Growth strategy determines the memory and structural properties of brain networks.

The interplay between structure and function affects the emerging properties of many natural systems. Here we use an adaptive neural network model that couples activity and topological dynamics and reproduces the experimental temporal profiles of synaptic density observed in the brain. We prove that the existence of a transient period of relatively high synaptic connectivity is critical for the development of the system under noise circumstances, such that the resulting network can recover stored memories. Moreover, we show that intermediate synaptic densities provide optimal developmental paths with minimum energy consumption, and that ultimately it is the transient heterogeneity in the network that determines its evolution. These results could explain why the pruning curves observed in actual brain areas present their characteristic temporal profiles and they also suggest new design strategies to build biologically inspired neural networks with particular information processing capabilities.

Entropic origin of disassortativity in complex networks.

Why are most empirical networks, with the prominent exception of social ones, generically degree-degree anticorrelated? To answer this long-standing question, we define the ensemble of correlated networks and obtain the associated Shannon entropy. Maximum entropy can correspond to either assortative (correlated) or disassortative (anticorrelated) configurations, but in the case of highly heterogeneous, scale-free networks a certain disassortativity is predicted--offering a parsimonious explanation for the question above. Our approach provides a neutral model from which, in the absence of further knowledge regarding network evolution, one can obtain the expected value of correlations. When empirical observations deviate from the neutral predictions--as happens for social networks--one can then infer that there are specific correlating mechanisms at work.

Instabilities in attractor networks with fast synaptic fluctuations and partial updating of the neurons activity.

We present and study a probabilistic neural automaton in which the fraction of simultaneously-updated neurons is a parameter, rhoin(0,1). For small rho, there is relaxation towards one of the attractors and a great sensibility to external stimuli and, for rho > or = rho(c), itinerancy among attractors. Tuning rho in this regime, oscillations may abruptly change from regular to chaotic and vice versa, which allows one to control the efficiency of the searching process. We argue on the similarity of the model behavior with recent observations, and on the possible role of chaos in neurobiology.

Concurrence of form and function in developing networks and its role in synaptic pruning.

A fundamental question in neuroscience is how structure and function of neural systems are related. We study this interplay by combining a familiar auto-associative neural network with an evolving mechanism for the birth and death of synapses. A feedback loop then arises leading to two qualitatively different types of behaviour. In one, the network structure becomes heterogeneous and dissasortative, and the system displays good memory performance; furthermore, the structure is optimised for the particular memory patterns stored during the process. In the other, the structure remains homogeneous and incapable of pattern retrieval. These findings provide an inspiring picture of brain structure and dynamics that is compatible with experimental results on early brain development, and may help to explain synaptic pruning. Other evolving networks-such as those of protein interactions-might share the basic ingredients for this feedback loop and other questions, and indeed many of their structural features are as predicted by our model.

Control of neural chaos by synaptic noise.

We study neural automata - or neurobiologically inspired cellular automata - which exhibits chaotic itinerancy among the different stored patterns or memories. This is a consequence of activity-dependent synaptic fluctuations, which continuously destabilize the attractor and induce irregular hopping to other possible attractors. The nature of these irregularities depends on the dynamic details, namely, on the intensity of the synaptic noise and the number of sites of the network, which are synchronously updated at each time step. Varying these factors, different regimes occur, ranging from regular to chaotic dynamics. As a result, and in absence of external agents, the chaotic behavior may turn regular after tuning the noise intensity. It is argued that a similar mechanism might be on the basis of self-controlling chaos in natural systems.

Metastability, nucleation, and noise-enhanced stabilization out of equilibrium.

We study metastability and nucleation in a kinetic two-dimensional Ising model that is driven out of equilibrium by a small random perturbation of the usual dynamics at temperature T. We show that, at a mesoscopic/cluster level, a nonequilibrium potential describes in a simple way metastable states and their decay. We thus predict noise-enhanced stability of the metastable phase and resonant propagation of domain walls at low T. This follows from the nonlinear interplay between thermal and nonequilibrium fluctuations, which induces reentrant behavior of the surface tension as a function of T. Our results, which are confirmed by Monte Carlo simulations, can be also understood in terms of a Langevin equation with competing additive and multiplicative noises.

Prevention of disabling and fatal strokes by successful carotid endarterectomy in patients without recent neurological symptoms: randomised controlled trial.

BACKGROUND: Among patients with substantial carotid artery narrowing but no recent neurological symptom (stroke or transient ischaemia), the balance of surgical risks and long-term benefits from carotid endarterectomy (CEA) was unclear. METHODS: During 1993-2003, 3120 asymptomatic patients with substantial carotid narrowing were randomised equally between immediate CEA (half got CEA by 1 month, 88% by 1 year) and indefinite deferral of any CEA (only 4% per year got CEA) and were followed for up to 5 years (mean 3.4 years). Kaplan-Meier analyses of 5-year risks are by allocated treatment. FINDINGS: The risk of stroke or death within 30 days of CEA was 3.1% (95% CI 2.3-4.1). Comparing all patients allocated immediate CEA versus all allocated deferral, but excluding such perioperative events, the 5-year stroke risks were 3.8% versus 11% (gain 7.2% [95% CI 5.0-9.4], p<0.0001). This gain chiefly involved carotid territory ischaemic strokes (2.7% vs 9.5%; gain 6.8% [4.8-8.8], p<0.0001), of which half were disabling or fatal (1.6% vs 5.3%; gain 3.7% [2.1-5.2], p<0.0001), as were half the perioperative strokes. Combining the perioperative events and the non-perioperative strokes, net 5-year risks were 6.4% versus 11.8% for all strokes (net gain 5.4% [3.0-7.8], p<0.0001), 3.5% versus 6.1% for fatal or disabling strokes (net gain 2.5% [0.8-4.3], p=0.004), and 2.1% versus 4.2% just for fatal strokes (net gain 2.1% [0.6-3.6], p=0.006). Subgroup-specific analyses found no significant heterogeneity in the perioperative hazards or (apart from the importance of cholesterol) in the long-term postoperative benefits. These benefits were separately significant for males and females; for those with about 70%, 80%, and 90% carotid artery narrowing on ultrasound; and for those younger than 65 and 65-74 years of age (though not for older patients, half of whom die within 5 years from unrelated causes). Full compliance with allocation to immediate CEA or deferral would, in expectation, have produced slightly bigger differences in the numbers operated on, and hence in the net 5-year benefits. The 10-year benefits are not yet known. INTERPRETATION: In asymptomatic patients younger than 75 years of age with carotid diameter reduction about 70% or more on ultrasound (many of whom were on aspirin, antihypertensive, and, in recent years, statin therapy), immediate CEA halved the net 5-year stroke risk from about 12% to about 6% (including the 3% perioperative hazard). Half this 5-year benefit involved disabling or fatal strokes. But, outside trials, inappropriate selection of patients or poor surgery could obviate such benefits.

Effects of static and dynamic disorder on the performance of neural automata.

We report on both analytical and numerical results concerning stochastic Hopfield-like neural automata exhibiting the following (biologically inspired) features: (1) Neurons and synapses evolve in time as in contact with respective baths at different temperatures; (2) the connectivity between neurons may be tuned from full connection to high random dilution, or to the case of networks with the small-world property and/or scale-free architecture; and (3) there is synaptic kinetics simulating repeated scanning of the stored patterns. Although these features may apparently result in additional disorder, the model exhibits, for a wide range of parameter values, an extraordinary computational performance, and some of the qualitative behaviors observed in natural systems. In particular, we illustrate here very efficient and robust associative memory, and jumping between pattern attractors.

Lennard-Jones and lattice models of driven fluids.

We introduce a nonequilibrium off-lattice model for anisotropic phenomena in fluids. This is a Lennard-Jones generalization of the driven lattice-gas model in which the particles' spatial coordinates vary continuously. A comparison between the two models allows us to discuss some exceptional, hardly realistic features of the original discrete system--which has been considered a prototype for nonequilibrium anisotropic phase transitions. We thus help to clarify open issues, and discuss on the implications of our observations for future investigation of anisotropic phase transitions.

Brain Performance versus Phase Transitions.

We here illustrate how a well-founded study of the brain may originate in assuming analogies with phase-transition phenomena. Analyzing to what extent a weak signal endures in noisy environments, we identify the underlying mechanisms, and it results a description of how the excitability associated to (non-equilibrium) phase changes and criticality optimizes the processing of the signal. Our setting is a network of integrate-and-fire nodes in which connections are heterogeneous with rapid time-varying intensities mimicking fatigue and potentiation. Emergence then becomes quite robust against wiring topology modification--in fact, we considered from a fully connected network to the Homo sapiens connectome--showing the essential role of synaptic flickering on computations. We also suggest how to experimentally disclose significant changes during actual brain operation.

Efficient transmission of subthreshold signals in complex networks of spiking neurons.

We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances--that naturally balances the network with excitatory and inhibitory synapses--and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.

Reentrant behavior of the spinodal curve in a nonequilibrium ferromagnet.

The metastable behavior of a kinetic Ising-type ferromagnetic model system in which a generic type of microscopic disorder induces nonequilibrium steady states is studied by computer simulation and a mean-field approach. We pay attention, in particular, to the spinodal curve or intrinsic coercive field that separates the metastable region from the unstable one. We find that, under strong nonequilibrium conditions, this exhibits reentrant behavior as a function of temperature. That is, metastability does not happen in this regime for both low and high temperatures, but instead emerges for intermediate temperature, as a consequence of the nonlinear interplay between thermal and nonequilibrium fluctuations. We argue that this behavior, which is in contrast with equilibrium phenomenology and could occur in actual impure specimens, might be related to the presence of an effective multiplicative noise in the system.

Robust short-term memory without synaptic learning.

Short-term memory in the brain cannot in general be explained the way long-term memory can--as a gradual modification of synaptic weights--since it takes place too quickly. Theories based on some form of cellular bistability, however, do not seem able to account for the fact that noisy neurons can collectively store information in a robust manner. We show how a sufficiently clustered network of simple model neurons can be instantly induced into metastable states capable of retaining information for a short time (a few seconds). The mechanism is robust to different network topologies and kinds of neural model. This could constitute a viable means available to the brain for sensory and/or short-term memory with no need of synaptic learning. Relevant phenomena described by neurobiology and psychology, such as local synchronization of synaptic inputs and power-law statistics of forgetting avalanches, emerge naturally from this mechanism, and we suggest possible experiments to test its viability in more biological settings.

Stochastic resonance crossovers in complex networks.

Here we numerically study the emergence of stochastic resonance as a mild phenomenon and how this transforms into an amazing enhancement of the signal-to-noise ratio at several levels of a disturbing ambient noise. The setting is a cooperative, interacting complex system modelled as an Ising-Hopfield network in which the intensity of mutual interactions or "synapses" varies with time in such a way that it accounts for, e.g., a kind of fatigue reported to occur in the cortex. This induces nonequilibrium phase transitions whose rising comes associated to various mechanisms producing two types of resonance. The model thus clarifies the details of the signal transmission and the causes of correlation among noise and signal. We also describe short-time persistent memory states, and conclude on the limited relevance of the network wiring topology. Our results, in qualitative agreement with the observation of excellent transmission of weak signals in the brain when competing with both intrinsic and external noise, are expected to be of wide validity and may have technological application. We also present here a first contact between the model behavior and psychotechnical data.

Unstable dynamics, nonequilibrium phases, and criticality in networked excitable media.

Excitable systems are of great theoretical and practical interest in mathematics, physics, chemistry, and biology. Here, we numerically study models of excitable media, namely, networks whose nodes may occasionally be dormant and the connection weights are allowed to vary with the system activity on a short-time scale, which is a convenient and realistic representation. The resulting global activity is quite sensitive to stimuli and eventually becomes unstable also in the absence of any stimuli. Outstanding consequences of such unstable dynamics are the spontaneous occurrence of various nonequilibrium phases--including associative-memory phases and one in which the global activity wanders irregularly, e.g., chaotically among all or part of the dynamic attractors--and 1/f noise as the system is driven into the phase region corresponding to the most irregular behavior. A net result is resilience which results in an efficient search in the model attractor space that can explain the origin of some observed behavior in neural, genetic, and ill-condensed matter systems. By extensive computer simulation we also address a previously conjectured relation between observed power-law distributions and the possible occurrence of a "critical state" during functionality of, e.g., cortical networks, and describe the precise nature of such criticality in the model which may serve to guide future experiments.