Lake Michigan 2018

I study the stochastic dynamics of complex biological and social systems, with a focus on computational biology of aging and chronic disease. My work develops probabilistic and PDE-based frameworks to model how damage, mutations, and cellular signaling errors accumulate over time, leading to systemic transitions such as disease onset or organ failure. Current projects include first-passage time models of aging, Bayesian state-space prediction of dialysis initiation in diabetic kidney disease, and mean field game models of mitochondrial–nuclear signaling under environmental stress. These projects integrate mathematical theory, computational simulation, and biological data, with the goal of building tractable models that connect microscopic mechanisms to macroscopic health outcomes.

I pursue a parallel line of research on stochastic control, agent-based modeling, and network resilience, motivated by parallels between biological systems and economic/social networks. I study how large populations of agents with partial information coordinate, fail, or undergo phase transitions, using tools from mean field games, optimal transport, and large deviation theory. This dual program aims to advance both the mathematical foundations of decentralized decision-making under uncertainty and their applications to urgent problems in aging, chronic disease, and systemic risk in complex adaptive systems.

(Some of these may not be up to date, so please reach out if you’d like to learn more)

Publications

1. Mean Field Modeling of Mitochondrial-Nuclear Signaling Games Under Environmental Stress [Under Review] [PDF]

   The mitochondrial-nuclear signaling interface represents a critical evolutionary partnership that maintains cellular homeostasis. We present a mean field game (MFG) framework to model how environmental stress disrupts this signaling equilibrium, leading to genomic instability and disease. By formulating mitochondrial-nuclear communication as a large-population signaling game with asymmetric information, we derive a coupled system of Hamilton-Jacobi-Bellman and Fokker-Planck equations that characterize equilibrium signaling strategies. Environmental perturbations are modeled as exogenous forcing terms that degrade signal fidelity and increase mutation risk. We prove that beyond critical exposure thresholds, the system undergoes equilibrium breakdowns corresponding to biological pathologies like cancer. The model provides quantitative predictions for mutation accumulation and suggests therapeutic interventions based on equilibrium restoration.

2. An Optimal Transport Characterization of Mean Field Games with Asymmetric Information [Under Review] [PDF]

   We study a class of Mean Field Games (MFGs) with asymmetric information, where a principal seeks to design an optimal signaling mechanism to influence the equilibrium behavior of a continuum of agents. Each agent observes a private signal drawn from a policy-dependent channel and updates their belief about an unobserved parameter affecting their dynamics. We prove the existence of an informed Mean Field Nash Equilibrium (MFNE) under general convexity, Lipschitz, and Bayesian regularity conditions using a fixed-point argument in the space of belief augmented distributions. Our main result establishes a novel duality between the principal’s signaling problem and a regularized optimal transport (OT) problem. Specifically, we show that the principal’s expected reward, optimized over signal distributions, is dual to a Sinkhorn-type entropy-regularized transport cost between prior and posterior-induced population distributions. This result links incentive design with convex geometry and provides an algorithmically tractable formulation for learning optimal signals. We generalize classical Bayesian persuasion by incorporating endogenous dynamics and strategic coupling across agents through the mean field, offering new insights into information design in large populations.

3. Free Energy, Phase Transitions, and Large Deviations in Random Graphs [Under Review] [PDF]

   This exposition presents a series of theorems motivated by the study of free energy in randomly growing networks. Inspired by the Azuma–Hoeffding inequality and Ising-like energy functions on random graphs, we develop rigorous tools to analyze phase transitions, graphon identification, and large deviations. The results draw on statistical mechanics, probability theory, and graph limit theory.

4. Aging as a First-Passage Process: Stochastic Thresholds, Repair Dynamics, and Mortality Emergence [Under Review] [PDF]

   Aging can be modeled as a stochastic accumulation of damage leading to system failure when a critical threshold is crossed. We analyze this process via the mean first-passage time (MFPT) of a standard stochastic differential equation of the form dXt = µ dt + σ dWt, where Xt denotes cumulative damage and failure occurs when Xt ≥ Xc. We derive several exact and asymptotic results for the MFPT and its dependence on control interventions, boundary thresholds, and repair dynamics. Specifically, we show that the MFPT is convex in the damage threshold Xc, revealing diminishing returns to resilience-enhancing interventions. We also establish that under optimal stochastic control, the control intensity scales super-linearly with damage, implying a biologically interpretable prioritization of repair with advancing age. Moreover, we prove that under broad classes of repair-enhanced models, the distribution of first-passage times converges to a Generalized Inverse Gaussian (GIG) form. In the state dependent regime we find the MFPT also offers a natural bridge to the Gompertz law and the conditions under which it fails. Taken together, these results unify a set of control-theoretic and probabilistic insights into the aging process, providing a quantitative framework to study the efficacy, limitations, and trade-offs of biological repair.

5. How Mitochondrial Signaling Games May Shape and Stabilize Nuclear-Mitochondrial Symbiosis (with Will Casey, Steven Massey, and Bud Mishra) [Biology 13(3), 187] [PDF]

   The eukaryotic lineage has enjoyed a long-term “stable” mutualism between nucleus and mitochondrion, since mitochondrial endosymbiosis began about 2 billion years ago. This mostly cooperative interaction has provided the basis for eukaryotic expansion and diversification, which has profoundly altered the forms of life on Earth. While we ignore the exact biochemical details of how the alpha-proteobacterial ancestor of mitochondria entered into endosymbiosis with a proto-eukaryote, in more general terms, we present a signaling games perspective of how the cooperative relationship became established, and has been maintained. While games are used to understand organismal evolution, information-asymmetric games at the molecular level promise novel insights into endosymbiosis. Using a previously devised biomolecular signaling games approach, we model a sender–receiver information asymmetric game, in which the informed mitochondrial sender signals and the uninformed nuclear receiver may take actions (involving for example apoptosis, senescence, regeneration and autophagy/mitophagy). The simulation shows that cellularization is a stabilizing mechanism for Pareto efficient sender/receiver strategic interaction. In stark contrast, the extracellular environment struggles to maintain efficient outcomes, as senders are indifferent to the effects of their signals upon the receiver. Our hypothesis has translational implications, such as in cellular therapy, as mitochondrial medicine matures. It also inspires speculative conjectures about how an analogous human–AI endosymbiosis may be engineered.

1. A Stochastic First Passage Time Framework for Predictive Modeling of Diabetic Kidney Disease Progression

   Diabetic Kidney Disease (DKD) is a leading cause of end-stage renal disease (ESRD) worldwide. Current predictive models, while effective for population-level risk stratification, fail to provide individualized, time-sensitive predictions about renal failure progression. We propose a novel approach using first-passage time (FPT) theory, conceptualizing kidney damage as a latent stochastic process subject to both endogenous drift and random biological fluctuations. This formulation yields closed-form survival functions, risk scores, and expected time-to-event estimates that are both analytically tractable and clinically interpretable. Crucially, our model can incorporate intervention effects as modifications to the drift and diffusion terms, enabling simulation of counterfactual trajectories. This work provides a new foundation for precision nephrology by offering forward-looking, personalized forecasts that integrate time, uncertainty, and treatment response.

2. Agent Based Models of International Electricity Supergrids: Physical Flows, Investments, and Welfare

   The accelerating shift toward renewable energy has revived interest in large-scale electricity supergrids as a means to smooth variability, improve reliability, and enhance welfare across regions. Yet the economic and systemic consequences of such integration remain uncertain, particularly in Asia where proposals for a regional supergrid face both technical and political barriers. This paper develops a mathematically rigorous agent-based model (ABM) of interconnected electricity grids that couples DC power-flow dynamics with adaptive agent behavior. Countries are modeled as heterogeneous agents making production, trade, and grid investment decisions, while transmission constraints, stochastic renewable generation, and market clearing are enforced through optimal power flow. Agents adapt policies such as carbon pricing and renewable mandates via reinforcement learning, and outcomes are evaluated in terms of social welfare, distributional gains and losses, and systemic fragility. The model is calibrated and validated using data from European cross-border electricity flows and Chinese ultra-high-voltage (UHV) projects, allowing us to benchmark the framework against real-world integration efforts. Counterfactual simulations of an Asian supergrid assess the potential costs, benefits, and vulnerabilities under alternative cooperation regimes and political frictions. Results highlight both the aggregate efficiency gains of deep interconnection and the uneven distribution of benefits, underscoring the need for institutional mechanisms to share costs and manage risks. By uniting physical power-system modeling with adaptive agent behavior, this paper provides a new quantitative foundation for evaluating the feasibility and robustness of regional electricity supergrids.

3. From Disorder to Design: Information-Theoretic Frameworks for Biological Aging

   Aging has traditionally been modeled as the progressive accumulation of damage, but this perspective alone cannot fully capture the systemic, information-rich nature of biological decline. Here we develop and compare three information-theoretic paradigms of aging. First, in the entropy model, aging corresponds to rising systemic uncertainty, reflecting the loss of regulatory coherence within cells and tissues. Second, in the mutual information model, aging is characterized as a decline in the capacity of one biological level (e.g., genotype, epigenome) to transmit useful information to another (e.g., phenotype, cellular function). Third, drawing on rate-distortion theory, we frame aging not as failure, but as the expected distortion that arises when biological systems optimize fidelity under metabolic and evolutionary constraints. Each framework highlights different aspects of decline: entropy captures disorder, mutual information reveals regulatory decoupling, and rate-distortion exposes fundamental trade-offs in design. Together, these perspectives suggest that aging is best understood not as a single process of decay, but as the convergence of uncertainty, communication breakdown, and constrained optimization across biological scales. This integrative framework offers both testable predictions (through entropy and information loss metrics) and a unifying principle linking cellular dynamics, tissue coordination, and evolutionary design.

Work in Progress