**RESEARCH**

**Dr.**
**Zinovi
Krougly **

**University
of Western Ontario
**

1151 Richmond Street North

Western Science Centre 270

London, Ontario, Canada, N6A 5B9

**http://www.stats.uwo.ca/faculty/krougly/default.htm**** **

·
Scientific
Computing, Numerical Analysis, Optimization

·
Stochastic
Modeling, Simulation

·
Big Data
Analysis & Data Visualization and Object Oriented Programming

Used: SQL
Server Database Engine, SQL Server Compact Database, MS Access Database

·
High-precision
Numerical Computing

·
Operations
Research, Queuing Networks, Performance Analysis

·
Use of
Technology in the Teaching of Mathematics, Statistics and Related Disciplines

·
Machine
Learning, Cluster Analysis

·
Programming
Languages C++, C\#, Matlab, R, Mathematica.

**Big Data Analysis & Data Visualization ****and Object Oriented Programming**

KEY WORDS that
best describe the research:

Big Data
Analysis; C\#, SQL server database and Excel Integration; Interpolation Methods
and Optimization, Machine Learning and Classification Algorithms, Classes and
C# Advances Features.

The software
includes:

Data selection,
import Excel data files, reading and visualizing data in C\# and import large
scale Excel files (C# and Excel integration), trend chart, ability to select
start and end time in the chart, tool tips and data markers.

Used SQL Server
or SQL Server Compact (SQL CE) databases.

Some of the C#
classes are the following:

ClassLogisticRegression, ClassLibraryArray and ClassLibraryInterpolator,
ClassHistogram, ClassDescriptiveStatisticss
(mean, standard deviation, median, mode, F95 (95% percentile), F90, F75, F50,
F25, F10, F05), ClassClusterAnalysis.

Library
Interpolator class includes curve fitting option, polynomial curve fit
algorithm, cubic spline interpolation for logistic curve fit (sigmoid
function).

ClusterAnalysis class
(for optimizing or controlling groups called clusters) of multiple source
(wells). The objective is to divide the source with similar functions based on
properties learned from training data (classification and data clustering
analysis).

**High-precision
Numerical Computing**

We presented a
multiple precision libraries with applications to numerical analysis, queueing
networks and stochastic modelling [9, 15]. For maximum efficiency, arithmetic
operators and algebraic functions are implemented in the *mpreal* class. We investigate the
accuracy of numerical solutions in double precision and multiple precision in
all three areas. Our examples are chosen to reflect the diversity of types of
problems for which multiple precision can play a useful role.

A multiple precision library for
ﬂoating-point calculations to any number of digits has been implemented
in Matlab and C++.
One application is discussed in detail, namely the evaluation in the
complex plane of special functions in regions of bad conditioning [9, 10].
Through the use of Matlab classes, all the basic
arithmetic operations are accessible using Matlab
syntax, even though the fundamental operations are coded in C++. Arithmetic supports both real and complex
data to arbitrary precision. The level of the precision being used can be
changed at any time. Many elementary functions are also available in Matlab syntax, although not all of them are offered for
complex arguments.

**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, 4, 12, 16]. 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

Forest Fire Modelling Examples

http://www.stats.uwo.ca/faculty/krougly/ffSimulation/ForestFireSimulation_v2.htm

**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 [1]. 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.

**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,
10, 11]. Algorithms for computing critical levels and
power of the likelihood ratio test by the

**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, 13]. 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, 13] 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 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, work in progress).

__Papers
in Refereed Journals__

1. A stochastic model for generating disturbance patterns within landscapes (2009),

`Krougly, Z.L., Creed, I.F., Stanford D.A., Computers & Geosciences 35, 1451-1459.`

2. Stochastic forest fire growth models (2009), Boychuk, D., Braun, W.J., Kulperger, R.J., Krougly, Z.L., Stanford, D.A., Environmental and Ecological Statistics 16, 133-151.

3. 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.`

__JSS Article __http://www.stats.uwo.ca/faculty/aim/2007/ltsa/default.htm

__R Packag__e http://www.stats.uwo.ca/faculty/aim/2007/ltsa/default.htm

CRAN:ltsa http://cran.us.r-project.org/web/packages/ltsa/index.html

4. 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.

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.

__Refereed
Conference Proceedings__

9. __Software implementation of numerical
algorithms in arbitrary precision, Krougly, Z.L., Jeffrey, D.J, Tsarapkina, D., 15th International Symposium on Symbolic
and Numeric Algorithms for Scientific Computing (SYNASC 2013), Editors: N. Bjorner et al., IEEE Computer Society, (2014), p. 132-138.__

10. Implementation and application of
extended precision in Matlab (2009), Krougly, Z.L.,
Jeffrey D.J., Proceedings of the Applied Computing Conference ACC '09, Editors:
N. Mastorakis et al., WSEAS Press, pp 103—108.

11. 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,

12. 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,

13. 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.

14. 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.

15. 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.

__Preprints and Work in Progress__

16.
__Numerical Laplace Transform and Inversion with Extended
Precision for Probability Distributions and Stochastic Modeling, __Krougly, Z.L., Stanford, D.A.

17.
__Extended Precision with Applications to Stochastic
Modeling, 26 pages, __Krougly,
Z.L.,
Stanford, D.A.

18.
Spot Fires and firebrand Distribution, Krougly, Z.L., Kulperger
D.J.,
Stanford, D.A.

__Software Packages in C++__

__List of C++ software
packages developed for and used in the aforementioned papers follows.__

__[1] Terrain disturbance
simulator (TDSimulator package) (2009).__

__ [2], [4], [13] Stochastic forest fire
simulator (FFSimulator package) (2009).__

__[3] Linear time series
analysis (ltsa package ).__

__R computer code can be
download from the following programming resources:__

__- R source package ltsa, version 1.4.2 (2012),
http://CRAN.R-project.org/package=ltsa.__

__- R source package FGN:Fractional gaussian
noise, estimation and simulation, version 1.4__

__ (2011), http://www.jstatsoft.org/v23/i05.\\__

__ [5], [14] Stochastic modeling of networks and
queues (ZEDNED package), 2005.__

__[6], [11], [12]
Almost-lack-of-memory distributions (ALM package) (2004), Revised November
2012.__

__ [9], [10] Multiple precision numerical
computing and complex analysis library (MPREC package), 2009-2015.__

__ [10] Matlab
double-double precision numerical computing and complex analysis library
(DDPREC package), 2009.__

**SOFTWARE PACKAGES in C# (in progress)**

__Big Data Analysis and
Object Oriented Programming, 2013 - 2015__