Related papers: Effective computation of $\mathrm{SO}(3)$ and $\ma…
Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…
This paper gives simple distributed algorithms for the fundamental problem of computing graph distances in the Congested Clique model. One of the main components of our algorithms is fast matrix multiplication, for which we show an…
This paper is about: (1) bounds on the number of cliques in a graph in a particular class, and (2) algorithms for listing all cliques in a graph. We present a simple algorithm that lists all cliques in an $n$-vertex graph in O(n) time per…
Answering a question of Shuzhou Wang we give a description of quantum $\SO(3)$ groups of Podle\'s as universal objects. We use this result to give a complete classification of all continuous compact quantum group actions on $M_2$.
A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group-subgroup chains is presented. While the canonical U(3)->U(2)->U(1) coupling and recoupling coefficients are applicable to any…
Assuming the Tate conjecture and the computability of \'etale cohomology with finite coefficients, we give an algorithm that computes the N\'eron-Severi group of any smooth projective geometrically integral variety, and also the rank of the…
We perform a classification of third order integrable systems of evolution equations with respect to higher symmetries. Applying it, we consider polynomial systems that are 0-homogeneous under a suitable weighting of variables with main…
For each integer $n$ we present an explicit formulation of a compact linear program, with $O(n^3)$ variables and constraints, which determines the satisfiability of any 2SAT formula with $n$ boolean variables by a single linear…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
We give an algorithm for computing Segre classes of subschemes of arbitrary projective varieties by computing degrees of a sequence of linear projections. Based on the fact that Segre classes of projective varieties commute with…
Let $A \in \{0,1\}^{n \times n}$ be a matrix with $z$ zeroes and $u$ ones and $x$ be an $n$-dimensional vector of formal variables over a semigroup $(S, \circ)$. How many semigroup operations are required to compute the linear operator…
An update of the ODEtools Maple package, for the analytical solving of 1st and 2nd order ODEs using Lie group symmetry methods, is presented. The set of routines includes an ODE-solver and user-level commands realizing most of the relevant…
We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term $\propto r^4$. This term breaks the U(3) symmetry of the HO, resulting in a spherical…
We show a general method allowing the solution calculation, in the form of a power series, for a very large class of nonlinear Ordinary Differential Equations (ODEs), namely the real analytic $\sigma\pi$-ODEs (and, more in general, the real…
We compute the image of any choice of complex conjugation on the Galois representations associated to regular algebraic cuspidal automorphic representations and to torsion classes in the cohomology of locally symmetric spaces for $GL_n$…
We present an algorithm for computing the set of all coset leaders of a binary code $\mathcal C \subset \mathbb{F}_2^n$. The method is adapted from some of the techniques related to the computation of Gr\"obner representations associated…
For enumerative problems, i.e. computable functions f from N to Z, we define the notion of an effective (or closed) formula. It is an algorithm computing f(n) in the number of steps that is polynomial in the combined size of the input n and…
For every linear binary code $C$, we construct a geometric triangular configuration $\Delta$ so that the weight enumerator of $C$ is obtained by a simple formula from the weight enumerator of the cycle space of $\Delta$. The triangular…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is…