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Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
In this paper we propose an efficiently preconditioned Newton method for the computation of the leftmost eigenpairs of large and sparse symmetric positive definite matrices. A sequence of preconditioners based on the BFGS update formula is…
We consider a variant of VASS extended with integer counters, denoted VASS+Z. These are automata equipped with N and Z counters; the N-counters are required to remain nonnegative and the Z-counters do not have this restriction. We study the…
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…
Designing component-based constraint solvers is a complex problem. Some components are required, some are optional and there are interdependencies between the components. Because of this, previous approaches to solver design and…
While considerable advances have been made in estimating high-dimensional structured models from independent data using Lasso-type models, limited progress has been made for settings when the samples are dependent. We consider estimating…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
We introduce a framework for the description of a large class of delay-differential algebraic systems, in which we study three core problems: first we characterize abstractly the well-posedness of the initial-value problem, then we design a…
The goal of this presentation is to build an efficient non-parametric Bayes classifier in the presence of large numbers of predictors. When analyzing such data, parametric models are often too inflexible while non-parametric procedures tend…
Uniform preconditioners for operators of negative order discretized by (dis)continuous piecewise polynomials of any order are constructed from a boundedly invertible operator of opposite order discretized by continuous piecewise linears.…
Quadric hypersurfaces are well-known to satisfy the Hasse principle. However, this is no longer true in the case of the Hasse principle for integral points, where counter-examples are known to exist in dimension 1 and 2. This work explores…
We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data…
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…
First-order logic fragments mixing quantifiers, arithmetic, and uninterpreted predicates are often undecidable, as is, for instance, Presburger arithmetic extended with a single uninterpreted unary predicate. In the SMT world, difference…
Pushdown Vector Addition Systems with States (PVASS) consist of finitely many control states, a pushdown stack, and a set of counters that can be incremented and decremented, but not tested for zero. Whether the reachability problem is…
We show that the regular separability problem of VASS reachability languages is decidable and $\mathbf{F}_{\omega}$-complete. At the heart of our decision procedure are doubly-marked graph transition sequences, a new proof object that…
I study definable sets in affine continuous logic. Let $T$ be an affine theory. After giving some general results, it is proved that if $T$ has a first order model, its extremal theory is a complete first order theory and first order…
A special case of the satisfiability problem, in which the clauses have a hierarchical structure, is shown to be solvable in linear time, assuming that the clauses have been represented in a convenient way.
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
We study the classic sliding cube model for programmable matter under parallel reconfiguration in three dimensions, providing novel algorithmic and surprising complexity results in addition to generalizing the best known bounds from two to…