## Professor and Graduate Program Coordinator

Department of Mathematics

California State University San Marcos

bjoshi at csusm dot edu

Administrative Building, Room 6232

## Professional Trajectory

Currently I am the Graduate Program Coordinator. Contact me if you are interested in pursuing a Masters degree in Mathematics at CSUSM.

- 2023-present: Professor at California State University San Marcos.
- 2018-2023: Associate Professor at California State University San Marcos.
- 2013-2018: Assistant Professor at California State University San Marcos.
- 2012-2013: Postdoctoral Fellow at University of Minnesota.
- 2009-2012: Assistant Research Professor at Duke University.
- 2009: PhD in Mathematics, Ohio State University.
- 2004: MS in Physics, Ohio State University.
## Teaching:

I have been teaching several graduate classes recently including:My research area is mathematical biology. In recent years, I've been working mostly on the theory and applications of reaction networks. Reaction network theory draws on mathematical tools from real analysis, dynamical systems, algebraic geometry, graph theory, and stochastic processes to understand the dynamics of biochemical reaction networks.

- Mathematics of Biochemical Reaction Networks (Math 490), Spring 2024,
- General Topology (Math 555), Fall 2023,
- Calculus of Variations (Math 537), Spring 2023,
- Ordinary differential equations (Math 532), Fall 2022,
- Stochastic Processes (Math 570), Spring 2022,
- Partial differential equations (Math 534), Fall 2021.
## Preprints

Chemical mass-action systems as analog computers: implementing arithmetic computations at specified speed, with David F. Anderson, arXiv, submitted April 2024.

## Research Publications

Bifunctional enzyme provides absolute concentration robustness in multisite covalent modification networks, with Tung D. Nguyen,Journal of Mathematical Biology, Vol. 88, 36 (2024). arXiv.

Development of the sleep-wake switch in rats during the P2-P21 early infancy period, with Mainak Patel,Frontiers in Network Physiology: Networks in Sleep and Circadian Systems, Vol. 3, 2023.

Power-engine-load form for dynamic absolute concentration robustness, with Gheorghe Craciun,SIAM Journal on Applied Mathematics, Vol. 83, Iss. 6, (2023). arXiv.

Prevalence of multistationarity and absolute concentration robustness in reaction networks, with Nidhi Kaihnsa, Tung D. Nguyen, and Anne Shiu,SIAM Journal on Applied Mathematics, Vol. 83, Iss. 6, (2023). arXiv.

Reaction Network Motifs for Static and Dynamic Absolute Concentration Robustness, with Gheorghe Craciun,SIAM Journal on Applied Dynamical Systems, Vol. 22, No. 2, pp. 501-526, (2023). arXiv.

Foundations of Static and Dynamic Absolute Concentration Robustness, with Gheorghe Craciun,Journal of Mathematical Biology, Vol. 85, 53 (2022), arXiv.

Transition graph decomposition for complex balanced reaction networks with non-mass-action kinetics, with Daniele Cappelletti,Stochastic methods for biological systems, special issue ofMathematical Biosciences and Engineering, Vol. 19, Issue 8, (2022), arXiv.

Multistationarity in cyclic sequestration-transmutation networks, with Gheorghe Craciun, Casian Pantea, and Ike Tan,Bulletin of Mathematical Biology, 84:65 (2022), arXiv.

Autocatalytic recombination systems: A reaction network perspective, with Gheorghe Craciun, Abhishek Deshpande, and Polly Y. Yu,Mathematical Biosciences, Vol. 345 (2022) 108784, arXiv.

On reaction network implementations of neural networks, with David F. Anderson, and Abhishek Deshpande,Journal of Royal Society Interface, Vol. 18, Issue 177 (April 2021). arXiv.

Autocatalytic Networks: An Intimate Relation between Network Topology and Dynamics, with Gheorghe Craciun,SIAM Journal on Applied Mathematics, Vol. 81, issue:4, pp.1623-1644 (August 2021), arXiv.

Detailed balance = complex balance + cycle balance: A graph-theoretic proof for reaction networks and Markov chains, with Stefan Müller, arXiv,Bulletin of Mathematical Biology, Vol. 82, Article number: 116 (September 2020).

Graphically balanced equilibria and stationary measures of reaction networks, with Daniele Cappelletti,SIAM Journal on Applied Dynamical Systems, Vol. 17, pp.2146-2175 (August 2018). arXiv.

Deterministic Stability Regimes and Noise-Induced Quasistable Behavior in a Pair of Reciprocally Inhibitory Neurons, with Mainak Patel,Journal of Theoretical Biology, Vol. 441, pp.68-83 (March 2018), Link.

Which small reaction networks are multistationary?, with Anne Shiu,SIAM Journal on Applied Dynamical Systems, Vol. 1618, No.2, pp.802-833 (April 2017). arXiv.

Modeling the Evolving Oscillatory Dynamics of the Rat Locus Coeruleus Through Early Infancy, with Mainak Patel,Brain Research, 1618, pp. 181-193 (August 2015), Link.

A survey of methods for deciding whether a reaction network is multistationary, with Anne Shiu,Chemical Dynamicsspecial issue of Mathematical Modelling of Natural Phenomena, 10, pp. 47-67 (August 2015) arXiv.

A detailed balanced reaction network is sufficient but not necessary for its Markov chain to be detailed balanced,Discrete and Continuous Dynamical Systems - Series B, 20, pp. 1077-1105 (June 2015), arXiv,

Encoding Whisker Deflection Velocity within the Rodent Barrel Cortex using Phase-Delayed Inhibition, with Runjing Liu and Mainak Patel,Journal of Computational Neuroscience, 37, pp. 387-401 (December 2014), Link.

Switching mechanisms and bout times in a pair of reciprocally inhibitory neurons, with Mainak Patel.Journal of Computational Neuroscience, 36, pp. 177-191 (February 2014), Link.

Decoding synchronized oscillations within the brain: phase-delayed inhibition provides a robust mechanism for creating a sharp synchrony filter, with Mainak Patel.Journal of Theoretical Biology, 334, pp. 13-25 (October 2013), Preprint version (contains supplementary information), Link.

Encoding with synchrony: phase-delayed inhibition allows for reliable and specific stimulus detection, with Mainak Patel.Journal of Theoretical Biology, 328, pp. 26-32 (July 2013), Link.

Complete characterization by multistationarity of fully open networks with one non-flow reaction,Applied Mathematics and Computation, 219:12, pp. 6931-6945 (February 2013). arXiv

Atoms of multistationarity in chemical reaction networks, with Anne Shiu.Journal of Mathematical Chemistry, 51:1, pp. 153-178 (2013). arXiv

Simplifying the Jacobian criterion for precluding multistationarity in chemical reaction networks, with Anne Shiu.SIAM J. Appl. Math., 72:3, pp. 857-876 (2012). arXiv

Order of magnitude time-reversible Markov chains and characterization of clustering processes(October 2011). arXiv

A doubly stochastic Poisson process for wake-sleep cycling, Ph.D. Dissertation, July 2009.

On immunotherapies and cancer vaccination protocols: A mathematical modelling approach, with Xueying Wang, Sayanti Banerjee, Haiyan Tian, Anastasios Matzavinos, and Mark A.J. Chaplain.Journal of Theoretical Biology, 259:4, pp.820-827 (August 2009), Link.

Developmental emergence of power-law wake behavior depends upon the functional integrity of the Locus Coeruleus, with Andrew Gall, Janet Best, Virginia R. Florang, Jonathan A. Doorn and Mark Blumberg.Sleep, 32:7 (2009), Link.