Chaos, Solitons & Fractals

Neuronal dynamics such as brain criticality have recently been attributed to optimal information processing. Brain criticality attempts to elucidate the collective dynamics of a large number of neurons. It posits that the brain operates near critical to the critical point, although the field is rife with controversies and contrasting evidence. Similar computational capacities are observed during sharp wave ripples in the hippocampus prompting the need to correlate their dynamics. In the current study, the measures of avalanche criticality including neuronal avalanches, branching process, crackling noise relation, and deviation from criticality coefficient and Hurst exponents for long-range temporal correlations in rodent hippocampus during sharp wave ripples are reported. The evidence for mixed subcritical to critical dynamics in the hippocampus and minimal difference between ripple and no ripple times across measured metrics was found. The evidence demonstrates heterogeneity in signatures of criticality among animals and brain areas, indicating the presence of broad-range neuronal dynamics.

Obesity is one of the biggest public health problems in the world, and its pathophysiological characteristics include chronic inflammation with an increase in various circulating inflammatory markers, such as acute inflammatory cytokines. Complications in the respiratory tract are related to bodily problems, which lead to a restriction of lung function due to reduced volume, inducing an increase in respiratory work. SARS-CoV-2 has a high potential for contamination by respiratory secretions and, therefore, obesity is one of the main risk factors for complications due to the association established between obesity, chronic inflammation and respiratory infection. The objective was to analyze the complex relationships between obesity and COVID-19 in a meta-analysis study using complex network modeling and the theoretical knockouts technique. Here, we identify and justify through a mathematical analysis the relationships between all the immunological agents added to the proposed immunological networks, considered as a simple evident interaction, relationship, influence, response, activation, based on our quantifiers. They performed the knockouts of all 52 vertices in the COVID-19 network and obesity - regardless of the environment, which would result in nonsense - and the COVID-19 infection network without considering obesity. The stationary flow vector (flow profile), for some knockouts of immunological interest in COVID-19 infections, was chosen IFN, IL-6, IL-10, IL-17 and TNF. This initial study pointed out the importance of chronic inflammation in the obese individual as an important factor in potentiating the disease caused by covid-19 and, in particular, the importance on IL-17.

We are surrounded with many fractal and self-similar patterns which has been area of many researches in the recent years. We can perceive self-similarities in various spatial and temporal scales; however, the underlying neural mechanism needs to be well understood. In this study, we hypothesized that complexity of visual stimuli directly influence complexity of information processing in the brain. Therefore, changes in fractal pattern of EEG signal must follow change in fractal dimension of animation. To investigate this hypothesis, we recorded EEG signal of fifteen healthy participants while they were exposed to several 2D fractal animations. Fractal dimension of each frame of the animation was estimated by box counting method. Subsequently, fractal dimensions of 32 EEG channels were estimated in a frequency specific manner. Then, association between pattern of fractal dimensions of the animations and pattern of fractal dimensions of EEG signals were calculated using the Pearsons correlation algorithm. The results indicated that fractal animation complexity is mainly sensed by changes in fractal dimension of EEG signals at the centro-parietal and parietal regions. It may indicate that when the complexity of visual stimuli increases the mechanism of information processing in the brain also enhances its complexity to better attend and comprehend the stimuli.

Multiple Sclerosis (MS) is an autoimmune diseases that affects the central nervous system. It can lead to inflammation, neurodegeneration, and physical or cognitive disability. Currently, no cure for MS exists, but medications are available to slow its progression. To date, mathematical modelling of MS has focussed on a few aspects of the disease, but an overall modelling framework is missing. In this paper, we propose a new paradigm for the mathematical modelling of MS. Based on biological principles, we propose six consecutive modelling levels and develop the first three model levels in this work using systems of ordinary differential equations. We test if these models can describe known effects related to MS disease risk, with particular focus on estrogen, vitamin D, Epstein-Barr virus (EBV) and HLA-DR mutations. We first show that periodic disease outbreaks are possible in this framework through interactions by antigen-presenting cells, regulatory cells and memory B cells. We show that the presence of Epstein-Barr virus infections can initiate the disease, low and high levels of estrogen and vitamin D deficiency can alleviate it, mutations in the HLA-DR gene can promote MS, and we find that memory B-cells play a dominant role in the disease progression. We hope that this framework may serve as a reference for the development and comparative evaluation of future mathematical and computational models of MS.

This paper is concerned with the theoretical investigation of game theory concepts in analyzing the behavior of dynamically coupled oscillators. Here, we claim that the coupling strength in any neuronal oscillators can be modeled as a game. We formulate the game to describe the effect of pure-strategy Nash equilibrium on two neuron systems of Hopf-oscillator and later demonstrate the application of the same assumptions and methods to N x N neuronal sheet. We also demonstrate the effect of the proposed method on MNIST data to show the equilibrium behavior of neurons in a N x N neuronal grid for all different digits. A significant outcome of the paper is a modified Hebbian algorithm, which adapts the coupling weights to neural potential resulting in a stable phase difference. Which in turn, makes it possible for an individual neuron to encode input information.

AO_SCPLOWBSTRACTC_SCPLOWSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a highly transmissible RNA virus that emerged in China at the end of 2019 and caused a large global outbreak. The interaction between SARS-CoV-2 and the immune response is complex because it is regulated by various processes taking part at the intracellular, tissue, and host levels. To gain a better understanding of the pathogenesis and progression of COVID-19, we formulate a multiscale model that integrate the main mechanisms which regulate the immune response to SARS-CoV-2 across multiple scales. The model describes the effect of type I interferon on the replication of SARS-CoV-2 inside cells. At the tissue level, we simulate the interactions between infected cells and immune cells using a hybrid agent-based representation. At the same time, we model the dynamics of virus spread and adaptive immune response in the host organism. After model validation, we demonstrate that a moderately weak inhibition of virus replication by type I IFN could elicit a strong adaptive immune response which accelerates the clearance of the virus. Furthermore, numerical simulations suggest that the deficiency of lymphocytes and not dendritic cells could lead to unfavourable outcomes in the elderly population.

The relationship between ratios of excitatory to inhibitory neurons and the brains dynamic range of cortical activity is crucial. However, its full understanding within the context of cortical scale-free dynamics remains an ongoing investigation. To provide insightful observations that can improve the current understanding of this impact, and based on studies indicating that a fully excitatory neural network can induce critical behavior under the influence of noise, it is essential to investigate the effects of varying inhibition within this network. Here, the impact of varying ratios on neural avalanches and phase transition diagrams, considering a range of control parameters in a leaky integrate-and-fire model network, is examined. Our computational results show that the network exhibits critical, sub-critical, and super-critical behavior across different control parameters. In particular, a certain ratio leads to a significantly extended dynamic range compared to others and increases the probability of the system being in the critical regime. To address differences between various ratios, we utilized the Kuramoto order parameter and conducted a finite-size scaling analysis to determine the critical exponents associated with phase transitions. In order to characterize the criticality, we examined the distribution of neuronal avalanches at the critical point and the scaling behavior characterized by specific exponents.

Humans modulate the behavior flexibly after timely receiving and processing information from the environment. To better understand and measure human behavior in the driving process, we integrate humans and the environment as a system. The eye-movement methodologies are used to provide a bridge between humans and environment. Thus, we conduct a goal-directed task in virtual driving to investigate the law of eye-movement that could characterize the humans (internal) and environmental (external) state measured by fixation distribution and optical flows distribution. The analysis of eye-movement data combined with the information-theoretic tool, transfer entropy, active information storage, quantify the humans cognitive effort and receiving information, and in fact, there is a balance (optimal) range between two, because of the mutual synergy and inhibition, whose quantified value is named balance of information processing. Subsequently, we update a system-level model, finding that those information measurements, transfer entropy, active information storage, and balance of information processing, all are included. This information set is information flow, which is quantified by the square root of Jensen-Shannon divergence (SRJSD), named information flow gain. Whats more, results also demonstrate that the influence of system-level information flow correlated with behavioral performance stronger than the separate measurements. In conclusion, we research humans eye-movement based on information theory to analyze behavioral performance. Besides driving, these measurements may be a predictor for other behaviors such as walking, running, etc. Still, the limitation is that the information flow may be a proxy of determinants of behavior.

As social beings, humans make decisions partly based on social interaction. Observing the behavior of others can lead to learning from and about them, potentially increasing trust and prompting trust-based behavioral changes. Observation-based decision making involves different neural structures. The orbitofrontal cortex (OFC) and lateral prefrontal cortex (LPFC) are known as neural structures mainly involved in processing emotional and cognitive decision values, respectively, while the anterior cingulate cortex (ACC) plays a pivotal role as a social hub, integrating the afferent expectancy signals from OFC and LPFC. This paper presents a neurocomputational model of the interplay between observational learning and trust, as well as their role in individual decision-making. Our model elucidates and predicts the emotional and rational behavioral changes of an individual influenced by observing the action-outcome association of an alleged expert. We have modeled the neurodynamics of three cortical structures (OFC, LPFC, and ACC) and their interactions, where the neural oscillatory properties, modeled with Dynamic Bayesian Probability, represent the observers attitude towards the expert and the decision options. As an example of an everyday behavioral situation related to climate change, we use the choice of transportation between home and work. The EEG-like simulation outputs from our model represent the presumed brain activity of an individual making such a choice, assuming the decision-maker is exposed to social information.

Neurodegenerative diseases are frequently associated with aggregation and propagation of toxic proteins. In particular, it is well known that along with amyloid-beta, the tau protein is also driving Alzheimers disease. Multiscale reaction-diffusion models can assist in our better understanding of the evolution of the disease. We have modified the heterodimer model in such a way that it can now capture some of critical characteristics of this evolution such as the conversion time from healthy to toxic proteins. We have analyzed the modified model theoretically and validated the theoretical findings with numerical simulations.

The novel coronavirus disease (namely COVID-19) has taken attention because of its deadliness across the globe, causing a massive death as well as critical situation around the world. It is an infectious disease which is caused by newly discovered coronavirus. Our study demonstrates with a nonlinear model of this devastating COVID-19 which narrates transmission from human-to-human in the society. Pontryagins Maximum principle has also been applied in order to obtain optimal control strategies where the maintenance of social distancing is the major control. The target of this study is to find out the most fruitful control measures of averting coronavirus infection and eventually, curtailed of the COVID-19 transmission among people. The model is investigated analytically by using most familiar necessary conditions of Pontryagins maximum principle. Furthermore, numerical simulations have been performed to illustrate the analytical results. The analysis reveals that implementation of educational campaign, social distancing and developing human immune system are the major factors which can be able to plunge the scenario of becoming infected.

The brain is a source of continuous electrical activity, which include one dimensional voltage pulses (action potentials) that propagate along nerve fibres, transient localised oscillations, and persistent surface oscillations in five distinct frequency bands. However, a unified theoretical framework for modelling these excitations is lacking. In this paper we provide such a framework by constructing a special surface network in which all observed brain-like signals, including surface oscillations, can be generated by topological means. Analytic expressions for all these excitations are found and the values of the five frequency bands of surface oscillations are correctly predicted. It is shown how input signals of the system produce their own communication code to encode the information they carry and how the response output propagating signals produced carry this input information with them and can transfer it to the pathways they traverse as a non-transient topological memory structure of aligned spin-half protons. It is conjectured that the memory structure is located in the insulating sheaths of nerve fibres and are stable only if the pathways between assembly of neurons, that represents a memory structure, includes loops. The creation time and size of memory structures is estimated and a memory specific excitation frequencies for a memory structure is identified and determined, which can be used to recall memories.

In this paper, we investigate briefly the appropriateness of the widely used logistic growth curve modeling with focus on COVID-19 spread, from a data-driven perspective. Specifically, we suggest the Gumbel growth model for behaviour of COVID-19 cases in European countries in addition to the United States of America (US), for better detecting the growth and prediction. We provide a suitable fit and predict the growth of cases for some selected countries as illustration. Our contribution will stimulate the correct growth spread modeling for this pandemic outbreak.

Working memory is a system that helps us to store, retrieve, and manipulate information for a short period. The improper function of working memory is highly reported in people with attention deficit disorder. Attention deficit disorder is one of the most common disruptive behavioral disorders in children. Finding the actual reasons that may lead to inattentive symptoms is still an enigma for scientists. In this study, a model was proposed to show the flow of information through sensory, long-term, and working memory based on the Petri net approach. A new "selective updating" mechanism is also suggested. It is speculated that the central executive part of working memory uses this mechanism for updating the less important content with new incoming essential inputs. The analysis of the proposed model shows how an abnormality in the time setting or unexpected delays in information transmission may lead to some symptoms of inattention. These predictions about the possible causes of inattentive symptoms would be valuable for psychologists to find new possible treatments. This study also illustrates the great potential of Petri net approach for modeling and analysis of biological systems.

Visual scanning plays an important role in sampling visual information from the surrounding environments for a lot of everyday sensorimotor tasks, such as walking and car driving. In this paper, we consider the problem of visual scanning mechanism underpinning sensorimotor tasks in 3D dynamic environments. We exploit the use of eye tracking data as a behaviometric, for indicating the visuo-motor behavioral measures in the context of virtual driving. A new metric of visual scanning efficiency (VSE), which is defined as a mathematical divergence between a fixation distribution and a distribution of optical flows induced by fixations, is proposed by making use of a widely-known information theoretic tool, namely the square root of Jensen-Shannon divergence. Based on the proposed efficiency metric, a cognitive effort measure (CEM) is developed by using the concept of quantity of information. Psychophysical eye tracking studies, in virtual reality based driving, are conducted to reveal that the new metric of visual scanning efficiency can be employed very well as a proxy evaluation for driving performance. In addition, the effectiveness of the proposed cognitive effort measure is demonstrated by a strong correlation between this measure and pupil size change. These results suggest that the exploitation of eye tracking data provides an effective behaviometric for sensorimotor activity.

There is growing evidence that many forms of neural computation may be implemented by low-dimensional dynamics unfolding at the population scale. However, neither the connectivity structure nor the general capabilities of these embedded dynamical processes are currently understood. In this work, the two most common formalisms of firing-rate models are evaluated using tools from analysis, topology and nonlinear dynamics in order to provide plausible explanations for these problems. It is shown that low-rank structured connectivity predicts the formation of invariant and globally attracting manifolds in both formalisms, which generalizes existing theories to different neural models. Regarding the dynamics arising in these manifolds, it is proved they are topologically equivalent across the considered formalisms. It is also stated that under the low-rank hypothesis, dynamics emerging in neural models are universal. These include input-driven systems, which broadens previous findings. It is then explored how low-dimensional orbits can bear the production of continuous sets of muscular trajectories, the implementation of central pattern generators and the storage of memory states. It is also proved these dynamics can robustly simulate any Turing machine over arbitrary bounded memory strings, virtually endowing rate models with the power of universal computation. In addition, it is shown how the low-rank hypothesis predicts the parsimonious correlation structure observed in cortical activity. Finally, it is discussed how this theory could provide a useful tool from which to study neuropsychological phenomena using mathematical methods.

The persistent neural activity at a global scale, either stationary or oscillatory, can be explained by the use of the excitatory-inhibitory neural network models. This state of the network, as can be inferred, is crucial for the information processing and the memorizing ability of the brain. Though the goal for persistence to exist is apparent; from where the network achieves its ability to show a rich variety of the persistent dynamical states is unclear. The following study investigates the possible reasons for the persistence of neuronal networks in two parts; numerically and analytically. Presently, it shows that the action of the inhibitory components, among other favourable factors, plays a key role in starting and stabilizing neural activity. The results strongly support previous research conducted with both simpler and more specialized neural network models, as well as neurophysiological experiments. PACS numbers (2006 scheme)05.40.-a, 05.45.-a, 87.00, 89.00

In recent years, a vertiginous advance has occurred within the Neural Field Theory with the development of the so-called Next Generation Neural Field models. Unlike the phenomenological models, these models manage to describe neuronal activity, macroscopically, from the thermodynamic limit of microscopic laws under the assumption of a homogeneous density of neurons. The study of neural activity during neurodegenerative processes associated to Alzheimers, Parkinsons or Glioblastomas, should include a variable density of neurons. In this work, we propose an update of the Next Generation Neural Field model, extracted from the thermodynamic limit of the quadratic integration-and-fire model with realistic synaptic coupling and a variable density of neurons at the microscopic level. The thermodynamic limit of the system will allow us to study the patterns of synchronized neural activity that appear as the result of different spatial distribution of neurodegeneration. In particular, we demonstrate that during neurodegenerative processes, the relationship established between the thermodynamic states of the Neural Field and the Kuramoto order parameter (Measure of Neural Synchronization) differs from the classic results of the Next Generation Neural Field literature. Instead, the variation in neuron density directly modifies the Kuramoto order parameter. This might help us explain the diverse patterns of activity that can be found in different neurodegenerative processes and that could become experimental biomarkers of such pathologies.

Recently SIQR model was proposed by Odagaki as the modification of conventional SIR model by adding the term for isolation of infected persons, Q(Quarantined). The exponent{lambda} of the exponential function expressing the number of newly tested positive persons was defined as an linear equation explicitly with three important parameters, transmission coefficient, social distancing ratio x and isolation rate q. In this study, applying this model to the number of positive persons in publicly available database, daily{lambda} values are regression analyzed, and social distancing ratio and isolation rate are derived. Analyses for 7 countries including Japan, Taiwan, South Korea, and western countries are performed and determine the dynamic locus of q-x relation on the q-x plane during epidemic propagation. Finally, the remaining parameter, the transmission coefficient is shown to closely relate to the maximum {lambda}, {lambda}max, and {lambda}max (transmission coefficient) is characterized as a specific value for each country. Then, the magnitude of {lambda}max is combined with the value of {lambda}min to influence the total number of new cases until the convergence stage.

How the brain stores and retrieves memories is an important unsolved problem in neuroscience. It is commonly believed that memories are represented in the brain by distinct patterns of neural activity. Attractor dynamics has been proposed as one of the theoretical frameworks for learning and memory in neural networks. However, most of the prior theoretical work typically assumes that the neural network consists of fully-connected, binary neurons and that neuronal representations of memories are uncorrelated. In this paper, we propose a model consisting of continuously varying, rate-based, sparse neural network with a local learning rule which stores correlated patterns organized into multiple uncorrelated classes. We perform analytical calculations to compute maximum storage capacity and basin of attraction. It is found that increasing pattern correlation decreases storage capacity, and increasing the memory load decreases basin of attraction. We also study rate-based and spiking based neural network with separate excitatory and inhibitory populations and tight EI balance. Recent experimental work indicates that piriform cortex exhibits attractor dynamics and possibly stores hierarchically correlated patterns. So, we consider this work as a model for olfactory memory storage.