Related papers: Book inequalities
We study holographic entropy inequalities and their structural properties by making use of a judicious grouping of terms into certain multipartite information quantities. This allows us to recast cumbersome entropic expressions into much…
We show that two essentially conditional linear inequalities for Shannon's entropies (including the Zhang-Yeung'97 conditional inequality) do not hold for asymptotically entropic points. This means that these inequalities are non-robust in…
We consider a generalization of an important class of high-dimensional inference problems, namely spiked symmetric matrix models, often used as probabilistic models for principal component analysis. Such paradigmatic models have recently…
The $book$ $embedding$ of a graph $G$ is to place the vertices of $G$ on the spine and draw the edges to the pages so that the edges in the same page do not cross with each other. The book embedding is $matching$ if the pages have maximum…
Kinser developed a hierarchy of inequalities dealing with the dimensions of certain spaces constructed from a given quantity of subspaces. These inequalities can be applied to the rank function of a matroid, a geometric object concerned…
Document classification is the detection specific content of interest in text documents. In contrast to the data-driven machine learning classifiers, knowledge-based classifiers can be constructed based on domain specific knowledge, which…
One of the most useful and correct methodological approaches in bibliometrics is ranking. In the context of highly skewed bibliometric distributions and severe distortions caused by outliers, it is often the preferable way of analysis.…
Information has an entropic character which can be analyzed within the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is…
A new information theoretic condition is presented for reconstructing a discrete random variable $X$ based on the knowledge of a set of discrete functions of $X$. The reconstruction condition is derived from Shannon's 1953 lattice theory…
The rank of partitions play an important role in the combinatorial interpretations of several Ramanujan's famous congruence formulas. In 2005 and 2008, the $D$-rank and $M_2$-rank of an overpartition were introduced by Lovejoy,…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
A popular method in combinatorial optimization is to express polytopes P, which may potentially have exponentially many facets, as solutions of linear programs that use few extra variables to reduce the number of constraints down to a…
In this paper, we study contact structures supported by open book decompositions whose pages are four-punctured spheres. The paper is split into two parts. In the first part, we find infinitely many overtwisted, right-veering monodromies on…
We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…
We investigate how to measure and define the entropy of a simple chaotic system, three hard spheres on a ring. A novel approach is presented, which does not assume the ergodic hypothesis. It consists of transforming the particles collision…
Back in the Eighties, Heath showed that every 3-planar graph is subhamiltonian and asked whether this result can be extended to a class of graphs of degree greater than three. In this paper we affirmatively answer this question for the…
Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which…
This is a foundational paper in tropical linear algebra, which is linear algebra over the min-plus semiring. We introduce and compare three natural definitions of the rank of a matrix, called the Barvinok rank, the Kapranov rank and the…
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…
Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside…