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Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
Humans experience small fluctuations in their gait when walking on uneven terrain. The fluctuations deviate from the steady, energy-minimizing pattern for level walking, and have no obvious organization. But humans often look ahead when…
Dormancy is a widespread adaptive strategy that enables populations to persist in fluctuating environments, yet how its benefits depend on the temporal structure of environmental variability remains unclear. We examine how dormancy…
The effects of fluid viscosity on the kinematics of a small swimmer at low Reynolds number are investigated in both experiments and in a simple model. The swimmer is the nematode Caenorhabditis elegans, which is an undulating roundworm…
Navigating toward a known target in a noisy environment is a fundamental problem shared across biological, physical, and engineered systems. Although optimal strategies are often framed in terms of continuous, fine-grained feedback, we show…
The shape of allele-frequency clines maintained by migration-selection balance depends not only on the properties of migration and selection, but also on the dominance relations among alleles and on linkage to other loci under selection. We…
A central problem of neuroscience involves uncovering the principles governing the organization of nervous systems which ensure robustness in brain development. The nematode Caenorhabditis elegans provides us with a model organism for…
The pursuit-evasion problem is widespread in nature, engineering, and societal applications. It is commonly observed in nature that predators often exhibit faster speeds than their prey but have less agile maneuverability. Over millions of…
In this paper, we conduct a literature review of laws of motion based on stochastic search strategies which are mainly focused on exploring highly dynamic environments. In this regard, stochastic search strategies represent an interesting…
Principles of self-organization play an increasingly central role in models of human activity. Notably, individual human displacements exhibit strongly recurrent patterns that are characterized by scaling laws and can be mechanistically…
Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for…
Limbless crawling is ubiquitous in biology, from cells to organisms. We develop and analyze a model for the dynamics of one-dimensional elastic crawlers, subject to active stress and deformation-dependent friction with the substrate. We…
We demonstrate a spiking neural network for navigation motivated by the chemotaxis network of Caenorhabditis elegans. Our network uses information regarding temporal gradients in the tracking variable's concentration to make navigational…
The nematode Caenorhabditis elegans, with information on neural connectivity, three-dimensional position and cell linage provides a unique system for understanding the development of neural networks. Although C. elegans has been widely…
A variety of swimming microorganisms, called ciliates, exploit the bending of a large number of small and densely-packed organelles, termed cilia, in order to propel themselves in a viscous fluid. We consider a spherical envelope model for…
Our understanding of the neural basis of locomotor behavior can be informed by careful quantification of animal movement. Classical descriptions of legged locomotion have defined discrete locomotor gaits, characterized by distinct patterns…
Efficient transportation, a hot topic in nonlinear science, is essential for modern societies and the survival of biological species. Biological evolution has generated a rich variety of successful solutions, which have inspired engineers…
Colonies of ants are systems of interacting living organisms in which interactions between individuals and their environment can produce a reliable performance of a complex tasks without the need for centralised control. Particularly…
From bacteria and sperm cells to artificial microrobots, self-propelled microscopic objects at low Reynolds numbers often perceive fluctuating mechanical and chemical stimuli and contact exterior wall boundaries both in nature and the…
We model and analyze a herding problem, where the drivers try to steer the evaders' trajectories while the evaders always move away from the drivers. This problem is motivated by the guidance-by-repulsion model [Escobedo, R., Iba\~nez, A.…