Time delays and stimulus-dependent pattern formation in periodic environments in isolated neurons

The dynamical characteristics of a single isolated Hopfield-type neuron with dissipation and time-delayed self-interaction under periodic stimuli are studied. Sufficient conditions for the hetero-associative stable encoding of periodic external stimuli are obtained. Both discrete and continuously distributed delays are included

Neuronal assembly dynamics in supervised and unsupervised learning scenarios

The dynamic formation of groups of neurons—neuronal assemblies—is believed to mediate cognitive phenomena at many levels, but their detailed operation and mechanisms of interaction are still to be uncovered. One hypothesis suggests that synchronized oscillations underpin their formation and functioning, with a focus on the temporal structure of neuronal signals. In this context, we investigate neuronal assembly dynamics in two complementary scenarios: the first, a supervised spike pattern classification task, in which noisy variations of a collection of spikes have to be correctly labeled; the second, an unsupervised, minimally cognitive evolutionary robotics tasks, in which an evolved agent has to cope with multiple, possibly conflicting, objectives. In both cases, the more traditional dynamical analysis of the system’s variables is paired with information-theoretic techniques in order to get a broader picture of the ongoing interactions with and within the network. The neural network model is inspired by the Kuramoto model of coupled phase oscillators and allows one to fine-tune the network synchronization dynamics and assembly configuration. The experiments explore the computational power, redundancy, and generalization capability of neuronal circuits, demonstrating that performance depends nonlinearly on the number of assemblies and neurons in the network and showing that the framework can be exploited to generate minimally cognitive behaviors, with dynamic assembly formation accounting for varying degrees of stimuli modulation of the sensorimotor interactions

Global Attractivity of a Circadian Pacemaker Model in a Periodic Environment

In this paper, we propose a delay differential equation with continuous periodic parameters to model the circadian pacemaker in a periodic environment. First, we show the existence of a positive periodic solution by using the theory of coincidence degree. Then we establish the global attractivity of the periodic solution under two su±cient conditions. These conditions are easily verifiable and are independent of each other. Some numerical simulations are also performed to demonstrate the main results

Synchronization of Coupled and Periodically Forced Chemical Oscillators

Physiological rhythms are essential in all living organisms. Such rhythms are regulated through the interactions of many cells. Deviation of a biological system from its normal rhythms can lead to physiological maladies. The tremor and symptoms associated with Parkinson\u27s disease are thought to emerge from abnormal synchrony of neuronal activity within the neural network of the brain. Deep brain stimulation is a therapeutic technique that can remove this pathological synchronization by the application of a periodic desynchronizing signal. Herein, we used the photosensitive Belousov--Zhabotinsky (BZ) chemical reaction to test the mechanism of deep brain stimulation. A collection of oscillators are initially synchronized using a regular light signal. Desynchronization is then attempted using an appropriately chosen desynchronizing signal based on information found in the phase response curve.;Coupled oscillators in various network topologies form the most common prototypical systems for studying networks of dynamical elements. In the present study, we couple discrete BZ photochemical oscillators in a network configuration. Different behaviors are observed on varying the coupling strength and the frequency heterogeneity, including incoherent oscillations to partial and full frequency entrainment. Phase clusters are organized symmetrically or non-symmetrically in phase-lag synchronization structures, a novel phase wave entrainment behavior in non-continuous media. The behavior is observed over a range of moderate coupling strengths and a broad frequency distribution of the oscillators

Nonlinear dynamics of pattern recognition and optimization

We associate learning in living systems with the shaping of the velocity vector field of a dynamical system in response to external, generally random, stimuli. We consider various approaches to implement a system that is able to adapt the whole vector field, rather than just parts of it - a drawback of the most common current learning systems: artificial neural networks. This leads us to propose the mathematical concept of self-shaping dynamical systems. To begin, there is an empty phase space with no attractors, and thus a zero velocity vector field. Upon receiving the random stimulus, the vector field deforms and eventually becomes smooth and deterministic, despite the random nature of the applied force, while the phase space develops various geometrical objects. We consider the simplest of these - gradient self-shaping systems, whose vector field is the gradient of some energy function, which under certain conditions develops into the multi-dimensional probability density distribution of the input. We explain how self-shaping systems are relevant to artificial neural networks. Firstly, we show that they can potentially perform pattern recognition tasks typically implemented by Hopfield neural networks, but without any supervision and on-line, and without developing spurious minima in the phase space. Secondly, they can reconstruct the probability density distribution of input signals, like probabilistic neural networks, but without the need for new training patterns to have to enter the network as new hardware units. We therefore regard self-shaping systems as a generalisation of the neural network concept, achieved by abandoning the "rigid units - flexible couplings'' paradigm and making the vector field fully flexible and amenable to external force. It is not clear how such systems could be implemented in hardware, and so this new concept presents an engineering challenge. It could also become an alternative paradigm for the modelling of both living and learning systems. Mathematically it is interesting to find how a self shaping system could develop non-trivial objects in the phase space such as periodic orbits or chaotic attractors. We investigate how a delayed vector field could form such objects. We show that this method produces chaos in a class systems which have very simple dynamics in the non-delayed case. We also demonstrate the coexistence of bounded and unbounded solutions dependent on the initial conditions and the value of the delay. Finally, we speculate about how such a method could be used in global optimization

Cortical-hippocampal processing: prefrontal-hippocampal contributions to the spatiotemporal relationship of events

The hippocampus and prefrontal cortex play distinct roles in the generation and retrieval of episodic memory. The hippocampus is crucial for binding inputs across behavioral timescales, whereas the prefrontal cortex is found to influence retrieval. Spiking of hippocampal principal neurons contains environmental information, including information about the presence of specific objects and their spatial or temporal position relative to environmental and behavioral cues. Neural activity in the prefrontal cortex is found to map behavioral sequences that share commonalities in sensory input, movement, and reward valence. Here I conducted a series of four experiments to test the hypothesis that external inputs from cortex update cell assemblies that are organized within the hippocampus. I propose that cortical inputs coordinate with CA3 to rapidly integrate information at fine timescales. Extracellular tetrode recordings of neurons in the orbitofrontal cortex were performed in rats during a task where object valences were dictated by the spatial context in which they were located. Orbitofrontal ensembles, during object sampling, were found to organize all measured task elements in inverse rank relative to the rank previously observed in the hippocampus, whereby orbitofrontal ensembles displayed greater differentiation for object valence and its contextual identity than spatial position. Using the same task, a follow-up experiment assessed coordination between prefrontal and hippocampal networks by simultaneously recording medial prefrontal and hippocampal activity. The circuit was found to coordinate at theta frequencies, whereby hippocampal theta engaged prefrontal signals during contextual sampling, and the order of engagement reversed during object sampling. Two additional experiments investigated hippocampal temporal representations. First, hippocampal patterns were found to represent conjunctions of time and odor during a head-fixed delayed match-to-sample task. Lastly, I assessed the dependence of hippocampal firing patterns on intrinsic connectivity during the delay period versus active navigation of spatial routes, as rats performed a delayed-alternation T-maze. Stimulation of the ventral hippocampal commissure induced remapping of hippocampal activity during the delay period selectively. Despite temporal reorganization, different hippocampal populations emerged to predict temporal position. These results show hippocampal representations are guided by stable cortical signals, but also, coordination between cortical and intrinsic circuitry stabilizes flexible CA1 temporal representations