相关论文: Differential Invariants under Gamma Correction

It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of non-linear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the…

Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…

We develop a gauge invariant canonical perturbation scheme for perturbations around symmetry reduced sectors in generally covariant theories, such as general relativity. The central objects of investigation are gauge invariant observables…

The method of statistical differentials, which approximates the mean and variance of transformations of random variables is used in many areas of mathematics. This paper will discuss the conditions under which such an approximation will be…

Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…

Renormalization-Group (RG) improvement has been frequently applied to capture the effect of quantum corrections on cosmological and black-hole spacetimes. This work utilizes an algebraically complete set of curvature invariants to establish…

Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being…

General invariants of a geometric mapping of a symmetric affine connection space are obtained in this paper. These invariants are generalizations of the previous obtained basic invariants (see [16]). Moreover, these invariants are related…

An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on the an arbitrary background spacetime which admits ADM decomposition is discussed. We explicitly construct the…

Generative Adversarial Networks (GANs) have recently demonstrated to successfully approximate complex data distributions. A relevant extension of this model is conditional GANs (cGANs), where the introduction of external information allows…

(2+1) dimensional diffusion equation is considered within the framework of equivalence transformations. Generators for the group are obtained and admissible transformations between linear and nonlinear equations are examined. It is shown…

The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then,…

Integral discriminants provide a simple and fundamental model for non-Gaussian integrals, associated with homogeneous polynomials of degree r in n variables. We argue that, in this context, the study of correlators is equally if not more…

We draw attention to a novel type of geometric gauge invariance relating the autoparallel equations of motion in different Riemann-Cartan spacetimes with each other. The novelty lies in the fact that the equations of motion are invariant…

One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According…

We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…

The convolution of a function with an isotropic Gaussian appears in many contexts such as differential equations, computer vision, signal processing, and numerical optimization. Although this convolution does not always have a closed form…

A frequent and well-founded criticism of the maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimates of a continuous parameter \gamma taking values in a differentiable manifold \Gamma is that they are not invariant to…

Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms…

Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…