We discuss in this paper the conformal geometry of bi-invariant metrics on compact semisimple Lie groups. For this purpose we develop a conformal Cartan calculus adapted to this problem. In particular, we derive an explicit formula for the holonomy algebra of the normal conformal Cartan connection of a bi-invariant metric. As an example, we apply this calculus to the group SO(4). Its conformal ...

In this paper we investigate properties of rank correlation coefficients that can be derived from right-invariant generalized metrics on the symmetric group. We prove some new inequalities between a number of generalized metrics, and we characterize the sample sizes for which several (right-invariant) rank correlation coefficients can equal zero. Using the Hausdorff generalized metric, we show ...

Linear time-invariant filter is presented for state estimation in LTI systems with bounded noise. The filter is optimal in the sense that it guarantees minimal error bounds (minimal invariant ellipsoid for errors of filtering). Both continuous-time and discrete-time cases are covered. The key role plays LMI technique and new version of S-theorem. Double pendulum velocity estimation is considere...

Probabilistic state-estimation approaches offer a principled foundation for designing localization systems, because they naturally integrate sequences of imperfect motion and exteroceptive sensor data. Recently, probabilistic systems utilizing appearance-invariant visual place recognition (VPR) methods as the primary have demonstrated state-of-the-art performance in presence substantial appeara...

Recognition of human poses and actions is crucial for autonomous systems to interact smoothly with people. However, cameras generally capture in 2D as images videos, which can have significant appearance variations across viewpoints that make the recognition tasks challenging. To address this, we explore recognizing similarity 3D body from information, has not been well-studied existing works. ...

We determine the probability, structure dependent, that block Wiedemann algorithm correctly computes leading invariant factors. This leads to a tight lower bound for independent. show, using size slightly larger than r, r factors are computed with high probability over any field. Moreover, an is provided compute given matrix and thus select needed obtain desired probability. The worst case impr...

We explore the connection between Hilbertian metrics and positive definite kernels on the real line. In particular, we look at a well-known characterization of translation invariant Hilbertian metrics on the real line by von Neumann and Schoenberg (1941). Using this result we are able to give an alternate proof of Bochner’s theorem for translation invariant positive definite kernels on the real...

A Riemannian metric is said to be Einstein if the Ricci curvature is a constant multiple of the metric. Given a manifold M , one can ask whether M carries an Einstein metric, and if so, how many. This fundamental question in Riemannian geometry is for the most part unsolved (cf. [Bes]). As a global PDE or a variational problem, the question is intractible. It becomes more manageable in the homo...

An upper bound on the first S invariant eigenvalue of the Laplacian for S invariant metrics on S is used to find obstructions to the existence of isometric embeddings of such metrics in (R, can). As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the surface of revolution cannot be isometrically embedded in (R, can). This leads to a generalization of a...