arXiv research

Investigates the long-only minimum variance portfolio in factor models.

Invariant description of SU(2)-structures on 5-manifolds developed.

Probabilistic programming languages represent complex data with intermingled models in a few lines of code. Efficient inference algorithms in probabilistic programming languages make possible to build unified frameworks to compute interesting probabilities of various large, real-world problems. When the structure of mo…

Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of time-series data by treating unknown time-series data nonparametrically using GP with …

A new method for one-class classification using ellipsoidal encapsulation.

SVDD and Deep SVDD improve radar target detection in clutter.

We give coordinate formula and geometric description of the curvature of the tensor product connection of linear connections on vector bundles with the same base manifold. We define the covariant differential of geometric fields of certain types with respect to a pair of a linear connection on a vector bundle and a lin…

Summary of para-Hermitian geometry for T-duality in string theory.

The curvature tensor of a pseudo-Riemannian metric, and its covariant derivatives, satisfy certain identities that hold on any manifold of dimension less or equal than $n$. In this paper, we re-elaborate recent results by Gilkey-Park-Sekigawa regarding $p$-covariant dimensional curvature identities, for $p=0,2$. To thi…

CDL index improves clustering validation for non-convex data.

Building on the Utiyama principle we formulate an approach to Lagrangian field theory in which exterior covariant differentials of vector-valued forms replace partial derivatives, in the sense that they take up the role played by the latter in the usual jet bundle formulation. Actually a natural Lagrangian can be writt…

We consider the geometric formulation of the Hamiltonian formalism for field theory in terms of {\em Hamiltonian connections} and {\em multisymplectic forms}. In this framework the covariant Hamilton equations for Mechanics and field theory are defined in terms of multisymplectic $(n+2)$--forms, where $n$ is the dimens…

In the preceding note math.DG/0610917 the $Λ_{k-1}\mathcal{C}$--spectral sequence, whose first term is composed of \emph{secondary iterated differential forms}, was constructed for a generic diffiety. In this note the zero and first terms of this spectral sequence are explicitly computed for infinite jet spaces. In par…

In this letter we provide an invariant characterization for all spacetimes with all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives vanishing except those zeroth order curvature invariants expressed as polynomials in $Λ$, the cosmological constant. Using this invariant des…

A new formulation of theories of supergravity as theories satisfying a generalized Principle of General Covariance is given. It is a generalization of the superspace formulation of simple 4D-supergravity of Wess and Zumino and it is designed to obtain geometric descriptions for the supergravities that correspond to the…

Neural networks speed up covariance estimation in spatial Gaussian processes.

We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical data and constraints. In special cases, we recover general relativity with and with…

Scalable GP model handles functional covariates and multitasks.

The space of Gaussian measures on a Euclidean space is geodesically convex in the $L^2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By restricting to the space of Gaussian measures inside the $L^2$-Wasserstein space, we manag…

In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives, which guarantees that the structure of the equations is invari…

A unified framework for Poisson and Jacobi structures from 2-covariant tensors

A Python tool generates synthetic data for cluster analysis from high-level descriptions.

Our article considers a Gaussian variational approximation of the posterior density in a high-dimensional state space model. The variational parameters to be optimized are the mean vector and the covariance matrix of the approximation. The number of parameters in the covariance matrix grows as the square of the number …

This paper offers a precise analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto gaussian variables whose covariance …

We study non-conservative like SODEs admitting explicit Lagrangian descriptions. Such systems are equivalent to the system of Lagrange equations of some Lagrangian $L$, including a covariant force field which represents non-conservative forces. We find necessary and sufficient conditions for the existence of a differen…

A flag area measure on an $n$-dimensional euclidean vector space is a continuous translation-invariant valuation with values in the space of signed measures on the flag manifold consisting of a unit vector $v$ and a $(p+1)$-dimensional linear subspace containing $v$ with $0 \leq p \leq n-1$. Using local parallel sets, …

SDR outperforms IDR in multimodal data analysis, especially with fewer samples.

HSIC loss improves robust regression and classification models.

Study eigenvalues and eigenvectors in neural networks, focusing on signal propagation.

Study connections on Lie and Courant algebroids, defining basic curvature and Atiyah cocycle.

A brief history of the investigation of the Weil-Petersson curvature and a summary of Teichmüller theory are provided. A report is presented on the program to describe an intrinsic geometry with the Weil-Petersson metric and geodesic-length functions. Formulas for the metric, covariant derivative and formulas for the c…

New Transformer architecture prevents rank degeneracy in deep attention models.

Fefferman and Graham showed some time ago that four dimensional conformal geometries could be analyzed in terms of six dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit…

We give an explicit description of the full asymptotic expansion of the Schwartz kernel of the complex powers of $m$-Laplace type operators $L$ on compact Riemannian manifolds in terms of Riesz distributions. The constant term in this asymptotic expansion turns turns out to be given by the local zeta function of $L$. I…

Develops a test for conditional local independence of counting processes.

We study the dependence of geometric quantization of the standard symplectic torus on the choice of invariant polarization. Real and mixed polarizations are interpreted as degenerate complex structures. Using a weak version of the equations of covariant constancy, and the Weil-Brezin expansion to describe distributiona…

A method for representing and comparing categorical trajectories using multivariate functional principal components.

Proposes a new AFT model for nonlinear survival data.

We establish a bijective correspondence between affine connections and a class of semi-holonomic jets of local diffeomorphisms of the underlying manifold called symmetry jets in the text. The symmetry jet corresponding to a torsion free connection consists in the family of $2$-jets of the geodesic symmetries. Conversel…

Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analogue of a covariant derivative compatible with a given fiber-wise metric. Imposing further conditions resembling standard Levi-Civita connect…

Following the point of view of Gray and Hervella, we derive detailed conditions which characterize each one of the classes of almost quaternion-Hermitian $4n$-manifolds, $n>1$. Previously, by completing a basic result of A. Swann, we give explicit descriptions of the tensors contained in the space of covariant derivati…

We propose and discuss recursive formulas for conformally covariant powers $P_{2N}$ of the Laplacian (GJMS-operators). For locally conformally flat metrics, these describe the non-constant part of any GJMS-operator as the sum of a certain linear combination of compositions of lower order GJMS-operators (primary part) a…

Unified description of p-brane QP-manifolds connects two recent tensor hierarchy descriptions.

We define a new geometric framework for string theory.

Study reveals limits of PLS in multi-modal learning with correlated signals.

Develops a new geometric formulation for abelian gauge theories.

Develops Green operators for quantum fields on low-regularity spacetimes.

Enhances SVM for uncertain data with probabilistic Gaussian distributions.