Codes with Locality for Two Erasures

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated with small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan et al, in which recovery from a single erasure is considered. By studying the generalized Hamming weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Turan graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from 2 erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.

Benchmarking sustainability of Indian electricity system: An indicator approach

India needs to significantly increase its electricity consumption levels, in a sustainable manner, if it has to ensure rapid economic development, a goal that remains the most potent tool for delivering adaptation capacity to its poor who will suffer the worst consequences of climate change. Resource/supply constraints faced by conventional energy sources, techno-economic constraints faced by renewable energy sources, and the bounds imposed by climate change on fossil fuel use are likely to undermine India's quest for having a robust electricity system that can effectively contribute to achieving accelerated, sustainable and inclusive economic growth. One possible way out could be transitioning into a sustainable electricity system, which is a trade-off solution having taken into account the economic, social and environmental concerns. As a first step toward understanding this transition, we contribute an indicator based hierarchical multidimensional framework as an analytical tool for sustainability assessment of electricity systems, and validate it for India's national electricity system. We evaluate Indian electricity system using this framework by comparing it with a hypothetical benchmark sustainable electrical system, which was created using best indicator values realized across national electricity systems in the world. This framework, we believe, can be used to examine the social, economic and environmental implications of the current Indian electricity system as well as setting targets for future development. The analysis with the indicator framework provides a deeper understanding of the system, identify and quantify the prevailing sustainability gaps and generate specific targets for interventions. We use this framework to compute national electricity system sustainability index (NESSI) for India. (C) 2014 Elsevier Ltd. All rights reserved.

Rainbow matchings in strongly edge-colored graphs

A rainbow matching of an edge-colored graph G is a matching in which no two edges have the same color. There have been several studies regarding the maximum size of a rainbow matching in a properly edge-colored graph G in terms of its minimum degree 3(G). Wang (2011) asked whether there exists a function f such that a properly edge-colored graph G with at least f (delta(G)) vertices is guaranteed to contain a rainbow matching of size delta(G). This was answered in the affirmative later: the best currently known function Lo and Tan (2014) is f(k) = 4k - 4, for k >= 4 and f (k) = 4k - 3, for k <= 3. Afterwards, the research was focused on finding lower bounds for the size of maximum rainbow matchings in properly edge-colored graphs with fewer than 4 delta(G) - 4 vertices. Strong edge-coloring of a graph G is a restriction of proper edge-coloring where every color class is required to be an induced matching, instead of just being a matching. In this paper, we give lower bounds for the size of a maximum rainbow matching in a strongly edge-colored graph Gin terms of delta(G). We show that for a strongly edge-colored graph G, if |V(G)| >= 2 |3 delta(G)/4|, then G has a rainbow matching of size |3 delta(G)/4|, and if |V(G)| < 2 |3 delta(G)/4|, then G has a rainbow matching of size |V(G)|/2] In addition, we prove that if G is a strongly edge-colored graph that is triangle-free, then it contains a rainbow matching of size at least delta(G). (C) 2015 Elsevier B.V. All rights reserved.

GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

Jet substructure and probes of CP violation in Vh production

We analyse the hVV (V = W, Z) vertex in a model independent way using Vh production. To that end, we consider possible corrections to the Standard Model Higgs Lagrangian, in the form of higher dimensional operators which parametrise the effects of new physics. In our analysis, we pay special attention to linear observables that can be used to probe CP violation in the same. By considering the associated production of a Higgs boson with a vector boson (W or Z), we use jet substructure methods to define angular observables which are sensitive to new physics effects, including an asymmetry which is linearly sensitive to the presence of CP odd effects. We demonstrate how to use these observables to place bounds on the presence of higher dimensional operators, and quantify these statements using a log likelihood analysis. Our approach allows one to probe separately the hZZ and hWW vertices, involving arbitrary combinations of BSM operators, at the Large Hadron Collider.

Sulfate Chemistry for High-Voltage Insertion Materials: Synthetic, Structural and Electrochemical Insights

Rechargeable batteries based on Li and Na ions have been growing leaps and bounds since their inception in the 1970s. They enjoy significant attention from both the fundamental science point of view and practical applications ranging from portable electronics to hybrid vehicles and grid storage. The steady demand for building better batteries calls for discovery, optimisation and implementation of novel positive insertion (cathode) materials. In this quest, chemists have tried to unravel many future cathode materials by taking into consideration their eco-friendly synthesis, material/process economy, high energy density, safety, easy handling and sustainability. Interestingly, sulfate-based cathodes offer a good combination of sustainable syntheses and high energy density owing to their high-voltage operation, stemming from electronegative SO42- units. This review delivers a sneak peak at the recent advances in the discovery and development of sulfate-containing cathode materials by focusing on their synthesis, crystal structure and electrochemical performance. Several family of cathodes are independently discussed. They are 1) fluorosulfates AMSO(4)F], 2) bihydrated fluorosulfates AMSO(4)F2H(2)O], 3) hydroxysulfate AMSO(4)OH], 4) bisulfates A(2)M(SO4)(2)], 5) hydrated bisulfates A(2)M(SO4)(2)nH(2)O], 6) oxysulfates Fe-2(SO4)(2)O] and 7) polysulfates A(2)M(2)(SO4)(3)]. A comparative study of these sulfate-based cathodes has been provided to offer an outlook on the future development of high-voltage polyanionic cathode materials for next-generation batteries.

Exploring CP violation in the MSSM

We explore the prospects for observing CP violation in the minimal supersymmetric extension of the Standard Model (MSSM) with six CP-violating parameters, three gaugino mass phases and three phases in trilinear soft supersymmetry-breaking parameters, using the CPsuperH code combined with a geometric approach to maximise CP-violating observables subject to the experimental upper bounds on electric dipole moments. We also implement CP-conserving constraints from Higgs physics, flavour physics and the upper limits on the cosmological dark matter density and spin-independent scattering. We study possible values of observables within the constrained MSSM (CMSSM), the non-universal Higgs model (NUHM), the CPX scenario and a variant of the phenomenological MSSM (pMSSM). We find values of the CP-violating asymmetry A(CP) in b -> s gamma decay that may be as large as 3 %, so future measurements of ACP may provide independent information about CP violation in the MSSM. We find that CP-violating MSSM contributions to the B-s meson mass mixing term Delta M-Bs are in general below the present upper limit, which is dominated by theoretical uncertainties. If these could be reduced, Delta M-Bs could also provide an interesting and complementary constraint on the six CP-violating MSSM phases, enabling them all to be determined experimentally, in principle. We also find that CP violation in the h(2,3)tau(+)tau(-) and h(2,3) (t) over bart couplings can be quite large, and so may offer interesting prospects for future pp, e(+) e(-), mu(+) mu(-) and gamma gamma colliders.

Heterochromatic paths in edge colored graphs without small cycles and heterochromatic-triangle-free graphs

Conditions for the existence of heterochromatic Hamiltonian paths and cycles in edge colored graphs are well investigated in literature. A related problem in this domain is to obtain good lower bounds for the length of a maximum heterochromatic path in an edge colored graph G. This problem is also well explored by now and the lower bounds are often specified as functions of the minimum color degree of G - the minimum number of distinct colors occurring at edges incident to any vertex of G - denoted by v(G). Initially, it was conjectured that the lower bound for the length of a maximum heterochromatic path for an edge colored graph G would be 2v(G)/3]. Chen and Li (2005) showed that the length of a maximum heterochromatic path in an edge colored graph G is at least v(G) - 1, if 1 <= v(G) <= 7, and at least 3v(G)/5] + 1 if v(G) >= 8. They conjectured that the tight lower bound would be v(G) - 1 and demonstrated some examples which achieve this bound. An unpublished manuscript from the same authors (Chen, Li) reported to show that if v(G) >= 8, then G contains a heterochromatic path of length at least 120 + 1. In this paper, we give lower bounds for the length of a maximum heterochromatic path in edge colored graphs without small cycles. We show that if G has no four cycles, then it contains a heterochromatic path of length at least v(G) - o(v(G)) and if the girth of G is at least 4 log(2)(v(G)) + 2, then it contains a heterochromatic path of length at least v(G) - 2, which is only one less than the bound conjectured by Chen and Li (2005). Other special cases considered include lower bounds for the length of a maximum heterochromatic path in edge colored bipartite graphs and triangle-free graphs: for triangle-free graphs we obtain a lower bound of 5v(G)/6] and for bipartite graphs we obtain a lower bound of 6v(G)-3/7]. In this paper, it is also shown that if the coloring is such that G has no heterochromatic triangles, then G contains a heterochromatic path of length at least 13v(G)/17)]. This improves the previously known 3v(G)/4] bound obtained by Chen and Li (2011). We also give a relatively shorter and simpler proof showing that any edge colored graph G contains a heterochromatic path of length at least (C) 2015 Elsevier Ltd. All rights reserved.

A Critical Assessment of the Flux Transport Dynamo

We first discuss how the flux transport dynamo with reasonably high diffusion can explain both the regular and the irregular features of the solar cycle quite well. Then, we critically examine the inadequacies of the model and the challenge posed by some recent observational data about meridional circulation, arriving at a conclusion that this model can still work within the bounds of observational data.

Relay Selection with Channel Probing in Sleep-Wake Cycling Wireless Sensor Networks

In geographical forwarding of packets in a large wireless sensor network (WSN) with sleep-wake cycling nodes, we are interested in the local decision problem faced by a node that has ``custody'' of a packet and has to choose one among a set of next-hop relay nodes to forward the packet toward the sink. Each relay is associated with a ``reward'' that summarizes the benefit of forwarding the packet through that relay. We seek a solution to this local problem, the idea being that such a solution, if adopted by every node, could provide a reasonable heuristic for the end-to-end forwarding problem. Toward this end, we propose a local relay selection problem consisting of a forwarding node and a collection of relay nodes, with the relays waking up sequentially at random times. At each relay wake-up instant, the forwarder can choose to probe a relay to learn its reward value, based on which the forwarder can then decide whether to stop (and forward its packet to the chosen relay) or to continue to wait for further relays to wake up. The forwarder's objective is to select a relay so as to minimize a combination of waiting delay, reward, and probing cost. The local decision problem can be considered as a variant of the asset selling problem studied in the operations research literature. We formulate the local problem as a Markov decision process (MDP) and characterize the solution in terms of stopping sets and probing sets. We provide results illustrating the structure of the stopping sets, namely, the (lower bound) threshold and the stage independence properties. Regarding the probing sets, we make an interesting conjecture that these sets are characterized by upper bounds. Through simulation experiments, we provide valuable insights into the performance of the optimal local forwarding and its use as an end-to-end forwarding heuristic.

Generalized Spatial Modulation in Large-Scale Multiuser MIMO Systems

Generalized spatial modulation (GSM) uses n(t) transmit antenna elements but fewer transmit radio frequency (RF) chains, n(rf). Spatial modulation (SM) and spatial multiplexing are special cases of GSM with n(rf) = 1 and n(rf) = n(t), respectively. In GSM, in addition to conveying information bits through n(rf) conventional modulation symbols (for example, QAM), the indices of the n(rf) active transmit antennas also convey information bits. In this paper, we investigate GSM for large-scale multiuser MIMO communications on the uplink. Our contributions in this paper include: 1) an average bit error probability (ABEP) analysis for maximum-likelihood detection in multiuser GSM-MIMO on the uplink, where we derive an upper bound on the ABEP, and 2) low-complexity algorithms for GSM-MIMO signal detection and channel estimation at the base station receiver based on message passing. The analytical upper bounds on the ABEP are found to be tight at moderate to high signal-to-noise ratios (SNR). The proposed receiver algorithms are found to scale very well in complexity while achieving near-optimal performance in large dimensions. Simulation results show that, for the same spectral efficiency, multiuser GSM-MIMO can outperform multiuser SM-MIMO as well as conventional multiuser MIMO, by about 2 to 9 dB at a bit error rate of 10(-3). Such SNR gains in GSM-MIMO compared to SM-MIMO and conventional MIMO can be attributed to the fact that, because of a larger number of spatial index bits, GSM-MIMO can use a lower-order QAM alphabet which is more power efficient.

Two player game variant of the Erdos-Szekeres problem

The classical Erdos-Szekeres theorem states that a convex k-gon exists in every sufficiently large point set. This problem has been well studied and finding tight asymptotic bounds is considered a challenging open problem. Several variants of the Erdos-Szekeres problem have been posed and studied in the last two decades. The well studied variants include the empty convex k-gon problem, convex k-gon with specified number of interior points and the chromatic variant. In this paper, we introduce the following two player game variant of the Erdos-Szekeres problem: Consider a two player game where each player playing in alternate turns, place points in the plane. The objective of the game is to avoid the formation of the convex k-gon among the placed points. The game ends when a convex k-gon is formed and the player who placed the last point loses the game. In our paper we show a winning strategy for the player who plays second in the convex 5-gon game and the empty convex 5-gon game by considering convex layer configurations at each step. We prove that the game always ends in the 9th step by showing that the game reaches a specific set of configurations.

Inner Bound on the GDOF of the K-User MIMO Gaussian Symmetric Interference Channel

The K-user multiple input multiple output (MIMO) Gaussian symmetric interference channel where each transmitter has M antennas and each receiver has N antennas is studied from a generalized degrees of freedom (GDOF) perspective. An inner bound on the GDOF is derived using a combination of techniques such as treating interference as noise, zero forcing (ZF) at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, as a function of the number of antennas and the log INR/log SNR level. Several interesting conclusions are drawn from the derived bounds. It is shown that when K > N/M + 1, a combination of the HK and IA schemes performs the best among the schemes considered. When N/M < K <= N/M + 1, the HK-scheme outperforms other schemes and is found to be GDOF optimal in many cases. In addition, when the SNR and INR are at the same level, ZF-receiving and the HK-scheme have the same GDOF performance.

DETERMINATION OF THE MASS OF IGR J17091-3624 FROM ``SPECTRO-TEMPORAL'' VARIATIONS DURING THE ONSET PHASE OF THE 2011 OUTBURST

The 2011 outburst of the black hole candidate IGR J17091-3624 followed the canonical track of state transitions along with the evolution of quasi-periodic oscillation (QPO) frequencies before it began exhibiting various variability classes similar to GRS 1915+105. We use this canonical evolution of spectral and temporal properties to determine the mass of IGR J17091-3624, using three different methods: photon index (Gamma)-QPO frequency (nu) correlation, QPO frequency (nu)-time (day) evolution, and broadband spectral modeling based on two-component advective flow (TCAF). We provide a combined mass estimate for the source using a naive Bayes based joint likelihood approach. This gives a probable mass range of 11.8 M-circle dot-13.7 M-circle dot. Considering each individual estimate and taking the lowermost and uppermost bounds among all three methods, we get a mass range of 8.7 M-circle dot-15.6 M-circle dot with 90% confidence. We discuss the possible implications of our findings in the context of two-component accretion flow.

Converses For Secret Key Agreement and Secure Computing

We consider information theoretic secret key (SK) agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the SK length, which is derived using a reduction of binary hypothesis testing to multiparty SK agreement. Building on this basic result, we derive new converses for multiparty SK agreement. Furthermore, we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to SK agreement. Finally, we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data, using an interactive public communication that by itself does not give away the value of the function. In many cases, we strengthen and improve upon previously known converse bounds. Our results are single-shot and use only the given joint distribution of the correlated observations. For the case when the correlated observations consist of independent and identically distributed (in time) sequences, we derive strong versions of previously known converses.