Related papers: Spatio-temporal canards in neural field equations
Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…
Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications,…
In continuous attractor neural networks (CANNs), spatially continuous information such as orientation, head direction, and spatial location is represented by Gaussian-like tuning curves that can be displaced continuously in the space of the…
Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…
We extend the theory of neural fields which has been developed in a deterministic framework by considering the influence spatio-temporal noise. The outstanding problem that we here address is the development of a theory that gives rigorous…
The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…
We investigate new models for scalar fields in flat and curved spacetime. We note that the global reflection symmetry of the potential that identify the scalar field model does not exclude the presence of internal asymmetries that give rise…
Inspired by the operation of biological brains, Spiking Neural Networks (SNNs) have the unique ability to detect information encoded in spatio-temporal patterns of spiking signals. Examples of data types requiring spatio-temporal processing…
Cascades arise in many contexts (e.g., neuronal avalanches, social contagions, and system failures). Despite evidence that propagations often involve higher-order dependencies, cascade theory has largely focused on models with…
Many classes of active matter develop spatial memory by encoding information in space, leading to complex pattern formation. It has been proposed that spatial memory can lead to more efficient navigation and collective behaviour in…
Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…
We have found various families of two-dimensional spatiotemporal solitons in quadratically nonlinear waveguide arrays. The families of unstaggered odd, even and twisted stationary solutions are thoroughly characterized and their stability…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…
Nonlinear reaction-diffusion systems admit a wide variety of spatiotemporal patterns or structures. In this lecture, we point out that there is certain advantage in studying discrete arrays, namely cellular neural/nonlinear networks (CNNs),…
We analyze canard explosions in delayed differential equations with a one-dimensional slow manifold. This study is applied to explore the dynamics of the van der Pol slow-fast system with delayed self-coupling. In the absence of delays,…
Biological neural networks exist in physical space where distance influences communication delays: a fundamental coupling between space and time absent in most artificial neural networks. While recent work has separately explored spatial…
Spatio-temporal graph learning is a fundamental problem in modern urban systems. Existing approaches tackle different tasks independently, tailoring their models to unique task characteristics. These methods, however, fall short of modeling…
Networks of neural mass nodes with delayed interactions are increasingly being used as models for large-scale brain activity. To complement the growing number of computational studies of such networks, it is timely to develop new…
We deal with the comparison of space-time covariance kernels having, either, full, spatially dynamical, or space-time compact support. Such a comparison is based on compatibility of these covariance models under fixed domain asymptotics,…
In this work, we introduce two spatio-temporal colored bounded noises, based on the zero-dimensional Cai-Lin and Tsallis-Borland noises. We then study and characterize the dependence of the defined bounded noises on both a temporal…