Narrow Results

We present several equivalent conditions for C*-finitely correlated states defined on the UHF algebras to be factor states and consider the types of factors generated by them. Subfactors generated by generalized quantum Markov chains defined on the gauge-invariant parts of the UHF algebras are also discussed.

The aim of this work is to predict the economic convergence among countries by using a generalization of Ehrenfest's urn. In particular this work shows that the Ehrenfest model captures the convergence among countries. A empirical analysis is presented on the European Union countries, the G7 countries and the emerging countries.

In this paper, scale-free networks and their functional robustness with respect to structural perturbations of the network are studied. Two types of perturbations are distinguished: random perturbations and attacks. The robustness of directed and undirected scale-free networks is studied numerically for two different measures and the obtained results are compared. For random perturbations, the results indicate that the strength of the perturbation plays a crucial role. In general, directed scale-free networks are more robust than undirected scale-free networks.

In this paper, we propose a new model for computer virus attacks and recovery at the level of information packets. The model we propose is based on one hand on the susceptible-infected (SI) and susceptible-infected-recovered (SIR) stochastic epidemic models for computer virus propagation and on the other hand on the time-discrete Markov chain of the minimal traffic routing protocol. We have applied this model to the scale free Barabasi–Albert network to determine how the dynamics of virus propagation is affected by the traffic flow in both the free-flow and the congested phases. The numerical results show essentially that the proportion of infected and recovered packets increases when the rate of infection $\lambda$ and the recovery rate $\beta$ increase in the free-flow phase while in the congested phase, the number of infected (recovered) packets presents a maximum (minimum) at certain critical value of $\beta$ characterizing a certain competition between the infection and the recovery rates.

The Decoupled Data-Driven (D³) architecture has shown promising results from performance evaluations based upon deterministic simulations. This paper provides performance evaluations of the D³ architecture through the formulation and analysis of a stochastic model. The D³ architecture is a hybrid control/dataflow approach that takes advantage of inherent parallelism present in a program by dynamically scheduling program threads based on data availability and it also takes advantage of locality through the use of conventional processing elements that execute the program threads. The model is validated by comparing the deterministic and stochastic model responses. After model validation, various input parameters are varied such as the number of available processing elements and average threadlength, then the performance of the architecture is evaluated. The stochastic model is based upon a closed queueing network and utilizes the concepts of available parallelism and virtual queues in order to be reduced to a Markovian system. Experiments with varying computation engine threadlengths and communication latencies indicate a high degree of tolerance with respect to exploited parallelism.

In an attempt to examine the effect of dependencies in the arrival process on the steady state queue length process in single server queueing models with exponential service time distribution, four different models for the arrival process, each with marginally distributed exponential inter-arrivals to the queueing system, are considered. Two of these models are based upon the upper and lower bounding joint distribution functions given by the Fréchet bounds for bivariate distributions with specified marginals, the third is based on Downton's bivariate exponential distribution and fourthly the usual M/M/1 model. The aim of the paper is to compare conditions for stability and explore the queueing behavior of the different models.

This paper presents a mathematical model, linking the classical Markov models for brand switching and models for product life cycles, to forecast competition analysis and market share. This integrated model can be used to forecast market shares of all competitors, and their market shares, including customers retained, customers gained from market growth, and customers gained from competitors over the product life cycle. Such information provides forecasters with valuable insight about their market positions. The model is generic and can be applied to different types of products and services, under different types and patterns of product life cycle curves. A numerical example on a typical mobile telecommunication industry is used to illustrate the application of the proposed approach.

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.

In this paper, we introduce the effect of neighbors on the infection of packets by computer virus in the SI and SIR models using the minimal traffic routing protocol. We have applied this model to the Barabasi–Albert network to determine how intrasite and extrasite infection rates affect virus propagation through the traffic flow of information packets in both the free-flow and the congested phases. The numerical results show that when we change the intrasite infection rate ${\lambda }_1$ while keeping constant the extrasite infection rate ${\lambda }_2$, we get normal behavior in the congested phase: in the network, the proportion of infected packets increases to reach a peak and then decreases resulting in a simultaneous increase of the recovered packets. In contrast, when the intrasite infection rate ${\lambda }_1$ is kept fixed, an increase of the extrasite infection rate results in two regimes: The first one is characterized by an increase of the proportion of infected packets until reaching some peak value and then decreases smoothly. The second regime is characterized by an increase of infected packets to some stationary value.

Data clustering has been widely used in many areas, such as data mining, statistics, machine learning and so on. A variety of clustering approaches have been proposed so far, but most of them are not qualified to quickly cluster a large-scale high-dimensional database. This paper is devoted to a novel data clustering approach based on a generalized particle model (GPM). The GPM transforms the data clustering process into a stochastic process over the configuration space on a GPM array. The proposed approach is characterized by the self-organizing clustering and many advantages in terms of the insensitivity to noise, quality robustness to clustered data, suitability for high-dimensional and massive data sets, learning ability, openness and easier hardware implementation with the VLSI systolic technology. The analysis and simulations have shown the effectiveness and good performance of the proposed GPM approach to data clustering.

By using the restricted and complementary relationship of the principle and secondary indexes, providing the description of the compound quantification of the fuzzy number, and analyzing the essential characteristic of fuzzy decision, we propose a kind of fuzzy genetic algorithm based on the principle index (PO-FGA for short) to deal with the fuzzy optimization and programming problems with fuzzy coefficients, fuzzy variables and fuzzy constraints. The concrete solution method is presented in accordance with the strategy of the unconditional penality transformation with conditional constrains. Then consider its convergence by using Markov chain theory and analyze its performance through two examples. All these indicate that this kind of algorithm is of faster speed of convergence, smaller number of iterations, has lower chances of trapping into the state of premature convergence and can be widely used in many problems of optimization.

Stochastic context-free grammars are an important tool in syntactic pattern analysis and other applications as well. This paper discusses major results in single-type and multitype branching processes used to study a grammar’s stochastic derivations. Probability generating functions are well-established as a tool in this area and are used extensively here.

As real-time systems continue to grow, performance evaluation plays a critical role in the design of these systems since the computation time, the service time, and the responsive actions must satisfy the time constraints. One of these systems is the real-time distributed multimedia-on-demand (MOD) service system. The MOD system usually fails when it misses a task deadline. The main units of the MOD system usually communicate with each other and work concurrently under timing constraints. The MOD system is designed to store, retrieve, schedule, synchronize and communicate objects comprising of mixed data types including images, text, video and audio, in real-time. In the MOD system, such data types represent the main concept of movie files. Modeling of such concurrency, communication, timing, and multimedia service (e.g., store, retrieve) is essential for evaluating the real-time MOD system. To illustrate how to model and analyze the important multimedia aspects of the MOD system, we use the Real-net (R-net) modeling technique. We choose R-net as an extension of Time Petri Net due to its ability to specify hard real-time process interaction, represent the synchronization of multimedia entities, describe concurrent multimedia activities, and illustrate the inter-process timing relationships as required for multimedia presentation. Based on modular techniques, we build three R-net performance models for describing the dynamic behavior of the MOD service system. The first model adopts the Earliest Deadline First (EDF) disk scheduling algorithm. The other models adopt the Scan-EDF algorithm. These algorithms help us to illustrate how the real-time user requests can be satisfied within the specified deadline times. Since R-nets are amenable to analysis including Markov process modeling, the interesting performance measures of the MOD service system such as the quality of service, the request response time, the disk scheduling algorithm time, and the actual retrieval time can be easily computed. In the performance analysis of the MOD models, we use our R-NET package.

In this paper, we propose a Markov chain modeling of complicated phenomena observed from coupled chaotic oscillators. Once we obtain the transition probability matrix from computer simulation results, various statistical quantities can be easily calculated from the model. It is shown that various statistical quantities are easily calculated by using the Markov chain model. Various features derived from the Markov chain models of chaotic wandering of synchronization states and switching of clustering states are compared with those obtained from computer simulations of original circuit equations.

In system level design or architecture design stage of SoCs, it is important to estimate the system parameters such as bus utilization and buffer capacity. A novel bus modeling method which was derived from Markov model for obtaining these parameters of an on-chip-bus system has been proposed in this paper. This modeling approach employs Markov chain to describe the state change of the system. This method was used in architecture design verification of a video format converting (VFC) chip. By comparing the simulation result and the pessimistic estimate value, the rationality and high efficiency of this method were verified, and more than 55% of FIFOs size are saved. It is suitable for analyzing various bus systems, such as user-defined buses, industrial standard buses, multi-core and multi-bus systems.

We analyze prediction schemes for stochastic time series data. We propose that under certain conditions a scalar time series, obtained from a vector-valued Markov process, can be modeled as a finite memory Markov process in the observable. The transition rules of the process are easily computed using simple nonlinear time series predictors originally proposed for deterministic chaotic signals. The optimal time lag entering the embedding procedure is shown to be significantly smaller than in the deterministic case. The same concept can be extended to nonstationary stochastic processes, where an increase of the embedding dimension can help to identify instantaneous dynamical properties, and where redundant information in the past is exploited in an optimal way.

The Ricker model is one of the simplest and most widely-used ecological models displaying complex nonlinear dynamics. We study a discrete-time population model, which is derived from simple assumptions concerning individual organisms’ behavior, using the “site-based” approach, developed by Brännström, Broomhead, Johansson and Sumpter. In the large-population limit the model converges to the Ricker model, and can thus be considered a mechanistic version of the Ricker model, derived from basic ecological principles, and taking into account the demographic stochasticity inherent to finite populations. We employ several analytical and precise numerical methods to study the model, showing how each approach contributes to understanding the model’s dynamics. Expressing the model as a Markov chain, we employ the concept of quasi-stationary distributions, which are computed numerically, and used to examine the interaction between complex deterministic dynamics and demographic stochasticity, as well as to calculate mean times to extinction. A Gaussian Markov chain approximation is used to obtain quantitative asymptotic approximations for the size of fluctuations of the stochastic model’s time series around the deterministic trajectory, and for the correlations between successive fluctuations. Results of these approximations are compared to results obtained from quasi-stationary distributions and from direct simulations, and are shown to be in good agreement.

Correctly measuring the reliability and availability of a cloud-based system is critical for evaluating its system performance. Due to the promised high reliability of physical facilities provided for cloud services, software faults have become one of the major factors for the failures of cloud-based systems. In this paper, we focus on the software aging phenomenon where system performance may be progressively degraded due to exhaustion of system resources, fragmentation and accumulation of errors. We use a proactive technique, called software rejuvenation, to counteract the software aging problem. The dynamic fault tree (DFT) formalism is adopted to model the system reliability before and during a software rejuvenation process in an aging cloud-based system. A novel analytical approach is presented to derive the reliability function of a cloud-based Hot SPare (HSP) gate, which is further verified using Continuous Time Markov Chains (CTMC) for its correctness. We use a case study of a cloud-based system to illustrate the validity of our approach. Based on the reliability analytical results, we show how cost-effective software rejuvenation schedules can be created to keep the system reliability consistently staying above a predefined critical level.

Exponent matrices appear in the theory of tiled orders over a discrete valuation ring. Many properties of such an order and its quiver are fully determined by its exponent matrix. We prove that an arbitrary strongly connected simply laced quiver with a loop in every vertex is realized as the quiver of a reduced exponent matrix. The relations between exponent matrices and finite posets, Markov chains, and doubly stochastic matrices are discussed.

The Tsetlin library is a very well-studied model for the way an arrangement of books on a library shelf evolves over time. One of the most interesting properties of this Markov chain is that its spectrum can be computed exactly and that the eigenvalues are linear in the transition probabilities. In this paper, we consider a generalization which can be interpreted as a self-organizing library in which the arrangements of books on each shelf are restricted to be linear extensions of a fixed poset. The moves on the books are given by the extended promotion operators of Ayyer, Klee and Schilling while the shelves, bookcases, etc. evolve according to the move-to-back moves as in the the self-organizing library of Björner. We show that the eigenvalues of the transition matrix of this Markov chain are $\pm 1$ integer combinations of the transition probabilities if the posets that prescribe the restrictions on the book arrangements are rooted forests or more generally, if they consist of ordinal sums of a rooted forest and so called ladders. For some of the results, we show that the monoids generated by the moves are either ${ℛ}$-trivial or, more generally, in $DO(Ab)$ and then we use the theory of left random walks on the minimal ideal of such monoids to find the eigenvalues. Moreover, in order to give a combinatorial description of the eigenvalues in the more general case, we relate the eigenvalues when the restrictions on the book arrangements change only by allowing for one additional transposition of two fixed books.