Mathematical tools of the kinetic theory of active particles with some reasoning on the modelling progression and heterogeneity

The mathematical approach proposed in this paper refers to the modelling, and related mathematical problems, of large systems of interacting entities whose microscopic state includes not only geometrical and mechanical variables (typically position and velocity), but also peculiar functions or specific activities. The number of the above entities is sufficiently large for describing the overall state of the system using a suitable probability distribution over the microscopic state. The first part of the paper is devoted to the derivation of suitable mathematical structures which can be properly used to model a variety of models in different fields of applied sciences. Then some research perspectives are analyzed, focussed on applications to biological systems.     

Cellular Simulation

Cellular simulation, a method of organizing simulation models to improve experimental efficiency, is described and shown to have the further advantages of reconciling the event based approach with the activity approach to simulation modelling and to have implication for modelling large systems.     

A model for monolayer deposition with interacting particles

We present a very versatile three-dimensional growth model with random initial conditions for the deposition of a monolayer of particles out of a gas beam on a substrate. The flexibility of the model is guaranteed by the inclusion of parameters like the substrate temperature and the chemical binding whose variation changes strongly the lateral diffusion and the morphology of the developing disordered structure. In the modelling of the potential we can use in principle data coming from experiment and quantum mechanical computations. The use of short-range potentials allows to apply the model to covalent systems. We find a variety of patterns which resemble structures found in the experiment and in other theoretical models. The important parameters have simple physical and chemical interpretations, whereas the simulation of static properties may be done with more complicated potentials for specific materials. Our approach allows to look for particular growth conditions and dynamical processes of large structures with moderate use of computational resources.     

On the modelling of heat exchangers and heat exchanger network dynamics using bond graphs

ABSTRACT

Heat exchanger networks are important systems in most thermal engineering systems and are found in applications ranging from power plants and the process industry to domestic heating. Achieving cost-effective design of heat exchanger networks relies heavily on mathematical modelling and simulation-based design. Today, stationary design calculations are carried out for all new designs, but for some special applications, the transient response of complete networks has been researched. However, simulating large heat exchanger networks poses challenges due to computational speed and stiff initial value problems when flow equations are cast in differential algebraic form. In this article, a systems approach to heat exchanger and heat exchanger network modelling is suggested. The modelling approach aims at reducing the cost of system model development by producing modular and interchangeable models. The approach also aims at improving the capability for large and complex network simulation by suggesting an explicit formulation of the network flow problem.     

Variational Bayes and the Reduced Dependence Approximation for the Autologistic Model on an Irregular Grid With Applications

Discrete Markov random field models provide a natural framework for representing images or spatial datasets. They model the spatial association present while providing a convenient Markovian dependency structure and strong edge-preservation properties. However, parameter estimation for discrete Markov random field models is difficult due to the complex form of the associated normalizing constant for the likelihood function. For large lattices, the reduced dependence approximation to the normalizing constant is based on the concept of performing computationally efficient and feasible forward recursions on smaller sublattices, which are then suitably combined to estimate the constant for the entire lattice. We present an efficient computational extension of the forward recursion approach for the autologistic model to lattices that have an irregularly shaped boundary and that may contain regions with no data; these lattices are typical in applications. Consequently, we also extend the reduced dependence approximation to these scenarios, enabling us to implement a practical and efficient nonsimulation-based approach for spatial data analysis within the variational Bayesian framework. The methodology is illustrated through application to simulated data and example images. The online supplementary materials include our C++ source code for computing the approximate normalizing constant and simulation studies.     

Choice of modelling technique for evaluating health care interventions

Economic evaluation, such as cost effectiveness analysis, provides a method for comparing healthcare interventions. These evaluations often use modelling techniques such as decision trees, Markov processes and discrete event simulations (DES). With the aid of examples from coronary heart disease, the use of these techniques in different health care situations is discussed. Guidelines for the choice of modelling technique are developed according to the characteristics of the health care intervention.The choice of modelling technique is shown to depend on the acceptance of the modelling technique, model ‘error’, model appropriateness, dimensionality and ease and speed of model development. Generally decision trees are suitable for acute interventions but they cannot model recursion and Markov models are suitable for simple chronic interventions. It is further recommended that population based models be used in order to provide health care outcomes for the likely cost, health benefits and cost effectiveness of the intervention. The population approach will complicate the construction of the model. DES will allow the modeller to construct more complex, dynamic and accurate systems but these may involve a corresponding increase in development time and expense. The modeller will need to make a judgement on the necessary complexity of the model in terms of interaction of individuals and model size and whether queuing for resources, resource constraints or the interactions between individuals are significant issues in the health care system.     

中国证券市场知情交易概率的动态马尔科夫状态转移模型研究

对指令驱动市场知情交易的研究是近年来的热点问题。常用的EKOP模型存在一些缺陷,本文放宽了EKOP模型关于日内信息均匀释放以及交易者行为独立性的假设,用动态的马尔科夫状态转移模型对该模型进行了改进,并检验了改进后的知情交易概率模型在中国证券市场的适用性。通过模拟数据以及对中国证券市场交易数据的实证研究发现动态的马尔科夫状态转移模型克服了EKOP模型受买卖方数据影响而产生的系统偏误,估计的知情交易概率更符合事后检验。     

A statistical Markov chain approximation of transient hospital inpatient inventory

Inventory levels are critical to the operations, management, and capacity decisions of inventory systems but can be difficult to model in heterogeneous, non-stationary throughput systems. The inpatient hospital is a complicated throughput system and, like most inventory systems, hospitals dynamically make managerial decisions based on short term subjective demand predictions. Specifically, short term hospital staffing, resource capacity, and finance decisions are made according to hospital inpatient inventory predictions. Inpatient inventory systems have non-stationary patient arrival and service processes. Previously developed models present poor inventory predictions due to model subjectivity, high model complexity, solely expected value predictions, and assumed stationary arrival and service processes. Also, no models present statistical testing for model significance and quality-of-fit. This paper presents a Markov chain probability model that uses maximum likelihood regression to predict the expectations and discrete distributions of transient inpatient inventories. The approach has a foundation in throughput theory, has low model complexity, and provides statistical significance and quality-of-fit tests unique to this Markov chain. The Markov chain is shown to have superior predictability over Seasonal ARIMA models.     

Probabilistic verification of a biodiesel production system using statistical model checking

Biochemical system designers are increasingly using formal modelling, simulation, and verification methods to improve the understanding of complex systems. Probabilistic models can incorporate realistic stochastic dynamics, but creating and analysing probabilistic models in a formal way is challenging. In this work, we present a stochastic model of biodiesel production that incorporates an inexpensive test of fuel quality, and we validate the model using statistical model checking, which can be used to evaluate simple or complex temporal properties efficiently. We also describe probabilistic simulation and analysis techniques for stochastic hybrid system (SHS) models to demonstrate the properties of our model. We introduce a variety of properties for various configurations of the reactor as well as results of testing our model against the properties.     

Approximate solution for two stage open networks with Markov-modulated queues minimizing the state space explosion problem

Analytical solutions for two-dimensional Markov processes suffer from the state space explosion problem. Two stage tandem networks are effectively used for analytical modelling of various communication and computer systems which have tandem system behaviour. Performance evaluation of tandem systems with feedbacks can be handled with these models. However, because of the numerical difficulties caused by large state spaces, considering server failures and repairs at the second stage employing multiple servers has not been possible. The solution proposed in this paper is approximate with a high degree of accuracy. Using this approach, two stage open networks with multiple servers, break downs, and repairs at the second stage as well as feedback can be modelled as three-dimensional Markov processes and solved for performability measures. Results show that, unlike other approaches such as spectral expansion, the steady state solution is possible regardless of the number of servers employed.     

THE EFFECT OF DECREASING SYSTEM SIZE ON BIRTH AND DEATH MODELS OF OPEN-ACCESS FISHERIES AND PREDATOR-PREY ECOSYSTEMS

Birth and death simulation, developed by Pielou, is a form of Markov stochastic process for describing the time evolution of populations. Applied to modelling the human element of a fishery, it expresses two features of fishing effort dynamics absent in systems of differential equations: (1) discreteness of events, such as a fishing trip or entry of a vessel into the fleet, and (2) demography stochasticity, expressed as randomness in the time occurrence of successive events. Birth and death simulation is based on randomly selecting the waiting time between events from a negative exponential distribution, derived under the assumption of Markov. Histograms from commercial landings data of waiting times between events of boats returning to port in a Nova Scotia fishery yielded good agreement with the predicted negative exponential. Algorithms are presented for stochastically modelling two processes: (1) catch and (2) the open-access hypothesis for changes in fleet size in response to changing levels of profit. The solutions qualitatively diverge from that predicted by differential equations: As the numbers of vessels and fish schools decline (i.e., as the system size scale shrinks), a birth and death formulation predicts increasing instability of the predator-prey cycle solution about the deterministically stable open-access equilibrium. Open-access models are a form of predator-prey model. In choosing the minimum wilderness preserve area needed to sustain a population of top predators, numbered in the low hundreds, a predator-prey model formulated with differential equations could underestimate instability and thus the risk of extinction, when the discreteness and randomness of predator-prey birth, death, and capture events is significant.     

Spatially varying SAR models and Bayesian inference for high-resolution lattice data

We discuss a new class of spatially varying, simultaneous autoregressive (SVSAR) models motivated by interests in flexible, non-stationary spatial modelling scalable to higher dimensions. SVSAR models are hierarchical Markov random fields extending traditional SAR models. We develop Bayesian analysis using Markov chain Monte Carlo methods of SVSAR models, with extensions to spatio-temporal contexts to address problems of data assimilation in computer models. A motivating application in atmospheric science concerns global CO emissions where prediction from computer models is assessed and refined based on high-resolution global satellite imagery data. Application to synthetic and real CO data sets demonstrates the potential of SVSAR models in flexibly representing inhomogeneous spatial processes on lattices, and their ability to improve estimation and prediction of spatial fields. The SVSAR approach is computationally attractive in even very large problems; computational efficiencies are enabled by exploiting sparsity of high-dimensional precision matrices.     

Large deviations for random dynamical systems and applications to hidden Markov models

In this paper, we prove the large deviation principle (LDP) for the occupation measures of not necessarily irreducible random dynamical systems driven by Markov processes. The LDP for not necessarily irreducible dynamical systems driven by i.i.d. sequence is derived. As a further application we establish the LDP for extended hidden Markov models, filling a gap in the literature, and obtain large deviation estimations for the log-likelihood process and maximum likelihood estimator of hidden Markov models.     

Simulation modelling of emergency medical services

This paper deals with the problem of application of simulation modelling in Emergency Medical Services (EMS) systems. Approaches to modelling of EMS are discussed and a review of EMS simulation models is presented. A simple simulation model of a rural EMS system in Poland is described. Some results of the initial application of the model are presented. Possibilities of simulation modelling for solving EMS managerial and planning problems are briefly analysed.     

Comparing conventional and distributed approaches to simulation in a complex supply-chain health system

Decision making in modern supply chains can be extremely daunting due to their complex nature. Discrete-event simulation is a technique that can support decision making by providing what-if analysis and evaluation of quantitative data. However, modelling supply chain systems can result in massively large and complicated models that can take a very long time to run even with today's powerful desktop computers. Distributed simulation has been suggested as a possible solution to this problem, by enabling the use of multiple computers to run models. To investigate this claim, this paper presents experiences in implementing a simulation model with a ‘conventional’ approach and with a distributed approach. This study takes place in a healthcare setting, the supply chain of blood from donor to recipient. The study compares conventional and distributed model execution times of a supply chain model simulated in the simulation package Simul8. The results show that the execution time of the conventional approach increases almost linearly with the size of the system and also the simulation run period. However, the distributed approach to this problem follows a more linear distribution of the execution time in terms of system size and run time and appears to offer a practical alternative. On the basis of this, the paper concludes that distributed simulation can be successfully applied in certain situations.     

Reliability assessment of multi-state phased mission system with non-repairable multi-state components

Phased mission systems (PMSs) like satellites and spacecraft perform their functions over non-overlapping mission periods, called phases. One of the challenges in assessing reliability of PMSs comes from considering the s-dependence among phases, and the consideration on the multi-state behavior of components and systems makes the reliability analysis even more difficult. To effectively address this problem, a multi-state multivalued decision diagram algorithm for PMS and a multi-state multi-valued decision diagram model for phased mission system (PMS-MMDD) method is developed for the reliability modelling of non-repairable multi-state components. Based on the Semi-Markov process, a Markov renewal equation-based method is developed to deal with non-exponential multi-state components and a numerical method, the trapezoidal integration method, is used to compute the complex integrals in the path probability evaluation. A case study of a multi-state attitude and orbit control system in a spacecraft is analyzed to illustrate the proposed PMS-MMDD model and the Markov renewal equation-based evaluation method. The accuracy and computation efficiency of the proposed method are verified by the Monte Carlo simulation method.     

A multivariate Markov chain model for categorical data sequences and its applications in demand predictions

Markov models are commonly used in modelling many practicalsystems such as telecommunication systems, manufacturing systemsand inventory systems. In this paper we propose a multivariateMarkov chain model for modelling multiple categorical data sequences.We develop efficient estimation methods for the model parameters.We then apply the model and method to demand predictions fora soft-drink company in Hong Kong.     

Online clustering of switching models based on a subspace framework

This paper deals with the modelling of switching systems and focuses on the characterization of the local functioning modes using the online clustering approach. The system considered is represented as a weighted sum of local linear models where each model could have its own structure. This implies that the parameters and the order of the switching system could change when the system switches. Moreover, possible constants of the local models are also unknown. The method presented consists of two steps. First, an online estimation method of the Markov parameters matrix of the local linear models is established. Secondly, the labelling of these parameters is done using a dynamical decision space worked out with learning techniques; each local model being represented by a cluster. The paper ends with an example and a discussion with an aim of illustrating the method’s performance.