Related papers: Discrete correlation of order 2 of generalized Rud…
We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the $s$-uniform variant of the problem is…
Pseudo-splines of integer order $(m,\ell)$ were introduced by Daubechies, Han, Ron, and Shen as a family which allows interpolation between the classical B-splines and the Daubechies' scaling functions. The purpose of this paper is to…
In our recent work we described conditions under which a multi-parameter random simplicial complex is connected and simply connected. We showed that the Betti numbers of multi-parameter random simplicial complexes in one specific dimension…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
The term "strong approximation" is used to describe phenomena where an arithmetic group as well as all of its Zariski dense subgroups have a large image in the congruence quotients. We exhibit analogues of such phenomena in a probabilistic,…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
Low correlation (finite length) sequences are used in communications and remote sensing. One seeks codebooks of sequences in which each sequence has low aperiodic autocorrelation at all nonzero shifts, and each pair of distinct sequences…
Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of…
Continuous spline functions are defined as piecewise polynomials on the faces of a polyhedral complex that agree on the intersections of two faces. Splines are used in approximation theory and numerical analysis, with applications in data…
Although squaring integers is deterministic, squares modulo a prime, $p$, appear to be random. First, because they are all generated by the multiplicative linear congruential equation, $x_{i+1} = g^2 x_i \mod p$, where $x_0 = 1$ and $g$ is…
Neural networks are known to use spurious correlations such as background information for classification. While prior work has looked at spurious correlations that are widespread in the training data, in this work, we investigate how…
It has been proven that, when normalized by $n$, the expected length of a longest common subsequence of $d$ random strings of length $n$ over an alphabet of size $\sigma$ converges to some constant that depends only on $d$ and $\sigma$.…
In this study we introduce a second type of higher order generalised geometric polynomials. This we achieve by examining the generalised stirling numbers $S(n; k;\alpha;\beta;\gamma)$ [Hsu & Shiue,1998] for some negative arguments. We study…
Recently, Okounkov, Lazarsfeld and Mustata, and Kaveh and Khovanskii have shown that the growth of a graded linear series on a projective variety over an algebraically closed field is asymptotic to a polynomial. We give a complete…
We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and…
We investigate symbolic sequences and in particular information carriers as e.g. books and DNA-strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is…
The number of comparisons X_n used by Quicksort to sort an array of n distinct numbers has mean mu_n of order n log n and standard deviation of order n. Using different methods, Regnier and Roesler each showed that the normalized variate…
Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters…
Delsarte, Goethals, and Seidel (1977) used the linear programming method in order to find bounds for the size of spherical codes endowed with prescribed inner products between distinct points in the code. In this paper, we develop the…
We study the convergence rates of the semi-discrete (SD) method originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics,…