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A causal, stochastic model of networked computers, based on information theory and nonequilibrium dynamical systems is presented. This provides a simple explanation for recent experimental results revealing the structure of information in network transactions. The model is based on non-Poissonian stochastic variables and pseudo-periodic functions. It explains the measured patterns seen in resource variables on computers in network communities. Weakly non-Poissonian behavior can be eliminated by a conformal scaling transformation and leads to a mapping onto statistical field theory. From this, it is possible to calculate the exact profile of the spectrum of fluctuations. This work has applications to anomaly detection and time-series analysis of computer transactions.

We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one individual of each species or can be empty. The system evolves in time according to a probabilistic cellular automaton composed by a set of local rules which describe interactions between species individuals and mimic the process of birth, death and predation. By performing computational simulations, we found that, depending on the values of the parameters of the model, the following states can be reached: a prey absorbing state and active states of two types. In one of them both species coexist in a stationary regime with population densities constant in time. The other kind of active state is characterized by local coupled time oscillations of prey and predator populations. We focus on the self-organized structures arising from spatio-temporal dynamics of the coexistence. We identify distinct spatial patterns of prey and predators and verify that they are intimally connected to the time coexistence behavior of the species.

We analyze the absorbing state phase transition exhibited by two distinct unidimensional delayed contact process (CP). The first is characterized by the introduction of an infection period and the second by an immune period in the dynamics of the original model. We characterize these CP by the quantities t_d (infection or disease period) and t_i (immune period). The quantity t_d corresponds to the period interval an individual remains infected after being contaminated, while the period t_i is the time interval an individual remains immune after being cured. We used Monte Carlo simulations to compute the critical parameters associated with the absorbing state phase transition exhibited by these models. We find two distinct power-law scale relations for the critical infection rate and the critical cure rate . For the CP delayed by the minimum infection period we find μ_d = 0.98, while we obtained μ_i = 0.80 for the case of a delay due to immunity. In addition, we used a finite-size scaling analysis to estimate the critical exponents β/ν and ν, and found that these models belong to the universality class of directed percolation irrespective to the time delay.

In this work we present an agent-based model for the spread of tuberculosis where the individuals can be infected with either drug-susceptible or drug-resistant strains and can also receive a treatment. The dynamics of the model and the role of each one of the parameters are explained. The whole set of parameters is explored to check their importance in the numerical simulation results. The model captures the beneficial impact of the adequate treatment on the prevalence of tuberculosis. Nevertheless, depending on the treatment parameters range, it also captures the emergence of drug resistance. Drug resistance emergence is particularly likely to occur for parameter values corresponding to less efficacious treatment, as usually found in developing countries.

A stochastic cage model for the orientational dynamics of a molecule in isotropic and nematic phases of a liquid crystal has been developed, following the methodology introduced in Refs. 1, 2. The model has been parameterized on the basis of statistical data obtained from the analysis of Molecular Dynamics (MD) simulations of a Gay–Berne mesogen and is based on the general assumption of a timescale separation between the fast inertial librational motion inside the instantaneous cage potential and the slow diffusive motion of the cage itself. The model is able to reproduce single molecule time correlation functions both for the angular momentum and the reorientation of the long molecular axis of the molecule. A complete description of the dynamics of a Gay–Berne particle is given with a single set of physical parameters, from a very fast (hundreds of femtoseconds) timescale up to a timescale of nanoseconds.

Since the onset of the COVID-19 outbreak in Wuhan, China, numerous forecasting models have been proposed to project the trajectory of coronavirus infection cases. Most of these forecasts are based on epidemiology models that utilize deterministic differential equations and have resulted in widely varying predictions. We propose a new discrete-time Markov chain model that directly incorporates stochastic behavior and for which parameter estimation is straightforward from available data. Using such data from China’s Hubei province (for which Wuhan is the provincial capital city and which accounted for approximately 82% of the total reported COVID-19 cases in the entire country), the model is shown to be flexible, robust, and accurate. As a result, it has been adopted by the first Shanghai assistance medical team in Wuhan’s Jinyintan Hospital, which was the first designated hospital to take COVID-19 patients in the world. The forecast has been used for preparing medical staff, intensive care unit (ICU) beds, ventilators, and other critical care medical resources and for supporting real-time medical management decisions.

The breakdown of trusted sources of information is probably one of the most serious problems today, since in the absence of a common ground, it will be impossible to address the problems that trouble our contemporary world. The COVID-19 pandemic is just a recent situation where the lack of agreed stances has led to failure and hopelessness. In fact, disinformation surrounding the COVID-19 has been a distinctive feature of this pandemic since its very beginning and has hampered what is perhaps the most important initiative to prevent the spread of the coronavirus, viz., an effective communication between scientifically minded health authorities and the general public. To investigate how disinformation threatens epistemic security, here we propose and solve analytically an evolutionary game-theoretic model where the individuals must accurately estimate some property of their hazardous environment. They can either explore the environment or copy the estimate from another individual, who may display a distorted version of its estimate. We find that the exploration-only strategy is optimal when the environment is relatively safe and the individuals are not reliable. In this doomsday scenario, disinformation erodes trust and suppresses the ability of the individuals to share information with one another.

In the evolution literature, sympatric speciation is the origin of two, or more, species from a single local population. Many models have been developed to study the role of ecological competition and sexual selection in sympatric speciation.

In this paper we propose a methodology for systematically deriving efficient computational models to study speciation in populations evolving with overlapping generations. As a particular case, we consider sympatric speciation by sexual selection and we follow an individual based approach: a population is represented as a set of individuals that can mate and survive according to given probabilities.

We use our methodology to construct four different models for sympatric speciation, based on male traits and female preferences. These models differ in the genotypical representation of the individuals. Results of simulations in the different models are shown and discussed.

The study of the models show that sympatric speciation by sexual selection is unlikely, also with a favorable distribution of genotypes in the initial population.

Computer simulations have been conducted to provide a realistic model of tumor recurrence in a cancer patient, following treatment. The simulation model incorporates description of the temporal organization of various biological processes underlying tumor development at the cellular level: proliferation, differentiation, death of tumor cells, growth control in neoplastic tissues along with the tumor treatment effect. The prime object of our concern is whether the simple parametric model of tumor recurrence proposed by Hoang et al. [6] allows estimation of actual value of the tumor growth potential. A good fit has been demonstrated of the parametric model when applied to the samples of simulated tumor recurrence times as well as to real data samples of tumor recurrence in breast cancer patients with various regimen of radiotherapy.

The evaluation of cancer treatment efficiency is often based on the risk of local recurrence. When applied to the statistical analysis of tumor recurrence data, a pertinent parametric method has the following distinct advantages: (1) it allows a natural interpretation in terms of parameters bearing clear biological meaning, (2) it provides a prediction of the recurrence risk forward in time beyond the follow-up period, (3) it offers a means of estimating survival fraction (probability of tumor cure) from the time-to-recurrence observations. This paper discusses a stochastic model of tumor recurrence based on the consideration of biological processes of tumor latency within the random minima framework. A parametric family of distributions is obtained that allows for a survival fraction, thereby providing an estimate of the probability of tumor cure. When applying the model to data on breast cancer, we estimate the expected number of clonogens which give rise to early and late recurrences and their progression rate parameters. The prime object of our concern is discrimination between true recurrence and spontaneuos carcinogenesis on the basis of the temporal characteristics of the tumor latency. As evidenced by the data analysis, such a discrimination is feasible and allows to conclude that the contralateral breast cancer may be interpreted as a preexisting subclinical tumor at the time of treatment.

We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of stochastic correlations. For this purpose, we construct an ensemble of random correlation matrices and average the normal distribution over this ensemble. The resulting distribution contains a modified Bessel function of the second kind whose behavior differs significantly from the multivariate normal distribution, in the central part as well as in the tails. This result is then applied to asset returns. We compare with empirical return distributions using daily data from the NASDAQ Composite Index in the period from 1992 to 2012. The comparison reveals good agreement, the average portfolio return distribution describes the data well especially in the central part of the distribution. This in turn confirms our ansatz to model the nonstationarity by an ensemble average.

The objective of this paper is to explore the impact of stochastic inputs on the buckling and post-buckling response of structural frames. In particular, we examine the impact of random member stiffness on the buckling load, and the initial slope and curvature of the post-buckling response of three example frames. A finite element implementation of Koiter's perturbation method is employed to efficiently examine the post-buckling response. Monte Carlo simulations where the member stiffness is treated as a random variable, as well as correlated and uncorrelated random fields, are completed. The efficiency of Koiter's perturbation method is the key to the feasibility of applying Monte Carlo simulation techniques, which typically requires a large number of sample simulations. In an attempt to curtail the need for multiple sample calculations, an alternative first-order perturbation expansion is proposed for approximating the mean and variance of the post-buckling behavior. However, the limitations of this first-order perturbation approximation are demonstrated to be significant. The simulations indicate that deterministic characteristics of the post-buckling response can be inadequate in the face of input randomness. In one case, a frame that is stable symmetric in the deterministic case is found to be asymmetric when randomness in the input is incorporated; therefore, this frame has real potential for imperfection sensitivity. The importance of random field models for the member stiffness as opposed to random variable models is highlighted. The simulations indicate that the post-buckling response can magnify input randomness, as variability in the post-buckling parameters can be greater than the variability in the input parameters.

A general concept is presented which allows of setting up mathematical models for stochastic and quasi deterministic dynamic processes in social systems.

The basis of this concept is the master equation for the probability distribution over appropriately chosen personal and material macrovariables of the society. The probabilistic transition rates depend on motivation potentials governing the decisions and actions of the social agents. The transition from the probability distribution to quasi-meanvalues leads to in general nonlinear coupled differential equations for the macrovariables of the chosen social sector. Up to now several models about population dynamics, collective political opinion formation, dynamics of economic processes and the formation of settlements have been published.

Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual difference is one of the main obstacles one has to overcome in order to characterize analytically economic models. In this paper, we build both on statistical mechanics and the game theory notion of Potential Function to introduce a rigorous generalization of the physicist's free energy, which includes individual dynamics. Our approach paves the way to analytical treatments of a wide range of socio-economic models and might bring new insights into them. As first examples, we derive solutions for a congestion model and a residential segregation model.

This paper treats the infinite horizon discounted cost control problem for partially observable Markov decision processes. Sondik studied the class of finitely transient policies and showed that their value functions over an infinite time horizon are piecewise linear (p.w.l) and can be computed exactly by solving a system of linear equations. However, the condition for finite transience is stronger than is needed to ensure p.w.l. value functions. In this paper, we introduce alternatively the class of periodic policies whose value functions turn out to be also p.w.l. Moreover, we examine a more general condition than finite transience and periodicity that ensures p.w.l. value functions. We implement these ideas in a replacement problem under Markovian deterioration, investigate for periodic policies and give numerical examples.

In this article, a stochastic SIR-type model for COVID-19 epidemic is built using the standard field theoretical language based on creation and annihilation operators. From the model, we derive the time evolution of the mean number of infectious (active cases) and deceased individuals. In order to capture the effects of lockdown and social distancing, we use a time-dependent infection rate. The results are in good agreement with the data for three different waves of epidemic activity in South Korea.

Sensitivity analysis (SA) is a critical part of modeling any biological system due to the inherent uncertainty in model output, as introduced by parameter values that have not been experimentally determined. SA therefore provides deeper understanding of the system by painting a picture of the extent to which certain model outputs vary in relationship to changes in model parameters. Here we explore two types of global SA for recently developed models of nascent focal adhesion formation, a key step in cellular movement. While many SA methods have been used for deterministic methods, we utilize methods for both stochastic and deterministic models, providing a more complete description of the parameters to which the focal adhesion model is most sensitive. Specific recommendations for further experimentation in the process of cellular motility are proposed in response to the SA.

Following the 2009 G-20 clearing mandate, international standard setting bodies (SSBs) have outlined a set of principles for central counterparty (CCP) risk management. They have also devised formulaic CCP risk capital requirements on clearing members for their central counterparty exposures. There is still no consensus among CCP regulators and bank regulators on how central counterparty risk should be measured coherently in practice. A conceptually sound and logically consistent definition of the CCP risk capital in the absence of a unifying CCP risk measurement framework is challenging. Incoherent CCP risk capital requirements may create an obscure environment disincentivizing the central clearing of over the counter (OTC) derivatives transactions. Based on novel applications of well-known mathematical models in finance, this paper introduces a risk measurement framework that coherently specifies all layers of the default waterfall resources of typical derivatives CCPs. The proposed framework gives the first risk sensitive definition of the CCP risk capital based on which less risk sensitive non-model-based methods can be evaluated.

In this paper, a refined Barndorff-Nielsen and Shephard (BN-S) model is implemented to find an optimal hedging strategy for commodity markets. The refinement of the BN-S model is obtained with various machine and deep learning algorithms. The refinement leads to the extraction of a deterministic parameter from the empirical data set. The problem is transformed to an appropriate classification problem with a couple of different approaches — the volatility approach and the duration approach. The analysis is implemented to the Bakken crude oil data and the aforementioned deterministic parameter is obtained for a wide range of data sets. With the implementation of this parameter in the refined model, the resulting model performs much better than the classical BN-S model.

The healthcare system is no stranger to resource challenges in the face of unlimited demand to fulfill healthcare objectives of satisfying patients, maintaining service quality, and maximizing profit. An emergency medical services (EMSs) system plays a crucial role in stabilizing and transporting seriously injured patients to hospitals within healthcare systems. The EMS function is influenced by several criteria, such as call rate, traffic condition, setup, and operating costs. Therefore, the optimal design of EMS systems, including determining the location of emergency medical bases and allocating ambulances, helps improve service performance. This chapter explains the methodology and empirical results of a mathematical modeling and simulation-based optimization approach aimed at identifying the optimal location of emergency medical centers and assigning ambulances to the selected centers to maximize survival rates and minimize the total cost of the EMS system. A case study of the city of Isfahan in Iran is presented to demonstrate the applicability and efficacy of the proposed approach. The simulation-based optimization model was implemented in four selected municipal regions of Isfahan to obtain an appropriate design for emergency center locations and ambulances allocation with three types of patients (classified by the urgency of help required) and two types of ambulances. Six scenarios were defined to simulate the model in a dynamic environment and measure the survival rate and total cost of each scenario. In view of the survival rate and costs, data envelopment analysis (DEA) was then used to rank scenarios and select the best ones. The patient type was found to have a significant effect on the DEA rankings of the different input scenarios. An analysis across scenarios showed that adding portable stations in the regions that have the highest percentage of urgent patient calls can help increase the survival rate at a lower cost.