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Provenance for database queries or scientific workflows is often motivated as providing explanation, increasing understanding of the underlying data sources and processes used to compute the query, and reproducibility, the capability to…
We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings…
We determine all permutations in two large classes of polynomials over finite fields, where the construction of the polynomials in each class involves the denominators of a class of rational functions generalizing the classical Redei…
We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formulas involve certain kinds of plethystic…
In this paper I present a conjecture for a recursive algorithm that finds each permutation of combining two sets of objects (AKA the Shuffle Product). This algorithm provides an efficient way to navigate this problem, as each atomic…
Recurrence properties of systems and associated sets of integers that suffice for recurrence are classical objects in topological dynamics. We describe relations between recurrence in different sorts of systems, study ways to formulate…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
The structure of three pattern classes Av(2143, 4321), Av(2143, 4312) and Av(1324, 4312) is determined using the machinery of monotone grid classes. This allows the permutations in these classes to be described in terms of simple diagrams…
We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations…
In this article, the reproducing kernel Hilbert space [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
In this paper, we study the relationship among left peaks, interior peaks and up-down runs of simsun permutations. Properties of the generating polynomials, including the recurrence relation, generating function and real-rootedness are…
We investigate a family of integrals involving modified Bessel functions that arise in the context of neutrino scattering. Recursive formulas are derived for evaluating these integrals and their asymptotic expansions are computed. We prove…
Perron-Frobenius theory developed for irreducible non-negative kernels deals with so-called $R$-positive recurrent kernels. If kernel $M$ is $R$-positive recurrent, then the main result determines the limit of the scaled kernel iterations…
In many instances one has to deal with parametric models. Such models in vector spaces are connected to a linear map. The reproducing kernel Hilbert space and affine- / linear- representations in terms of tensor products are directly…
Every binary De~Bruijn sequence of order n satisfies a recursion 0=x_n+x_0+g(x_{n-1}, ..., x_1). Given a function f on (n-1) bits, let N(f; r) be the number of functions generating a De Bruijn sequence of order n which are obtained by…
We study recurrence, and multiple recurrence, properties along the $k$-th powers of a given set of integers. We show that the property of recurrence for some given values of $k$ does not give any constraint on the recurrence for the other…
We present the multiplicative recurrent neural network as a general model for compositional meaning in language, and evaluate it on the task of fine-grained sentiment analysis. We establish a connection to the previously investigated…
Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the…
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…