Related papers: Exploiting Single-Cycle Symmetries in Continuous C…
An emerging and challenging area in mathematical control theory called Ensemble Control encompasses a class of problems that involves the guidance of an uncountably infinite collection of structurally identical dynamical systems, which are…
We present a polyhedral algorithm to manipulate positive dimensional solution sets. Using facet normals to Newton polytopes as pretropisms, we focus on the first two terms of a Puiseux series expansion. The leading powers of the series are…
We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring…
The construction and role of symmetries for difference equations are now well known. In this paper, the symmetry analysis of the discrete Painleve equations is considered. We assume that the characteristics depend on $n$ and $u_n$ only and…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…
The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same…
We present a comprehensive analysis of an algorithm for evaluating high-dimensional polynomials that are invariant under permutations and rotations. The key bottleneck is the contraction of a high-dimensional symmetric and sparse tensor…
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synthesizing at the same time a controller and an…
In this paper and in its sequel [BKLV], we investigate the cone ${\rm Pseff}_n(C_d)$ of pseudoeffective $n$-cycles in the symmetric product $C_d$ of a smooth curve $C$. In the present paper, we study the convex-geometric properties of the…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
We consider the problem of sampling from solutions defined by a set of hard constraints on a combinatorial space. We propose a new sampling technique that, while enforcing a uniform exploration of the search space, leverages the reasoning…
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…
The predictive advantage of combining several different predictive models is widely accepted. Particularly in time series forecasting problems, this combination is often dynamic to cope with potential non-stationary sources of variation…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
One common type of symmetry is when values are symmetric. For example, if we are assigning colours (values) to nodes (variables) in a graph colouring problem then we can uniformly interchange the colours throughout a colouring. For a…