Ando, Matsuzawa, Thom, and Törnquist have resolved a problem by Sorin Popa constructing an example of Polish group unitary operators with the strong operator topology, whose left right uniform structures coincide, but which does not embed into

is precompact in the C1,α topology. Here R denotes the Riemann curvature tensor, vol the volume and diam the diameter of (M,g). Thus, for any sequence of metrics gi on n-manifolds Mi satisfying (1.1), there is a subsequence, also called gi, and diffeomorphisms φi : M∞ → Mi such that the metrics φi gi converge in the C 1,α topology to a limit metric g∞ onM∞, for any α < 1. In particular, there a...

Feedback stabilization of an ensemble of non interacting half spins described by Bloch equations is considered. This system may be seen as a prototype for infinite dimensional systems with continuous spectrum. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibr...

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

This paper tackles the task of estimating the topology of filamentary networks such as retinal vessels and road networks. Building on top of a global model that performs a dense semantical classification of the pixels of the image, we design a Convolutional Neural Network (CNN) that predicts the local connectivity between the central pixel of an input patch and its border points. By iterating t...

Wireless communication networks have received strong interest for applications in industrial environments. The use of wireless networks in automation systems introduces stringent requirements regarding real-time communication, reliability and security. The WirelessHART protocol aims to meet these requirements. In this protocol, a device known as Network Manager is responsible for the entire net...

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

An algorithm for $n-1$-strong-equillibrium for distributed consensus in a ring with rational agents was proposed by Afek et al. (2014). A proof of impossibility of $n-1$-strong-equillibrium for distributed consensus in every topology with rational agents, when $n$ is even, is presented. Furthermore, we show that the algorithm proposed by Afek et al. is the only algorithm which can solve the pro...

ABSTRACT. The paper considers the stability and strong convergence to equilibrium of solutions to the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Under the usual cut-off condition on the collision kernel, we prove a strong stability in L-topology at any finite time interval, and, for hard and Maxwellian potentials, we prove that the solutions converge strongly in L to eq...

In adult humans, the ventral temporal cortex (VTC) represents faces in a reproducible topology. However, it is unknown what role visual experience plays in the development of this topology. Using functional magnetic resonance imaging in children and adults, we found a sequential development, in which the topology of face-selective activations across the VTC was matured by age 7, but the spatial...