The Recurrent Hopfield Mass Model (RHoMM) is a novel generative model developed for the estimation of large-scale effective connectivity from magnetoencephalography (MEG) Band Limited Power signals. This binary mass model, compared to the other popular generative models, has the advantages of being data-driven and in principle scalable to encode large-scale systems interactions. The aim of this work is to evaluate the scalability of the RHoMM and to optimize it at different network sizes (20-200 nodes). Specifically, using simulated objective networks with different architectures, we analysed the effects of L1 rows' normalization and of the addition of a bias in the training. We obtained that in RHoMM without normalization wider intervals of larger learning rates and convergence speeds, associated with lower errors in the inference of the effective connectivity matrix, can be obtained compared to the implementation with normalization, independently from the objective network architecture. Thus, the selection of the learning rate in this case is less critical than with normalization. To also validate the model on experimental data, we employed a dataset of MEG recordings from 10 subjects and a network size of 155 nodes. The obtained results suggest that the model could be effectively scaled to estimate standard-size MEG connectomes.

It is shown that the activity of a whole-brain model based on a Hopfield recurrent neural network exhibits a scaling regime whose exponents depend on both the number of parcels and the decay length of the coupling strength. This scaling regime recovers the picture introduced by Deco et al., whereby information transfer within the human brain generates spatially correlated patterns qualitatively similar to those displayed by turbulent flows, although with a lower exponent, 1/2 instead of 2/3, indicating less regularity. Both models employ coupling strengths which decay exponentially with the Euclidean distance between nodes, as informed by experimental work on the brain topology. Given that the Hopf oscillators model and the Hopfield neural network are mathematically very different, their convergence under the same data parameters, suggests an intriguing robustness of the scaling picture. The present analysis further shows that the Hopfield model brain remains functional after removing connections above about five decay lengths, which corresponds to roughly one sixth of the size of the whole brain. This suggests that, in terms of connectivity decay length, the Hopfield brain functions in an intermediate "turbulent liquid"-like regime, in which the essential connections lie between the connectivity decay length and the global size of the brain. The sensitivity of the numerical value of the scaling exponent to both the decay length, and the number of brain parcels employed, invites great caution in formulating a quantitative assessment on the specific nature of underlying mechanisms sustaining the scaling regime.

The architecture of communication within the brain, represented by the human connectome, has gained a paramount role in the neuroscience community. Several features of this communication, e.g., the frequency content, spatial topology, and temporal dynamics are currently well established. However, identifying generative models providing the underlying patterns of inhibition/excitation is very challenging. To address this issue, we present a novel generative model to estimate large-scale effective connectivity from MEG. The dynamic evolution of this model is determined by a recurrent Hopfield neural network with asymmetric connections, and thus denoted Recurrent Hopfield Mass Model (RHoMM). Since RHoMM must be applied to binary neurons, it is suitable for analyzing Band Limited Power (BLP) dynamics following a binarization process. We trained RHoMM to predict the MEG dynamics through a gradient descent minimization and we validated it in two steps. First, we showed a significant agreement between the similarity of the effective connectivity patterns and that of the interregional BLP correlation, demonstrating RHoMM's ability to capture individual variability of BLP dynamics. Second, we showed that the simulated BLP correlation connectomes, obtained from RHoMM evolutions of BLP, preserved some important topological features, e.g, the centrality of the real data, assuring the reliability of RHoMM. Compared to other biophysical models, RHoMM is based on recurrent Hopfield neural networks, thus, it has the advantage of being data-driven, less demanding in terms of hyperparameters and scalable to encompass large-scale system interactions. These features are promising for investigating the dynamics of inhibition/excitation at different spatial scales.

MOTIVATION: Thermal properties of proteins are of great importance for a number of theoretical and practical implications. Predicting the thermal stability of a protein is a difficult and still scarcely addressed task. RESULTS: Here, we introduce Thermometer, a webserver to assess the thermal stability of a protein using structural information. Thermometer is implemented as a publicly available, user-friendly interface. AVAILABILITY AND IMPLEMENTATION: Our server can be found at the following link (all major browser supported): http://service.tartaglialab.com/new_submission/thermometer_file. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network dilution measures the fraction of neuron couples that are connected, and the network asymmetry measures to what extent the underlying connectivity matrix is asymmetric. For each given neural network, we study the dynamical evolution of all the different initial conditions, thus characterizing the full dynamical landscape without imposing any learning rule. Because of the deterministic dynamics, each trajectory converges to an attractor, that can be either a fixed point or a limit cycle. These attractors form the set of all the possible limit behaviors of the neural network. For each network we then determine the convergence times, the limit cycles' length, the number of attractors, and the sizes of the attractors' basin. We show that there are two network structures that maximize the number of possible limit behaviors. The first optimal network structure is fully-connected and symmetric. On the contrary, the second optimal network structure is highly sparse and asymmetric. The latter optimal is similar to what observed in different biological neuronal circuits. These observations lead us to hypothesize that independently from any given learning model, an efficient and effective biologic network that stores a number of limit behaviors close to its maximum capacity tends to develop a connectivity structure similar to one of the optimal networks we found.