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The first step in investigating fractional difference maps, which do not have periodic points except fixed points, is to find asymptotically periodic points and bifurcation points and draw asymptotic bifurcation diagrams. Recently derived…
Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…
We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. The algorithm is obtained by the sign analysis of the itineraries of…
We report our experiences with the generalized integration-by-parts algorithm [hep-ph/9609429] in the context of calculations of a realistic one-loop subset of diagrams.
By holonomic guessing, we denote the process of finding a linear differential equation with polynomial coefficients satisfied by the generating function of a sequence, for which only a few first terms are known. Holonomic guessing has been…
Studying 2 degree-of-freedom (DOF) Hamiltonian dynamical systems often involves the computation of stable & unstable manifolds of periodic orbits, due to the homoclinic & heteroclinic connections they can generate. Such study is generally…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
In this paper, we study the hardness of solving graph-structured linear systems with coefficients over a finite field $\mathbb{Z}_p$ and over a polynomial ring $\mathbb{F}[x_1,\ldots,x_t]$. We reduce solving general linear systems in…
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…
In this paper, we address the problem of safety verification of interval hybrid systems in which the coefficients are intervals instead of explicit numbers. A hybrid symbolic-numeric method, based on SOS relaxation and interval arithmetic…
LP relaxation-based message passing algorithms provide an effective tool for MAP inference over Probabilistic Graphical Models. However, different LP relaxations often have different objective functions and variables of differing…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…
We investigate means of efficient computation of the simulation relation over symbolic finite automata (SFAs), i.e., finite automata with transitions labeled by predicates over alphabet symbols. In one approach, we build on the algorithm by…
In this paper we present a Maple library (MOPs) for computing Jack, Hermite, Laguerre, and Jacobi multivariate polynomials, as well as eigenvalue statistics for the Hermite, Laguerre, and Jacobi ensembles of Random Matrix theory. We also…
The Dirichlet forms methods, in order to represent errors and their propagation, are particularly powerful in infinite dimensional problems such as models involving stochastic analysis encountered in finance or physics, cf. [5]. Now, coming…
Standard answer set programming (ASP) targets at solving search problems from the first level of the polynomial time hierarchy (PH). Tackling search problems beyond NP using ASP is less straightforward. The class of disjunctive logic…
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of…
In this work, we propose a data-driven approach for the construction of finite abstractions (a.k.a., symbolic models) for discrete-time deterministic control systems with unknown dynamics. We leverage notions of so-called alternating…
This work is devoted to study the existence of periodic solutions for a family of discontinuous differential systems $Z(x,y;\epsilon)$ with many zones. We show that for $\epsilon$ sufficiently small the averaged functions at any order…
This work provides a systematic recipe for computing accurate high order Fourier expansions of quasiperiodic invariant circles in area preserving maps. The recipe requires only a finite data set sampled from the quasiperiodic circle. Our…