Constraint-based reachability

Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with standard backward or forward exploration strategies. An approach that we call Constraint-based reachability, is proposed to address reachability problems by exploring program states using a constraint model of the whole program. The keypoint of the approach is to interpret imperative constructions such as conditionals, loops, array and memory manipulations with the fundamental notion of constraint over a computational domain. By combining constraint filtering and abstraction techniques, Constraint-based reachability is able to solve reachability problems which are usually outside the scope of backward or forward exploration strategies. This paper proposes an interpretation of classical filtering consistencies used in Constraint Programming as abstract domain computations, and shows how this approach can be used to produce a constraint solver that efficiently generates solutions for reachability problems that are unsolvable by other approaches.Comment: In Proceedings Infinity 2012, arXiv:1302.310

Estimating Multidimensional Persistent Homology through a Finite Sampling

An exact computation of the persistent Betti numbers of a submanifold $X$ of a Euclidean space is possible only in a theoretical setting. In practical situations, only a finite sample of $X$ is available. We show that, under suitable density conditions, it is possible to estimate the multidimensional persistent Betti numbers of $X$ from the ones of a union of balls centered on the sample points; this even yields the exact value in restricted areas of the domain. Using these inequalities we improve a previous lower bound for the natural pseudodistance to assess dissimilarity between the shapes of two objects from a sampling of them. Similar inequalities are proved for the multidimensional persistent Betti numbers of the ball union and the one of a combinatorial description of it

A pattern mining approach for information filtering systems

It is a big challenge to clearly identify the boundary between positive and negative streams for information filtering systems. Several attempts have used negative feedback to solve this challenge; however, there are two issues for using negative relevance feedback to improve the effectiveness of information filtering. The first one is how to select constructive negative samples in order to reduce the space of negative documents. The second issue is how to decide noisy extracted features that should be updated based on the selected negative samples. This paper proposes a pattern mining based approach to select some offenders from the negative documents, where an offender can be used to reduce the side effects of noisy features. It also classifies extracted features (i.e., terms) into three categories: positive specific terms, general terms, and negative specific terms. In this way, multiple revising strategies can be used to update extracted features. An iterative learning algorithm is also proposed to implement this approach on the RCV1 data collection, and substantial experiments show that the proposed approach achieves encouraging performance and the performance is also consistent for adaptive filtering as well

Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown