Related papers: It is not a Coincidence! On Curious Patterns in Ca…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has…
The problem of computing the index of a coincidence isometry of the hyper cubic lattice $\mathbb{Z}^{n}$ is considered. The normal form of a rational orthogonal matrix is analyzed in detail, and explicit formulas for the index of certain…
Different mathematical models of recognition processes are known. In the present paper we consider a pattern recognition algorithm as an oracle computation on a Turing machine. Such point of view seems to be useful in pattern recognition as…
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
The study of pattern avoidance in permutations, and specifically in flattened partitions is an active area of current research. In this paper, we count the number of distinct flattened partitions over [n] avoiding a single pattern, as well…
Non-overlapping codes are block codes that have arisen in diverse contexts of computer science and biology. Applications typically require finding non-overlapping codes with large cardinalities, but the maximum size of non-overlapping codes…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present the specific structure of nonsmooth optimization problems appearing in machine…
Maximum subarray is a classical problem in computer science that given an array of numbers aims to find a contiguous subarray with the largest sum. We focus on its use for a noisy statistical problem of localizing an interval with a mean…
Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual…
In this work we study randomised reduction strategies,a notion already known in the context of abstract reduction systems, for the $\lambda$-calculus. We develop a simple framework that allows us to prove a randomised strategy to be…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
Nature features a plethora of extraordinary photonic architectures that have been optimized through natural evolution. While numerical optimization is increasingly and successfully used in photonics, it has yet to replicate any of these…
In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…
In this paper some new properties and computational tools for finding KL-optimum designs are provided. KL-optimality is a general criterion useful to select the best experimental conditions to discriminate between statistical models. A…