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Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
Slow adaption processes, like synaptic and intrinsic plasticity, abound in the brain and shape the landscape for the neural dynamics occurring on substantially faster timescales. At any given time the network is characterized by a set of…
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…
This review provides a dynamical systems perspective on psychiatric symptoms and disease, and discusses its potential implications for diagnosis, prognosis, and treatment. After a brief introduction into the theory of dynamical systems, we…
Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to…
Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we…
We formulate a novel technique for the detection of functional clusters in discrete event data. The advantage of this algorithm is that no prior knowledge of the number of functional groups is needed, as our procedure progressively combines…
These notes introduce probabilistic landscape models defined on high-dimensional discrete sequence spaces. The models are motivated primarily by fitness landscapes in evolutionary biology, but links to statistical physics and computer…
This short paper presents an abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
Neural population activity relating to behaviour is assumed to be inherently low-dimensional despite the observed high dimensionality of data recorded using multi-electrode arrays. Therefore, predicting behaviour from neural population…
Recent years have witnessed an explosion of extensive geolocated datasets related to human movement, enabling scientists to quantitatively study individual and collective mobility patterns, and to generate models that can capture and…
From the sandpoint of neural network dynamics we consider dynamical system of special type pesesses gradient (symmetric) and Hamiltonian (antisymmetric) flows. The conditions when Hamiltonian flow properties are dominant in the system are…
The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yield valuable insights into the time dynamics of functional…
Fractional gradient descent has been studied extensively, with a focus on its ability to extend traditional gradient descent methods by incorporating fractional-order derivatives. This approach allows for more flexibility in navigating…
Cells move differently on substrates with different elasticities. In particular, the persistence time of their motion is higher on stiffer substrates. We show that this behavior will result in a net transport of cells directed up a…
Neuromorphic computing seeks to replicate the remarkable efficiency, flexibility, and adaptability of the human brain in artificial systems. Unlike conventional digital approaches, which suffer from the Von Neumann bottleneck and depend on…