Related papers: Open-source tools for dynamical analysis of Liley'…

A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…

The primary motor cortex appears to be in the center of transcranial magnetic stimulation (TMS). It is one of few locations that provide directly observable responses, and its physiology serves as model or reference for almost all other TMS…

We study a problem of designing ``robust'' external excitations for control and synchronization of an assembly of homotypic harmonic oscillators representing so-called theta neurons. The model of theta neurons (Theta model) captures, in…

Metastable brain dynamics are characterized by abrupt, jump-like modulations so that the neural activity in single trials appears to unfold as a sequence of discrete, quasi-stationary states. Evidence that cortical neural activity unfolds…

Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models;…

Lattices abound in nature - from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. Such regular arrangements provide solutions for optimally dense packings, efficient resource…

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical…

Artificial Intelligence (AI) systems based solely on neural networks or symbolic computation present a representational complexity challenge. While minimal representations can produce behavioral outputs like locomotion or simple…

We study the asymptotic stability of a two-dimensional mean-field equation, which takes the form of a nonlocal transport equation and generalizes the time-elapsed neuron network model by the inclusion of a leaky memory variable. This…

There exist very few ways to isolate cognitive processes, historically defined via highly controlled laboratory studies, in more ecologically valid contexts. Specifically, it remains unclear as to what extent patterns of neural activity…

Recent research is revealing how cognitive processes are supported by a complex interplay between the brain and the rest of the body, which can be investigated by the analysis of physiological features such as breathing rhythms, heart rate,…

Questions about information encoded by the brain demand statistical frameworks for inferring relationships between neural firing and features of the world. The landmark discovery of grid cells demonstrates that neurons can represent spatial…

Alzheimer's disease gradually affects several components including the cerebral dimension with brain atrophies, the cognitive dimension with a decline in various functions and the functional dimension with impairment in the daily living…

Modeling and interpreting spike train data is a task of central importance in computational neuroscience, with significant translational implications. Two popular classes of data-driven models for this task are autoregressive Point Process…

The elapsed time model has been widely studied in the context of mathematical neuroscience with many open questions left. The model consists of an age-structured equation that describes the dynamics of interacting neurons structured by the…

Process data, temporally ordered categorical observations, are of recent interest due to its increasing abundance and the desire to extract useful information. A process is a collection of time-stamped events of different types, recording…

We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our…

Continuous-time neural processes are performant sequential decision-makers that are built by differential equations (DE). However, their expressive power when they are deployed on computers is bottlenecked by numerical DE solvers. This…

Neuroimaging data, particularly from techniques like MRI or PET, offer rich but complex information about brain structure and activity. To manage this complexity, latent representation models - such as Autoencoders, Generative Adversarial…

Large and diverse datasets have been the cornerstones of many impressive advancements in artificial intelligence. Intelligent creatures, however, learn by interacting with the environment, which changes the input sensory signals and the…