Rainbow Connection Number and Connectivity

The rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges, so that every pair of vertices is connected by at least one path in which no two edges are colored the same. Our main result is that rc(G) <= inverted right perpendicularn/2inverted left perpendicular for any 2-connected graph with at least three vertices. We conjecture that rc(G) <= n/kappa + C for a kappa-connected graph G of order n, where C is a constant, and prove the conjecture for certain classes of graphs. We also prove that rc(G) < (2 + epsilon)n/kappa + 23/epsilon(2) for any epsilon > 0.

Real-time monitoring of critical nodes with minimal number of Phasor Measurement Units

This paper presents a method for placement of Phasor Measurement Units, ensuring the monitoring of vulnerable buses which are obtained based on transient stability analysis of the overall system. Real-time monitoring of phase angles across different nodes, which indicates the proximity to instability, the very purpose will be well defined if the PMUs are placed at buses which are more vulnerable. The issue is to identify the key buses where the PMUs should be placed when the transient stability prediction is taken into account considering various disturbances. Integer Linear Programming technique with equality and inequality constraints is used to find out the optimal placement set with key buses identified from transient stability analysis. Results on IEEE-14 bus system are presented to illustrate the proposed approach.

Rainbow connection number and connected dominating sets

The rainbow connection number of a connected graph is the minimum number of colors needed to color its edges, so that every pair of its vertices is connected by at least one path in which no two edges are colored the same. In this article we show that for every connected graph on n vertices with minimum degree delta, the rainbow connection number is upper bounded by 3n/(delta + 1) + 3. This solves an open problem from Schiermeyer (Combinatorial Algorithms, Springer, Berlin/Hiedelberg, 2009, pp. 432437), improving the previously best known bound of 20n/delta (J Graph Theory 63 (2010), 185191). This bound is tight up to additive factors by a construction mentioned in Caro et al. (Electr J Combin 15(R57) (2008), 1). As an intermediate step we obtain an upper bound of 3n/(delta + 1) - 2 on the size of a connected two-step dominating set in a connected graph of order n and minimum degree d. This bound is tight up to an additive constant of 2. This result may be of independent interest. We also show that for every connected graph G with minimum degree at least 2, the rainbow connection number, rc(G), is upper bounded by Gc(G) + 2, where Gc(G) is the connected domination number of G. Bounds of the form diameter(G)?rc(G)?diameter(G) + c, 1?c?4, for many special graph classes follow as easy corollaries from this result. This includes interval graphs, asteroidal triple-free graphs, circular arc graphs, threshold graphs, and chain graphs all with minimum degree delta at least 2 and connected. We also show that every bridge-less chordal graph G has rc(G)?3.radius(G). In most of these cases, we also demonstrate the tightness of the bounds.

Vaporization dynamics of functional droplets in a hot laminar air jet

The vaporization characteristics of pendant droplets of various chemical compositions (like conventional fuels, alternative fuels and nanosuspensions) subjected to convective heating in a laminar air jet have been analyzed. Different heating conditions were achieved by controlling the air temperature and velocity fields around the droplet. A hybrid timescale has been proposed which incorporates the effects of latent heat of vaporization, saturation vapor pressure and thermal diffusivity. This timescale in essence encapsulates the different parameters that influence the droplet vaporization rate. The analysis further permits the evaluation of the effect of various parameters such as surrounding temperature, Reynolds number, far-field vapor presence, impurity content and agglomeration dynamics (nanosuspensions) in the droplet. Flow visualization has been carried out to understand the role of internal recirculation on the vaporization rate. The visualization indicates the presence of a single vortex cell within the droplet on account of the rotation and oscillation of the droplet due to aerodynamic load. External heating induced agglomeration in nanofluids leads to morphological changes during the vaporization process. These morphological changes and alteration in vaporization behavior have been assessed using high speed imaging of the diameter regression and Scanning Electron Microscopy images of the resultant precipitate. (C) 2012 Elsevier Ltd. All rights reserved.

Cubicity, degeneracy, and crossing number

A $k$-box $B=(R_1,...,R_k)$, where each $R_i$ is a closed interval on the real line, is defined to be the Cartesian product $R_1\times R_2\times ...\times R_k$. If each $R_i$ is a unit length interval, we call $B$ a $k$-cube. Boxicity of a graph $G$, denoted as $\boxi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-boxes. Similarly, the cubicity of $G$, denoted as $\cubi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-cubes. It was shown in [L. Sunil Chandran, Mathew C. Francis, and Naveen Sivadasan: Representing graphs as the intersection of axis-parallel cubes. MCDES-2008, IISc Centenary Conference, available at CoRR, abs/cs/ 0607092, 2006.] that, for a graph $G$ with maximum degree $\Delta$, $\cubi(G)\leq \lceil 4(\Delta +1)\log n\rceil$. In this paper, we show that, for a $k$-degenerate graph $G$, $\cubi(G) \leq (k+2) \lceil 2e \log n \rceil$. Since $k$ is at most $\Delta$ and can be much lower, this clearly is a stronger result. This bound is tight. We also give an efficient deterministic algorithm that runs in $O(n^2k)$ time to output a $8k(\lceil 2.42 \log n\rceil + 1)$ dimensional cube representation for $G$. An important consequence of the above result is that if the crossing number of a graph $G$ is $t$, then $\boxi(G)$ is $O(t^{1/4}{\lceil\log t\rceil}^{3/4})$ . This bound is tight up to a factor of $O((\log t)^{1/4})$. We also show that, if $G$ has $n$ vertices, then $\cubi(G)$ is $O(\log n + t^{1/4}\log t)$. Using our bound for the cubicity of $k$-degenerate graphs we show that cubicity of almost all graphs in $\mathcal{G}(n,m)$ model is $O(d_{av}\log n)$, where $d_{av}$ denotes the average degree of the graph under consideration. model is O(davlogn).

Effects of two-wheelers on saturation flow at signalized intersections in developing countries

Two-wheelers (TW) constitute a major proportion of urban traffic in developing countries and therefore their effect on the saturation flow at signalized intersections could be substantial. This paper attempts to study and analyze the effect of two-wheelers on the saturation flow of signalized intersections by collecting data at a few signalized intersections in Bangalore, India. A strong correlation is observed between the measured saturation flow and the proportion of two-wheeler traffic, which suggest that two-wheelers have significant impact and should be considered in the capacity analysis of signalized intersections. In this paper, the effect of two-wheelers on saturation flow rate is incorporated in a previous model by calibrating and introducing a new adjustment factor for two-wheelers. Results show that saturation flow measured using the modified HCM equation is closer to observed saturation flow values.

Coulomb-hole summations and energies for GW calculations with limited number of empty orbitals: a modified static remainder approach

Ab initio GW calculations are a standard method for computing the spectroscopic properties of many materials. The most computationally expensive part in conventional implementations of the method is the generation and summation over the large number of empty orbitals required to converge the electron self-energy. We propose a scheme to reduce the summation over empty states by the use of a modified static remainder approximation, which is simple to implement and yields accurate self-energies for both bulk and molecular systems requiring a small fraction of the typical number of empty orbitals.

Optimal design of timer-based, distributed selection with unknown number of nodes

The timer-based selection scheme is a popular, simple, and distributed scheme that is used to select the best node from a set of available nodes. In it, each node sets a timer as a function of a local preference number called a metric, and transmits a packet when its timer expires. The scheme ensures that the timer of the best node, which has the highest metric, expires first. However, it fails to select the best node if another node transmits a packet within Delta s of the transmission by the best node. We derive the optimal timer mapping that maximizes the average success probability for the practical scenario in which the number of nodes in the system is unknown but only its probability distribution is known. We show that it has a special discrete structure, and present a recursive characterization to determine it. We benchmark its performance with ad hoc approaches proposed in the literature, and show that it delivers significant gains. New insights about the optimality of some ad hoc approaches are also developed.

On the Chern number of I-admissible filtrations of ideals

Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e(1)(I) of the Hilbert polynomial of an I-admissible filtration I is called the Chern number of I. A formula for the Chern number has been derived involving the Euler characteristic of subcomplexes of a Koszul complex. Specific formulas for the Chern number have been given in local rings of dimension at most two. These have been used to provide new and unified proofs of several results about e(1)(I).

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

A dynamical instability is observed in experimental studies on micro-channels of rectangular cross-section with smallest dimension 100 and 160 mu m in which one of the walls is made of soft gel. There is a spontaneous transition from an ordered, laminar flow to a chaotic and highly mixed flow state when the Reynolds number increases beyond a critical value. The critical Reynolds number, which decreases as the elasticity modulus of the soft wall is reduced, is as low as 200 for the softest wall used here (in contrast to 1200 for a rigid-walled channel) The instability onset is observed by the breakup of a dye-stream introduced in the centre of the micro-channel, as well as the onset of wall oscillations due to laser scattering from fluorescent beads embedded in the wall of the channel. The mixing time across a channel of width 1.5 mm, measured by dye-stream and outlet conductance experiments, is smaller by a factor of 10(5) than that for a laminar flow. The increased mixing rate comes at very little cost, because the pressure drop (energy requirement to drive the flow) increases continuously and modestly at transition. The deformed shape is reconstructed numerically, and computational fluid dynamics (CFD) simulations are carried out to obtain the pressure gradient and the velocity fields for different flow rates. The pressure difference across the channel predicted by simulations is in agreement with the experiments (within experimental errors) for flow rates where the dye stream is laminar, but the experimental pressure difference is higher than the simulation prediction after dye-stream breakup. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modelled as a neo-Hookean elastic solid, and the simulation results for the mean velocity and pressure gradient from the CFD simulations are used as inputs. The stability analysis accurately predicts the Reynolds number (based on flow rate) at which an instability is observed in the dye stream, and it also predicts that the instability first takes place at the downstream converging section of the channel, and not at the upstream diverging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation; if we assume a parabolic velocity profile with the pressure gradient given by the plane Poiseuille law, the flow is always found to be stable.

Design and Analysis of an Acknowledgment-Aware Asynchronous MPR MAC Protocol for Distributed WLANs

Multi-packet reception (MPR) promises significant throughput gains in wireless local area networks (WLANs) by allowing nodes to transmit even in the presence of ongoing transmissions in the medium. However, the medium access control (MAC) layer must now be redesigned to facilitate rather than discourage - these overlapping transmissions. We investigate asynchronous MPR MAC protocols, which successfully accomplish this by controlling the node behavior based on the number of ongoing transmissions in the channel. The protocols use the backoff timer mechanism of the distributed coordination function, which makes them practically appealing. We first highlight a unique problem of acknowledgment delays, which arises in asynchronous MPR, and investigate a solution that modifies the medium access rules to reduce these delays and increase system throughput in the single receiver scenario. We develop a general renewal-theoretic fixed-point analysis that leads to expressions for the saturation throughput, packet dropping probability, and average head-of-line packet delay. We also model and analyze the practical scenario in which nodes may incorrectly estimate the number of ongoing transmissions.

Effect of steady rotation on low Reynolds number vortex shedding behind a circular cylinder

In this paper control of oblique vortex shedding in the wake behind a straight circular cylinder is explored experimentally and computationally. Towards this, steady rotation of the cylinder about its axis is used as a control device. Some limited studies are also performed with a stepped circular cylinder, where at the step the flow is inevitably three-dimensional irrespective of the rotation rate. When there is no rotation, the vortex shedding pattern is three dimensional as described in many previous studies. With a non-zero rotation rate, it is demonstrated experimentally as well as numerically that the shedding pattern becomes more and more two-dimensional. At sufficiently high rotation rates, the vortex shedding is completely suppressed.

Effect of myonuclear number and mitochondrial fusion on Drosophila indirect flight muscle organization and size

Mechanisms involved in establishing the organization and numbers of fibres in a muscle are not completely understood. During Drosophila indirect flight muscle (IFM) formation, muscle growth is achieved by both incorporating hundreds of nuclei, and hypertrophy. As a result, IFMs provide a good model with which to understand the mechanisms that govern overall muscle organization and growth. We present a detailed analysis of the organization of dorsal longitudinal muscles (DLMs), a subset of the IFMs. We show that each DLM is similar to a vertebrate fascicle and consists of multiple muscle fibres. However, increased fascicle size does not necessarily change the number of constituent fibres, but does increase the number of myofibrils packed within the fibres. We also find that altering the number of myoblasts available for fusion changes DLM fascicle size and fibres are loosely packed with myofibrils. Additionally, we show that knock down of genes required for mitochondrial fusion causes a severe reduction in the size of DLM fascicles and fibres. Our results establish the organization levels of DLMs and highlight the importance of the appropriate number of nuclei and mitochondrial fusion in determining the overall organization, growth and size of DLMs. (C) 2013 Elsevier Inc. All rights reserved.

EFFICIENT QUANTUM RANDOM NUMBER GENERATION USING QUANTUM INDISTINGUISHABILITY

In this paper, we propose a quantum method for generation of random numbers based on bosonic stimulation. Randomness arises through the path-dependent indeterministic amplification of two competing bosonic modes. We show that the process provides an efficient method for macroscopic extraction of microscopic randomness.

Optimal Timer-Based Best Node Selection for Wireless Systems with Unknown Number of Nodes

The distributed, low-feedback, timer scheme is used in several wireless systems to select the best node from the available nodes. In it, each node sets a timer as a function of a local preference number called a metric, and transmits a packet when its timer expires. The scheme ensures that the timer of the best node, which has the highest metric, expires first. However, it fails to select the best node if another node transmits a packet within Delta s of the transmission by the best node. We derive the optimal metric-to-timer mappings for the practical scenario where the number of nodes is unknown. We consider two cases in which the probability distribution of the number of nodes is either known a priori or is unknown. In the first case, the optimal mapping maximizes the success probability averaged over the probability distribution. In the second case, a robust mapping maximizes the worst case average success probability over all possible probability distributions on the number of nodes. Results reveal that the proposed mappings deliver significant gains compared to the mappings considered in the literature.