refinements thereof. We find lack of vulnerability to heresthetic manipulation is contrary to many desirable properties of choice functions, notably majoritarian support.
DA - 2016/7//
PY - 2016/7//
DO - 10.1177/0951629814568398
VL - 28
IS - 3
SP - 385-407
SN - 1460-3667
KW - Banks set
KW - collective choice
KW - heresthetically stable set
KW - needing
KW - tournament solution
KW - week covering
ER -
TY - JOUR
TI - GENERALIZED SPLINES ON ARBITRARY GRAPHS
AU - Gilbert, Simcha
AU - Tymoczko, Julianna
AU - Viel, Shira
T2 - PACIFIC JOURNAL OF MATHEMATICS
AB - Let G be a graph whose edges are labeled by ideals of a commutative ring. We introduce a generalized spline, which is a vertex-labeling of G by elements of the ring so that the difference between the labels of any two adjacent vertices lies in the corresponding edge ideal. Generalized splines arise naturally in combinatorics (em algebraic splines of Billera and others) and in algebraic topology (certain equivariant cohomology rings, described by Goresky-Kottwitz-MacPherson and others). The central question of this manuscript asks when an arbitrary edge-labeled graph has nontrivial generalized splines. The answer is `always', and we prove the stronger result that generalized splines contain a free submodule whose rank is the number of vertices in G. We describe all generalized splines when G is a tree, and give several ways to describe the ring of generalized splines as an intersection of generalized splines for simpler subgraphs of G. We also present a new tool which we call the GKM matrix, an analogue of the incidence matrix of a graph, and end with open questions.
DA - 2016/4//
PY - 2016/4//
DO - 10.2140/pjm.2016.281.333
VL - 281
IS - 2
SP - 333-364
SN - 0030-8730
KW - splines
KW - GKM theory
KW - equivariant cohomology
KW - algebraic graph theory
ER -
TY - JOUR
TI - Enhanced Information Exclusion Relations
AU - Xiao, Yunlong
AU - Jing, Naihuan
AU - Li-Jost, Xianqing
T2 - SCIENTIFIC REPORTS
AB - Abstract In Hall’s reformulation of the uncertainty principle, the entropic uncertainty relation occupies a core position and provides the first nontrivial bound for the information exclusion principle. Based upon recent developments on the uncertainty relation, we present new bounds for the information exclusion relation using majorization theory and combinatoric techniques, which reveal further characteristic properties of the overlap matrix between the measurements.
DA - 2016/7/27/
PY - 2016/7/27/
DO - 10.1038/srep30440
VL - 6
SP -
SN - 2045-2322
ER -
TY - JOUR
TI - Comparison of the Windkessel model and structured-tree model applied to prescribe outflow boundary conditions for a one-dimensional arterial tree model
AU - Guan, Debao
AU - Liang, Fuyou
AU - Gremaud, Pierre A.
T2 - JOURNAL OF BIOMECHANICS
AB - One-dimensional (1D) modeling is a widely adopted approach for studying wave propagation phenomena in the arterial system. Despite the frequent use of the Windkessel (WK) model to prescribe outflow boundary conditions for 1D arterial tree models, it remains unclear to what extent the inherent limitation of the WK model in describing wave propagation in distal vasculatures affect hemodynamic variables simulated at the arterial level. In the present study, a 1D model of the arterial tree was coupled respectively with a WK boundary model and a structured-tree (ST) boundary model, yielding two types of arterial tree models. The effective resistances, compliances and inductances of the WK and ST boundary models were matched to facilitate quantitative comparisons. Obtained results showed that pressure/flow waves simulated by the two models were comparable in the aorta, whereas, their discrepancies increased towards the periphery. Wave analysis revealed that the differences in reflected waves generated by the boundary models were the major sources of pressure wave discrepancies observed in large arteries. Additional simulations performed under aging conditions demonstrated that arterial stiffening with age enlarged the discrepancies, but with the effects being partly counteracted by physiological aortic dilatation with age. These findings suggest that the method adopted for modeling the outflow boundary conditions has considerable influence on the performance of a 1D arterial tree model, with the extent of influence varying with the properties of the arterial system.
DA - 2016/6/14/
PY - 2016/6/14/
DO - 10.1016/j.jbiomech.2016.03.037
VL - 49
IS - 9
SP - 1583-1592
SN - 1873-2380
KW - One-dimensional model
KW - Arterial tree
KW - Outflow boundary conditions
KW - Windkessel model
KW - Structured-tree model
KW - Pressure wave
ER -
TY - JOUR
TI - Classification of Some Solvable Leibniz Algebras
AU - Demir, Ismail
AU - Misra, Kailash C.
AU - Stitzinger, Ernie
T2 - ALGEBRAS AND REPRESENTATION THEORY
AB - Leibniz algebras are certain generalization of Lie algebras. In this paper we give classification of non-Lie solvable (left) Leibniz algebras of dimension $\leq 8$ with one dimensional derived subalgebra. We use the canonical forms for the congruence classes of matrices of bilinear forms to obtain our result. Our approach can easily be extended to classify these algebras of higher dimensions. We also revisit the classification of three dimensional non-Lie solvable (left) Leibniz algebras.
DA - 2016/4//
PY - 2016/4//
DO - 10.1007/s10468-015-9580-5
VL - 19
IS - 2
SP - 405-417
SN - 1572-9079
KW - Leibniz algebra
KW - Solvability
KW - Nilpotency
KW - Classification
ER -
TY - JOUR
TI - A delay differential equation model of follicle waves in women
AU - Panza, Nicole M.
AU - Wright, Andrew A.
AU - Selgrade, James F.
T2 - JOURNAL OF BIOLOGICAL DYNAMICS
AB - This article presents a mathematical model for hormonal regulation of the menstrual cycle which predicts the occurrence of follicle waves in normally cycling women. Several follicles of ovulatory size that develop sequentially during one menstrual cycle are referred to as follicle waves. The model consists of 13 nonlinear, delay differential equations with 51 parameters. Model simulations exhibit a unique stable periodic cycle and this menstrual cycle accurately approximates blood levels of ovarian and pituitary hormones found in the biological literature. Numerical experiments illustrate that the number of follicle waves corresponds to the number of rises in pituitary follicle stimulating hormone. Modifications of the model equations result in simulations which predict the possibility of two ovulations at different times during the same menstrual cycle and, hence, the occurrence of dizygotic twins via a phenomenon referred to as superfecundation. Sensitive parameters are identified and bifurcations in model behaviour with respect to parameter changes are discussed. Studying follicle waves may be helpful for improving female fertility and for understanding some aspects of female reproductive ageing.
DA - 2016///
PY - 2016///
DO - 10.1080/17513758.2015.1115564
VL - 10
IS - 1
SP - 200-221
SN - 1751-3766
KW - Estradiol
KW - parameter
KW - pituitary gland
KW - superfecundation
KW - bifurcation
ER -
TY - JOUR
TI - A CONVEX ANALYSIS APPROACH TO OPTIMAL CONTROLS WITH SWITCHING STRUCTURE FOR PARTIAL DIFFERENTIAL EQUATIONS
AU - Clason, Christian
AU - Ito, Kazufumi
AU - Kunisch, Karl
T2 - ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
AB - Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality system that allows an explicit pointwise characterization and whose Moreau–Yosida regularization is amenable to a semismooth Newton method in function space. This approach is especially suited for computing switching controls for partial differential equations. In this case, the optimality gap between the original functional and its relaxation can be estimated and shown to be zero for controls with switching structure. Numerical examples illustrate the effectiveness of this approach.
DA - 2016///
PY - 2016///
DO - 10.1051/cocv/2015017
VL - 22
IS - 2
SP - 581-609
SN - 1262-3377
KW - Optimal control
KW - switching control
KW - partial differential equations
KW - nonsmooth optimization
KW - convexification
KW - semi-smooth Newton method
ER -
TY - JOUR
TI - Validation of a mathematical model for green algae (Raphidocelis Subcapitata) growth and implications for a coupled dynamical system with Daphnia magna
AU - Stemkovski, M.
AU - Baraldi, R.
AU - Flores, K. B.
AU - Banks, H. T.
T2 - Applied Sciences-Basel
DA - 2016///
PY - 2016///
VL - 6
IS - 5
ER -
TY - JOUR
TI - Universal and Overlap Cycles for Posets, Words, and Juggling Patterns
AU - King, Adam
AU - Laubmeier, Amanda
AU - Orans, Kai
AU - Godbole, Anant
T2 - GRAPHS AND COMBINATORICS
AB - We discuss results dealing with universal cycles (ucycles) and s-overlap cycles, and contribute to the body of those results by proving existence of universal cycles of naturally labeled posets (NL posets), s-overlap cycles of words of weight k, and juggling patterns. The result on posets is, to the best of our knowledge, the first demonstration of the existence of a ucycle whose length is unknown.
DA - 2016/5//
PY - 2016/5//
DO - 10.1007/s00373-015-1632-4
VL - 32
IS - 3
SP - 1013-1025
SN - 1435-5914
KW - Universal cycles
KW - Arc digraph
KW - Labeled posets
ER -
TY - JOUR
TI - TRIANGULABLE LEIBNIZ ALGEBRAS
AU - Burch, Tiffany
AU - Stitzinger, Ernie
T2 - COMMUNICATIONS IN ALGEBRA
AB - A converse to Lie's theorem for Leibniz algebras is found and generalized. The result is used to find cases in which the generalized property, called triangulable, is 2-recognizable; that is, if all 2-generated subalgebras are triangulable, then the algebra is also. Triangulability joins solvability, supersolvability, strong solvability, and nilpotentcy as a 2-recognizable property for classes of Leibniz algebras.
DA - 2016///
PY - 2016///
DO - 10.1080/00927872.2015.1085997
VL - 44
IS - 8
SP - 3622-3625
SN - 1532-4125
KW - Leibniz
KW - Lie's theorem
KW - Triangulable
KW - Two recognizable
ER -
TY - JOUR
TI - Optimization with hidden constraints and embedded Monte Carlo computations
AU - Chen, Xiaojun
AU - Kelley, C. T.
T2 - OPTIMIZATION AND ENGINEERING
AB - In this paper we explore the convergence properties of deterministic direct search methods when the objective function contains a stochastic or Monte Carlo simulation. We present new results for the case where the objective is only defined on a set with certain minimal regularity properties. We present two numerical examples to illustrate the ideas.
DA - 2016/3//
PY - 2016/3//
DO - 10.1007/s11081-015-9302-1
VL - 17
IS - 1
SP - 157-175
SN - 1573-2924
KW - Sampling methods
KW - Monte Carlo simulation
KW - Water resource policy
KW - Hidden constraints
ER -
TY - JOUR
TI - On linear conic relaxation of discrete quadratic programs
AU - Nie, Tiantian
AU - Fang, Shu-Cherng
AU - Deng, Zhibin
AU - Lavery, John E.
T2 - OPTIMIZATION METHODS & SOFTWARE
AB - A special reformulation-linearization technique based linear conic relaxation is proposed for discrete quadratic programming (DQP). We show that the proposed relaxation is tighter than the traditional positive semidefinite programming relaxation. More importantly, when the proposed relaxation problem has an optimal solution with rank one or two, optimal solutions to the original DQP problem can be explicitly generated. This rank-two property is further extended to binary quadratic optimization problems and linearly constrained DQP problems. Numerical results indicate that the proposed relaxation is capable of providing high quality and robust lower bounds for DQP.
DA - 2016/8//
PY - 2016/8//
DO - 10.1080/10556788.2015.1134528
VL - 31
IS - 4
SP - 737-754
SN - 1029-4937
KW - discrete quadratic program
KW - linear conic relaxation
KW - RLT method
ER -
TY - JOUR
TI - On analytical and numerical approaches to division and label structured population models
AU - Banks, H. T.
AU - Flores, Kevin B.
AU - Sindi, Suzanne S.
T2 - APPLIED MATHEMATICS LETTERS
AB - Even among cells in the same population, the concentration of a protein or cellular constituent can vary considerably. This heterogeneity can arise from several sources, including differences in kinetic rates between cells and distribution of cellular constituents through cell division. Compartmental models have been used to describe the distribution of the number of divisions undergone by cells in a population. More recently, such models have been coupled with the dynamics of intracellular labels and analytical solutions to the division and label structured population equations have been found. However, such approaches have thus far focused on simple models of intracellular dynamics such as the decay of an intracellular label. In this work, we demonstrate that analytical solutions are possible for more general forms of intracellular dynamics offering the promise to lend mathematical insight into population dynamics in more realistic biological settings.
DA - 2016/10//
PY - 2016/10//
DO - 10.1016/j.aml.2016.04.009
VL - 60
SP - 81-88
SN - 0893-9659
KW - Division-structured population model
KW - Heterogeneous cell populations
KW - Protein dynamics
ER -
TY - JOUR
TI - Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits
AU - Maiden, Michelle D.
AU - Lowman, Nicholas K.
AU - Anderson, Dalton V.
AU - Schubert, Marika E.
AU - Hoefer, Mark A.
T2 - PHYSICAL REVIEW LETTERS
AB - Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here we report on a novel dispersive hydrodynamics testbed: the effectively frictionless dynamics of interfacial waves between two high contrast, miscible, low Reynolds' number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening while normal stresses give rise to dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multi-phase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.
DA - 2016/4/28/
PY - 2016/4/28/
DO - 10.1103/physrevlett.116.174501
VL - 116
IS - 17
SP -
SN - 1079-7114
ER -
TY - JOUR
TI - Integrating Transgenic Vector Manipulation with Clinical Interventions to Manage Vector-Borne Diseases
AU - Okamoto, Kenichi W.
AU - Gould, Fred
AU - Lloyd, Alun L.
T2 - PLOS Computational Biology
AB - Many vector-borne diseases lack effective vaccines and medications, and the limitations of traditional vector control have inspired novel approaches based on using genetic engineering to manipulate vector populations and thereby reduce transmission. Yet both the short- and long-term epidemiological effects of these transgenic strategies are highly uncertain. If neither vaccines, medications, nor transgenic strategies can by themselves suffice for managing vector-borne diseases, integrating these approaches becomes key. Here we develop a framework to evaluate how clinical interventions (i.e., vaccination and medication) can be integrated with transgenic vector manipulation strategies to prevent disease invasion and reduce disease incidence. We show that the ability of clinical interventions to accelerate disease suppression can depend on the nature of the transgenic manipulation deployed (e.g., whether vector population reduction or replacement is attempted). We find that making a specific, individual strategy highly effective may not be necessary for attaining public-health objectives, provided suitable combinations can be adopted. However, we show how combining only partially effective antimicrobial drugs or vaccination with transgenic vector manipulations that merely temporarily lower vector competence can amplify disease resurgence following transient suppression. Thus, transgenic vector manipulation that cannot be sustained can have adverse consequences—consequences which ineffective clinical interventions can at best only mitigate, and at worst temporarily exacerbate. This result, which arises from differences between the time scale on which the interventions affect disease dynamics and the time scale of host population dynamics, highlights the importance of accounting for the potential delay in the effects of deploying public health strategies on long-term disease incidence. We find that for systems at the disease-endemic equilibrium, even modest perturbations induced by weak interventions can exhibit strong, albeit transient, epidemiological effects. This, together with our finding that under some conditions combining strategies could have transient adverse epidemiological effects suggests that a relatively long time horizon may be necessary to discern the efficacy of alternative intervention strategies.
DA - 2016/3/10/
PY - 2016/3/10/
DO - 10.1371/journal.pcbi.1004695
VL - 12
IS - 3
SP - e1004695
J2 - PLoS Comput Biol
LA - en
OP -
SN - 1553-7358
UR - http://dx.doi.org/10.1371/journal.pcbi.1004695
DB - Crossref
ER -
TY - JOUR
TI - Fine numerical analysis of the crack-tip position for a Mumford-Shah minimizer
AU - Li, Zhilin
AU - Mikayelyan, Hayk
T2 - INTERFACES AND FREE BOUNDARIES
AB - A new algorithm to determine the position of the crack (discontinuity set) of certain minimizers of Mumford-Shah functional in situations when a crack-tip occurs is introduced. The conformal mapping $w=\sqrt{z}$ in the complex plane is used to transform the free discontinuity problem to a new type of free boundary problem, where the symmetry of the free boundary is an additional constraint of a non-local nature. Instead of traditional Jacobi or Newton iterative methods, we propose a simple iteration method which does not need the Jacobian but is way fast than the Jacobi iteration. In each iteration, a Laplace equation needs to be solved on an irregular domain with a Dirichlet boundary condition on the fixed part of the boundary; and a Neumann type boundary condition along the free boundary. The augmented immersed interface method is employed to solve the potential problem. The numerical results agree with the analytic analysis and provide insight into some open questions in free discontinuity problems.
DA - 2016///
PY - 2016///
DO - 10.4171/ifb/357
VL - 18
IS - 1
SP - 75-90
SN - 1463-9971
KW - Free discontinuity
KW - free boundary
KW - crack-tip
KW - Mumford-Shah energy
KW - augmented immersed interface method
KW - fast/Poisson solver
KW - irregular domain
ER -
TY - JOUR
TI - EXTENDING THE LATENT MULTINOMIAL MODEL WITH COMPLEX ERROR PROCESSES AND DYNAMIC MARKOV BASES
AU - Bonner, Simon J.
AU - Schofield, Matthew R.
AU - Noren, Patrik
AU - Price, Steven J.
T2 - ANNALS OF APPLIED STATISTICS
AB - The latent multinomial model (LMM) of Link et al. [Biometrics 66 (2010) 178–185] provides a framework for modelling mark-recapture data with potential identification errors. Key is a Markov chain Monte Carlo (MCMC) scheme for sampling configurations of the latent counts of the true capture histories that could have generated the observed data. Assuming a linear map between the observed and latent counts, the MCMC algorithm uses vectors from a basis of the kernel to move between configurations of the latent data. Schofield and Bonner [Biometrics 71 (2015) 1070–1080] shows that this is sufficient for some models within the framework but that a larger set called a Markov basis is required when errors are more complex. We address two further challenges: (1) that models with complex error mechanisms may not fit within the LMM framework and (2) that Markov bases can be difficult to compute for studies of even moderate size. We extend the framework to model the capture/demographic and error processes separately and develop a new MCMC algorithm using dynamic Markov bases. Our work is motivated by a study of queen snakes (Regina septemvittata) and we use simulation to compare estimates of survival rates when snakes are marked with PIT tags which have perfect identification versus brands which are prone to error.
DA - 2016/3//
PY - 2016/3//
DO - 10.1214/15-aoas889
VL - 10
IS - 1
SP - 246-263
SN - 1932-6157
KW - Bayesian inference
KW - Markov basis
KW - Markov chain Monte Carlo
KW - mark-recapture
KW - misidentification
KW - queen snake (Regina septemvittata)
ER -
TY - JOUR
TI - An upper bound of fully entangled fraction of mixed states
AU - Huang, X. F.
AU - Jing, Naihuan
AU - Zhang, T. G.
T2 - Communications in Theoretical Physics
AB - We study the fully entangled fraction of a quantum state. An upper bound is obtained for arbitrary bipartite system. This upper bound only depends on the Frobenius norm of the state.
DA - 2016///
PY - 2016///
DO - 10.1088/0253-6102/65/6/701
VL - 65
IS - 6
SP - 701–704
ER -
TY - JOUR
TI - A note on the path interval distance
AU - Coons, Jane Ivy
AU - Rusinko, Joseph
T2 - JOURNAL OF THEORETICAL BIOLOGY
AB - The path interval distance accounts for global congruence between locally incongruent trees. We show that the path interval distance provides a lower bound for the nearest neighbor interchange distance. In contrast to the Robinson-Foulds distance, random pairs of trees are unlikely to be maximally distant from one another under the path interval distance. These features indicate that the path interval distance should play a role in phylogenomics where the comparison of trees on a fixed set of taxa is becoming increasingly important.
DA - 2016/6/7/
PY - 2016/6/7/
DO - 10.1016/j.jtbi.2016.03.027
VL - 398
SP - 145-149
SN - 1095-8541
KW - Tree metrics
KW - Phylogenetics
KW - Cophylogenetics
ER -
TY - JOUR
TI - A Sparse Grid Stochastic Collocation Method for Elliptic Interface Problems with Random Input
AU - Zhang, Qian
AU - Li, Zhilin
AU - Zhang, Zhiyue
T2 - JOURNAL OF SCIENTIFIC COMPUTING
DA - 2016/4//
PY - 2016/4//
DO - 10.1007/s10915-015-0080-x
VL - 67
IS - 1
SP - 262-280
SN - 1573-7691
KW - Sparse grids
KW - Stochastic inputs
KW - Interface
KW - Immersed finite element
KW - Smolyak construction
ER -
TY - JOUR
TI - Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis
AU - Fancher, Chris M.
AU - Han, Zhen
AU - Levin, Igor
AU - Page, Katharine
AU - Reich, Brian J.
AU - Smith, Ralph C.
AU - Wilson, Alyson G.
AU - Jones, Jacob L.
T2 - Scientific Reports
AB - A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method.
DA - 2016/8//
PY - 2016/8//
DO - 10.1038/srep31625
VL - 6
IS - 1
J2 - Sci Rep
LA - en
OP -
SN - 2045-2322
UR - http://dx.doi.org/10.1038/srep31625
DB - Crossref
ER -
TY - JOUR
TI - Uniform Entanglement Frames
AU - Xiao, Yunlong
AU - Jing, Naihuan
AU - Li-Jost, Xianqing
AU - Fei, Shao-Ming
T2 - INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
AB - We present several criteria for genuine multipartite entanglement from universal uncertainty relations based on majorization theory. Under non-negative Schur-concave functions, the vector-type uncertainty relation generates a family of infinitely many detectors to check genuine multipartite entanglement. We also introduce the concept of $k$-separable circles via geometric distance for probability vectors, which include at most $(k-1)$-separable states. The entanglement witness is also generalized to a universal entanglement witness which is able to detect the $k$-separable states more accurately.
DA - 2016/8//
PY - 2016/8//
DO - 10.1007/s10773-016-2976-0
VL - 55
IS - 8
SP - 3492-3505
SN - 1572-9575
KW - Entanglement detector
KW - Genuine entanglement
KW - Majorization
KW - Universal uncertainty relations
ER -
TY - JOUR
TI - The immersed finite volume element method for some interface problems with nonhomogeneous jump conditions
AU - Zhu, L.
AU - Zhang, Z. Y.
AU - Li, Z. L.
T2 - International Journal of Numerical Analysis and Modeling
DA - 2016///
PY - 2016///
VL - 13
IS - 3
SP - 368-382
ER -
TY - JOUR
TI - Isomorphy classes of involutions of SP(2n, k), n > 2 (vol 25, pg 903, 2015)
AU - Benim, R. W.
AU - Helminck, A. G.
AU - Ward, F. J.
T2 - Journal of Lie Theory
DA - 2016///
PY - 2016///
VL - 26
IS - 1
SP - 293-295
ER -
TY - JOUR
TI - In celebration of the 60th birthday of Professor Alemdar Hasanoglu (Hasanov)
AU - Andreev, V. B.
AU - Banks, H. T.
AU - Dulikravich, G. S.
AU - Hofmann, B.
AU - Kabanikhin, S. I.
AU - Kuchuk, F. J.
AU - Lesnic, D.
AU - Nashed, M. Z.
AU - Neubauer, A.
AU - Romanov, V. G.
AU - Slodicka, M.
AU - Vasin, V. V.
AU - Yagola, A. G.
AU - Zirilli, F.
T2 - Journal of Inverse and Ill-Posed Problems
DA - 2016///
PY - 2016///
VL - 24
IS - 2
SP - 109-110
ER -
TY - JOUR
TI - Expansion shock waves in regularized shallow-water theory
AU - El, Gennady A.
AU - Hoefer, Mark A.
AU - Shearer, Michael
T2 - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
AB - We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularised shallow water equations that include the Benjamin-Bona-Mahoney (BBM) and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock.
DA - 2016/5//
PY - 2016/5//
DO - 10.1098/rspa.2016.0141
VL - 472
IS - 2189
SP - 20160141
J2 - Proc. R. Soc. A
LA - en
OP -
SN - 1364-5021 1471-2946
UR - http://dx.doi.org/10.1098/rspa.2016.0141
DB - Crossref
KW - Lax entropy condition
KW - non-local dispersion
KW - Benjamin-Bona-Mahony equation
KW - Boussinesq equations
ER -
TY - JOUR
TI - Combinatorial Frameworks for Cluster Algebras
AU - Reading, Nathan
AU - Speyer, David E.
T2 - INTERNATIONAL MATHEMATICS RESEARCH NOTICES
AB - We develop a general approach to finding combinatorial models for cluster algebras. The approach is to construct a labeled graph called a framework. When a framework is constructed with certain properties, the result is a model incorporating information about exchange matrices, principal coefficients, g-vectors, and g-vector fans. The idea behind frameworks arises from Cambrian combinatorics and sortable elements, and in this paper, we use sortable elements to construct a framework for any cluster algebra with an acyclic initial exchange matrix. This Cambrian framework yields a model of the entire exchange graph when the cluster algebra is of finite type. Outside of finite type, the Cambrian framework models only part of the exchange graph. In a forthcoming paper, we extend the Cambrian construction to produce a complete framework for a cluster algebra whose associated Cartan matrix is of affine type.
DA - 2016///
PY - 2016///
DO - 10.1093/imrn/rnv101
VL - 2016
IS - 1
SP - 109-173
SN - 1687-0247
UR - https://doi.org/10.1093/imrn/rnv101
ER -
TY - JOUR
TI - An augmented iim for helmholtz/poisson equations on irregular domains in complex space
AU - Zhang, S. D. M.
AU - Li, Z. L.
T2 - International Journal of Numerical Analysis and Modeling
DA - 2016///
PY - 2016///
VL - 13
IS - 1
SP - 166-178
ER -
TY - JOUR
TI - An augmented Cartesian grid method for Stokes-Darcy fluid-structure interactions
AU - Li, Zhilin
T2 - INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
AB - Summary
A new finite difference method based on Cartesian meshes is proposed for solving the fluid–structure interaction between a fluid flow modeled by the Stokes equations and a porous media modeled by the Darcy's law. The idea is to introduce several augmented variables along the interface between the fluid flow and the porous media so that the problem can be decoupled as several Poisson equations. The augmented variables should be chosen so that the Beavers–Joseph–Saffman and other interface conditions are satisfied. In the discretization, the augmented variables have co-dimension one compared with that of the primitive variables and are solved through the Schur complement system. A non-trivial analytic solution with a circular interface is constructed to check second-order convergency of the proposed method. Numerical examples with various interfaces and parameters are also presented. Some simulations show interesting behaviors of the fluid–structure interaction between the fluid flow and the porous media. The computational framework can be applied to other multi-phase and multi-physics problems. Copyright © 2015 John Wiley & Sons, Ltd.
DA - 2016/5/18/
PY - 2016/5/18/
DO - 10.1002/nme.5131
VL - 106
IS - 7
SP - 556-575
SN - 1097-0207
KW - Stokes-Darcy fluid-structure interaction
KW - augmented immersed interface method
KW - fast Poisson solver
KW - BJS interface condition
KW - analytic solution of Stokes and Darcy coupling
ER -
TY - JOUR
TI - AN ADAPTIVE FEEDBACK METHODOLOGY FOR DETERMINING INFORMATION CONTENT IN STABLE POPULATION STUDIES
AU - Banks, H. T.
AU - Banks, John E.
AU - Everett, R. A.
AU - Stark, John D.
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - We develop statistical and mathematical based methodologies for determining (as the experiment progresses) the amount of information required to complete the estimation of stable population parameters with pre-specified levels of confidence. We do this in the context of life table models and data for growth/death for three species of Daphniids as investigated by J. Stark and J. Banks [17]. The ideas developed here also have wide application in the health and social sciences where experimental data are often expensive as well as difficult to obtain.
DA - 2016/8//
PY - 2016/8//
DO - 10.3934/mbe.2016013
VL - 13
IS - 4
SP - 653-671
SN - 1551-0018
KW - Demographic data
KW - inverse problem
KW - ordinary least squares
KW - information content
KW - adaptive feedback
ER -
TY - JOUR
TI - Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing Karhunen-Loeve expansion
AU - Saibaba, Arvind K.
AU - Lee, Jonghyun
AU - Kitanidis, Peter K.
T2 - NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
AB - We describe randomized algorithms for computing the dominant eigenmodes of the generalized Hermitian eigenvalue problem Ax = λBx, with A Hermitian and B Hermitian and positive definite. The algorithms we describe only require forming operations Ax,Bx and B−1x and avoid forming square roots of B (or operations of the form, B1/2x or B−1/2x). We provide a convergence analysis and a posteriori error bounds and derive some new results that provide insight into the accuracy of the eigenvalue calculations. The error analysis shows that the randomized algorithm is most accurate when the generalized singular values of B−1A decay rapidly. A randomized algorithm for the generalized singular value decomposition is also provided. Finally, we demonstrate the performance of our algorithm on computing an approximation to the Karhunen–Loève expansion, which involves a computationally intensive generalized Hermitian eigenvalue problem with rapidly decaying eigenvalues. Copyright © 2015 John Wiley & Sons, Ltd.
DA - 2016/3//
PY - 2016/3//
DO - 10.1002/nla.2026
VL - 23
IS - 2
SP - 314-339
SN - 1099-1506
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84956611207&partnerID=MN8TOARS
KW - randomized algorithms
KW - generalized Hermitian eigenvalue problems
KW - Karhunen-Loeve expansion
ER -
TY - JOUR
TI - On the first degree Fejer-Riesz factorization and its applications to X plus A*X(-1)A = Q
AU - Chu, Moody T.
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - Given a Laurent polynomial with matrix coefficients that is positive semi-definite over the unit circle in the complex plane, the Fejér–Riesz theorem asserts that it can always be factorized as the product of a polynomial with matrix coefficients and its adjoint. This paper exploits such a factorization in its simplest form of degree one and its relationship with the nonlinear matrix equation X + A ⁎ X − 1 A = Q . In particular, the nonlinear equation can be recast as a linear Sylvester equation subject to unitary constraint. The Sylvester equation is readily obtainable from hermitian eigenvalue computation. The unitary constraint can be enforced by a hybrid of a straightforward alternating projection for low precision estimation and a coordinate-free Newton iteration for high precision calculation. This approach offers a complete parametrization of all solutions and, in contrast to most existent algorithms, makes it possible to find all solutions if so desired.
DA - 2016/1/15/
PY - 2016/1/15/
DO - 10.1016/j.laa.2015.09.051
VL - 489
SP - 123-143
SN - 1873-1856
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84945151931&partnerID=MN8TOARS
KW - Fejer-Riesz factorization
KW - Nonlinear matrix equation
KW - Alternating projection method
KW - Coordinate-free Newton method
ER -
TY - JOUR
TI - On the commutative quotient of Fomin-Kirillov algebras
AU - Liu, Ricky Ini
T2 - EUROPEAN JOURNAL OF COMBINATORICS
AB - The Fomin–Kirillov algebra En is a noncommutative algebra with a generator for each edge of the complete graph on n vertices. For any graph G on n vertices, let EG be the subalgebra of En generated by the edges in G. We show that the commutative quotient of EG is isomorphic to the Orlik–Terao algebra of G. As a consequence, the Hilbert series of this quotient is given by (−t)nχG(−t−1), where χG is the chromatic polynomial of G. We also give a reduction algorithm for the graded components of EG that do not vanish in the commutative quotient and show that their structure is described by the combinatorics of noncrossing forests.
DA - 2016/5//
PY - 2016/5//
DO - 10.1016/j.ejc.2015.12.003
VL - 54
SP - 65-75
SN - 1095-9971
ER -
TY - JOUR
TI - Geometric transformations of multidimensional color images based on NASS
AU - Fan, Ping
AU - Zhou, Ri-Gui
AU - Jing, Naihuan
AU - Li, Hai-Sheng
T2 - INFORMATION SCIENCES
AB - We present quantum algorithms to realize geometric transformations (two-point swappings, symmetric flips, local flips, orthogonal rotations, and translations) based on an $n$-qubit normal arbitrary superposition state (NASS). These transformations are implemented using quantum circuits consisting of basic quantum gates, which are constructed with polynomial numbers of single-qubit and two-qubit gates. Complexity analysis shows that the global operators (symmetric flips, local flips, orthogonal rotations) can be implemented with $O(n)$ gates. The proposed geometric transformations are used to facilitate applications of quantum images with low complexity.
DA - 2016/5/1/
PY - 2016/5/1/
DO - 10.1016/j.ins.2015.12.024
VL - 340
SP - 191-208
SN - 1872-6291
KW - Geometric transformations
KW - Quantum image processing
KW - Quantum circuits
KW - Quantum computing
ER -
TY - JOUR
TI - Development of a human physiologically based pharmacokinetic (PBPK) model for dermal permeability for lindane
AU - Sawyer, Megan E.
AU - Evans, Marina V.
AU - Wilson, Charles A.
AU - Beesley, Lauren J.
AU - Leon, Lider S.
AU - Eklund, Chris R.
AU - Croom, Edward L.
AU - Pegram, Rex A.
T2 - TOXICOLOGY LETTERS
AB - Lindane is a neurotoxicant used for the treatment of lice and scabies present on human skin. Due to its pharmaceutical application, an extensive pharmacokinetic database exists in humans. Mathematical diffusion models allow for calculation of lindane skin permeability coefficients using human kinetic data obtained from in vitro and in vivo experimentation as well as a default compound-specific calculation based on physicochemical characteristics used in the absence of kinetic data. A dermal model was developed to describe lindane diffusion into the skin, where the skin compartment consisted of homogeneous dermal tissue. This study utilized Fick's law of diffusion along with chemical binding to protein and lipids to determine appropriate dermal absorption parameters which were then incorporated into a physiologically based pharmacokinetic (PBPK) model to describe in vivo kinetics. The estimation of permeability coefficients using chemical binding in combination with in vivo data demonstrates the advantages of combining physiochemical properties with a PBPK model to predict dermal absorption.
DA - 2016/3/14/
PY - 2016/3/14/
DO - 10.1016/j.toxlet.2016.01.008
VL - 245
SP - 106-109
SN - 1879-3169
KW - PBPK
KW - Lindane
KW - Dermal permeability
ER -
TY - JOUR
TI - Computational model of the fathead minnow hypothalamic–pituitary–gonadal axis: Incorporating protein synthesis in improving predictability of responses to endocrine active chemicals
AU - Breen, Miyuki
AU - Villeneuve, Daniel L.
AU - Ankley, Gerald T.
AU - Bencic, David
AU - Breen, Michael S.
AU - Watanabe, Karen H.
AU - Lloyd, Alun L.
AU - Conolly, Rory B.
T2 - Comparative Biochemistry and Physiology Part C: Toxicology & Pharmacology
AB - There is international concern about chemicals that alter endocrine system function in humans and/or wildlife and subsequently cause adverse effects. We previously developed a mechanistic computational model of the hypothalamic-pituitary-gonadal (HPG) axis in female fathead minnows exposed to a model aromatase inhibitor, fadrozole (FAD), to predict dose-response and time-course behaviors for apical reproductive endpoints. Initial efforts to develop a computational model describing adaptive responses to endocrine stress providing good fits to empirical plasma 17β-estradiol (E2) data in exposed fish were only partially successful, which suggests that additional regulatory biology processes need to be considered. In this study, we addressed short-comings of the previous model by incorporating additional details concerning CYP19A (aromatase) protein synthesis. Predictions based on the revised model were evaluated using plasma E2 concentrations and ovarian cytochrome P450 (CYP) 19A aromatase mRNA data from two fathead minnow time-course experiments with FAD, as well as from a third 4-day study. The extended model provides better fits to measured E2 time-course concentrations, and the model accurately predicts CYP19A mRNA fold changes and plasma E2 dose-response from the 4-d concentration-response study. This study suggests that aromatase protein synthesis is an important process in the biological system to model the effects of FAD exposure.
DA - 2016/5//
PY - 2016/5//
DO - 10.1016/j.cbpc.2016.02.002
VL - 183-184
SP - 36-45
J2 - Comparative Biochemistry and Physiology Part C: Toxicology & Pharmacology
LA - en
OP -
SN - 1532-0456
UR - http://dx.doi.org/10.1016/j.cbpc.2016.02.002
DB - Crossref
KW - Adaptation
KW - Computational model
KW - Endocrine disrupting chemicals
KW - Fadrozole
KW - Fish
KW - Hypothalamic-pituitary-gonadal axis
KW - Protein synthesis
KW - Toxicology
ER -
TY - JOUR
TI - Acoustic sequences in non-human animals: a tutorial review and prospectus
AU - Kershenbaum, Arik
AU - Blumstein, Daniel T.
AU - Roch, Marie A.
AU - Akcay, Caglar
AU - Backus, Gregory
AU - Bee, Mark A.
AU - Bohn, Kirsten
AU - Cao, Yan
AU - Carter, Gerald
AU - Caesar, Cristiane
AU - Coen, Michael
AU - DeRuiter, Stacy L.
AU - Doyle, Laurance
AU - Edelman, Shimon
AU - Ferrer-i-Cancho, Ramon
AU - Freeberg, Todd M.
AU - Garland, Ellen C.
AU - Gustison, Morgan
AU - Harley, Heidi E.
AU - Huetz, Chloe
AU - Hughes, Melissa
AU - Bruno, Julia Hyland
AU - Ilany, Amiyaal
AU - Jin, Dezhe Z.
AU - Johnson, Michael
AU - Ju, Chenghui
AU - Karnowski, Jeremy
AU - Lohr, Bernard
AU - Manser, Marta B.
AU - McCowan, Brenda
AU - Mercado, Eduardo, III
AU - Narins, Peter M.
AU - Piel, Alex
AU - Rice, Megan
AU - Salmi, Roberta
AU - Sasahara, Kazutoshi
AU - Sayigh, Laela
AU - Shiu, Yu
AU - Taylor, Charles
AU - Vallejo, Edgar E.
AU - Waller, Sara
AU - Zamora-Gutierrez, Veronica
T2 - BIOLOGICAL REVIEWS
AB - Animal acoustic communication often takes the form of complex sequences, made up of multiple distinct acoustic units. Apart from the well-known example of birdsong, other animals such as insects, amphibians, and mammals (including bats, rodents, primates, and cetaceans) also generate complex acoustic sequences. Occasionally, such as with birdsong, the adaptive role of these sequences seems clear (e.g. mate attraction and territorial defence). More often however, researchers have only begun to characterise - let alone understand - the significance and meaning of acoustic sequences. Hypotheses abound, but there is little agreement as to how sequences should be defined and analysed. Our review aims to outline suitable methods for testing these hypotheses, and to describe the major limitations to our current and near-future knowledge on questions of acoustic sequences. This review and prospectus is the result of a collaborative effort between 43 scientists from the fields of animal behaviour, ecology and evolution, signal processing, machine learning, quantitative linguistics, and information theory, who gathered for a 2013 workshop entitled, 'Analysing vocal sequences in animals'. Our goal is to present not just a review of the state of the art, but to propose a methodological framework that summarises what we suggest are the best practices for research in this field, across taxa and across disciplines. We also provide a tutorial-style introduction to some of the most promising algorithmic approaches for analysing sequences. We divide our review into three sections: identifying the distinct units of an acoustic sequence, describing the different ways that information can be contained within a sequence, and analysing the structure of that sequence. Each of these sections is further subdivided to address the key questions and approaches in that area. We propose a uniform, systematic, and comprehensive approach to studying sequences, with the goal of clarifying research terms used in different fields, and facilitating collaboration and comparative studies. Allowing greater interdisciplinary collaboration will facilitate the investigation of many important questions in the evolution of communication and sociality.
DA - 2016/2//
PY - 2016/2//
DO - 10.1111/brv.12160
VL - 91
IS - 1
SP - 13-52
SN - 1469-185X
KW - acoustic communication
KW - information
KW - information theory
KW - machine learning
KW - Markov model
KW - meaning
KW - network analysis
KW - sequence analysis
KW - vocalisation
ER -
TY - JOUR
TI - Weighted Uncertainty Relations
AU - Xiao, Yunlong
AU - Jing, Naihuan
AU - Li-Jost, Xianqing
AU - Fei, Shao-Ming
T2 - SCIENTIFIC REPORTS
AB - Recently, Maccone and Pati have given two stronger uncertainty relations based on the sum of variances and one of them is nontrivial when the quantum state is not an eigenstate of the sum of the observables. We derive a family of weighted uncertainty relations to provide an optimal lower bound for all situations and remove the restriction on the quantum state. Generalization to multi-observable cases is also given and an optimal lower bound for the weighted sum of the variances is obtained in general quantum situation.
DA - 2016/3/17/
PY - 2016/3/17/
DO - 10.1038/srep23201
VL - 6
SP -
SN - 2045-2322
ER -
TY - JOUR
TI - The entry-exit function and geometric singular perturbation theory
AU - De Maesschalck, Peter
AU - Schecter, Stephen
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - For small ε>0, the system x˙=ε, z˙=h(x,z,ε)z, with h(x,0,0)<0 for x<0 and h(x,0,0)>0 for x>0, admits solutions that approach the x-axis while x<0 and are repelled from it when x>0. The limiting attraction and repulsion points are given by the well-known entry–exit function. For h(x,z,ε)z replaced by h(x,z,ε)z2, we explain this phenomenon using geometric singular perturbation theory. We also show that the linear case can be reduced to the quadratic case, and we discuss the smoothness of the return map to the line z=z0, z0>0, in the limit ε→0.
DA - 2016/4/15/
PY - 2016/4/15/
DO - 10.1016/j.jde.2016.01.008
VL - 260
IS - 8
SP - 6697-6715
SN - 1090-2732
KW - Entry-exit function
KW - Geometric singular perturbation theory
KW - Bifurcation delay
KW - Blow-up
KW - Turning point
ER -
TY - JOUR
TI - Special issue on the conference ISSAC 2014: Symbolic computation and computer algebra Foreword
AU - Nagasaka, Kosaku
AU - Szanto, Agnes
AU - Winkler, Franz
T2 - JOURNAL OF SYMBOLIC COMPUTATION
DA - 2016///
PY - 2016///
DO - 10.1016/j.jsc.2015.10.002
VL - 75
SP - 1-3
SN - 0747-7171
ER -
TY - JOUR
TI - Sparse multivariate function recovery with a small number of evaluations
AU - Kaltofen, Erich L.
AU - Yang, Zhengfeng
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - In Kaltofen and Yang (2014) we give an algorithm based algebraic error-correcting decoding for multivariate sparse rational function interpolation from evaluations that can be numerically inaccurate and where several evaluations can have severe errors (“outliers”). Our 2014 algorithm can interpolate a sparse multivariate rational function from evaluations where the error rate 1/q is quite high, say q=5. For the algorithm with exact arithmetic and exact values at non-erroneous points, one avoids quadratic oversampling by using random evaluation points. Here we give the full probabilistic analysis for this fact, thus providing the missing proof to Theorem 2.1 in Section 2 of our ISSAC 2014 paper. Our argumentation already applies to our original 2007 sparse rational function interpolation algorithm (Kaltofen et al., 2007), where we have experimentally observed that for T unknown non-zero coefficients in a sparse candidate ansatz one only needs T+O(1) evaluations rather than O(T2) (cf. Candès and Tao sparse sensing), the latter of which we have proved in 2007. Here we prove that T+O(1) evaluations at random points indeed suffice.
DA - 2016///
PY - 2016///
DO - 10.1016/j.jsc.2015.11.015
VL - 75
SP - 209-218
SN - 0747-7171
KW - Error correcting coding
KW - Fault tolerance
KW - Cauchy interpolation
KW - Multivariate rational function model
ER -
TY - JOUR
TI - Solving the Helmholtz equation for general smooth geometry using simple grids
AU - Medvinsky, M.
AU - Tsynkov, S.
AU - Turkel, E.
T2 - Wave Motion
AB - The method of difference potentials was originally proposed by Ryaben’kii, and is a generalized discrete version of the method of Calderon’s operators. It handles non-conforming curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity of the solver at the level of a finite-difference scheme on a regular structured grid. Compact finite difference schemes enable high order accuracy on small stencils and so require no additional boundary conditions beyond those needed for the differential equation itself. Previously, we have used difference potentials combined with compact schemes for solving transmission/scattering problems in regions of a simple shape. In this paper, we generalize our previous work to incorporate smooth general shaped boundaries and interfaces, including a formulation that involves multiple scattering.
DA - 2016/4//
PY - 2016/4//
DO - 10.1016/j.wavemoti.2015.12.004
VL - 62
SP - 75-97
J2 - Wave Motion
LA - en
OP -
SN - 0165-2125
UR - http://dx.doi.org/10.1016/j.wavemoti.2015.12.004
DB - Crossref
KW - Difference potentials
KW - Boundary projections
KW - Calderon's operators
KW - Curvilinear boundaries
KW - High order compact differencing
KW - Multiple scattering
ER -
TY - JOUR
TI - Root Multiplicities of the Indefinite Kac-Moody Algebra HDn(1)
AU - Misra, Kailash C.
AU - Wilson, Evan A.
T2 - COMMUNICATIONS IN ALGEBRA
AB - In this article, we study the root multiplicities of the indefinite type Kac–Moody algebra . We obtain the multiplicities of infinite family of roots and conjecture that they are polynomials in n of certain degree. Our approach is to view the roots of as weights of certain integrable -modules and then use the path realization of crystal bases for these modules and Kang's multiplicity formula to find their multiplicities. In particular, we prove that mult(−2α−1 − kδ) is a polynomial in n of degree k. We observe that Frenkel's conjectured root multiplicity bound holds in this case.
DA - 2016///
PY - 2016///
DO - 10.1080/00927872.2015.1027369
VL - 44
IS - 4
SP - 1599-1614
SN - 1532-4125
KW - Crystal bases
KW - Kac-Moody algebras
KW - Quantum groups
ER -
TY - JOUR
TI - Real quantifier elimination for the synthesis of optimal numerical algorithms (Case study: Square root computation)
AU - Erascu, Madalina
AU - Hong, Hoon
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We report on our 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 x and its width is less than or equal to ε. A typical numerical algorithm starts with an initial interval and repeatedly updates it by applying a “refinement map” on it until it becomes narrow enough. Thus the synthesis amounts to finding a refinement map that ensures the correctness and optimality of the resulting algorithm. This problem can be formulated as a real quantifier elimination. Hence, in principle, the synthesis can be carried out automatically. However, the computational requirement is huge, making the automatic synthesis practically impossible with the current general real quantifier elimination software. We overcame the difficulty by (1) carefully reducing a complicated quantified formula into several simpler ones and (2) automatically eliminating the quantifiers from the resulting ones using the state-of-the-art quantifier elimination software. As the result, we were able to synthesize semi-automatically an optimal quadratically1 convergent map, which is better than the well known hand-crafted Secant-Newton map. Interestingly, the optimal synthesized map is not contracting as one would naturally expect.
DA - 2016///
PY - 2016///
DO - 10.1016/j.jsc.2015.11.010
VL - 75
SP - 110-126
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2015.11.010
KW - Synthesis
KW - Optimal quadratically convergent algorithm
KW - Square root
KW - Real quantifier elimination
ER -
TY - JOUR
TI - Periodic behaviour of nonlinear, second-order discrete dynamical systems
AU - Maroncelli, Daniel
AU - Rodriguezb, Jesus
T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
AB - In this work we provide conditions for the existence of periodic solutions to nonlinear, second-order difference equations of the form \begin{equation*} y(t+2)+by(t+1)+cy(t)=g(t,y(t)) \end{equation*} where $c\neq 0$, and $g:\mathbb{Z}^+\times\mathbb{R}\to \mathbb{R}$ is continuous and periodic in $t$. Our analysis uses the Lyapunov-Schmidt reduction in combination with fixed point methods and topological degree theory.
DA - 2016///
PY - 2016///
DO - 10.1080/10236198.2015.1083016
VL - 22
IS - 2
SP - 280-294
SN - 1563-5120
KW - Periodic difference equations
KW - resonance
KW - Lyapunov-Schmidt procedure
KW - Schauder's fixed point theorem
KW - topological degree
ER -
TY - JOUR
TI - On the computation of the parameterized differential Galois group for a second-order linear differential equation with differential parameters
AU - Arreche, Carlos E.
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We present algorithms to compute the differential Galois group G associated via the parameterized Picard–Vessiot theory to a parameterized second-order linear differential equation∂2∂x2Y+r1∂∂xY+r0Y=0, where the coefficients r1 and r0 belong to the field of rational functions F(x) over a computable Π-field F of characteristic zero, and the finite set of commuting derivations Π is thought of as consisting of derivations with respect to parameters. This work relies on earlier procedures developed by Dreyfus and by the present author to compute G under the assumption that r1=0, which guarantees that G is unimodular. When r1≠0, we reinterpret a classical change-of-variables procedure in Galois-theoretic terms in order to reduce the computation of G to the computation of an associated unimodular differential Galois group H. We establish a parameterized version of the Kolchin–Ostrowski theorem and apply it to give more direct proofs than those found in the literature of the fact that the required computations can be performed effectively. We then extract from these algorithms a complete set of criteria to decide whether any of the solutions to a parameterized second-order linear differential equation is Π-transcendental over the underlying Π-field of F(x). We give various examples of computation and some applications to differential transcendence.
DA - 2016///
PY - 2016///
DO - 10.1016/j.jsc.2015.11.006
VL - 75
SP - 25-55
SN - 0747-7171
KW - Parameterized differential equation
KW - Parameterized Picard-Vessiot theory
KW - Linear differential algebraic group
KW - Unipotent radical
KW - Creative telescoping
ER -
TY - JOUR
TI - On finite-dimensional representations of two-parameter quantum affine algebras
AU - Jing, Naihuan
AU - Zhang, Honglian
T2 - JOURNAL OF ALGEBRA AND ITS APPLICATIONS
AB - A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.
DA - 2016/4//
PY - 2016/4//
DO - 10.1142/s0219498816500547
VL - 15
IS - 3
SP -
SN - 1793-6829
KW - Two-parameter quantum affine algebra
KW - Drinfeld realization
KW - evaluation representation
KW - finite-dimensional representation
ER -
TY - JOUR
TI - Augmented immersed finite element methods for some elliptic partial differential equations
AU - Ji, Haifeng
AU - Chen, Jinru
AU - Li, Zhilin
T2 - INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
AB - Augmented immersed finite element methods are proposed to solve elliptic interface problems with non-homogeneous jump conditions. The non-homogeneous jump conditions are treated as source terms using the singularity removal technique. For the piecewise constant coefficient case, we transform the original interface problem to a Poisson equation with the same jump in the solution, but an unknown flux jump (augmented variable) which is chosen such that the original flux jump condition is satisfied. The GMRES iterative method is used to solve the augmented variable. The core of each iteration involves solving a Poisson equation using a fast Poisson solver and an interpolation scheme to interpolate the flux jump condition. With a little modification, the method can be applied to solve Poisson equations on irregular domains. Numerical experiments show that not only the computed solution but also the normal derivative are second-order accurate in the L∞ norm.
DA - 2016/3/3/
PY - 2016/3/3/
DO - 10.1080/00207160.2015.1005010
VL - 93
IS - 3
SP - 540-558
SN - 1029-0265
KW - level set function
KW - singularity removal technique
KW - irregular domain
KW - interface problem
KW - non-homogeneous jump condition
KW - 35J60
KW - 65N30
KW - 65N15
ER -
TY - JOUR
TI - A Generally Applicable Calibration Algorithm for Digitally Reconfigurable Self-Healing RFICs
AU - Wyers, Eric J.
AU - Morton, Matthew A.
AU - Sollner, T. C. L. Gerhard
AU - Kelley, C. T.
AU - Franzon, Paul D.
T2 - IEEE Transactions on Very Large Scale Integration (VLSI) Systems
AB - A generally applicable calibration technique for digitally reconfigurable self-healing radio frequency integrated circuits based on a hybrid of the Nelder-Mead and Hooke-Jeeves direct search algorithms is presented. The proposed algorithm is applied to the multiobjective problem of gain error and phase error minimization for a self-healing phase rotator test case. For the 8-D phase rotator calibration problem, we show that the proposed hybrid Nelder-Mead and Hooke-Jeeves calibration algorithm is capable of reducing the gain error and phase error of the phase rotator output to less than a maximum of 0.5 dB and 2°, respectively, relative to the chosen gain and phase targets. A 3-GHz self-healing phase rotator test chip was fabricated in a 45-nm silicon-on-insulator CMOS process, and the measured data were obtained to validate the performance of the proposed calibration algorithm.
DA - 2016/3//
PY - 2016/3//
DO - 10.1109/tvlsi.2015.2424211
VL - 24
IS - 3
SP - 1151-1164
J2 - IEEE Trans. VLSI Syst.
OP -
SN - 1063-8210 1557-9999
UR - http://dx.doi.org/10.1109/TVLSI.2015.2424211
DB - Crossref
KW - Calibration
KW - digitally reconfigurable radio frequency integrated circuits (RFICs)
KW - Hooke-Jeeves algorithm
KW - Nelder-Mead algorithm
KW - self-healing
ER -
TY - JOUR
TI - A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problems
AU - Alexanderian, Alen
AU - Petra, Noemi
AU - Stadler, Georg
AU - Ghattas, Omar
T2 - SIAM Journal on Scientific Computing
AB - We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs). The inverse problem seeks to infer an infinite-dimensional parameter from experimental data observed at a set of sensor locations and from the governing PDEs. The goal of the OED problem is to find an optimal placement of sensors so as to minimize the uncertainty in the inferred parameter field. Specifically, we seek an optimal subset of sensors from among a fixed set of candidate sensor locations. We formulate the OED objective function by generalizing the classical A-optimal experimental design criterion using the expected value of the trace of the posterior covariance. This expected value is computed through sample averaging over the set of likely experimental data. To cope with the infinite-dimensional character of the parameter field, we construct a Gaussian approximation to the posterior at the maximum a posteriori probability (MAP) point, and use the...
DA - 2016/1//
PY - 2016/1//
DO - 10.1137/140992564
VL - 38
IS - 1
SP - A243-A272
J2 - SIAM J. Sci. Comput.
LA - en
OP -
SN - 1064-8275 1095-7197
UR - http://dx.doi.org/10.1137/140992564
DB - Crossref
KW - optimal experimental design
KW - A-optimal design
KW - Bayesian inference
KW - sensor placement
KW - nonlinear inverse problems
KW - randomized trace estimator
KW - sparsified designs
ER -
TY - JOUR
TI - WONDER OF SINE-GORDON Y-SYSTEMS
AU - Nakanishi, Tomoki
AU - Stella, Salvatore
T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - The sine-Gordon Y-systems and the reduced sine-Gordon Y-systems were introduced by Tateo in the 90's in the study of the integrable deformation of conformal field theory by the thermodynamic Bethe ansatz method. The periodicity property and the dilogarithm identities concerning these Y-systems were conjectured by Tateo, and only a part of them have been proved so far. In this paper we formulate these Y-systems by the polygon realization of cluster algebras of types A and D, and prove the conjectured periodicity and dilogarithm identities in full generality. As it turns out, there is a wonderful interplay among continued fractions, triangulations of polygons, cluster algebras, and Y-systems.
DA - 2016/10//
PY - 2016/10//
DO - 10.1090/tran/6505
VL - 368
IS - 10
SP - 6835-6886
SN - 1088-6850
ER -
TY - JOUR
TI - Quality of positive root bounds
AU - Herman, Aaron
AU - Hong, Hoon
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - In this paper, we study the quality of positive root bounds. A positive root bound of a polynomial is an upper bound on the largest positive root. Higher quality means that the relative over-estimation (the ratio of the bound and the largest positive root) is smaller. We report three findings. Most known positive root bounds can be arbitrarily bad; that is, the relative over-estimation can approach infinity, even when the degree and the coefficient size are fixed. When the number of sign variations is the same as the number of positive roots, the relative over-estimation of a positive root bound due to Hong (BH) is at most linear in the degree, no matter what the coefficient size is. When the number of sign variations is one, the relative over-estimation of BH is at most constant, in particular 4, no matter what the degree and the coefficient size are.
DA - 2016///
PY - 2016///
DO - 10.1016/j.jsc.2015.09.006
VL - 74
SP - 592-602
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2015.09.006
KW - Polynomial roots
KW - Positive root bounds
KW - Absolute positiveness
ER -
TY - JOUR
TI - Modelling immune response to BK virus infection and donor kidney in renal transplant recipients
AU - Banks, H. T.
AU - Hu, Shuhua
AU - Link, Kathryn
AU - Rosenberg, Eric S.
AU - Mitsuma, Sheila
AU - Rosario, Lauren
T2 - INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
AB - In this paper, we develop and validate with bootstrapping techniques a mechanistic mathematical model of immune response to both BK virus infection and a donor kidney based on known and hypothesized mechanisms in the literature. The model presented does not capture all the details of the immune response but possesses key features that describe a very complex immunological process. We then estimate model parameters using a least squares approach with a typical set of available clinical data. Sensitivity analysis combined with asymptotic theory is used to determine the number of parameters that can be reliably estimated given the limited number of observations.
DA - 2016/1/2/
PY - 2016/1/2/
DO - 10.1080/17415977.2015.1017484
VL - 24
IS - 1
SP - 127-152
SN - 1741-5985
KW - renal transplant
KW - human polyomavirus type 1 (BKV)
KW - mathematical model
KW - inverse problem
KW - sensitivity analysis
KW - 62F12
KW - 65L09
KW - 92B05
ER -
TY - JOUR
TI - Desingularization of Ore operators
AU - Chen, Shaoshi
AU - Kauers, Manuel
AU - Singer, Michael F.
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We show that Ore operators can be desingularized by calculating a least common left multiple with a random operator of appropriate order, thereby turning a heuristic used for many years in several computer algebra systems into an algorithm. Our result can be viewed as a generalization of a classical result about apparent singularities of linear differential equations.
DA - 2016///
PY - 2016///
DO - 10.1016/j.jsc.2015.11.001
VL - 74
SP - 617-626
SN - 0747-7171
KW - D-finite functions
KW - Apparent singularities
KW - Computer algebra
KW - Ore operators
ER -
TY - JOUR
TI - An assessment of coupling algorithms for nuclear reactor core physics simulations
AU - Hamilton, Steven
AU - Berrill, Mark
AU - Clarno, Kevin
AU - Pawlowski, Roger
AU - Toth, Alex
AU - Kelley, C. T.
AU - Evans, Thomas
AU - Philip, Bobby
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - This paper evaluates the performance of multiphysics coupling algorithms applied to a light water nuclear reactor core simulation. The simulation couples the k-eigenvalue form of the neutron transport equation with heat conduction and subchannel flow equations. We compare Picard iteration (block Gauss–Seidel) to Anderson acceleration and multiple variants of preconditioned Jacobian-free Newton–Krylov (JFNK). The performance of the methods are evaluated over a range of energy group structures and core power levels. A novel physics-based approximation to a Jacobian-vector product has been developed to mitigate the impact of expensive on-line cross section processing steps. Numerical simulations demonstrating the efficiency of JFNK and Anderson acceleration relative to standard Picard iteration are performed on a 3D model of a nuclear fuel assembly. Both criticality (k-eigenvalue) and critical boron search problems are considered.
DA - 2016/4/15/
PY - 2016/4/15/
DO - 10.1016/j.jcp.2016.02.012
VL - 311
SP - 241-257
SN - 1090-2716
KW - Multiphysics
KW - Jacobian-free Newton-Krylov
KW - Anderson acceleration
KW - Nuclear reactor analysis
ER -
TY - JOUR
TI - Additional symmetries of the extended bigraded Toda hierarchy
AU - Bakalov, Bojko
AU - Wheeless, William
T2 - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
AB - The extended bigraded Toda hierarchy (EBTH) is an integrable system satisfied by the total descendant potential of $\mathbb{CP}^1$ with two orbifold points. We construct additional symmetries of the EBTH and describe explicitly their action on the Lax operator, wave operators, and tau-function of the hierarchy. In particular, we obtain infinitesimal symmetries of the EBTH that act on the tau-function as a subalgebra of the Virasoro algebra, generalizing those of Dubrovin and Zhang.
DA - 2016///
PY - 2016///
DO - 10.1088/1751-8113/49/5/055201
VL - 49
IS - 5
SP -
SN - 1751-8121
KW - extended bigraded Toda hierarchy
KW - Lax operator
KW - tau-function
KW - Virasoro algebra
KW - wave function
KW - wave operator Mathematics Subject Classification: Primary 37K35
KW - Secondary 37K10
KW - 53D45
ER -
TY - JOUR
TI - A new augmented immersed finite element method without using SVD interpolations
AU - Ji, Haifeng
AU - Chen, Jinru
AU - Li, Zhilin
T2 - NUMERICAL ALGORITHMS
DA - 2016/2//
PY - 2016/2//
DO - 10.1007/s11075-015-9999-0
VL - 71
IS - 2
SP - 395-416
SN - 1572-9265
KW - Interface problem
KW - Piecewise constant coefficient
KW - Immersed finite element
KW - Augmented immersed finite element method
KW - Poisson equation on irregular domain
KW - Fast poisson solver
KW - Least squares interpolation using SVD
ER -
TY - JOUR
TI - On using Lazard's projection in CAD construction
AU - McCallum, Scott
AU - Hong, Hoon
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - In 1994 Lazard proposed an improved projection operation for cylindrical algebraic decomposition (CAD). For the proof he introduced a certain notion of valuation of a multivariate Puiseux series at a point. However a gap in one of the key supporting results for the improved projection was subsequently noticed. In this paper we show that Lazard's projection is valid for CAD construction for so-called well-oriented polynomial sets. Our proof does not make use of Lazard's notion of valuation, however.
DA - 2016///
PY - 2016///
DO - 10.1016/j.jsc.2015.02.001
VL - 72
SP - 65-81
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2015.02.001
KW - Cylindrical algebraic decomposition
KW - Projection operation
KW - Theorem of Abhyankar and Jung
ER -
TY - JOUR
TI - Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme
AU - Daleo, Noah S.
AU - Hauenstein, Jonathan D.
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - In numerical algebraic geometry, a witness point set W is a key object for performing numerical computations on a projective scheme X of pure dimension d>0 defined over C. If X is arithmetically Cohen–Macaulay, W can also be used to obtain information about X, such as the initial degree of the ideal generated by X and its Castelnuovo–Mumford regularity. Due to this relationship, we develop a new numerical algebraic geometric test for deciding if X is arithmetically Cohen–Macaulay using points which lie (approximately) on a general curve section C of X. For any curve, we also compute other information such as the arithmetic genus and index of regularity. Several examples are presented showing the effectiveness of this method, even when the ideal of X is unknown.
DA - 2016///
PY - 2016///
DO - 10.1016/j.jsc.2015.01.001
VL - 72
SP - 128-146
SN - 0747-7171
KW - Numerical algebraic geometry
KW - Witness set
KW - Arithmetically Cohen-Macaulay
KW - Castelnuovo-Mumford regularity
KW - Arithmetic genus
ER -
TY - JOUR
TI - Numerical methods for fourth-order elliptic equations with nonlocal boundary conditions
AU - Pao, C. V.
AU - Wang, Yuan-Ming
T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
AB - This paper is concerned with some numerical methods for a fourth-order semilinear elliptic boundary value problem with nonlocal boundary condition. The fourth-order equation is formulated as a coupled system of two second-order equations which are discretized by the finite difference method. Three monotone iterative schemes are presented for the coupled finite difference system using either an upper solution or a lower solution as the initial iteration. These sequences of monotone iterations, called maximal sequence and minimal sequence respectively, yield not only useful computational algorithms but also the existence of a maximal solution and a minimal solution of the finite difference system. Also given is a sufficient condition for the uniqueness of the solution. This uniqueness property and the monotone convergence of the maximal and minimal sequences lead to a reliable and easy to use error estimate for the computed solution. Moreover, the monotone convergence property of the maximal and minimal sequences is used to show the convergence of the maximal and minimal finite difference solutions to the corresponding maximal and minimal solutions of the original continuous system as the mesh size tends to zero. Three numerical examples with different types of nonlinear reaction functions are given. In each example, the true continuous solution is constructed and is used to compare with the computed solution to demonstrate the accuracy and reliability of the monotone iterative schemes.
DA - 2016/1/15/
PY - 2016/1/15/
DO - 10.1016/j.cam.2015.07.018
VL - 292
SP - 447-468
SN - 1879-1778
KW - Fourth-order elliptic equation
KW - Nonlocal boundary condition
KW - Finite difference system
KW - Method of upper and lower solutions
KW - Monotone iterations
KW - Convergence
ER -
TY - JOUR
TI - Dynamics of food-chain models with density-dependent diffusion and ratio-dependent reaction function
AU - Pao, C. V.
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - This paper is concerned with a 3-species and a 2-species food-chain reaction diffusion systems in a bounded domain where the diffusion coefficients may be density dependent and the reaction functions are ratio-dependent. These equations are quasilinear where the diffusion coefficients may be degenerate on the boundary of the domain. Three basic types of Dirichlet, Neumann and Robin boundary conditions are considered, and in each case some very simple conditions are obtained to ensure the dynamical behavior of the time-dependent solution in relation to some positive solutions or quasi-solutions of the steady-state problem, including the existence of these solutions. This dynamical behavior leads to the coexistence and global attractor of the food-chain systems. In the case of Neumann boundary condition sufficient conditions are given to ensure that the steady-state problem has a unique positive constant solution which is a global attractor of the time-dependent system.
DA - 2016/1/1/
PY - 2016/1/1/
DO - 10.1016/j.jmaa.2015.05.075
VL - 433
IS - 1
SP - 355-374
SN - 1096-0813
KW - Food-chain reaction diffusion system
KW - Degenerate diffusion
KW - Ratio-dependent reaction
KW - Dynamical behavior
KW - Global attractor
KW - Stability
ER -
TY - JOUR
TI - Complete branching rules for Specht modules
AU - Liu, Ricky Ini
T2 - JOURNAL OF ALGEBRA
AB - We give a combinatorial description for when the Specht module of an arbitrary diagram admits a (complete) branching rule. This description, given in terms of the maximal rectangles of the diagram, generalizes all previously known branching rules for Specht modules, such as those given by Reiner and Shimozono for northwest diagrams and by the present author for forest diagrams.
DA - 2016/1/15/
PY - 2016/1/15/
DO - 10.1016/j.jalgebra.2015.09.008
VL - 446
SP - 77-102
SN - 1090-266X
KW - Symmetric group
KW - Specht modules
KW - Branching rule
ER -
TY - JOUR
TI - Central-upwind scheme for shallow water equations with discontinuous bottom topography
AU - Bernstein, Andrew
AU - Chertock, Alina
AU - Kurganov, Alexander
T2 - BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
DA - 2016/3//
PY - 2016/3//
DO - 10.1007/s00574-016-0124-3
VL - 47
IS - 1
SP - 91-103
SN - 1678-7714
UR - https://doi-org.prox.lib.ncsu.edu/10.1007/s00574-016-0124-3
KW - hyperbolic system of conservation and balance laws
KW - semi-discrete central-upwind scheme
KW - Saint Venant system of shallow water equations
ER -
TY - JOUR
TI - Modules for double affine Lie algebras
AU - Jing, Naihuan
AU - Wang, Chunhua
T2 - FRONTIERS OF MATHEMATICS IN CHINA
AB - Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.
DA - 2016/2//
PY - 2016/2//
DO - 10.1007/s11464-015-0447-1
VL - 11
IS - 1
SP - 89-108
SN - 1673-3576
KW - Double affine Lie algebra
KW - Verma module
KW - irreducibility
KW - Weyl module
ER -