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Monte Carlo (MC) simulations have been performed for a refined estimation of the correction-to-scaling exponent omega in the 2D phi^4 model. The best estimate omega=1.546(30) has been obtained from the finite-size scaling of the susceptibility data in the range of linear lattice sizes L from 128 to 2048 at the critical value of the Binder cumulant, this result is confirmed also by several other MC estimations. It served as a basis for a critical reconsideration of some earlier theoretical conjectures and scaling assumptions. In particular, we have corrected and refined our previous analysis by grouping Feynman diagrams. The renewed analysis gives omega = 4-d-2 eta as some approximation for spatial dimensions d<4, or omega approximately 1.5 in two dimensions. Our MC value is comparable with the known results of the epsilon-expansion., Comment: 17 pages, 8 tables

Non-charge based logic in single-hole spin of semiconductor quantum dots (QDs) can be controlled by anisotropic gate potentials providing a notion for making next generation solid-state quantum devices. In this study, we investigate the isotropic and anisotropic behavior of phonon mediated spin relaxation of heavy-hole spin hot spots in QDs. For the electron spin in isotropic QDs, hot spots are known to be always present due to the Rashba spin-orbit coupling. But for heavy holes in isotropic dots, we show that the occurrences of spin hot spots are sensitive to the bulk g-factor. The hot spot for Rashba coupling in InAs and GaSb dots arises because these materials possess negative bulk g-factor, while that for the Dresselhaus coupling in GaAs and InSb dots is found due to their positive bulk g-factor. For anisotropic QDs, on the other hand, the spin hot spot is universally present due to their broken in-plane rotational symmetry. Further, the increasing electric field, that strengthens the Rashba coupling, is shown to cover a wide range of magnetic field by the hot spots. Results demonstrate that the magnetic field, choice of dot materials and size anisotropy can act as effective control parameters which can be experimentally used to design the device for detecting the phonon mediated heavy-hole spin-relaxation behavior of III-V semiconductor QDs., Comment: 15 pages, 11 figures

In bio-social models, cooperative behaviour has evolved as an adaptive strategy, playing multi-functional roles. One of such roles in populations is to increase the success of survival and reproduction of individuals and their families or social groups. Moreover, collective decision-making in cooperative behaviour is an aspect that is used to study the dynamic behaviour of individuals within a social group. In this paper, we have focused on population dynamics by considering a predator-prey model as our main exemplification, where the generalist predator has adopted a cooperative hunting strategy while consuming their prey. In particular, we have analyzed the dynamic nature of the system when a nonlocal term is introduced in the cooperation. First, the Turing instability condition has been studied for the local model around the coexisting steady-state, followed by the Turing and non-Turing patterns in the presence of the nonlocal interaction term. This work is also concerned with the existence of travelling wave solutions for predator-prey interaction with the nonlocal cooperative hunting strategy. Such solutions are reported for local as well as for nonlocal models. We have characterized the invading speed of the predator with the help of the minimal wave speed of travelling wave solutions connecting the predator-free state to the co-existence state. The travelling waves are found to be non-monotonic in this system. The formation of wave trains has been demonstrated for an extended range of nonlocal interactions. Finally, the importance of psychological effects in shaping the dynamics of nonlocal collective behaviour is demonstrated with several representative examples., Comment: 39 pages, 34 figures

In functionally complex systems, higher-order connectivity is often revealed in the underlying geometry of networked units. Furthermore, such systems often show signatures of self-organized criticality, a specific type of non-equilibrium collective behaviour associated with an attractor of internal dynamics with long-range correlations and scale invariance, which ensures the robust functioning of complex systems, such as the brain. Here, we highlight the intertwining of features of higher-order geometry and self-organized critical dynamics as a plausible mechanism for the emergence of new properties on a larger scale, representing the central paradigm of the physical notion of complexity. Considering the time scale of the structural evolution with the known separation of the time scale in self-organized criticality, i.e., internal dynamics and external driving, we distinguish three classes of geometries that can shape the self-organized dynamics on them differently. We provide an overview of current trends in the study of collective dynamics phenomena, such as the synchronization of phase oscillators and discrete spin dynamics with higher-order couplings embedded in the faces of simplicial complexes. For a representative example of self-organized critical behaviour induced by higher-order structures, we present a more detailed analysis of the dynamics of field-driven spin reversal on the hysteresis loops in simplicial complexes composed of triangles. These numerical results suggest that two fundamental interactions representing the edge-embedded and triangle-embedded couplings must be taken into account in theoretical models to describe the influence of higher-order geometry on critical dynamics., Comment: 12 pages, 4 figures

This study presents a computational framework to investigate and predict the complicated multiphase properties of eco-friendly lead-free piezoelectric materials, which are crucial for sustainable technological progress. Although their electromechanical properties vary by phase, lead-free piezoelectric materials show a considerable thermo-electromechanical response. Lead-free materials such as Bi$_{0.5}$Na$_{0,5}$TiO$_{3}$ (BNT) and other BNT-type piezoelectric materials transition to rhombohedral (R3c), orthorhombic (Pnma), tetragonal (P4bm), and cubic (Cc) phases with temperature variation. These phases are determined by the symmetry and alignment of the ferroelectric domains. Multiple phases can occur simultaneously under specific thermal, electrical, and mechanical conditions, leading in complex multiphase behaviour. These materials' performance must be assessed by studying such behaviour. This study uses Landau-Ginzburg-Devonshire theory to simulate material micro-domain phase transitions. The computational model for BNT-type piezoelectric material covers temperature-induced ferroelectric domain switching and phase transitions. Therefore, the developed computational approach will assist us in better understanding the influence of these materials' complex multiphase behaviour on creating sustainable solutions with green technologies.

Living tissues experience various external forces on cells, influencing their behaviour, physiology, shape, gene expression, and destiny through interactions with their environment. Despite much research done in this area, challenges remain in our better understanding of the behaviour of the cell in response to external stimuli, including the arrangement, quantity, and shape of organelles within the cell. This study explores the electromechanical behaviour of biological cells, including organelles like microtubules, mitochondria, nuclei, and cell membranes. Two distinct cell structures have been developed to explore the cell responses to mechanical displacement, resembling actual cell shapes. The finite element method has been utilized to integrate the linear piezoelectric and non-local flexoelectric effects accurately. It is found that the longitudinal stress is absent and only the transverse stress plays a crucial role when the mechanical load is imposed on the top side of the cell through compressive displacement. The impact of flexoelectricity is elucidated by introducing a new parameter called the maximum electric potential ratio ($V_{\text{R,max}}$). It has been found that $V_{\text{R,max}}$ depends upon the orientation angle and shape of the microtubules. Further, the study reveals that the number of microtubules significantly impacts effective elastic and piezoelectric coefficients, affecting cell behaviour based on structure, microtubule orientation, and mechanical stress direction. The insight obtained from the current study can assist in advancements in medical therapies such as tissue engineering and regenerative medicine.

Nonlocality is important in realistic mathematical models of physical and biological systems at small-length scales. It characterizes the properties of two individuals located in different locations. This review illustrates different nonlocal mathematical models applied to biology and life sciences. The major focus has been given to sources, developments, and applications of such models. Among other things, a systematic discussion has been provided for the conditions of pattern formations in biological systems of population dynamics. Special attention has also been given to nonlocal interactions on networks, network coupling and integration, including models for brain dynamics that provide us with an important tool to better understand neurodegenerative diseases. In addition, we have discussed nonlocal modelling approaches for cancer stem cells and tumor cells that are widely applied in the cell migration processes, growth, and avascular tumors in any organ. Furthermore, the discussed nonlocal continuum models can go sufficiently smaller scales applied to nanotechnology to build biosensors to sense biomaterial and its concentration. Piezoelectric and other smart materials are among them, and these devices are becoming increasingly important in the digital and physical world that is intrinsically interconnected with biological systems. Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue growth and shrinkage, and other areas increasingly important in biomedical and bioengineering applications. Finally, we provided a comprehensive summary of emerging trends and highlighted future directions in this rapidly expanding field., Comment: 71 pages

In recent times, there have been notable advancements in haptic technology, particularly in screens found on mobile phones, laptops, LED screens, and control panels. However, it is essential to note that the progress in high-temperature haptic applications is still in the developmental phase. Due to its complex phase and domain structures, lead-free piezoelectric materials such as BNT-based haptic technology behave differently at high temperatures than ambient conditions. Therefore, it is essential to investigate the aspects of thermal management and thermal stability, as temperature plays a vital role in the phase and domain transition of BNT material. A two-dimensional thermo-electromechanical model has been proposed in this study to analyze the thermal stability of BNT material by analyzing the impact of temperature on effective electromechanical properties and mechanical and electric field parameters. However, the thermo-electromechanical modelling of BNT ceramics examines the macroscopic effects of the applied thermal field on mechanical and electric field parameters as phase change and microdomain dynamics are not considered in this model. This study analyzes the impact of thermo-electromechanical coupling on the performance of BNT-type piezoelectric materials compared to conventional electromechanical coupling. The results predicted a significant improvement in piezoelectric response compared to electromechanical coupling due to increased thermoelectric effect in absence of phase change and microdomain switching for temperature boundary conditions below depolarization temperature ($T_{d}$~200$^{\circ}$C for pure BNT material)., Comment: 37 pages, 13 figures

Patterns in a semiarid ecosystem are important because they directly and indirectly affect ecological processes, biodiversity, and ecosystem resilience. Understanding the causes and effects of these patterns is critical for long-term land surface management and conservation efforts in semiarid regions, which are especially sensitive to climate change and human-caused disturbances. It is known that there is a regular connection between the vegetation and the living species in a habitat since some animals evolved to live in a semiarid ecosystem and rely on plants for food. In this work, we have constructed a coupled mathematical model to connect the water resource, vegetation and living organisms and have investigated how the soil surface affects the resulting patterns for the long term. This study contributes to a better understanding of ecological patterns and processes in semiarid environments by shedding light on the complex interaction mechanisms that depend on the structure of semiarid ecosystems. The findings provide further critical insight into the influence of efforts for improving ecosystem resilience and adjusting to the challenges posed by climate change and human activities., Comment: 21 pages, 6 figures, 1 table

In a predator-prey interaction, many factors are present that affect the growth of the species, either positively or negatively. Fear of predation is such a factor that causes psychological stress in a prey species, so their overall growth starts to decline. In this work, a predator-prey model is proposed where the prey species faces a reduction in their growth out of fear, and the predator is also provided with an alternative food source that helps the prey to hide in a safer place. The dynamics produce a wide range of interesting results, including the significance of the presence of a certain amount of fear or even prey refuge for population coexistence. The analysis is extended later to the nonlocal model to analyze how the non-equilibrium phenomena influence the dynamical behaviour. It is observed through numerical simulations that the scope of pattern formation reduces with the increase of fear level in the spatio-temporal model, whereas the incorporation of nonlocal interaction further increases the chance of species colonization., Comment: 26 pages, 28 figures

In this chapter, we consider probabilistic drift-diffusion models and Bayesian inference frameworks to address this issue, assisting better social human decision-making. We provide details of the models, as well as representative numerical examples, and discuss the decision-making process with a representative example of the escape route decision-making phenomena by further developing the drift-diffusion models and Bayesian inference frameworks. In the latter context, we also give a review of recent developments in human collective decision-making and its applications with brain network models. Furthermore, we provide illustrative numerical examples to discuss the role of neuromodulation, reinforcement learning in decision-making processes. Finally, we call attention to existing challenges, open problems, and promising approaches in studying social dynamics and collective human decision-making, including those arising from nonequilibrium considerations of the associated processes., Comment: 39 pages,10 pages

Alzheimer's disease (AD) is a prominent, worldwide, age-related neurodegenerative disease that currently has no systemic treatment. Strong evidence suggests that permeable amyloid-beta peptide (Abeta) oligomers, astrogliosis and reactive astrocytosis cause neuronal damage in AD. A large amount of Abeta is secreted by astrocytes, which contributes to the total Abeta deposition in the brain. This suggests that astrocytes may also play a role in AD, leading to increased attention to their dynamics and associated mechanisms. Therefore, in the present study, we developed and evaluated novel stochastic models for Abeta growth using ADNI data to predict the effect of astrocytes on AD progression in a clinical trial. In the AD case, accurate prediction is required for a successful clinical treatment plan. Given that AD studies are observational in nature and involve routine patient visits, stochastic models provide a suitable framework for modelling AD. Using the approximate Bayesian computation (ABC) approach, the AD etiology may be modelled as a multi-state disease process. As a result, we use this approach to examine the weak and strong influence of astrocytes at multiple disease progression stages using ADNI data from the baseline to 2-year visits for AD patients whose ages ranged from 50 to 90 years. Based on ADNI data, we discovered that the strong astrocyte effect (i.e., a higher concentration of astrocytes as compared to Abeta) could help to lower or clear the growth of Abeta, which is a key to slowing down AD progression., Comment: 10, figures and 30 pages

The abnormal aggregation of extracellular amyloid-$\beta$ (A\beta) in senile plaques resulting in calcium (Ca^{+2}) dyshomeostasis is one of the primary symptoms of Alzheimer's disease (AD). Significant research efforts have been devoted in the past to better understand the underlying molecular mechanisms driving A\beta deposition and Ca^{+2} dysregulation. To better understand this interaction, we report a novel stochastic model where we analyze the positive feedback loop between A\beta and Ca^{+2} using ADNI data. A good therapeutic treatment plan for AD requires precise predictions. Stochastic models offer an appropriate framework for modelling AD since AD studies are observational in nature and involve regular patient visits. The etiology of AD may be described as a multi-state disease process using the approximate Bayesian computation method. So, utilizing ADNI data from $2$-year visits for AD patients, we employ this method to investigate the interplay between A\beta and Ca^{+2} levels at various disease development phases. Incorporating the ADNI data in our physics-based Bayesian model, we discovered that a sufficiently large disruption in either A\beta metabolism or intracellular Ca^{+2} homeostasis causes the relative growth rate in both Ca^{+2} and A\beta, which corresponds to the development of AD. The imbalance of Ca^{+2} ions causes A\beta disorders by directly or indirectly affecting a variety of cellular and subcellular processes, and the altered homeostasis may worsen the abnormalities of Ca^{+2} ion transportation and deposition. This suggests that altering the Ca^{+2} balance or the balance between A\beta and Ca^{+2} by chelating them may be able to reduce disorders associated with AD and open up new research possibilities for AD therapy., Comment: 20 pages, 6 figures

We consider the problem of analyzing spin-flip qubit gate operation in presence of Random Telegraph Noise (RTN). Our broad approach is the following. We calculate the spin-flip probability of qubit driven by composite pulses, (Constant pulse (C-pulse), Quantum Well pulse (QW-pulse) and Barrier Potential pulse (BP-pulse)) in the presence of RTN using Feynman disentangling method. When composite pulses and RTN act in x-direction and z-direction respectively, we calculate the optimal time to achieve 100% spin-flip probability of qubit. We report the shortcut of spin-flip qubit, which can be achieved by using C-pulse, followed by BP-pulse and QW-pulse. When jumps time in RTN are very fast, tuning of perfect fidelity or spin-flip probability extends to large RTN correlation time. On the other hand, when the jumps in RTN are very slow, the BP-pulse can be used to recover the lost fidelities. Nevertheless, the fidelities of qubit gate operation are larger than 90%, regardless of RTN jumps environments which may be beneficial in quantum error correction. For more general case, we have tested several pulse sequences for achieving high fidelity quantum gates, where we have used the pulses acting in different directions. From the calculations, we find high fidelity of qubit gate operation in presence of RTN is achieved when QW-pulse, BP-pulse and C-pulse act in x-direction, y-direction and z-direction, respectively., Comment: 8 pages, 7 figures. arXiv admin note: text overlap with arXiv:2005.05493

Alzheimer's disease (AD) is a common neurodegenerative disorder nowadays. Amyloid-beta (A$\beta$) and tau proteins are among the main contributors to the development or propagation of AD. In AD, A$\beta$ proteins clump together to form plaques and disrupt cell functions. On the other hand, the abnormal chemical change in the brain helps to build sticky tau tangles that block the neuron's transport system. Astrocytes generally maintain a healthy balance in the brain by clearing the A$\beta$ plaques (toxic A$\beta$). However, over-activated astrocytes release chemokines and cytokines in the presence of A$\beta$ and react to pro-inflammatory cytokines, further increasing the production of A$\beta$. In this paper, we construct a mathematical model that can capture astrocytes' dual behaviour. Furthermore, we reveal that the disease propagation depends on the current time instance and the disease's earlier status, called the ``memory effect''. We consider a fractional order network mathematical model to capture the influence of such memory effect on AD propagation. We have integrated brain connectome data into the model and studied the memory effect, the dual role of astrocytes, and the brain's neuronal damage. Based on the pathology, primary, secondary, and mixed tauopathies parameters are considered in the model. Due to the mixed tauopathy, different brain nodes or regions in the brain connectome accumulate different toxic concentrations of A$\beta$ and tau proteins. Finally, we explain how the memory effect can slow down the propagation of such toxic proteins in the brain, decreasing the rate of neuronal damage., Comment: 16 pages, 8 figures, 3 tables

Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the long-range diffusion occurs, and the usual reaction-diffusion (RD) model can not capture such phenomena. The nonlocal RD model, on the other hand, can fill the gap. Analytical derivation of the amplitude equations (AE) for an RD system is a valuable tool to predict the pattern selections, in particular, the stationary Turing patterns when they occur. In this paper, we analyze the conditions for the Turing bifurcation for the nonlocal model and also derive the AE for the nonlocal RD model near the Turing bifurcation threshold to describe the reason behind the pattern selections. This derivation of the AE is not only limited to the nonlocal prey-predator model, as shown in our representative example but also can be applied to other nonlocal models near the Turing bifurcation threshold. The analytical prediction agrees with numerical simulation near the Turing bifurcation threshold. Moreover, the analytical and numerical results fit each other well even more remote from the Turing bifurcation threshold for the small values of the nonlocal parameter but not for the higher values., Comment: 21 pages, 7 figures

Population dynamics with complex biological interactions, accounting for uncertainty quantification, is critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation of the corresponding problems faces the challenge that the corresponding stochastic processes should, in most cases, be considered in bounded domains. We propose a model based on a coupled system of reflecting Skorokhod-type stochastic differential equations with jump-like exit from a boundary. The setting describes the population dynamics of active and passive populations. As main working techniques, we use compactness methods and Skorokhod's representation of solutions to SDEs posed in bounded domains to prove the well-posedness of the system. This functional setting is a new point of view in the field of modelling and simulation of population dynamics. We provide the details of the model, as well as representative numerical examples, and discuss the applications of a Wilson-Cowan-type system, modelling the dynamics of two interacting populations of excitatory and inhibitory neurons. Furthermore, the presence of random input current, reflecting factors together with Poisson jumps, increases firing activity in neuronal systems., Comment: 20 pages, 3 figures. arXiv admin note: text overlap with arXiv:2006.00232

Working memory (WM) has been intensively used to enable the temporary storing of information for processing purposes, playing an important role in the execution of various cognitive tasks. Recent studies have shown that information in WM is not only maintained through persistent recurrent activity but also can be stored in activity-silent states such as in short-term synaptic plasticity (STSP). Motivated by important applications of the STSP mechanisms in WM, the main focus of the present work is on the analysis of the effects of random inputs on a leaky integrate-and-fire (LIF) synaptic conductance neuron under STSP. Furthermore, the irregularity of spike trains can carry the information about previous stimulation in a neuron. A LIF conductance neuron with multiple inputs and coefficient of variation (CV) of the inter-spike-interval (ISI) can bring an output decoded neuron. Our numerical results show that an increase in the standard deviations in the random input current and the random refractory period can lead to an increased irregularity of spike trains of the output neuron., Comment: 14 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:2202.09482

Artificial neural networks (ANNs) have been extensively used for the description of problems arising from biological systems and for constructing neuromorphic computing models. The third generation of ANNs, namely, spiking neural networks (SNNs), inspired by biological neurons enable a more realistic mimicry of the human brain. A large class of the problems from these domains is characterized by the necessity to deal with the combination of neurons, spikes and synapses via integrate-and-fire neuron models. Motivated by important applications of the integrate-and-fire of neurons in neuromorphic computing for bio-medical studies, the main focus of the present work is on the analysis of the effects of additive and multiplicative types of random input currents together with a random refractory period on a leaky integrate-and-fire (LIF) synaptic conductance neuron model. Our analysis is carried out via Langevin stochastic dynamics in a numerical setting describing a cell membrane potential. We provide the details of the model, as well as representative numerical examples, and discuss the effects of noise on the time evolution of the membrane potential as well as the spiking activities of neurons in the LIF synaptic conductance model scrutinized here. Furthermore, our numerical results demonstrate that the presence of a random refractory period in the LIF synaptic conductance system may substantially influence an increased irregularity of spike trains of the output neuron., Comment: 16 pages, 11 figures. arXiv admin note: text overlap with arXiv:2112.12932

The modelling of human crowd behaviors offers many challenging questions to science in general. Specifically, the social human behavior consists of many physiological and psychological processes which are still largely unknown. To model reliably such human crowd systems with complex social interactions, stochastic tools play an important role for the setting of mathematical formulations of the problems. In this work, using the description based on an exclusion principle, we study a statistical-mechanics-based lattice gas model for active-passive population dynamics with an application to human crowd behaviors. We provide representative numerical examples for the evacuation dynamics of human crowds, where the main focus in our considerations is given to an interacting particle system of active and passive human groups. Furthermore, our numerical results show that the communication between active and passive humans strongly influences the evacuation time of the whole population even when the "faster-is-slower" phenomenon is taken into account. To provide an additional inside into the problem, a stationary state of our model is analyzed via current representations and heat map techniques. Finally, future extensions of the proposed models are discussed in the context of coupled data-driven modelling of human crowds and traffic flows, vital for the design strategies in developing intelligent transportation systems., Comment: 12 figures, 23 pages

Our brain is a complex information processing network in which the nervous system receives information from the environment to quickly react to incoming events or learns from experience to sharp our memory. In the nervous system, the brain states translate collective activities of neurons interconnected via synaptic connections. In this paper, we study coupled effects of channels and synaptic dynamics under the stochastic influence of healthy brain cells with applications to Parkinson's disease (PD). In particular, we investigate the effects of random inputs in a subthalamic nucleus (STN) cell membrane potential model. The STN bursting phenomena and parkinsonian hypokinetic motor symptoms are closely connected, as electrical and chemical maneuvers modulating STN bursts are sufficient to ameliorate or mimic parkinsonian motor deficits. Deep brain stimulation (DBS) of the STN is an important surgical technique used in the treatment to improve PD symptoms. Our numerical results show that the random inputs strongly affect the spiking activities of the STN neuron not only in the case of healthy cells but also in the case of PD cells in the presence of DBS treatment. Specifically, the existence of a random refractory period together with random input current in the system may substantially influence an increased irregularity of spike trains of the output neurons., Comment: 23 pages, 16 figures

It is well known that today nearly one in six of the world's population has to deal with neurodegenerative disorders. While a number of medical devices have been developed for the detection, prevention, and treatments of such disorders, some fundamentals of the progression of associated diseases are in urgent need of further clarification. In this paper, we focus on Alzheimer's disease, where it is believed that the concentration changes in amyloid-beta and tau proteins play a central role in its onset and development. A multiscale model is proposed to analyze the propagation of these concentrations in the brain connectome. In particular, we consider a modified heterodimer model for the protein-protein interactions. Higher toxic concentrations of amyloid-beta and tau proteins destroy the brain cell. We have studied these propagations for the primary and secondary and their mixed tauopathy. We model the damage of a brain cell by the nonlocal contributions of these toxic loads present in the brain cells. With the help of rigorous analysis, we check the stability behaviour of the stationary points corresponding to the homogeneous system. After integrating the brain connectome data into the developed model, we see that the spreading patterns of the toxic concentrations for the whole brain are the same, but their concentrations are different in different regions. Also, the time to propagate the damage in each region of the brain connectome is different., Comment: 15 pages, 9 figures, 4 tables

Deep brain stimulation (DBS) can alleviate the movement disorders like Parkinson's disease (PD). Indeed, it is known that aberrant beta (13-30Hz)oscillations and the loss of dopaminergic neurons in the basal ganglia-thalamus (BGTH) and cortex characterize the akinesia symptoms of PD. However, the relevant biophysical mechanism behind this process still remains unclear. Based on the prior striatal inhibitory model, we propose an extended BGTH model incorporating medium spine neurons (MSNs) and fast-spiking interneurons (FSIs) along with the effect of DBS. We are focusing in this paper on an open-loop DBS mode, where the stimulation parameters stay constant independent of variations in the disease state, and modifications of parameters rely mainly on trial and error of medical experts. Additionally, we propose a novel combined model of the cerebellar-basal-ganglia thalamocortical network, MSNs, and FSIs, and show new results that indicate that Parkinsonian oscillations in the beta-band frequency range emerge from the dynamics of such a network. Our model predicts that DBS can be used to suppress beta oscillations in globus pallidus pars interna (GPi) neurons. This research will help our better understanding of the changes in brain activity caused by DBS, providing new insight for studying PD in the future., Comment: 15 pages, 7 figures

To model reliably behavioral systems with complex bio-social interactions, accounting for uncertainty quantification, is critical for many application areas. However, in terms of the mathematical formulation of the corresponding problems, one of the major challenges is coming from the fact that corresponding stochastic processes should, in most cases, be considered in bounded domains, possibly with obstacles. This has been known for a long time and yet, very little has been done for the quantification of uncertainties in modelling complex behavioral systems described by such stochastic processes. In this paper, we address this challenge by considering a coupled system of Skorokhod-type stochastic differential equations (SDEs) describing interactions between active and passive participants of a mixed-population group. In developing a multi-fidelity modelling methodology for such behavioral systems, we combine low- and high-fidelity results obtained from (a) the solution of the underlying coupled system of SDEs and (b) simulations with a statistical-mechanics-based lattice gas model, where we employ a kinetic Monte Carlo procedure. Furthermore, we provide representative numerical examples of healthcare systems, subject to an epidemic, where the main focus in our considerations is given to an interacting particle system of asymptomatic and susceptible populations., Comment: 12 pages, 3 figures

Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these domains is characterized by the necessity to deal with several distinct groups of populations, which are usually labeled as "active" and "passive". Motivated by important applications of queueing networks and neuroscience, the main focus of the present work is on the analysis of reflecting stochastic dynamics of such mixed populations. We develop a general mathematical modeling framework to describe the reflecting stochastic dynamics for active-passive populations. The analysis of this model is carried out via a combination of low- and high-delity results obtained from the solution of the underlying coupled system of SDEs and from the simulations with a statistical-mechanics-based lattice gas model, where we employ a kinetic Monte Carlo procedure. We provide details of the queueing theory and neuronal models and discuss a relationship between reflecting SDEs and a model of queueing theory via a limit theorem. Furthermore, we present several representative numerical examples, and discuss an intrinsic interconnection between active and passive particles in the underlying stochastic process. Finally, possible extensions of the proposed methodology have been highlighted., Comment: 25 pages, 9 figures

Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human connectome can be crucial for the brain complex dynamics. In this context, the best-connected brain areas, designated as hub nodes, play a central role in supporting integrated brain function. Here, we study the structure of simplicial complexes attached to eight global hubs in the female and male connectomes and identify the core networks among the affected brain regions. These eight hubs (Putamen, Caudate, Hippocampus and Thalamus-Proper in the left and right cerebral hemisphere) are the highest-ranking according to their topological dimension, defined as the number of simplexes of all orders in which the node participates. Furthermore, we analyse the weight-dependent heterogeneity of simplexes. We demonstrate changes in the structure of identified core networks and topological entropy when the threshold weight is gradually increased. These results highlight the role of higher-order interactions in human brain networks and provide additional evidence for (dis)similarity between the female and male connectomes., Comment: 14 pages, 6 figures

Cooperative self-assembly can result in complex nano-networks with new hyperbolic geometry. However, the relation between the hyperbolicity and spectral and dynamical features of these structures remains unclear. Using the model of aggregation of simplexes introduced in I [Sci. Rep., 8:1987, 2018], here we study topological and spectral properties of a large class of self-assembled structures consisting of monodisperse building blocks (cliques of size $n=3,4,5,6$) which self-assemble via sharing the geometrical shapes of a lower order. The size of the shared sub-structure is tunned by varying the chemical affinity $\nu$ such that for significant positive $\nu$ sharing the largest face is the most probable, while for $\nu < 0$, attaching via a single node dominates. Our results reveal that, while the parameter of hyperbolicity remains $\delta_{max}=1$ across the assemblies, their structure and spectral dimension $d_s$ vary with the size of cliques $n$ and the affinity when $\nu \geq 0$. In this range, we findthat $d_s >4$ can be reached for $n\geq 5$ and sufficiently large $\nu$. For the aggregates of triangles and tetrahedra, the spectral dimension remains in the range $d_s\in [2,4)$, as well as for the higher cliques at vanishing affinity. On the other end, for $\nu < 0$, we find $d_s\eqsim 1.57$ independently on $n$. Moreover, the spectral distribution of the normalised Laplacian eigenvalues has a characteristic shape with peaks and a pronounced minimum, representing the hierarchical architecture of the simplicial complexes. These findings show how the structures compatible with complex dynamical properties can be assembled by controlling the higher-order connectivity among the building blocks., Comment: 9 pages, 7 figures included

Mapping the brain imaging data to networks, where each node represents a specific area of the brain, has enabled an objective graph-theoretic analysis of human connectome. However, the latent structure on higher-order connections remains unexplored, where many brain regions acting in synergy perform complex functions. Here we analyse this hidden structure using the simplicial complexes parametrisation where the shared faces of simplexes encode higher-order relationships between groups of nodes and emerging hyperbolic geometry. Based on data collected within the Human Connectome Project, we perform a systematic analysis of consensus networks of 100 female (F-connectome) and 100 male (M-connectome) subjects by varying the number of fibres launched. Our analysis reveals that the functional geometry of the common F\&M-connectome coincides with the M-connectome and is characterized by a complex architecture of simplexes to the 14th order, which is built in six anatomical communities, and short cycles among them. Furthermore, the F-connectome has additional connections that involve different brain regions, thereby increasing the size of simplexes and introducing new cycles. By providing new insights into the internal organisation of anatomical brain modules as well as into the links between them that are essential to dynamics, these results also highlight the functional gender-related differences, Comment: 13 pages, 7 figures

An odd number of zigzag edges in armchair graphene nanoribbons and their mechanical properties (e.g., Young's modulus, Poisson ratio and shear modulus) have potential interest for bandgap engineering in graphene based optoelectronic devices. In this paper, we consider armchair graphene nanoribbons passivated with hydrogen at the armchair edges and then apply the strain for tuning the bandgaps. Using density functional theory calculations, our study finds that the precise control of strain can allow tuning the bandgap from semiconductor to mettalic and then again switching back to semiconductor. In addition, we also show that the strained graphene nanoribbon passivated with hydrogen molecules can have large out-of-plane deformations demonstrating the properties of relaxed shape graphene. We express the strain induced by hydrogen in terms of binding energy. Finally, we characterise the effect of strain on the mechanical properties that can be used for making straintronic devices based on graphene nanoribbons., Comment: 7 pages and 7 figures

Modern applications require a robust and theoretically solid tool for the realistic modeling of electronic states in low dimensional nanostructures. The $k \cdot p$ theory has fruitfully served this role for the long time since its establishment. During the last three decades several problems have been detected in connection with the application of the $k \cdot p$ approach to such nanostructures. These problems are closely related to the violation of the ellipticity conditions for the underlying model, the fact that has been largely overlooked in the literature. We derive ellipticity conditions for $6 \times 6$, $8\times 8$ and $14 \times 14$ Hamiltonians obtained by the application of Luttinger-Kohn theory to the bulk zinc blende (ZB) crystals, and demonstrate that the corresponding models are non-elliptic for many common crystalline materials. With the aim to obtain the admissible (in terms of ellipticity) parameters, we further develop and justify a parameter rescaling procedure for $8\times 8$ Hamiltonians. This allows us to calculate the admissible parameter sets for GaAs, AlAs, InAs, GaP, AlP, InP, GaSb, AlSb, InSb, GaN, AlN, InN. The newly obtained parameters are then optimized in terms of the bandstructure fit by changing the value of the inversion asymmetry parameter $B$ that is proved to be essential for ellipticity of $8\times 8$ Hamiltonian. The consecutive analysis, performed here for all mentioned $k \cdot p$ Hamiltonians, indicates the connection between the lack of ellipticity and perturbative terms describing the influence of out-of-basis bands on the structure of the Hamiltonian. This enables us to quantify the limits of models' applicability material-wise and to suggest a possible unification of two different $14 \times 14$ models, analysed in this work., Comment: 19 pages, 6 figures

Veselago lens focusing in graphene p-n junction is promising for realizations of new generation electron optics devices. However, the effect of the strain-induced Aharonov-Bohm interference in a p-n junction has not been discussed before. We provide an experimentally feasible setup based on the Veselago lens in which the presence of strain can result in both the valley-dependent Lorentz force and Aharonov-Bohm interference. In particular, by employing the Green's function and tight binding methods, we study the strain induced by dislocations and line defects in a p-n junction and show how the resulting Aharonov-Bohm phase and interference can be detected. Furthermore, for a different strain configuration, e.g. corresponding to corrugated graphene, we find strong signatures of valley splitting induced by the fictitious magnetic field. Our proposal can be useful for mapping elastic deformations and defects, and for studying valley dependent effects in graphene., Comment: 8 pages, 9 figures