LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification

The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a time-invariant nonlinear dynamical system. A sufficient condition guaranteeing the Input-to-State (ISS) stability property of this class of systems is provided. The ISS property entails the boundedness of the output reachable set of the LSTM. In light of this result, a novel approach for the safety verification of the network, based on the Scenario Approach, is devised. The proposed method is eventually tested on a pH neutralization process.Comment: Accepted for Learning for dynamics & control (L4DC) 202

Motor imagery and motor illusion: from plasticity to a translational approach

Motor imagery e illusione motoria: dalla plasticit\ue0 ad un approccio traslazional

LE PROBLEMATICHE VALUTATIVE DEL PROCESSO DI AFFIDAMENTO BANCARIO IN UNA PMI. ASPETTI TEORICI E CONSIDERAZIONI OPERATIVE

La tesi ha l'obiettivo di evidenziare il procedimento di rilascio di una pratica di affidamento. La tesi è suddivisa in due parti: una teorica ed una pratica nella quale viene descritto un caso pratico affrontato in uno stage presso una banca cooperativa. Nello specifico, il primo capitolo focalizza l’attenzione sulle peculiarità e specificità delle PMI italiane; viene analizzato il fabbisogno di finanziamento e le varie modalità di copertura. Un’ampia parte è dedicata alle caratteristiche delle banche locali e in special modo delle Banche di Credito Cooperativo, cercando di evidenziare le principali differenze che è possibile riscontrare nei confronti delle banche a vocazione universale. Il secondo capitolo, invece, tratta in maniera teorica l’intera procedura di affidamento analizzando nello specifico tutte le fasi che compongono l’istruttoria di fido. Il terzo deriva da un’esperienza personale effettuata presso la Banca di Credito Cooperativo di Fornacette e intende mostrare una pratica di affidamento richiesta da una PMI operante nel territorio di insediamento dell’istituto locale. L’obiettivo principale è quello di evidenziare le principali differenze che è possibile incontrare nella realtà rispetto a quello che invece viene evidenziato a livello teorico

Baseline Micronuclei Frequency in Children: Estimates from Meta- and Pooled Analyses

The number of studies evaluating the effect of environmental exposure to genotoxic agents in children has rapidly increased in the last few years. The frequency of micronuclei (MN) in peripheral blood lymphocytes determined with the cytokinesis block assay is among the most popular biomarkers used for this purpose, although large inter- and intralaboratory variability of this end point has been observed in population studies. The availability of reference measures is therefore necessary for laboratories to validate protocols and analytical procedures, and for molecular epidemiologists, as well, to estimate the statistical power of studies and to assess the quality of data. In this article, we provide estimates of the baseline frequency of MN in children, conducting a meta-analysis of MN frequency reported by field studies in children and a pooled analysis of individual data [available from published studies and from the Human Micronucleus International Collaborative Study (HUMN) database]. Thirteen articles were selected for meta-analysis, and individual data included in the pooled analysis were retrieved from the databases of 12 laboratories. Overall means of 4.48 [95% confidence interval (CI), 3.35–5.98] and 5.70 (95% CI, 4.29–7.56) MN per 1,000 binucleated cells were estimated by the meta- and pooled analysis, respectively. A clear effect of age was detected, even within the restricted range of pediatric age considered, with significantly lower frequency values in newborns. No influence of sex was found. The study showed the advantage of using data from large collaborative studies and suggested a synergistic use of meta- and pooled analysis

Stability of discrete-time feed-forward neural networks in NARX configuration

The idea of using Feed-Forward Neural Networks (FFNNs) as regression functions for Nonlinear AutoRegressive eXogenous (NARX) models, leading to models herein named Neural NARXs (NNARXs), has been quite popular in the early days of machine learning applied to nonlinear system identification, owing to their simple structure and ease of application to control design. Nonetheless, few theoretical results are available concerning the stability properties of these models. In this paper we address this problem, providing a sufficient condition under which NNARX models are guaranteed to enjoy the Input-to-State Stability (ISS) and the Incremental Input-to-State Stability ({\delta}ISS) properties. This condition, which is an inequality on the weights of the underlying FFNN, can be enforced during the training procedure to ensure the stability of the model. The proposed model, along with this stability condition, are tested on the pH neutralization process benchmark, showing satisfactory results.Comment: This work has been submitted to IFAC for possible publicatio

LSTM neural networks: Input to state stability and probabilistic safety verification

The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a time-invariant nonlinear dynamical system. A sufficient condition guaranteeing the Input-to-State (ISS) stability property of this class of systems is provided. The ISS property entails the boundedness of the output reachable set of the LSTM. In light of this result, a novel approach for the safety verification of the network, based on the Scenario Approach, is devised. The proposed method is eventually tested on a pH neutralization process