Glassy phases in Random Heteropolymers with correlated sequences

We develop a new analytic approach for the study of lattice heteropolymers, and apply it to copolymers with correlated Markovian sequences. According to our analysis, heteropolymers present three different dense phases depending upon the temperature, the nature of the monomer interactions, and the sequence correlations: (i) a liquid phase, (ii) a ``soft glass'' phase, and (iii) a ``frozen glass'' phase. The presence of the new intermediate ``soft glass'' phase is predicted for instance in the case of polyampholytes with sequences that favor the alternation of monomers. Our approach is based on the cavity method, a refined Bethe Peierls approximation adapted to frustrated systems. It amounts to a mean field treatment in which the nearest neighbor correlations, which are crucial in the dense phases of heteropolymers, are handled exactly. This approach is powerful and versatile, it can be improved systematically and generalized to other polymeric systems

Drift of invariant manifolds and transient chaos in memristor Chua's circuit

The article shows that transient chaos phenomena can be observed in a generalized memristor Chua's circuit where a nonlinear resistor is introduced to better model the real memristor behaviour. The flux-charge analysis method is used to explain the origin of transient chaos, that is attributed to the drift of the index of the memristor circuit invariant manifolds caused by the charge flowing into the nonlinear resistor

Multiple abnormalities in the skull of a prostitute. An autopsy report (1900)

OBJECTIVE: The study presents and comments on the publication of an autopsy report. CASE REPORT: In 1900 De Blasio published an article entitled "Multiple abnormalities in a prostitute's skull" in the "Journal of Psychiatry, Criminal Anthropology and related sciences". In this work De Blasio related anomalies at the cranial level to the presence of mental pathologies. The skull belonged to a 24-year-old prostitute who died of syphilitic hepatitis. In his article, De Blasio described the life of the woman, after which he gave a macroscopic description of the skull. De Blasio believed that the subject's amoral behavior was caused by the anomalous shape of the subject's skull. CONCLUSION: From the study, it is evident that the school of criminal anthropology influenced De Blasio's autopsy medical practice, and it is interesting to note the interpretation of anthropologists of the time who tried to describe the link between physical and behavioral anomalies

Convergence of Discrete-Time Cellular Neural Networks with Application to Image Processing

The paper considers a class of discrete-time cellular neural networks (DT-CNNs) obtained by applying Euler's discretization scheme to standard CNNs. Let T be the DT-CNN interconnection matrix which is defined by the feedback cloning template. The paper shows that a DT-CNN is convergent, i.e. each solution tends to an equilibrium point, when T is symmetric and, in the case where T + En is not positive-semidefinite, the step size of Euler's discretization scheme does not exceed a given bound (En is the n × n unit matrix). It is shown that two relevant properties hold as a consequence of the local and space-invariant interconnecting structure of a DT-CNN, namely: (1) the bound on the step size can be easily estimated via the elements of the DT-CNN feedback cloning template only; (2) the bound is independent of the DT-CNN dimension. These two properties make DT-CNNs very effective in view of computer simulations and for the practical applications to high-dimensional processing tasks. The obtained results are proved via Lyapunov approach and LaSalle's Invariance Principle in combination with some fundamental inequalities enjoyed by the projection operator on a convex set. The results are compared with previous ones in the literature on the convergence of DT-CNNs and also with those obtained for different neural network models as the Brain-State-in-a-Box model. Finally, the results on convergence are illustrated via the application to some relevant 2D and 1D DT-CNNs for image processing tasks

Necessary and Sufficient Topological Conditions for Identifiability of Dynamical Networks

This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. We are interested in graph-theoretic conditions for identifiability of such dynamical networks, where we assume that only a subset of nodes is measured but the underlying graph structure of the network is known. This problem has recently been investigated from a generic viewpoint. Roughly speaking, generic identifiability means that the transfer functions in the network can be identified for "almost all" network matrices associated with the graph. In this paper, we investigate the stronger notion of identifiability for all network matrices. To this end, we introduce a new graph-theoretic concept called the graph simplification process. Based on this process, we provide necessary and sufficient topological conditions for identifiability. Notably, we also show that these conditions can be verified by polynomial time algorithms. Finally, we explain how our results generalize existing sufficient conditions for identifiability.Comment: 13 page

Resilience against misbehaving nodes in asynchronous networks

When dealing with network systems, a fundamental challenge is to ensure their functioning even when some of the network nodes do not operate as intended due to faults or attacks. The objective of this paper is to address the problem of resilient consensus in a context where the nodes have their own clocks, possibly operating in an asynchronous way, and can make updates at arbitrary time instants. The results represent a first step towards the development of resilient event-triggered and self-triggered coordination protocols. (C) 2019 Elsevier Ltd. All rights reserved