Related papers: Ribbons from Independence Structure: Hypercontract…
For a continuous map $f$ on a compact metric space we study the geometry and entropy of the generalized rotation set $\R(\Phi)$. Here $\Phi=(\phi_1,...,\phi_m)$ is a $m$-dimensional continuous potential and $\R(\Phi)$ is the set of all…
We address the mechanics of an elastic ribbon subjected to twist and tensile load. Motivated by the classical work of Green and a recent experiment that discovered a plethora of morphological instabilities, we introduce a comprehensive…
Inference and learning are commonly cast in terms of optimisation, yet the fundamental constraints governing uncertainty reduction remain unclear. This work presents a first-principles framework inherent to Bayesian updating, termed…
Given a hypergraph $H$ with $m$ hyperedges and a set $X$ of $m$ \emph{pins}, i.e.\ globally fixed subspaces in Euclidean space $\mathbb{R}^d$, a \emph{pinned subspace-incidence system} is the pair $(H, X)$, with the constraint that each pin…
We introduce a notion called entropic independence that is an entropic analog of spectral notions of high-dimensional expansion. Informally, entropic independence of a background distribution $\mu$ on $k$-sized subsets of a ground set of…
Our aim is to provide a short and self contained synthesis which generalise and unify various related and unrelated works involving what we call Phi-Sobolev functional inequalities. Such inequalities related to Phi-entropies can be seen in…
Quantifying integrated information is a leading approach towards building a fundamental theory of consciousness. Integrated Information Theory (IIT) has gained attention in this regard due to its theoretically strong framework. However, it…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…
The properties of complex networked systems arise from the interplay between the dynamics of their elements and the underlying topology. Thus, to understand their behaviour, it is crucial to convene as much information as possible about…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
A sheet of graphene under magnetic bias attains anisotropic surface conductivity, opening the door for realizing compact devices such as Faraday rotators, isolators and circulators. In this paper, an accurate and analytical method is…
Mixture distributions are a workhorse model for multimodal data in information theory, signal processing, and machine learning. Yet even when each component density is simple, the differential entropy of the mixture is notoriously hard to…
We take the paradigm of interacting spin chains, the Heisenberg spin-$\frac{1}{2}$ XXZ model, as a reference system and consider interacting models that are related to it by Jordan-Wigner transformations and restrictions to sub-chains. An…
The Partial Information Decomposition (PID) [arXiv:1004.2515] provides a theoretical framework to characterize and quantify the structure of multivariate information sharing. A new method (Idep) has recently been proposed for computing a…
We introduce a new measure of interdependence among the components of a random vector along the main diagonal of the vector copula, i.e. along the line $u_{1}=\ldots=u_{J}$, for $\left(u_{1},\ldots,u_{J}\right)\in\left[0,1\right]^{J}$. Our…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
Measuring the dependence of data plays a central role in statistics and machine learning. In this work, we summarize and generalize the main idea of existing information-theoretic dependence measures into a higher-level perspective by the…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
We investigate the statistical mechanics of long developable ribbons of finite width and very small thickness. The constraint of isometric deformations in these ribbon-like structures that follows from the geometric separation of scales…