Control and Synchronization of Neuron Ensembles

Synchronization of oscillations is a phenomenon prevalent in natural, social, and engineering systems. Controlling synchronization of oscillating systems is motivated by a wide range of applications from neurological treatment of Parkinson's disease to the design of neurocomputers. In this article, we study the control of an ensemble of uncoupled neuron oscillators described by phase models. We examine controllability of such a neuron ensemble for various phase models and, furthermore, study the related optimal control problems. In particular, by employing Pontryagin's maximum principle, we analytically derive optimal controls for spiking single- and two-neuron systems, and analyze the applicability of the latter to an ensemble system. Finally, we present a robust computational method for optimal control of spiking neurons based on pseudospectral approximations. The methodology developed here is universal to the control of general nonlinear phase oscillators.Comment: 29 pages, 6 figure

Born to learn: The inspiration, progress, and future of evolved plastic artificial neural networks

Biological plastic neural networks are systems of extraordinary computational capabilities shaped by evolution, development, and lifetime learning. The interplay of these elements leads to the emergence of adaptive behavior and intelligence. Inspired by such intricate natural phenomena, Evolved Plastic Artificial Neural Networks (EPANNs) use simulated evolution in-silico to breed plastic neural networks with a large variety of dynamics, architectures, and plasticity rules: these artificial systems are composed of inputs, outputs, and plastic components that change in response to experiences in an environment. These systems may autonomously discover novel adaptive algorithms, and lead to hypotheses on the emergence of biological adaptation. EPANNs have seen considerable progress over the last two decades. Current scientific and technological advances in artificial neural networks are now setting the conditions for radically new approaches and results. In particular, the limitations of hand-designed networks could be overcome by more flexible and innovative solutions. This paper brings together a variety of inspiring ideas that define the field of EPANNs. The main methods and results are reviewed. Finally, new opportunities and developments are presented

Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis

We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of simulated annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker-Planck describing the evolving probability density function of the corresponding coarse-grained observables

Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons

First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and multifunctionality in neural networks that produce and control rhythmical motor patterns. In some cases, isolating the neurons from their synaptic network revealsirregular, complex signatures that have been regarded as evidence of intrinsic, chaotic behavior. We show that incorporation of dynamical noise into minimal neuron models of square-wave bursting (either conductance-based or abstract) produces signatures akin to those observed in biological examples, without the need for fine-tuning of parameters or ad hoc constructions for inducing chaotic activity. The form of the stochastic term is not strongly constrained, and can approximate several possible sources of noise, e.g. random channel gating or synaptic bombardment. The cornerstone of this signature generation mechanism is the rich, transient, but deterministic dynamics inherent in the square-wave (saddle-node/homoclinic) mode of neuronal bursting. We show that noise causes the dynamics to populate a complex transient scaffolding or skeleton in state space, even for models that (without added noise) generate only periodic activity (whether in bursting or tonic spiking mode).Comment: REVTeX4-1, 18 pages, 9 figure

Can biological quantum networks solve NP-hard problems?

There is a widespread view that the human brain is so complex that it cannot be efficiently simulated by universal Turing machines. During the last decades the question has therefore been raised whether we need to consider quantum effects to explain the imagined cognitive power of a conscious mind. This paper presents a personal view of several fields of philosophy and computational neurobiology in an attempt to suggest a realistic picture of how the brain might work as a basis for perception, consciousness and cognition. The purpose is to be able to identify and evaluate instances where quantum effects might play a significant role in cognitive processes. Not surprisingly, the conclusion is that quantum-enhanced cognition and intelligence are very unlikely to be found in biological brains. Quantum effects may certainly influence the functionality of various components and signalling pathways at the molecular level in the brain network, like ion ports, synapses, sensors, and enzymes. This might evidently influence the functionality of some nodes and perhaps even the overall intelligence of the brain network, but hardly give it any dramatically enhanced functionality. So, the conclusion is that biological quantum networks can only approximately solve small instances of NP-hard problems. On the other hand, artificial intelligence and machine learning implemented in complex dynamical systems based on genuine quantum networks can certainly be expected to show enhanced performance and quantum advantage compared with classical networks. Nevertheless, even quantum networks can only be expected to efficiently solve NP-hard problems approximately. In the end it is a question of precision - Nature is approximate.Comment: 38 page