Related papers: Edge modes as dynamical frames: charges from post-…
We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…
Conserved charges in theories with gauge symmetries are supported on codimension-2 surfaces in the bulk spacetime. It has recently been suggested that various classical formulations of gravity dynamics display different symmetries, and…
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism…
Alignment, the tendency of adjacent weight matrices in deep networks to develop compatible subspace orientations, underlies gradient flow, Neural Collapse, and representation similarity across architectures. Despite extensive empirical…
The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space-time dimensions [arXiv:0903.3680]. In this formalism, the kinematic information of an interacting elementary…
Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced…
Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Discussed is a model of collective and internal degrees of freedom with kinematics based on affine group and its subgroups. The main novelty in comparison with the previous attempts of this kind is that it is not only kinematics but also…
Infinite sets of asymptotic soft-charges were recently shown to be related to new symmetries of the $S$-matrix, spurring a large amount of research on this and related questions. Notwithstanding, the raison-d'\^etre of these soft-charges…
We describe a new type of gravity-matter models where modified f(R)=R+R^2 gravity couples non-canonically to a scalar "inflaton", to the bosonic sector of the electroweak particle model and to a special nonlinear gauge field with a…
We discuss a geometrical method to define a preferred reference frame for precessing binary systems and the gravitational waves they emit. This minimal-rotation frame is aligned with the angular-momentum axis and fixes the rotation about…
Since the proposal of the AdS/CFT correspondence, made by Maldacena and Witten, there has been some controversy about the definition of conserved Noether charges associated to asymptotic isometries in asymptotically AdS spacetimes, namely,…
In this paper, we propose a Bayesian approach for multiscale problems with the availability of dynamic observational data. Our method selects important degrees of freedom probabilistically in a Generalized multiscale finite element method…
Gravity, and the puzzle regarding its energy, can be understood from a gauge theory perspective. Gravity, i.e., dynamical spacetime geometry, can be considered as a local gauge theory of the symmetry group of Minkowski spacetime: the…
We consider the algebra associated to a group of transformations which are symmetries of a regular mechanical system (i.e. system free of constraints). For time dependent coordinate transformations we show that a central extension may…
Unsupervised learning of depth and ego-motion, two fundamental 3D perception tasks, has made significant strides in recent years. However, most methods treat ego-motion as an auxiliary task, either mixing all motion types or excluding…
We illustrate how the different kinds of constraints acting on an impulsive mechanical system can be clearly described in the geometric setup given by the configuration space--time bundle $\pi_t:\mathcal{M} \to \mathbb{E}$ and its first jet…
We study simultaneous inference for multiple matrix-variate Gaussian graphical models in high-dimensional settings. Such models arise when spatiotemporal data are collected across multiple sample groups or experimental sessions, where each…
The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the…