Hubble's law and faster than light expansion speeds

Naively applying Hubble's law to a sufficiently distant object gives a receding velocity larger than the speed of light. By discussing a very similar situation in special relativity, we argue that Hubble's law is meaningful only for nearby objects with non-relativistic receding speeds. To support this claim, we note that in a curved spacetime manifold it is not possible to directly compare tangent vectors at different points, and thus there is no natural definition of relative velocity between two spatially separated objects in cosmology. We clarify the geometrical meaning of the Hubble's receding speed v by showing that in a Friedmann-Robertson-Walker spacetime if the four-velocity vector of a comoving object is parallel-transported along the straight line in flat comoving coordinates to the position of a second comoving object, then v/c actually becomes the rapidity of the local Lorentz transformation, which maps the fixed four-velocity vector to the transported one.Comment: 5 pages, 2 figures, to appear in Am. J. Phy

Squeezed States and Hermite polynomials in a Complex Variable

Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].Comment: 15 page

Coherent States on Hilbert Modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert $C^*$-modules which have a natural left action from another $C^*$-algebra say, $\mathcal A$. The coherent states are well defined in this case and they behave well with respect to the left action by $\mathcal A$. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive kernel between two $C^*$-algebras, in complete analogy to the Hilbert space situation. Related to this there is a dilation result for positive operator valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory

LCrowdV: Generating Labeled Videos for Simulation-based Crowd Behavior Learning

We present a novel procedural framework to generate an arbitrary number of labeled crowd videos (LCrowdV). The resulting crowd video datasets are used to design accurate algorithms or training models for crowded scene understanding. Our overall approach is composed of two components: a procedural simulation framework for generating crowd movements and behaviors, and a procedural rendering framework to generate different videos or images. Each video or image is automatically labeled based on the environment, number of pedestrians, density, behavior, flow, lighting conditions, viewpoint, noise, etc. Furthermore, we can increase the realism by combining synthetically-generated behaviors with real-world background videos. We demonstrate the benefits of LCrowdV over prior lableled crowd datasets by improving the accuracy of pedestrian detection and crowd behavior classification algorithms. LCrowdV would be released on the WWW

The Network Slicing and Performance Analysis of 6G Networks using Machine Learning

6G technology is designed to provide users with faster and more reliable data  transfer as compared to the current 5G technology. 6G is rapidly evolving and provides a large bandwidth, even in underserved areas. This technology is extremely anticipated and is currently booming for its ability to deliver massive network capacity, low latency, and a highly improved user experience. Its scope is immense, and it’s designed to connect everyone and everything in the world. It includes new deployment models and services with extended user capacity. This study proposes a network slicing simulator that uses hardcoded base station coordinates to randomly distribute client locations to help analyse the performance of a particular base station architecture. When a client wants to locate the closest base station, it queries the simulator, which stores base station coordinates in a K-Dimensional tree. Throughout the simulation, the user follows a pattern that continues until the time limit is achieved. It gauges multiple statistics such as client connection ratio, client count per second, Client count per slice, latency, and the new location of the client. The K-D tree handover algorithm proposed here allows the user to connect to the nearest base stations after fulfilling the required criteria. This algorithm ensures the quality requirements and decides among the base stations the user connects to

Supersymmetric Effects on Isospin Symmetry Breaking and Direct CP Violation in B→ργB \to \rho \gamma

We argue that one can search for physics beyond the standard model through measurements of the isospin-violating quantity $\Delta^{-0} \equiv \Gamma(B^- \to \rho^- \gamma)/2\Gamma(B^0 \to \rho^0 \gamma)-1$, its charge conjugate $\Delta^{+0}$, and direct CP violation in the partial decay rates of $B^\pm \to \rho^\pm \gamma$. We illustrate this by working out theoretical profiles of the charge-conjugate averaged ratio $\Delta \equiv {1 \over 2}(\Delta^{+0} +\Delta^{-0})$ and the CP asymmetry $A_{CP}(B^\pm \to \rho^\pm \gamma)$ in the standard model and in some variants of the minimal supersymmetric standard model. We find that chargino contributions in the large $\tan \beta$ region may modify the magnitudes and flip the signs of $\Delta$ and $A_{CP}(B^\pm \to \rho^\pm \gamma)$ compared to their standard-model values, providing an unmistakeable signature of supersymmetry.Comment: 10 pages, 7 figures (requires graphicx

Gazeau−-Klauder squeezed states associated with solvable quantum systems

A formalism for the construction of some classes of Gazeau$-$Klauder squeezed states, corresponding to arbitrary solvable quantum systems with a known discrete spectrum, are introduced. As some physical applications, the proposed structure is applied to a few known quantum systems and then statistical properties as well as squeezing of the obtained squeezed states are studied. Finally, numerical results are presented.Comment: 18 pages, 12 figure

Asymmetry of bipartite quantum discord

It is known from the analysis of the density matrix for bipartite systems that the quantum discord (as a measure of quantum correlations) depends on the particular subsystem chosen for the projective measurements. We study asymmetry of the discord in a simple physical model of two spin-1/2 particles with the dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous magnetic field. The dependence of the above discord asymmetry on the Larmour frequencies at both T=0 (the ground state) and $T>0$ has been investigated. It is demonstrated, in particular, that the asymmetry is negligible for high temperatures but it may become significant with the decrease in temperature.Comment: 5 pages 3 figure

Rare exclusive semileptonic b -> s transitions in the Standard Model

We study long-distance effects in rare exclusive semileptonic decays B -> (K, K*) (l+ l-, nu bar{nu}) and analyze dilepton spectra and asymmetries within the framework of the Standard Model. The form factors, describing the meson transition amplitudes of the effective Hamiltonian are calculated within the lattice-constrained dispersion quark model: the form factors are given by dispersion representations through the wave functions of the initial and final mesons, and these wave functions are chosen such that the B -> K* transition form factors agree with the lattice results at large q**2. We calculate branching ratios of semileptonic B -> K, K* transition modes and study the sensitivity of observables to the long-distance contributions. The shape of the forward-backward asymmetry and the longitudinal lepton polarization asymmetry are found to be independent of the long-distance effects and mainly determined by the values of the Wilson coefficients in the Standard Model.Comment: revtex, 17 pp., 5 figures with epsfig.st

Standard Model CP violation in Polarised b->d l^+ l^-

In the standard model, we study CP violating rate asymmetries in the decay b->d l^+ l^- when one of the leptons is polarised. We find an asymmetry of (5 -- 15)% in the polarised decay spectrum which is comparable to known results for the unpolarised case. In the kinematic region separating the rho-omega and $c \bar c$ resonances, which is also theoretically cleanest, the polarised contribution to the asymmetry is larger than the unpolarised results. In order to observe a 3 sigma signal for direct CP violation in the polarised spectrum, assuming 100% efficiency, about 10^10 $B \bar B$ pairs are required at a B factory. Our results indicate an asymmetric contribution from the individual polarisation states to the unpolarised CP asymmetry. Taking advantage of this, one can attribute any new physics to be most sensitive to a specific polarisation state.Comment: 23 pages, one reference adde