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### Javad Tavakoli, PhD

#### Professor

###### Mathematics

**Other Titles:**Adjunct Professor, Carleton University

**Office:**SCI 114

**Office Hours:**Tuesdays and Thursdays from 3:30pm to 4:30pm

**Phone:**(250) 317-5373

**Email:**javad.tavakoli@ubc.ca

Graduate student supervisor

## Research Summary

Information geometry, topological data analysis, queueing theory and applications in telecommunication systems, random walks in quarter plane and applications in probability modeling.

## Courses & Teaching

Recent teaching: Algebraic Number Theory, Abstract Algebra I & II, Stochastic Processes, Queueing Theory, Calculus (all levels), Topology, Algebraic Topology, Topological Data Analysis, Applied Probability, and many Directed Studies in different areas in Math.

## Biography

Founded on a university career of more than 40 years, my teaching experience spans a wide range of courses in mathematics for graduate and undergraduate students in science, education and engineering. I have taught in several Canadian universities including UBC Okanagan, Carleton University, and the Univ. of Sask. My specialty at undergrad level covers most of the courses such as (linear) algebra, complex analysis, calculus and more, while at the graduate level my interests cover algebra (groups, rings, and homological), (algebraic) topology, stochastic process, applied probability, queuing theory, complex geometry, sheaf theory, category theory, complex functions theory, fuzzy (logic) sets. My commitment to diversity, equity and inclusion is evident in the fact that my (grad) students come from diverse backgrounds and cultures. I take pride in seeing my students succeed and the fact that my teaching experience has led to rewarding collaborations with Canadian and foreign universities.

## Degrees

Postdoc, Dalhousie University

PhD, Dalhousie University

MSc Shiraz University

## Research Interests & Projects

My research activities have centered around key or fundamental issues in probability modeling and performance analysis for complex systems, especially, application of Markov decision process (MDP) incorporated with the reinforcement learning (RL) in health, application of random walks and recently working on robust optimization with applications on health and finance. My HQP training has largely focused on these areas. My research program deals with addressing fundamental and challenging topics in these research fields, motivated by innovative applications in health, finance, telecommunications and computer networks.

Graduates (supervised):

- Maryam Bayat, PhD: “Riemannian learning and it application in finance”
- Nima Eslami, PhD: “robust optimization & ML”
- Mohamad Mosaffa, MSc: “application of deep learning in waiting time queuing systems.”
- Amirhossein Salami, MSc: “digital marketplace platform inventory”
- Nick Rieske, MSc: “algebraic number theory”
- Ruichao Jaing, Postdoc Fellow: “information geometry”
- Yann Vestring, PhD: “steady state Markov chain solution by simulation”
- Marjan Yaghoubi, MSc: “an application of ML in Alzheimer disease”
- Ruichao Jiang, PhD: “a problem in differential manifold)
- Chad Davis, PhD: algebraic number theory”
- Araz Sholehkerdar, PhD: “image processing”
- Elham Kiyani, PhD: “Non-convex Vector Optimization”
- Ali Tirdad, PhD: “an application of queueing system in ER”
- Maryam Sadeghi, MSc: “an application of coding in computers”
- Morgan Roosenmaallen, MSc: “kinematic topological modeling of RNA”
- Cody Epema, MSc: “application of BVP in random walk in the quarter plane”
- Zafar Zafari, MSc: “random walk in the half plane”
- Banani Battacharja, MSc: “an algorithm to obtain the stationary solution of Markov chains”
- And more than 20 undergraduate research assistant (URA & USRA) in the different areas mentioned above.

## Selected Publications & Presentations

**Books**

- Numerical Methods for Solving Discrete Event Systems with Applications to Queueing Systems Springer 2022, 361 pages.
- Mathematics from an Aboriginal Perspective, 4th edition 2018, UBC Publication.

**Published Papers**

- Laplacian Operator on Statistical Manifold, submitted to Information Geometry,2022, Doi: 10.1007/s41884-022-00070-0.
- A new image fusion quality measure based on localized edge strength and mutual information, accepted with minor revision, IEEE Access, 2023.
- An upper bound and criteria for the Galois group of weighted walks with rational coefficients in the quarter plane, Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 563-576.
- Non-convex Vector Optimization and Optimality Conditions for Proper Efficiency. Int. J. Anal. Appl. (2022), 20:11.
- Optimal Conditions for Approximate Solutions of Set-valued Optimization Problems in Real Linear Spaces. TWMS J. App. and Eng. Math. V.11, N.2, 2021, pp. 395-407.
- Weyl Prior and Bayesian Statistics. Entropy (2020), 22(4), 467; doi:10.3390/e22040467.
- Theoretical Analysis of Image Fusion Quality Measure Based on T-Sallies Entropy. Information Fusion 58 (2020) 69–81.
- The distribution of the line length in a discrete GI/G/1 queue. Performance Evaluation, 131 (2019) 43-53.
- A Numerical method to determine the waiting time and the idle time distributions of a GI/G/1 queue when inter-arrival times and / or service times have geometric tails. INFOR: Information Systems and Operational Research. DOI:10.1080/03155986.2018.1533775, (published on line 23 Jan 2019).
- In-depth analysis of Tsallis entropy-based measures for image fusion quality assessment. Optical Engineering 58(3), 033102 (March 2019).
- Optimal Policies of M(t)/M/c/c Queues with Two Different Level of Servers. European Journal of Operational Research (EJOR), 249 (3), pp 1124-1130, 2016.
- Efficient Methods to Find the Equilibrium Distribution of the Number in GI/M/c Queues. INFOR, Vol. 52, No. 4, 2015.
- Analysis of Exact Tail Asymptotic for Singular Random Walks in the Quarter Plane. Queueing Systems, DOI 10.1007/s11134-012-9321y, 2012.
- New Approach for Fuzzy Control and Analysis of Queueing Systems with Flexible Service Time. Lecture Notes in Engineering and Computer Science, 2189(1): 1139 – 1143, 2011.
- Comparing Some Algorithms for Solving QBD Processes Exhibiting Special Structures. INFOR, Vol. 48, No 3, 2010, pp. 133-141.
- Transient Solutions for Multi-server Queues with Infinite Buffers. Queueing Systems, 65:35-49, 2009.
- Spectrum of Certain Tridiagonal Matrices when their Dimension goes to Infinity. Linear Algebra and Its Applications, 431:1208-1217, 2009.
- The Continuous Spectrum for M/M/c Queue. Linear and Multilinear Algebra, 56, No. 3: 319-331, 2008.
- Stochastic and Substochastic Solutions for Infinite-state Markov Chains with Applications to Matrix Analytic Methods. Advances in Applied Probability, 40.4: 1157-1173, 2008.
- A Bayesian Approach to Find Random-time Probabilities from Embedded Markov Chain Probabilities. Probability in the Engineering and Informational Sciences, 21: 551-556, 2007.
- Two-station Queuing Networks with Moving Servers, Blocking, and Customer Loss. The Electronic Journal of Linear Algebra, 13: 72 – 89, 2005.
- A Tandem Queue with a Movable Server: An Eigenvalue Approach. SIAM Journal on Matrix Analysis & Applications. 24.2: 465 – 474, 2002.
- Categorical Constructions in C*-Algebras Theory. Journal of the Australian Mathematical Society. 73.1: 97 – 113, 2002.
- Tiny Objects in the Category of M-sets. Italian Journal of Pure and Applied Mathematics. 10: 153 – 162, 2001.
- On the Category of M-sets. Far East Journal of Mathematical Sciences. 2.2: 251 – 260, 2000.
- Locally Free Vector Spaces in a Topos. Communications in Algebra. 24.4: 1199 – 1205, 1996.
- Sheaves on Posets. Proceedings of the 25th Annual Iranian Mathematics Conference. Tehran, Iran (1994). T
- A Note on the Sheaf Functor. Bulletin of the Iranian Mathematical Society.18.1: 1 – 7, 1992.
- On Topologies in a Topos. Bulletin of the Australian Mathematical Society. 41.3: 387 – 392, 1990.
- Tensor Products on Modules in a Topos. Bulletin of the Iranian Mathematical Society. 11.1-2: 23 – 32, 1988.
- A Characterization of Geometric Fields in a Topos. Communications in Algebra. 13.1: 101 – 111, 1985.
- On Products of Modules in a Topos”. Journal of the Australian Mathematical Society. 38.3: 416 – 420, 1985.
- Normal Forms of Matrices in Topoi. Cahiers de topologie et géométrie différentielle. 23.3: 317 – 340, 1982.
- Elements of Free Modules in Topoi. Communications in Algebra. 10.2: 171 – 201, 1982.

**Presentations**

Numerous research presentations in Canada and abroad.

## Selected Grants & Awards

NSERC Grants