Effects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons

The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore consider that the neuron dynamics may occur at a (shorter) time scale than synaptic plasticity and consider the possibility of learning rules with passive forgetting. We show that the application of such Hebbian learning leads to drastic changes in the network dynamics and structure. In particular, the learning rule contracts the norm of the weight matrix and yields a rapid decay of the dynamics complexity and entropy. In other words, the network is rewired by Hebbian learning into a new synaptic structure that emerges with learning on the basis of the correlations that progressively build up between neurons. We also observe that, within this emerging structure, the strongest synapses organize as a small-world network. The second effect of the decay of the weight matrix spectral radius consists in a rapid contraction of the spectral radius of the Jacobian matrix. This drives the system through the "edge of chaos" where sensitivity to the input pattern is maximal. Taken together, this scenario is remarkably predicted by theoretical arguments derived from dynamical systems and graph theory.     

Cooperative recurrent modular neural networks for constrained optimization: a survey of models and applications

Constrained optimization problems arise in a wide variety of scientific and engineering applications. Since several single recurrent neural networks when applied to solve constrained optimization problems for real-time engineering applications have shown some limitations, cooperative recurrent neural network approaches have been developed to overcome drawbacks of these single recurrent neural networks. This paper surveys in details work on cooperative recurrent neural networks for solving constrained optimization problems and their engineering applications, and points out their standing models from viewpoint of both convergence to the optimal solution and model complexity. We provide examples and comparisons to shown advantages of these models in the given applications.     

The frustrated brain: from dynamics on motifs to communities and networks

Cognitive function depends on an adaptive balance between flexible dynamics and integrative processes in distributed cortical networks. Patterns of zero-lag synchrony likely underpin numerous perceptual and cognitive functions. Synchronization fulfils integration by reducing entropy, while adaptive function mandates that a broad variety of stable states be readily accessible. Here, we elucidate two complementary influences on patterns of zero-lag synchrony that derive from basic properties of brain networks. First, mutually coupled pairs of neuronal subsystems—resonance pairs—promote stable zero-lag synchrony among the small motifs in which they are embedded, and whose effects can propagate along connected chains. Second, frustrated closed-loop motifs disrupt synchronous dynamics, enabling metastable configurations of zero-lag synchrony to coexist. We document these two complementary influences in small motifs and illustrate how these effects underpin stable versus metastable phase-synchronization patterns in prototypical modular networks and in large-scale cortical networks of the macaque (CoCoMac). We find that the variability of synchronization patterns depends on the inter-node time delay, increases with the network size and is maximized for intermediate coupling strengths. We hypothesize that the dialectic influences of resonance versus frustration may form a dynamic substrate for flexible neuronal integration, an essential platform across diverse cognitive processes.     

Implementing behaviour in individual-based models using neural networks and genetic algorithms

Even though individual-based models (IBMs) have become very popular in ecology during the last decade, there have been few attempts to implement behavioural aspects in IBMs. This is partly due to lack of appropriate techniques. Behavioural and life history aspects can be implemented in IBMs through adaptive models based on genetic algorithms and neural networks (individual-based-neural network-genetic algorithm, ING). To investigate the precision of the adaptation process, we present three cases where solutions can be found by optimisation. These cases include a state-dependent patch selection problem, a simple game between predators and prey, and a more complex vertical migration scenario for a planktivorous fish. In all cases, the optimal solution is calculated and compared with the solution achieved using ING. The results show that the ING method finds optimal or close to optimal solutions for the problems presented. In addition it has a wider range of potential application areas than conventional techniques in behavioural modelling. Especially the method is well suited for complex problems where other methods fail to provide answers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Neurogenesis and neuronal communication on micropatterned neurochips

Neural networks are formed by accurate connectivity of neurons and glial cells in the brain. These networks employ a three-dimensional bio-surface that both assigns precise coordinates to cells during development and facilitates their connectivity and functionality throughout life. Using specific topographic and chemical features, we have taken steps towards the development of poly(dimethylsiloxane; PDMS) neurochips that can be used to generate and study synthetic neural networks. These neurochips have micropatterned structures that permit adequate cell positioning and support cell survival. Within days of plating, cells differentiate into neurons displaying excitability and communication, as evidenced by intracellular calcium oscillations and action potentials. The structural and functional capacities of such simple neural networks open up new opportunities to study synaptic communication and plasticity.     

Elements for a general memory structure: properties of recurrent neural networks used to form situation models

We study how individual memory items are stored assuming that situations given in the environment can be represented in the form of synaptic-like couplings in recurrent neural networks. Previous numerical investigations have shown that specific architectures based on suppression or max units can successfully learn static or dynamic stimuli (situations). Here we provide a theoretical basis concerning the learning process convergence and the network response to a novel stimulus. We show that, besides learning “simple” static situations, a nD network can learn and replicate a sequence of up to n different vectors or frames. We find limits on the learning rate and show coupling matrices developing during training in different cases including expansion of the network into the case of nonlinear interunit coupling. Furthermore, we show that a specific coupling matrix provides low-pass-filter properties to the units, thus connecting networks constructed by static summation units with continuous-time networks. We also show under which conditions such networks can be used to perform arithmetic calculations by means of pattern completion.     

Neural networks for clustered and longitudinal data using mixed effects models

Although most statistical methods for the analysis of longitudinal data have focused on retrospective models of association, new advances in mobile health data have presented opportunities for predicting future health status by leveraging an individual's behavioral history alongside data from similar patients. Methods that incorporate both individual-level and sample-level effects are critical to using these data to its full predictive capacity. Neural networks are powerful tools for prediction, but many assume input observations are independent even when they are clustered or correlated in some way, such as in longitudinal data. Generalized linear mixed models (GLMM) provide a flexible framework for modeling longitudinal data but have poor predictive power particularly when the data are highly nonlinear. We propose a generalized neural network mixed model that replaces the linear fixed effect in a GLMM with the output of a feed-forward neural network. The model simultaneously accounts for the correlation structure and complex nonlinear relationship between input variables and outcomes, and it utilizes the predictive power of neural networks. We apply this approach to predict depression and anxiety levels of schizophrenic patients using longitudinal data collected from passive smartphone sensor data.     

富硒板党对低氧耐受小鼠兴奋性氨基酸的影响

目的：探讨富硒板党对小鼠低氧耐受形成中脑组织兴奋性氨基酸（EAA）含量的影响。方法：将小鼠用富硒板党处理后,建立小鼠急性重复低氧耐受模型,观察富硒板党对小鼠低氧耐受形成中的脑组织谷氨酸（Glu）、天冬氨酸（Asp）、γ-氨基丁酸（GABA）和甘氨酸（Gly）的影响。结果：富硒板党对正常小鼠脑组织EAA含量无影响,可使低氧耐受形成中脑组织Glu、Asp含量降低,对GABA、Gly无明显影响。结论：富硒板党能明显降低低氧小鼠脑组织中EAA含量,从而发挥对脑损伤的保护作用。     

Attractor analysis of asynchronous Boolean models of signal transduction networks

Prior work on the dynamics of Boolean networks, including analysis of the state space attractors and the basin of attraction of each attractor, has mainly focused on synchronous update of the nodes’ states. Although the simplicity of synchronous updating makes it very attractive, it fails to take into account the variety of time scales associated with different types of biological processes. Several different asynchronous update methods have been proposed to overcome this limitation, but there have not been any systematic comparisons of the dynamic behaviors displayed by the same system under different update methods. Here we fill this gap by combining theoretical analysis such as solution of scalar equations and Markov chain techniques, as well as numerical simulations to carry out a thorough comparative study on the dynamic behavior of a previously proposed Boolean model of a signal transduction network in plants. Prior evidence suggests that this network admits oscillations, but it is not known whether these oscillations are sustained. We perform an attractor analysis of this system using synchronous and three different asynchronous updating schemes both in the case of the unperturbed (wild-type) and perturbed (node-disrupted) systems. This analysis reveals that while the wild-type system possesses an update-independent fixed point, any oscillations eventually disappear unless strict constraints regarding the timing of certain processes and the initial state of the system are satisfied. Interestingly, in the case of disruption of a particular node all models lead to an extended attractor. Overall, our work provides a roadmap on how Boolean network modeling can be used as a predictive tool to uncover the dynamic patterns of a biological system under various internal and environmental perturbations.     

Firing synchronization and temporal order in noisy neuronal networks

Noise-induced complete synchronization and frequency synchronization in coupled spiking and bursting neurons are studied firstly. The effects of noise and coupling are discussed. It is found that bursting neurons are easier to achieve firing synchronization than spiking ones, which means that bursting activities are more important for information transfer in neuronal networks. Secondly, the effects of noise on firing synchronization in a noisy map neuronal network are presented. Noise-induced synchronization and temporal order are investigated by means of the firing rate function and the order index. Firing synchronization and temporal order of excitatory neurons can be greatly enhanced by subthreshold stimuli with resonance frequency. Finally, it is concluded that random perturbations play an important role in firing activities and temporal order in neuronal networks.     

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective, communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires the know-how of all the methodological steps of the pipeline that manipulate the input brain signals and extract the functional network properties. On the other hand, knowledge of the neural phenomenon under study is required to perform physiologically relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.     

Advances in defining signaling networks for the establishment of neuronal polarity

Neurons are highly polarized cells that have structurally and functionally distinct processes called axons and dendrites. How neurons establish polarity is one of the fundamental questions of neuroscience. In the last decade, significant progress has been made in identifying and understanding the molecular mechanisms responsible for neuronal polarization, primarily through researches conducted on cultured neurons. Advances in phosphoproteomics technologies and molecular tools have enabled comprehensive signal analysis and visualization and manipulation of signaling molecules for analyzing neuronal polarity. Furthermore, advances in gene transfer techniques have revealed the role of extracellular and intracellular signaling molecules in neuronal polarization in vivo. This review discusses the latest insights and techniques for the elucidation of the molecular mechanisms that control neuronal polarity.     

Modularity and robustness of frontal cortical networks

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Organization of receptive fields in networks with Hebbian learning: the connection between synaptic and phenomenological models

In this paper we address the question of how interactions affect the formation and organization of receptive fields in a network composed of interacting neurons with Hebbian-type learning. We show how to partially decouple single cell effects from network effects, and how some phenomenological models can be seen as approximations to these learning networks. We show that the interaction affects the structure of receptive fields. We also demonstrate how the organization of different receptive fields across the cortex is influenced by the interaction term, and that the type of singularities depends on the symmetries of the receptive fields.     

Differential control of active and silent phases in relaxation models of neuronal rhythms

Rhythmic bursting activity, found in many biological systems, serves a variety of important functions. Such activity is composed of episodes, or bursts (the active phase, AP) that are separated by quiescent periods (the silent phase, SP). Here, we use mean field, firing rate models of excitatory neural network activity to study how AP and SP durations depend on two critical network parameters that control network connectivity and cellular excitability. In these models, the AP and SP correspond to the network's underlying bistability on a fast time scale due to rapid recurrent excitatory connectivity. Activity switches between the AP and SP because of two types of slow negative feedback: synaptic depression—which has a divisive effect on the network input/output function, or cellular adaptation—a subtractive effect on the input/output function. We show that if a model incorporates the divisive process (regardless of the presence of the subtractive process), then increasing cellular excitability will speed up the activity, mostly by decreasing the silent phase. Reciprocally, if the subtractive process is present, increasing the excitatory connectivity will slow down the activity, mostly by lengthening the active phase. We also show that the model incorporating both slow processes is less sensitive to parameter variations than the models with only one process. Finally, we note that these network models are formally analogous to a type of cellular pacemaker and thus similar results apply to these cellular pacemakers. Action Editor: Misha Tsodyks     

Neural hierarchical models of ecological populations

Neural networks are increasingly being used in science to infer hidden dynamics of natural systems from noisy observations, a task typically handled by hierarchical models in ecology. This article describes a class of hierarchical models parameterised by neural networks – neural hierarchical models. The derivation of such models analogises the relationship between regression and neural networks. A case study is developed for a neural dynamic occupancy model of North American bird populations, trained on millions of detection/non‐detection time series for hundreds of species, providing insights into colonisation and extinction at a continental scale. Flexible models are increasingly needed that scale to large data and represent ecological processes. Neural hierarchical models satisfy this need, providing a bridge between deep learning and ecological modelling that combines the function representation power of neural networks with the inferential capacity of hierarchical models.     

Interactive properties of human glioblastoma cells with brain neurons in culture and neuronal modulation of glial laminin organization

The harmonious development of the central nervous system depends on the interactions of the neuronal and glial cells. Extracellular matrix elements play important roles in these interactions, especially laminin produced by astrocytes, which has been shown to be a good substrate for neuron growth and axonal guidance. Glioblastomas are the most common subtypes of primary brain tumors and may be astrocytes in origin. As normal laminin-producing glial cells are the preferential substrate for neurons, and glial tumors have been shown to produce laminin, we questioned whether glioblastoma retained the same normal glial-neuron interactive properties with respect to neuronal growth and differentiation. Then, rat neurons were co-cultured onto rat normal astrocytes or onto three human glioblastoma cell lines obtained from neurosurgery. The co-culture confirmed that human glioblastoma cells as well as astrocytes maintained the ability to support neuritogenesis, but non-neural normal or tumoral cells failed to do so. However, glioblastoma cells did not distinguish embryonic from post-natal neurons in relation to neurite pattern in the co-cultures, as normal astrocytes did. Further, the laminin organization on both normal and tumoral glial cells was altered from a filamentous arrangement to a mixed punctuate/filamentous pattern when in co-culture with neurons. Together, these results suggest that glioblastoma cells could identify neuronal cells as partners, to support their growth and induce complex neurites, but they lost the normal glia property to distinguish neuronal age. In addition, our results show for the first time that neurons modulate the organization of astrocytes and glioblastoma laminin on the extracellular matrix.