Instability of frozen-in states in synchronous Hebbian neural networks

The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of frozen-in states that appear in the absence of both kinds of noise. Both, the numerical simulation procedure of Eissfeller and Opper and a new alternative procedure that allows to follow the dynamics over larger time scales have been used in this work. It is shown that synaptic noise destabilizes the frozen-in states and yields either retrieval or paramagnetic states for not too large stochastic noise. The indications are that the same results may follow in the absence of synaptic noise, for low stochastic noise.Comment: 14 pages and 4 figures; accepted for publication in J. Phys. A: Math. Ge

Impact of COVID-19 on maxillofacial surgery practice: a worldwide survey

The outbreak of coronavirus disease 2019 (COVID-19) is rapidly changing our habits. To date, April 12, 2020, the virus has reached 209 nations, affecting 1.8 million people and causing more than 110,000 deaths. Maxillofacial surgery represents an example of a specialty that has had to adapt to this outbreak, because of the subspecialties of oncology and traumatology. The aim of this study was to examine the effect of this outbreak on the specialty of maxillofacial surgery and how the current situation is being managed on a worldwide scale. To achieve this goal, the authors developed an anonymous questionnaire which was posted on the internet and also sent to maxillofacial surgeons around the globe using membership lists from various subspecialty associations. The questionnaire asked for information about the COVID-19 situation in the respondent's country and in their workplace, and what changes they were facing in their practices in light of the outbreak. The objective was not only to collect and analyse data, but also to highlight what the specialty is facing and how it is handling the situation, in the hope that this information will be useful as a reference in the future, not only for this specialty, but also for others, should COVID-19 or a similar global threat arise again

Symmetric sequence processing in a recurrent neural network model with a synchronous dynamics

The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction is studied in this work allowing for the presence of a self-interaction for each unit. Phase diagrams of stationary states are obtained exhibiting phases of retrieval, symmetric and period-two cyclic states as well as correlated and frozen-in states, in the absence of noise. The frozen-in states are destabilised by synaptic noise and well separated regions of correlated and cyclic states are obtained. Excitatory or inhibitory self-interactions yield enlarged phases of fixed-point or cyclic behaviour.Comment: Accepted for publication in Journal of Physics A: Mathematical and Theoretica

Statistics of opinion domains of the majority-vote model on a square lattice

The existence of juxtaposed regions of distinct cultures in spite of the fact that people's beliefs have a tendency to become more similar to each other's as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size $L$ and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with $L^2$ whereas the size of the largest cluster grows with $\ln L^2$. The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model -- Axelrod's model -- we found that these opinion domains are unstable to the effect of a thermal-like noise

Mean-field analysis of the majority-vote model broken-ergodicity steady state

We study analytically a variant of the one-dimensional majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. The individuals are fixed in the sites of a ring of size $L$ and can interact with their nearest neighbors only. The interesting feature of this model is that it exhibits an infinity of spatially heterogeneous absorbing configurations for $L \to \infty$ whose statistical properties we probe analytically using a mean-field framework based on the decomposition of the $L$-site joint probability distribution into the $n$-contiguous-site joint distributions, the so-called $n$-site approximation. To describe the broken-ergodicity steady state of the model we solve analytically the mean-field dynamic equations for arbitrary time $t$ in the cases n=3 and 4. The asymptotic limit $t \to \infty$ reveals the mapping between the statistical properties of the random initial configurations and those of the final absorbing configurations. For the pair approximation ($n=2$) we derive that mapping using a trick that avoids solving the full dynamics. Most remarkably, we find that the predictions of the 4-site approximation reduce to those of the 3-site in the case of expectations involving three contiguous sites. In addition, those expectations fit the Monte Carlo data perfectly and so we conjecture that they are in fact the exact expectations for the one-dimensional majority-vote model

A Population Genetic Approach to the Quasispecies Model

A population genetics formulation of Eigen's molecular quasispecies model is proposed and several simple replication landscapes are investigated analytically. Our results show a remarcable similarity to those obtained with the original kinetics formulation of the quasispecies model. However, due to the simplicity of our approach, the space of the parameters that define the model can be explored. In particular, for the simgle-sharp-peak landscape our analysis yelds some interesting predictions such as the existence of a maximum peak height and a mini- mum molecule length for the onset of the error threshold transition.Comment: 16 pages, 4 Postscript figures. Submited to Phy. Rev.

Comportamento a fatica di strutture meccaniche in piena scala: risultati sperimentali e previsioni

Il lavoro si propone di presentare le principali attività di ricerca svolte, negli ultimi anni, presso il Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione (DIMNP) dell’Università di Pisa, anche in collaborazione con l’Università di Trento, nel campo della resistenza a fatica delle strutture meccaniche, in particolare per quanto riguarda la conduzione di “test” su componenti in piena scala e la loro interpretazione. Viene quindi condotta un’illustrazione di alcune recenti campagne sperimentali (Es.: giunzioni filettate in acciaio, elementi di sospensione in alluminio, ingranaggi ad elevate prestazioni), alla quale segue una descrizione delle attività di caratterizzazione di base e di modellazione condotte al fine di costituire una adeguata base di conoscenze per la interpretazione. Infine, vengono analizzati i risultati ottenuti, evidenziando alcuni problemi aperti, sia sul piano concettuale che su quello applicativo

Error threshold in the evolution of diploid organisms

The effects of error propagation in the reproduction of diploid organisms are studied within the populational genetics framework of the quasispecies model. The dependence of the error threshold on the dominance parameter is fully investigated. In particular, it is shown that dominance can protect the wild-type alleles from the error catastrophe. The analysis is restricted to a diploid analogue of the single-peaked landscape.Comment: 9 pages, 4 Postscript figures. Submitted to J. Phy. A: Mat. and Ge

Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random, Gaussian interactions of order p >= 2, and deterministic self-interactions u <= 0. We show that for nonzero u the effect of increasing the order of the interactions is to make the system more cooperative, in the sense that the fraction of extinct species is greatly reduced. Furthermore, we find that for p > 2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.Comment: 7 pages, 4 Postscript figure