Related papers: Generalized Parikh Matrices For Tracking Subsequen…
In the present paper we generate binary pseudorandom sequences using generalized polynomials. A generalized polynomial is a function in whose description we not only allow addition and product (as it is the case in usual polynomials) but…
Frequent sequence mining methods often make use of constraints to control which subsequences should be mined. A variety of such subsequence constraints has been studied in the literature, including length, gap, span, regular-expression, and…
Let P be a poset and let P* be the set of all finite length words over P. Generalized subword order is the partial order on P* obtained by letting u \leq w if and only if there is a subword u' of w having the same length as u such that each…
In this text, we are concerned with ring epimorphisms, and more specifically universal localisations, from path algebras to matrix algebras. We are mainly focused on constructing ring epimorphisms and universal localisations by extending…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
A parametric approach is developed to the method of S-tree diagrams and its generalization for investigation of the hierarchical substructure of $N$-body nonlinearly interacting systems (e.g., clusters of galaxies). The introduction of a…
In this paper we present the notions of trail (pseudo-)division, generalized subresultants and generalized subresultant algorithm.
We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map from the hull(closure of the set of translates) to the sequence of embedding operations through which we…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
Generalized Pascal matrix whose elements are generalized binomial coefficients is included in the group of generalized Riordan arrays. There is a special set of generalized Riordan arrays defined by parameter $q$. If $q=0$, they are…
The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern…
This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
We determine the conditions for the existence or not of cycles for several families of generalized 3x + 1 mappings and develop a method to find them.
Efficiently representing real world data in a succinct and parsimonious manner is of central importance in many fields. We present a generalized greedy pursuit framework, allowing us to efficiently solve structured matrix factorization…
Predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees…
We generalize the notion of linear chord diagrams to the case of matched sets of size $k$, which we call $k$-chord diagrams. We provide formal generating functions and recurrence relations enumerating these $k$-chord diagrams by the number…
The concept of sequency holds a fundamental significance in signal analysis using Walsh basis functions. In this study, we closely examine the concept of sequency and explore the properties of sequency-complete and sequency-ordered…
The Pascal matrix, $P$, is an upper diagonal matrix whose entries are the binomial coefficients. In 1993 Call and Velleman demonstrated that it satisfies the beautiful relation $P=\exp(H)$ in which $H$ has the numbers 1, 2, 3, etc. on its…