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A function is said to be additive if, similar to mutual information, expands by a factor of $n$, when evaluated on $n$ i.i.d. repetitions of a source or channel. On the other hand, a function is said to satisfy the tensorization property if…
The elastic response is studied of a single flexible chain grafted on a rigid plane and an ensemble of non-interacting tethered chains. It is demonstrated that the entropic theory of rubber elasticity leads to conclusions that disagree with…
Combinatorial rigidity theory seeks to describe the rigidity or flexibility of bar-joint frameworks in R^d in terms of the structure of the underlying graph G. The goal of this article is to broaden the foundations of combinatorial rigidity…
In a neural network (NN), *weight matrices* linearly transform inputs into *preactivations* that are then transformed nonlinearly into *activations*. A typical NN interleaves multitudes of such linear and nonlinear transforms to express…
In this work we derive a number of chain rules for mutual information quantities, suitable for analyzing quantum cryptography with imperfect devices that leak additional information to an adversary. First, we derive a chain rule between…
In multivariate analysis, uncertainty arises from two sources: the marginal distributions of the variables and their dependence structure. Quantifying the dependence structure is crucial, as it provides valuable insights into the…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
I study the mutual information between spatial subsystems in a variety of scale invariant quantum field theories. While it is derived from the bare entanglement entropy, the mutual information offers a more refined probe of the entanglement…
Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling…
In this article, we unravel an intimate relationship between two seemingly unrelated concepts: elasticity, that defines the local relations between stress and strain of deformable bodies, and topology that classifies their global shape.…
We study a proper definition of R\'enyi mutual information (RMI) in quantum field theory as defined via the Petz R\'enyi relative entropy. Unlike the standard definition, the RMI we compute is a genuine measure of correlations between…
We study the electronic structure of gated graphene sheets. We consider both infinite graphene and finite width ribbons. The effect of Coulomb interactions between the electrically injected carriers and the coupling to the external gate are…
We find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. We do so by generalizing the notion of independence entropy, originally studied in the…
The entropy region is constructed from vectors of random variables by collecting Shannon entropies of all subvectors. Its shape is studied here by means of polymatroidal constructions, notably by convolution. The closure of the region is…
Using the maximum-entropy method, we calculate the end-to-end distance distribution of the force stretched chain from the moments of the distribution, which can be obtained from the extension-force curves recorded in single-molecule…
We calculate upper and lower bounds on the modulus of the pion electro magnetic form factor on the unitarity cut below the $\omega\pi$ inelastic threshold, using as input the phase in the elastic region known via the Fermi-Watson theorem…
The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distribution is the variable part under fixed marginals. We aim to minimize and…
The diversity of the symbols of the information source is calculated following the definition that entropy is the information loss and following a new entropy-symbol similarity relation after the rejection of the Gibbs paradox statement.…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
The aim of this paper is to investigate various information-theoretic measures, including entropy, mutual information, and some systematic measures that based on mutual information, for a class of structured spiking neuronal network. In…