Related papers: Multisequences with high joint nonlinear complexit…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the…
We obtain smoothing estimates for certain nonlinear convolution operators on prime fields, leading to quantitative nonlinear Roth type theorems. Compared with the usual linear setting (i.e. arithmetic progressions), the nonlinear nature of…
We consider a family of higher-order Boussinesq equations with an arbitrary nonlinearity. We determine the classes of equations so that a certain type of Lie symmetry algebra is admitted in this family. In case of a quadratic nonlinearity…
Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to…
Infinite sequences are of tremendous theoretical and practical importance, and in the Information Age sequences of 0s and 1s are of particular interest. Over the past century, the field of symbolic dynamics has developed to study sequences…
We calculate the probability that random polynomial matrices over a finite field with certain structures are right prime or left prime, respectively. In particular, we give an asymptotic formula for the probability that finitely many…
We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and…
The aim of this article is to investigate the issues of multiplicative inverses and composition in the set of formal Laurent series. We show the lack of general uniqueness of inverses of formal Laurent series; necessary and sufficient…
Working over a field ${\mathbb{k}}$ of characteristic $\ne 2$, we study what we call bisector fields, which are arrangements of paired lines in the plane that have the property that each line in the arrangement crosses the paired lines in…
Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded…
We establish recursions counting various classes of chains in the noncrossing partition lattice of a finite Coxeter group. The recursions specialize a general relation which is proven uniformly (i.e. without appealing to the classification…
We obtain lower bounds for the cardinality of $k$-fold sum-sets of reciprocals of elements of suitable defined short intervals in high degree extensions of finite fields. Combining our results with bounds for multilinear character sums we…
We construct, for any finite commutative ring $R$, a family of representations of the general linear group $\mathrm{GL}_n(R)$ whose intertwining properties mirror those of the principal series for $\mathrm{GL}_n$ over a finite field.
The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited numerically. When the wave complex amplitudes are independent, with a gaussian distribution, the quasilinear approximation is found to always…
Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different…
We present new families of weighted homogeneous and Newton non-degenerate line singularities that satisfy the Zariski multiplicity conjecture.
In this paper, first we introduce a new mapping for finding a common fixed point of an infinite family of nonexpansive mappings then we consider iterative method for finding a common element of the set of fixed points of an infinite family…
We provide estimators for a large class of inverse problems, including nonlinear inverse problems. Using complexity regularization technics we provide adaptive estimators achieving the best rate over the collection of models.
The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of the Goresky-MacPherson approach to similar homology calculations is proposed.