arXiv research

New extensions for homogeneous distributions on deformations to the normal cone.

Study finds homogeneous spaces with geodesic orbits but no integrable distributions.

We classify multiply transitive homogeneous real (2,3,5) distributions up to local diffeomorphism equivalence.

Classifies homogeneous Pfaffian forms on graded manifolds.

Survey shows deformations of homogeneous metrics in curvature homogeneous manifolds.

A homogeneously saturated equation for the time development of the price of a financial asset is presented and investigated for the pricing of European call options using noise that is distributed as a Student's t-distribution. In the limit that the saturation parameter of the equation equals zero, the standard model o…

We consider automorphisms of homogeneous parabolic geometries with a fixed point. Parabolic geometries carry the distinguished distributions and we study those automorphisms which enjoy natural actions on the distributions at the fixed points. We describe the sets of such automorphisms on homogeneous parabolic geometri…

Characterizes connections on normal distributions manifold.

Introduces homogeneity supermanifolds for studying graded structures.

Distributions of Monge type are a class of strongly regular bracket-generating distributions introduced by I. Anderson, Zh. Nie and P. Nurowski. Their symbol algebras prolong to simple graded Lie algebras, thus allowing one to associate a parabolic geometry to any given Monge distribution. This article is devoted to th…

The time development of the price of a financial asset is considered by constructing and solving Langevin equations for a homogeneously saturated model, and for comparison, for a standard model and for a logistic model. The homogeneously saturated model uses coupled rate equations for the money supply and for the price…

The paper introduces new uniformity and homogeneity concepts for Cosserat media.

An almost para-CR structure on a manifold $M$ is given by a distribution $HM \subset TM$ together with a field $K \in Γ({\rm End}(HM))$ of involutive endomorphisms of $HM$. If $K$ satisfies an integrability condition, then $(HM,K)$ is called a para-CR structure. The notion of maximally homogeneous para-CR structure of …

The paper proposes deep normalization to improve speaker recognition performance.

New method calibrates local volatility models to marginal distributions.

We propose to investigate test statistics for testing homogeneity in reproducing kernel Hilbert spaces. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed and local alternatives is assessed. Finally, experimental evidence of the performance of the proposed approach on both ar…

We present a rigorous homogenization theorem for distributed dislocations. We construct a sequence of locally-flat Riemannian manifolds with dislocation-type singularities. We show that this sequence converges, as the dislocations become denser, to a flat non-singular Weitzenböck manifold, i.e. a flat manifold endowed …

The paper examines risk aggregation under mixtures of marginals, finding that more homogeneous distributions lead to larger uncertainty.

In this paper, extending our previous joint work (Hu et al., Math Nachr 291:343--373, 2018), we initiate the study of Hopf hypersurfaces in the homogeneous NK (nearly Kähler) manifold $\mathbf{S}^3\times\mathbf{S}^3$. First, we show that any Hopf hypersurface of the homogeneous NK $\mathbf{S}^3\times\mathbf{S}^3$ does …

The paper extends distributions by singular curves, revealing structural equivalences.

New compact ECS manifolds with rank 2 discovered, differing from previous rank 1 examples.

A groupoid $Ω\left( \mathcal{B} \right)$ called material groupoid is naturally associated to any simple body $\mathcal{B}$. The material distribution is introduced due to the (possible) lack of differentiability of the material groupoid. Thus, the inclusion of these new objects in the theory of material bodies opens th…

In federated distributed learning, the goal is to optimize a global training objective defined over distributed devices, where the data shard at each device is sampled from a possibly different distribution (a.k.a., heterogeneous or non i.i.d. data samples). In this paper, we generalize the local stochastic and full gr…

We provide a complete characterization of the class of one-dimensional time-homogeneous diffusions consistent with a given law at an exponentially distributed time using classical results in diffusion theory. To illustrate we characterize the class of diffusions with the same distribution as Brownian motion at an expon…

The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot completely characterize the homogeneity of two high-dimensional distributions in …

SHIFT method optimally estimates heterogeneous discrete distributions with limited communication.

We prove a singular Darboux type theorem for homogeneous polynomial closed $2$-forms of degree one on $\mathbb{C}^n$. As application, we classify non-integrable codimension one distributions, of degree one, and arbitrary classes on projective spaces.

Study of ants' movement rules on a 6D space, revealing distribution structures and singular trajectories.

The 1950's foundational literature on rational mechanics exhibits two somewhat distinct paradigms to the representation of continuous distributions of defects in solids. In one paradigm, the fundamental objects are geometric structures on the body manifold, e.g., an affine connection and a Riemannian metric, which repr…

Effective estimates for lattice orbits in homogeneous spaces.

Parallel transport map over reductive spaces is an affine submersion.

We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient point-wise homogeneous OHLC volatility estimators, valid for any price processes. We intr…

In this paper we propose a simple and efficient method to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. We give the analytical expressions for the ordered default time distributions with recursive…

The author discusses in some detail the old definitions of the curvature tensors for rigged metrized distributions on manifolds given by Schouten, Wagner, and Solov'ev. To calculate the Solov'ev sectional and Ricci curvatures for homogeneous sub-Riemannian manifolds, the author suggests to use in some cases special rig…

Characterizes uncertainty in low-rank matrix completion with noisy data.

We survey the use of dynamics of $SL(2, \R)$-actions to understand gap distributions for various sequences of subsets of $[0, 1)$, particularly those arising from special trajectories of various two-dimensional dynamical systems. We state and prove an abstract theorem that gives a unified explanation for some of the ex…

Polynomial-time tester-learner for general halfspaces with Gaussian adversarial noise.

The study shows that the visible range from a point on harmonic manifolds follows an exponential distribution.

We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $ν$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that give a deep insight of such spaces. In particular, there must exist an order-two tr…

Study learning halfspaces with Massart noise under Gaussian distribution, improving previous results.

Extends Sasakian structures to arbitrary contact manifolds.

The space of invariant affine connections on every $3$-Sasakian homogeneous manifold of dimension at least $7$ is described. In particular, the remarkable subspaces of invariant affine metric connections, and the subclass with skew-torsion, are also determined. To this aim, an explicit construction of all $3$-Sasakian …

In this paper we are investigating variational homogeneous second order differential equations by considering the questions of how many different variational principles exist for a given spray. We focus our attention on h(2)-variationality; that is, the regular Lagrange function is homogeneous of degree two in the dire…

Introduces new types of homogeneous spaces and their properties.

We present an algorithm for classification tasks on big data. Experiments conducted as part of this study indicate that the algorithm can be as accurate as ensemble methods such as random forests or gradient boosted trees. Unlike ensemble methods, the models produced by the algorithm can be easily interpreted. The algo…

WaveletGAN improves GANs by homogenizing noise through multi-channel wavelet filtering.

Heavy-tailed distributions emerge in SGD's parameter evolution.

Unified analysis of federated learning with compression for various data distributions.