Related papers: Computing Tropical Prevarieties with Satisfiabilit…
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finite. The aim is to combine approaches for solving a system of polynomial equations with dual…
Bit-vectors, which are integers in a finite number of bits, are ubiquitous in software and hardware systems. In this work, we consider the satisfiability modulo theories (SMT) of bit-vectors. Unlike normal integers, the arithmetics of…
Tropical varieties capture combinatorial information about how coordinates of points in a classical variety approach zero or infinity. We present algorithms for computing the rays of a complex and real tropical curve defined by polynomials…
Tropical implicitization means computing the tropicalization of a unirational variety from its parametrization. In the case of a hypersurface, this amounts to finding the Newton polytope of the implicit equation, without computing its…
Can algebraic geometry enhance the sharpness, robustness, and interpretability of modern neural reasoning models by equipping them with a mathematically grounded inductive bias? To answer this, we introduce Tropical Attention, an attention…
Satisfiability Modulo Theories (SMT) solvers check the satisfiability of quantifier-free first-order logic formulas. We consider the theory of non-linear real arithmetic where the formulae are logical combinations of polynomial constraints.…
We consider decision problems of rating alternatives based on their pairwise comparisons according to two criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall scores of the alternatives. We…
Matrix factorization methods are linear models, with limited capability to model complex relations. In our work, we use tropical semiring to introduce non-linearity into matrix factorization models. We propose a method called Sparse…
The paper introduces a novel algorithm for computing the output admissible set of linear discrete-time systems subject to input saturation. The proposed method takes advantage of the piecewise-affine dynamics to propagate the output…
Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI.…
Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and $L_2$-norm.…
In many applications, SMT solvers are utilized to solve similar or identical tasks over time. Significant variations in performance due to small changes in the input are not uncommon and lead to frustration for users. This sort of stability…
We propose a novel polyhedral uncertainty set for robust optimization, termed the smooth uncertainty set, which captures dependencies of uncertain parameters by constraining their pairwise differences. The bounds on these differences may be…
We examine a multidimensional optimisation problem in the tropical mathematics setting. The problem involves the minimisation of a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield subject to linear…
We are considering a two-stage optimal scheduling problem, which involves two similar projects with the same starting times for workers and the same deadlines for tasks. It is required that the starting times for workers and deadlines for…
Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step in checking for possible errors in LTL assertions. Extant LTL satisfiability checkers use a variety of different search procedures. With the sole exception of LTL…