Related papers: Robin Milner's Work on Concurrency: An Appreciatio…
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
Interdisciplinary collaborations now sweep most fields of the natural and life sciences, necessary to tackle the world's most challenging problems. Yet, the scientific enterprise continues to be dominated by old stereotypes:…
We study the distribution of primes from a topological viewpoint. Certain conjecture is introduced, and we show that it is equivalent to the Riemann Hypothesis.
Collaborative competitions have gained popularity in the scientific and technological fields. These competitions involve defining tasks, selecting evaluation scores, and devising result verification methods. In the standard scenario,…
Analogical proportions compare pairs of items (a, b) and (c, d) in terms of their differences and similarities. They play a key role in the formalization of analogical inference. The paper first discusses how to improve analogical inference…
I survey recent progress on a classic and challenging problem in social choice: the fair division of indivisible items. I discuss how a computational perspective has provided interesting insights into and understanding of how to divide…
We present a comprehensive insight into counting distributions from the perspective of the combinants extracted from them. In particular, we focus on cases where these combinants exhibit oscillatory behavior that can provide an invaluable…
This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…
Many categories have been used to model concurrency. Using any of these, the challenge is to reduce a given model to a smaller representation which nevertheless preserves the relevant computer-scientific information. That is, one wants to…
The robotics research field lacks formalized definitions and frameworks for evaluating advanced capabilities including generalizability (the ability for robots to perform tasks under varied contexts) and reproducibility (the performance of…
Reproducibility is a cornerstone of science, as the replication of findings is the process through which they become knowledge. It is widely considered that many fields of science are undergoing a reproducibility crisis. This has led to the…
These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation.
We give a presentation of abelian class field theory.
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
This paper considers derivation of $f$-divergence inequalities via the approach of functional domination. Bounds on an $f$-divergence based on one or several other $f$-divergences are introduced, dealing with pairs of probability measures…
In this work, we consider a binary classification problem and cast it into a binary hypothesis testing framework, where the observations can be perturbed by an adversary. To improve the adversarial robustness of a classifier, we include an…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
Vladimir Andreevich Uspensky [1930-2018] was one of the Soviet pioneers of the theory of computation and mathematical logic in general (and my teacher and thesis advisor). This paper is the survey of his mathematical works and their…
Convergence theory is an extension of general topology. In contrast with topology, it is closed under some important operations, like exponentiation. With all its advantages, convergence theory remains rather unknown. It is an aim of this…
This paper proposes that the mathematical relationship between an entropy distribution and its limit offers some new insight into system performance. This relationship is used to quantify variation among the entities of a system, where…