Kinematic Self-Similar Cylindrically Symmetric Solutions

This paper is devoted to find out cylindrically symmetric kinematic self-similar perfect fluid and dust solutions. We study the cylindrically symmetric solutions which admit kinematic self-similar vectors of second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the parallel case gives contradiction both in perfect fluid and dust cases. The orthogonal perfect fluid case yields a vacuum solution while the orthogonal dust case gives contradiction. It is worth mentioning that the tilted case provides solution both for the perfect as well as dust cases.Comment: 22 pages, accepted for publication in Int. J. of Mod. Phys.

Kinematic Self-Similar Plane Symmetric Solutions

This paper is devoted to classify the most general plane symmetric spacetimes according to kinematic self-similar perfect fluid and dust solutions. We provide a classification of the kinematic self-similarity of the first, second, zeroth and infinite kinds with different equations of state, where the self-similar vector is not only tilted but also orthogonal and parallel to the fluid flow. This scheme of classification yields twenty four plane symmetric kinematic self-similar solutions. Some of these solutions turn out to be vacuum. These solutions can be matched with the already classified plane symmetric solutions under particular coordinate transformations. As a result, these reduce to sixteen independent plane symmetric kinematic self-similar solutions.Comment: 29 pages, accepted for publication in Classical Quantum Gravit

On Physical Properties of Cylindrically Symmetric Self-Similar Solutions

This paper is devoted to discuss some of the features of self-similar solutions of the first kind. We consider the cylindrically symmetric solutions with different homotheties. We are interested in evaluating the quantities acceleration, rotation, expansion, shear, shear invariant and expansion rate. These kinematical quantities are discussed both in co-moving as well as in non-co-moving coordinates (only in radial direction). Finally, we would discuss the singularity feature of these solutions. It is expected that these properties would help in exploring some interesting features of the self-similar solutions.Comment: 16 pages, accepted for publication in Int. J. of Mod. Phys.

How much does transmit correlation affect the sum-rate scaling of MIMO Gaussian broadcast channels?

This paper considers the effect of spatial correlation between transmit antennas on the sum-rate capacity of the MIMO Gaussian broadcast channel (i.e., downlink of a cellular system). Specifically, for a system with a large number of users n, we analyze the scaling laws of the sum-rate for the dirty paper coding and for different types of beamforming transmission schemes. When the channel is i.i.d., it has been shown that for large n, the sum rate is equal to M log log n + M log P/M + o(1) where M is the number of transmit antennas, P is the average signal to noise ratio, and o(1) refers to terms that go to zero as n → ∞. When the channel exhibits some spatial correlation with a covariance matrix R (non-singular with tr(R) = M), we prove that the sum rate of dirty paper coding is M log log n + M log P/M + log det(R) + o(1). We further show that the sum-rate of various beamforming schemes achieves M log log n + M log P/M + M log c + o(1) where c ≤ 1 depends on the type of beamforming. We can in fact compute c for random beamforming proposed in and more generally, for random beamforming with preceding in which beams are pre-multiplied by a fixed matrix. Simulation results are presented at the end of the paper

Cold Plasma Wave Analysis in Magneto-Rotational Fluids

This paper is devoted to investigate the cold plasma wave properties. The analysis has been restricted to the neighborhood of the pair production region of the Kerr magnetosphere. The Fourier analyzed general relativistic magnetohydrodynamical equations are dealt under special circumstances and dispersion relations are obtained. We find the $x$-component of the complex wave vector numerically. The corresponding components of the propagation vector, attenuation vector, phase and group velocities are shown in graphs. The direction and dispersion of waves are investigated.Comment: 22 pages, 18 figures, accepted for publication in Astrophys. Space Sc

Electrodynamics in Friedmann-Robertson-Walker Universe: Maxwell and Dirac fields in Newman-Penrose formalism

Maxwell and Dirac fields in Friedmann-Robertson-Walker spacetime is investigated using the Newman-Penrose method. The variables are all separable, with the angular dependence given by the spin-weighted spherical harmonics. All the radial parts reduce to the barrier penetration problem, with mostly repulsive potentials representing the centrifugal energies. Both the helicity states of the photon field see the same potential, but that of the Dirac field see different ones; one component even sees attractive potential in the open universe. The massless fields have the usual exponential time dependencies; that of the massive Dirac field is coupled to the evolution of the cosmic scale factor $a$. The case of the radiation filled flat universe is solved in terms of the Whittaker function. A formal series solution, valid in any FRW universe, is also presented. The energy density of the Maxwell field is explicitly shown to scale as $a^{-4}$. The co-moving particle number density of the massless Dirac field is found to be conserved, but that of the massive one is not. Particles flow out of certain regions, and into others, creating regions that are depleted of certain linear and angular momenta states, and others with excess. Such current of charged particles would constitute an electric current that could generate a cosmic magnetic field. In contrast, the energy density of these massive particles still scales as $a^{-4}$.Comment: 18 pages including 9 figure

Fault Sneaking Attack: a Stealthy Framework for Misleading Deep Neural Networks

Despite the great achievements of deep neural networks (DNNs), the vulnerability of state-of-the-art DNNs raises security concerns of DNNs in many application domains requiring high reliability.We propose the fault sneaking attack on DNNs, where the adversary aims to misclassify certain input images into any target labels by modifying the DNN parameters. We apply ADMM (alternating direction method of multipliers) for solving the optimization problem of the fault sneaking attack with two constraints: 1) the classification of the other images should be unchanged and 2) the parameter modifications should be minimized. Specifically, the first constraint requires us not only to inject designated faults (misclassifications), but also to hide the faults for stealthy or sneaking considerations by maintaining model accuracy. The second constraint requires us to minimize the parameter modifications (using L0 norm to measure the number of modifications and L2 norm to measure the magnitude of modifications). Comprehensive experimental evaluation demonstrates that the proposed framework can inject multiple sneaking faults without losing the overall test accuracy performance.Comment: Accepted by the 56th Design Automation Conference (DAC 2019

Impact of incomplete ventricular coverage on diagnostic performance of myocardial perfusion imaging.

In the context of myocardial perfusion imaging (MPI) with cardiac magnetic resonance (CMR), there is ongoing debate on the merits of using technically complex acquisition methods to achieve whole-heart spatial coverage, rather than conventional 3-slice acquisition. An adequately powered comparative study is difficult to achieve given the requirement for two separate stress CMR studies in each patient. The aim of this work is to draw relevant conclusions from SPECT MPI by comparing whole-heart versus simulated 3-slice coverage in a large existing dataset. SPECT data from 651 patients with suspected coronary artery disease who underwent invasive angiography were analyzed. A computational approach was designed to model 3-slice MPI by retrospective subsampling of whole- heart data. For both whole-heart and 3-slice approaches, the diagnostic performance and the stress total perfusion deficit (TPD) score-a measure of ischemia extent/severity-were quantified and compared. Diagnostic accuracy for the 3-slice and whole-heart approaches were similar (area under the curve: 0.843 vs. 0.855, respectively; P = 0.07). The majority (54%) of cases missed by 3-slice imaging had primarily apical ischemia. Whole-heart and 3-slice TPD scores were strongly correlated (R2 = 0.93, P < 0.001) but 3-slice TPD showed a small yet significant bias compared to whole-heart TPD (- 1.19%; P < 0.0001) and the 95% limits of agreement were relatively wide (- 6.65% to 4.27%). Incomplete ventricular coverage typically acquired in 3-slice CMR MPI does not significantly affect the diagnostic accuracy. However, 3-slice MPI may fail to detect severe apical ischemia and underestimate the extent/severity of perfusion defects. Our results suggest that caution is required when comparing the ischemic burden between 3-slice and whole-heart datasets, and corroborate the need to establish prognostic thresholds specific to each approach

Energy Content of Colliding Plane Waves using Approximate Noether Symmetries

This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. It is shown that in both cases, there does not existComment: 18 pages, accepted for publication in Brazilian J Physic

Phaeanthine and Limacine from Phaeanthus crassipetalus Becc.

Phaeanthus crassipetalus Becc.(Fam: Annonaceae) has been studied. Two major alkaloids have been isolated and characterised based on their spectral information. The alkaloids, phaeanthine (l) and limacine (II), show antibacterial properties against Gram positive and Gram negative bacteria