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Researcher profile

Aanjaneya Kumar

Aanjaneya Kumar contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
cond-mat.stat-mechmath.PRPopulations and EvolutionBiological Physicsphysics.soc-phSocial and Information Networks

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4 published item(s)

preprint2026arXiv

Branching under First-Passage Resetting

Many biological processes, from cell division to viral lysis, are triggered when an internal stochastic variable reaches a threshold. Here we introduce Branching under First-Passage Resetting, a general framework in which replication events arise endogenously from first-passage dynamics rather than from externally imposed lifetime clocks. We show that the resulting population dynamics obey an exact renewal equation linking single-trajectory first-passage statistics to the population growth rate. This mapping shows that, for fixed offspring number and fixed mean replication time, stochastic timing fluctuations necessarily enhance growth relative to a deterministic clock. When offspring yield depends on the first-passage time, however, fluctuations have non-trivial effects and expose a fundamental yield-delay trade-off: waiting longer can increase the number of descendants, but delays all future lineages. Our framework allows us to address this optimization problem analytically, and upon application to bacteriophage lysis, gives an optimal lysis time and growth rate consistent with empirical data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The evolution of trust and trustworthiness

Trust and trustworthiness form the basis for continued social and economic interactions, and they are also fundamental for cooperation, fairness, honesty, and indeed for many other forms of prosocial and moral behavior. However, trust entails risks, and building a trustworthy reputation requires effort. So how did trust and trustworthiness evolve, and under which conditions do they thrive? To find answers, we operationalize trust and trustworthiness using the trust game with the trustor's investment and the trustee's return of the investment as the two key parameters. We study this game on different networks, including the complete network, random and scale-free networks, and in the well-mixed limit. We show that in all but one case the network structure has little effect on the evolution of trust and trustworthiness. Specifically, for well-mixed populations, lattices, random and scale-free networks, we find that trust never evolves, while trustworthiness evolves with some probability depending on the game parameters and the updating dynamics. Only for the scale-free network with degree non-normalized dynamics, we find parameter values for which trust evolves but trustworthiness does not, as well as values for which both trust and trustworthiness evolve. We conclude with a discussion about mechanisms that could lead to the evolution of trust and outline directions for future work.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Improved Upper Bounds on the Asymptotic Growth Velocity of Eden Clusters

We consider the asymptotic shape of clusters in the Eden model on a d-dimensional hypercubical lattice. We discuss two improvements for the well-known upper bound to the growth velocity in different directions by that of the independent branching process (IBP). In the IBP, each cell gives rise to a daughter cell at a neighboring site at a constant rate. In the first improvement, we do not allow such births along the bond connecting the cell to its mother cell. In the second, we iteratively evolve the system by a growth as IBP for a duration $Δ$ t, followed by culling process in which if any cell produced a descendant within this interval, who occupies the same site as the cell itself, then the descendant is removed. We study the improvement on the upper bound on the velocity for different dimensions d. The bounds are asymptotically exact in the large-d limit. But in $d =2$, the improvement over the IBP approximation is only a few percent.

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preprint2019arXiv

TASEP Speed Process: An Effective Medium Approach

We discuss the approximate phenomenological description of the motion of a single second-class particle in a two-species totally asymmetric simple exclusion process (TASEP) on a 1D lattice. Initially, the second class particle is located at the origin and to its left, all sites are occupied with first class particles while to its right, all sites are vacant. Ferrari and Kipnis proved that in any particular realization, the average velocity of the second class particle tends to a constant, but this mean value has a wide variation in different histories. We discuss this phenomena, here called the TASEP Speed Process, in an approximate effective medium description, in which the second class particle moves in a random background of the space-time dependent average density of the first class particles. We do this in three different approximations of increasing accuracy, treating the motion of the second-class particle first as a simple biassed random walk in a continuum Langevin equation, then as a biased Markovian random walk with space and time dependent jump rates, and finally as a Non-Markovian biassed walk with a non-exponential distribution of waiting times between jumps. We find that, when the displacement at time $T$ is $x_0$, the conditional expectation of displacement, at time $zT$ ($z>1$) is $zx_0$, and the variance of the displacement only varies as $z(z-1)T$. We extend this approach to describe the trajectories of a tagged particle in the case of a \emph{finite} lattice, where there are $L$ classes of particles on an $L$-site line, initially placed in the order of increasing class number. Lastly, we discuss a variant of the problem in which the exchanges between adjacent particles happened at rates proportional to the difference in their labels.

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