Related papers: Rhythms of the nervous system: mathematical themes…
Recurrent Neural Network models have elucidated the interplay between structure and dynamics in biological neural networks, particularly the emergence of irregular and rhythmic activities in cortex. However, most studies have focused on…
This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the…
The brain may be thought of as a many-body architecture with a spatio-temporal dynamics described by neuronal structures. The oscillatory nature of brain activity allows these structures (nodes) to be described as a set of coupled…
Recent advances in sleep neurobiology have allowed development of physiologically based mathematical models of sleep regulation that account for the neuronal dynamics responsible for the regulation of sleep-wake cycles and allow detailed…
Complexity in the temporal organization of neural systems may be a reflection of the diversity of its neural constituents. These constituents, excitatory and inhibitory neurons, comprise an invariant ratio in vivo and form the substrate for…
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…
The central nervous system is composed of many individual units -- from cells to areas -- that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
Rhythm patterns can be performed with a wide variation of tempi. This presents a challenge for many music information retrieval (MIR) systems; ideally, perceptually similar rhythms should be represented and processed similarly, regardless…
The glow of a starry night sky, the smell of a freshly brewed cup of coffee or the sound of ocean waves breaking on the beach are representations of the physical world that have been created by the dynamic interactions of thousands of…
Given a population of interconnected input-output agents repeatedly exposed to independent random inputs, we talk of correlated variability when agents' outputs are variable (i.e., they change randomly at each input repetition) but…
Understanding how brain networks learn and manage multiple tasks simultaneously is of interest in both neuroscience and artificial intelligence. In this regard, a recent research thread in theoretical neuroscience has focused on how…
Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics…
Biological rhythms are generated by pacemaker organs, such as the heart pacemaker organ (the sinoatrial node) and the master clock of the circadian rhythms (the suprachiasmatic nucleus), which are composed of a network of autonomously…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…
Neural circuits comprise multiple interconnected regions, each with complex dynamics. The interplay between local and global activity is thought to underlie computational flexibility, yet the structure of multiregion neural activity and its…
In neurosciences, the brain processes information via the firing patterns of connected neurons operating across a spectrum of frequencies. To better understand the effects of these frequencies in the neuron dynamics, we have simulated a…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
Sleep is essential for the maintenance of the brain and the body, yet many features of sleep are poorly understood and mathematical models are an important tool for probing proposed biological mechanisms. The most well-known mathematical…
Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In…