In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

[Q]: This papers shows that using separators, which is a pair of two complementary contractors, we can easily and efficiently solve the localization problem of a robot with sonar measurements in an unstructured environment. We introduce separators associated with the Minkowski sum and the Minkowski difference in order to facilitate the resolution. A test-case is given in order to illustrate the principle of the approach.
[A]: Minkowski Operations of Sets with Application to Robot Localization


[Q]: We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions (e.g., pi) and iterated connectives ∨ or ∧ ranging over intervals parameterized by arithmetic variables (e.g., ∧n i=1 pi, where n is a parameter). The satisfiability problem is shown to be undecidable for this new logic, but we introduce a very general class of schemata, called bound-linear, for which this problem becomes decidable. This result is obtained by reduction to a particular class of schemata called regular, for which we provide a sound and complete terminating proof procedure. This schemata calculus (called stab) allows one to capture proof patterns corresponding to a large class of problems specified in propositional logic. We also show that the satisfiability problem becomes again undecidable for slight extensions of this class, thus demonstrating that bound-linear schemata represent a good compromise between expressivity and decidability.
[A]: Decidability and Undecidability Results for Propositional Schemata


[Q]: Functional neuroimaging can measure the brain’s response to an external stimulus. It is used to perform brain mapping: identifying from these observations the brain regions involved. This problem can be cast into a linear supervised learning task where the neuroimaging data are used as predictors for the stimulus. Brain mapping is then seen as a support recovery problem. On functional MRI (fMRI) data, this problem is particularly challenging as i) the number of samples is small due to limited acquisition time and ii) the variables are strongly correlated. We propose to overcome these difficulties using sparse regression models over new variables obtained by clustering of the original variables. The use of randomization techniques, e.g. bootstrap samples, and clustering of the variables improves the recovery properties of sparse methods. We demonstrate the benefit of our approach on an extensive simulation study as well as two fMRI datasets.
[A]:
Small-sample brain mapping: sparse recovery on spatially correlated designs with randomization and clustering