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The population model of Wilson-Cowan is perhaps the most popular in the history of computational neuroscience. It embraces the nonlinear mean field dynamics of excitatory and inhibitory neuronal populations provided via a temporal coarse-graining technique. The traditional Wilson-Cowan equations exhibit either steady-state regimes or else limit cycle competitions for an appropriate range of parameters. As these equations lower the resolution of the neural system and obscure vital information, we assess the validity of mass-type model approximations for complex neural behaviors. Using a large-scale network of Hodgkin-Huxley style neurons, we derive implicit average population dynamics based on mean field assumptions. Our comparison of the microscopic neural activity with the macroscopic temporal profiles reveals dependency on the binary state of interacting subpopulations and the random property of the structural network at the Hopf bifurcation points when different synaptic weights are considered. For substantial configurations of stimulus intensity, our model provides further estimates of the neural population's dynamics official, ranging from simple periodic to quasi-periodic and aperiodic patterns, as well as phase transition regimes. While this shows its great potential for studying the collective behavior of individual neurons particularly concentrating on the occurrence of bifurcation phenomena, we must accept a quite limited accuracy of the Wilson-Cowan approximations-at least in some parameter regimes. Additionally, we report that the complexity and temporal diversity of neural dynamics, especially in terms of limit cycle trajectory, and synchronization can be induced by either small heterogeneity in the degree of various types of local excitatory connectivity or considerable diversity in the external drive to the excitatory pool., Comment: 25 pages, 10 figures

We investigate the dynamical properties of a network of coupled neural oscillators with identical Jansen-Rit masses. The connections between nodes follow the regular Watts-Strogatz topology. Each node receives deterministic external input plus internal input based on the output signal from the neighbors. This paper aims to change these two inputs and analyze the generated results. First, we attempt to analyze the model using the mean-field approximation, i.e., identical inputs for all nodes. Then, this assumption is relaxed. A more detailed analysis of these two states is discussed. We use the Pearson correlation coefficient to measure the amount of synchronization. As a result of the mean-field approach, we find that despite observed changes in behavior, there is no phase transition. Surprisingly, both the first (discontinuous) and second (continuous) phase transition occurs by relaxing the mean-field assumption. We also demonstrate how changes in input can result in pathological oscillations similar to those observed in epilepsy. Results show that coupled Jansen-Rit masses emerge a variety of behaviors influenced by various external and internal inputs. Moreover, our findings indicate that delta waves can be generated by altering these inputs in a network of Jansen-Rit neural mass models, which has not been previously observed in a single Jansen-Rit neural mass model analysis. \\ Overall, a wide range of behavioral patterns, including epilepsy, healthy behavior, and the transition between synchrony, and asynchrony are examined comprehensively in this paper. Moreover, this work highlights the putative contribution of external and internal inputs in studying the phase transition and synchronization of neural mass models.

Type 2 diabetes (T2D) is a challenging metabolic disorder characterized by a substantial loss of $\beta$-cell mass and alteration of $\beta$-cell function in the islets of Langerhans, disrupting insulin secretion and glucose homeostasis. The mechanisms for deficiency in $\beta$-cell mass and function during the hyperglycemia development and T2D pathogenesis are complex. To study the relative contribution of $\beta$-cell mass to $\beta$-cell function in T2D, we make use of a comprehensive electrophysiological model of human $\beta$-cell clusters. We find that defect in $\beta$-cell mass causes a functional decline in single $\beta$-cell, impairment in intra-islet synchrony, and changes in the form of oscillatory patterns of membrane potential and intracellular $\textrm{Ca}^{2+}$ concentration, which can lead to changes in insulin secretion dynamics and in insulin levels. The model demonstrates a good correspondence between suppression of synchronizing electrical activity and published experimental measurements. We then compare the role of gap junction-mediated electrical coupling with both $\beta$-cell synchronization and metabolic coupling in the behavior of $\textrm{Ca}^{2+}$ concentration dynamics within human islets. Our results indicate that inter-$\beta$-cellular electrical coupling depicts a more important factor in shaping the physiological regulation of islet function and in human T2D. We further predict that varying the whole-cell conductance of delayed rectifier $\textrm{K}^{+}$ channels modifies oscillatory activity patterns of $\beta$-cell population lacking intercellular coupling, which significantly affect $\textrm{Ca}^{2+}$ concentration and insulin secretion.

How does society work? How do groups emerge within society? What are the effects of emotions and memory on our everyday actions? George Homans, like us, had a perspective on what society is, except that he was a sociologist. Homans theory, which is an exchange theory, is based on a few propositions about the fundamental actions of individuals, and how values, memory, and expectations affect their behavior. In this paper, our main interest and purpose are to find out whether these propositions can satisfy our conception of society and generate essential properties of it computationally. To do so, Based on Homans' prepositions, we provide the opportunity for each agent to exchange with other agents. That is, each agent transacts with familiar agents based on his previous history with them and transacts with newly found agents through exploration. One novelty of our work is the investigation of implications of the base theory while covering its flaws with minimal intervention; flaws which are inevitable in a non-mathematical theory. The importance of our work is that we have scrutinized the consequences of an actual sociological theory. At the end of our investigation, we propose another proposition to Homans theory, which makes the theory more appealing, and we discuss other possible directions for further research.

A causal interpretation of the quantum world needs second quantization in order to cover phenomena like creation and annihilation of particles, and this leads to quantum field theory. The causal effects of the second quantization can be described through a new quantum potential. In this article we have dealt with the second quantization of Schrodinger and its effects on the path of a particle. This generalization leads to a modified Schrodinger which affects the particle through a modified quantum potential and a new term in the continuity equation. We have shown that these effects can provide a framework for the explanation of the creation and annihilation phenomena and other effects of quantum field theory on the development of a particle., Comment: 8 pages, This manuscript has been published in Heliyon as ,SupA, of article entitled ,A proposed mechanism for mind-brain interaction using extended Bohmian quantum mechanics in Avicenna's monotheistic perspective

Cyborg in the brain-machine interface field has attracted more attention in recent years. To control a creature via a machine called cyborg method, three stages are considerable: stimulation of neurons, neural response, and the behavioral reaction of the subject. Our main concern was to know how electrical stimulation induces neural activity and leads to a behavioral response. Additionally, we were interested to explore which type of electrical stimulation is optimal from different aspects such as maximum response with minimum induction stimulus field, minimum damage of the tissue and the electrode, reduction of the noxiousness of stimuli or pain in the living creature. In this article, we proposed a new model for the induction of neural activity led to locomotion responses through electrical stimulation. Furthermore, based on this model, we developed a new approach of electrical neural stimulation to provide a better locomotion control of living beings. This approach was verified through the empirical data of fish cyborg. We stimulated the fish brain by use of an ultra-high frequency signal which careered by a random low frequency. According to our model, we could control the locomotion of fish in a novel and innovative way. In this study, we categorized the different cyborg methods based on the nervous system areas and the stimulation signal properties to reach the better and optimal behavioral control of creature. According to this, we proposed a new stimulation method theoretically and confirmed it experimentally.

Nerve stimulation via micro-electrode implants is one of the neurostimulation approaches which is used frequently in the medical treatment of some brain disorders, neural prosthetics, brain-machine interfaces and also in the cyborg. In this method, the electrical stimulation signal can be categorized by the frequency band: low frequency, high frequency, and ultra-high frequency. The stimulation should be less destructive, more smooth, and controllable. In this article, we present a brief description of the mechanism underlying the ultra-high frequency stimulation. In the flowing, from an informatics perspective, we propose a state-of-the-art, low destructive, and highly efficient stimulation method at the low amplitude ultra-high frequency signal. In this method, we have tried to reduce the adaptation of the nerve system by modulating the stimulation signal via a low frequency rectangular random wave. By this method, we could reach the "almost zero discharge" with minimum destructive effect in the experimental test on the fish nervous system.

Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon that can be seen in the brain. The network topology has a remarkable impact on both the function and the dynamics of neural networks. In this research, synchronization of neural networks is scrutinized through creating various topologies. These networks include both excitatory and inhibitory neurons. We investigate the dynamics of different networks by random rewiring of the synaptic connections. In this manner, a regular network transforms into a small-world network and then becomes a random network. Coherence level which is measured and utilized as the criteria to analyze synchronicity, experiencing a sharp increase as the network changes into the small-world network and growing steadily by the end. On the other hand, a decreasing trend of coherence level is revealed starting from a complete excitatory network and gradually increasing of inhibitory neurons. Thus, the coherence level reaches approximately zero in a complete inhibitory network. By increasing the number of neurons in the network, the degree of synchronization follows a power-law distribution; however, the number of synaptic connections of each neuron and their conductance have a positive impact on synchronization. By applying the model to a C-elegance neural network, not only the mentioned parameters but also the role of the degree distribution are highlighted.

Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by standard linear equation (SLE) mostly owing to shape memory effect during deformation. Recently, researchers have been applying fractional calculus in order for probing viscoelasticity of such materials with a high precision. Fractional calculus is a powerful tool for modeling complex phenomenon. In this tutorial based paper, we try present clear descriptions of the fractional calculus, its techniques and its implementation. The intention is to keep the details to a minimum while still conveying a good idea of what and how can be done with this powerful tool. We try to expose the reader to the basic techniques that are used to solve the fractional equations analytically and/or numerically. More specifically, modeling the shape memory phenomena with this powerful tool are studied from different perspectives, as well as presented some physical interpretation in this case. Moreover, in order to show the relationship between fractional models and standard linear equations, a fractal system comprising spring and damper elements is considered, and the constitutive equation is approximated with a fractional element. Finally, after a brief literature review, two fractional models are utilized to investigate the viscoelasticity of the cell, and the comparison is made among them, experimental data, and previous models. Verification results indicate that not only does the fractional model match the experimental data well, but it also can be a good substitute for previously used models., Comment: 36 pages

We have developed a two dimensional stochastic molecular dynamics model for the description of intra cellular collective motion of bio motors, in particular Kinesins, on a microtubular track. The model is capable or reproducing the hand-over-hand mechanism of the directed motion along the microtubule. The model gives the average directed velocity and the current of Kinesins along the microtubule. It is shown that beyond a certain density of Kinesins, the average velocity and current undergo notable decrease which is due to formation of traffic jams in the system., Comment: 8 pages, 14 eps figures