RESEARCH
Dr. Zinovi Krougly
University of Western Ontario
Department of Statistical &
Actuarial Sciences
1151 Richmond Street North
Western Science Center 262
London, Ontario, Canada, N6A 5B9
Phone: 661-2111 ext. 86281
Fax: (519) 661-3813
Email: zkrougly@stats.uwo.ca;
http://www.stats.uwo.ca/faculty/krougly/default.htm
Expertise and Research Interests
 Numerical Analysis and Optimization / Computational Mathematics
 Stochastic Modelling / Simulation
 Statistical Data Analysis and Visualization
 Operations Research / Queueing Theory and Queueing Networks , Performance
Analysis
 High-precision Numerical Computing
 High Performance Computing / Parallel and Distributed Computing
 Use of Technology in the Teaching of Mathematics and Statistics
Forestry Project, Stochastic Modelling and Visualization of Fire Spread Natural
Phenomena
We consider a stochastic fire growth model, with the aim of predicting the behaviour of
large forest fires. Such a model can describe not only average growth, but also the
variability of the growth. Implementing such a model, based on cellular automata
simulations, in a computing environment allows one to obtain probability contour plots, burn
size distributions, and distributions of time to specified events [2, 3, 11]. Such a model also
allows the incorporation of a stochastic spotting mechanism. We have also used it to
generate phenomena such as the large fire event at Dogrib in Alberta in 2001. The
applications are written in C++.
Forest Fire Modelling Examples
A Stochastic Model for Generating Disturbance Patterns within Landscapes
A stochastic model for generating disturbances in landscapes that interfaces with
geographic information systems (GIS) is presented in [4]. The model operates on a lattice
(rectangular array of points) using a space-time Markov process, which gives a stochastic
simulation of growth patterns in terms of parameters of the local region. The model
generates disturbance patterns on the landscape based on the total area disturbed and the
number of patches to be disturbed.
The model is developed in a C++ software package named “TDsimulator” (“Terrain
Disturbance Simulator”) which can be used to predict terrain changes under a variety of
stochastic scenarios described herein. The software comprises a set of a geographic
information system GIS routines that collectively yield the disturbance patterns. A
demonstration of the stochastic model is provided for simulating fire behavior in a forested
landscape. The numerical examples illustrate disturbance impact and map-visualization
under different initial stochastic conditions and scenarios.
Forestry Project, Stochastic Modelling and Visualization of Fire Spread Natural
Phenomena
We consider a stochastic fire growth model, with the aim of predicting the behaviour of
large forest fires. Such a model can describe not only average growth, but also the
variability of the growth. Implementing such a model, based on cellular automata
simulations, in a computing environment allows one to obtain probability contour plots, burn
size distributions, and distributions of time to specified events [2, 3, 11]. Such a model also
allows the incorporation of a stochastic spotting mechanism. We have also used it to
generate phenomena such as the large fire event at Dogrib in Alberta in 2001. The
applications are written in C++ and R.
http://www.stats.uwo.ca/faculty/krougly/ffSimulation/ForestFireSimulation_v2.htm
Simulation Distributions with Almost-lack-of Memory (ALM) Property, Hypothesis
Testing and Computing the Corresponding Statistics
Time-varying periodic flows of events occur in numerous applications, particularly in data
transfer networks, communication systems, reliability models, ecological data descriptions,
etc. Recently a new class of probability distributions known as the class of ALM
distributions was introduced to properly model phenomena possessing periodical behavior.
Certain characterization properties of time-varying periodic Poisson flows are studied in terms
of ALM distributions. Statistical parameter estimation and testing of hypothesis for such
distributions are studied. We consider some new properties of this class of distributions,
compare estimation of their parameters and propose the likelihood ratio test for testing an
ALM distribution versus other competing distributions, particular another ALM or non-ALM
distributions [6, 9, 10]. Algorithms for computing critical levels and power of the likelihood ratio
test by the Monte Carlo method are designed. The Monte-Carlo methods in testing
hypotheses about ALM distributions based on the Neyman-Pierson theorem. Applications are
written in C++.
Performance Evaluation and Optimization of Computer - Communication Systems
and Queueing Networks
In the design and performance analysis of computer networks, closed queueing networks have
played a key role [5, 7, 8, 12]. Whereas product-form network models have become invaluable
tools in this regard, a whole host of real networks do not satisfy the necessary conditions to
make use of them. For such situations, various approximations have been proposed. The
present work presents a new approximation, with the main focus being networks employing a
preemptive priority discipline at one or more service centers.
The novel role is that it resorts to sensitivity analysis based on partial derivatives for
various performance measures. This method has been previously used in [7, 8] to obtain
such derivative information as functions of the service demands and service rates. A
unified nonlinear programming approach has been presented [5, 12] to arrive at an
approximate solution. In fact, two main optimizing approaches are followed; one which
employs the derivative information to develop efficient techniques to reach the optimal
solution, and the other which does not.
The performance evaluation algorithms use a nonlinear programming approach to obtain
approximate solutions in queueing network models. A number of algorithms are proposed
to determine the numerical results for priority approximation and other models. Using
sensitivity analysis, an efficient iterative technique has been developed for closed queueing
networks.
This work introduced the minimization criteria and used a direct search procedure with
efficient algorithms based on the calculation of derivative information to perform the
optimization. We compare the approximate solutions obtained from our approach with the
global balance solution, illustrate the accuracy of the approximation, and compare the
efficiency of the different optimization methods we have implemented. The applications are
written in C++.
Forecasting, Time Series Analysis with C++, Mathematica and R Packages
The Trench algorithm is implemented in C++ and is interfaced to Mathematica and R [1].
This algorithm computes the inverse of a Positive-definite Toepliz matrix, and can be used
to evaluate the inverse of the covariance matrix of n successive observations from a
stationary time series as well as its determinant. The Trench Inverse package is provided
in both of these high-level quantitative programming environments.
The Trench Inverse package is suitable for exact maximum likelihood estimation in many
linear time series models as well as for use in many other types of problems in time series
analysis. The use of Trench Inverse is illustrated with another package, FGN, which we
developed for fitting fractional Gaussian noise models. Examples are given which illustrate
the efficiency of the algorithms we have implemented.
High-Precision Numerical Computing
We have explored high-precision complex arithmetic, complex exponentials and other
complex- valued functions to perform numerical calculations in C++ and Matlab. A Mprec
package in double-double and arbitrary precision computations are proposed. For
maximum efficiency most of the Matlab functions in arbitrary precision use C++ interface to
Matlab. The C++ and Matlab versions incorporate some advance algorithms, for ordinary
differential equations, eigensystems, matrix exponentials, Gamma, Erf, Lambert W and
other functions.
We investigate the existence of solutions and the convergence of algorithms.
Numerical examples are reflected a variety of scientific calculation problems (C++ and
Matlab software, paper in preparation)
High Performance Computing
High performance computing in stochastic modelling and simulation, Windows and Linux
environments, integrating with Mathlink and Mathematica (C++ and Mathematica software).
Used LAM/MPI C++ communication standard for parallel and distributed computers
(SHARCNET infrastructure).
C++ Implementation of Algorithms for Matrix Analytic Methods in Stochastic
Modeling
Calculations of performance measures for a wide class of stochastic models,
implementation of the concept of object-oriented programming techniques, class vector
and class matrix development, implementation of quadratically convergent logarithmic
reduction algorithm (C++ software, paper in preparation).
Refetrences
1.
Algorithms for linear time series analysis: with R package (2007), McLeod, A.I.,
Yu, Hao, Krougly, Z.L., Journal of Statistical Software 23(5), 1-26.
2.
A stochastic model for forest fire growth (2007), Boychuk, D., Braun, W.J.,
Kulperger, R.J., Krougly, Z.L., Stanford, D.A., Information Systems and Operational
Research (Special Issue on Forestry) 45, 9-16.
3.
Stochastic forest fire growth models (2009), Boychuk, D., Braun, W.J., Kulperger,
R.J., Krougly, Z.L., Stanford, D.A., Environmental and Ecological Statistics,
DOI10.1007/s10651-007-0079-z, 19 pp (In Press).
4.
A stochastic model for generating disturbance patterns within landscapes (2009),
Krougly, Z.L., Creed, I.F., Stanford D.A., Computers & Geosciences,
doi:10.1016/j.cageo.2008.05.01016 pp (In Press).
5.
Iterative algorithms for performance evaluation of closed network models (2005),
Krougly, Z.L., Stanford, D.A., Performance Evaluation 61 (2005), 41-64.
6.
Periodic Poisson processes and almost-lack-of-memory distributions (2004),
Dimitrov, B.D., Rykov, V.V, Krougly, Z.L., Automation and Remote Control 65,
1597-1610.
7.
Computational algorithms of optimization of closed queueing networks (1990),
Krougly, Z.L., Murshtein, M.S., Automation and Remote Control 49, 926-936.
8.
Optimization of closed stochastic networks (1987), Vishnevsky, V.M., Krougly,
Z.L., Automation and Remote Control 46, 173-183.
9.
Periodic non-stationary arrival processes in queueing networks and their
characterization (2003), Dimitrov, B.D., Rykov, V.V, Krougly, Z.L., Distributed
Computer and Communication Networks (DCCN-2003): Stochastic Modelling and
Optimization, Technosphera, Moscow, 64-72.
10. B. Dimitrov, V. Rykov, Z. Krougly, M. Ghitany, On properties and statistical
estimation of ALM distributions(2003), Dimitrov, B.D., Rykov, V.V, Krougly, Z.L.,
Ghitany, M., Proceedings of Hawaii International Conference on Statistics and
Related Fields, Honolulu: (CD ISSN#1539-7211).
11. A stochastic forest fire spread model (2005), Kulperger, R.J., Krougly, Z.L.,
Stanford, D.A., Proceedings of the 5th Saint Petersburg Workshop on Simulation,
St. Petersburg, 401-406.
12. Nonlinear programming algorithms for performance modelling of computer
networks (2003) Krougly, Z.L., Stanford, D.A., Distributed Computer and
Communication Networks: Stochastic Modelling and Optimization (DCCN-2003),
Technosphera, Moscow, 11-22.
13. Experimental data analysis and software applications for Indicator
spectrophotometric method for the determination of acidic and basic properties of
solid surfaces (2004), Krougly, Z.L., Glibin, V.P., 87th Canadian Chemistry
Conference and Exhibition of the CSC, 934.
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