Related papers: Algorithm to Detect Periodicity by Interleaving Se…
In this paper we present a method for obtaining tail-bounds for random variables satisfying certain probabilistic recurrences that arise in the analysis of randomized parallel divide and conquer algorithms. In such algorithms, some…
The ability to quickly and accurately detect anomalous structure within data sequences is an inference challenge of growing importance. This work extends recently proposed post-hoc (offline) anomaly detection methodology to the sequential…
The tail-dependence compatibility problem is introduced. It raises the question whether a given $d\times d$-matrix of entries in the unit interval is the matrix of pairwise tail-dependence coefficients of a $d$-dimensional random vector.…
Statistical approaches to cyber-security involve building realistic probability models of computer network data. In a data pre-processing phase, separating automated events from those caused by human activity should improve statistical…
A sequential pattern with negation, or negative sequential pattern, takes the form of a sequential pattern for which the negation symbol may be used in front of some of the pattern's itemsets. Intuitively, such a pattern occurs in a…
This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular…
Cyclic reduction is a method for the solution of (block-)tridiagonal linear systems. In this note we review the method tailored to hermitian positive definite banded linear systems. The reviewed method has the following advantages: It is…
This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: (1) {\em filtering}, or assigning a belief or likelihood to each…
Mining frequent episodes aims at recovering sequential patterns from temporal data sequences, which can then be used to predict the occurrence of related events in advance. On the other hand, gradual patterns that capture co-variation of…
Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). The recovered period for the sequence of the first 10000 prime numbers is equal to…
By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.
The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, $k$-error linear complexity, the minimum error and the $k$-error linear complexity…
Time-periodic form or expression is a ubiquitous natural and man-made phenomenon observable in all the scientific and engineering disciplines. In this article, we propose a theory of periodic sequence (TPS), which can be formulated as a…
The paper established sufficient conditions of predictability with degeneracy for the spectrum at $M$-periodically located isolated points on the unit circle. It is also shown that $m$-periodic subsequences of these sequences are also…
Many theorems of mathematics have the form that for a certain problem, e.g. a differential equation or polynomial (in)equality, there exists a solution. The sequential version then states that for a sequence of problems, there is a sequence…
We propose and study a generalized continued fraction algorithm that can be executed in an arbitrary imaginary quadratic field, the novelty being a non-restriction to the five Euclidean cases. Many hallmark properties of classical continued…
We give a polynomial-time algorithm for detecting very long cycles in dense regular graphs. Specifically, we show that, given $\alpha \in (0,1)$, there exists a $c=c(\alpha)$ such that the following holds: there is a polynomial-time…
We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of…
In the present paper, as a generalization of the classical periodic rings, we explore those rings whose elements are additively generated by two (or more) periodic elements by calling them additively periodic. We prove that, in some major…
To design efficient parallel algorithms, some recent papers showed that many sequential iterative algorithms can be directly parallelized but there are still challenges in achieving work-efficiency and high-parallelism. Work-efficiency can…