Noticias en español
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in English. If not, they will be marked as Spanish Only.
Teaching conics sections at the school.
ABSTRACT: We discuss a possible way of teaching conics sections at the level of the grade 6 and 7 of the elementary school through experimental mathematics in optics and equilibria.
History of Conics.
ABSTRACT: We shall discuss the history of the conics sections from the very beginning (350 BC) to Newton (1685) and their applications to equilibria, optics and celestial mechanics.
Machine Learning for Financial Statement Fraud
Abstract: Financial statement fraud (FSF) is a global concern representing a significant threat to financial system stability. In recent years, data-informed quantitative models have been developed to automate and reduce the manual auditing processes. Although the existing techniques have improved the detection rate of FSF, these are very limited and can be improved in terms of data, accuracy and efficiency, leading to more targeted and effective examinations. The main objective of this study is to develop four machine learning methods...
How neuroscience can benefit from advances in machine learning? the example of high-resolution retinal prosthesis.
Abstract: Recent advances in experimental techniques have enabled large-scale recordings and stimulation of neural populations (e.g. multi-electro arrays, optogenetics) comprising thousands of neurons or even entire brains. The central question now is how do we make sense of these huge volumes of data: if methods for processing massive datasets were available, we could, for example, enable the online control of the activity of populations of neurons. This talk is concerned with the data-processing methods that are necessary to make possible...
Statistics and philosophy of probability – six degrees of separation
Abstract: I will discuss some topics from my book “The search for certainty. On the clash of science and philosophy of probability.” My main claims are (i) The philosophy of probability is a complete intellectual failure. (ii) Frequency statistics has nothing in common with the frequency philosophy of probability of von Mises. (iii) Bayesian statistics has nothing in common with the subjective philosophy of probability of de Finetti. (iv) A few simple laws summarize well the science of...
Terrorists never congregate in even numbers (or: some strange results in fragmentation-coalescence)
Abstract: We analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while fragmentation breaks up a cluster into a collection of singletons. Under mild conditions on the coalescence rates, we show that the distribution of cluster sizes becomes non-random in the large-scale limit. Moreover, we discover that, in the limit of small fragmentation rate, these processes exhibit a universal...
Fully convex optimal control problems and impulsive systems.
Abstract: We are interested in fully convex optimal control problems, that is, problems whose Lagrangian is jointly convex in the state and the velocity. Problems of this kind have been widely investigated by Rockafellar and collaborators in the absence of state constraints. In particular, it has been established that the adjoint state (which is an absolutely continuous arc as well as the state of the system) solves a dual optimal control problem, and that the dual value function is the conjugate function of the primal value function....
Hierarchy of pre-strained behaviors for thin materials
ABSTRACT: A hierarchy of four models for thin structures was first obtained by means of a syste- matic, but formal, approach in [5]. Namely, the nonlinear membrane model, the nonlinear bending model, the slightly nonlinear von Ka`rm`an model and the linear model were reco- vered. Emphasis was put on the loading order of magnitude and on the induced magnitude of the deformations. A rigorous variational derivation of the nonlinear membrane model was then given in [7]. In particular, the degeneracy under compression was exhibited. Then, [6]...
“Smoothness of the Metric Projection onto Nonconvex Bodies in Hilbert Spaces”
Abstract: “Based on a fundamental work of R. B. Holmes from 1973, we study differentiability properties of the metric projection onto prox-regular sets. We show that if the set is a nonconvex body with a Cp+1-smooth boundary, then the projection is Cp-smooth near suitable open truncated normal rays, which are determined only by the function of prox-regularity. A local version of the same result is established as well, namely, when the smoothness of the boundary and the prox-regularity of the set are assumed only near a fixed...
Some percolation processes with infinite-range dependencies and with inhomogeneous lines.
ABSTRACT: Consider the hyper-cubic lattice and remove the lines parallel to the coordinate axis independently at random. Does the set of remaining vertices undergo a sharp phase transition as the probability of removing the lines vary? How many connected components are there? In this talk we discuss these question for this model and for a continuous analogous model in which we remove cylinders from the Euclidian space in a isometry invariant way. We also discuss for Bernoulli bond percolation processes in the square lattice, how...
