Bit Error Probability Analysis of SSK in DF Relaying with Threshold-Based Best Relay Selection and Selection Combining

In this letter, we analyze the end-to-end average bit error probability (ABEP) of space shift keying (SSK) in cooperative relaying with decode-and-forward (DF) protocol, considering multiple relays with a threshold based best relay selection, and selection combining of direct and relayed paths at the destination. We derive an exact analytical expression for the end-to-end ABEP in closed-form for binary SSK, where analytical results agree with simulation results. For non-binary SSK, approximate analytical and simulation results are presented.

Correlation between local structural dynamics of proteins inferred from NMR ensembles and evolutionary dynamics of homologues of known structure

Conformational changes in proteins are extremely important for their biochemical functions. Correlation between inherent conformational variations in a protein and conformational differences in its homologues of known structure is still unclear. In this study, we have used a structural alphabet called Protein Blocks (PBs). PBs are used to perform abstraction of protein 3-D structures into a 1-D strings of 16 alphabets (a-p) based on dihedral angles of overlapping pentapeptides. We have analyzed the variations in local conformations in terms of PBs represented in the ensembles of 801 protein structures determined using NMR spectroscopy. In the analysis of concatenated data over all the residues in all the NMR ensembles, we observe that the overall nature of inherent local structural variations in NMR ensembles is similar to the nature of local structural differences in homologous proteins with a high correlation coefficient of .94. High correlation at the alignment positions corresponding to helical and beta-sheet regions is only expected. However, the correlation coefficient by considering only the loop regions is also quite high (.91). Surprisingly, segregated position-wise analysis shows that this high correlation does not hold true to loop regions at the structurally equivalent positions in NMR ensembles and their homologues of known structure. This suggests that the general nature of local structural changes is unique; however most of the local structural variations in loop regions of NMR ensembles do not correlate to their local structural differences at structurally equivalent positions in homologues.

Ramachandran analysis of conserved glycyl residues in homologous proteins of known structure

High conservation of glycyl residues in homologous proteins is fairly frequent. It is commonly understood that glycine tends to be highly conserved either because of its unique Ramachandran angles or to avoid steric clash that would arise with a larger side chain. Using a database of aligned 3D structures of homologous proteins we identified conserved Gly in 288 alignment positions from 85 families. Ninety-six of these alignment positions correspond to conserved Gly residue with (phi, ) values allowed for non-glycyl residues. Reasons for this observation were investigated by in-silico mutation of these glycyl residues to Ala. We found in 94% of the cases a short contact exists between the C atom of the introduced Ala with the atoms which are often distant in the primary structure. This suggests the lack of space even for a short side chain thereby explaining high conservation of glycyl residues even when they adopt (phi, ) values allowed for Ala. In 189 alignment positions, the conserved glycyl residues adopt (phi, ) values which are disallowed for Ala. In-silico mutation of these Gly residues to Ala almost always results in steric hindrance involving C atom of Ala as one would expect by comparing Ramachandran maps for Ala and Gly. Rare occurrence of the disallowed glycyl conformations even in ultrahigh resolution protein structures are accompanied by short contacts in the crystal structures and such disallowed conformations are not conserved in the homologues. These observations raise the doubt on the accuracy of such glycyl conformations in proteins.

Features in visual search combine linearly

Single features such as line orientation and length are known to guide visual search, but relatively little is known about how multiple features combine in search. To address this question, we investigated how search for targets differing in multiple features ( intensity, length, orientation) from the distracters is related to searches for targets differing in each of the individual features. We tested race models (based on reaction times) and coactivation models ( based on reciprocal of reaction times) for their ability to predict multiple feature searches. Multiple feature searches were best accounted for by a co-activation model in which feature information combined linearly (r = 0.95). This result agrees with the classic finding that these features are separable i.e., subjective dissimilarity ratings sum linearly. We then replicated the classical finding that the length and width of a rectangle are integral features-in other words, they combine nonlinearly in visual search. However, to our surprise, upon including aspect ratio as an additional feature, length and width combined linearly and this model outperformed all other models. Thus, length and width of a rectangle became separable when considered together with aspect ratio. This finding predicts that searches involving shapes with identical aspect ratio should be more difficult than searches where shapes differ in aspect ratio. We confirmed this prediction on a variety of shapes. We conclude that features in visual search co-activate linearly and demonstrate for the first time that aspect ratio is a novel feature that guides visual search.

Upper Bounds on the Size of Grain-Correcting Codes

In this paper, we revisit the combinatorial error model of Mazumdar et al. that models errors in high-density magnetic recording caused by lack of knowledge of grain boundaries in the recording medium. We present new upper bounds on the cardinality/rate of binary block codes that correct errors within this model. All our bounds, except for one, are obtained using combinatorial arguments based on hypergraph fractional coverings. The exception is a bound derived via an information-theoretic argument. Our bounds significantly improve upon existing bounds from the prior literature.

Digestive ripening and green synthesis of ultra-small (r < 2 nm) stable ZnO quantum dots

Given the recent reports pertaining to novel optical properties of ultra-small quantum dots (QDs) (r <2 nm), this nanomaterial is of relevance to both technology and science. However it is well known that in these size regimes most chalocogenide QD dispersions are unstable. Since applications often require use of QD dispersions (e.g. for deployment on a substrate), stabilizing these ultra-small particles is of practical relevance. In this work we demonstrate a facile, green, solution approach for synthesis of stable, ultra-small ZnO QDs having radius less than 2 nm. The particle size is calculated using Brits' equation and confirmed by transmission electron micrographs. ZnO QDs reported remain stable for > 120 days in ethanol (at similar to 298-303 K). We report digestive ripening (DR) in TEA capped ZnO QDs; this occurs rapidly over a short duration of 5 min. To explain this observation we propose a suitable mechanism based on the Lee's theory, which correlates the tendency of DR with the observed zeta potentials of the dispersed medium. To the best of our knowledge this is the (i) first report on DR in oxide QDs, as well as the first direct experimental verification of Lee's theory, and (ii) most rapid DR reported so far. The facile nature of the method presented here makes ultra-small ZnO readily accessible for fundamental exploration and technologically relevant applications. (C) 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

BELIEF PROPAGATION FOR OPTIMAL EDGE COVER IN THE RANDOM COMPLETE GRAPH

We apply the objective method of Aldous to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge costs. The limit, as the number of vertices goes to infinity, of the expected minimum cost for this problem is known via a combinatorial approach of Hessler and Wastlund. We provide a proof of this result using the machinery of the objective method and local weak convergence, which was used to prove the (2) limit of the random assignment problem. A proof via the objective method is useful because it provides us with more information on the nature of the edge's incident on a typical root in the minimum-cost edge cover. We further show that a belief propagation algorithm converges asymptotically to the optimal solution. This can be applied in a computational linguistics problem of semantic projection. The belief propagation algorithm yields a near optimal solution with lesser complexity than the known best algorithms designed for optimality in worst-case settings.

Constraints on the omega pi form factor from analyticity and unitarity

Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic omega pi form factor and certain experimental data, we investigate this form factor using analyticity and unitarity in a framework known as the method of unitarity bounds. We use a QCD correlator computed on the spacelike axis by operator product expansion and perturbative QCD as input, and exploit unitarity and the positivity of its spectral function, including the two-pion contribution that can be reliably calculated using high-precision data on the pion form factor. From this information, we derive upper and lower bounds on the modulus of the omega pi form factor in the elastic region. The results provide a significant check on those obtained with standard dispersion relations, confirming the existence of a disagreement with experimental data in the region around 0.6 GeV.

LOWER BOUNDS FOR BOXICITY

An axis-parallel b-dimensional box is a Cartesian product R-1 x R-2 x ... x R-b where R-i is a closed interval of the form a(i),b(i)] on the real line. For a graph G, its boxicity box(G) is the minimum dimension b, such that G is representable as the intersection graph of boxes in b-dimensional space. Although boxicity was introduced in 1969 and studied extensively, there are no significant results on lower bounds for boxicity. In this paper, we develop two general methods for deriving lower bounds. Applying these methods we give several results, some of which are listed below: 1. The boxicity of a graph on n vertices with no universal vertices and minimum degree delta is at least n/2(n-delta-1). 2. Consider the g(n,p) model of random graphs. Let p <= 1 - 40logn/n(2.) Then with high `` probability, box(G) = Omega(np(1 - p)). On setting p = 1/2 we immediately infer that almost all graphs have boxicity Omega(n). Another consequence of this result is as follows: For any positive constant c < 1, almost all graphs on n vertices and m <= c((n)(2)) edges have boxicity Omega(m/n). 3. Let G be a connected k-regular graph on n vertices. Let lambda be the second largest eigenvalue in absolute value of the adjacency matrix of G. Then, the boxicity of G is a least (kappa(2)/lambda(2)/log(1+kappa(2)/lambda(2))) (n-kappa-1/2n). 4. For any positive constant c 1, almost all balanced bipartite graphs on 2n vertices and m <= cn(2) edges have boxicity Omega(m/n).

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.

Lower bounds for testing triangle-freeness in Boolean functions

Given a Boolean function , we say a triple (x, y, x + y) is a triangle in f if . A triangle-free function contains no triangle. If f differs from every triangle-free function on at least points, then f is said to be -far from triangle-free. In this work, we analyze the query complexity of testers that, with constant probability, distinguish triangle-free functions from those -far from triangle-free. Let the canonical tester for triangle-freeness denotes the algorithm that repeatedly picks x and y uniformly and independently at random from , queries f(x), f(y) and f(x + y), and checks whether f(x) = f(y) = f(x + y) = 1. Green showed that the canonical tester rejects functions -far from triangle-free with constant probability if its query complexity is a tower of 2's whose height is polynomial in . Fox later improved the height of the tower in Green's upper bound to . A trivial lower bound of on the query complexity is immediate. In this paper, we give the first non-trivial lower bound for the number of queries needed. We show that, for every small enough , there exists an integer such that for all there exists a function depending on all n variables which is -far from being triangle-free and requires queries for the canonical tester. We also show that the query complexity of any general (possibly adaptive) one-sided tester for triangle-freeness is at least square root of the query complexity of the corresponding canonical tester. Consequently, this means that any one-sided tester for triangle-freeness must make at least queries.

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.

Performance of OFDM Systems With Best-m Feedback, Scheduling, and Delays for Uniformly Correlated Subchannels

Contemporary cellular standards, such as Long Term Evolution (LTE) and LTE-Advanced, employ orthogonal frequency-division multiplexing (OFDM) and use frequency-domain scheduling and rate adaptation. In conjunction with feedback reduction schemes, high downlink spectral efficiencies are achieved while limiting the uplink feedback overhead. One such important scheme that has been adopted by these standards is best-m feedback, in which every user feeds back its m largest subchannel (SC) power gains and their corresponding indices. We analyze the single cell average throughput of an OFDM system with uniformly correlated SC gains that employs best-m feedback and discrete rate adaptation. Our model incorporates three schedulers that cover a wide range of the throughput versus fairness tradeoff and feedback delay. We show that, for small m, correlation significantly reduces average throughput with best-m feedback. This result is pertinent as even in typical dispersive channels, correlation is high. We observe that the schedulers exhibit varied sensitivities to correlation and feedback delay. The analysis also leads to insightful expressions for the average throughput in the asymptotic regime of a large number of users.

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.

Lower bounds on Ricci flow invariant curvatures and geometric applications

We consider Ricci flow invariant cones C in the space of curvature operators lying between the cones ``nonnegative Ricci curvature'' and ``nonnegative curvature operator''. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies R + epsilon I is an element of C at the initial time, then it satisfies R + epsilon I is an element of C on some time interval depending only on the scalar curvature control. This allows us to link Gromov-Hausdorff convergence and Ricci flow convergence when the limit is smooth and R + I is an element of C along the sequence of initial conditions. Another application is a stability result for manifolds whose curvature operator is almost in C. Finally, we study the case where C is contained in the cone of operators whose sectional curvature is nonnegative. This allows us to weaken the assumptions of the previously mentioned applications. In particular, we construct a Ricci flow for a class of (not too) singular Alexandrov spaces.