arXiv subjects

Thi Kim Thoa Thieu

Publications and source records attributed to Thi Kim Thoa Thieu.

8 recordsLinked to original sources

arXiv2023

Modelling the behavior of human crowds as coupled active-passive dynamics of interacting particle systems

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.

physics.soc-ph↗

arXiv2022

Coupled effects of channels and synaptic dynamics in stochastic modelling of healthy and Parkinson's-disease-affected brains

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.

q-bio.NC↗

arXiv2022

Coupled stochastic systems of Skorokhod type: well-posedness of a mathematical model and its applications

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.

math.DS↗

arXiv2022

Effects of noise on leaky integrate-and-fire neuron models for neuromorphic computing applications

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.

q-bio.NC↗

arXiv2022

Effects of random inputs and short-term synaptic plasticity in a LIF conductance model for working memory applications

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.

q-bio.NC↗

arXiv2021

Combining Coupled Skorokhod SDEs and Lattice Gas Frameworks for Multi-fidelity Modelling of Complex Behavioral Systems

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.

physics.data-an↗

arXiv2021

Reflecting stochastic dynamics of active-passive populations with applications in operations research and neuroscience

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.

math.NA↗

arXiv2021

Well-posedness of a coupled system of Skorohod-like stochastic differential equations

We study the well-posedness of a coupled system of Skorohod-like stochastic differential equations with reflecting boundary condition. The setting describes the evacuation dynamics of a mixed crowd composed of both active and passive pedestrians moving through a domain with obstacles, fire and smoke. As main working techniques, we use compactness methods and the Skorohod's representation of solutions to SDEs posed in bounded domains. This functional setting is a new point of view in the field of modeling and simulation pedestrian dynamics. The main challenge is to handle the coupling in the model equations together with the multiple-connectedness of the domain and the pedestrian-obstacle interaction.

math.PR↗