22 research outputs found
Cooperative Phenomena in Networks of Oscillators With Non-Identical Interactions and Dynamics
No full textThe incipience of synchrony in a diverse population of phase oscillators with non-identical interactions is an intriguing phenomenon. We study frequency synchronization of such oscillators composing networks with arbitrary topology in the context of the Kuramoto model and we show that its synchronization manifold is exponentially stable when the coupling has certain properties. Several example systems with periodic linear, cubic and sinusoidal coupling functions were examined, some including frustration and external fields. The numerical results confirmed the analytic findings and revealed some other interesting occurrences, like phase clustering in a synchronized network of strongly coupled oscillators. We also analyze the effects of the topology by considering random weighted network
Estimation of the basic reproduction number of COVID-19 from the incubation period distribution
No full textThe estimates of the future course of spreading of the SARS-CoV-2 virus are frequently based on Markovian models in which the duration of residence in any compartment is exponentially distributed. Accordingly, the basic reproduction number [Formula: see text] is also determined from formulae where it is related to the parameters of such models. The observations show that the start of infectivity of an individual appears nearly at the same time as the onset of symptoms, while the distribution of the incubation period is not an exponential. Therefore, we propose a method for estimation of [Formula: see text] for COVID-19 based on the empirical incubation period distribution and assumed very short infectivity period that lasts only few days around the onset of symptoms. We illustrate this venerable approach to estimate [Formula: see text] for six major European countries in the first wave of the epidemic. The calculations show that even if the infectivity starts 2 days before the onset of symptoms and stops instantly when they appear (immediate isolation), the value of [Formula: see text] is larger than that from the classical, SIR model. For more realistic cases, when only individuals with mild symptoms spread the virus for few days after onset of symptoms, the respective values are even larger. This implies that calculations of [Formula: see text] and other characteristics of spreading of COVID-19 based on the classical, Markovian approaches should be taken very cautiously
Energy-efficiency in decentralized wireless networks: A game-theoretic approach inspired by evolutionary biology
No full textEnergy efficiency is gaining importance in wireless communication networks which have nodes with limited energy supply and signal processing capabilities. We present a numerical study of cooperative communication scenarios based on simple local rules. This is in contrast to most of the approaches in the literature which enforce cooperation by using complex algorithms and require strategic complexity of the network nodes. The approach is motivated by recent results in evolutionary biology which suggest that, if certain mechanism is at work, cooperation can be favored by natural selection, i. e. even selfish actions of the individual nodes can lead to emergence of cooperative behavior in the network. The results of the simulations in the context of wireless communication networks verify these observations and indicate that uncomplicated local rules, followed by simple fitness evaluation, can generate network behavior which yields global energy efficiency
Random Walk with Memory on Complex Networks
No full textWe 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
Emergence of Cooperation in Decentralized Wireless Networks
No full textThe paper investigates the mechanisms for promotion
of cooperation in decentralized wireless networks. The main
objective is to determine whether cooperation can emerge in
these networks in the same way it emerges in biological systems.
The approach is motivated by recent results in evolutionary
biology which suggest that cooperation can be favored by natural
selection, if a certain mechanism is at work. We are interested in
promoting cooperation based on simple rules, in contrast to most
of the approaches which enforce cooperation by using complex
algorithms and require strategic complexity of the network nodes.
We present a model of a wireless network as a graph, and
associate benefits and costs with the strategy that the network
users follow at a certain time instant (cooperation or defection).
We define fitness function based on the amount of power each
node has to transmit and allow the users to update their strategy
based on the observed change of fitness. The objective is to
demonstrate that cooperative behavior, if introduced by chance,
can persists over time in the wireless network
Some Probabilistic Interpretations Related to the Next-Generation Matrix Theory: A Review with Examples
No full textThe fact that the famous basic reproduction number R0, i.e., the largest eigenvalue of the next generation matrix FV−1, sometimes has a probabilistic interpretation is not as well known as it deserves to be. It is well understood that half of this formula, −V, is a Markovian generating matrix of a continuous-time Markov chain (CTMC) modeling the evolution of one individual on the compartments. It has also been noted that the not well-enough-known rank-one formula for R0 of Arino et al. (2007) may be interpreted as an expected final reward of a CTMC, whose initial distribution is specified by the rank-one factorization of F. Here, we show that for a large class of ODE epidemic models introduced in Avram et al. (2023), besides the rank-one formula, we may also provide an integral renewal representation of R0 with respect to explicit “age kernels” a(t), which have a matrix exponential form.This latter formula may be also interpreted as an expected reward of a probabilistic continuous Markov chain (CTMC) model. Besides the rather extensively studied rank one case, we also provide an extension to a case with several susceptible classes
