arXiv research

This study investigates global normalization in neural models, showing its effectiveness in search-aware training.

Problem of global integration of geometric structures arising in the theory of dynamical systems admitting the normal shift is considered. In the case when such integration is possible the problem of globalization for shift maps is studied.

Formula for the force field of Newtonian dynamical systems admitting the normal shift of hypersurfaces in Riemannian manifolds is considered. Problem of globalization for geometric structures associated with this formula is studied.

Normal forms found for meromorphic connections over a specific F-manifold.

This paper analyzes how normalization layers improve neural network training.

The article constructs Feynman propagators for normally hyperbolic operators on curved spacetimes.

Employing Morse theory for the global control of monodromy and the method of analytic discs for local extension, we establish a version of the global Hartogs extension theorem in a singular setting: for every domain D of an (n-1)-complete normal complex space X of pure dimension n >= 2 and for every compact set K in D …

For orthonormal normal sections of two-dimensional immersions in R^4 we define torsion coefficients and a functional for the total torsion. We discuss normal sections which are critical for this functional. In particular, a global estimate for the torsion coefficients of a critical normal section in terms of the curvat…

Example shows no global coordinates on 2-torus's cover.

We study the determination of the second-order normal form for perturbed Hamiltonians $H_ε=H_0 +εH_1 +\frac{ε^2}{2} H_2$, relative to the periodic flow of the unperturbed Hamiltonian $H_0$. The formalism presented here is global, and can be easily implemented in any CAS. We illustrate it by means of two examples: the H…

Stability proved for open Milne spacetime, showing gravity's long-term behavior.

Classifies normal stable Horikawa surfaces with smoothable singularities.

Neural collapse occurs in normalized features over a Riemannian manifold.

We prove that a normal homogeneous space with the property that every Jacobi field along a geodesic vanishing at two points is the restriction of a Killing field along that geodesic is a globally symmetric space.

In this paper we form relations for the determination of the elements of the Eötvös matrix of the Earth's normal gravity field. In addition a relation between the Gauss curvature of the normal equipotential surface and the Gauss curvature of the actual equipotential surface both passing through the point P is presented…

The main drawback of the Frenet frame is that it is undefined at those points where the curvature is zero. Further- more, in the case of planar curves, the Frenet frame does not agree with the standard framing of curves in the plane. The main drawback of the Bishop frame is that the principle normal vector N is not in …

We prove a global residual formula in terms of logarithmic indices for one-dimensional holomorphic foliations, with isolated singularities, and logarithmic along normal crossing divisors. We also give a formula for the total sum of the logarithmic indices if the singular set of the foliation is contained in the invaria…

The study verifies a conjecture about homogeneous quotients of manifolds with positive curvature.

Study analyzes Airbnb booking lead times during global crises using a new metric.

Local normal forms for symmetrical contact structures on 3-manifolds.

The paper studies matrix normalization and graph balancing using a new functional and gradient descent.

Normal forms for Q-structures on graded manifolds explained.

Global covariance pooling improves deep CNNs' representation and generalization.

We give the global picture of the normalized Ricci flow on generalized flag manifolds with two or three isotropy summands. The normalized Ricci flow for these spaces descents to a parameter depending system of two or three ordinary differential equations, respectively. We present here the qualitative study of these sys…

Study geometric isomorphisms between spacetime solutions using paracausal metrics.

New Monte Carlo method outperforms existing strategy for estimating Sobol' indices.

The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous example of a global conformal invariant is the Willmore energy of a surface. In …

In this paper, we investigate the behavior of the normalized Ricci flow on asymptotically hyperbolic manifolds. We show that the normalized Ricci flow exists globally and converges to an Einstein metric when starting from a non-degenerate and sufficiently Ricci pinched metric. More importantly we use maximum principles…

We show that the scalar curvature is uniformly bounded for the normalized Kahler-Ricci flow on a Kahler manifold with semi-ample canonical bundle. In particular, the normalized Kahler-Ricci flow has long time existence if and only if the scalar curvature is uniformly bounded, for Kahler surfaces, projective manifolds o…

Local bifurcation theory typically deals with the response of a degenerate but isolated equilibrium state or periodic orbit of a dynamical system to perturbations controlled by one or more independent parameters, and characteristically uses tools from singularity theory. There are many situations, however, in which the…

We describe the flat surfaces with flat normal bundle and regular Gauss map immersed in R^4 using spinors and Lorentz numbers. We obtain a new proof of the local structure of these surfaces. We also study the flat tori in the sphere S^3 and obtain a new representation formula. We then deduce new proofs of their global …

SAM optimizer struggles to converge to global minima or stationary points in practical settings.

iREPA shows spatial structure, not global semantic, drives generation performance in REPA.

In this paper we obtain an existence theorem for normal geodesics joining two given submanifolds in a globally hyperbolic stationary spacetime. The proof is based on both variational and geometric arguments involving the causal structure of the spacetime, the completeness of suitable Finsler metrics associated to it an…

This article concerns cotangent-lifted Lie group actions; our goal is to find local and ``semi-global'' normal forms for these and associated structures. Our main result is a constructive cotangent bundle slice theorem that extends the Hamiltonian slice theorem of Marle, Guillemin and Sternberg. The result applies to a…

We show that in any triangulated 3-manifold, every index n topologically minimal surface can be transformed to a surface which has local indices (as computed in each tetrahedron) that sum to at most n. This generalizes classical theorems of Kneser and Haken, and more recent theorems of Rubinstein and Stocking, and is t…

Locally convex compact immersed hypersurfaces in Finsler-Hadamard manifolds with bounded T-curvature are considered. We prove that such hypersurfaces are embedded as the boundary of convex body under certain conditions on the normal curvatures

Study integrability of geodesic flow on specific Lie groups.

In this paper we analyze the local and global boundary rigidity problem for general Riemannian manifolds with boundary $(M,g)$. We show that the boundary distance function, i.e., $d_g|_{\partial M\times\partial M}$, known near a point $p\in \partial M$ at which $\partial M$ is strictly convex, determines $g$ in a suita…

We prove that the universal covering of a complete locally symmetric normal metric contact pair manifold is a Calabi-Eckmann manifold. Moreover we show that a complete, simply connected, normal metric contact pair manifold such that the foliation induced by the vertical subbundle is regular and reflections in the integ…

Local and global rigidity results for Lie group actions on pseudo-Riemannian manifolds.

Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.

Layer normalization improves federated learning with skewed labels.

Normalization techniques such as Batch Normalization have been applied successfully for training deep neural networks. Yet, despite its apparent empirical benefits, the reasons behind the success of Batch Normalization are mostly hypothetical. We here aim to provide a more thorough theoretical understanding from a clas…

The paper solves the Cauchy problem for Friedrichs systems on specific spacetime manifolds.

New method bypasses global fit for LISA's Galactic binaries, extracting population parameters directly.

Novel approach combines local and global brain changes for AD prediction.

For a subRiemannian manifold and a given Riemannian extension of the metric, we define a canonical global connection. This connection coincides with both the Levi-Civita connection on Riemannian manifolds and the Tanaka-Webster connection on strictly pseudoconvex CR manifolds. We define a notion of normality generalizi…