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Abstract: The Single-Allocation Ordered Median Hub Location problem is a recent hub model introduced by Puerto et al. (2011) [32] that provides a unifying analysis of the class of hub location models. Indeed, considering ordered objective functions in hub location models is a powerful tool in modeling classic and alternative location paradigms, that can be applied with success to a large variety of problems providing new distribution patterns induced by the different users’ roles within the supply chain network. In this paper, we present a new formulation for the Single-Allocation Ordered Median Hub Location problem and a branch-and-bound-and-cut (B&B&Cut) based algorithm to solve optimally this model. A simple illustrative example is discussed to demonstrate the technique, and then a battery of test problems with data taken from the AP library are solved. The paper concludes that the proposed B&B&Cut approach performs well for small to medium sized problems. [Copyright &y& Elsevier]

Abstract: A general repairable k-out-of-n:G system with non-identical components, which is a common form of redundancy, is considered in this paper. The number of repairmen is assumed to be r (1≤r≤n−k+1) while components can have similar or different repair priorities. The objective of this work is to address the problem of efficient evaluation of the system''s availability in a way that steady state solutions can be obtained systematically in a reasonable computational time. This problem is modeled as a finite state-dependent non-homogeneous quasi-birth–death (QBD) process. An algorithm is introduced to systematically generate the system state vectors and transition rate matrix and then an iterative method based on the Block Gauss–Seidel method is employed to determine the steady state probabilities. These are the novel contributions made in this paper. An analog Monte Carlo simulation is presented to demonstrate the correctness and the efficiency of the proposed method. [Copyright &y& Elsevier]

This paper presents a general mathematical optimization model and the related deterministic algorithm for synthesizing heat-exchanger networks (HEN). The methodologies commonly used to solve a HEN problem are based on heuristic methods. These algorithms reach a presumed best solution with respect to the investigated set of process streams, whereas our approach determines the optimal configuration. In this paper the proposed method is applied to the solution of a few simple HEN synthesis problems and the results are compared with those obtained utilizing heuristic or meta-heuristic methods. HEN''s problem is represented by a general mathematical model that can be applied to small and medium sized problems and is solved by using a deterministic method with a reasonably brief computation time. Notably, this approach can represent a unique general model of a wide class of heat-exchanger networks, independently of their specific physical configuration. [Copyright &y& Elsevier]

Delirium and dementia represent an emerging global crisis in healthcare. Attempts have been made to identify the pathognomonic feature that would make delirium stand out from dementia but unfortunately the global neural dysfunction of both disorders has made the establishment of a direct measurement difficult. Modern conceptualisations of delirium have been influenced by the assessment tools used to assess, detect, and analyse its complex and transient nature. Recent publication of the DSM-V criteria for delirium has marginally altered the previous DSM-IV criteria with a focus upon inattention with vague terms such as consciousness downplayed. Such an alteration has been found to be restrictive and thus impact upon delirium case identification. Although these findings are approximating the empirical state of delirium as measured by validated instruments, a more refined neuroscientifically informed phenomenological framework is required in order to enhance the theoretical understanding of delirium assessment and resolve these challenges. One such application is the predictive coding (PC) model, also known as the hierarchical Bayesian inference model, to interpreting delirium pathophysiology. Therefore, the aims of this paper are to 1) propose the hypothesis that delirium pathophysiology can be explained in terms of the PC model, 2) support this hypothesis by applying this model to current methods of assessing delirium phenomenology, particularly attention, and 3) outline a future programme of research to test many of the parameters of this application. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops a sequential scheduling algorithm for consultation periods not divided into slots. Patients call a scheduler and request appointments with a specified provider. The scheduler provides the patient with an appointment time before the call terminates. In making the appointment, the scheduler cannot alter the appointments of previously scheduled patients. Service times are random and each scheduled patient has a probability of “no-showing” for the appointment. Each arriving patient generates a given amount of revenue, and costs are incurred from patient waiting and provider overtime. The scheduling method selects the calling patient's appointment time by minimizing the total expected cost. We prove that total expected cost is a convex function of appointment times and that the expected profit of the schedule is unimodal, which provides a unique stopping criterion for the scheduling algorithm. Computational studies compare this approach with no-show based sequential scheduling methods for out-patient clinics where a predefined slot structure is assumed. The new method yields higher expected profit and less overtime than when service periods are pre-divided into slots. Because slot scheduling is ingrained in healthcare, we use the model to design slot structures that account for no-show and service time variation. [Copyright &y& Elsevier]

Abstract: It is well known that evaluation of parameters for any mathematical model is always very important and often a very difficult problem. This is especially true for agents-based models because as a rule the evaluation of an agent's parameters can be made only based on available information from the higher levels of a complex system. Such problems can be ill-posed or even have a non-unique solution. That is why there is no general algorithm for solving these problems and a researcher has to search for it for every specific model type. In this paper the problem of evaluating transmission probabilities for different age groups during an influenza epidemic/pandemic in a city will be considered. In order to solve this problem a regularization procedure based on illness attack rates for several age groups (cumulated numbers of infected residents as functions of time) is proposed and validated. It can be used for past epidemics to estimate the efficiency or inefficiency of undertaken interventions, to propose new ones and to reveal its advantages and shortcomings. Under some conditions it can be used to model the possible dynamics of a coming epidemic. [Copyright &y& Elsevier]

Abstract: External control of some genes in a genetic regulatory network is useful for avoiding undesirable states associated with some diseases. For this purpose, a number of stochastic optimal control approaches have been proposed. Probabilistic Boolean networks (PBNs) as powerful tools for modeling gene regulatory systems have attracted considerable attention in systems biology. In this paper, we deal with a problem of optimal intervention in a PBN with the help of the theory of discrete time Markov decision process. Specifically, we first formulate a control model for a PBN as a first passage model for discrete time Markov decision processes and then find, using a value iteration algorithm, optimal effective treatments with the minimal expected first passage time over the space of all possible treatments. In order to demonstrate the feasibility of our approach, an example is also displayed. [Copyright &y& Elsevier]

Abstract: The probability hypothesis density (PHD) filter is a promising algorithm for multitarget tracking, which can be extended for jump Markov systems (JMS). Since the existing multiple model sequential Monte Carlo PHD (MM SMC-PHD) filter is not interacting, two extensions of the SMC-PHD filters are developed in this paper. The interacting multiple-model (IMM) SMC-PHD filter approximates the model conditional PHD of target states by particles, and performs the interaction by resampling without any a priori assumption of the noise. The IMM Rao-Blackwellized particle (RBP) PHD filter uses the idea of Rao-Blackwellized to further enhance the performance of target state estimation for JMS with mixed linear/nonlinear state space models. The simulation results show that the proposed algorithms have better performances than the existing MM SMC-PHD filter in terms of state filtering and target number estimation. [Copyright &y& Elsevier]

Abstract: In this paper the problem of performing external validation of the semantic coherence of topic models is considered. The Fowlkes–Mallows index, a known clustering validation metric, is generalized for the case of overlapping partitions and multi-labeled collections, thus making it suitable for validating topic modeling algorithms. In addition, we propose new probabilistic metrics inspired by the concepts of recall and precision. The proposed metrics also have clear probabilistic interpretations and can be applied to validate and compare other soft and overlapping clustering algorithms. The approach is exemplified by using the Reuters-21578 multi-labeled collection to validate LDA models, then using Monte Carlo simulations to show the convergence to the correct results. Additional statistical evidence is provided to better understand the relation of the metrics presented. [Copyright &y& Elsevier]

Abstract: Modeling fire spread in a building is a key factor of a fire risk analysis used for fire safety designs of large buildings. In this paper, a dynamic model of fire spread considering fire spread in both horizontal and vertical directions is described. The algorithms for simulating the fire spread process in buildings and calculating dynamic probability of fire spread for each compartment at each time step of simulation are proposed. The formulae used in calculating the input data for the dynamic fire spread model are derived. The dynamic fire spread model can easily be applied for any building including high-rise buildings. A detailed example of calculation of fire spread in a two-storey office building is described. [Copyright &y& Elsevier]

Abstract: The blocking probability in wavelength-routed all optical networks is very important measure of performance of the network, which can be affected by many factors such as network topology, traffic load, number of links, algorithms employed and whether wavelength conversion is available or not. In this paper, we have proposed a mathematical model to reduce the blocking probability of the WDM optical network for wavelength-convertible networks. The model can be used to evaluate the blocking performance of any network topology also it can be useful to improve its blocking performance of the given network topology. The blocking probability variation of the network for a particular load (per link) has been studied based on the load variation and total number of wavelengths used in the network. This model gives good results for high load (per link). [Copyright &y& Elsevier]

Abstract: The truncation error of fixed-point multiplication is commonly modelled as white noise with a uniform distribution. This paper shows the inaccuracy of this assumption by using a bitwise approach. A probabilistic bit-pattern analysis of the fixed-point multiplication is presented from which an accurate probability model for the truncation error is derived. Using this PDF model, exact values for the mean and variance of the truncation error in the output of the fixed-point multiplication are formulated for the first time. The proposed PDF model, mean and variance values are compact and usable in word-length optimization algorithms. [Copyright &y& Elsevier]

Abstract: Finite source retrial G-queues are good mathematical models of communication systems and networks, so their investigation is important for theory and applications. In this paper, we analyze the MAP/PH/N retrial queue with finite number of sources and MAP arrivals of negative customers operating in a finite state Markovian random environment. The arrival of a negative customer with equal probability goes to any busy server to remove the customer being in service. The multi-dimensional Markov chain describing the behavior of the system is investigated. The algorithms for calculating the stationary state probabilities are elaborated. Main performance measures are obtained. Illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

Abstract: There exist primarily three different types of algorithms for computing nonparametric maximum likelihood estimates (NPMLEs) of mixing distributions in the literature, which are the EM-type algorithms, the vertex direction algorithms such as VDM and VEM, and the algorithms based on general constrained optimization techniques such as the projected gradient method. It is known that the projected gradient algorithm may run into stagnation during iterations. When a stagnation occurs, VDM steps need to be added. We argue that the abrupt switch to VDM steps can significantly reduce the efficiency of the projected gradient algorithm, and is usually unnecessary. In this paper, we define a group of partially projected directions, which can be regarded as hybrids of ordinary projected gradient directions and VDM directions. Based on these directions, four new algorithms are proposed for computing NPMLEs of mixing distributions. The properties of the algorithms are discussed and their convergence is proved. Extensive numerical simulations show that the new algorithms outperform the existing methods, especially when a NPMLE has a large number of support points or when high accuracy is required. [Copyright &y& Elsevier]

Abstract: The wavelength assignment algorithm is a method to improve the performance in respect of blocking probability and to provide cost effective communication system. In this paper, we have developed a simple mathematical model which is used for the calculation of blocking probability of an OBS network. The implementation of the proposed model has less complexity and the computation used is quite efficient. This model can be implemented on different network topologies. The validity of model is supported by simulation results. [Copyright &y& Elsevier]

While most evidence types considered by forensic scientists result from the interactions between criminals, objects or victims at crime scenes, dust evidence arises from the mere presence of individuals and objects at locations of interest. Dust is ubiquitous. Yet, the use of dust evidence is anecdotical and is limited to cases where rare and characteristic particles are observed. The dust at any given location contains a large number of particles from different types and the dust present on an object or individual traveling across locations may be indicative of the locations recently visited by an individual, and, in particular, of the presence of an individual at a particular site of interest, e.g., the scene of a crime. In this paper, we propose to represent dust mixtures as vectors of counts of the individual particles, which can be characterised by any appropriate analytical technique. This strategy enables us to describe a dust mixture as a mixture of multinomial distributions over a fixed number of dust particle types. Using a latent Dirichlet allocation model, we make inference on (a) the contributions of sites of interest to a dust mixture, and (b) the particle profiles associated with these sites. [ABSTRACT FROM AUTHOR]