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

Lifting degeneracies in Higgs couplings using single top production in association with a Higgs boson

Current Higgs data show an ambiguity in the value of the Yukawa couplings to quarks and leptons. Not so much because of still large uncertainties in the measurements but as the result of several almost degenerate minima in the coupling profile likelihood function. To break these degeneracies, it is important to identify and measure processes where the Higgs coupling to fermions interferes with other coupling(s). The most prominent example, the decay of $h \to \gamma \gamma$, is not sufficient to give a definitive answer. In this Letter, we argue that $t$-channel single top production in association with a Higgs boson, with $h\to b\bar b$, can provide the necessary information to lift the remaining degeneracy in the top Yukawa. Within the Standard Model, the total rate is highly reduced due to an almost perfect destructive interference in the hard process, $W b \rightarrow t h$. We first show that for non-standard couplings the cross section can be reliably computed without worrying about corrections from physics beyond the cutoff scale $\Lambda\gtrsim 10\,\mathrm{TeV}$, and that it can be enhanced by more than one order of magnitude compared to the SM. We then study the signal $p p \rightarrow t h j (b)$ with 3 and 4 $b$'s in the final state, and its main backgrounds at the LHC. We find the 8 TeV run dataset to be sensitive to the sign of the anomalous top Yukawa coupling, while already a moderate integrated luminosity at 14 TeV should lift the degeneracy completely.Comment: 17 pages, 7 figures. v2: inclusive signal cross sections at NLO in QCD added; new comment on sensitivity of the analysis to t tbar h process. Matches version accepted by JHE

Mathematical Models for Some Aspects of Blood Microcirculation

Blood rheology is a challenging subject owing to the fact that blood is a mixture of a fluid (plasma) and of cells, among which red blood cells make about 50% of the total volume. It is precisely this circumstance that originates the peculiar behavior of blood flow in small vessels (i.e., roughly speaking, vessel with a diameter less than half a millimeter). In this class we find arterioles, venules, and capillaries. The phenomena taking place in microcirculation are very important in supporting life. Everybody knows the importance of blood filtration in kidneys, but other phenomena, of not less importance, are known only to a small class of physicians. Overviewing such subjects reveals the fascinating complexity of microcirculation

Influence of artificial mouth’s directivity in determining Speech Transmission Index

In room acoustics, one of the most used parameters for evaluating the speech intelligibility is the Speech Transmission Index (STI). The experimental evaluation of this STI generally employs an artificial speaker (binaural head) and listener (artificial mouth). In this study, the influence on the measurements of the emission directivity of the artificial mouth was investigated for different acoustic environments and we have found that, in many cases (i.e. big rooms or systems of telecommunications) the results is not sensitive to modifications of the directivity; on the contrary, inside cars, the shape of the whole balloon of directivity is important for determining correct and comparable values and the different mouth studied gives really different results in the same situation

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

Harmony of transitions in assessing interpersonal motivations in transcripts analysis can discriminate between Adult Attachment Interview secure and disorganized individuals

SUMMARY. Aim. Assessing Interpersonal Motivations in Transcripts (AIMIT) is a validated coding system to assess the activation of interpersonal motivational systems (IMS) in the transcripts of psychotherapy sessions. The Transition Index (TI) is an AIMIT measure that reflects the levels of organisation, synchronisation and harmony amongst two or more IMS when they are rapidly shifting or simultaneously in the clinical dialogue. It is supposed to be a measure of integration and coherence of the patient’s state of mind within the psychotherapeutic sessions. It has also been hypothesized that low TI could be a marker for disorganization of attachment of the patient leading to difficulties in the therapeutic relationships and ruptures in the therapeutic alliance. In order to assess this hypothesis we tested its capability to discriminate between Adult Attachment Interview (AAI) organized and disorganized individuals. Methods. Two groups of 15 transcriptions of AAI matched for age and sex, one classified as free-autonomous and one as disorganized, were analysed by the AIMIT method. Results. Compared to organized individuals, disorganized patients at AAI reported lower TI scores (3.7±0.63 vs 3.0±0.53; F=2.98, p=0.005). Furthermore, TI showed a good discriminant capability (Wilks’ Lambda=0.77, p=0.004). Discussion and Conclusion. This result seems to confirm the usefulness and reliability of AIMIT analysis in evaluating the interpersonal difficulties which often characterize the therapeutic relationship with disorganized attachment patient