Related papers: Applications of Metric Coinduction
A method for certifying exact input trackability for constrained discrete time linear systems is introduced in this paper. A signal is assumed to be drawn from a reference set and the system must track this signal with a linear combination…
In Bounded Model Checking both the system model and the checked property are translated into a Boolean formula to be analyzed by a SAT-solver. We introduce a new encoding technique which is particularly optimized for managing quantitative…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
The main goal of quantum metrology is to obtain accurate values of physical parameters using quantum probes. In this context, we show that abstention, i.e., the possibility of getting an inconclusive answer at readout, can drastically…
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…
Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…
Quantum metrology theory has up to now focused on the resolution gains obtainable thanks to the entanglement among N probes. Typically, a quadratic gain in resolution is achievable, going from the 1/sqrt(N) of the central limit theorem to…
Guided by the theory of graph limits, we investigate a variant of the cut metric for limit objects of sequences of discrete probability distributions. Apart from establishing basic results, we introduce a natural operation called {\em…
We present coincidence and common fixed point results of selfmappings satisfying a contraction type in partially ordered metric spaces. As an application, we give an existence theorem for a common solution of integral equations.
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
Metric approximate categories, or metagories, for short, are metrically enriched graphs. Their structure assigns to every directed triangle in the graph a value which may be interpreted as the area of the triangle; alternatively, as the…
Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving…
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
We provide an introduction to the signature method, focusing on its theoretical properties and machine learning applications. Our presentation is divided into two parts. In the first part, we present the definition and fundamental…
Metric search is concerned with the efficient evaluation of queries in metric spaces. In general,a large space of objects is arranged in such a way that, when a further object is presented as a query, those objects most similar to the query…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…
In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…