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We consider a simple neural field model in which the state variable is dendritic voltage, and in which somas form a continuous one-dimensional layer. This neural field model with dendritic processing is formulated as an integro-differential…
Epileptic seizure activity shows complicated dynamics in both space and time. To understand the evolution and propagation of seizures spatially extended sets of data need to be analysed. We have previously described an efficient filtering…
This research focuses on an innovative task of extracting equations from incomplete data, moving away from traditional methods used for complete solutions. The study addresses the challenge of extracting equations from data, particularly in…
We try to perform geometrization of cognitive science and psychology by representing information states of cognitive systems by points of {\it mental space} given by a hierarchic $m$-adic tree. Associations are represented by balls and…
This paper studies data-driven iterative learning control (ILC) for linear time-invariant (LTI) systems with unknown dynamics, output disturbances and input box-constraints. Our main contributions are: 1) using a non-parametric data-driven…
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…
Advances in neuroscience and artificial intelligence have enabled preliminary decoding of brain activity. However, despite the progress, the interpretability of neural representations remains limited. A significant challenge arises from the…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
Linear models are a core component for statistical software that analyzes treatment effects. They are used in experimentation platforms where analysis is automated, as well as scientific studies where analysis is done locally and manually.…
Physical simulations based on partial differential equations typically generate spatial fields results, which are utilized to calculate specific properties of a system for engineering design and optimization. Due to the intensive…
Here we describe an "information based exchange" model of brain function that ascribes to neocortex, basal ganglia, and thalamus distinct network functions. The model allows us to analyze whole brain system set point measures, such as the…
Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…
The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
Probabilistic inference offers a principled framework for understanding both behaviour and cortical computation. However, two basic and ubiquitous properties of cortical responses seem difficult to reconcile with probabilistic inference:…
Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…
The Ising Model has recently received much attention for the statistical description of neural spike train data. In this paper, we propose and demonstrate its use for building decoders capable of predicting, on a millisecond timescale, the…
The fundamental, powerful process of computation in the brain has been widely misunderstood. The paper [1] associates the general failure to build intelligent thinking machines with current reductionist principles of temporal coding and…
Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners…
We explore training deep neural network models in conjunction with physics simulations via partial differential equations (PDEs), using the simulated degrees of freedom as latent space for a neural network. In contrast to previous work,…