Related papers: From Dimension-Free Manifolds to Dimension-varying…
We study multidimensional cosmological models with a higher-dimensional product manifold, that consists of spherical and flat spaces, in the presence of a minimal free scalar field. Dynamical behaviour of the model is analyzed both in…
Diffusion models have shown remarkable results for image generation, editing and inpainting. Recent works explore diffusion models for 3D shape generation with neural implicit functions, i.e., signed distance function and occupancy…
The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output…
Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…
We present a novel Eulerian meshless method for two-phase flows with arbitrary embedded geometries. The spatial derivatives are computed using the meshless generalized finite difference method (GFDM). The sharp phase interface is tracked…
Classification is an important topic in statistics and machine learning with great potential in many real applications. In this paper, we investigate two popular large margin classification methods, Support Vector Machine (SVM) and Distance…
In the framework of deterministic finslerian models, a mechanism producing dissipative dynamics at the Planck scale is discussed. It is based on a geometric evolution from Finsler to Riemann structures defined on the fiber bundle ${ TM}\to…
Unsigned distance fields (UDFs) offer broader modeling capabilities than signed distance fields (SDFs), enabling the representation of shapes with open boundaries, non-manifold structures or mixed curve and surface parts. However,…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
A cascade model is described based on multiplier distributions determined from 3D direct numerical simulations (DNS) of turbulent particle laden flows, which include two-way coupling between the phases at global mass loadings equal to…
In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…
We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to…
Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…
It is generally believed that any quantum theory of gravity should have a generic feature --- a quantum of length. We provide a physical ansatz to obtain an effective non-local metric tensor starting from the standard metric tensor such…
The D-dimensional cosmological model on the manifold $M = R \times M_{1} \times M_{2}$ describing the evolution of 2 Einsteinian factor spaces, $M_1$ and $M_2$, in the presence of multicomponent perfect fluid source is considered. The…
How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…
We introduce Non-Euclidean-MDS (Neuc-MDS), an extension of classical Multidimensional Scaling (MDS) that accommodates non-Euclidean and non-metric inputs. The main idea is to generalize the standard inner product to symmetric bilinear forms…
A disentangled representation of a data set should be capable of recovering the underlying factors that generated it. One question that arises is whether using Euclidean space for latent variable models can produce a disentangled…
The ability to extract generative parameters from high-dimensional fields of data in an unsupervised manner is a highly desirable yet unrealized goal in computational physics. This work explores the use of variational autoencoders (VAEs)…
A higher dimensional modified gravity theory with an action that includes dimensionally continued Euler-Poincar\'e forms up to second order in curvatures is considered. The variational field equations are derived. Matter in the universe at…