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A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or…
Immune cells recognize and discriminate antigens through immunological synapses - dynamic intercellular junctions exhibiting highly organized receptor-ligand patterns. While much work has focused on molecular kinetics and passive mechanisms…
Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect…
A group of cooperative aerial robots can be deployed to efficiently patrol a terrain, in which each robot flies around an assigned area and shares information with the neighbors periodically in order to protect or supervise it. To ensure…
Nature provides us with abundant examples of how large numbers of individuals can make decisions without the coordination of a central authority. Social insects, birds, fishes, and many other living collectives, rely on simple interaction…
The incorporation of structured light techniques into vision science has enabled more selective probes of polarization related entoptic phenomena. Diverse sets of stimuli have become accessible in which the spatially dependant optical…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
The human visual system uses two parallel pathways for spatial processing and object recognition. In contrast, computer vision systems tend to use a single feedforward pathway, rendering them less robust, adaptive, or efficient than human…
In many species, genomic data have revealed pervasive adaptive evolution indicated by the fixation of beneficial alleles. However, when selection pressures are highly variable along a species range or through time adaptive alleles may…
Orphans are genes restricted to a single phylogenetic lineage and emerge at high rates. While this predicts an accumulation of genes, the gene number has remained remarkably constant through evolution. This paradox has not yet been…
Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Most theoretical approaches describe them as purely deterministic or stochastic dynamical…
The Continuous-Variable Firing Rate (CVFR) model, widely used in neuroscience to describe the intertangled dynamics of excitatory biological neurons, is here trained and tested as a veritable dynamically assisted classifier. To this end the…
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…
Differentiable particle filters provide a flexible mechanism to adaptively train dynamic and measurement models by learning from observed data. However, most existing differentiable particle filters are within the bootstrap particle…
In contrast to the neutral population cycles of the deterministic mean-field Lotka--Volterra rate equations, including spatial structure and stochastic noise in models for predator-prey interactions yields complex spatio-temporal structures…
The time required to transcribe genes with long primary transcripts may limit their ability to be expressed in cells with short mitotic cycles, a phenomenon termed intron delay. As such short cycles are a hallmark of the earliest stages of…
The functioning of a living cell is largely determined by the structure of its regulatory network, comprising non-linear interactions between regulatory genes. An important factor for the stability and evolvability of such regulatory…
In many animals, rhythmic motor activity is governed by neural limit cycle oscillations under the control of sensory feedback. In the fruit fly Drosophila melanogaster, the wingbeat rhythm is generated myogenically by stretch-activated…