Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Numerical analysis (3)
- Galerkin methods (2)
- Polynomials (2)
- Algorithms (1)
- Biological networks (1)
-
- Boundary value problems (1)
- Chaotic behavior in systems (1)
- Commutative algebra (1)
- Comparative studies (1)
- Computer algorithms (1)
- Computer science (1)
- Differential geometry (1)
- Discontinuous functions (1)
- Distribution (Probability theory) (1)
- Dynamical Systems (1)
- Dynamical systems (1)
- Dynamics -- Mathematical models (1)
- Dynamics -- Statistics -- Testing (1)
- Exponential functions (1)
- Fermat's theorem (1)
- Finite fields (Algebra) (1)
- Helmholtz equation (1)
- Instrumental variables (Statistics) (1)
- Laplace's equation (1)
- Markov processes (1)
- Mathematical optimization (1)
- Mathematical statistics (1)
- Mathematics (1)
- Nonlinear systems (1)
- Plane geometry (1)
Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Nonsmooth Algorithms And Nesterov's Smoothing Technique For Generalized Fermat-Torricelli Problems, Nguyen Mau Nam, Nguyen Thai An, R. Blake Rector, Jie Sun
Nonsmooth Algorithms And Nesterov's Smoothing Technique For Generalized Fermat-Torricelli Problems, Nguyen Mau Nam, Nguyen Thai An, R. Blake Rector, Jie Sun
Mathematics and Statistics Faculty Publications and Presentations
We present algorithms for solving a number of new models of facility location which generalize the classical Fermat--Torricelli problem. Our first approach involves using Nesterov's smoothing technique and the minimization majorization principle to build smooth approximations that are convenient for applying smooth optimization schemes. Another approach uses subgradient-type algorithms to cope directly with the nondifferentiability of the cost functions. Convergence results of the algorithms are proved and numerical tests are presented to show the effectiveness of the proposed algorithms.
Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman
Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped harmonic oscillators in R with completely decentralized nearest neighbor interaction. We then use the theory to establish that in a certain range of the parameters transients grow linearly in the number of agents (and faster outside that range). Finally, in the regime where this linear growth occurs we give the constant of proportionality as a function of the signal velocities …
Exact Tests For Singular Network Data, Ian H. Dinwoodie, Kruti Pandya
Exact Tests For Singular Network Data, Ian H. Dinwoodie, Kruti Pandya
Mathematics and Statistics Faculty Publications and Presentations
We propose methodology for exact statistical tests of hypotheses for models of network dynamics. The methodology formulates Markovian exponential families, then uses sequential importance sampling to compute expectations within basins of attraction and within level sets of a sufficient statistic for an over-dispersion model. Comparisons of hypotheses can be done conditional on basins of attraction. Examples are presented.
Vanishing Configurations In Network Dynamics With Asynchronous Updates, Ian H. Dinwoodie
Vanishing Configurations In Network Dynamics With Asynchronous Updates, Ian H. Dinwoodie
Mathematics and Statistics Faculty Publications and Presentations
We consider Boolean dynamics for biological networks where stochasticity is introduced through asynchronous updates. An exact method is given for finding states which can reach a steady state with positive probability, and a method is given for finding states which cannot reach other steady states. These methods are based on computational commutative algebra. The algorithms are applied to dynamics of a cell survival network to determine node assignments that exclude termination in a cancerous state
Stochastic Order Relations Among Parallel Systems From Weibull Distributions, Nuria Torrado, Subhash C. Kochar
Stochastic Order Relations Among Parallel Systems From Weibull Distributions, Nuria Torrado, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
In this article, we focus on stochastic orders to compare the magnitudes of two parallel systems from Weibull distributions when one set of scale parameters majorizes the other. The new results obtained here extend some of those proved by Dykstra et al. (1997) and Joo and Mi (2010) from exponential to Weibull distributions. Also, we present some results for parallel systems from multiple-outlier Weibull models.
An Analysis Of The Practical Dpg Method, Jay Gopalakrishnan, Weifeng Qiu
An Analysis Of The Practical Dpg Method, Jay Gopalakrishnan, Weifeng Qiu
Mathematics and Statistics Faculty Publications and Presentations
We give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space consisting of polynomials of degree p on each mesh element. Earlier works showed that there is a "trial-to-test" operator T, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator T is local: it can be applied element-by-element. However, an infinite dimensional problem on each mesh element needed to be solved to apply T. In practical computations, …
Conditional Tests On Basins Of Attraction With Finite Fields, Ian H. Dinwoodie
Conditional Tests On Basins Of Attraction With Finite Fields, Ian H. Dinwoodie
Mathematics and Statistics Faculty Publications and Presentations
An iterative method is given for computing the polynomials that vanish on the basin of attraction of a steady state in discrete polynomial dynamics with finite field coefficients. The algorithm is applied to dynamics of a T cell survival network where it is used to compare transition maps conditional on a basin of attraction.
Convergence Rates Of The Dpg Method With Reduced Test Space Degree, Timaeus Bouma, Jay Gopalakrishnan, Ammar Harb
Convergence Rates Of The Dpg Method With Reduced Test Space Degree, Timaeus Bouma, Jay Gopalakrishnan, Ammar Harb
Mathematics and Statistics Faculty Publications and Presentations
This paper presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree
Regularity Of Mediatrices In Surfaces, Pilar Herreros, Mario Ponce, J. J. P. Veerman
Regularity Of Mediatrices In Surfaces, Pilar Herreros, Mario Ponce, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. This paper establishes additional geometric regularity properties of mediatrices. We show that mediatrices have the radial linearizability property, which implies that at each point they have a geometrically defined derivative in the branching directions. Also, we study the particular case of mediatrices on spheres, by showing that they are Lipschitz simple closed curves …
Dispersive And Dissipative Errors In The Dpg Method With Scaled Norms For Helmholtz Equation, Jay Gopalakrishnan, Ignacio Muga, Nicole Olivares
Dispersive And Dissipative Errors In The Dpg Method With Scaled Norms For Helmholtz Equation, Jay Gopalakrishnan, Ignacio Muga, Nicole Olivares
Mathematics and Statistics Faculty Publications and Presentations
This paper studies the discontinuous Petrov--Galerkin (DPG) method, where the test space is normed by a modified graph norm. The modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter. The main finding is that as the parameter approaches zero, better results are obtained, under some circumstances, when the method is applied to the Helmholtz equation. The main tool used is a dispersion analysis on the multiple interacting stencils that form the DPG method. The analysis shows that the discrete wavenumbers of the method are complex, explaining the numerically observed artificial dissipation in the …