相关论文: Decompositions of factor codes and embeddings betw…
This paper studies several aspects of symbolic factors of $\mathcal{S}$-adic subshifts of finite alphabet rank. First, we address a problem raised in [DDPM20] about the topological rank of symbolic factors of $\mathcal{S}$-adic subshifts…
Whereas Shannon entropy is related to the growth rate of multinomial coefficients, we show that the quadratic entropy (Tsallis 2-entropy) is connected to their $q$-deformation; when $q$ is a prime power, these $q$-multinomial coefficients…
By solving a differential-functional equation inposed by the MaxEnt principle we obtain a class of two-parameter deformed logarithms and construct the corresponding two-parameter generalized trace-form entropies. Generalized distributions…
We introduce "embedding dimensions" of a family of generators of a finite von Neumann algebra when the von Neumann algebra can be faithfully embedded into the ultrapower of the hyperfinite II$_1$ factor. These embedding dimensions are von…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
Integrable difference equations commonly have more low-order conservation laws than occur for nonintegrable difference equations of similar complexity. We use this empirical observation to sift a large class of difference equations, in…
Multivariate multiplicity codes (Kopparty, Saraf, and Yekhanin, J. ACM 2014) are linear codes where the codewords are described by evaluations of multivariate polynomials (with a degree bound) and their derivatives up to a fixed order, on a…
We show how real-number codes can be used to compress correlated sources, and establish a new framework for lossy distributed source coding, in which we quantize compressed sources instead of compressing quantized sources. This change in…
Whether the system under study is a shoal of fish, a collection of neurons, or a set of interacting atmospheric and oceanic processes, transfer entropy measures the flow of information between time series and can detect possible causal…
Intersecting codes are linear codes where every two nonzero codewords have non-trivially intersecting support. In this article we expand on the theory of this family of codes, by showing that nondegenerate intersecting codes correspond to…
One of the main objectives of topological data analysis is the study of discrete invariants for persistence modules, in particular when dealing with multiparameter persistence modules. In many cases, the invariants studied for these…
The article describes prime intervals into the prime factorization of the middle binomial coefficient. Prime factors and prime powers are distributed in layers. Each layer consists of non-repeated prime numbers which are chosen (not…
Some of the most interesting quantities associated with a factor graph are its marginals and its partition sum. For factor graphs \emph{without cycles} and moderate message update complexities, the sum-product algorithm (SPA) can be used to…
Quantum systems with short range interactions are known to respect an area law for the entanglement entropy: the von Neumann entropy $S$ associated to a bipartition scales with the boundary $p$ between the two parts. Here we study the case…
This paper is the first in a series of articles devoted to the construction and study of synthetic deformations of $\infty$-categories in the unstable context: that is, deformations of $\infty$-categories that categorify spectral sequence…
The decomposition into interaction subspaces is an important result for graphical models and plays a central role for results on the linearized marginal problem; similarly the Chaos decomposition plays an important role in statistical…
The need for improved functionalities is driving the search for more complicated multi-component materials. Despite the factorially increasing composition space, ordered compounds with 4 or more species are rare. Here, we unveil the…
The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…
We introduce a new spin chain which is a deformation of the Fredkin spin chain and has a phase transition between bounded and extensive entanglement entropy scaling. In this chain, spins have a local interaction of three nearest neighbors.…
$S$-gap shifts are a well-studied class of shift spaces, which has led to several proposed generalizations. This paper introduces a new class of shift spaces called $\mathcal{S}$-graph shifts whose essential structure is encoded in a novel…