Mathematical and computer modelling reports

Modelling Vol. 13, No. 10, pp. 85-100, Press plc. Printed in Great Britain

1990

Math1 Comput. Pergamon

MATHEMATICAL

AND

COMPUTER

MODELLING

REPORTS

This section aims to provide our readers with the title, abstract and other essential data concerning mathematical models that were reported on in other journals, and as selected by our editors. Our readers are encouraged and requested to submit for publication reports of additional mathematical models, in the form here presented. Our own survey extends only to scientific journals published by Pergamon Press; although our readers are invited to contribute from any other source by submitting a tearsheet or good-quality camera-ready copy of the title page including the abstract direct from the journal concerned, providing permission to reproduce has been obtained. Please send all such submissions to Dr D. N. P. Murthy, Department of Mechanical Engineering, University of Queensland, St Lucia, Qld 4067, Australia.

Journal

of Statistical

Planning

EXPERT IMPERFECT

and Inference Vol. 20, pp. 245-277,

SYSTEM MODELS KNOWLEDGE:

1988

FOR INFERENCE A COMPARATIVE

WITH STUDY

AMBROSE GOICOECHEA School for Information

Technology

and Engineering,

Fairfax, VA 22030, Abstract-This on imperfect Cohen’s

paper presents a detailed comparative knowledge:

system

presented

probabilities,

leading methods

Purposely,

the assumptions,

and (6) a class of nonmonotonic

reasoning methods.

Each method

(5) is

and a list of strengths and

the same numerical example is addressed by each method such that we are able to highlight

and computational

Words-Inference

for reasoning based

theory, (3) fuzzy set theory, (4) MYCIN Model,

and discussed in terms of theoretical content, a detailed numerical example,

limitations.

Key

study of six major,

(1) Bayes’ rule, (2) Dempster-Shafer

of inductive

George Mason University,

U.S.A.

requirements

models, expert systems,

that are specific to each method

imperfect knowledge, uncertainty,

in a consistent

manner.

decision support systems,

infer-

ence network, evidential reasoning.

Biometrics

Vol. 44, pp. 635-655,

1988

THE PREVALENCE OF MALARIA IN GARKI, NIGERIA: DOUBLE SAMPLING WITH A FALLIBLE EXPERT JERRY NEDELMAN Department

of Mathematical

Clemson, Abstract-Data of Plasmodium

Sciences, Clemson

South Carolina

2963.4-1907,

University,

U.S.A.

from the Garki Project are analyzed to assess how misdiagnosis falciparum.

Three double-sampling

affects the estimated

prevalence

models that account for the fallibility of the expert are derived Typeset 85

by A,#-‘QX

MATHEMATICAL AND

86

COMPUTER MODELLING REPORTS

and applied. The models incorporate information about the density of parasites in the blood to varying degrees. The error in the estimation of prevalence is quantified; and its dependence on calendar time, age, prevalence, and density is investigated. Prevalence and average density are discovered to be good predictors of the error, with the latter being better. Implications of the double-sampling models for the design of epidemiological surveys similar to the one in Garki are investigated. Key Words-Misclassification,

Stand.

Actuarial

misdiagnosis, plaamodium falciparum.

.I. pp. 129-137, 1988

A RATING

MODEL

FOR

LOSS

OF PROFITS

INSURANCE

TERJE AVEN Rogaland University Center and Hanne Myre, University of Oslo Abstract-In this paper we present a rating model for loss of profits insurance for a production system consisting of n production units. Explicit expressions for the company’s long run expected average claims expenditures are derived. A numerical example is given. Key Words-Loss of profits insurance, indemnity period, long run expected average claims expenditures, SemiMarkov model, regenerative process.

Biometrics

Vol. 44, pp. 787-801, 1988

A RANDOM

EFFECTS MODEL FROM DEPENDENT

FOR BINARY SAMPLES

DATA

MARY COFFEY Department of Mathematical

Sciences, Oakland University, Rochester, Michigan 48063, U.S.A.

Abstract-A model is proposed for the binary data analog of the paired t situation. In this model the success probabilities vary across strata and have a specified probability distribution. The parameters can be estimated by moments or likelihood methods; various large-sample tests are proposed. The esimates and tests do not require fixed sample sizes. The model can be applied to case-control studies in which at least some cases have multiple controls and to other nested designs that have two treatments per stratum and small samples in each treatmentstratum combination. Key Words-Case-control

Znt. J.

Systems

Sci.

studies, categorical data, extra-binomial

variation.

Vol. 19, No. 11, pp. 2291-2306, 1988

DIAGNOSIS

MODEL FOR DYNAMICAL PART 1. DISCRETE SYSTEM

SYSTEMS

YOSHITERU ISHIDA and HIDEKATSU TOKUMARU Division of Applied Systems Science, Faculty of Engineering, Kyoto University, Kyoto 606, Japan Abstract-Many static diagnosis models, which express the static relation between faults and syndrome, have been studied extensively. However, it is difficult to apply these static models to dynamical systems in which the syndrome changes dynamically. In order to construct diagnostic systems for dynamical systems, a dynamic

Mathematical

diagnosis

model

that

propose

a failure

system.

Two

designed

can express

propagation

concepts

Biometrics

Vol.

the dynamic

model

of dynamic

to evaluate

which

705-715,

MODEL

relation

explicitly

diagnosabilities

these diagnosabilities

44, pp.

and Computer

Modelling

of fault propagation expresses

are defined

of the model

87

Reports

should be studied.

some dynamic for the model.

as well as to locate

aspects

In this paper,

of failure

Algorithms a primary

propagation

are presented failure

from

we in a

which are

a syndrome.

1988

SELECTION

AND VALIDATION WITH INTERACTION

FOR YIELD

TRIALS

HUGH G. GAUCH, JR. Department Abstract-The

additive

analysis

of variance

analysis

(PCA)

of Agronomy,

main

(ANOVA)

model

given

a large

trial

to two-way

to the residual

University,

data,

from the additive

of the more familiar

genotype-by-environment

and postdictive

Cornell

and multiplicative

model

trial data is a useful extension predictive

effects

model, Model

14853, U.S.A. model

first

the multiplicative

that is, to the interaction. PCA,

and linear

selection

using data splitting

and

and F-tests,

validation

the additive components

AMMI

regression

respectively.

applies prinipal

analysis

procedures,

are considered A New York

of yield

particularly from

both

soybean

yield

serves as an example.

Z
Analysis

of variance,

components

soybean,

validation.

analysis,

J. Math. Biol Vol.

26, pp. 635-649,

MODELS

Universitlit

P.

biplot,

interaction,

FORMATION

HADELER,

Abstract-Birth, conditions

death,

Tiibingen,

Lehrstuhl

for existence

ZCey Words-Pair

Research

pair formation,

differential

formation,

Policy Vol.

equations.

and global

17, pp. 315-328,

THE

Federal

qualitative

Abstract-This universities,

Change paper mainly

shows that

Research

principal

POPULATIONS

Auf der Morgenstelle

10,

of Germany by a system

of the system

of three nonlinear

are investigated,

homoge-

in particular

the

state. evolution

equation.

DETERMINATION OF RESEARCH IN BRITISH UNIVERSITIES

Centre,

Heriot-Watt

support

and GEOFFREY University,

for restructuring

of research resources.

for such concentration

OUTPUT

WYATT

31-35 Grassmarket,

some of the recent proposals

a process of concentration

there is little

prediction,

1988

begins by noting

through

postdiction,

W&Z-BUSEKROS

are described

homogeneous

PAUL HARE Technological

Republic

properties

of the bisexual

population,

and A.

fur Biomathematik,

and separation

The

stability

two-sex

MODELLING

sequence,

IN BISEXUAL

Ft. WALDST~TTER,

D-7400 Tubingen,

neous ordinary

model

1988

FOR PAIR K.

which

New York (AMMI)

and then applies

ANOVA,

interaction.

perspectives,

Ithaca,

interaction

except

Edinburgh

EHl

research

activity

We then review

in the most

2HT,

the available

resource-intensive

U.K.

in British evidence, disciplines.

MATHEMATICAL AND COMPUTER MODELLINC REPORTS

88

Since there is little &m information about the shape of “research production functions”, either for institutions or for the system as a whole, the core of the paper studies the factors likely to be important in such functions and investigates the consequences of particular functional forms. Finally, it is concluded that more research is needed to gain a better understanding of the research process in universities, and that in the meantime it would be unwise to embark on a wholesale restructuring of the system.

Int. J. Systems

Sci. Vol. 19, No. 11, pp. 2367-2379, 1988

MODELLING

AND

IDENTIFICATION WITH GENERAL

OF OFFSHORE DAMPING

TOWERS

K. A. MOUSTAFA Department

of Design and Production

Engineering, Faculty of Engineering, Aim-Shams University, Abbassia, Cairo, Egypt K. ASFAR and F. DRIES

Department of Mechanical Engineering, Jordan University of Science and Technology, Irbid, Jordan Abstract-The modelling problem of offshore towers is considered. A model is proposed which includes viscous and hydrodynamic drag damping and takes into account the stochastic nature of the problem. The model is decoupled into a set of modal equations by using the complex mode theory. A technique is developed to identify the modal parameters and the complex mode shapes by using the noisy excitation and response measurements. This technique is computationally efficient and accurate in the sense of minimizing a criterion function of the estimates variance. A simulation example is presented to demonstrate the results.

J. Appl.

Prob.

Vol. 25, pp. 492-500, 1988

AN IMPROVED

STOCHASTIC AMONG

MODEL ALLOWING INDIVIDUALS

INTERACTION

P. B. CERRITO Department

of Mathematics,

University of South Florida, Tampa, FL 33620, USA

Abstract-The purpose of this paper is to explore the properties of a new model which can describe the interaction among individuals. Various other models have been proposed, but all assume that each individual acts independently of others. Our model permits the assumption that individuals can be influenced and dominated by other individuals. We also demonstrate how this model can describe the interaction of various species in an ecosystem. This model will lead naturally to the definition of a population index of diversity. A means of estimating the values of the model will also be given. ICey Words-Markov

chains, behavior interaction, diversity index, estimation, regular semigroup

Mathematical

Int.

J. Systems

SC;. Vol.

19, No.

and Computer

11, pp. 2307-2319,

Modelling

Reports

89

1988

DIAGNOSIS MODEL FOR DYNAMICAL SYSTEMS PART 2. CONTINUOUS SYSTEM ISHIDA and HIDEKATSU TOKUMARU

YO~HITERU Division of Applied Abstract-While

Systems

most existing systems

are static.

Consequently,

dynamical

systems.

Although

model of differential equations

this model-based systems.

in qualitative

discussed.

theory.

The distinguishability

are derived by these qualitative

Journal

of Dynamics,

BOND

We interpret these qualitative

Strategies for monitoring

Abstract-The

physical

systems

products

generalizing

We propose a diagnosis which has been

stabilities of the model

is also studied with a new concept

of invariant

as well as for the diagnosis of the dynamical

Engineering,

modeling

University

IN FINITE

systems

variables and transformer

the power flow and modulation

of Texas, Austin,

deformation.

Texas 78712 to represent the hysteretic

Second and fourth order tensors rep

or gyrator moduli, respectively, calculations

STRAIN

WV

theory of bond graphs may be employed

solids in finite strain elastic-plastic

resent stress power conjugate

mode.

and Control Vol. 110, 1988

of Mechanical

of continuous

diagnosis of

results in terms of the diagnosis

MODELING OF CONTINUOUS SOLIDS ELASTIC-PLASTIC DEFORMATION

Department

for diagnosis

results.

Measurement

GRAPH

proposed

it is not used much in practice

The dynamic aspects of the qualitative

of the sign pattern

E. P. FAHRENTHOLD and A.

deformation

most models

606, Japan

The model can be expressed by a signed directed-graph,

matrix

fault pattern defined in the model.

Kyoto

is used for a model-based

diagnosis has been well studied,

and also present new results for the model.

are mainly

University,

difficulty and the difficulty of obtaining the mathematical

model for continuous dynamical studied extensively

Kyoto

requiring diagnosis are dynamical,

a mathematical

owing to the computation

model,

Science, Faculty of Engineering,

with corresponding

of scalar and vector bond graphs.

inner

Capacitors

and resistors of a tensor type suitably represent strain energy storage, associated flow rules in plasticity, and other familiar concepts.

An important

application

of this simulation

technique arises in constitutive

modeling

studies

of nonlinear materials.

Journal

of Dynamic

Measurement,

Syslems,

MODELING

AND

and Control

SIMULATION

RAYMOND MERALA, Mechanical Abstract-A

dynamic

Engineering

configuration.

MONT

Department,

model is developed

tively arbitrary geometric

Vol.

110, 1988

OF A SUPERCHARGER

HUBBARD,

and TAKASHI MIYANO

University of California,

for simulating

and predicting

A thermodynamic

Davis, CA 95616

performance

used to derive continuity and energy equations linking the various control volumes. and understand

the casual implications

Heat transfer is neglected.

Simulation

for superchargers

of laws governing flows between

Bond graphs also serve to study

control volumes

outputs include time histories of pressure,

with each control volume, time histories of the various flows in the supercharger,

efficiency.

Volumetric

within three percent of experimentally supercharger

performance

measured

over a wide range of speed/pressure values.

The simulation

to several key design parameters,

and side plate clearance distances.

including

and system

temperature,

associated

efficiencies are predicted

of rels

control volume approach and bond graph models are dynamics. and energy

and overall volumetric

ratio combinations

is used to investigate

rotor-rotor

mass,

separation,

and are

the sensitivity

of

and rotor-housing

MATHEMATICAL AND COMPUTER MODELLINC REPORTS

90

Journal of Dynamic

MODELING

Systems,

AND

Measurement,

and Control Vol. 110, 1988

IDENTIFICATION SYSTEMS WITH

OF A CLASS OF SERVOMECHANISM STICK-SLIP FRICTION

KA C. CHEOK, HONGXING Hu, and NAN K. LOH Center for Robotics

and Advanced Automation,

Oaklaud University, Rochester, MI 48309

Abstract-This paper describes a technique for modeling and identifying a class of nonlinear servomechanism systems with stick-slip friction. The physics of the stick-slip friction is considered in modeling the process. Identification of the system parameters is formulated as a nonlinear optimization problem. A modified simplex algorithm is proposed as the optimization procedure. The difficulties encountered in choosing identification algorithm and input signals for the problem are discussed. A simulation example of a servomotor system is provided.

Mathematical

Biosciences

Vol. 92, pp. 119-199, 1988

MODELING THE

AND ANALYZING HIV TRANSMISSION: EFFECT OF CONTACT PATTERNS JOHN A. JACQUEZ

Departments of Biostatics and Physiology, The University of Michigan, Ann Arbor, Michigan CARL P. SIMON Departments of Mathematics,

Economics, and Public Policy, The University of Michigan, Ann Arbor, Michigan JAMES KOOPMAN

Department of Epidemiology,

The University of Michigan, Ann Arbor, Michigan LISA SATTENSPIEL

Department of Anthropology,

University of Missouri, Columbia, Missouri

TIMOTHY PERRY Departments

of Physiology

and Internal Medicine, The University of Michigan, Ann Arbor, Michigan

Abstract-A compartmental model is presented for the spread of HIV in a homosexual population divided into subgroups by degree of sexual activity. The model includes constant recruitment rates for the susceptibles in the subgroups. It incorporates the long infectious period of HIV-infected individuals and allows one to vary infectiousness over the infectious period. A new pattern of mixing, termed preferred mixing, is defined, in which a fraction of a group’s contacts can be reserved for within-group contacts, the remainder being subject to proportional mixing. The fraction reserved may differ among groups. In addition, the classic definition of reproductive number is generalized to show that for heterogeneous population in general the endemic threshold is PDcy, where cy is the mean number of contacts per infective. The most important finding is that the pattern of contacts between the different groups has a major effect on the spread of HIV, an effect inadequately recognized or studied heretofore.

Mathematical

Biosciences

Vol. 92, pp. 201-229, 1988

A METHODOLOGICAL STUDY OF AN AIDS

OF A STOCHASTIC EPIDEMIC

MODEL

CHARLES J. MODE, HERMAN E. GOLLWITZER, and NRA HERRMANN Department of Mathematics

and Computer Science, Drexel University, Philadelphia,

Pennsylvania 19104

Abstract-A model of an AIDS epidemic in a population of male homosexuals was formulated as a stochastic population process. The paper is a methodological study in the sense that computer-intensive methods were used to investigate some properties of the model statistically rather than relying solely on classical methods of deductive mathematics. Three factors of importance in the evolution of an AIDS epidemic were studied in a numerical factorial experiment. These factors were the distribution of the latent period of HIV, the probability of

Mathematical

and Computer Modelling Reports

91

infection with HIV per sexual contact with an infected individual, and the distribution of the number of contacts per sexual partner per month. The numerical experiment suggested that the distribution of the latent period of HIV will have a decisive impact on the evolution of an AIDS epidemic but this impact will depend crucially on the levels of the other two factors. A Monte Carlo experiment suggested that if forecasts of an epidemic were made solely on the basis of deterministic nonlinear difference equations embedded in the stochastic population process, then prediction of the number of individuals infected with HIV and AIDS cases may be overly pessimistic.

SIAM

J. Appl.

Math.

Vol. 48, No. 6, 1988

MARTINGALE

APPROACH

FOR MODELING

DNA

SYNTHESIS

A. GERARDI and G. NAPPO Dipartimento

di Matematica,

Universitb di Roma “La Sapiensa,” P. Pe Aldo More, 00100 Rome, Italy

Abstract-The relation between continuous and discrete models for DNA synthesis is treated. A law of large numbers is given when cells can die during the mitotic period. In the critical case the fluctuations around an equilibrium state are studied. In particular the convergence to an Ornstein-Uhlenbecktype process is proved. Key

Word.+-Martingales,

J. Math.

weak convergence, nuclear spaces.

Biol. Vol. 27, pp. 29-48, 1989

STATISTICAL

MODELLING

OF MITOCHONDRIAL

POWER

SUPPLY

A. T. JAMES and J. T. WISKICH Departments of Statistics and Botany, The University of Adelaide, Adelaide, S.A. 5000 Ft. A. J. CONYERS Department of Biochemistry, Alfred Hospital, Melbourne, Victoria 3181, Australia Abstract-By experiment and theory, formulae are derived to calculate the response of mitochondrial power supply, in flux and potential, to an ATP consuming enzyme load, incorporating effects of varying amounts of (i) enzyme, (ii) total circulating adenylate, and (iii) inhibition of the ATP/ADP translocclse. The formulae, which apply between about 20% and 80% of maximum respiration, are the same as for the current and voltage of an electrical circuit in which a battery with potential, linear in the logarithm of the total adenylate, charges another battery whose opposing potential is also linear in the same logarithm, through three resistances. These resistances produce loss of potential due to d&equilibrium of (i) intramitochondrial oxidative phosphorylation, (ii) the ATP/ADP translocase, and (iii) the ATP-consuming enzyme load. The model is represented geometrically by the following configuration: when potential is plotted against flux, the points lie on two pencils of lines each concurrent at zero respiration, the two pencils describing the respective characteristics of the mitochondrion and enzyme. Control coefficients and elasticities are calculated from the formulae. Key Wo&-Mitochondria,

respiration, ATP/ADP

ratio, kinetics, thermodynamics, ,data-modelling

MATHEMATICAL AND

92

J. Math.

Biol.

COMPUTER MODELLING REPORTS

Vol 27., pp. 49-64, 1989

AN EPIDEMIOLOGICAL NONLINEAR

MODEL WITH A DELAY INCIDENCE RATE

AND

A

H. W. HETHCOTE Department of Mathematics,

University of Iowa, Iowa City, IA 52242, USA M. A. LEWIS

Centre for Mathematical

Biology, Mathematical

Department of Mathematics,

Institute, 24-29 St. Giles, Oxford OX1 3LB, UK and

University of Victoria, B.C. V8W 2Y2, Canada

P. VAN DEN DRIESSCHE Department of Mathematics,

University of Victoria,

B.C. V8W 2Y2, Canada

Abstract-An epidemiological model with both a time delay in the removed class and a nonlinear incidence rate is analysed to determine the equilibria and their stability. This model is for diseases where individuals are first susceptible, then infected, then removed with temporary immunity and then susceptible again when they lose their immunity. There are multiple equilibria for some parameter values, and, for certain of these, periodic solutions arise by Hopf bifurcation from the large nontrivial equilibrium state. Key Words-Epidemiological

J. Math.

Biol.

model, Hopf bifurcation, nonlinear incidence, time delay.

Vol 27., pp. 81-90, 1989

NUMERICAL

SIMULATION OF A STOCHASTIC MODEL CELLS SUBMITTED TO CHEMOTHERAPY

FOR

CANCEROUS

M. ABUNDO and C. Ross1 Dipartimento

di Matematica,

11Universita di Roma, Via Orazio Raimondo, I-00173 La Romanina (Roma),

Italy

Abstract-A stochastic model is proposed to study the problem of inherent resistance by cell populations when chemotherapeutic agents are used to control tumor growth. Stochastic differential equations are introduced and numerically integrated to simulate expected response to the chemotherapeutic strategies as a function of different parameters. Satisfactory demonstration runs of the model indicate that it could represent a useful tool in verifying the results of experimental and clinical chemotherapy courses and planning treatment strategies. Some types of behaviour are illustrated graphically. ZCey Word.+-Cell

J. Math.

Biol.

LOCAL

resistance, stochastic models, simulation.

Vol 27., pp. 65-80, 1989

VS. NON-LOCAL

INTERACTIONS

IN POPULATION

DYNAMICS

J. FURTER and M. GRINFELD Department of Mathematics,

Heriot-Watt

University, Riccarton, Edinburgh, EH14 4AS, Scotland, UK

Abstract-In this work we examine two models of single-species dynamics which incorporate non-local effects. The emphasis is on the ability of these models to generate stable patterns. Global behavior of the bifurcating branches is also investigated. Key Words-Reaction-diffusion

equations, non-local effects, stable patterns.

Mathematical J. Math.

and Computer Modelling Reports

93

Vol 27., pp. 105-113, 1989

Biol.

ON STOCHASTIC

COMPARTMENTAL

MODELS

Rudjer Bor(kovif. Institute, POB 1016, Yu-41001 Zagreb, Yugoslavia Abstract-The statistical averaging of compartmental models with parameters being random processes is derived for the case of vanishing input and uniformly bounded input. the difference of resulting models is discussed. Key Words-Compartmental

Appl.

Math.

Modelling

models, stochastic models.

Vol 13., 1989

MATHEMATICAL

MODELLING OF STIMULUS-SECRETION COUPLING IN THE PANCREATIC B-CELL VI. CELLULAR HETEROGENEITY AND RECRUITMENT WILLY J. MALAESE and ANN OWEN

Laboratory

of Experimental

Medicine and Department of Endocrinology,

(Erasmus Hospital),

Brussels Free University, Brussels, Belgium Abstract-Insulin release from the pancreatic B-cell may display rhythmic oscillations between basal and stimulated values, reflecting comparable fluctuations in the rate of Ca *+ inflow. The mathematical modelling of such a process allows simulation fo the biphasic pattern of insulin release and its dependence on glucose concentration, when allowance is made for the heterogeneity of both the time course of secretory events and threshold glucose concentration for stimulation of insulin release in distinct B-cells. It is proposed that such a heterogeneity and the consequent recruitment of cells at increasing concentrations of the hexose indeed play an essential role in the dynamics of hormonal release. Key

Worda-Insulin

Optimal

Control

secretion, mathematical

Applications

MODELLING

Ed Methods

AND CONTROL

modelling, pancreatic islet.

Vol lo., pp. 2138,

1989

OF A ROTARY

CRANE WITH A FLEXIBLE

JOINT

TADASHI YOSHIMOTO and YOSHIYLJKISAKAWA Department of Control Engineering, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan Abstract-A dynamical model is derived for the control of a rotary crane, which has a flexible joint and makes three kinds of motion (rotation, load hoisting and boom hoisting) simultaneously. The goal is to transfer a load to a desired place in such a way that at the end of the transfer the swing of the load decays as quickly as possible. A new open-loop plus feedback control scheme is proposed.

Key Words-Flexible

rotary crane, open-loop plus feedback control, observer, stabilization of swing

MATHEMATICAL

94

Quality

and Reliability

Engineering

A MULTI-FAILURE

RAPONE,

system

considers

mathematical

by applying

WordsTransit

system,

SIMPLE

TWO

and GIANPAOLO Motori,

1 80125 Naples,

operating

a new

transit

may be delayed are compared

to a common

service

dependability,

Models

Vol 5., No.

DIMENSIONAL

literature

as an effective policy

model

with those relative

from

failure which

in a trip.

by using the Monte

to different

of

is proposed,

of more than one failure are overcome

measure

and maintainability

and recovery

dependability

variables

Council,

with reliability

characteristics

by the occurrence

of random

Research

Italy

reliability

system

FOR TRANSIT

PULCINI

National

link system dependability

special

model

the model

Statist.-Stochastic

Common.

REPORTS

1989

in the transportation

with the algebra

The results of the proposed

Istituto

e Matteucci,

In this paper

associated

CALABRIA

models

incorporating

system.

that a passenger

difficulties

the literature, Key

transit

the possibility

method.

Dependability

of subsystems,

of each particular

Barsanti

has been recognized

service quality.

characteristics

RAFFAELA

and Reliability,

Piazza

transit

Vol 5., pp. 47-52,

International

of Statistics

Abstract-Dependability

MODELLING

ADDITIVE DEPENDABILITY MODEL SYSTEM EFFECTIVENESS ANALYSIS

MARIO Department

COMPUTER

AND

modelling

The Carlo

approaches

in

test scenario. Monte

1, pp.

Carlo

131-159,

MODELS

simulation.

1989

FOR THE

SPREAD

OF A DISEASE

DAVID GREENHALGH Control

and Management

Systems

Division,

Cambridge

Cambridge, Abstract-A a fixed

simple

population.

assumptions

versions

counterexamples

Prob.

Vol.

the

the optimal

25., pp. 649-662,

Abstract-A

drug addiction Expressions

also developed. a competing Key

This

death

of Statistics,

Mill Lane,

to model

which

Chain Binomial

make

epidemic

of people

the spread assumptions models.

infected.

of a disease

The epidemic

Some

amongst

corresponding

results,

to the

is controlled

conjectures

process

The

ADDICTION and P. W. University

in which individuals

drug addiction

A.

MODEL DAYANANDA

of Georgia,

Athens,

GA

in a closed population

and factorial

moments

process can be viewed

30602, USA can become

are obtained.

as a particular

addicts

A generalized

or pushers model

addicts,

pushers,

state probabilities,

factorial

moments,

is

case of what may be called

process.

Worda-Susceptibles,

and

are presented.

for the state probabilities

generalized

Department,

England

is proposed

number

Engineering

1988

L. BILLARD

is modelled.

lRX,

are obtained

expected policy

A DRUG

Department

model

and Reed-Frost

so as to minimize concerning

stochastic

of this model

made in the Greenwood

by immunization

J. Appl.

two dimensional Two

CB2

University

competing

death

process.

Mathematical

Reliability

Engineering

and

AN ACCELERATED

Vol 24., pp.

Safety

System

LIFE

and Computer

TEST

Modelling

223-230,

MODEL

Department

of Industrial

Engineering,

Korea

Advanced

Chongryang, Abstract-Constant Weibull

and progressive

lifetime

distributions

prior distribution to estimate

and other parameters

the model

of Marketing

Jou~sal

in which

Institute

life

constants.

POWER

LAW

and Technology,

PO

Box 150,

of Korea based

on the

inverse

power

law

and

scale parameter at use condition has a gamma Bayes and maximum likelihood methods are used

parameters.

Monte

Carlo study is performed

Vol 53., pp.

80-88,

1989

MODELING

INVERSE

of Science

test models

the Weibull

are unknown

THE

CHUNG

Seoul, Republic

stress accelerated

are proposed

95

1989

WITH

D. S. BAI and S. W.

Reports

to investigate

THE DECISION TO ADD NEW BY CHANNEL INTERMEDIARIES

the behaviour

of the estimators.

PRODUCTS

VITHALO R. RAO Johnson

Graduate

School of Management,

Cornell

University

EDWARD W. MCLAUGHLIN Department Abstract-Using logistic

data collected

regression

how different validation

variables system

on new products

to describe

influence

performance.

the marketing

Journal

models

of Agricultural

presented

the intermediary’s

those decisions.

Implications

Economics,

The

Cornell

to a major

accept/reject logistic

model

of these results for marketing

University

channel intermediary,

the authors

decisions for those products. is shown

to fit extremely

strategies

estimate

Results indicate

well with excellent

and for improving

performance

of

are discussed.

of Forecasting

Vol 8., pp.

A DYNAMIC

85-96,

LINEAR

1989

MODEL TIME

APPROACH FOR DISAGGREGATING SERIES DATA

M. AL-OSH King Abstract-An aggregate

approach series, it,

is proposed

of k period

problem

in a dynamic

filtering

techniques.

linear

An

from

the observed

model

ICey

Word+--Aggregation,

hood

estimation.

Saud University,

for obtaining

non-overlapping

model

form.

ad hoc procedure of the aggregates. d&aggregation,

Then

estimates

of the basic (disaggregated)

sums of Zi’s is available. estimates

is introduced

process,

The

approach

of Zi can be obtained

for deriving

An application ARIMA

Saudi Arabia

a model

of this approach dynamic

linear

series, Zi, when only an is based on casting

by application

the

of the Kalman

form for the unobserved

basic series

to a set of real data is given. model,

state

space,

maximum

likeli-

MATHEMATICAL AND

96

Journal

of Forecasting

TIME

Vol 8., pp.

SERIES

75-83,

COMPUTER MODELLINC REPORTS

1989

FORECASTS

AND

EXTRA-MODEL

INFORMATION

ALAN PANKRATZ Department Abstract-Often

of Economics

and Management,

a forecaster has supplementary

that cannot be included

DePauw University,

information

directly in a time series model.

Greencastle,

(e.g. field reports or forecasts from another source)

Especially

interesting

are cases where this information

is given at time intervals that are different from those of the time series model forecasts. considered a numerical and a model-based with ARIMA regression

model forecasts.

statistical

Key

(transfer function)

Words-ARIMA

European

Journal

for combining

This paper extends both methods model forecasts.

arises as a special case of the model-based

transfer function,

method

extra-model

to vector ARMA

Previous

authors have

information

of this type

model forecasts and dynamic

It is also shown that a Lagrange multiplier

procedure.

models, benchmarking,

IN, USA

numerical

procedure

dynamic

regression,

An empirical example is given.

composite

forecasts,

distributed

lag regression,

vector ARMA.

of Operational

Research

Vol 39., pp. 231-242,

COMPETITIVE

SPATIAL H. A.

Faculty of Administration,

University

1989

MODELS

EI~ELT

of New Brunswick,

Fredericton,

New Brunswick,

Canada

E3B 5A3

G. LAPORTE Centre de recherche sur les transports, Mont&al, Abstract-A models

de MontrBal, C.P. 6128,

actions.

Succursale

A,

QuCbec, Canada H3C 357

large number of decision situations can be modeled as spatial problems.

allow only one firm or facility to locate,

competitors’

Universitt

competitive

models permit

Whereas

the other facilities

the usual location to react to their

One question is then not only where an individual facility will locate but if repeated relocation

of the facilities involved does converge towards a predictable described in the literature.

pattern.

Many competitive

spatial models have been

In this review we first formalize the general model and delineate its components.

we survey some of the major results and put them into perspective.

We conclude

Then

the review with a number

of

research ideas which may be explored in the future. Key

Words-Competitive

models,

location

problems,

Nash

equilibria,

Hotelling

models,

spatial

optimization,

social optima.

Appl.

Statist.

Vol 38., No.

A PROBABILISTIC

1, pp. 95-110,

MODEL

1989

OF SQUASH:

STRATEGIES

AND

APPLICATIONS

JOHN SIMMONS Department Abstract-Optimal

of Physics and Astronomy,

strategies

chain. Further implications

Glasgow University,

for squash are presented

assuming

Glasgow,

G12 SQQ,

that the game can be modelled

of this model are discussed in relation to handicapping

The validity of the model is briefly discussed in the light of data.

Key

Markov

chains, scoring rules, squash.

a~ a Markov

and the correspondence

different scoring systems. WordtEstimation,

UK

between

Mathematical

Appl.

Statist.

Vol 38., No.

1, pp.

l-50,

and Computer

Modelling

Reports

97

1989

SPACE-TIME MODELLING WITH LONG-MEMORY DEPENDENCE: ASSESSING IRELAND’S WIND POWER RESOURCE JOHN HASLETT Department

of Statistics,

Trinity

ADRIAN University Abstract-We

consider

a site for which

few data

meteorological which

short-memory kriging,

of Washington,

Seattle,

USA

on wind

the main

features

of wind

autocorrelation

modelling

estimator,

2, Ireland

of the long term average power output from a wind turbine generator at Long term records of wind speeds at the 12 synoptic speeds are available. Inference is based on a simple and parsimonious approximating model are also used.

temporal

ARMA

as a point

for

Dublin

estimation

stations

accounts

College,

E. RAFTERY

speeds

in Ireland,

and long-memory

and fractional

and good interval

differencing estimators

temporal

in a natural

namely seasonal effects, spatial correlation, It synthesizes deseasonalization, dependence. way. A simple kriging estimator performs well

result from the model.

The resulting

procedure

is easy to apply

in practice. I
W&P-Deseasonalization,

Appl.

Statist.

fractional

Vol 38., No.

1, pp.

differencing,

127-138,

MULTIPLE-SPELL

kriging,

REGRESSION

of Statistics,

Abstract-General

models

how the successive special

cases of the general

timescales

MODELS

without

model

common

further

analysing

programming.

Icey Words-Completely

Finally,

and partially duration

Appl.

Vol 13., 1989

Modelling

TWO-EQUATION

Abstract-The

derivation

of conservation and

the

corresponding

constraints closure that

imposed

assumptions)

the model

are considered.

Konstanz, A general

stochastic

of different

DATA

such as Markov

models

are applied

models,

different

hazard

theory

Germany which

indicates Various

are investigated:

processes

different

or semi-Markov

GLIM

and RATE

to the duration

timescales,

West

process is presented.

timescales

data such as SAS, BMDP,

transition-specific

of a two-equation balance

balance

processes. can be used

of unemployment,

and

and conclusions.

maximum

likelihood

estimation,

rate.

laws

for

to within

model

conservation

the mean

turbulent

stress tensor,

of predicting

VALENTINE

Clarkson

of energy, buoyant

NY,

is presented.

and entropy

flow

field

are used to formulate heat

Potsdam,

USA

with the second law of thermodynamics

approximation

the heat flux vector,

nongradient

University,

consistent

the Boussinesq

law of thermodynamics

for the turbulent

and D. T.

Engineering,

turbulence

of momentum,

by the second

has the capability

G. AHMADI,

and Industrial

the effects of buoyancy

of mass,

5560, D-7750

is shown to lead to false interpretations

G. TANNOUS,

of Mechanical

that takes into account

processes

parameterized

model,

DURATION

THERMODYNAMICAL MODEL FOR TURBULENT BUOYANT FLOWS. PART I: THEORY A.

Department

data

The implications

multiple-spell

FOR

by an underlying

for duration

framework

multistate-multiepisode

Math.

duration

stochastic

programs

the data in a single-spell

Postfach

are generated

are discussed.

underlying

computer

persistence.

HAMERLE

of Konstanz,

for multiple-spell

lead to different

Occasionally

University

spells of an individual

interpolation,

1989

ALFRED Department

optimal

inequality

The

are averaged,

are developed.

The

the constitutive

equations

and the energy

diffusion.

The equations

new

flux vector.

model

contains

physical (or

It is shown empirical

MATHEMATICAL

98 constants data.

that are determined

Furthermore,

turbulence Key

with added

SOME

solutions

the model

equations

REPORTS

of limiting reduce

turbulent

flows with experimental

to those of the common

k-c model

for

terms.

buoyant

Modelling

Math.

MODELLING

of analytical

simplifications

buoyancy

Word-Turbulent

Appl.

via comparison

with certain

COMPUTER

AND

flow,

two-equation

model,

fluid mechanics.

Vol 13., 1989

NONLINEAR

OPTIMIZATION MODELLING FOR PLANNING OF LARGE MARKET-ORIENTED SYSTEMS: WITH AN APPLICATION TO REAL HEALTH DATA

OBJECTIVES

R. S. SECALL

Department Abstract-This prediction

paper

of patient

of its mathematical constrained model their

form

Massachusetts of the origin

derivations

hospitals.

with certain constrained derives

on objectives

This

Math.

of Lowell,

article

model

has been

efficiency,

model

States better

and formulations

and accessibility.

This

model

The

to predict predict

the flows

An application

of the equity

optimization

models,

Laboratorio

systems a finite Key

mathematical curve

of differential

equations

associated

bar left initially

Word-Schock

National

model

the stress-strain

of the general

of

assumptions

form.

This paper

programming

objective

from

in the state

models

to real health

equity,

efficiency,

accessibility,

market

systems.

Vol 13., 1989

Modelling

ROGCRIO

which

flows

is presented.

MODELING AND NUMERICAL SIMULATION OF SOME PHENOMENA INVOLVING ELASTIC-NONLINEAR

Abstract-A

constrained

of patients

the underlying

nonlinear

for the bases all

than the destination

than the destination

of several

article

destination

patient

However,

modelling

sequential rather

article.

and Europe

of some variables.

in the United

constrained

in the earlier

USA

mathematical

domain.

used to accurately

to the definition

MA,

presented

form of the gravity

and used in England

fit the situation

the origin

which

Lowell,

a large geographical

constrained

model

modifications

of equity,

Words-Nonlinear

Appl.

within

an origin

validated,

data for the state of Massachusetts Key

of a previous

“80~s”

upon

developed,

to acute

mathematically based

is a continuation

client customer

University

which was used for the basis of the modelling

was initially homes

of Mathematics,

is proposed

Glimm’s

Cientifica,

method,

Rio de Janeiro,

to analyze the dynamical This phenomenon results obtained

Brazil

behavior of elastic-nonlinear bars in is governed by nonlinear hyperbolic

shock waves in their solution.

and some typical

in a nonequilibrium

DA GAMA

points.

that may present problem

SALDANHA

de Computa@o

has no inflection

RiemaM

waves,

MARTINS

DYNAMICAL BARS

We present

numerically

state. nonlinear

elasticity,

elastic rod, vibrations.

the complete

by Glimm’s

solution

method

for

Mathematical and Computer Modelling Reports in the Engineering and Informational

Probability

MODELING

POWER

99

Sciences Vol. 2, pp. 435-459, 1988

OF STOCHASTIC

PETRI NETS FOR SIMULATION

PETER J. HAAS and GERALD S. SHEDLER IBM Ahnaden Research Center, San Jose, California 95120-6099 Abstract-Generalized semi-Markov processes and stochastic Petri nets have been proposed as general franu+ works for a discrete even simulation on a countable state space. The two formal systems differ, however, with respect to the clock setting (event scheduling) mechanism, the state transition mechanism, and the form of the state space. We obtain conditions under which the marking process of a stochastic Petri net ‘mimics” a generalized semi-Markov process in the sense that the two processes (and their underlying general state-space Markov chains) have the same finite dimensional distributions. The results imply that stochastic Petri nets have at least the modeling power of generalized semi-Markov processes for discrete event simulation.

Statistics

in Medicine Vol. 8, pp. 259-262, 1989

AN APPLICATION OF A MATHEMATICAL MODEL FOR TIME LAG IN CASE REPORTING

TO ADJUST

KUNG- JONG Lur Biometrics Branch, Division of Injury Epidemiology and Control, Center for Environmental Health and Injury Control, Centers for Disease Control, Atlanta, GA 36333, U.S.A. RICHARD K. RUDY Gillis W. Long Hansens Disease, Regional Hansens Disease Program, Carville, LA 70721, U.S.A. Abstract-In a dynamic, fluctuating surveillance system, the time lag case of reporting often causes an artificial plateau in an epidemic curve. Arbitrarily ignoring data reported in the most recent period to avoid this bias causes the loss of valuable information. In this report, we propose an application of a mathematical model to adjust for the underreporting bias owing to the time lag of the reporting process. We present an example using the acquired immunodeficiency syndrome incidence data for the homosexual group in the San Francisco surveillance system to illustrate and evaluate prospectively this proposed technique. The results show that the adjusted incidence obtained with the model agrees reasonably well with the true incidence, except for the last month of the period under consideration. ZCey Words-Surveillance,

Appl.

Math.

acquired i-unodeficiency

syndrome, homosexual,

Modelling Vol. 13, 1989

A NUMERICAL

MODEL FOR SIMULATING TWO-PHASE THROUGH POROUS MEDIA

FLOW

ANANT R. KUKRETI and YATENDRA RAJAPAK~A School of Civil Engineering and Environmental Science, The University of Oklahoma, Norman, OK, USA Abstract-A numerical model is developed for flow of immiscible and incompressible fluids through porous media, representing subsurface oil reservoirs. The spatial domain is discretized by using finite element theory, and the element matrices are obtained by Gale&in’s method. The resulting nonlinear equations are solved in the time domain by subdividing the total simulation time into small time increments and approximating the variation of the variables by a polynominal of time within each time increment. The coefficients of the polynominal are determined iteratively. The iterative algorithm is presented for a linear and quadratic approximation. The method is demonstrated for two-phase flow through a homogeneous square domain. Results of a sensitivity study conducted to investigate the effect of the type of element, mesh configuration, size of time increment adopted, and the order

MATHEMATICAL AND COMPUTER MODELLING REPORTS

100

of approximation used on the accuracy, convergence, and computational presented. The results are also compared to those of another method. Key Wordthmniscible,

efficiency of the results predicted

are

flow, two-phase, porous media, finite element.

Statistics in Medicine Vol. 8, pp. 263-266, 1989

A MODEL-BASED

APPROACH TO THE IMPUTATION HOME INJURY INCIDENCES

OF MISSING

DATA:

JUDITH M. CONN, KUNG-JONG LUI and DANIEL L. MCGEE Biometrics Branch, Division of Injury Epidemiology

and Control, Center for Environmental

Health and Injury

Control, Centers for Disease Control, Public Health Service, U.S. Department of Health and Human Services, Atlanta, Georgia, 30333, U.S.A. Abstract-Missing or incomplete data cases are a problem in all types of statistical analyses. In disease surveillance, this problem inhibits determining the actual incidence of a disease event and monitoring the disease occurrence. Several statistical techniques have been developed to impute values for incomplete data cases. We present a model-based approach to the imputation of missing data elements as applied to determining the incidence of home injury deaths. Key

Words-Imputation,

Automatica

incomplete data, logistic regression, partially missing data.

Vol. 25, No. 2, pp. 185-206, 1989

DEVELOPMENT

AND APPLICATION SUPPORT

OF AN INTERACTIVE SYSTEM

MODELING

Y. NAKAMORI Department of Applied Mathematics,

Konan University, 8-9-l

Okamoto, Higashinada-ku, Kobe 658 Japan

Abstract-This paper outlines an interactive modeling support system that helps model building for complex large-scale systems involving hum& behavioral aspects. The system consists of combined modeling techniques using statistical and graph-theoretical approaches, and multi-stage person-computer dialogues. It assists flexible determination of the model structure according to the advice of experts, and clear definition of the model objective with conviction. Three examples are presented to show its applicability to the wide range of concrete problems. I(ey Words-Man-machine interfaces and dialogue systems, mental models, human decision making, decision support systems, computer-assisted modeling.