Related papers: On congruence schemes for constant terms and their…
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the…
Let phi and psi be endomorphisms of the projective line of degree at least 2, defined over a noetherian commutative ring R with unity. From a dynamical perspective, a significant question is to determine whether phi and psi are conjugate…
In this paper, we study a class of cellular automata (CA) called stable cellular automata (SCA) that preserve stability by reflection, modulo-recurrent, and richness. After applying these automata to Sturmian words, we determine some of…
Association schemes are combinatorial objects that allow us solve problems in several branches of mathematics. They have been used in the study of permutation groups and graphs and also in the design of experiments, coding theory, partition…
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
Regularized factorization is proposed to simulate time evolution for quantum lattice systems. Transcending the Trotter decomposition, the resulting compact structure of the propagator indicates a high-order Baker-Campbell-Hausdorff series.…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
The problem of learning a minimal consistent model from a set of labeled sequences of symbols is addressed from a satisfiability modulo theories perspective. We present two encodings for deterministic finite automata and extend one of these…
A recurrence scheme is defined for the numerical determination of high degree polynomial approximations to functions as, for instance, inverse powers near zero. As an example, polynomials needed in the two-step multi-boson (TSMB) algorithm…
In the course of the proof of the irrationality of zeta(2) R. Apery introduced numbers b_n = \sum_{k=0}^n {n \choose k}^2{n+k \choose k}. Stienstra and Beukers showed that for the prime p > 3 Apery numbers satisfy congruence b((p-1)/2) =…
Probabilistic programming languages (PPLs) allow programmers to construct statistical models and then simulate data or perform inference over them. Many PPLs restrict models to a particular instance of simulation or inference, limiting…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…
Several sequences of free cumulants that count binary plane trees correspond to sequences of classical cumulants that count the decreasing versions of the same trees. Using two new operations on colored binary plane trees that we call…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
Consistent Recalibration models (CRC) have been introduced to capture in necessary generality the dynamic features of term structures of derivatives' prices. Several approaches have been suggested to tackle this problem, but all of them,…
We study polynomials interpolating the (rational) constant terms of certain meromorphic modular forms for Hecke groups. We make observations about the divisibility properties of the constant terms and connect them to several sequences, for…
In this paper, we consider the iterative solution of linear algebraic equations under the condition that matrix-vector products with the coefficient matrix are computed only partially. At the same time, non-computed entries are set to…
Property Specification Patterns (PSPs) have been proposed to solve recurring specification needs, to ease the formalization of requirements, and enable automated verification thereof. In this paper, we extend PSPs by considering Boolean as…