The relation between the complexity of a time-switched dynamics and the complexity of its control sequence depends critically on the concept of a non-autonomous pullback attractor. For instance, the switched dynamics associated with scalar dissipative affine maps has a pullback attractor consisting of singleton component sets. This entails that the complexity of the control sequence and switche...

This paper studies an incompressible non-Newtonian fluid with delays in two-dimensional bounded domains. We first prove the existence and uniqueness of solutions. Then we establish the existence of pullback attractors {AC H (t)}t∈R (has L-regularity), {AC W (t)}t∈R (has H-regularity), and {AE2 H (t)}t∈R (has L-regularity), {A E2 W (t)}t∈R (has H-regularity) corresponding to two different proces...

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 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...

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...

Intracoronary optical frequency domain imaging (OFDI) provides high resolution, three-dimensional views of coronary artery microstructure, but requires a non-occlusive saline/contrast purge to displace blood for clear artery views. Recent studies utilized manual pullback initiation/termination based on real-time image observation. Automated pullback initiation/termination by real-time OFDI sign...

INTRODUCTION AND OBJECTIVES The development of second-generation optical coherence tomography (i.e. Fourier domain optical coherence tomography, FD-OCT) has made it possible to perform high speed pullbacks during image acquisition without the need for transient occlusion of the coronary artery. The objective of this study was to assess the reproducibility of FD-OCT systems for characterizing pl...

In this paper we present a general differential-geometric framework for learning Riemannian metrics or distance functions for dynamical models, given a training set which can be either labeled or unlabeled. Given a training set of models, the optimal metric is selected among a family of pullback metrics induced by a parameterized automorphism of the space of models. The problem of classifying m...

The purpose of this paper is to outline a new approach to the classii-cation of nitely generated indecomposable modules over certain kinds of pullback rings. If R is the pullback of two hereditary noetherian serial rings over a common semi{simple artinian ring, then this classiication can be divided into the classiica-tion of indecomposable artinian modules and those modules over the coordinate...

We study the local geometry of the pullback of a variety via a finite holomorphic map. In particular, we are looking for properties of V = F(W ) such that if V has the property A, then W must have the property A. We show that A can be the property of normality or prefactoriality. We also show that A can be the property of smoothness, under extra assumptions.