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Many mechanical structures, both engineered and biological, combine heavy rigid elements such as bones and beams with lightweight flexible ones such as cables and membranes. These are referred to as tensegrities, reflecting that cables can…
Conventional information-theoretic quantities assume access to probability distributions. Estimating such distributions is not trivial. Here, we consider function-based formulations of cross entropy that sidesteps this a priori estimation…
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
We explore a large class of correlation measures called the $\alpha-z$ R\'enyi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of R\'enyi entropies, the $\alpha-z$ RMIs are positive…
We propose a unified information-geometric framework that formalizes understanding in learning as a trade-off between informativeness and geometric simplicity. An encoder phi is evaluated by U(phi) = I(phi(X); Y) - beta * C(phi), where…
Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…
In this paper, we study modulation instabilities (MI) in a one-dimensional chain configuration of a flexible mechanical metamaterial (flexMM). Using the lumped element approach, flexMMs can be modeled by a coupled system of discrete…
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…
We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs--Shannon entropy into more general framework - Renyi's information entropy. We address the…
A new heuristic based on vertex invariants is developed to rapidly distinguish non-isomorphic graphs to a desired level of accuracy. The method is applied to sample subgraphs from an E.coli protein interaction network, and as a probe for…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…
We investigate the low-lying excitation spectrum and ground-state properties of narrow graphene nanoribbons with zigzag edge configurations. Nanoribbons of comparable widths have been synthesized very recently [P. Ruffieux, \emph{et al.}…
Information theory is a powerful tool to express principles to drive autonomous systems because it is domain invariant and allows for an intuitive interpretation. This paper studies the use of the predictive information (PI), also called…
We show how Fisher's information already known particular character as the fundamental information geometric object which plays the role of a metric tensor for a statistical differential manifold, can be derived in a relatively easy manner…
Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction $\phi_R$.…
We study the continuity of the maximum-entropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong continuity of the set-valued inverse numerical range map. This gives a…
We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to…
This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes. We show that Shannon's entropy function has a…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…