Related papers: Computing Semi-algebraic Invariants for Polynomial…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
Despite the crucial need for formal safety and security verification of programs, discovering loop invariants remains a significant challenge. Static analysis is a primary technique for inferring loop invariants but often relies on…
In the last chapter of his book "The Algebraic Theory of Modular Systems " published in 1916, F. S. Macaulay developped specific techniques for dealing with " unmixed polynomial ideals " by introducing what he called " inverse systems ".…
In this paper, partially invariant solutions (PISs) method is applied in order to obtain new four-dimensional Einstein Walker manifolds. This method is based on subgroup classification for the symmetry group of partial differential…
It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using $(s\,d)^{O(n)}$ arithmetic operations, where $n$ and $s$ are the numbers of…
Traditional variable selection methods could fail to be sign consistent when irrepresentable conditions are violated. This is especially critical in high-dimensional settings when the number of predictors exceeds the sample size. In this…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
We present a new deep learning paradigm for the generation of sparse approximate inverse (SPAI) preconditioners for matrix systems arising from the mesh-based discretization of elliptic differential operators. Our approach is based upon the…
The modeling of dynamical systems is essential in many fields, but applying machine learning techniques is often challenging due to incomplete or noisy data. This study introduces a variant of stochastic interpolation (SI) for probabilistic…
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…
Semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities. In this paper, we consider the problem of deciding whether two given points in a semi-algebraic set are connected. We restrict to the case…
In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant difference from the classical method, which relies on repeated…
This paper presents a maximum principle-based approach in the establishment of input-to-state stability (ISS) for a class of nonlinear parabolic partial differential equations (PDEs) over higher dimensional domains with variable…
Program invariants are important for defect detection, program verification, and program repair. However, existing techniques have limited support for important classes of invariants such as disjunctions, which express the semantics of…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
We propose a probabilistic semantic filtering framework in which parameters of a dynamical system are inferred and associated with a closed set of semantic classes in a map. We extend existing methods to a multi-parameter setting using a…
We examine applications of polynomial Lie algebras $sl_{pd}(2)$ to solve physical tasks in $G_{inv}$-invariant models of coupled subsystems in quantum physics. A general operator formalism is given to solve spectral problems using…
We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose…
We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie-B\"acklund…
The traditional Pi-theorem tells us that for any dimensionally invariant relation there exists a full set of independent dimensionless "Pi groups" which can be used to nondimensionalise the relation. In this paper, we seek to understand…