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A graph is well-(edge-)dominated if every minimal (edge) dominating set is minimum. A graph is equimatchable if every maximal matching is maximum. We study these concepts on strong product graphs. We fully characterize well-edge-dominated…

Combinatorics · Mathematics 2024-07-02 Yixin Cao , Guiqiang Mou , Jianxin Wang

Universal source coding at short blocklengths is considered for an exponential family of distributions. The \emph{Type Size} code has previously been shown to be optimal up to the third-order rate for universal compression of all memoryless…

Information Theory · Computer Science 2016-12-21 Nematollah Iri , Oliver Kosut

For many real-life Bayesian networks, common knowledge dictates that the output established for the main variable of interest increases with higher values for the observable variables. We define two concepts of monotonicity to capture this…

Artificial Intelligence · Computer Science 2012-07-19 Linda C. van der Gaag , Hans L. Bodlaender , Ad Feelders

In 2011, Fici and Lipt\'ak introduced prefix normal words. A binary word is prefix normal if it has no factor (substring) that contains more occurrences of the letter 1 than the prefix of the same length. Among the open problems regarding…

Combinatorics · Mathematics 2025-08-28 Duncan Adamson , Moritz Dudey , Pamela Fleischmann , Annika Huch

We establish sufficient conditions for perfect simulation of chains of infinite order on a countable alphabet. The new assumption, localized continuity, is formalized with the help of the notion of context trees, and includes the…

Probability · Mathematics 2013-01-18 Sandro Gallo , Nancy L. Garcia

A common complaint about adaptive prefix coding is that it is much slower than static prefix coding. Karpinski and Nekrich recently took an important step towards resolving this: they gave an adaptive Shannon coding algorithm that encodes…

Information Theory · Computer Science 2008-12-18 Travis Gagie , Yakov Nekrich

Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint…

Logic in Computer Science · Computer Science 2014-05-01 Amir M. Ben-Amram , Michael Vainer

The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal…

Functional Analysis · Mathematics 2012-12-19 Jonathan M. Borwein , Liangjin Yao

We study the problem of invariance of indices of thematic factorizations. Such factorizations were introduced in [PY1] for studying superoptimal approximation by bounded analytic matrix functions. As shown in [PY1], the indices may depend…

Functional Analysis · Mathematics 2007-05-23 R. B. Alexeev , V. V. Peller

A real arithmetic function f is multiplicatively monotonous if f (mn) -- f (m) has constant sign for m, n positive integers. Properties and examples of such functions are discussed, with applications to positive hermitian…

Number Theory · Mathematics 2018-09-25 Michel Balazard

This article employs techniques from convex analysis to present characterizations of (maximal) $n-$monotonicity, similar to the well-established characterizations of (maximal) monotonicity found in the existing literature. These…

Functional Analysis · Mathematics 2024-11-19 M. D. Voisei

We present a new algorithm for dynamic prefix-free coding, based on Shannon coding. We give a simple analysis and prove a better upper bound on the length of the encoding produced than the corresponding bound for dynamic Huffman coding. We…

Information Theory · Computer Science 2007-07-16 Travis Gagie

First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…

Optimization and Control · Mathematics 2023-10-04 Baptiste Goujaud , Aymeric Dieuleveut , Adrien Taylor

By employing the residue polynomials, a construction of constant-composition codes is given. This construction generalizes the one proposed by Xing[16]. It turns out that when d=3 this construction gives a lower bound of…

Information Theory · Computer Science 2016-11-15 Yang Ding

We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…

Information Theory · Computer Science 2021-05-07 Rawad Bitar , Serge Kas Hanna , Nikita Polyanskii , Ilya Vorobyev

We encode/decode Prolog terms as unique natural numbers. Our encodings have the following properties: a) are bijective b) natural numbers always decode to syntactically valid terms c) they work in low polynomial time in the bitsize of the…

Programming Languages · Computer Science 2011-12-19 Paul Tarau

We show that a coded system is mixing if and only if it is totally transitive and if in addition it has a relatively prime generator, then it has strong property P. We continue by showing that a mixing half-synchronized system has such a…

Dynamical Systems · Mathematics 2015-07-30 Dawoud Ahmadi Dastjerdi , Maliheh Dabbaghian Amiri

The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…

Artificial Intelligence · Computer Science 2008-02-03 G. Brewka

An edge-colouring is {\em strong} if every colour class is an induced matching. In this work we give a formulae that determines either the optimal or the optimal plus one strong chromatic index of bipartite outerplanar graphs. Further, we…

Discrete Mathematics · Computer Science 2013-12-20 Valentin Borozan , Leandro Montero , Narayanan Narayanan

In the first part of the note we prove that a sufficient condition (due to Simons) for the convexity of the closure of the domain/range of a monotone operator is also necessary when the operator has bounded domain and is maximal. Simons'…

Functional Analysis · Mathematics 2012-12-13 Maria Elena Verona , Andrei Verona