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A critical mystery in neuroscience lies in determining how anatomical structure impacts the complex functional dynamics of human thought. How does large-scale brain circuitry constrain states of neuronal activity and transitions between…
Analysis of brain activity in resting-state is of fundamental importance in identifying functional characteristics of neuronal system. Although resting brain has been extensively investigated for low frequency synchrony between brain…
We present a new paradigm in the study of brain mental dynamics on the basis of the stable transient activity neural networks observed in experiments. This new approach is in contrast to traditional system analysis usually adopted in…
Understanding the dynamics of neural networks in different width regimes is crucial for improving their training and performance. We present an exact solution for the learning dynamics of a one-hidden-layer linear network, with…
Understanding the evolution of brain functional networks over time is of great significance for the analysis of cognitive mechanisms and the diagnosis of neurological diseases. Existing methods often have difficulty in capturing the…
Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity pattern is hippocampal replay, which is critical for memory…
Finding an appropriate representation of dynamic activities in the brain is crucial for many downstream applications. Due to its highly dynamic nature, temporally averaged fMRI (functional magnetic resonance imaging) can only provide a…
Non-reciprocal interactions are a defining feature of many complex systems, biological, ecological, and technological, often pushing them far from equilibrium and enabling rich dynamical responses. These asymmetries can arise at multiple…
A neuron transforms its input into output spikes, and this transformation is the basic unit of computation in the nervous system. The spiking response of the neuron to a complex, time-varying input can be predicted from the detailed…
Human brain dynamics can be profitably viewed through the lens of statistical mechanics, where neurophysiological activity evolves around and between local attractors representing preferred mental states. Many physically-inspired models of…
Physics perfectly describes neuronal operation, provided that we take into account that biology uses slow, positively charged ions rather than electrons as charge carriers and remove untested ad hoc hypotheses that contradict science's…
Dynamics of a chaotic spiking neuron model are being studied mathematically and experimentally. The Nonlinear Dynamic State neuron (NDS) is analysed to further understand the model and improve it. Chaos has many interesting properties such…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
It has become increasingly popular to study the brain as a network due to the realization that functionality cannot be explained exclusively by independent activation of specialized regions. Instead, across a large spectrum of behaviors,…
The functional network of the brain continually adapts to changing environmental demands. The environmental changes closely connect with changes of active cognitive processes. In recent years, the network approach has emerged as a promising…
Neuroscientists and computer vision researchers use model-brain alignment benchmarks to compare artificial and biological vision systems. These benchmarks rank models according to alignment measures such as the similarity of…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
Conventional neuroimaging analyses have revealed the computational specificity of localized brain regions, exploiting the power of the subtraction technique in fMRI and event-related potential analyses in EEG. Moving beyond this convention,…
Further analysis and experimentation is carried out in this paper for a chaotic dynamic model, viz. the Nonlinear Dynamic State neuron (NDS). The analysis and experimentations are performed to further understand the underlying dynamics of…
The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule. Previous works have analyzed the dynamical equations describing learning in the relatively simplified…