Adaptation Shapes Local Cortical Reactivity: From Bifurcation Diagram and Simulations to Human Physiological and Pathological Responses.

Human studies employing intracerebral and transcranial perturbations suggest that the input-output properties of cortical circuits are dramatically affected during sleep in healthy subjects as well as in awake patients with multifocal and focal brain injury. In all these conditions, cortical circuits react to direct stimulation with an initial activation followed by suppression of activity (Off-period) that disrupts the build-up of sustained causal interactions typically observed in healthy wakefulness. The transition to this stereotypical response has important clinical implications, being associated with loss of consciousness or loss of functions. Here, we provide a mechanistic explanation of these findings by means of simulations of a cortical-like module endowed with activity-dependent adaptation and mean-field theory. First, we show that fundamental aspects of the local responses elicited in humans by direct cortical stimulation can be replicated by systematically varying the relationships between adaptation strength and excitation level in the network. Then, we reveal a region in the adaptation-excitation parameter space of crucial relevance for both physiological and pathologic conditions, where spontaneous activity and responses to perturbation diverge in their ability to reveal Off-periods. Finally, we substantiate through simulations of connected cortical-like modules the role of adaptation mechanisms in preventing cortical neurons from engaging in reciprocal causal interactions, as suggested by empirical studies. These modeling results provide a general theoretical framework and a mechanistic interpretation for a body of neurophysiological measurements that bears critical relevance for physiological states as well as for the assessment and rehabilitation of brain-injured patients.

Deterministic and Stochastic Components of Cortical Down States: Dynamics and Modulation.

Slow oscillations are an emergent activity of the cerebral cortex network consisting of alternating periods of activity (Up states) and silence (Down states). Up states are periods of persistent cortical activity that share properties with that of underlying wakefulness. However, the occurrence of Down states is almost invariably associated with unconsciousness, both in animal models and clinical studies. Down states have been attributed relevant functions, such as being a resetting mechanism or breaking causal interactions between cortical areas. But what do Down states consist of? Here, we explored in detail the network dynamics (e.g., synchronization and phase) during these silent periods in vivo (male mice), in vitro (ferrets, either sex), and in silico, investigating various experimental conditions that modulate them: anesthesia levels, excitability (electric fields), and excitation/inhibition balance. We identified metastability as two complementary phases composing such quiescence states: a highly synchronized "deterministic" period followed by a low-synchronization "stochastic" period. The balance between these two phases determines the dynamical properties of the resulting rhythm, as well as the responsiveness to incoming inputs or refractoriness. We propose detailed Up and Down state cycle dynamics that bridge cortical properties emerging at the mesoscale with their underlying mechanisms at the microscale, providing a key to understanding unconscious states.SIGNIFICANCE STATEMENT The cerebral cortex expresses slow oscillations consisting of Up (active) and Down (silent) states. Such activity emerges not only in slow wave sleep, but also under anesthesia and in brain lesions. Down states functionally disconnect the network, and are associated with unconsciousness. Based on a large collection of data, novel data analysis approaches and computational modeling, we thoroughly investigate the nature of Down states. We identify two phases: a highly synchronized "deterministic" period, followed by a low-synchronization "stochastic" period. The balance between these two phases determines the dynamic properties of the resulting rhythm and responsiveness to incoming inputs. This finding reconciles different theories of slow rhythm generation and provides clues about how the brain switches from conscious to unconscious brain states.

Slow waves form expanding, memory-rich mesostates steered by local excitability in fading anesthesia.

In the arousal process, the brain restores its integrative activity from the synchronized state of slow wave activity (SWA). The mechanisms underpinning this state transition remain, however, to be elucidated. Here we simultaneously probed neuronal assemblies throughout the whole cortex with micro-electrocorticographic recordings in mice. We investigated the progressive shaping of propagating SWA at different levels of isoflurane. We found a form of memory of the wavefront shapes at deep anesthesia, tightly alternating posterior-anterior-posterior patterns. At low isoflurane, metastable patterns propagated in more directions, reflecting an increased complexity. The wandering across these mesostates progressively increased its randomness, as predicted by simulations of a network of spiking neurons, and confirmed in our experimental data. The complexity increase is explained by the elevated excitability of local assemblies with no modifications of the network connectivity. These results shed new light on the functional reorganization of the cortical network as anesthesia fades out.

Cost of Coexisting with a Relict Large Carnivore Population: Impact of Apennine Brown Bears, 2005-2015.

Human-carnivore conflicts are a major conservation issue. As bears are expanding their range in Europe's human-modified landscapes, it is increasingly important to understand, prevent, and address human-bear conflicts and evaluate mitigation strategies in areas of historical coexistence. Based on verified claims, we assessed costs, patterns, and drivers of bear damages in the relict Apennine brown bear population in the Abruzzo Lazio and Molise National Park (PNALM), central Italy. During 2005-2015, 203 ± 71 (SD) damage events were verified annually, equivalent to 75,987 ± 30,038 €/year paid for compensation. Most damages occurred in summer and fall, with livestock depredation, especially sheep and cattle calves, prevailing over other types of damages, with apiaries ranking second in costs of compensation. Transhumant livestock owners were less impacted than residential ones, and farms that adopted prevention measures loaned from the PNALM were less susceptible to bear damages. Livestock farms chronically damaged by bears represented 8 ± 3% of those annually impacted, corresponding to 24 ± 6% of compensation costs. Further improvements in the conflict mitigation policy adopted by the PNALM include integrated prevention, conditional compensation, and participatory processes. We discuss the implications of our study for Human-bear coexistence in broader contexts.

Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays.

Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics. In biological neuron networks this is due in part to local synaptic filtering of exchanged spikes, and in part to the distribution of the axonal transmission delays. How differently these two kinds of communication protocols affect the network dynamics is still an open issue due to the difficulties in dealing with the non-Markovian nature of synaptic transmission. Here, we develop a mean-field dimensional reduction yielding to an effective Markovian dynamics of the population density of the neuronal membrane potential, valid under the hypothesis of small fluctuations of the synaptic current. Within this limit, the resulting theory allows us to prove the formal equivalence between the two transmission mechanisms, holding for any synaptic time scale, integrate-and-fire neuron model, spike emission regimes and for different network states even when the neuron number is finite. The equivalence holds even for larger fluctuations of the synaptic input, if white noise currents are incorporated to model other possible biological features such as ionic channel stochasticity.

Emerging Heterogeneities in Italian Customs and Comparison with Nearby Countries.

In this work we apply techniques and modus operandi typical of Statistical Mechanics to a large dataset about key social quantifiers and compare the resulting behaviors of five European nations, namely France, Germany, Italy, Spain and Switzerland. The social quantifiers considered are i. the evolution of the number of autochthonous marriages (i.e., between two natives) within a given territorial district and ii. the evolution of the number of mixed marriages (i.e., between a native and an immigrant) within a given territorial district. Our investigations are twofold. From a theoretical perspective, we develop novel techniques, complementary to classical methods (e.g., historical series and logistic regression), in order to detect possible collective features underlying the empirical behaviors; from an experimental perspective, we evidence a clear outline for the evolution of the social quantifiers considered. The comparison between experimental results and theoretical predictions is excellent and allows speculating that France, Italy and Spain display a certain degree of internal heterogeneity, that is not found in Germany and Switzerland; such heterogeneity, quite mild in France and in Spain, is not negligible in Italy and highlights quantitative differences in the habits of Northern and Southern regions. These findings may suggest the persistence of two culturally distinct communities, long-term lasting heritages of different and well-established customs. Also, we find qualitative differences between the evolution of autochthonous and of mixed marriages: for the former imitation in decisional mechanisms seems to play a key role (and this results in a square root relation between the number of autochthonous marriages versus the percentage of possible couples inside that country), while for the latter the emerging behavior can be recovered (in most cases) with elementary models with no interactions, suggesting weak imitation patterns between natives and migrants (and this translates in a linear growth for the number of mixed marriages versus the percentage of possible mixed couples in the country). However, the case of mixed marriages displays a more complex phenomenology, where further details (e.g., the provenance and the status of migrants, linguistic barriers, etc.) should also be accounted for.

Topological properties of hierarchical networks.

Hierarchical networks are attracting a renewal interest for modeling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the Dyson hierarchical construction for ferromagnets, neural networks, and spin glasses, recently analyzed from a statistical-mechanics perspective, and we focus on the topological properties of the underlying structures. In particular, we find that such structures are weighted graphs that exhibit a high degree of clustering and of modularity, with a small spectral gap; the robustness of such features with respect to the presence of thermal noise is also studied. These outcomes are then discussed and related to the statistical-mechanics scenario in full consistency. Last, we look at these weighted graphs as Markov chains and we show that in the limit of infinite size, the emergence of ergodicity breakdown for the stochastic process mirrors the emergence of metastabilities in the corresponding statistical mechanical analysis.

Hierarchical neural networks perform both serial and parallel processing.

In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet available, after a streamlined introduction to the state of the art via that route, the problem is consistently approached through signal-to-noise technique and extensive numerical simulations. Focusing on the low-storage regime, where the amount of stored patterns grows at most logarithmical with the system size, we prove that these non-mean-field Hopfield-like networks display a richer phase diagram than their classical counterparts. In particular, these networks are able to perform serial processing (i.e. retrieve one pattern at a time through a complete rearrangement of the whole ensemble of neurons) as well as parallel processing (i.e. retrieve several patterns simultaneously, delegating the management of different patterns to diverse communities that build network). The tune between the two regimes is given by the rate of the coupling decay and by the level of noise affecting the system. The price to pay for those remarkable capabilities lies in a network's capacity smaller than the mean field counterpart, thus yielding a new budget principle: the wider the multitasking capabilities, the lower the network load and vice versa. This may have important implications in our understanding of biological complexity.

Retrieval capabilities of hierarchical networks: from Dyson to Hopfield.

We consider statistical-mechanics models for spin systems built on hierarchical structures, which provide a simple example of non-mean-field framework. We show that the coupling decay with spin distance can give rise to peculiar features and phase diagrams much richer than their mean-field counterpart. In particular, we consider the Dyson model, mimicking ferromagnetism in lattices, and we prove the existence of a number of metastabilities, beyond the ordered state, which become stable in the thermodynamic limit. Such a feature is retained when the hierarchical structure is coupled with the Hebb rule for learning, hence mimicking the modular architecture of neurons, and gives rise to an associative network able to perform single pattern retrieval as well as multiple-pattern retrieval, depending crucially on the external stimuli and on the rate of interaction decay with distance; however, those emergent multitasking features reduce the network capacity with respect to the mean-field counterpart. The analysis is accomplished through statistical mechanics, Markov chain theory, signal-to-noise ratio technique, and numerical simulations in full consistency. Our results shed light on the biological complexity shown by real networks, and suggest future directions for understanding more realistic models.

Multitasking attractor networks with neuronal threshold noise.

We consider the multitasking associative network in the low-storage limit and we study its phase diagram with respect to the noise level T and the degree d of dilution in pattern entries. We find that the system is characterized by a rich variety of stable states, including pure states, parallel retrieval states, hierarchically organized states and symmetric mixtures (remarkably, both even and odd), whose complexity increases as the number of patterns P grows. The analysis is performed both analytically and numerically: Exploiting techniques based on partial differential equations, we are able to get the self-consistencies for the order parameters. Such self-consistency equations are then solved and the solutions are further checked through stability theory to catalog their organizations into the phase diagram, which is outlined at the end. This is a further step towards the understanding of spontaneous parallel processing in associative networks.

Parallel processing in immune networks.

In this work, we adopt a statistical-mechanics approach to investigate basic, systemic features exhibited by adaptive immune systems. The lymphocyte network made by B cells and T cells is modeled by a bipartite spin glass, where, following biological prescriptions, links connecting B cells and T cells are sparse. Interestingly, the dilution performed on links is shown to make the system able to orchestrate parallel strategies to fight several pathogens at the same time; this multitasking capability constitutes a remarkable, key property of immune systems as multiple antigens are always present within the host. We also define the stochastic process ruling the temporal evolution of lymphocyte activity and show its relaxation toward an equilibrium measure allowing statistical-mechanics investigations. Analytical results are compared with Monte Carlo simulations and signal-to-noise outcomes showing overall excellent agreement. Finally, within our model, a rationale for the experimentally well-evidenced correlation between lymphocytosis and autoimmunity is achieved; this sheds further light on the systemic features exhibited by immune networks.

Parallel retrieval of correlated patterns: from Hopfield networks to Boltzmann machines.

In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a modification of the Hebbian prescription, which induces a coupling between consecutive patterns and this effect is tuned by a parameter a. In the latter case, dilution is introduced in pattern entries, in such a way that a fraction d of them is blank. Then, we merge these two extensions to obtain a system able to retrieve several patterns in parallel and the quality of retrieval, encoded by the set of Mattis magnetizations {m(µ)}, is reminiscent of the correlation among patterns. By tuning the parameters d and a, qualitatively different outputs emerge, ranging from highly hierarchical to symmetric. The investigations are accomplished by means of both numerical simulations and statistical mechanics analysis, properly adapting a novel technique originally developed for spin glasses, i.e. the Hamilton-Jacobi interpolation, with excellent agreement. Finally, we show the thermodynamical equivalence of this associative network with a (restricted) Boltzmann machine and study its stochastic dynamics to obtain even a dynamical picture, perfectly consistent with the static scenario earlier discussed.

Multitasking associative networks.

We introduce a bipartite, diluted and frustrated, network as a sparse restricted Boltzmann machine and we show its thermodynamical equivalence to an associative working memory able to retrieve several patterns in parallel without falling into spurious states typical of classical neural networks. We focus on systems processing in parallel a finite (up to logarithmic growth in the volume) amount of patterns, mirroring the low-level storage of standard Amit-Gutfreund-Sompolinsky theory. Results obtained through statistical mechanics, the signal-to-noise technique, and Monte Carlo simulations are overall in perfect agreement and carry interesting biological insights. Indeed, these associative networks pave new perspectives in the understanding of multitasking features expressed by complex systems, e.g., neural and immune networks.