arXiv research

Formal normal form created for real-smooth hypersurfaces.

Adapts Hölder smoothness with normalized gradients.

We prove that smooth cube manifolds have normal smooth structures.

We prove that strictly hyperbolized smooth cube manifolds admit normal smooth structures.

New algorithm tackles nonconvex machine learning problems with adaptive normalization and independent sampling.

In this article, we shall investigate the relationship between the existence or non-existence of non-singular solutions to the normalized Ricci flow and smooth structures on closed 4-manifolds, where non-singular solutions to the normalized Ricci flow are solutions which exist for all time $t \in [0, \infty)$ with unif…

Article studies symmetry in smooth vector bundles using advanced operations.

Formal Normal Form created for special CR singularities.

Kernel smoothing on unknown manifolds with bounds and asymptotic normality.

In this paper we show that if the minimal good resolution graph of a normal surface singularity contains at least two nodes (i.e. vertex with valency at least 3) then the singularity does not admit a smoothing with Milnor fiber having rational homology equal to the rational homology of the 4-disk $D^4$ (called a ration…

We prove the existence of a local smooth Levi decomposition for smooth Poisson structures and Lie algebroids near a singular point. In the appendix of this paper, we show an abstract Nash-Moser normal form theorem, which generalizes our Levi decomposition result and which may be helpful in the study of other smooth nor…

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

The study proves that in normal tilings, at least two vertices are required per cell.

A solution to the normalized Ricci flow is called non-singular if it exists for all time with uniformly bounded sectional curvature. By using the techniques developed by the present authors, we study the existence or non-existence of non-singular solutions of the normalized Ricci flow on 4-manifolds with non-trivial fu…

Stochastic approximation proves asymptotic normality for non-smooth problems.

A new technique normalizes nodes within groups to improve GNN performance.

In this paper we study the main geometric properties of the Carnot-Carathéodory (abbreviated CC) distance $\dc$ in the setting of $k$-step sub-Riemannian Carnot groups from many different points of view. An extensive study of the so-called normal CC-geodesics is given. We state and prove some related variational formul…

We deal with a notion of weak binormal and weak principal normal for non-smooth curves of the Euclidean space with finite total curvature and total absolute torsion. By means of piecewise linear methods, we first introduce the analogous notation for polygonal curves, where the polarity property is exploited, and then m…

New algorithm for differentially private distributed optimization of smooth, non-convex problems.

A new proof shows almost every normal to a smooth convex body intersects at least 6 normals from different points.

We find an obstruction to the existence of non-singular solutions to the normalized Ricci flow on four-manifolds with $b^+=1$. By using this obstruction, we study the relationship between the existence or non-existence of non-singular solutions of the normalized Ricci flow and exotic smooth structures on the topologica…

Defines mass for non-smooth hyperbolic spaces using a modified flow.

We suggest an algorithm allowing to obtain some new integral-geometric formulae from the existing formulae of Crofton type. These new formulae are applied to get smooth versions of BKK theorem. The algorithm is based on the calculations in the ring of normal densities on a manifold.

Defines weak normals for irregular curves in high-dimensional spaces.

We construct normal rationally connected varieties (of arbitrarily large dimension) not containing any smooth rational curves.

It is constructed a normal form for a class of real-smooth surfaces M\subset\mathbb{C}^{2} defined near a degenerate CR singularity.

We investigate a method of construction of Calabi--Yau manifolds, that is, by smoothing normal crossing varieties. We develop some theories for calculating the Picard groups of the Calabi--Yau manifolds obtained in this method. Some applications are included, such as construction of new examples of Calabi--Yau 3-folds …

Smooth flows for physical systems with smooth energies and forces.

Polytopes in high dimensions have at least 2n+4 normals.

Paper explores whether gradient normalization can replace clipping for SGD in heavy-tailed noise.

In this paper we complete the study of the normal holonomy groups of complex submanifolds (non nec. complete) of Cn or CPn. We show that irreducible but non transitive normal holonomies are exactly the Hermitian s-representations of [CD09, Table 1] (see Corollary 1.1). For each one of them we construct a non necessaril…

Efficient EP algorithm improves smoothing distribution inference in financial models.

In this paper we prove that the Kähler-Einstein metrics for a degeneration family of Kähler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete Kähler-Einstein metric on the smooth part of the central fiber when the central fiber has only normal crossing singularities inside smooth total sp…

It is well known that a k-dimensional smooth surface in a Euclidean space cannot be tangent to a non-involutive distribution of k-dimensional planes. In this paper we discuss the extension of this statement to weaker notions of surfaces, namely integral and normal currents. We find out that integral currents behave to …

Study immersions and embeddings of manifolds with trivial normal bundles.

Extends normalizing flows to arbitrary smooth manifolds.

Generalizes Poincaré-Hopf Theorem for piecewise smooth boundaries.

Researchers relax the CVF's smoothness requirement to create more flexible flow models.

Study on algebraic curves' invariants and vanishing criteria.

Classifies singularities of smooth vector fields on the line.

The paper strengthens the classical result of MLE convergence to a Gaussian distribution.

The paper proves a theorem and characterizes connections over normal varieties.

Normal forms for equivariant maps in infinite dimensions established.

New optimizers control network width scaling, improving stability and transfer across different model sizes.

This paper presents a tensor multiplication based smoothing algorithm that follows a two step denoising method. Unlike other traditional averaging approaches, our approach uses an element based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a l…

Gradient descent on normalized networks reveals sparsity preferences.

We give a comprehensive theoretical characterization of a nonparametric estimator for the $L_2^2$ divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is $\sqrt{n}$-consistent provided the densities are sufficiently smooth. In this smooth regime, we t…

For an arbitrary Riemannian manifold $X$ and Hermitian vector bundles $E$ and $F$ over $X$ we define the notion of the normal symbol of a pseudodifferential operator $P$ from $E$ to $F$. The normal symbol of $P$ is a certain smooth function from the cotangent bundle $T^*X$ to the homomorphism bundle $Hom (E,F)$ and dep…