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The fundamental relationship between the mesoscopic structure of neuronal circuits and organismic functions they subserve is one of the major challenges in contemporary neuroscience. Formation of structurally connected modules of neurons…
We use immobility as an origin and reference for the measurement of locomotor behavior; speed, the direction of walking and the direction of facing as the three degrees of freedom shaping fly locomotor behavior, and cocaine as the parameter…
Undulatory locomotion, as seen in the nematode \emph{Caenorhabditis elegans}, is a common swimming gait of organisms in the low Reynolds number regime, where viscous forces are dominant. While the nematode's motility is expected to be a…
Unentangled wormlike micelle solutions relax stress through a dynamic interplay of reversible scission and intrachain relaxation involving a hierarchy of molecular timescales whose relationship to linear viscoelastic response remains…
Animal behavior spans many timescales, from short, seconds-scale actions to circadian rhythms over many hours to life-long changes during aging. Most quantitative behavior studies have focused on short-timescale behaviors such as locomotion…
We demonstrate the phenomenon of cumulative inertia in intracellular transport involving multiple motor proteins in human epithelial cells by measuring the empirical survival probability of cargoes on the microtubule and their detachment…
The purpose of this paper is to implement a random death process into a persistent random walk model which produces subballistic superdiffusion (L\'{e}vy walk). We develop a Markovian model of cell motility with the extra residence variable…
Advances in GPS telemetry technology have enabled analysis of animal movement in open areas. Ecologists today are utilizing modern analytic tools to study animal behaviors from large quantity of GPS coordinates. Analytic tools with…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
Understanding the dynamical behavior of complex systems from their underlying network architectures is a long-standing question in complexity theory. Therefore, many metrics have been devised to extract network features like motifs,…
1. Spatial memory plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in…
Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks and theoretical methods, we can begin to probe the complex lives of microscopic motile…
We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…
Life presents fascinating examples of self-organization and emergent phenomena. In multi-cellular organisms, a multitude of cells interact to form and maintain highly complex body plans of well-defined size. In this thesis, we investigate…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
Animal movement exhibits complex behavior which can be influenced by unobserved environmental conditions. We propose a model which allows for a spatially-varying movement rate and spatially-varying drift through a semiparametric potential…
Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null…
Many living and artificial systems show a similar emergent behavior and collective motions on different scales, starting from swarms of bacteria to synthetic active particles, herds of mammals and crowds of people. What all these systems…
Motile biological cells in tissue often display the phenomenon of durotaxis, i.e. they tend to move towards stiffer parts of substrate tissue. The mechanism for this behavior is not completely understood. We consider simplified models for…