arXiv subjects

Lasko Basnarkov

Publications and source records attributed to Lasko Basnarkov.

At least 19 recordsLinked to original sources

arXiv2026

A Persistent Random-Walk Model of Molecular Transport in Neuronal Dendritic Trees

A two-level analytical framework is presented for modeling random walk transport of messenger ribonucleic acid (mRNA) molecules along neuronal microtubules from soma to synapses. Motivated by empirical observations of mRNA cargo motion, the transport within a dendrite is modeled by a persistent telegraph process with pauses. Theoretical expressions for the probability of traversing the dendrite and the mean time for such travel are derived for different and equal probabilities of persistence. These results are used for the construction of a semi-Markov model of motion of mRNA cargo within the whole neuron. The semi-Markov model provides the probabilities of absorption at a given synapse and corresponding mean first-passage times (MFPTs) from the soma, where mRNA is transcribed. The theoretical expressions, together with experimentally obtained parameter values, are used to calculate MFPTs for neurons with empirically reconstructed morphology. The model predicts that when retrograde persistence is stronger, the MFPT to each synapse is effectively the same. Otherwise, when the persistence is more pronounced in the anterograde direction, the transport in the neuron resembles the motion along a single dendrite -- nearly linear dependence of MFPT on the distance between soma and synapse. These findings are theoretically justified when the lengths of dendrites are considerably longer than the distance traversed during a typical run.

q-bio.SC↗

arXiv2025

On the Similarity between Epidemiologic Strains, Minimal Self-Replicable Siphons, and autocatalytic cores in (Chemical) Reaction Networks: Towards a Unifying Framework

We aim to study boundary stability and persistence of positive odes in mathematical epidemiology models by importing structural tools from chemical reaction networks. This is largely a review work, which attempts to bring closer together the fields of mathematical epidemiology (ME), and chemical reaction networks (CRNs), based on several observations. We started by observing the conceptual correspondence between epidemiologic strains and both critical minimal siphons and minimal autocatalytic sets (cores) in an underlying CRN, and confirmed this in all the models we studied. We leverage this to provide a definition of the disease free equilibrium (DFE) face/infected set as the union of either all minimal siphons, or of all cores (they coincide always in our examples). Next, we provide a proposed definition of ME models, as models which have a unique boundary fixed point on the DFE face, and for which the Jacobian of the infected subnetwork admits a regular splitting, which allows defining the famous next generating matrix (NGM). We then define the interaction graph on minimal siphons (IGMS), whose vertices are minimal siphons, and whose edges indicate the existence of reactions producing species in one siphon from species in another. When this graph is acyclic, we say the model exhibits a Acyclic Minimal Siphon Decomposition (AMSD). For AMSD models whose minimal siphons partition the infection species, we show that the NGM is block triangular after permutation, which implies the classical max structure of the reproduction number R0 for multi-strain models. We implement algorithms to compute IGMS and detect AMSD in the Epid-CRN Mathematica package (https://github.com/florinav/EpidCRNmodels) (which contains already modules to identify minimal siphons, criticality, drainability, self-replicability, etc).

math.DS↗

arXiv2025

Semi-Markov random walk on complex networks

We present a semi-Markov model of random walk on complex networks in discrete and continuous-time scenario. In the general setting of the semi-Markov chains, the duration of stay at given node - the sojourn time - is random, and the probability to transition to a neighbor depends on the sojourn time. Analytical formulae for the average sojourn time and the node occupation probability of infinite walk are presented and verified with Monte Carlo simulations for two examples. We propose an application of the semi-Markovian random walk for ranking web pages determined by the fraction of time that infinite random surfer spends on a web page - time rank, as an alternative to the existing PageRank that relies on the fraction of visits - visit rank.

physics.soc-ph↗

arXiv2025

Response to an external field of a generalized Langevin equation with stochastic resetting of the memory kernel

We study a generalized Langevin equation (GLE) framework that incorporates stochastic resetting of a truncation power-law memory kernel. The inclusion of stochastic resetting enables the emergence of resonance phenomena even in parameter regimes where conventional settings (without resetting) do not exhibit such behavior. Specifically, we explore the response of the system to an external field under three scenarios: (i) a free particle, (ii) a particle in a harmonic potential, and (iii) the effect of truncation in the memory kernel. In each case, the primary focus is on understanding how the resetting mechanism interacts with standard parameters to induce stochastic resonance. In addition, we explore the effect of resetting on the dielectric loss.

cond-mat.stat-mech↗

arXiv2024

Comparative study of random walks with one-step memory on complex networks

We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph mean first passage times as an indicator for the searching efficiency. The experiments with generated and real networks show that biasing based on inverse degree, persistence and local two-hop paths can lead to smaller searching times. Moreover, these biasing approaches can be combined to achieve a more robust random search strategy. Our findings can be applied in the modeling and solution of various real-world problems.

cs.CY↗

arXiv2023

Algorithmic approach for an unique definition of the next generation matrix

The basic reproduction number R0 is a concept which originated in population dynamics, mathematical epidemiology, and ecology and is closely related to the mean number of children in branching processes.We offer below three new contributions to the literature: 1) We order a universal algorithmic definition of a (F, V) gradient decomposition (and hence of the resulting R0), which requires a minimal input from the user, namely the specification of an admissible set of disease/infection variables. We also present examples where other choices may be more reasonable, with more terms in F, or more terms in V . 2) We glean out from the works of Bacaer a fixed point equation (8) for the extinction probabilities of a stochastic model associated to a deterministic ODE model, which may be expressed in terms of the (F, V ) decomposition. The fact that both R0 and the extinction probabilities are functions of (F, V ) underlines the centrality of this pair, which may be viewed as more fundamental than the famous next generation matrix FV^{-1}. 3) We suggest introducing a new concept of sufficient/minimal disease/infection set (sufficient for determining R0). More precisely, our universal recipe of choosing "new infections" once the "infections" are specified suggests focusing on the choice of the latter, which is also not unique. The maximal choice of choosing all compartments which become 0 at the given boundary point seems to always work, but is the least useful for analytic computations, therefore we propose to investigate the minimal one. As a bonus, this idea seems useful for understanding the Jacobian factorization approach for computing R0 . Last but not least, we offer Mathematica scripts and implement them for a large variety of examples, which illustrate that our recipe others always reasonable results, but that sometimes other reasonable (F, V ) decompositions are available as well.

q-bio.PE↗

arXiv2022

On matrix-SIR Arino models with linear birth rate, loss of immunity, disease and vaccination fatalities, and their approximations

In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of which we review and combine. Our main result shows that for simple "matrix epidemic models" introduced in [1], an explicit general formula for the reproduction number and the corresponding "weak stability alternative" still holds, under small modifications, for models with nonconstant population size, and even when the model allows for vaccination and loss of immunity. The importance of this result is clear once we note that the models of [1] include a large number of viral and bacterial models of epidemic propagation, including for example the totality of homogeneous COVID-19 models. To better understand the nature of the result, we emphasize that the models proposed in [1] and considered here are extensions of the SIR-PH model, which is essentially characterized by a phase-type distribution that models transitions between the "disease/infectious compartments". In these cases, the reproduction number and a certain Lyapunov function for the disease free equilibrium are explicitly expressible. Not surprisingly, accounting for varying demography, loss of immunity, and vaccinations lead to several challenges. One of the most important is that a varying population size leads to multiple endemic equilibrium points: this is in contrast with "classic models" which in general admit unique disease-free and endemic equilibria. As a special case of our analysis, we consider a "first approximation" (FA) of our model, which coincides with the constant-demography model often studied in the literature, and for which more explicit results are available. Furthermore, we propose a second heuristic approximation named "intermediate approximation" (IA).

math.OC↗

arXiv2021

Endemic state equivalence between non-Markovian SEIS and Markov SIS model in complex networks

In the light of several major epidemic events that emerged in the past two decades, and emphasized by the COVID-19 pandemics, the non-Markovian spreading models occurring on complex networks gained significant attention from the scientific community. Following this interest, in this article, we explore the relations that exist between the non-Markovian SEIS (Susceptible--Exposed--Infectious--Susceptible) and the classical Markov SIS, as basic re-occurring virus spreading models in complex networks. We investigate the similarities and seek for equivalences both for the discrete-time and the continuous-time forms. First, we formally introduce the continuous-time non-Markovian SEIS model, and derive the epidemic threshold in a strict mathematical procedure. Then we present the main result of the paper that, providing certain relations between process parameters hold, the stationary-state solutions of the status probabilities in the non-Markovian SEIS may be found from the stationary state probabilities of the Markov SIS model. This result has a two-fold significance. First, it simplifies the computational complexity of the non-Markovian model in practical applications, where only the stationary distribution of the state probabilities is required. Next, it defines the epidemic threshold of the non-Markovian SEIS model, without the necessity of a thrall mathematical analysis. We present this result both in analytical form, and confirm the result trough numerical simulations. Furthermore, as of secondary importance, in an analytical procedure we show that each Markov SIS may be represented as non-Markovian SEIS model.

physics.soc-ph↗

arXiv2021

Non-Markovian SIR epidemic spreading model

We introduce non-Markovian SIR epidemic spreading model inspired by the characteristics of the COVID-19, by considering discrete- and continuous-time versions. The incubation period, delayed infectiousness and the distribution of the recovery period are modeled with general functions. By taking corresponding choice of these functions, it is shown that the model reduces to the classical Markovian case. The epidemic threshold is analytically determined for arbitrary functions of infectivity and recovery and verified numerically. The relevance of the model is shown by modeling the first wave of the epidemic in Italy, in the spring, 2020.

physics.soc-ph↗

arXiv2020

Generalised geometric Brownian motion: Theory and applications to option pricing

Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics due to irregularities found when comparing its properties with empirical distributions. As a solution, we develop a generalisation of GBM where the introduction of a memory kernel critically determines the behavior of the stochastic process. We find the general expressions for the moments, log-moments, and the expectation of the periodic log returns, and obtain the corresponding probability density functions by using the subordination approach. Particularly, we consider subdiffusive GBM (sGBM), tempered sGBM, a mix of GBM and sGBM, and a mix of sGBMs. We utilise the resulting generalised GBM (gGBM) to examine the empirical performance of a selected group of kernels in the pricing of European call options. Our results indicate that the performance of a kernel ultimately depends on the maturity of the option and its moneyness.

q-fin.PR↗

arXiv2020

SEAIR epidemic spreading model of COVID-19

We study Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic spreading model of COVID-19. It captures two important characteristics of the infectiousness of COVID-19: delayed start and its appearance before onset of symptoms, or even with total absence of them. The model is theoretically analyzed in continuous-time compartmental version and discrete-time version on random regular graphs and complex networks. We show analytically that there are relationships between the epidemic thresholds and the equations for the susceptible populations at the endemic equilibrium in all three versions, which hold when the epidemic is weak. We provide theoretical arguments that eigenvector centrality of a node approximately determines its risk to become infected.

physics.soc-ph↗

arXiv2019

Evolution of cooperation in networked heterogeneous fluctuating environments

Fluctuating environments are situations where the spatio-temporal stochasticity plays a significant role in the evolutionary dynamics. The study of the evolution of cooperation in these environments typically assumes a homogeneous, well mixed population, whose constituents are endowed with identical capabilities. In this paper, we generalize these results by developing a systematic study for the cooperation dynamics in fluctuating environments under the consideration of structured, heterogeneous populations with individual entities subjected to general behavioral rules. Considering complex network topologies, and a behavioral rule based on generalized reciprocity, we perform a detailed analysis of the effect of the underlying interaction structure on the evolutionary stability of cooperation. We find that, in the presence of environmental fluctuations, the cooperation dynamics can lead to the creation of multiple network components, each with distinct evolutionary properties. This is paralleled to the freezing state in the Random Energy Model. We utilize this result to examine the applicability of our generalized reciprocity behavioral rule in a variety of settings. We thereby show that the introduced rule leads to steady state cooperative behavior that is always greater than or equal to the one predicted by the evolutionary stability analysis of unconditional cooperation. As a consequence, the implementation of our results may go beyond explaining the evolution of cooperation. In particular, they can be directly applied in domains that deal with the development of artificial systems able to adequately mimic reality, such as reinforcement learning.

q-bio.PE↗

arXiv2019

Lead-lag Relationships in Foreign Exchange Markets

Lead-lag relationships among assets represent a useful tool for analyzing high frequency financial data. However, research on these relationships predominantly focuses on correlation analyses for the dynamics of stock prices, spots and futures on market indexes, whereas foreign exchange data have been less explored. To provide a valuable insight on the nature of the lead-lag relationships in foreign exchange markets here we perform a detailed study for the one-minute log returns on exchange rates through three different approaches: i) lagged correlations, ii) lagged partial correlations and iii) Granger causality. In all studies, we find that even though for most pairs of exchange rates lagged effects are absent, there are many pairs which pass statistical significance tests. Out of the statistically significant relationships, we construct directed networks and investigate the influence of individual exchange rates through the PageRank algorithm. The algorithm, in general, ranks stock market indexes quoted in their respective currencies, as most influential. In contrast to the claims of the efficient market hypothesis, these findings suggest that all market information does not spread instantaneously.

q-fin.ST↗

arXiv2019

Random Walk with Memory on Complex Networks

We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs of nodes, for a random walk with a memory of one step. We have analyzed one particular model of random walk, where the transition probabilities depend on the number of paths to the second neighbors. The numerical experiments on paradigmatic complex networks verify the validity of the theoretical expressions, and also indicate that the flattening of the stationary occupation probability accompanies a nearly optimal random search.

physics.soc-ph↗

arXiv2019

Cooperation dynamics in the networked geometric Brownian motion

Recent works suggest that pooling and sharing may constitute a fundamental mechanism for the evolution of cooperation in well-mixed fluctuating environments. The rationale is that, by reducing the amplitude of fluctuations, pooling and sharing increases the steady-state growth rate at which the individuals self-reproduce. However, in reality interactions are seldom realized in a well-mixed structure, and the underlying topology is in general described by a complex network. Motivated by this observation, we investigate the role of the network structure on the cooperative dynamics in fluctuating environments, by developing a model for networked pooling and sharing of resources undergoing environmental fluctuations, represented through geometric Brownian motion. The study reveals that, while in general cooperation increases the individual steady state growth rates (i.e. is evolutionary advantageous), the interplay with the network structure may yield large discrepancies in the observed individual resource endowments. We comment possible biological and social implications and discuss relations to econophysics.

nlin.AO↗

arXiv2019

Option Pricing with Heavy-Tailed Distributions of Logarithmic Returns

A growing body of literature suggests that heavy tailed distributions represent an adequate model for the observations of log returns of stocks. Motivated by these findings, here we develop a discrete time framework for pricing of European options. Probability density functions of log returns for different periods are conveniently taken to be convolutions of the Student's t-distribution with three degrees of freedom. The supports of these distributions are truncated in order to obtain finite values for the options. Within this framework, options with different strikes and maturities for one stock rely on a single parameter -- the standard deviation of the Student's t-distribution for unit period. We provide a study which shows that the distribution support width has weak influence on the option prices for certain range of values of the width. It is furthermore shown that such family of truncated distributions approximately satisfies the no-arbitrage principle and the put-call parity. The relevance of the pricing procedure is empirically verified by obtaining remarkably good match of the numerically computed values by our scheme to real market data.

q-fin.PR↗

arXiv2019

Correlation Patterns in Foreign Exchange Markets

The value of an asset in a financial market is given in terms of another asset known as numeraire. The dynamics of the value is non-stationary and hence, to quantify the relationships between different assets, one requires convenient measures such as the means and covariances of the respective log returns. Here, we develop transformation equations for these means and covariances when one changes the numeraire. The results are verified by a thorough empirical analysis capturing the dynamics of numerous assets in a foreign exchange market. We show that the partial correlations between pairs of assets are invariant under the change of the numeraire. This observable quantifies the relationship between two assets, while the influence of the rest is removed. As such the partial correlations uncover intriguing observations which may not be easily noticed in the ordinary correlation analysis.

q-fin.ST↗

arXiv2019

Cooperation dynamics of generalized reciprocity in state-based social dilemmas

We introduce a framework for studying social dilemmas in networked societies where individuals follow a simple state-based behavioral mechanism based on generalized reciprocity, which is rooted in the principle "help anyone if helped by someone". Within this general framework, which applies to a wide range of social dilemmas including, among others, public goods, donation and snowdrift games, we study the cooperation dynamics on a variety of complex network examples. By interpreting the studied model through the lenses of nonlinear dynamical systems, we show that cooperation through generalized reciprocity always emerges as the unique attractor in which the overall level of cooperation is maximized, while simultaneously exploitation of the participating individuals is prevented. The analysis elucidates the role of the network structure, here captured by a local centrality measure which uniquely quantifies the propensity of the network structure to cooperation, by dictating the degree of cooperation displayed both at microscopic and macroscopic level. We demonstrate the applicability of the analysis on a practical example by considering an interaction structure that couples a donation process with a public goods game.

q-bio.PE↗