Related papers: Landscape of solutions in constraint satisfaction …

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…

In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all…

We establish a framework that allows us to transfer results between some constraint satisfaction problems with infinite templates and promise constraint satisfaction problems. On the one hand, we obtain new algebraic results for…

Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…

Methods are described for the solution of linear inference problems subject to deterministic constraints. The approach builds on work by Backus (1970a,b,c) and Parker (1977), but a range useful advances are suggested to address both…

A novel artificial neural network approach to constraint satisfaction problems is presented. Based on information-theoretical considerations, it differs from a conventional mean-field approach in the form of the resulting free energy. The…

Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…

We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…

We investigate the problem of learning the structure of a Markov network from data. It is shown that the structure of such networks can be described in terms of constraints which enables the use of existing solver technology with…

Diagrammatic reasoning (DR) is pervasive in human problem solving as a powerful adjunct to symbolic reasoning based on language-like representations. The research reported in this paper is a contribution to building a general purpose DR…

We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…

Probabilistic graphical models (PGMs) are tools for solving complex probabilistic relationships. However, suboptimal PGM structures are primarily used in practice. This dissertation presents three contributions to the PGM literature. The…

Some basic features of confinement are reviewed, in particular the symmetry patterns of the dual dynamics. Open problems and possible directions of progress are discussed.

The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and…

Computational modeling is widely used to study how humans and organizations search and solve problems in fields such as economics, management, cultural evolution, and computer science. We argue that current computational modeling research…

Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored:…

We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of…