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Unsupervised disentanglement of content and transformation is significantly important for analyzing shape-focused scientific image datasets, given their efficacy in solving downstream image-based shape-analyses tasks. The existing relevant…

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…

We show that the superconformal symmetries of the (1,1) sigma model decompose into a set of more refined symmetries when the target space admits projectors $P_{\pm}$, and the orthogonal complements $Q_{\pm}$, covariantly constant with…

Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these…

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…

This paper proposes a geometric interpretation of the angles and scales which the orientation- and scale-covariant feature detectors, e.g. SIFT, provide. Two new general constraints are derived on the scales and rotations which can be used…

The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with…

Deformable image registration is a fundamental task in medical image analysis, aiming to establish a dense and non-linear correspondence between a pair of images. Previous deep-learning studies usually employ supervised neural networks to…

We extend the framework of submanifolds in Riemannian geometry to Riemann-Cartan geometry, which addresses connections with torsion. This procedure naturally introduces a 2-form on submanifolds associated with the nontrivial ambient…

We consider the conformal group of a space of dim n=p+q, with SO(p,q) metric. The quotient of this group by its homogeneous Weyl subgroup gives a principal fiber bundle with 2n-dim base manifold and Weyl fibers. The Cartan generalization to…

Graph diffusion models have gained significant attention in graph generation tasks, but they often inherit and amplify topology biases from sensitive attributes (e.g. gender, age, region), leading to unfair synthetic graphs. Existing fair…

The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…

Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…

Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…

The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…

Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…

Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…

The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of…

We introduce Probabilistic Coordinate Fields (PCFs), a novel geometric-invariant coordinate representation for image correspondence problems. In contrast to standard Cartesian coordinates, PCFs encode coordinates in correspondence-specific…

We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…