Giacomo Aletti

Giacomo Aletti, Davide Lonardoni, Giovanni Naldi et al.

One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity and how information processing occurs in the neural circuits. At the cellular and molecular level, mechanisms of signal transduction have been studied intensively and a better knowledge and understanding of some basic processes of information handling by neurons has been achieved. In contrast, little is known about the organization and function of complex neuronal networks. Experimental methods are now available to simultaneously monitor electrical activity of a large number of neurons in real time. Then, the qualitative and quantitative analysis of the spiking activity of individual neurons is a very valuable tool for the study of the dynamics and architecture of the neural networks. Such activity is not due to the sole intrinsic properties of the individual neural cells but it is mostly consequence of the direct influence of other neurons. The deduction of the effective connectivity between neurons, whose experimental spike trains are observed, is of crucial importance in neuroscience: first for the correct interpretation of the electro-physiological activity of the involved neurons and neural networks, and, for correctly relating the electrophysiological activity to the functional tasks accomplished by the network. In this work we propose a novel method for the identification of connectivity of neural networks using recorded voltages. Our approach is based on the assumption that the network has a topology with sparse connections. After a brief description of our method we will report the performances and compare it to the cross-correlation computed on the spike trains, that represents a gold standard method in the field.

Giacomo Aletti

This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds. The class of FMa has reached a significant popularity in bigdata stream learning, and the attention of the literature has mainly been based on algorithmic aspects, basically complexity optimality, while the statistical analysis of these class of algorithms has been often faced heuristically. The analysis provided here shows deep connections with mathematical special functions and with extreme value theory. The latter connection may help in explaining heuristic considerations, while the first opens many numerical issues, faced at the end of the present paper. Finally, the algorithms are tested on an anonymized real data stream and MonteCarlo simulations are provided to support our analytical choice in this context.

Giacomo Aletti, Monica Moroni, Giovanni Naldi

In this paper we introduce and study a new feature-preserving nonlinear anisotropic diffusion for denoising signals. The proposed partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically detected parameter related to the local bounded variation and the local oscillating pattern of the noisy input signal. We provide a mathematical analysis of the existence of the solution of our nonlinear and nonlocal diffusion equation in the two dimensional case (images processing). Finally, we propose a numerical scheme with some numerical experiments which demonstrate the effectiveness of the new method.

Giacomo Aletti

In this paper, we face the problem of simulating discrete random variables with general and varying distributions in a scalable framework, where fully parallelizable operations should be preferred. The new paradigm is inspired by the context of discrete choice models. Compared to classical algorithms, we add parallelized randomness, and we leave the final simulation of the random variable to a single associative operation. We characterize the set of algorithms that work in this way, and those algorithms that may have an additive or multiplicative local noise. As a consequence, we could define a natural way to solve some popular simulation problems.