Averaging Transformations of Synaptic Potentials on Networks

The problem of the transformation of microscopic information to the macroscopic level is an intriguing challenge in computational neuroscience, but also of general mathematical importance. Here, a phenomenological mathematical model is introduced that simulates the internal information processing of brain compartments. Synaptic potentials are integrated over small number of realistically coupled neurons to obtain macroscopic quantities. The striatal complex, an important part of the basal ganglia circuit in the brain for regulating motor activity, has been investigated as an example for the validation of the model

The Predominance of Electric Transport in Synaptic Transmission

The quantitative description of the motion of neurotransmitters in the synaptic cleft appears to be one of the most difficult problems in the modeling of synapses. Here we show in contradiction to the common view, that this process is merely governed by electric transport than diffusion forces

ATP Hysteresis in Tripartite Synapses

Recent experimental studies strongly suggest the influence of glial purinergic transmission in the modulation of synaptic dynamics. By releasing adenosine triphosphate (ATP), which accumulates as adenosine, astrocytes tonically suppressed synaptic transmission. The delayed multi-step feedback of the glial adenosine with the neuron suggest the existence of hysteresis phenomena, which are investigated in the present study from the theoretical point of view. The model suggests that a memory operator, tripartite synaptic plasticity, governs the mysterious delayed feedback inhibition caused by the action of adenosine on neuronal $A_1$ receptors and provides a powerful tool for further dynamical modeling tasks on tripartite synapses

Signal detection in extracellular neural ensemble recordings using higher criticism

Information processing in the brain is conducted by a concerted action of multiple neural populations. Gaining insights in the organization and dynamics of such populations can best be studied with broadband intracranial recordings of so-called extracellular field potential, reflecting neuronal spiking as well as mesoscopic activities, such as waves, oscillations, intrinsic large deflections, and multiunit spiking activity. Such signals are critical for our understanding of how neuronal ensembles encode sensory information and how such information is integrated in the large networks underlying cognition. The aforementioned principles are now well accepted, yet the efficacy of extracting information out of the complex neural data, and their employment for improving our understanding of neural networks, critically depends on the mathematical processing steps ranging from simple detection of action potentials in noisy traces - to fitting advanced mathematical models to distinct patterns of the neural signal potentially underlying intra-processing of information, e.g. interneuronal interactions. Here, we present a robust strategy for detecting signals in broadband and noisy time series such as spikes, sharp waves and multi-unit activity data that is solely based on the intrinsic statistical distribution of the recorded data. By using so-called higher criticism - a second-level significance testing procedure comparing the fraction of observed significances to an expected fraction under the global null - we are able to detect small signals in correlated noisy time-series without prior filtering, denoising or data regression. Results demonstrate the efficiency and reliability of the method and versatility over a wide range of experimental conditions and suggest the appropriateness of higher criticism to characterize neuronal dynamics without prior manipulation of the data

Mathematical Modeling of the Neuronal Processes in Sugar Addiction

It has already been demonstrated that the body responds to enhanced intake of sugar and is conducive to a natural form of addiction. There are substantial neurochemical changes in the brain (especially dopamine and acetylcholine systems) similar to other addictive drugs. A mathematical model comprised by a system of delayed leaky integrate-and-re equations is established to simulate the effects of sugar on a reward-circuitry. Simulations with Neuron suggest agreement with the neurobiological hypotheses of hyperactivity of neural systems due to binge sugar intake

Mathematical Modelling of the Neurochemical Processes in Schizophrenia

Schizophrenia is an endogenous psychosis with a 1 \% prevalence in world population. Several pharmacological studies suggest that alterations in the function of different neurotransmitter systems such as dopamine or glutamate are related to schizophrenic symptoms. This thesis represents mathematical models that are constructed to investigate the dynamical behaviour of the neurochemical systems in the human brain. These models formulate the anatomical properties and physiological processes of synapses, single brain compartments and large neurochemical pathways involved in the regulation of behaviour such as the basal ganglia and the limbic system. The interaction between the neurochemical systems and the electrophysiological activities are considered by modelling in different scales. In the synaptic scale, it has been shown that the transport of neurotransmitters in the synaptic cleft is merely governed by electrical forces than diffusion. The intra-synaptic concentration of neurotransmitters is modelled using partial differential equations and is coupled to the Hodgkin-Huxley equation (neurochemical modification) to model the effect of neurotransmitter-receptor binding in the generation of post-synaptic potentials. Considering the morphological and ultra-morphological studies of brain compartments, the averaged electrophysiological activity is modelled by integral equations respecting these internal structures. A system comprised by nonlinear delay differential equations is constructed to simulate the dynamical behaviour of neurochemical concentrations, coupled to the local electrophysiological activity of the compartments, on the brain pathways. By parameter sensitivity analysis, we have also investigated qualitatively the influence of certain anti-psychotic agents. Synchronized oscillations are experienced in electrophysiological systems. The neurotransmitter concentrations also demonstrate an oscillatory behaviour. The resulting oscillatory dynamics of these processes reveals a profound view on the relation between the dynamical behaviour of the neurochemical systems and the occurrence of psychotic states. These facts led us to establish a hypothesis on this relation, called the oscillation hypothesis of psychosis. Because of the general formulation of the models, these are not only useful for schizophrenia, but also for the investigations of other neurological diseases

Strategizing niceness in co-opetition: The case of knowledge exchange in supply chain innovation projects

© 2015 Elsevier B.V. All rights reserved. Abstract In this paper, we take a novel approach to address the dilemma of innovation sharing versus protection among supply chain partners. The paper conducts an exploratory study that introduces factors affecting a firm\u27s optimum supply chain innovation strategy. We go beyond the conventional Prisoners\u27 Dilemma, with its limiting assumptions of players\u27 preferences and symmetry, to explore a larger pool of 2 × 2 games that may effectively model the problem. After classifying firm types according to collaboration motive and relative power, we use simulation to explore the effects of firm type, opponent type, and payoff structure on repeated innovation interactions (or, equivalently, long-term relations) and optimality of \u27niceness\u27. Surprisingly, we find that opponent type is essentially irrelevant in long-term innovation interactions, and focal firm type is only conditionally relevant. The paper contributes further by introducing reciprocation of strategy type (nice versus mean), showing that reciprocation is recommended, while identifying and explaining the exceptions to this conclusion