arXiv subjects

Konstantinos Spiliotis

Publications and source records attributed to Konstantinos Spiliotis.

9 recordsLinked to original sources

arXiv2026

Data-driven macroscopic dynamics of complex networks using Topological Data Analysis and the Equation-Free Method

In this work, we present a computational framework for exploring and analyzing the macroscopic dynamics of complex agent-based network models by integrating Topological Data Analysis with the Equation-Free Method. To demonstrate the effectiveness of our method, we apply it to Erdős--Rényi-type random networks. Central to our approach is a Topological Data Analysis-based filtration process driven by the density of activated network nodes (agents), from which we extract a coarse-grained macroscopic topological observable. This observable is defined via persistent Betti numbers, thus requiring significantly reduced data dimensionality while retaining essential topological features. Subsequently, within the Equation-Free Method framework, we show firstly that a \textit{lifting procedure} can be achieved using topological properties and secondly, a data-driven evolution law that governs the dynamics of this macroscopic variable. Finally, we perform a numerical bifurcation and stability analysis to investigate the global behavior and qualitative transitions of the emergent macroscopic dynamics.

math.DS↗

arXiv2023

Numerical Bifurcation Analysis of Turing and Symmetry Broken Patterns of a Vegetation PDE Model

We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water and one ordinary differential equation (ODE) describing the dependence of the toxicity on the biomass. We perform a linear stability analysis in the one-dimensional finite space, we derive analytically the conditions for the appearance of Turing instability that gives rise to spatio-temporal patterns emanating from the homogeneous solution, and provide its dependence with respect to the size of the domain. Furthermore, we perform a numerical bifurcation analysis in order to study the pattern formation of the inhomogeneous solution, with respect to the precipitation rate, thus analyzing the stability and symmetry properties of the emanating patterns. Based on the numerical bifurcation analysis, we have found new patterns, which form due to the onset of secondary bifurcations from the primary Turing instability, thus giving rise to a multistability of asymmetric solutions.

math.DS↗

arXiv2021

Optimal vaccine roll-out strategies with respect to social distancing measures for SARS-CoV-2 pandemic

Non-pharmacological interventions (NPIs), and in particular social distancing, in conjunction with the advent of effective vaccines at the end of 2020, aspired for the development of a protective immunity shield against the spread of SARS-CoV-2. The main question rose is related to the deployment strategy of the two doses with respect to the imposed NPIs and population age. In this study, an extended (SEIR) agent-based model on small-world networks was employed to identify the optimal policies against Covid 19 pandemic, including social distancing measures and mass vaccination. To achieve this, a new methodology is proposed to solve the inverse problem of calibrating an agent's infection rate with respect to vaccination efficacy. The results show that deploying the first vaccine dose across the whole population is sufficient to control the epidemic, with respect to deaths, even for low number of social contacts. Moreover, for the same range of social contacts, we found that there is an optimum ratio of vaccinating ages > 65 over the younger ones of 4/5.

math.DS↗

arXiv2021

A biophysical network model reveals the link between deficient inhibitory cognitive control and major neurotransmitter and neural connectivity hypotheses in schizophrenia

We address a biophysical network dynamical model to study how the modulation of dopamine (DA) activity and related N-methyl-d-aspartate (NMDA) glutamate receptor activity as well as the emerging Pre-Frontal Cortex (PFC) functional connectivity network (FCN) affect inhibitory cognitive function in schizophrenia in an antisaccade task. The values of the model parameters and the topology of the PFC-FCN were estimated by minimizing the differences between simulations and the observed distributions of reaction times (RT) during the performance of the antisaccade task in 30 patients with schizophrenia and 30 healthy controls. We show that the proposed model approximates remarkably well the predicted prefrontal cortical DA hypo-activity and the related NMDA receptor hypo-function as well as the FCN dysconnection pattern that are considered as the major etio-pathological hypotheses to explain cognitive deficits in schizophrenia.

q-bio.NC↗

arXiv2021

Deep brain stimulation for movement disorder treatment: Exploring frequency-dependent efficacy in a computational network model

A large scale computational model of the basal ganglia (BG) network is proposed to describes movement disorder including deep brain stimulation (DBS). The model of this complex network considers four areas of the basal ganglia network: the subthalamic nucleus (STN) as target area of DBS, globus pallidus, both pars externa and pars interna (GPe-GPi), and the thalamus (THA). Parkinsonian conditions are simulated by assuming reduced dopaminergic input and corresponding pronounced inhibitory or disinhibited projections to GPe and GPi. Macroscopic quantities can be derived which correlate closely to thalamic responses and hence motor programme fidelity. It can be demonstrated that depending on different levels of striatal projections to the GPe and GPi, the dynamics of these macroscopic quantities switch from normal conditions to parkinsonian. Simulating DBS on the STN affects the dynamics of the entire network, increasing the thalamic activity to levels close to normal, while differing from both normal and parkinsonian dynamics. Using the mentioned macroscopic quantities, the model proposes optimal DBS frequency ranges above 130 Hz.

q-bio.NC↗

arXiv2021

Coarse-scale PDEs from fine-scale observations via machine learning

Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through e.g. atomistic, agent-based or lattice models) based on first principles. Some of these processes can also be successfully modeled at the macroscopic level using e.g. partial differential equations (PDEs) describing the evolution of the right few macroscopic observables (e.g. concentration and momentum fields). Deriving good macroscopic descriptions (the so-called "closure problem") is often a time-consuming process requiring deep understanding/intuition about the system of interest. Recent developments in data science provide alternative ways to effectively extract/learn accurate macroscopic descriptions approximating the underlying microscopic observations. In this paper, we introduce a data-driven framework for the identification of unavailable coarse-scale PDEs from microscopic observations via machine learning algorithms. Specifically, using Gaussian Processes, Artificial Neural Networks, and/or Diffusion Maps, the proposed framework uncovers the relation between the relevant macroscopic space fields and their time evolution (the right-hand-side of the explicitly unavailable macroscopic PDE). Interestingly, several choices equally representative of the data can be discovered. The framework will be illustrated through the data-driven discovery of macroscopic, concentration-level PDEs resulting from a fine-scale, Lattice Boltzmann level model of a reaction/transport process. Once the coarse evolution law is identified, it can be simulated to produce long-term macroscopic predictions. Different features (pros as well as cons) of alternative machine learning algorithms for performing this task (Gaussian Processes and Artificial Neural Networks), are presented and discussed.

cs.LG↗

arXiv2019

Analytical and Numerical Bifurcation Analysis of a Forest-Grassland Ecosystem Model with Human Interaction

We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of forest/grassland value. The system displays multiple steady states corresponding to different forest densities as well as regimes characterized by both stable and unstable limit cycles. We derive analytically the conditions with respect to the model parameters that give rise to various types of codimension-one criticalities such as transcritical, saddle-node, and Andronov-Hopf bifurcations and codimension-two criticalities such as cusp and Bogdanov-Takens bifurcations. We also perform a numerical continuation of the branches of limit cycles. By doing so, we reveal turning points of limit cycles marking the appearance/disappearance of sustained oscillations. These far-from-equilibrium criticalities that cannot be detected analytically give rise to the abrupt loss of the sustained oscillations, thus leading to another mechanism of catastrophic shifts

math.NA↗

arXiv2014

Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model

We show how appropriate rewiring with the aid of Metropolis Monte Carlo computational experiments can be exploited to create network topologies possessing prescribed values of the average path length (APL) while keeping the same connectivity degree and clustering coefficient distributions. Using the proposed rewiring rules we illustrate how the emergent dynamics of the celebrated majority-rule model are shaped by the distinct impact of the APL attesting the need for developing efficient algorithms for tuning such network characteristics.

cs.SI↗

arXiv2011

On the effect of the path length and transitivity of small-world networks on epidemic dynamics

We show how one can trace in a systematic way the coarse-grained solutions of individual-based stochastic epidemic models evolving on heterogeneous complex networks with respect to their topological characteristics. In particular, we have developed algorithms that allow the tuning of the transitivity (clustering coefficient) and the average mean-path length allowing the investigation of the "pure" impacts of the two characteristics on the emergent behavior of detailed epidemic models. The framework could be used to shed more light into the influence of weak and strong social ties on epidemic spread within small-world network structures, and ultimately to provide novel systematic computational modeling and exploration of better contagion control strategies.

cs.SI↗