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Neural networks show a progressive increase in complexity during the time course of evolution. From diffuse nerve nets in Cnidaria to modular, hierarchical systems in macaque and humans, there is a gradual shift from simple processes…
To understand how neurons and nervous systems first evolved, we need an account of the origins of neural elongations: Why did neural elongations (axons and dendrites) first originate, such that they could become the central component of…
Cerebellar-like networks, in which input activity patterns are separated by projection to a much higher-dimensional space before classification, are a recurring neurobiological motif, present in the cerebellum, dentate gyrus, insect…
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…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…
Advances in optical neuroimaging techniques now allow neural activity to be recorded with cellular resolution in awake and behaving animals. Brain motion in these recordings pose a unique challenge. The location of individual neurons must…
Recent whole brain imaging experiments on $\textit{C. elegans}$ has revealed that the neural population dynamics encode motor commands and stereotyped transitions between behaviors on low dimensional manifolds. Efforts to characterize the…
Legged locomotion is commonly studied and expressed as a discrete set of gait patterns, like walk, trot, gallop, which are usually treated as given and pre-programmed in legged robots for efficient locomotion at different speeds. However,…
The brain's synaptic network, characterized by parallel connections and feedback loops, drives interaction pathways between neurons through a large system with infinitely many degrees of freedom. This system is best modeled by the graph…
Molecular transport in living systems regulates numerous processes underlying biological function. Although many cellular components exhibit anomalous diffusion, only recently has the subdiffusive motion been associated with nonergodic…
Human beings and other vertebrates show remarkable performance and efficiency in locomotion, but the functioning of their biological control systems for locomotion is still only partially understood. The basic patterns and timing for…
The asymmetric simple exclusion process with additional Langmuir kinetics, i.e. attachment and detachment in the bulk, is a paradigmatic model for intracellular transport. Here we study this model in the presence of randomly distributed…
Background: Caenorhabditis elegans is a major model system in biology, yet very little is known about its biology outside the laboratory. Especially, its unusual mode of reproduction with self-fertile hermaphrodites and facultative males…
C. elegans shows chemotaxis using klinokinesis where the worm senses the concentration based on a single concentration sensor to compute the concentration gradient to perform foraging through gradient ascent/descent towards the target…
Recently there has been a lot of interest in identifying modules at the level of genetic and metabolic networks of organisms, as well as in identifying single genes and reactions that are essential for the organism. A goal of computational…
Cortical circuits are characterized by exquisitely complex connectivity patterns that emerge during development from undifferentiated networks. The development of these circuits is governed by a combination of precise molecular cues that…
This paper presents a bio-inspired central pattern generator (CPG)-type architecture for learning optimal maneuvering control of periodic locomotory gaits. The architecture is presented here with the aid of a snake robot model problem…
Signal transduction pathways are largely conserved throughout the animal kingdom. The repertoire of pathways is limited and each pathway is used in different intercellular signaling events during the development of a given animal. For…
Neural systems show a modular and typically also a hierarchical organisation across different levels and across different species. Topology relates to function, but it is also influences dynamics as earlier studies showed its effect on…
Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling…