Related papers: Bandgap Extremization: Some Exact Results
Entropy maximization and free energy minimization are general physical principles for modeling the dynamics of various physical systems. Notable examples include modeling decision-making within the brain using the free-energy principle,…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…
The standard series expansion for the period of a finite amplitude pendulum as a function of energy (and hence amplitude) provides a lower limit on the period when the series is truncated. An adjustment to the last term in the truncated…
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…
This paper presents a new method for finding the node-disjoint paths with maximum combined bandwidth in communication networks. This problem is an NP-complete problem which can be optimally solved in exponential time using integer linear…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
This paper derives the maximum variance of a finite dataset of real numbers, given their mean, minimum and maximum. An example is provided in which the maximum variance is less than half of the Bhatia-Davis upper bound, (maximum -…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
We confirm a conjecture by Everett, Sinclair, and Dankelmann~[Some Centrality results new and old, J. Math. Sociology 28 (2004), 215--227] regarding the problem of maximizing closeness centralization in two-mode data, where the number of…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
The capacity of 1-D constraints is given by the entropy of a corresponding stationary maxentropic Markov chain. Namely, the entropy is maximized over a set of probability distributions, which is defined by some linear requirements. In this…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
We demonstrate an experimental method for measuring energy-time entanglement over almost 80 nm spectral bandwidth in a single shot with a quantum bit error rate below 0.5%. Our scheme is extremely cost-effective and efficient in terms of…
We prove upper bounds on the graph diameters of polytopes in two settings. The first is a worst-case bound for polytopes defined by integer constraints in terms of the height of the integers and certain subdeterminants of the constraint…
We prove a maximality theorem for one-parameter dynamical systems including multiplier one-parameter dynamical systems. Our main result is new even for one-parameter actions on commutative multiplier algebras including the algebra of…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
This paper introduces a computational approach to identify performance constraints in the time-domain, offering a way to design systems in pulse operation. This work presents a comprehensive application of convex optimization to determine…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral…