Professor of Mathematics
Department of Mathematics, California State University San Marcos
bjoshi at csusm dot edu · Google Scholar · ORCID · CV
After a PhD at Ohio State (2009) and postdoctoral positions at Duke University (2009–12) and the University of Minnesota (2012–13), I joined CSUSM in 2013 and was promoted to full Professor in 2023.
Computing max(a,b) as a composition of elementary chemical reaction gates (Anderson & Joshi 2025).
Chemical reactions are a powerful computational substrate, raising the exciting prospect of implementing computation using biomolecules inside a living cell. We use mathematical theory of reaction networks and dynamical systems to develop algorithms that complement and guide breakthroughs in synthetic biology.
An analog computer based on reaction networks is naturally suited to simulating continuous processes such as differential equations. Arithmetic and transcendental functions are also essential, and implementing them reliably on an analog substrate comes with unique challenges — especially since analog computers interface directly with continuous, real-world signals. One challenge we identified: for generic algorithms, computation speed can depend not only on the operation but on the specific input values. A single slow step can become rate-limiting. We developed novel reaction network algorithms that achieve input-independent speed for all arithmetic operations and for exponential and logarithmic functions, giving robust and fast analog molecular computation.
[30][32][34][20]
A substrate hypergraph (Joshi & Nguyen 2026) for a network with 3 composite reactions: Xp + Y → X + Yp, X + Ypp → Xp + Yp, 2Yp → Ypp + Y
The chemistry of life — biochemistry — has a unique structure that goes beyond ordinary chemistry. Biomolecules have special roles: substrates are the stars of the show, while enzymes direct the action. By focusing on substrates and codifying their interactions as a substrate hypergraph, we set aside the enzymes, intermediate compounds, and detailed internal reaction steps — not as a loss of information but as a gain in clarity, since major dynamical properties are agnostic to these hidden details, which may anyway be experimentally unknown. A graph-theoretic invariant we call hypergraph current turns out to be a key object: its structure governs existence, uniqueness, and stability of steady states, absolute concentration robustness, and bifurcation behavior — giving a unified dynamical portrait of the biochemical system from the hypergraph topology.
[31][33][29]
An atom of multistationarity and four descendants (Joshi & Shiu 2013).
The dynamics of a reaction network are difficult to characterize without knowing the reaction rate constants — and those constants aren’t truly constant, fluctuating with the environment in ways that are often unknown. Classical theory offers network conditions that rule out multistationarity, but not conditions that rule it in: the capacity to switch between distinct steady states, a behavior central to biological decision-making. We showed that multistationarity can be inherited: under well-defined conditions, a larger network acquires it from smaller networks embedded within. The smallest networks with this capacity we called atoms of multistationarity — the irreducible building blocks from which all multistationary behavior is assembled. Identifying new atoms and finding them operating inside real biochemical systems remains an active frontier.
[6][7][13][15][26][22]
Other research topics include:
static and dynamic absolute concentration robustness
[24][25][26][27] stochastic models of reaction networks
[12][17][23]
MATH 448: Mathematical Models and Methods in Biology — Fall 2026 (course materials, interactive tools, homework)
In September 2025, I ran my first ever marathon — the Ladakh Marathon in Leh, Ladakh, India, at an elevation of 11,155 ft (3,401 m), where the air holds just 65% of the oxygen at sea level. The route passes through villages whose children line the course to high-five the runners; somehow that energy almost makes up for the altitude. Since then I have run three marathons on three continents, a half marathon, and the Big Sur 21-miler — where runners cross the iconic Bixby Creek Bridge to the sound of a grand piano played live at the cliff’s edge above the Pacific.
In October 2025, I completed a 14-day trek to Everest Base Camp — my first ever multiday hike. Heavy unseasonal snowfall in the opening days brought weather warnings and fears of being stranded; as it turned out, those same snows made the final push to Base Camp all the more dramatic and unforgettable.
