Related papers: On pattern entropy of weak model sets
We consider the $k$th-power-free points in $n$-dimensional lattices and explicitly calculate their entropies and diffraction spectra. This is of particular interest since these sets have holes of unbounded inradius.
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
For continuous self-maps of compact metric spaces, we explore the relationship among the shadowable points, sensitive points, and entropy points. Specifically, we show that (1) if the set of shadowable points is dense in the phase space,…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
Semiconductor model is a system of parabolic partial differential equations with cross-diffusion phenomenon. Previous results showed that a weak solution exists and is not bounded in general. So semiconductor model was categorized as a…
Competitive on-line prediction (also known as universal prediction of individual sequences) is a strand of learning theory avoiding making any stochastic assumptions about the way the observations are generated. The predictor's goal is to…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
The entropy region is a fundamental object in information theory. An outer bound for the entropy region is defined by a minimal set of Shannon-type inequalities called elemental inequalities also referred to as the Shannon region. This…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
This chapter provides a comprehensive and self-contained discussion of the most recent developments of information theory of networks. Maximum entropy models of networks are the least biased ensembles enforcing a set of constraints and are…
Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications,…
In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases,…
This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied…
In supervised learning, the redundancy contained in random examples can be avoided by learning from queries. Using statistical mechanics, we study learning from minimum entropy queries in a large tree-committee machine. The generalization…
We consider the problem of succinctly encoding a static map to support approximate queries. We derive upper and lower bounds on the space requirements in terms of the error rate and the entropy of the distribution of values over keys: our…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…