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In this article, we investigate the optimal control problems of heterogeneous node-based information epidemics. A node-based susceptible–infected–recovered–susceptible model is introduced to describe the information diffusion processes taking into account heterogeneities in both network structures and individual characters. Aiming at guiding information dissemination processes toward the desired performance, we propose an optimal control framework with respect to two typical scenarios, i.e., impeding the spread of rumors and enhancing the spread of marketing or campaigning information. We prove the existence of the solutions and solve the optimal control problems by the Pontryagin maximum principle and the forward–backward sweep method. Moreover, numerical experiments validate the use of the node-based SIRS model by comparing it with the exact $3^N$ -state Markov chain model. The effectiveness of the proposed control rules is demonstrated on both models. Furthermore, discussion on the influence of the parameters provides insights into the strategies of guiding information diffusion processes.

This paper presents an N-state Markov-chain mixture distribution approach to model the clear-sky index. The model is based on dividing the clear-sky index data into bins of magnitude and determining probabilities for transitions between bins. These transition probabilities are then used to define a Markov-chain, which in turn is connected to a mixture distribution of uniform distributions. When trained on measured data, this model is used to generate synthetic data as output. The model is an N-state generalization of a previously published two-state Markov-chain mixture distribution model applied to the clear-sky index. The model is tested on clear-sky index data sets for two different climatic regions: Norrkoping, Sweden, and Oahu, Hawaii, USA. The model is also compared with the two-state model and a copula model for generating synthetic clear-sky index time-series as well as other existing clear-sky index generators in the literature. Results show that the N-state model is generally on par with, or superior to, state-of-the-art synthetic clear-sky index generators in terms of Kolmogorov–Smirnov test statistic, autocorrelation and computational speed.

Modern bulk material production processes are high volume and high quality processes. The manual grab sampling of bulk material is known to be biased and unrepresentative. Auto-samplers, which are robotic samplers of bulk material in small increments, provide for better representative samples of the production process. The amount and sampling frequency for an auto-sampler can be varied depending on the product type and quality characteristic of interest. This article presents a statistical methodology for determining the sampling frequency for auto-samplers using a two-state Markov chain model for detecting the foreign matter contamination in the production.

In this paper, we develop a resilience modelling and analysis framework for multistate systems. The developed framework is based on Markov reward processes, in which the performance degradation and recovery processes of the multistate system are modeled by a continuous time discrete state Markov chain, and the losses caused by disruptive events are modeled by reward rates. A numerical metric is defined to quantify resilience based on the losses the system suffered from the disruptive events. The developed methods are applied to analyze the resilience of a nuclear power plant under the threat of earthquakes.

This paper analysis a discrete time infinite capacity queueing system with correlated arrival and negative customers served by two state Markovian server. Positive customers are generated according to the first order Markovian arrival process with geometrically distributed lengths of On periods and Off periods. Further, the geometrically distributed arrival of negative customer removes the positive customers is any, and has no effect when the system is empty. The server state is a two state Markov chain which alternate between Good and Bad states with geometrically distributed service times. Closed-form expressions for mean queue length, unfinished work and sojourn time distributions are obtained. Numerical illustrations are also presented.

Probabilistic Boolean networks (PBNs) is a well-established computational framework for modelling biological systems. The steady-state dynamics of PBNs is of crucial importance in the study of such systems. However, for large PBNs, which often arise in systems biology, obtaining the steady-state distribution poses a significant challenge. In this paper, we revive the two-state Markov chain approach to solve this problem. This paper contributes in three aspects. First, we identify a problem of generating biased results with the approach and we propose a few heuristics to avoid such a pitfall. Secondly, we conduct an extensive experimental comparison of the extended two-state Markov chain approach and another approach based on the Skart method. We analyse the results with machine learning techniques and we show that statistically the two-state Markov chain approach has a better performance. Finally, we demonstrate the potential of the extended two-state Markov chain approach on a case study of a large PBN model of apoptosis in hepatocytes.

Using two simple examples, the continuous-time random walk as well as a two state Markov chain, the relation between generalized anomalous relaxation equations and semi-Markov processes is illustrated. This relation is then used to discuss continuous-time random statistics in a general setting, for statistics of convolution-type. Two examples are presented in some detail: the sum statistic and the maximum statistic., Comment: 12 pages, submitted to EPJB

Multi-objective optimization problems are very important, but it is hard to optimized or solved. Generalized ant colony optimization (GACO) algorithm is a new kind of ant colony optimization (ACO) algorithm developed in recent years. In this paper, we try to combine Multi-objective optimization problems with GACO algorithm, established a model for multi-objective GACO algorithm by absorbing state Markov chain, and present a method for estimating the convergence speed of multi-objective GACO algorithm. Simulation results show that the convergence speed of multi-objective GACO algorithm is faster than traditional multi-objective ACO algorithm.

This paper discusses the asymptotic behaviors of the longest run on a countable state Markov chain. Let \(\left\{ {X_a } \right\}_{a \in Z_ + }\) be a stationary strongly ergodic reversible Markov chain on countablestate space S = {1, 2, ...}. Let T ⊂ S be an arbitrary finite subset of S. Denote by L n the length of the longest run of consecutive i’s for i ∈ T, that occurs in the sequence X 1, ..., X n . In this paper, we obtain a limit law and a week version of an Erdos-Renyi type law for L n . A large deviation result of L n is also discussed.

The objective of the present study is the identification of the characteristics of monthly Sq variations for geomagnetic components D, H and Z for a time series at four Indian geomagnetic observatories, namely, Alibag (ALB), Hyderabad (HYD), Pondicherry (PON) and Visakhapatnam (VIZ). To study the behavior of Sq monthly variation, a two state Markov chain model is employed. With the help of Markov transition probabilities, one can guess the behavior of a time series data. Index Terms: Geomagnetic field – Geomagnetic Sq variation– Stochastic process – Markov chain model – Bernoulli trials

Este trabalho propõe uma abordagem para monitoramento da taxa média de defeitos por item produzido numa produção finita ou encomenda de N itens. A cada ciclo de m itens produzidos, inspecionam-se os últimos r itens. Em cada item inspecionado conta-se o número de defeitos e cada item é classificado como aprovado se o número de defeitos satisfizer o critério do limite de controle. Se todos os r itens forem aprovados, a produção continua, caso contrário interrompe-se a produção à procura de causas especiais. Os itens inspecionados são descartados somente quando há parada no processo. Após a produção de N itens, um lote adicional será produzido para completar a quantia encomendada, mas esses não passarão por inspeção. Será utilizada uma cadeia de Markov finita de estados discretos para determinar as probabilidades de mudança de estado. Elas são utilizadas nas expressões de custo para determinar a estratégia ótima de monitoração, que será obtida através da otimização de três parâmetros: intervalo amostral (m), tamanho da amostra retrospectiva (r) e o limite de controle (LC). Os parâmetros serão obtidos através de busca direta, de forma que se minimize a expressão do custo médio por item produzido. Um exemplo numérico ilustra a proposta. This paper proposes an approach for monitoring the average number of non-conformities per items in short-run productions of N items. After every m produced items, the last r items are inspected. For each inspected item, the number of defects is counted; each inspected item is classified as approved if it meets the control limit criterion. If all r inspected items are approved, then the production goes on, otherwise it is stopped for adjustment. The inspected items are all discarded in case of production stoppage. After a production of N items, an additional lot is produced to complete the size ordered, but this additional lot does suffer inspection. A finite discrete state Markov chain is used to determine the transitory probabilities, which will be considered in terms of cost, to determine the optimal strategy for monitoring, obtained by optimizing three parameters: sampling interval (m), retrospective sample size (r), and control limit (cl). These parameters are obtained computationally by direct search to minimize the expression of the average cost per item produced. A numerical example illustrates the proposal.

We consider a Markov chain X = {Xi, i = 1, 2, ...} with the state space {0, 1}, and define W = Σi=1nXiXi+1, which is the number of 2-runs in X before time n+1. In this paper, we prove that the negative binomial distribution is an appropriate approximation for \(\mathcal{L}W\) when VarW is greater than \(\mathbb{E}W\). The error estimate obtained herein improves the corresponding result in previous literatures.

The accurate prediction of the coal production in the future is an important basis for reasonably determining the production target and development planning. To combine the Grey system theory with the discrete – state Markov chain theory, the modified GM (1, 1) and Original Grey-Markov models were built based on the smoothing of the initial data of the 1998~2008 annual coal production in China over the years by way of a natural logarithm. The calculated results show that the predicted accuracy of the modified Markov model was significantly higher than the modified GM (1, 1) model. The predicted results are reliable and have certain universal practicability.

An approximation method based on discrete state Markov chain is developed to estimate the production rate of a series-parallel flow line with finite buffers. The proposed method's technique replace...

Nowadays, more and more oral anticancer chemotherapies are developed either for cytotoxic or new targeted drugs. But this relatively new route of administration in oncology drives to new problems in treatment management and particularly to non-compliance, i.e. the deviance of the actual way patients take their treatment with the prescription. Population PK-PD models and Monte-Carlo simulations allow to study the impact of non-compliance on toxicities. After a brief review on recent developments about oral chemotherapies, this work presents a simulation where non-compliance, modelled with a two state Markov chain defining four compliance profiles from excellent to poor, is linked to two dose-toxicity (continuous or categorical) population models. Simulated patients with the lowest compliance level were less exposed to treatment and therefore experienced less toxicity with shorter events. Nevertheless treatment efficacy is also lower, and this loss of efficacy may compromise patient's outcome. These results foresee the necessity of global simulations, combining compliance, toxicity and efficacy modelling.

© 2015, Springer-Verlag Berlin Heidelberg. Self-stabilization algorithms are very important in designing fault-tolerant distributed systems. In this paper we consider Herman’s self-stabilization algorithm and study its expected termination time. McIver and Morgan have conjectured the optimal upper bound being 0.148N2, where $$N$$N denotes the number of processors. We present an elementary proof showing a bound of 0.167N2, a sharp improvement compared with the best known bound 0.521N2. Our proof is inspired by McIver and Morgan’s approach: we find a nearly optimal closed form of the expected stabilization time for any initial configuration, and apply the Lagrange multipliers method to give an upper bound.

Let X-m+1, X-m+2,..., X0, X1, X2,..., Xn be a time-homogeneous {0, 1}-valued m-th order Markov chain. The probability distributions of numbers of runs of "1" of length k (k ≥ m) and of "1" of length k (k < m) in the sequence of a {0, 1}-valued m-th order Markov chain are studied. There are some ways of counting numbers of runs with length k. This paper studies the distributions based on four ways of counting numbers of runs, i.e., the number of non-overlapping runs of length k, the number of runs with length greater than or equal to k, the number of overlapping runs of length k and the number of runs of length exactly k.

In this paper we analyze an environment dependent (s, S) inventory system with renewal demands and lost sales where the environment goes through available and unavailable periods according to a two state Markov chain. An order which is placed in an available period is replenished instantaneously and that placed in an unavailable period is replenished at the end of that period. The transform of the various operating characteristics are obtained explicitly. The problem of minimizing the long-run expected cost rate is discussed and an efficient algorithm to compute optimal s and S is developed. Numerical illustration of the results are also provided.

This paper studies the functional of the path of a diffusion in which volatility switches between two states: high and low. For this two-state Markov-chain model, we derive a closed-form expression for the distribution function for the time spent in the high volatility state by guessing the form of, and calculating the coefficients in, the solution to a pair of integral equations.

A model of feed intake in group-penned swine was evaluated for six groups of four pigs each housed in three constant environmental conditions—one thermoneutral and two under different degrees of heat stress designed to reduce voluntary feed intake by 13% and 26%. The model used a five state Markov chain to simulate meal initiation and duration among a pen of animals. Feed intake rate was assumed to be a realization of a normally distributed random variable. The product of meal length and rate was used to simulate feed intake. Results of simulations were compared to measured results for the pigs during daylight hours over a three-week period when the animals were approximately 40 kg live weight. Simulated meal duration was found to correspond reasonably to measured data, but tended to overpredict the occurrence of shorter meals. Intake rate was found to be non-Gaussian, but did not influence the simulation results to any great extent and this model was concluded to be satisfactory. Simulation results for meal size were similar to those found in meal duration. Overall, the models provided an efficient means to simulate feed intake in group-penned swine.

We give an example of two distinct stationary processes {X n} and {X′ n} on {0, 1} for whichP[X0=1|X−1=a−1,X−2=a−2, …]=P[X′0=1|X′−1=a−1,X′−2=a−2, …] for all {a i},i=−1, −2, …, even though these probabilities are bounded away from 0 and 1, and are continuous in {a i}.

We study a possible model for neuron firing pattern as a two state Markov chain. We compare the qualitative predications of the model with various types of neural measurements available in the literature. It is shown that this model explains well several phenomena observed in different sensory systems of mammals.

In this paper, we present an analytic model for radio access unit selection in distributed radio system. The selection strategy is based on received signal strength measurements and described as a multiple state Markov chain. Performance analysis results show that numeric data achieved from the model are in good agreement with simulation results, which verifies the validity of the model. This model is helpful in designing seamless handoff schemes in distributed radio system.

An estimation method for a channel model using a three state Markov chain is presented. The model generates both random and burst errors, and it is suitable for representing actual channels. This estimation method is effective for estimating the model from experimentally measured values for actual channels.

An important question in stochastic modeling is whether a denumerable state Markov chain describing a system is stable or not. Adopting a general definition of stability, we discuss some conditions for instability. We extend slightly previous results on nonergodicity, and we present new criteria for moments of a chain to be infinite. Finally, we apply these instability conditions to study some multidimensional Markov chains that describe multiaccess protocols in a broadcast environment. In particular, we prove that the exponential backoff algorithm is unstable for λ > 0.461, and the decentralized dynamic control algorithm is unstable for λ > e−1 = 0.368.

A two state Markov chain model is used to describe and forecast the over time behavior of the best retail customers at Merrill Lynch. This model has 4 behaviorally meaningful parameters which capture the effect of recently being a prime customer, the differing average commissions generated across customers and the exiting of some of these customers from the Merrill Lynch system. This model helps management to understand the dynamics of the prime customers' behavior. In particular, the forecasts generated by the model allow for better analyses of possible strategies for providing special services for these very good customers. The model which was developed with 1976–1979 data is validated against the actual 1980 behavior of Merrill Lynch customers.

This paper develops and tests a continuous time discrete state Markov Chain as a model for change in group structure. Movement of triads among different states is focused upon. It is shown formally that a triad cannot move to a state where all the pair relationships are mutual without incurring intransitivity. An empirical test on the change in sociometric structures provides support for the model.

Success runs of a fixed length in a two-state Markov chain are discussed. The results are analogous to those in the case of independent Bernoulli trials. The generating function of the waiting time for the first occurrence of a success run is obtained from the theory of recurrent events. Under certain conditions, the distribution of the number of long runs in a large number of trials is shown to be Poisson.