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We introduce and study generalized holographic superconductors with higher derivative couplings between the field strength tensor and a complex scalar field, in four dimensional AdS black hole backgrounds. We study this theory in the probe…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Spectral graph neural networks learn graph filters, but their behavior with increasing depth and polynomial order is not well understood. We analyze these models in the graph Fourier domain, where each layer becomes an element-wise…
For a bounded domain equipped with a piecewise Lipschitz continuous Riemannian metric g, we consider harmonic map from $(\Omega, g)$ to a compact Riemannian manifold $(N,h)\subset\mathbb R^k$ without boundary. We generalize the notion of…
The possibility that the energy density of the Universe is dominated by a network of low-tension domain walls provides an alternative to the commonly discussed cosmological constant and scalar-field quintessence models of dark energy. We…
Graph neural networks are widely used tools for graph prediction tasks. Motivated by their empirical performance, prior works have developed generalization bounds for graph neural networks, which scale with graph structures in terms of the…
Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of…
We have studied the energy band structure of a Dirac particle in presence of a generalised uncertainty principle (GUP). We start from defining a modified momentum operator and derive corresponding modified dispersion relation (MDR) and GUP.…
The generalized Chaplygin gas (GCG) model allows for an unified description of the cosmologically recent accelerated expansion of the Universe and of the evolution of energy density perturbations. This dark energy - dark matter unification…
A fundamental challenge in understanding graph neural networks (GNNs) lies in characterizing their optimization dynamics and loss landscape geometry, critical for improving interpretability and robustness. While mode connectivity, a lens…
The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field…
Let $K$ be a number field, $\OK$ be its ring of integers. We introduce the notion of compactified representation of $GL_N(\OK)$ and, we see how to associate to a hermitian vector bundle $\E$ over $\Spec(\OK)$ and a compactified…
In this paper, we study generalized line bundles over $C_n$, a primitive multiple curve of arbitrary multiplicity $n$, where $n$ is a positive integer. In particular, we give a structure theorem for them and we characterize their…
We study conformal field theories describing two massless one-dimensional fields interacting at a single spatial point. The interactions we include are periodic functions of the bosonized fields separately plus a ``magnetic'' interaction…
We study harmonic maps from Riemannian manifolds into arbitrary non-positively curved and CAT(-1) metric spaces. First we discuss the domain variation formula with special emphasis on the error terms. Expanding higher order terms of this…
We investigate domain wall junctions in a generalized Wess-Zumino model with a Z(N) symmetry. We present a method to identify the junctions which are potentially BPS saturated. We then use a numerical simulation to show that those junctions…
We investigate the limit behaviour of sequences of free boundary minimal hypersurfaces with bounded index and volume, by presenting a detailed blow-up analysis near the points where curvature concentration occurs. Thereby, we derive a…
For a real bounded symmetric domain, G/K, we construct various natural enlargements to which several aspects of harmonic analysis on G/K and G have extensions. Our starting point is the realization of G/K as a totally real submanifold in a…
In this paper, we perform a systematic analysis of tachyon condensation over string Newton-Cartan (NC) geometry by probing the background with non BPS $ Dp $ brane. We construct the \textit{finite} tachyon effective action for NC geometry…
We develop an analytic model for the power spectra of polarized filamentary structures as a way to study the Galactic polarization foreground to the Cosmic Microwave Background. Our approach is akin to the cosmological halo-model framework,…