Modelli   Matematici per
 le Applicazioni

Dipartimento di Matematica, Sapienza, Università di Roma

Seminari 2023

Seminari degli anni precedenti: 2021-2020 -2019-2018-2017-

19 maggio

ore 12:00

Sala di Consiglio
Christophe Pouzat

Neuronal network structure inference by simulation

Neurophysiologists are nowadays able to record from a large number of extracellular electrodes and to extract, from the raw data, the sequences of action potentials or spikes generated by many neurons. Unfortunately these "many neurons" still represent only a tiny fraction of the neuronal population which constitutes the network. Using association statistics such as cross-correlograms, they try to infer the structure of the network formed by the recorded neurons. But this inference is compromised by the tremendous under-sampling of the neuronal population and by the errors made during the sequences reconstruction. This yields a "network picture" usually called a "functional network" whose features depend strongly on the recording conditions (such as the presence/absence of a stimulation). Considering that reconstructing the network formed by the recorded neurons is an ill-posed problem, I propose to focus instead on the "generative probability distribution" of the network: what is the probability to have a connection from a type A neuron to a type B neuron? Is the probability to have a connection from neuron Y of type B to neuron X of type A dependent on the presence of a connection from X to Y? To that end, the key idea is to simulate first the whole network using a simplified neuronal dynamics and different (parametrized) generative probability distributions. The association statistics obtained from the simulations and from the actual data are then compared and the model parameters are tuned in order to improve the match. This type of approach is now commonly used in several fields under different names like "Approximate Bayesian Computation" or "Simulation based Inference". I will illustrate on a idealized case, inspired by the first olfactory relay of an insect, how the "over representation of reciprocal connections" can be addressed.

31 Marzo

ore 12:00

Sala di Consiglio
Simon Guest

Zero-stiffness structures

The talk will provide a compendium of ’zero-stiffness’ structures, describing three classes of structures that remain in a neutral state of equilibrium, even while they undergo large (and clearly geometrically nonlinear) displacements, with part or all of each structure undergoing large (but elastic) deformations. The structures will not be abstract theoretical constructions, but real structures modelled using reasonable assumptions. Physical examples will be demonstrated.

24 Febbraio

ore 12:00

Aula Picone
Mirko Degli Esposti

Entropy, Irreversibility, DNA sequences… and Fake Faces

Entropy and irreversibility, two fundamental concepts underlying physical processes, and now also at the core of digital processes for simulation and evolution of artificial models. We will touch on some of these aspects, taking as our starting point the well-defined and well-explored mathematical context of infinite sequence spaces over finite alphabets. As we will see, universal estimators of typical signal entropy and cross entropy, based on the asymptotics of recurrences and waiting times, play an important role in information theory, and we will discuss some mathematical results. Starting from their construction, we will introduce and discuss universal estimators of typical signals of entropy production in the context of nonequilibrium statistical mechanics of one-sided shifts on finite alphabets. Finally, we will discuss some applications to DNA sequences, particularly in understanding the so-called Second Chargaff Rule, a still unexplained family of empirical symmetries present in "most" genetic sequences. We will conclude with some suggestions to show how concepts proper to statistical mechanics and thermodynamics, such as entropy and irreversibility, have become fundamental even in the most recent synthetic image generation models. In collaboration with Giampaolo Cristadoro Vojkan Jakšić, Renaud Raquépas.

27 Gennaio

ore 14.00

Sala di Consiglio
Laura Palagi

From black forests to interpretable trees: an overview and recent development on Optimal classification tree

In recent years there has been a growing attention to machine learning models which are able to give explanatory insights on the decisions made by the algorithm. Thanks to their interpretability, decision trees have been intensively studied for classification tasks, and, due to the remarkable advances in Mixed-Integer Programming (MIP), various approaches have been proposed to formulate the Optimal Classification Tree (OCT) problem as a MIP model starting from the seminal paper [Bertsimas D. and J. Dunn. "Optimal classification trees." Machine Learning 106.7 (2017)]. In this talk, we will make an overview on classification trees and random forests and on the optimal tree classification formulation. First, we present a novel formulation for binary classification using OCT and exploiting the generalization capabilities of another well know machine learning classifiers which are Support Vector Machines [Cortes C. , and V. Vapnik. "Support vector machine." Machine learning 20.3 (1995)]. In particular, the maximum MARGin Optimal Classification Tree (MARGOT) uses at each node of the decision tree a regularized Linear SVM to define a linear classifiers with maximum margin in a tree structure. The resulting model is a Mixed Integer Quadratic Programming problem. The model can also include feature selection constraints which allows to define a hierarchy on the subsets of features which mostly affect the outcome. We further present an OCT for approximating random forests with a single tree following a similar modelling approach. Numerical results on benchmark dataset are reported.

Joint work with: Giulia Di Teodoro, Marta Monaci, Federico D'onofrio, Giorgio Grani

Immagine generata con piattaforma DALL·E 2 (DALL·E 2 ( usando la
descrizione in linguaggio naturale "a decision tree painted by pietr mondrian"