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).

An Improved Outer Bound on the Storage-Repair-Bandwidth Tradeoff of Exact-Repair Regenerating Codes

While the tradeoff between the amount of data stored and the repair bandwidth of an (n, k, d) regenerating code has been characterized under functional repair (FR), the case of exact repair (ER) remains unresolved. It is known that there do not exist ER codes which lie on the FR tradeoff at most of the points. The question as to whether one can asymptotically approach the FR tradeoff was settled recently by Tian who showed that in the (4, 3, 3) case, the ER region is bounded away from the FR region. The FR tradeoff serves as a trivial outer bound on the ER tradeoff. In this paper, we extend Tian's results by establishing an improved outer bound on the ER tradeoff which shows that the ER region is bounded away from the FR region, for any (n; k; d). Our approach is analytical and builds upon the framework introduced earlier by Shah et. al. Interestingly, a recently-constructed, layered regenerating code is shown to achieve a point on this outer bound for the (5, 4, 4) case. This represents the first-known instance of an optimal ER code that does not correspond to a point on the FR tradeoff.

High Temperatures Result in Smaller Nurseries which Lower Reproduction of Pollinators and Parasites in a Brood Site Pollination Mutualism

In a nursery pollination mutualism, we asked whether environmental factors affected reproduction of mutualistic pollinators, non-mutualistic parasites and seed production via seasonal changes in plant traits such as inflorescence size and within-tree reproductive phenology. We examined seasonal variation in reproduction in Ficus racemosa community members that utilise enclosed inflorescences called syconia as nurseries. Temperature, relative humidity and rainfall defined four seasons: winter; hot days, cold nights; summer and wet seasons. Syconium volumes were highest in winter and lowest in summer, and affected syconium contents positively across all seasons. Greater transpiration from the nurseries was possibly responsible for smaller syconia in summer. The 3-5 degrees C increase in mean temperatures between the cooler seasons and summer reduced fig wasp reproduction and increased seed production nearly two-fold. Yet, seed and pollinator progeny production were never negatively related in any season confirming the mutualistic fig-pollinator association across seasons. Non-pollinator parasites affected seed production negatively in some seasons, but had a surprisingly positive relationship with pollinators in most seasons. While within-tree reproductive phenology did not vary across seasons, its effect on syconium inhabitants varied with season. In all seasons, within-tree reproductive asynchrony affected parasite reproduction negatively, whereas it had a positive effect on pollinator reproduction in winter and a negative effect in summer. Seasonally variable syconium volumes probably caused the differential effect of within-tree reproductive phenology on pollinator reproduction. Within-tree reproductive asynchrony itself was positively affected by intra-tree variation in syconium contents and volume, creating a unique feedback loop which varied across seasons. Therefore, nursery size affected fig wasp reproduction, seed production and within-tree reproductive phenology via the feedback cycle in this system. Climatic factors affecting plant reproductive traits cause biotic relationships between plants, mutualists and parasites to vary seasonally and must be accorded greater attention, especially in the context of climate change.

A Gaussian network model study suggests that structural fluctuations are higher for inactive states than active states of protein kinases

We performed Gaussian network model based normal mode analysis of 3-dimensional structures of multiple active and inactive forms of protein kinases. In 14 different kinases, a more number of residues (1095) show higher structural fluctuations in inactive states than those in active states (525), suggesting that, in general, mobility of inactive states is higher than active states. This statistically significant difference is consistent with higher crystallographic B-factors and conformational energies for inactive than active states, suggesting lower stability of inactive forms. Only a small number of inactive conformations with the DFG motif in the ``in'' state were found to have fluctuation magnitudes comparable to the active conformation. Therefore our study reports for the first time, intrinsic higher structural fluctuation for almost all inactive conformations compared to the active forms. Regions with higher fluctuations in the inactive states are often localized to the aC-helix, aG-helix and activation loop which are involved in the regulation and/or in structural transitions between active and inactive states. Further analysis of 476 kinase structures involved in interactions with another domain/protein showed that many of the regions with higher inactive-state fluctuation correspond to contact interfaces. We also performed extensive GNM analysis of (i) insulin receptor kinase bound to another protein and (ii) holo and apo forms of active and inactive conformations followed by multi-factor analysis of variance. We conclude that binding of small molecules or other domains/proteins reduce the extent of fluctuation irrespective of active or inactive forms. Finally, we show that the perceived fluctuations serve as a useful input to predict the functional state of a kinase.

Molecular and Functional Characterization of RecD, a Novel Member of the SF1 Family of Helicases, from Mycobacterium tuberculosis

Background: The heterotrimeric M. tuberculosis RecBCD complex, or each of its individual subunits, remains uncharacterized. Results: MtRecD exists as a homodimer in solution, catalyzes ssDNA-dependent ATP hydrolysis, unwinding of DNA replication/recombination intermediates, and interacts with RecA. Conclusion: MtRecD possesses strong 5 3- and weak 3 5-helicase activities. Significance: These findings provide insights into the mechanism underlying DSB repair and homologous recombination in mycobacteria. The annotated whole-genome sequence of Mycobacterium tuberculosis revealed the presence of a putative recD gene; however, the biochemical characteristics of its encoded protein product (MtRecD) remain largely unknown. Here, we show that MtRecD exists in solution as a stable homodimer. Protein-DNA binding assays revealed that MtRecD binds efficiently to single-stranded DNA and linear duplexes containing 5 overhangs relative to the 3 overhangs but not to blunt-ended duplex. Furthermore, MtRecD bound more robustly to a variety of Y-shaped DNA structures having 18-nucleotide overhangs but not to a similar substrate containing 5-nucleotide overhangs. MtRecD formed more salt-tolerant complexes with Y-shaped structures compared with linear duplex having 3 overhangs. The intrinsic ATPase activity of MtRecD was stimulated by single-stranded DNA. Site-specific mutagenesis of Lys-179 in motif I abolished the ATPase activity of MtRecD. Interestingly, although MtRecD-catalyzed unwinding showed a markedly higher preference for duplex substrates with 5 overhangs, it could also catalyze significant unwinding of substrates containing 3 overhangs. These results support the notion that MtRecD is a bipolar helicase with strong 5 3 and weak 3 5 unwinding activities. The extent of unwinding of Y-shaped DNA structures was approximate to 3-fold lower compared with duplexes with 5 overhangs. Notably, direct interaction between MtRecD and its cognate RecA led to inhibition of DNA strand exchange promoted by RecA. Altogether, these studies provide the first detailed characterization of MtRecD and present important insights into the type of DNA structure the enzyme is likely to act upon during the processes of DNA repair or homologous recombination.

Improvements to the Froissart bound from AdS/CFT

In this paper we consider the issue of the Froissart bound on the high energy behaviour of total cross sections. This bound, originally derived using principles of analyticity of scattering amplitudes, is seen to be satisfied by all the available experimental data on total hadronic cross sections. At strong coupling, gauge/gravity duality has been used to provide some insights into this behaviour. In this work, we find the subleading terms to the so-derived Froissart bound from AdS/CFT. We find that a (ln s/s0) term is obtained, with a negative coefficient. We see that the fits to the currently available data confirm improvement in the fits due to the inclusion of such a term, with the appropriate sign. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.

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.

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.

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.

Structures of substrate- and nucleotide-bound propionate kinase from Salmonella typhimurium: substrate specificity and phosphate-transfer mechanism

Kinases are ubiquitous enzymes that are pivotal to many biochemical processes. There are contrasting views on the phosphoryl-transfer mechanism in propionate kinase, an enzyme that reversibly transfers a phosphoryl group from propionyl phosphate to ADP in the final step of non-oxidative catabolism of L-threonine to propionate. Here, X-ray crystal structures of propionate- and nucleotide-bound Salmonella typhimurium propionate kinase are reported at 1.8-2.0 angstrom resolution. Although the mode of nucleotide binding is comparable to those of other members of the ASKHA superfamily, propionate is bound at a distinct site deeper in the hydrophobic pocket defining the active site. The propionate carboxyl is at a distance of approximate to 5 angstrom from the -phosphate of the nucleotide, supporting a direct in-line transfer mechanism. The phosphoryl-transfer reaction is likely to occur via an associative S(N)2-like transition state that involves a pentagonal bipyramidal structure with the axial positions occupied by the nucleophile of the substrate and the O atom between the - and the -phosphates, respectively. The proximity of the strictly conserved His175 and Arg236 to the carboxyl group of the propionate and the -phosphate of ATP suggests their involvement in catalysis. Moreover, ligand binding does not induce global domain movement as reported in some other members of the ASKHA superfamily. Instead, residues Arg86, Asp143 and Pro116-Leu117-His118 that define the active-site pocket move towards the substrate and expel water molecules from the active site. The role of Ala88, previously proposed to be the residue determining substrate specificity, was examined by determining the crystal structures of the propionate-bound Ala88 mutants A88V and A88G. Kinetic analysis and structural data are consistent with a significant role of Ala88 in substrate-specificity determination. The active-site pocket-defining residues Arg86, Asp143 and the Pro116-Leu117-His118 segment are also likely to contribute to substrate specificity.

Bearing Capacity Factors for Ring Foundations

Bearing capacity factors because of the components of cohesion, surcharge, and unit weight, respectively, have been computed for smooth and rough ring footings for different combinations of r(i)= r(o) and. by using lower and upper bound theorems of the limit analysis in conjunction with finite elements and linear optimization, where r(i) and r(o) refer to the inner and outer radii of the ring, respectively. It is observed that for a smooth footing with a given value of r(o), the magnitude of the collapse load decreases continuously with an increase in r(i). Conversely, for a rough base, for a given value of r(o), hardly any reduction occurs in the magnitude of the collapse load up to r(i)= r(o) approximate to 0.2, whereas for r(i)= r(o) > 0.2, the magnitude of the collapse load, similar to that of a smooth footing, decreases continuously with an increase in r(i)= r(o). The results from the analysis compare reasonably well with available theoretical and experimental data from the literature. (C) 2015 American Society of Civil Engineers.

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

Composite Guidance for Impact Angle Control Against Higher Speed Targets

In the literature, the impact angle control problem has been addressed mostly against lower speed or stationary targets. However, in the current defense scenario, targets of much higher speeds than interceptors are a reality. Moreover, approaching a higher speed target from a specified angle is important for effective seeker acquisition and enhanced warhead effectiveness. This paper proposes a composite proportional navigation guidance law using a combination of the standard proportional navigation and the recently proposed retroproportional navigation guidance laws for intercepting higher speed nonmaneuvering targets at specified impact angles in three-dimensional engagements. An analysis of the set of achievable impact angles by the composite proportional navigation guidance law is presented. It is shown that there exists an impulse bias that, when added to the composite proportional navigation guidance command, expands this set further by reversing the direction of the line-of-sight angular rotation vector. A bound on the magnitude of the bias is also derived. Finally, an implementation of this impulse bias, in the form of a series of pulses, is proposed and analyzed. Simulation results are also presented to support the analysis.

Composite Guidance for Impact Angle Control Against Higher Speed Targets

In the literature, the impact angle control problem has been addressed mostly against lower speed or stationary targets. However, in the current defense scenario, targets of much higher speeds than interceptors are a reality. Moreover, approaching a higher speed target from a specified angle is important for effective seeker acquisition and enhanced warhead effectiveness. This paper proposes a composite proportional navigation guidance law using a combination of the standard proportional navigation and the recently proposed retroproportional navigation guidance laws for intercepting higher speed nonmaneuvering targets at specified impact angles in three-dimensional engagements. An analysis of the set of achievable impact angles by the composite proportional navigation guidance law is presented. It is shown that there exists an impulse bias that, when added to the composite proportional navigation guidance command, expands this set further by reversing the direction of the line-of-sight angular rotation vector. A bound on the magnitude of the bias is also derived. Finally, an implementation of this impulse bias, in the form of a series of pulses, is proposed and analyzed. Simulation results are also presented to support the analysis.

A Closer Look at Multiple Forking: Leveraging (In)Dependence for a Tighter Bound

Boldyreva, Palacio and Warinschi introduced a multiple forking game as an extension of general forking. The notion of (multiple) forking is a useful abstraction from the actual simulation of cryptographic scheme to the adversary in a security reduction, and is achieved through the intermediary of a so-called wrapper algorithm. Multiple forking has turned out to be a useful tool in the security argument of several cryptographic protocols. However, a reduction employing multiple forking incurs a significant degradation of , where denotes the upper bound on the underlying random oracle calls and , the number of forkings. In this work we take a closer look at the reasons for the degradation with a tighter security bound in mind. We nail down the exact set of conditions for success in the multiple forking game. A careful analysis of the cryptographic schemes and corresponding security reduction employing multiple forking leads to the formulation of `dependence' and `independence' conditions pertaining to the output of the wrapper in different rounds. Based on the (in)dependence conditions we propose a general framework of multiple forking and a General Multiple Forking Lemma. Leveraging (in)dependence to the full allows us to improve the degradation factor in the multiple forking game by a factor of . By implication, the cost of a single forking involving two random oracles (augmented forking) matches that involving a single random oracle (elementary forking). Finally, we study the effect of these observations on the concrete security of existing schemes employing multiple forking. We conclude that by careful design of the protocol (and the wrapper in the security reduction) it is possible to harness our observations to the full extent.