Related papers: The Occurrence-in-subtuple problem
Individuals have an intuitive perception of what makes a good coincidence. Though the sensitivity to coincidences has often been presented as resulting from an erroneous assessment of probability, it appears to be a genuine competence,…
In this paper we study random optimization problems where random functions are investigated in sample paths. Some sufficient conditions ensuring the existence of random solutions to random optimization problems are proposed.
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
We suggest a reduction of the combinatorial problem of hypergraph partitioning to a continuous optimization problem.
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
Logical theories have been developed which have allowed temporal reasoning about eventualities (a la Galton) such as states, processes, actions, events, processes and complex eventualities such as sequences and recurrences of other…
A classification of ordinary differential equations and finite-difference equations in one variable having polynomial solutions (the generalized Bochner problem) is given. The method used is based on the spectral problem for a polynomial…
We revisit occurrence typing, a technique to refine the type of variables occurring in type-cases and, thus, capturesome programming patterns used in untyped languages. Although occurrence typing was tied from its inceptionto set-theoretic…
A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
The paper is devoted to the methods of solving simultaneous recurrences. Specifically, we discuss transformation of matrix recurrences to regular recurrences and propose a way of solving special matrix recurrences of order three by their…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
This is an informal discussion on one of the basic problems in the theory of empirical processes, addressed in our preprint "Combinatorics of random processes and sections of convex bodies", which is available at ArXiV and from our web…
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a…
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
In this article, we consider some simple combinatorial game and a winning strategy in this game. This game is then used to prove several known results about non-repetitive sequences and approximations with denominators from a lacunary…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…