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Stability of fractional functional differential equations

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arXiv 2018年

作者： Da C. Sousa, J. Vanterler De Oliveira, E. Capelas Rodrigues, F.G. Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computation University of Campinas - UNICAMP rua Sérgio Buarque de Holanda 651 Campinas SP13083-859 Brazil Departamento de Matemáticas Universidad de la Serena Benavente 980 La Serena Chile

26A33, 34A08, 34K37, 34K20In this paper, we present a study on the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the solution of the fractional functional differential equation using the Banach fixed point theorem.... 详细信息

关键词： Fixed point arithmetic

Characterizing the nonlinear structure of shared variability in cortical neuron populations using latent variable models

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arXiv 2019年

作者： Whiteway, Matthew R. Socha, Karolina Bonin, Vincent Butts, Daniel A. Program in Applied Mathematics and Statistics and Scientific Computation University of Maryland College ParkMD United States Neuro-Electronics Research Flanders Leuven Belgium Department of Biology Leuven Brain Institute KU Leuven Leuven Belgium VIB Leuven Belgium Department of Biology and Program in Neuroscience and Cognitive Sciences University of Maryland College ParkMD United States

Sensory neurons often have variable responses to repeated presentations of the same stimulus, which can significantly degrade the stimulus information contained in those responses. This information can in principle be preserved if variability is shared across many neurons, but depends on the structure of the shared variability and its relationship to sensory encoding at the population level. The structure of this shared variability in neural activity can be characterized by latent variable models, although they have thus far typically been used under restrictive mathematical assumptions, such as assuming linear transformations between the latent variables and neural activity. Here we introduce two nonlinear latent variable models for analyzing large-scale neural *** first present a general nonlinear latent variable model that is agnostic to the stimulus tuning properties of the individual neurons, and is hence well suited for exploring neural populations whose tuning properties are not well characterized. This motivates a second class of model, the Generalized Affine Model, which simultaneously determines each neuron's stimulus selectivity and a set of latent variables that modulate these stimulus-driven responses both additively and multiplicatively. While these approaches can detect very general nonlinear relationships in shared neural variability, we find that neural activity recorded in anesthetized primary visual cortex (V1) is best described by a single additive and single multiplicative latent variable, i.e., an "affine model". In contrast, application of the same models to recordings in awake macaque prefrontal cortex discover more general nonlinearities to compactly describe the population response variability. These results thus demonstrate how nonlinear latent variable models can be used to describe population variability, and suggest that a range of methods is necessary to study different brain regions under different experimental conditions. C

关键词： Neurons

Efficient learning of donor retention strategies for the American Red Cross 13

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Efficient learning of donor retention strategies for the Ame...

Simulation Winter Conference

作者： Bin Han Ilya O. Ryzhov Boris Defourny Applied Mathematics Statistics and Scientific Computation University of Maryland College Park MD USA Robert H. Smith School of Business University of Maryland College Park MD USA Operations Research & Financial Engineering Pinceton University Princeton NJ USA

ISBN: (纸本)9781479920778

We present a new sequential decision model for adaptively allocating a fundraising campaign budget for a non-profit organization such as the American Red Cross. The campaign outcome is related to a set of design features using linear regression. We derive the first simulation allocation procedure for simultaneously learning unknown regression parameters and unknown sampling noise. The large number of alternatives in this problem makes it difficult to evaluate the value of information. We apply convex approximation with a quantization procedure and derive a semidefinite programming relaxation to reduce the computational complexity. Simulation experiments based on historical data demonstrate the efficient performance of the approximation.

关键词： Bayes methods computational modeling Educational institutions Linear regression computational complexity Adaptation models Organizations

Validation of a fractional model for erythrocyte sedimentation rate

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arXiv 2018年

作者： da C. Sousa, J. Vanterler Dos Santos, Magun N.N. Magna, L.A. Capelas De Oliveira, E. Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computation University of Campinas - UNICAMP rua Sérgio Buarque de Holanda 651 Campinas SP13083-859 Brazil Department of Clinical Pathology School of Medical Sciences University of Campinas -UNICAMP Campinas SP13083-887 Brazil

We present the validation of a recent fractional mathematical model for erythrocyte sedimentation proposed by Sharma et al. [13]. The model uses a Caputo fractional derivative to build a time fractional diffusion equation suitable to predict blood sedimentation rates. This validation was carried out by means of erythrocyte sedimentation tests in laboratory. Data on sedimentation rates (percentages) were analyzed and compared with the analytical solution of the time fractional diffusion equation. The behavior of the analytical solution related to each blood sample sedimentation data was described and analyzed.26A06, 26A33, 33RXX, 34A30, 35KXX, 92BXX, 92DXX Copyright © 2018, The Authors. All rights reserved.

关键词： Blood

Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem

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arXiv 2023年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Applied Mathematics & Statistics and Scientific Computing Program University of Maryland College Park United States Department of Mathematics The University of Arizona United States

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Adaptive gridding results in more accurate computation of geometric quantities such as x-points associated with the *** Codes 65Z05, 65C05, 62P35, 35R35, 35R60 © 2023, CC BY.

关键词： Monte Carlo methods

Multilevel Monte Carlo Methods for the Grad-Shafranov Free Boundary Problem

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SSRN

SSRN 2023年

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costsby performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductionstypically on the order of 60 or more and possibly as large as 200. Adaptive gridding results in more accurate computation of geometric quantities such as x-points associated with the model. © 2023, The Authors. All rights reserved.

关键词： Monte Carlo methods

Equilibria in the tangle

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arXiv 2017年

作者： Popov, Serguei Saa, Olivia Finardi, Paulo Department of Statistics Institute of Mathematics Statistics and Scientific Computation University of Campinas UNICAMP rua Sérgio Buarque de Holanda 651 Campinas SP13083-859 Brazil Department of Applied Mathematics Institute of Mathematics and Statistics University of So Paulo USP rua do Matao 1010 So Paulo SP05508-090 Brazil Institute of Computing IC University of Campinas UNICAMP av. Albert Einstein 1251 Campinas SP13083-852 Brazil

We analyse the Tangle - a DAG-valued stochastic process where new vertices get attached to the graph at Poissonian times, and the attachment's locations are chosen by means of random walks on that graph. These new vertices, also thought of as "transactions", are issued by many players (which are the nodes of the network), independently. The main application of this model is that it is used as a base for the IOTA cryptocurrency system [1]. We prove existence of "almost symmetric" Nash equilibria for the system where a part of players tries to optimize their attachment strategies. Then, we also present simulations that show that the "selfish" players will nevertheless cooperate with the network by choosing attachment strategies that are similar to the "recommended" *** Codes 91A15 (Primary), 60J20, 68M14 (Secondary) Copyright © 2017, The Authors. All rights reserved.

关键词： Random processes

Surrogate approximation of the grad-shafranov free boundary problem via stochastic collocation on sparse grids

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arXiv 2021年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Applied Mathematics & Statistics and Scientific Computing Program University of Maryland College Park United States Courant Institute of Mathematical Sciences New York University Department of Mathematics The University of Arizona

In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. The use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over *** Codes 65C30, 65C05, 65N35, 65N99, 65Z05 Copyright © 2021, The Authors. All rights reserved.

关键词： Monte Carlo methods

Quantum Adversarial Learning in Emulation of Monte-Carlo Methods for Max-cut Approximation: QAOA is not optimal

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arXiv 2022年

作者： Unsal, Cem M. Brady, Lucas T. Quantum Artificial Intelligence Laboratory NASA Ames Research Center Moffett FieldCA94035 United States KBR 601 Jefferson St. HoustonTX77002 United States Applied Mathematics & Statistics and Scientific Computation University of Maryland College ParkMD20742 United States

One of the leading candidates for near-term quantum advantage is the class of Variational Quantum Algorithms, but these algorithms suffer from classical difficulty in optimizing the variational parameters as the number of parameters increases. Therefore, it is important to understand the expressibility and power of various ansätze to produce target states and distributions. To this end, we apply notions of emulation to Variational Quantum Annealing and the Quantum Approximate Optimization Algorithm (QAOA) to show that QAOA is outperformed by variational annealing schedules with equivalent numbers of parameters. Our Variational Quantum Annealing schedule is based on a novel polynomial parameterization that can be optimized in a similar gradient-free way as QAOA, using the same physical ingredients. In order to compare the performance of ansätze types, we have developed statistical notions of Monte-Carlo methods. Monte-Carlo methods are computer programs that generate random variables that approximate a target number that is computationally hard to calculate exactly. While the most well-known Monte-Carlo method is Monte-Carlo integration (e.g. Diffusion Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods