Related papers: Physiological Aging as an Infinitesimally Ratchete…
At the physiological level, aging is neither rigid nor unchangeable. Instead, the molecular and mechanisms driving aging are sufficiently plastic that a variety of diverse interventions--dietary, pharmaceutical, and genetic--have been…
Results on the behaviour of the rightmost particle in the $n$th generation in the branching random walk are reviewed and the phenomenon of anomalous spreading speeds, noticed recently in related deterministic models, is considered. The…
Aging, the dependence of the dynamics of a physical process on the time $t_a$ since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of…
As written by statistician George Box "All models are wrong, but some are useful", standard diffusion derivation or Feynman path ensembles use nonphysical infinite velocity/kinetic energy nowhere differentiable trajectories - what seems…
We investigate the role of a time and spin-dependent phase shift on the evolution of one-dimensional discrete-time quantum walks. By employing Floquet engineering, a time and spin-dependent phase shift ($\phi$) is imprinted onto the…
Author's early work on aging is developed to yield a relationship between life spans and the velocity of aging. The mathematical analysis shows that the mean extent of the advancement of aging throughout one's life is conserved, or…
As a model of market price, we introduce a new type of random walk in a moving potential which is approximated by a quadratic function with its center given by the moving average of its own trace. The properties of resulting random walks…
We consider the group of permutations of the vertices of a lattice. A random walk is generated by unit steps that each interchange two nearest neighbor vertices of the lattice. We study the heat equation on the permutation group, using the…
We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources.…
Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment…
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…
We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours…
We address the theory of records for integrated random walks with finite variance. The long-time continuum limit of these walks is a non-Markov process known as the random acceleration process or the integral of Brownian motion. In this…
We establish an analogy between the Fokker-Planck equation describing evolutionary landscape dynamics and the Schr\"{o}dinger equation which characterizes quantum mechanical particles, showing how a population with multiple genetic traits…
Consider a branching random walk evolving in a macroscopic time-inhomogeneous environment, that scales with the length $n$ of the process under study. We compute the first two terms of the asymptotic of the maximal displacement at time $n$.…
We construct a pathwise formulation of a growing population of cells, based on two different samplings of lineages within the population, namely the forward and backward samplings. We show that a general symmetry relation, called…
Once the problem of ensemble averaging is removed, correlations between the response of a single molecule to an external driving field $F$, with the history of fluctuations of the particle, become detectable. Exact analytical theory for the…
We present an analytical approximation scheme for the first passage time distribution on a finite interval of a random walker on a random forcing energy landscape. The approximation scheme captures the behavior of the distribution over all…
In empirical studies of random walks, continuous trajectories of animals or individuals are usually sampled over a finite number of points in space and time. It is however unclear how this partial observation affects the measured…