Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Mammalian Brain As a Network of Networks

Acknowledgements AZ, SG and AL acknowledge support from the Russian Science Foundation (16-12-00077). Authors thank T. Kuznetsova for Fig. 6.Peer reviewedPublisher PD

Functional Optimization in Complex Excitable Networks

We study the effect of varying wiring in excitable random networks in which connection weights change with activity to mold local resistance or facilitation due to fatigue. Dynamic attractors, corresponding to patterns of activity, are then easily destabilized according to three main modes, including one in which the activity shows chaotic hopping among the patterns. We describe phase transitions to this regime, and show a monotonous dependence of critical parameters on the heterogeneity of the wiring distribution. Such correlation between topology and functionality implies, in particular, that tasks which require unstable behavior --such as pattern recognition, family discrimination and categorization-- can be most efficiently performed on highly heterogeneous networks. It also follows a possible explanation for the abundance in nature of scale--free network topologies.Comment: 7 pages, 3 figure

Introducing Astrocytes on a Neuromorphic Processor: Synchronization, Local Plasticity and Edge of Chaos

While there is still a lot to learn about astrocytes and their neuromodulatory role in the spatial and temporal integration of neuronal activity, their introduction to neuromorphic hardware is timely, facilitating their computational exploration in basic science questions as well as their exploitation in real-world applications. Here, we present an astrocytic module that enables the development of a spiking Neuronal-Astrocytic Network (SNAN) into Intel's Loihi neuromorphic chip. The basis of the Loihi module is an end-to-end biophysically plausible compartmental model of an astrocyte that simulates the intracellular activity in response to the synaptic activity in space and time. To demonstrate the functional role of astrocytes in SNAN, we describe how an astrocyte may sense and induce activity-dependent neuronal synchronization, switch on and off spike-time-dependent plasticity (STDP) to introduce single-shot learning, and monitor the transition between ordered and chaotic activity at the synaptic space. Our module may serve as an extension for neuromorphic hardware, by either replicating or exploring the distinct computational roles that astrocytes have in forming biological intelligence.Comment: 9 pages, 7 figure