Related papers: Beyond Shapiro's problem: from cyclic sums to "gra…
In this note, the following basic question is explored: in a cyclic group, how are the Shannon entropies of the sum and difference of i.i.d. random variables related to each other? For the integer group, we show that they can differ by any…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
A class of generalized Schr\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume…
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
Ohno-Wakabayashi's cyclic sum formula for multiple zeta-star values is generalized by Igarashi with one or two parameters. In this article, we give a possible answer for one of his problems about a generalization with three parameters.
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
We continue our analysis of Yablo's coding of the liar paradox by infinite acyclic graphs. The present notes are based on and continue the author's previous results on the problem. In particular, our approach is often more systematic than…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
This is a survey of the exciting recent progress made in understanding the complexity of distributed subgraph finding problems. It overviews the results and techniques for assorted variants of subgraph finding problems in various models of…
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of…
Recent results about sums of cubes of Fibonacci numbers [Frontczak, 2018] are extended to arbitrary powers.
We prove a new bound to the exponential sum of the form $$ \sum_{h \sim H}\delta_h \mathop{\sum_{m\sim M}\sum_{n\sim N}}_{mn\sim x}a_{m}b_{n}\e\big(\alpha mn + h(mn + u)^{\gamma}\big), $$ by a new approach to the Type I sum. The sum can be…
We provide a new perspective on the divisor theory of graphs, using additive combinatorics. As a test case for this perspective, we compute the gonality of certain families of outerplanar graphs, specifically the strip graphs. The Jacobians…
\emph{Uncertain Graph} (also known as \emph{Probabilistic Graph}) is a generic model to represent many real\mbox{-}world networks from social to biological. In recent times analysis and mining of uncertain graphs have drawn significant…
An operation on species corresponding to the inner plethysm of their associated cycle index series is constructed. This operation, the inner plethysm of species, is generalized to n-sorted species. Polynomial maps on species are studied and…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between…
Let $G=(V,E)$ be a locally finite graph. Firstly, using calculus of variations, including a direct method of variation and the mountain-pass theory, we get sequences of solutions to several local equations on $G$ (the Schr\"odinger…
Influence diagrams are a decision-theoretic extension of probabilistic graphical models. In this paper we show how they can be used to solve the Goddard problem. We present results of numerical experiments with this problem and compare the…