Related papers: Persistent Dirac for molecular representation
Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider data from a…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
Recent years have witnessed a fast growth in mathematical artificial intelligence (AI). One of the most successful mathematical AI approaches is topological data analysis (TDA) via persistent homology (PH) that provides explainable AI (xAI)…
Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution…
In complex systems, groups of interacting objects may form prevalent and persistent spatiotemporal patterns, which we refer to as motifs. These motifs can exhibit features that reveal how individual objects interact with one another.…
Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic…
We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian $L^1$-potentials. The results are sharp in the non-relativistic or weak-coupling limit. In the massless case, the absence of…
Discrete fermionic and bosonic models for hyperbolic lattices have attracted significant attention across a range of fields since the experimental realization of hyperbolic lattices in metamaterial platforms, sparking the development of…
Cancer diagnosis, prognosis, and therapy response predictions from tissue specimens highly depend on the phenotype and topological distribution of constituting histological entities. Thus, adequate tissue representations for encoding…
Microscopic examination of slides prepared from tissue samples is the primary tool for detecting and classifying cancerous lesions, a process that is time-consuming and requires the expertise of experienced pathologists. Recent advances in…
4x4 Dirac (gamma) matrices (irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many calculations in quantum physics. Although the final physical results do not depend on the applied…
We propose a novel scheme for efficient Dirac mixture modeling of distributions on unit hyperspheres. A so-called hyperspherical localized cumulative distribution (HLCD) is introduced as a local and smooth characterization of the underlying…
We consider one-dimensional discrete Dirac models in vanishing random environments. In a previous work [6], we showed that these models exhibit a rich phase diagram in terms of their spectrum as a function of the rate of decay of the random…
Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details. Irreducible infinite-dimensional representations, being realized in the indefinite metric Hilbert space, are…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly…
The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic,…
The motion of a relativistic particle is linked to its spin by the Dirac equation. Remarkably, electrons in two-dimensional materials can mimic such Dirac particles but must always appear in pairs of opposite spin chirality. Using…
Understanding the dynamic nature of protein structures is essential for comprehending their biological functions. While significant progress has been made in predicting static folded structures, modeling protein motions on microsecond to…
The lattice studies in QCD demonstrate the nontrivial localization behavior of the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian of $4+1$ dimensional disordered system. We use the holographic viewpoint to provide…
We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability…