Related papers: Torus Graphs for Multivariate Phase Coupling Analy…
We introduce the notion of multiscale covariance tensor fields (CTF) associated with Euclidean random variables as a gateway to the shape of their distributions. Multiscale CTFs quantify variation of the data about every point in the data…
Topological phases have greatly improved our understanding of modern conception of phases of matter that go beyond the paradigm of symmetry breaking and are not described by local order parameters. Instead, characterization of topological…
The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This…
In our version of Watts and Strogatz's small world model, space is a d-dimensional torus in which each individual has in addition exactly one long-range neighbor chosen at random from the grid. This modification is natural if one thinks of…
Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed…
In signal processing, exploring complex systems through network representations has become an area of growing interest. This study introduces the modularity graph, a new graph-based feature, to highlight the relationship across the graph…
The chordal ring (CR) graphs are a well-known family of graphs used to model some interconnection networks for computer systems in which all nodes are in a cycle. Generalizing the CR graphs, in this paper, we introduce the families of…
Understanding the functional connectivity of the brain has become a major goal of neuroscience. In many situatons, the relative phase difference, together with coherence patterns, have been employed to infer the direction of the information…
Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience, to mention only a few. Recent studies have demonstrated that…
The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…
Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more…
2+1d topological phases are well characterized by the fusion rules and braiding/exchange statistics of fractional point excitations. In 4+1d, some topological phases contain only fractional loop excitations. What kind of loop statistics…
Recordings of electrical brain activity carry information about a person's cognitive health. For recording EEG signals, a very common setting is for a subject to be at rest with its eyes closed. Analysis of these recordings often involve a…
Coupled non-linear oscillators are ubiquitous in dynamical studies. A wealth of behaviors have been found mostly for globally coupled systems. From a complexity perspective, less studied have been systems with local coupling, which is the…
Inferring brain connectivity network and quantifying the significance of interactions between brain regions are of paramount importance in neuroscience. Although there have recently emerged some tests for graph inference based on…
We investigate the emergence of a myriad of phases in the strong coupling regime of the dipolar Hubbard model in two dimensions. By using a combination of numerically unbiased methods in finite systems with analytical perturbative…
Thanks to novel, powerful brain activity recording techniques, we can create data-driven models from thousands of recording channels and large portions of the cortex, which can improve our understanding of brain-states neuromodulation and…
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…
We study a class of (1+1)D symmetric random quantum circuits with two competing types of measurements in addition to random unitary dynamics. The circuit exhibits a rich phase diagram involving robust symmetry-protected topological (SPT),…
Entanglement transitions in quantum dynamics present a novel class of phase transitions in non-equilibrium systems. When a many-body quantum system undergoes unitary evolution interspersed with monitored random measurements, the…