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In this work, we study various properties of embedded hypersurfaces in $1+1+2$ decomposed spacetimes with a preferred spatial direction, denoted $e^{\mu}$, which are orthogonal to the fluid flow velocity of the spacetime and admit a proper…
Motivated by well-known obstacles to quantum gravity, I look for the most general geometrodynamical symmetries compatible with a reduced physical configuration space for metric gravity. I argue that they lead either to a completely static…
Dynamical realizations of the Lifshitz group are studied within the group-theoretic framework. A generalization of the 1d conformal mechanics is constructed, which involves an arbitrary dynamical exponent z. A similar generalization of the…
In this work are computed analytical solutions for orbital motion on a background described by an Expanding Locally Anisotropic (ELA) metric ansatz. This metric interpolates between the Schwarzschild metric near the central mass and the…
The Dijkstra algorithm is a classic path planning method, which operates in a discrete graph space to determine the shortest path from a specified source point to a target node or all other nodes based on non-negative edge weights. Numerous…
In this paper, we present new results on the Riemannian geometry of symmetric positive semi-definite (SPSD) matrices. First, based on an existing approximation of the geodesic path, we introduce approximations of the logarithmic and…
Let $G = (V,E)$ be an undirected graph with maximum degree $\Delta$ and vertex conductance $\Psi^*(G)$. We show that there exists a symmetric, stochastic matrix $P$, with off-diagonal entries supported on $E$, whose spectral gap…
Model merging offers a promising avenue for knowledge integration and parallel development without retraining. Yet, existing methods either ignore the geometry of the loss landscape or rely on intractable full-space Hessian approximations.…
The quotient of the conformal group of Euclidean 4-space by its Weyl subgroup results in a geometry possessing many of the properties of relativistic phase space, including both a natural symplectic form and non-degenerate Killing metric.…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
Deformation of any d-dimensional conformal field theory by a constant null source for a vector operator of dimension (d + z -1) is exactly marginal with respect to anisotropic scale invariance, of dynamical exponent z. The holographic duals…
We consider perturbations of a static and spherically symmetric background endowed with a metric tensor and a scalar field in the framework of the effective field theory of modified gravity. We employ the previously developed 2+1+1…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
Regression analysis for responses taking values in general metric spaces has received increasing attention, particularly for settings with Euclidean predictors $X \in \mathbb{R}^p$ and non-Euclidean responses $Y$ in metric spaces. While…
In this article we focus on constructing a new family of spatially anisotropic Lifshitz spacetimes with arbitrary dynamical exponent z and constant negative curvature in d+1 dimensions within the framework of the Einstein-Proca theory. The…
Lattice field theory is a very powerful tool to study Feynman's path integral non-perturbatively. However, it usually requires Euclidean background metrics to be well-defined. On the other hand, a recently developed regularization scheme…
We propose new optimal estimators for the Lipschitz frontier of a set of points. They are defined as kernel estimators being sufficiently regular, covering all the points and whose associated support is of smallest surface. The estimators…
The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and…
Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the…
The problem of constructing gauge-invariant actions for conformal higher-spin fields in curved backgrounds is known to be notoriously difficult. In this paper we present gauge-invariant models for conformal maximal depth fields with spin…