Potential Well Spectrum and Hitting Time in Renewal Processes

Miguel Abadi, Liliam Cardeño and Sandro Gallo

The potential well of a state can be interpreted physically as the energy that a stationary process needs to leave the state. We prove that for discrete time renewal processes, the potential well is the right scaling for the hitting and return time distributions of the state. We further detail the potential well spectrum of these processes by giving a complete classification of the states according to their potential well.

Estimating Parameters Associated with Monotone Properties

Carlos Hoppen, Yoshiharu Kohayakawa, Richard Lang, Hanno Lefmann and Henrique Stagni

There has been substantial interest in estimating the value of a graph parameter, i.e., of a real function defined on the set of finite graphs, by sampling a randomly chosen substructure whose size is independent of the size of the input. Graph parameters that may be successfully estimated in this way are said to be testable or estimable, and the sample complexity qz = qz(ε) of an estimable parameter z is the size of the random sample required to ensure that the value of z(G) may be estimated within error ε with probability at least 2/3. In this paper, we study the sample complexity of estimating two graph parameters associated with a monotone graph property, improving previously known results. To obtain our results, we prove that the vertex set of any graph that satisfies a monotone property P may be partitioned equitably into a constant number of classes in such a way that the cluster graph induced by the partition is not far from satisfying a natural weighted graph generalization of P. Properties for which this holds are said to be recoverable, and the study of recoverable properties may be of independent interest

NeuroMat initiative to address research and education on brachial plexus injuries

The Research, Innovation and Dissemination Center for Neuromathematics (RIDC NeuroMat) will soon launch a multidisciplinary initiative focusing on brachial plexus injuries, called the NeuroMat Action for the Brachial Plexus Injury, or ABRAÇO. This initiative will become a go-to reference for patients, patients’ relatives, health professionals, researchers and educators who are interested in this kind of injury, that has been in the rise in Brazil, especially associated to an increasing number of motorcycle riders and accidents.

Statistics applied to neuroscience

Neurology is often considered the most difficult area in medicine. The brain is by far the most complex organ of the human body, and many scientific fields investigate it. One of these fields is statistics. Eunylson Lopes, United Statisticians, 6/1/2017. (In Portuguese)

On the Number of Bh-Sets

Domingos Dellamonica, Yoshiharu Kohayakawa, Sang June Lee, Vojtěch Rödl and Wojciech Samotij

A set A of positive integers is a Bh-set if all sums of the form a1 + ··· + ah, with a1,...,ah ∈ A and a1 ··· ah, are distinct. We provide asymptotic bounds for the number of Bh-sets of a given cardinality contained in the interval [n] = {1,...,n}. As a consequence of our results, we address a problem of Cameron and Erd˝os (1990) in the context of Bh-sets.
We also use these results to estimate the maximum size of a Bh-set contained in a typical (random) subset of [n] with a given cardinality.

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The Research, Innovation and Dissemination Center for Neuromathematics is hosted by the University of São Paulo and funded by FAPESP (São Paulo Research Foundation).

 

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