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Understanding the nature of the changes exhibited by evolving neuronal dynamics from high-dimensional activity data is essential for advancing neuroscience, particularly in the study of neuronal network development and the pathophysiology…
Activity in the human brain moves between diverse functional states to meet the demands of our dynamic environment, but fundamental principles guiding these transitions remain poorly understood. Here, we capitalize on recent advances in…
Recent advancements in quantum hardware and classical computing simulations have significantly enhanced the accessibility of quantum system data, leading to an increased demand for precise descriptions and predictions of these systems.…
We analyze the complex networks associated with brain electrical activity. Multichannel EEG measurements are first processed to obtain 3D voxel activations using the tomographic algorithm LORETA. Then, the correlation of the current…
The human brain is a complex system defined by multi-way, higher-order interactions invisible to traditional pairwise network models. Although a diverse array of analytical methods has been developed to address this shortcoming, the field…
We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
Recently, the potential of dynamic brain networks as a neuroimaging biomarkers for mental illnesses is being increasingly recognized. However, there are several unmet challenges in developing such biomarkers, including the need for methods…
Recent works have highlighted the need for a new dynamical paradigm in the modeling of brain function and evolution. Specifically, these models should incorporate non-constant and asymmetric synaptic weights $T_{ij}$ in the neuron-neuron…
Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…
Using deep neural networks as computational models to simulate cognitive process can provide key insights into human behavioral dynamics. Challenges arise when environments are highly dynamic, obscuring stimulus-behavior relationships.…
Higher-order properties of functional magnetic resonance imaging (fMRI) induced connectivity have been shown to unravel many exclusive topological and dynamical insights beyond pairwise interactions. Nonetheless, whether these fMRI-induced…
We present a novel topological framework for analyzing functional brain signals using time-frequency analysis. By integrating persistent homology with time-frequency representations, we capture multi-scale topological features that…
A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie…
We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving "hidden"…
The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…
The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to…
Experimental fMRI studies have shown that spontaneous brain activity i.e. in the absence of any external input, exhibit complex spatial and temporal patterns of co-activity between segregated brain regions. These so-called large-scale…
Dynamic networks have been increasingly used to characterize brain connectivity that varies during resting and task states. In such characterizations, a connectivity network is typically measured at each time point for a subject over a…