Scale-free correlations in the dynamics of a small (N∼10000) cortical network.

The advent of novel optogenetics technology allows the recording of brain activity with a resolution never seen before. The characterization of these very large data sets offers new challenges as well as unique theory-testing opportunities. Here we discuss whether the spatial and temporal correlations of the collective activity of thousands of neurons are tangled as predicted by the theory of critical phenomena. The analysis shows that both the correlation length ξ and the correlation time τ scale as predicted as a function of the system size. With some peculiarities that we discuss, the analysis uncovers evidence consistent with the view that the large-scale brain cortical dynamics corresponds to critical phenomena.

Finite-size correlation behavior near a critical point: A simple metric for monitoring the state of a neural network.

In this article, a correlation metric κ_{c} is proposed for the inference of the dynamical state of neuronal networks. κ_{C} is computed from the scaling of the correlation length with the size of the observation region, which shows qualitatively different behavior near and away from the critical point of a continuous phase transition. The implementation is first studied on a neuronal network model, where the results of this new metric coincide with those obtained from neuronal avalanche analysis, thus well characterizing the critical state of the network. The approach is further tested with brain optogenetic recordings in behaving mice from a publicly available database. Potential applications and limitations for its use with currently available optical imaging techniques are discussed.

Tricritical behavior in a neural model with excitatory and inhibitory units.

While the support for the relevance of critical dynamics to brain function is increasing, there is much less agreement on the exact nature of the advocated critical point. Thus, a considerable number of theoretical efforts are currently concentrated on which mechanisms and what type(s) of transition can be exhibited by neuronal network models. In that direction, the present work describes the effect of incorporating a fraction of inhibitory neurons on the collective dynamics. As we show, this results in the appearance of a tricritical point for highly connected networks and a nonzero fraction of inhibitory neurons.

Universal dynamics of mitochondrial networks: a finite-size scaling analysis.

Evidence from models and experiments suggests that the networked structure observed in mitochondria emerges at the critical point of a phase transition controlled by fission and fusion rates. If mitochondria are poised at criticality, the relevant network quantities should scale with the system's size. However, whether or not the expected finite-size effects take place has not been demonstrated yet. Here, we first provide a theoretical framework to interpret the scaling behavior of mitochondrial network quantities by analyzing two conceptually different models of mitochondrial dynamics. Then, we perform a finite-size scaling analysis of real mitochondrial networks extracted from microscopy images and obtain scaling exponents comparable with critical exponents from models and theory. Overall, we provide a universal description of the structural phase transition in mammalian mitochondria.

Purified myelin lipids display a critical mixing point at low surface pressure.

Lipids extracted from Purified Myelin Membranes (LPMM) were spread as monomolecular films at the air/aqueous interface. The films were visualized by Brewster Angle Microscopy (BAM) at different lateral pressures (π) and ionic environments. Coexistence of Liquid-Expanded (LE) and cholesterol-enriched (CE) rounded domains persisted up to π ≈ 5 mN/m but the monolayers became homogeneous at higher surface pressures. Before mixing, the domains distorted to non-rounded domains. We experimentally measured the line tension (λ) for the lipid monolayers at the domain borders by a shape relaxation technique using non-homogeneous electric fields. Regardless of the subphase conditions, the obtained line tensions are of the order of pN and tended to decrease as lateral pressure increased toward the mixing point. From the mean square displacement of nested trapped domains, we also calculated the dipole density difference between phases (µ). A non-linear drop was detected in this parameter as the mixing point is approached. Here we quantitively evaluated the π-dependance of both parameters with proper power laws in the vicinity of the critical mixing surface pressure, and the exponents showed to be consistent with a critical phenomenon in the two-dimensional Ising universality class. This idea of bidimensionality was found to be compatible only for simplified lipidic systems, while for whole myelin monolayers, that means including proteins, no critical mixing point was detected. Finally, the line tension values were related with the thickness differences between phases (Δt) near the critical point.

Emergent dynamics in a robotic model based on the Caenorhabditis elegans connectome.

We analyze the neural dynamics and their relation with the emergent actions of a robotic vehicle that is controlled by a neural network numerical simulation based on the nervous system of the nematode Caenorhabditis elegans. The robot interacts with the environment through a sensor that transmits the information to sensory neurons, while motor neurons outputs are connected to wheels. This is enough to allow emergent robot actions in complex environments, such as avoiding collisions with obstacles. Working with robotic models makes it possible to simultaneously keep track of the dynamics of all the neurons and also register the actions of the robot in the environment in real time, while avoiding the complex technicalities of simulating a real environment. This allowed us to identify several relevant features of the neural dynamics associated with the emergent actions of the robot, some of which have already been observed in biological worms. These results suggest that some basic aspects of behaviors observed in living beings are determined by the underlying structure of the associated neural network.

Box scaling as a proxy of finite size correlations.

The scaling of correlations as a function of size provides important hints to understand critical phenomena on a variety of systems. Its study in biological structures offers two challenges: usually they are not of infinite size, and, in the majority of cases, dimensions can not be varied at will. Here we discuss how finite-size scaling can be approximated in an experimental system of fixed and relatively small extent, by computing correlations inside of a reduced field of view of various widths (we will refer to this procedure as "box-scaling"). A relation among the size of the field of view, and measured correlation length, is derived at, and away from, the critical regime. Numerical simulations of a neuronal network, as well as the ferromagnetic 2D Ising model, are used to verify such approximations. Numerical results support the validity of the heuristic approach, which should be useful to characterize relevant aspects of critical phenomena in biological systems.

Similar local neuronal dynamics may lead to different collective behavior.

This report is concerned with the relevance of the microscopic rules that implement individual neuronal activation, in determining the collective dynamics, under variations of the network topology. To fix ideas we study the dynamics of two cellular automaton models, commonly used, rather in-distinctively, as the building blocks of large-scale neuronal networks. One model, due to Greenberg and Hastings (GH), can be described by evolution equations mimicking an integrate-and-fire process, while the other model, due to Kinouchi and Copelli (KC), represents an abstract branching process, where a single active neuron activates a given number of postsynaptic neurons according to a prescribed "activity" branching ratio. Despite the apparent similarity between the local neuronal dynamics of the two models, it is shown that they exhibit very different collective dynamics as a function of the network topology. The GH model shows qualitatively different dynamical regimes as the network topology is varied, including transients to a ground (inactive) state, continuous and discontinuous dynamical phase transitions. In contrast, the KC model only exhibits a continuous phase transition, independently of the network topology. These results highlight the importance of paying attention to the microscopic rules chosen to model the interneuronal interactions in large-scale numerical simulations, in particular when the network topology is far from a mean-field description. One such case is the extensive work being done in the context of the Human Connectome, where a wide variety of types of models are being used to understand the brain collective dynamics.

Controlling a complex system near its critical point via temporal correlations.

Many complex systems exhibit large fluctuations both across space and over time. These fluctuations have often been linked to the presence of some kind of critical phenomena, where it is well known that the emerging correlation functions in space and time are closely related to each other. Here we test whether the time correlation properties allow systems exhibiting a phase transition to self-tune to their critical point. We describe results in three models: the 2D Ising ferromagnetic model, the 3D Vicsek flocking model and a small-world neuronal network model. We demonstrate that feedback from the autocorrelation function of the order parameter fluctuations shifts the system towards its critical point. Our results rely on universal properties of critical systems and are expected to be relevant to a variety of other settings.

Universal and nonuniversal neural dynamics on small world connectomes: A finite-size scaling analysis.

Evidence of critical dynamics has been found recently in both experiments and models of large-scale brain dynamics. The understanding of the nature and features of such a critical regime is hampered by the relatively small size of the available connectome, which prevents, among other things, the determination of its associated universality class. To circumvent that, here we study a neural model defined on a class of small-world networks that share some topological features with the human connectome. We find that varying the topological parameters can give rise to a scale-invariant behavior either belonging to the mean-field percolation universality class or having nonuniversal critical exponents. In addition, we find certain regions of the topological parameter space where the system presents a discontinuous, i.e., noncritical, dynamical phase transition into a percolated state. Overall, these results shed light on the interplay of dynamical and topological roots of the complex brain dynamics.

Three-state model with competing antiferromagnetic and pairing interactions.

Motivated by the rich phase diagram of the high-temperature superconductors, we introduce a pseudospin model with three state variables which can be interpreted as two states (spin ±1/2) particles and holes. The Hamiltonian has a term which favors antiferromagnetism and an additional competing interaction which favors bonding between pairs of antiparallel spins mediated by holes. For low concentration of holes the dominant interaction between particles has antiferromagnetic character, leading to an antiferromagnetic phase in the temperature-hole concentration phase diagram, qualitatively similar to the antiferromagnetic phase of doped Mott insulators. For growing concentration of holes antiferromagnetic order is weakened and a phase with a different kind of order mediated by holes appears. This last phase has the form of a dome in the T-hole concentration plane. The whole phase diagram resembles those of some families of high-T_{c} superconductors. We compute the phase diagram in the mean-field approximation and characterize the different phase transitions through Monte Carlo simulations.

Nrf2 stabilization prevents critical oxidative damage in Down syndrome cells.

Mounting evidence implicates chronic oxidative stress as a critical driver of the aging process. Down syndrome (DS) is characterized by a complex phenotype, including early senescence. DS cells display increased levels of reactive oxygen species (ROS) and mitochondrial structural and metabolic dysfunction, which are counterbalanced by sustained Nrf2-mediated transcription of cellular antioxidant response elements (ARE). Here, we show that caspase 3/PKCδdependent activation of the Nrf2 pathway in DS and Dp16 (a mouse model of DS) cells is necessary to protect against chronic oxidative damage and to preserve cellular functionality. Mitochondria-targeted catalase (mCAT) significantly reduced oxidative stress, restored mitochondrial structure and function, normalized replicative and wound healing capacity, and rendered the Nrf2-mediated antioxidant response dispensable. These results highlight the critical role of Nrf2/ARE in the maintenance of DS cell homeostasis and validate mitochondrial-specific interventions as a key aspect of antioxidant and antiaging therapies.

Mitochondrial network complexity emerges from fission/fusion dynamics.

Mitochondrial networks exhibit a variety of complex behaviors, including coordinated cell-wide oscillations of energy states as well as a phase transition (depolarization) in response to oxidative stress. Since functional and structural properties are often interwinded, here we characterized the structure of mitochondrial networks in mouse embryonic fibroblasts using network tools and percolation theory. Subsequently we perturbed the system either by promoting the fusion of mitochondrial segments or by inducing mitochondrial fission. Quantitative analysis of mitochondrial clusters revealed that structural parameters of healthy mitochondria laid in between the extremes of highly fragmented and completely fusioned networks. We confirmed our results by contrasting our empirical findings with the predictions of a recently described computational model of mitochondrial network emergence based on fission-fusion kinetics. Altogether these results offer not only an objective methodology to parametrize the complexity of this organelle but also support the idea that mitochondrial networks behave as critical systems and undergo structural phase transitions.

Magnetization reversal in mixed ferrite-chromite perovskites with non magnetic cation on the A-site.

In this work, we have performed Monte Carlo simulations in a classical model for RFe1-x Cr x O3 with R = Y and Lu, comparing the numerical simulations with experiments and mean field calculations. In the analyzed compounds, the antisymmetric exchange or Dzyaloshinskii-Moriya (DM) interaction induced a weak ferromagnetism due to a canting of the antiferromagnetically ordered spins. This model is able to reproduce the magnetization reversal (MR) observed experimentally in a field cooling process for intermediate x values and the dependence with x of the critical temperatures. We also analyzed the conditions for the existence of MR in terms of the strength of DM interactions between Fe(3+) and Cr(3+) ions with the x values variations.

The generalization complexity measure for continuous input data.

We introduce in this work an extension for the generalization complexity measure to continuous input data. The measure, originally defined in Boolean space, quantifies the complexity of data in relationship to the prediction accuracy that can be expected when using a supervised classifier like a neural network, SVM, and so forth. We first extend the original measure for its use with continuous functions to later on, using an approach based on the use of the set of Walsh functions, consider the case of having a finite number of data points (inputs/outputs pairs), that is, usually the practical case. Using a set of trigonometric functions a model that gives a relationship between the size of the hidden layer of a neural network and the complexity is constructed. Finally, we demonstrate the application of the introduced complexity measure, by using the generated model, to the problem of estimating an adequate neural network architecture for real-world data sets.

Finite-temperature phase diagram of ultrathin magnetic films without external fields.

We analyze the finite-temperature phase diagram of ultrathin magnetic films by introducing a mean-field theory, valid in the low-anisotropy regime, i.e., close to the spin reorientation transition. The theoretical results are compared with Monte Carlo simulations carried out on a microscopic Heisenberg model. Connections between the finite-temperature behavior and the ground-state properties of the system are established. Several properties of the stripe pattern, such as the presence of canted states, the stripe width variation phenomenon, and the associated magnetization profiles, are also analyzed.

Nonequilibrium structures and slow dynamics in a two-dimensional spin system with competing long-range and short-range interactions.

We present a lattice spin model that mimics a system of interacting particles through a short-range repulsive potential and a long-range attractive power-law decaying potential. We perform a detailed analysis of the general equilibrium phase diagram of the model at finite temperature, showing that the only possible equilibrium phases are the ferromagnetic and the antiferromagnetic ones. We then study the nonequilibrium behavior of the model after a quench to subcritical temperatures, in the antiferromagnetic region of the phase diagram region, where the pair interaction potential behaves in the same qualitative way as in a Lennard-Jones gas. We find that even in the absence of quenched disorder or geometric frustration, the competition between interactions gives rise to nonequilibrium disordered structures at low enough temperatures that strongly slow down the relaxation of the system. This nonequilibrium state presents several features characteristic of glassy systems such as subaging, nontrivial fuctuation dissipation relations, and possible logarithmic growth of free-energy barriers to coarsening.

Emergent self-organized complex network topology out of stability constraints.

Although most networks in nature exhibit complex topologies, the origins of such complexity remain unclear. We propose a general evolutionary mechanism based on global stability. This mechanism is incorporated into a model of a growing network of interacting agents in which each new agent's membership in the network is determined by the agent's effect on the network's global stability. It is shown that out of this stability constraint complex topological properties emerge in a self-organized manner, offering an explanation for their observed ubiquity in biological networks.

Cultural neuroeconomics of intertemporal choice.

According to theories of cultural neuroscience, Westerners and Easterners may have distinct styles of cognition (e.g., different allocation of attention). Previous research has shown that Westerners and Easterners tend to utilize analytical and holistic cognitive styles, respectively. On the other hand, little is known regarding the cultural differences in neuroeconomic behavior. For instance, economic decisions may be affected by cultural differences in neurocomputational processing underlying attention; however, this area of neuroeconomics has been largely understudied. In the present paper, we attempt to bridge this gap by considering the links between the theory of cultural neuroscience and neuroeconomic theory of the role of attention in intertemporal choice. We predict that (i) Westerners are more impulsive and inconsistent in intertemporal choice in comparison to Easterners, and (ii) Westerners more steeply discount delayed monetary losses than Easterners. We examine these predictions by utilizing a novel temporal discounting model based on Tsallis' statistics (i.e. a q-exponential model). Our preliminary analysis of temporal discounting of gains and losses by Americans and Japanese confirmed the predictions from the cultural neuroeconomic theory. Future study directions, employing computational modeling via neural networks, are outlined and discussed.

Nonequilibrium characterization of spinodal points using short time dynamics.

Although intuitively appealing, the concept of spinodal is rigorously defined only in systems with infinite range interactions (mean-field systems). In short-range systems, a pseudospinodal can be defined by extrapolation of metastable measurements, but the point itself is not reachable because it lies beyond the metastability limit. In this work we show that a sensible definition of spinodal points can be obtained through the short time dynamical behavior of the system deep inside the metastable phase by looking for a point where the system shows critical behavior. We show that spinodal points obtained by this method agree both with the thermodynamical spinodal point in mean-field systems and with the pseudospinodal point obtained by extrapolation of metaequilibrium behavior in short-range systems. With this definition, a practical determination can be achieved without regard for equilibration issues.