In this paper we present an unsupervised differential-geometric approach for learning Riemannian metrics for dynamical models. Given a training set of models the optimal metric is selected among a family of pullback metrics induced by the Fisher information tensor through a parameterized diffeomorphism. The problem of classifying motions, encoded as dynamical models of a certain class, can then...

The Hubble relation between distance and redshift is a purely cosmographic relation that depends only on the symmetries of a FLRW spacetime, but does not intrinsically make any dynamical assumptions. This suggests that it should be possible to estimate the parameters defining the Hubble relation without making any dynamical assumptions. To test this idea, we perform a number of inter-related co...

The dynamical evolution of the globular cluster systems in galaxies is predicted, based on the standard dynamical theory normalized to the example of the Milky Way. The major processes varying with the galactocentric distance are the tidal shocks and dynamical friction. Our simple model explains, on a quantitative basis, the observed diierences of the inner and outer populations of globular clu...

A general model of the equations of generalized thermoelasticity   for an infinite space weakened by a finite linear opening Mode-I crack is solving. The material is   homogeneous and has isotropic properties of elastic half space. The crack is subjected to prescribed temperature and stress distribution. The formulation is applied to generalized thermoelasticity theories, the Lord-Şhulman...

Consider the problem of classifying motions, encoded as dynamical models of a certain class. Standard nearest neighbor classification then reduces to find a suitable distance function in the space of the models. In this paper we present a supervised differentialgeometric method to learn a Riemannian metric for a given class of dynamical models in order to improve classification performances. Gi...

In action, activity or identity recognition it is sometimes useful, rather than to simply extract spatiotemporal features from the volumes representing motions, to explicitly encode their dynamics by means of dynamical systems. Hidden Markov models (HMMs) are a popular choice in that respect: actions can be then classified by measuring distances in the space of HMMs. However, using a fixed, arb...

Consider the problem of classifying motions, encoded as dynamical models of a certain class. Standard nearest neighbor classification then reduces to find a suitable distance function in the space of the models. In this paper we present a supervised differential-geometric method to learn a Riemannian metric for a given class of dynamical models in order to improve classification performances. G...

A recent generalization of Vinnicombe’s ν-gap metric accommodates linear time-varying (LTV) dynamics for a class of systems with graphs that admit normalized coprime representations. Such graph representations exist for systems generated by stabilizable and detectable LTV statespace models. In general, construction of normalized coprime representations is computationally challenging. In this pa...