arXiv subjects

Bhargav R. Karamched

Publications and source records attributed to Bhargav R. Karamched.

7 recordsLinked to original sources

arXiv2026

Navigating the Delicate Geometry of Beehive Mite Infestation with Optimal Control

The parasitic mite Varroa destructor poses a severe existential threat to global honey bee Apis mellifera populations. In this paper, we present a dynamical systems model of hive-mite interactions incorporating a eusocial Allee effect to evaluate the efficacy of chemical interventions. We partition treatments into ``soft'' miticides (targeting phoretic mites) and ``harsh'' miticides (penetrating the capped brood to target reproductive mites). Our bifurcation analysis reveals a fundamental trade-off: while harsh treatments effectively eradicate the protected mite reservoir by shifting the transcritical bifurcation boundary, they impose sublethal toxicity on the bees. We analytically show that exceeding a critical dosage threshold culminates in a catastrophic saddle-node bifurcation that guarantees colony collapse. To navigate this toxicity limit, we formulate an optimal control problem using Pontryagin's Maximum Principle. Numerical solutions reveal that a dynamic ``shock and maintain'' cocktail strategy optimally balances reservoir clearance with hive viability. Expanding the model to include treatment-resistant strains demonstrates that single-chemical reliance forces the hive onto a highly toxic, nearly unsustainable chemical treadmill. Finally, our mathematical framework yields a striking ecological prediction: because the eradication boundary scales intimately with the colony's carrying capacity, unchecked mite pressure will likely exert evolutionary forces that select for smaller, naturally resistant hives over the massive colonies favored by commercial agriculture.

q-bio.PE↗

arXiv2026

Entropic Collapse and Extreme First-Passage Times in Discrete Ballistic Transport

We investigate the extreme first-passage statistics of $N$ non-interacting random walkers on discrete, hierarchical networks. {By distinguishing between transport limited by escape from localized initial states (injection-limited) and transport limited by the extended network (bulk-limited), we identify a class of extreme value statistics that arises in geometries dominated by source traps (e.g., the Comet graph).} In this regime, the distribution of the minimum arrival time does not converge to any of the classical generalized extreme value distributions. Instead, it follows a discrete distribution with a {strict lower time bound} determined by the properties of the hierarchical network. We analytically derive the asymptotic behavior of this class and validate our predictions against Monte Carlo simulations. Crucially, we identify the mechanism of ``entropic collapse" that destroys this scaling in bulk-dominated geometries like the Bethe lattice, where the phase space of delayed paths diverges with distance. This work establishes a geometry-encoding function that acts as a diagnostic tool for ascertaining whether or not a given graph is hierarchical.

math-ph↗

arXiv2026

Macroscopic Dominance from Microscopic Extremes: Symmetry Breaking in Spatial Competition

How do competing populations convert a spatial advantage into macroscopic dominance? We introduce a stochastic model for resource competition that decouples the transient discovery phase from monopolization. Initial symmetry breaking is governed by extreme value statistics of first-passage times: a linear spatial disadvantage requires an exponentially larger population to overcome. However, transient superiority cannot stabilize dominance. A non-reciprocal interaction bias is strictly necessary to arrest local fluctuations and drive the system into a robust absorbing state.

q-bio.PE↗

arXiv2025

Dynamic homeostasis in relaxation and bursting oscillations

Homeostasis, broadly speaking, refers to the maintenance of a stable internal state when faced with external stimuli. Failure to manage these regulatory processes can lead to different diseases or death. Most physiologists and cell biologists around the world agree that homeostasis is a fundamental tenet of their disciplines. Nevertheless, a precise definition of homeostasis is hard to come by. Often times, homeostasis is simply defined as ``you know it when you see it''. Mathematical treatments of homeostasis involve studying equilibria of dynamical systems that are relatively invariant with respect to parameters. However, physiological processes are rarely static and often involve dynamic processes such as oscillations. In such dynamic environments, quantities such as average values may be relatively invariant with respect to parameters. This has been referred to as ``homeodynamics''. We present a general framework for homeodynamics involving systems with two or more time scales that elicits homeostasis in the temporal average of a species. The key point is that homeostasis manifests when measuring the slow variable responsible for driving oscillations and is not apparent in the fast variables. We demonstrate this in the Fitzhugh-Nagumo model for relaxation oscillations and then in two models for electrical bursting activity and calcium oscillations in pancreatic $β$-cells. One of these models has multiple slow variables, each driving the bursting oscillations in different parameter regimes, but homeodynamics is only present in the variable currently engaged in this role.

math.DS↗

arXiv2024

Fast decisions reflect biases, slow decisions do not

Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in large groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased, and hence make better choices. We obtain asymptotic expressions in the large population limit that quantify how agents' initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in non-trivial ways to determine the reliability of decisions in a group.

physics.soc-ph↗

arXiv2023

Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model where stochastic delays evolve by a continuous-time Markov chain, and between switching events, the system of interest evolves via a deterministic delay equation. Our main contribution is the calculation of an effective delay equation in the fast switching limit. This effective equation maintains the influence of all subsystem delays and cannot be replaced with a single effective delay. To illustrate the relevance of this calculation, we investigate a simple model of stochastically switching delayed feedback motivated by gene regulation. We show that sufficiently fast switching between two oscillatory subsystems can yield stable dynamics.

q-bio.MN↗

arXiv2023

Correlated Information Reduces Accuracy of Pioneering Decision-Makers

Normative models are often used to describe how humans and animals make decisions. These models treat deliberation as the accumulation of uncertain evidence that terminates with a commitment to a choice. When extended to social groups, such models often assume that individuals make independent observations. However, individuals typically gather evidence from common sources, and their observations are rarely independent. Here we ask: For a group of ideal observers who do not exchange information, what is the impact of correlated evidence on decision accuracy? We show that even when agents are identical, correlated evidence causes decision accuracy to depend on temporal decision order. Surprisingly, the first decider is less accurate than a lone observer. Early deciders are less accurate than late deciders. These phenomena occur despite the fact that the rational observers use the same decision criterion, so they are equally confident in their decisions. We analyze discrete and continuum evidence-gathering models to explain why the first decider is less accurate than a lone observer when evidence is correlated. Pooling the decisions of early deciders using a majority rule does not rescue accuracy in the sense that such pooling results in only modest accuracy gain. Although we analyze an idealized model, we believe that our analysis offers insights that do not depend on exactly how groups integrate evidence and form decisions.

physics.soc-ph↗