The Classification of Certain Four-Weight Spin Models

In this paper we show that if one of the matrices {Wi, 1 h i h 4} of a four-weight spin model (X, W1, W2, W3, W4; D) is equivalent to the matrix of a Potts model or a cyclic model as type II matrix and |X| S 5, then the spin model is gauge equivalent to a Potts model or a cyclic model up to simultaneous permutations on rows and columns. Using this fact and Nomura's result [12] we show that every four-weight spin model of size |X| = 5 is gauge equivalent to either a Potts model or a cyclic model up to simultaneous permutations on rows and columns.     

Exact Analysis of the State-Dependent Polling Model

We consider a polling model in which a number of queues are served, in cyclic order, by a single server. Each queue has its own distinct Poisson arrival stream, service time, and switchover time (the server's travel time from that queue to the next) distribution. A setup time is incurred if the polled queue has one or more customers present. This is the polling model with State-Dependent service (the SD model). The SD model is inherently complex; hence, it has often been approximated by the much simpler model with State-Independent service (the SI model) in which the server always sets up for a service at the polled queue, regardless of whether it has customers or not. We provide an exact analysis of the SD model and obtain the probability generating function of the joint queue length distribution at a polling epoch, from which the moments of the waiting times at the various queues are obtained. A number of numerical examples are presented, to reveal conditions under which the SD model could perform worse than the corresponding SI model or, alternately, conditions under which the SD model performs better than a corresponding model in which all setup times are zero. We also present expressions for a variant of the SD model, namely, the SD model with a patient server.     

Prediction of risers’ tubes temperature in water tube boilers

A dynamic model is developed which enables the prediction of risers’ tubes temperature of water tube boilers under various operating conditions. The model is composed of fluid dynamics model representing the fluid flow in the drum-downcomer-riser loop and a dynamic thermal model of the riser’s temperature. The model gives a detailed account of the two-phase heat transfer process which takes place between the risers’ inner walls and the water–steam mixture flow inside the tubes. The model is used to simulate various operational scenarios of water tube boilers. Results of the simulation provide insight into the dynamic interactions of the boiler’s main variables including the drum pressure, water volume, steam quality and risers’ temperature. Such a model is useful in checking operational scenarios before their actual plant implementation, can be a basis for developing boiler start up procedures and online temperature predictions to prevent eminent tube overheating.     

A nonstationary model of firespreading

A nonstationary (dynamical) model of the fire-spreading process is proposed in connection with firebreak designs, fire fighting policies and contingency for the people affected. The model is derived as a Stefan problem with the aid of the law of conservation of energy; firebrand-spotting and wind-blown effects are neglected. Also, the numerical examples of a laboratory scale fire are given; the results agree well, in the order of magnitude, with the experimental data reported. The stationary model is also derived from the dynamical model by use of Galilei's transformation and it is shown that a solution of the dynamical model approaches with time to a solution of the stationary model.     

Impedance of a three-dimensional head-spine model

A three-dimensional, discrete mathematical model of the human spine, torso, and head is decribed. The model consists of a system of rigid bodies representing the head, vertebrae, pelvis, and viscera, interconnected by deformable elements representing the intervertebral discs, ligaments, and other connective tissues. The model is a modified version of a previously developed head-spine model, the primary modifications being the incorporation of a detailed representation of the viscera-abdominal wall system and the determining of more accurate model damping parameters. Driving point impedances for vertical (+G_z) excitation were numerically determined for both the modified and the older model and compared to experimentally obtained driving point impedances of human volunteers. It is shown that the modified model's impedance is in much better agreement with the experimental results than that of the older model.     

Covering location problem of emergency service facilities in an uncertain environment

In practical location problems on networks, the response time between any pair of vertices and the demands of vertices are usually indeterminate. This paper employs uncertainty theory to address the location problem of emergency service facilities under uncertainty. We first model the location set covering problem in an uncertain environment, which is called the uncertain location set covering model. Using the inverse uncertainty distribution, the uncertain location set covering model can be transformed into an equivalent deterministic location model. Based on this equivalence relation, the uncertain location set covering model can be solved. Second, the maximal covering location problem is investigated in an uncertain environment. This paper first studies the uncertainty distribution of the covered demand that is associated with the covering constraint confidence level α. In addition, we model the maximal covering location problem in an uncertain environment using different modelling ideas, namely, the (α, β)-maximal covering location model and the α-chance maximal covering location model. It is also proved that the (α, β)-maximal covering location model can be transformed into an equivalent deterministic location model, and then, it can be solved. We also point out that there exists an equivalence relation between the (α, β)-maximal covering location model and the α-chance maximal covering location model, which leads to a method for solving the α-chance maximal covering location model. Finally, the ideas of uncertain models are illustrated by a case study.     

Properties of learning models in collective action: Rationality of backward-looking players

This article intends to clarify properties of learning models in simulation studies and to conduct a comparison of preceding learning models. Learning models are often used in many simulation studies, but there is no uniform rule of learning. We introduce three technical properties (monotonicity, condition of probability, neutrality) and three rational properties (rationality is fixed situations, rationality in first order stochastic domination, rationality with risk preference in stocahstic situations). We examine Michael Macy's model, the Erev & Roth model, and some others. We find that these models have different properties. Though learning is treated as one of the solutions of social dilemma from the results of Macy's model (Kollock, 1998), Macy's model is peculiar learning model. Learning is not always a solution of social dilemma. A comparison of learning models from a uniform point of view clarifies the properties of each model, and helps to probe conformity of a learning model and human behavior.     

Determination of the parameters of cancellous bone using high frequency acoustic measurements

The Biot model is widely used to model poroelastic media. Several authors have tested its applicability to cancellous bone, but to do so requires a priori estimation of the parameters of the Biot model, which is an uncertain and expensive endeavor. A method of computing acoustic pressure in the low 100 kHz range is developed.     

A review of credibilistic portfolio selection

This paper reviews the credibilistic portfolio selection approaches which deal with fuzzy portfolio selection problem based on credibility measure. The reason for choosing credibility measure is given. Several mathematical definitions of risk of an investment in the portfolio are introduced. Some credibilistic portfolio selection models are presented, including mean-risk model, mean-variance model, mean-semivariance model, credibility maximization model, α-return maximization model, entropy optimization model and game models. A hybrid intelligent algorithm for solving the optimization models is documented. In addition, as extensions of credibilistic portfolio selection approaches, the paper also gives a brief review of some hybrid portfolio selection models.     

Nonstandard models that are definable in models of Peano Arithmetic

In this paper, we investigate definable models of Peano Arithmetic PA in a model of PA. For any definable model N without parameters in a model M, we show that N is isomorphic to M if M is elementary extension of the standard model and N is elementarily equivalent to M. On the other hand, we show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M but N is not isomorphic to M. We also show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M, and N is isomorphic to M, but N is not definably isomorphic to M. And also, we give a generalization of Tennenbaum's theorem. At the end, we give a new method to construct a definable model by a refinement of Kotlarski's method. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonexistence of Markovian time dynamics for graphical models of correlated default

Filiz et al. (in arXiv:0809.1393 (2008)) proposed a model for the pattern of defaults seen among a group of firms at the end of a given time period. The ingredients in the model are a graph G=(V,E), where the vertices V correspond to the firms and the edges E describe the network of interdependencies between the firms, a parameter for each vertex that captures the individual propensity of that firm to default, and a parameter for each edge that captures the joint propensity of the two connected firms to default. The correlated default model can be rewritten as a standard Ising model on the graph by identifying the set of defaulting firms in the default model with the set of sites in the Ising model for which the {±1}-valued spin is +1. We ask whether there is a suitable continuous-time Markov chain (X _t ) _t??0 taking values in the subsets of V such that X ₀=?, X _r ?X _s for r??s (that is, once a firm defaults, it stays in default), the distribution of X _T for some fixed time T is the one given by the default model, and the distribution of X _t for other times t is described by a probability distribution in the same family as the default model. In terms of the equivalent Ising model, this corresponds to asking if it is possible to begin at time 0 with a configuration in which every spin is ?1 and then flip spins one at a time from ?1 to +1 according to Markovian dynamics so that the configuration of spins at each time is described by some Ising model and at time T the configuration is distributed according to the prescribed Ising model. We show for three simple but financially natural special cases that this is not possible outside of the trivial case where there is complete independence between the firms.     

Enhancing the generality of fuzzy relational models for control

A promising area of research in fuzzy control is the model-based fuzzy controller. At the heart of this approach is a fuzzy relational model of the process to be controlled. Since this model is identified directly from process input-output data it is likely that ‘holes’ will be present in the identified relational model. These holes are real problems when the model is incorporated into a model-based controller since the model will be unable to make any predictions whatsoever if the system drifts into an unknown region. The present work deals with the completeness of the fuzzy relational model which forms the core of the controller. This work proposes a scheme of post-processing to ‘fiil in’ the fuzzy relational model once it has been built and thereby improve its applicability for on-line control. A comparative study of the post-processed model and conventional relational model is presented for Box-Jenkins data identification system and a real-time, highly non-linear application of pH control identification.     

A scaled version of the double-mean-reverting model for VIX derivatives

As the Heston model is not consistent with VIX data in real market well enough, alternative stochastic volatility models including the double-mean-reverting model of Gatheral (in: Bachelier Congress, 2008) have been developed to overcome its limitation. The double-mean-reverting model is a three factor model successfully reflecting the empirical dynamics of the variance but there is no closed form solution for VIX derivatives and SPX options and thus calibration using conventional techniques may be slow. In this paper, we propose a fast mean-reverting version of the double-mean-reverting model. We obtain a closed form approximation for VIX derivatives and show how it is effective by comparing it with the Heston model and the double-mean-reverting model.     

On End-Extensions of Models of ¬exp

Every model of IΔ₀ is the tally part of a model of the stringlanguage theory Th-FO (a main feature of which consists in having induction on notation restricted to certain AC⁰. sets). We show how to “smoothly” introduce in Th-FO the binary length function, whereby it is possible to make exponential assumptions in models of Th-FO. These considerations entail that every model of IΔ₀ + ¬exp is a proper initial segment of a model of Th-FO and that a modicum of bounded collection is true in these models. Mathematics Subject Classification: 03F30, 03C62, 68Q15.     

Bayesian comparison of models with inequality and equality constraints

A Bayesian model selection procedure for comparing models subject to inequality and/or equality constraints is proposed. An encompassing prior approach is used, and a general form of the Bayes factor of a constrained model against the encompassing model is derived. A simple estimation method is proposed which can estimate the Bayes factors for all candidate models simultaneously by using one set of samples from the encompassing model. A simulation study and a real data analysis demonstrate performance of the method.     

Phenomenological model of interaction of a plate with a flow

In the present paper, a finite-dimensional phenomenological model of unsteady interaction of a rigid plate with a flow is proposed. It is assumed that the plate performs translational motion across the flow. The internal dynamics of the flow is modeled by the attached second order dynamical system. It is shown that the model allows satisfactory agreement with experimental data. With the developed model an inverse problem of dynamics is examined for the situation where the plate performing uniform translational motion at some moment begins uniform deceleration and finally stops. It is shown that for sufficiently large values of the plate acceleration for some time range the flow does not resist the motion of the plate but “accelerates” it. It is shown also that the equations of motion in the context of the proposed model can be reduced to the integro-differential form, and comparison with the known model of S. M. Belotserkovsky is performed. The structural resemblance of the motion equations for a body in flow in both models is noted. The domain of applicability of the quasi-stationary model is examined. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 7, pp. 43–62, 2005.     

基于三类模型的四大银行股票收益率预测研究

运用时间序列分析的预测方法,对四大银行的股票日对数收益率序列进行拟合与预测分析,分别构建ARMA模型、GARCH模型以及ARMA-GARCH组合模型,通过模型比较,实证分析表明:在拟合效果上,ARMA-GARCH模型的拟合优度优于ARMA模型和GARCH模型;在预测效果上,ARMA模型的预测效果最优,ARMA-GARCH模型次之.     

Simulation of quasi-dimensional combustion model for predicting diesel engine performance

In order to improve the precision of quasi-dimensional combustion model for predicting diesel engine performance and promote the real time operating performance of the simulation model, a new phase-divided spray mixing model is proposed and the quasi-dimensional combustion model of diesel engine working process is developed. The software MATLAB/Simulink is utilized to build the quasi-dimensional combustion model of diesel engine working process, and the performance for diesel engine is simulated. The simulation results agree with experimental data quite well. The comparisons between them show that the relative error of power and brake specific fuel consumption is less than 2.8% and the relative error of nitric oxide and soot emissions is less than 9.1%. By utilization of this simulation model with personal computer, the average computational time for one diesel engine working process is 36 s, which presents good real time operating performance of the model. At the same time, the influence of parameters in calculation of air entrainment on prediction precision of diesel engine’s simulation model is analyzed.