Shuffle-exchanges on augmented meshes

A mesh connected array of size N = two to the Kth power, K an integer, can be augmented by adding at most one edge per node such that it can perform a shuffle-exchange of size N/2 in constant time. A shuffle-exchange of size N is performed on this augmented array in constant time. This is done by combining the available perfect shuffle of size N/2 with the existing nearest neighbor connections of the mesh. By carefully scheduling the different permutations that are composed in order to achieve the shuffle, the time required is reduced to 5 steps, which is optimal for this network

Augmenting computer networks

Three methods of augmenting computer networks by adding at most one link per processor are discussed: (1) A tree of N nodes may be augmented such that the resulting graph has diameter no greater than 4log sub 2((N+2)/3)-2. Thi O(N(3)) algorithm can be applied to any spanning tree of a connected graph to reduce the diameter of that graph to O(log N); (2) Given a binary tree T and a chain C of N nodes each, C may be augmented to produce C so that T is a subgraph of C. This algorithm is O(N) and may be used to produce augmented chains or rings that have diameter no greater than 2log sub 2((N+2)/3) and are planar; (3) Any rectangular two-dimensional 4 (8) nearest neighbor array of size N = 2(k) may be augmented so that it can emulate a single step shuffle-exchange network of size N/2 in 3(t) time steps

Weyl collineations that are not curvature collineations

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality".Comment: 9 page

Proper Weyl Collineations in Kantowski-Sachs and Bianchi Type III Space-Times

A study of proper Weyl collineations in Kantowski-Sachs and Bianchi type III space-times is given by using the rank of the 6X6 Weyl matrix and direct integration techniques. Studying proper Weyl collineations in each of the above space-times, it is shown that there exists no such possibility when the above space-times admit proper Weyl collineations.Comment: 5 page

Cardiac acceleration as a marker of vagal withdrawal in heart rate control during exercise in humans

Objective: To investigate whether the time rate of change in heart rate i.e. cardiac acceleration, during aerobic exercise in human subjects could be used to differentiate vagal withdrawal from sympathetic stimulation.Methods: Fifteen male subjects exercised on a bicycle ergometer at 50 Watts (Step 1), then 100 Watts (Step 2), for 2 minutes each.Results: Heart rate (HR) was monitored from a resting value (mean +/- SD) of 80.3 +/- 12.9 to 113.8 +/- 13.6 beats min-1 in Step 1. In Step 2 exercise, HR increased from 113.8 +/- 13.6 to 145 +/- 20 beats min-1. At the initiation of Step 1, a rapid acceleration of HR was observed in the form of an overshoot response. In contrast to Step 1, a small overshoot response of cardiac acceleration was observed during Step 2. The difference between the mean cardiac acceleration at 10 seconds in Steps 1 and 2 was significant (2.40 +/- 0.19 and 0.71 +/- 0.12 beats min-1 sec-1, p \u3c 0.0001).CONCLUSION: The initial vagal withdrawal of exercise-induced tachycardia, as a frontline adaptive mechanism, can be indirectly identified from HR transients using cardiac acceleration as a new marker

Ricci Collineations of the Bianchi Type II, VIII, and IX Space-times

Ricci and contracted Ricci collineations of the Bianchi type II, VIII, and IX space-times, associated with the vector fields of the form (i) one component of $\xi^a(x^b)$ is different from zero and (ii) two components of $\xi^a(x^b)$ are different from zero, for $a,b=1,2,3,4$, are presented. In subcase (i.b), which is $\xi^a= (0,\xi^2(x^a),0,0)$, some known solutions are found, and in subcase (i.d), which is $\xi^a =(0,0,0,\xi^4(x^a))$, choosing $S(t)=const.\times R(t)$, the Bianchi type II, VIII, and IX space-times is reduced to the Robertson-Walker metric.Comment: 12 Pages, LaTeX, 1 Table, no figure

Survey on Vision-based Path Prediction

Path prediction is a fundamental task for estimating how pedestrians or vehicles are going to move in a scene. Because path prediction as a task of computer vision uses video as input, various information used for prediction, such as the environment surrounding the target and the internal state of the target, need to be estimated from the video in addition to predicting paths. Many prediction approaches that include understanding the environment and the internal state have been proposed. In this survey, we systematically summarize methods of path prediction that take video as input and and extract features from the video. Moreover, we introduce datasets used to evaluate path prediction methods quantitatively.Comment: DAPI 201

Inflating Lorentzian Wormholes

It has been speculated that Lorentzian wormholes of the Morris- Thorne type might be allowed by the laws of physics at submicroscopic, e.g. Planck, scales and that a sufficiently advanced civilization might be able to enlarge them to classical size. The purpose of this paper is to explore the possibility that inflation might provide a natural mechanism for the enlargement of such wormholes to macroscopic size. A new classical metric is presented for a Lorentzian wormhole which is imbedded in a flat deSitter space. It is shown that the throat and proper length of the wormhole inflate. The resulting properties and stress-energy tensor associated with this metric are discussed.Comment: 24 pg

Synthesis, structural and photo-physical studies of transition metal complexes with Mannich bases derived from 2-mercaptobenzimidazole

Two Mannich base ligands, [1-(di-n-butylamine-N-methyl)mercapto-1H-benz-imidazole] (L1) and [1-(diphenylamine-N-methyl)mercapto-1H-benzimidazole] (L2)have been synthesized and further reacted with Co(II), Ni(II), Cu(II) and Zn(II) ionsto afford their respective complexes. The progress of the reaction was monitored by thin layer chromatography. The structural elucidation of Mannich base ligands and their metal complexes was done by Fourier Transform Infrared (FTIR), UV-Visible, Nuclear Magnetic Resonance spectroscopy (1H NMR & 13C NMR) and Atomic absorption spectroscopy (AAS) / Inductively coupled plasma emission spectroscopy (ICPES). FTIR and NMR studies supported the monoanionic bidentate coordination mode of L1 and L2 while tetrahedral geometries of metal complexes were proposed on the basis of AAS/ICP, magnetic moment and electronic spectroscopic data. The synthesized compounds were also investigated for their luminescent behavior which exhibited broad emission bands indicating charge transfer nature of the involved transitions.               KEY WORDS: Metal complexes, Mannich bases, 2-Mercaptobenzimidazole, Luminescence Bull. Chem. Soc. Ethiop. 2018, 32(3), 481-490.DOI: https://dx.doi.org/10.4314/bcse.v32i3.

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