Power Controlled Reverse Channel Training Achieves an Infinite Diversity Order in a TDD-SIMO System with Perfect CSIR

In this letter, we analyze the Diversity Multiplexinggain Tradeoff (DMT) performance of a training-based reciprocal Single Input Multiple Output (SIMO) system. Assuming Channel State Information (CSI) is available at the Receiver (CSIR), we propose a channel-dependent power-controlled Reverse Channel Training (RCT) scheme that enables the transmitter to directly estimate the power control parameter to be used for the forwardlink data transmission. We show that, with an RCT power of (P) over bar (gamma), gamma > 0 and a forward data transmission power of (P) over bar, our proposed scheme achieves an infinite diversity order for 0 <= g(m) < L-c-L-B,L-tau/L-c min(gamma, 1) and r > 2, where g(m) is the multiplexing gain, L-c is the channel coherence time, L-B,L-tau is the RCT duration and r is the number of receive antennas. We also derive an upper bound on the outage probability and show that it goes to zero asymptotically as exp(-(P) over bar (E)), where E (sic) (gamma - g(m)L(c)/L-c-L-B,L-tau), at high (P) over bar. Thus, the proposed scheme achieves a significantly better DMT performance compared to the finite diversity order achieved by channel-agnostic, fixed-power RCT schemes.

Cubicity and Bandwidth

A unit cube in (or a k-cube in short) is defined as the Cartesian product R (1) x R (2) x ... x R (k) where R (i) (for 1 a parts per thousand currency sign i a parts per thousand currency sign k) is a closed interval of the form a (i) , a (i) + 1] on the real line. A k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that two vertices in G are adjacent if and only if their corresponding k-cubes have a non-empty intersection. The cubicity of G is the minimum k such that G has a k-cube representation. From a geometric embedding point of view, a k-cube representation of G = (V, E) yields an embedding such that for any two vertices u and v, ||f(u) - f(v)||(a) a parts per thousand currency sign 1 if and only if . We first present a randomized algorithm that constructs the cube representation of any graph on n vertices with maximum degree Delta in O(Delta ln n) dimensions. This algorithm is then derandomized to obtain a polynomial time deterministic algorithm that also produces the cube representation of the input graph in the same number of dimensions. The bandwidth ordering of the graph is studied next and it is shown that our algorithm can be improved to produce a cube representation of the input graph G in O(Delta ln b) dimensions, where b is the bandwidth of G, given a bandwidth ordering of G. Note that b a parts per thousand currency sign n and b is much smaller than n for many well-known graph classes. Another upper bound of b + 1 on the cubicity of any graph with bandwidth b is also shown. Together, these results imply that for any graph G with maximum degree Delta and bandwidth b, the cubicity is O(min{b, Delta ln b}). The upper bound of b + 1 is used to derive upper bounds for the cubicity of circular-arc graphs, cocomparability graphs and AT-free graphs in terms of the maximum degree Delta.

Stochastically driven instability in rotating shear flows

The origin of hydrodynamic turbulence in rotating shear flows is investigated, with particular emphasis on the flows whose angular velocity decreases but whose specific angular momentum increases with the increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain the observed data. Such a mismatch between the linear theory and the observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and then the corresponding turbulence therein is ruled out. This work explores the effect of stochastic noise on such hydrodynamic flows. We essentially concentrate on a small section of such a flow, which is nothing but a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disc. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities and hence large energy dissipations of perturbation, which presumably generate the instability. A range of angular velocity (Omega) profiles of the background flow, starting from that of a constant specific angular momentum (lambda = Omega r(2); r being the radial coordinate) to a constant circular velocity (v(phi) = Omega r), is explored. However, all the background angular velocities exhibit identical growth and roughness exponents of their perturbations, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand the origin of instability and turbulence in three-dimensional Rayleigh stable rotating shear flows by introducing additive noise to the underlying linearized governing equations. This has important implications to resolve the turbulence problem in astrophysical hydrodynamic flows such as accretion discs.

Trends and Variability of AVHRR-Derived NPP in India

In this paper, we estimate the trends and variability in Advanced Very High Resolution Radiometer (AVHRR)-derived terrestrial net primary productivity (NPP) over India for the period 1982-2006. We find an increasing trend of 3.9% per decade (r = 0.78, R-2 = 0.61) during the analysis period. A multivariate linear regression of NPP with temperature, precipitation, atmospheric CO2 concentration, soil water and surface solar radiation (r = 0.80, R-2 = 0.65) indicates that the increasing trend is partly driven by increasing atmospheric CO2 concentration and the consequent CO2 fertilization of the ecosystems. However, human interventions may have also played a key role in the NPP increase: non-forest NPP growth is largely driven by increases in irrigated area and fertilizer use, while forest NPP is influenced by plantation and forest conservation programs. A similar multivariate regression of interannual NPP anomalies with temperature, precipitation, soil water, solar radiation and CO2 anomalies suggests that the interannual variability in NPP is primarily driven by precipitation and temperature variability. Mean seasonal NPP is largest during post-monsoon and lowest during the pre-monsoon period, thereby indicating the importance of soil moisture for vegetation productivity.

The curvature of the liquid-vapor reduced pressure curve and its relation with the critical region

For most fluids, there exist a maximum and a minimum in the curvature of the reduced vapor pressure curve, p(r) = p(r)(T-r) (with p(r) = p/p(c) and T-r = T/T-c, p(c) and T-c being the pressure and temperature at the critical point). By analyzing National Institute of Standards and Technology (NIST) data on the liquid-vapor coexistence curve for 105 fluids, we find that the maximum occurs in the reduced temperature range 0.5 <= T-r <= 0.8 while the minimum occurs in the reduced temperature range 0.980 <= T-r <= 0.995. Vapor pressure equations for which d(2)p(r)/dT(r)(2) diverges at the critical point present a minimum in their curvature. Therefore, the point of minimum curvature can be used as a marker for the critical region. By using the well-known Ambrose-Walton (AW) vapor pressure equation we obtain the reduced temperatures of the maximum and minimum curvature in terms of the Pitzer acentric factor. The AW predictions are checked against those obtained from NIST data. (C) 2013 Elsevier Ltd. All rights reserved.

Influence of steric effect on the structural aspects of N,N `,N `'-triarylguanidine derived six-membered C,N] palladacycles

Guanidine derived six-membered C,N] palladacycles of the types (C,N)Pd(mu-OC(O)R)](2) (1a-d), (C,N)Pd(mu-Br)](2) (2a,b), cis-(C,N)PdBr(L)] (3a-d, 4, and 5), and ring contracted guanidine derived five-membered C,N] palladacycle, (C,N)PdBr(C NXy)] (6) were prepared in high yield following the established methods with a view aimed at understanding the influence of the substituents on the aryl rings of the guanidine upon the solid state structure and solution behaviour of palladacycles. Palladacycles were characterised by microanalytical, IR, NMR and mass spectral data. The molecular structures of 1a, 1c, 2a, 2b, 3a, 3c, 3d, and 4-6 were determined by single crystal X-ray diffraction data. Palladacycles 1a and 1c were shown to exist as a dimer in transoid in-in conformation in the solid state but as a mixture of a dimer in major proportion and a monomer (kappa(2)-O,O'-OAc) in solution as deduced from H-1 NMR data. Palladacycles 2a and 2b were shown to exist as a dimer in transoid conformation in the solid state but the former was shown to exist as a mixture of a dimer and presumably a trimer in solution as revealed by a variable temperature H-1 NMR data in conjunction with ESI-MS data. The cis configuration around the palladium atom in 3a, 3c, and 3d was ascribed to steric influence of the aryl moiety of =NAr unit and that in 4-6 was ascribed to antisymbiosis. The solution behaviour of 3d was studied by a variable concentration (VC) H-1 NMR data.

Six-membered C,N] cyclopalladated sym N,N `,N `'-tri(4-tolyl) guanidines: Synthesis, reactivity studies and structural aspects

Six-membered C,N] cyclopalladated sym N,N',N `'-tri(4-tolyl)guanidines, (ArNH)(2)C=NAr] (sym = symmetrical; Ar = 4-MeC6H4; LH24-tolyl) of the types (C,N)Pd(mu-OC(O)R)](2) (1 and 2), (C,N)Pd(mu-Br)](2) (3), cis-(C,N)PdLBr] (4-7), and (C,N)Pd(acac)] (8) were prepared in high yield by established methods with a view aimed at understanding the influence of the 4-tolyl substituent of the guanidine moiety upon the solution behaviour of 1-8. The composition of 1-8 was confirmed by elemental analysis, IR, and NMR spectroscopy, and mass spectrometry. The molecular structures of 1-6 were determined by single-crystal X-ray diffraction. Palladacycles 1-3 exist as a dimer in transoid conformation in the solid state while 4-6 exist as a monomer with cis configuration around the palladium atom as the Lewis base is placed cis to the Pd-C bond due to antisymbiosis. The NMR spectra of 1-8 revealed the presence of a single isomer in solution and this spectral feature is ascribed to the rapid inversion of the six-membered ``C,N]Pd'' ring due to the presence of sterically less hindered and more symmetrical 4-tolyl substituent in the =NAr unit of the guanidine moiety. (C) 2013 Elsevier B.V. All rights reserved.

On the Erdos-Szekeres n-interior-point problem

The n-interior-point variant of the Erdos Szekeres problem is the following: for every n, n >= 1, does there exist a g(n) such that every point set in the plane with at least g(n) interior points has a convex polygon containing exactly n interior points. The existence of g(n) has been proved only for n <= 3. In this paper, we show that for any fixed r >= 2, and for every n >= 5, every point set having sufficiently large number of interior points and at most r convex layers contains a subset with exactly n interior points. We also consider a relaxation of the notion of convex polygons and show that for every n, n >= 1, any point set with at least n interior points has an almost convex polygon (a simple polygon with at most one concave vertex) that contains exactly n interior points. (C) 2013 Elsevier Ltd. All rights reserved.

Coral diseases are major contributors to coral mortality in Shingle Island, Gulf of Mannar, southeastern India

The present study reports coral mortality, driven primarily by coral diseases, around Shingle Island, Gulf of Mannar (GOM), Indian Ocean. In total, 2910 colonies were permanently monitored to assess the incidence of coral diseases and consequent mortality for 2 yr. Four types of lesions consistent with white band disease (WBD), black disease (BD), white plaque disease (WPD), and pink spot disease (PSD) were recorded from 4 coral genera: Montipora, Pocillopora, Acropora, and Porites. Porites were affected by 2 disease types, while the other 3 genera were affected by only 1 disease type. Overall disease prevalence increased from 8% (n = 233 colonies) to 41.9% (n = 1219) over the 2 yr study period. BD caused an unprecedented 100% mortality in Pocillopora, followed by 20.4 and 13.1% mortality from WBD in Montipora and Acropora, respectively. Mean disease progression rates of 0.8 +/- 1.0 and 0.6 +/- 0.5 cm mo(-1) over live coral colonies were observed for BD and WBD. Significant correlations between temperature and disease progression were observed for BD (r = 0.86, R-2 = 0.75, p < 0.001) and WBD (R-2 = 0.76, p < 0.001). This study revealed the increasing trend of disease prevalence and progression of disease over live coral in a relatively limited study area; further study should investigate the status of the entire coral reef in the GOM and the role of diseases in reef dynamics.

Differentially Selective Chemosensor with Fluorescence Off-On Responses on Cu2+ and Zn2+ Ions in Aqueous Media and Applications in Pyrophosphate Sensing, Live Cell Imaging, and Cytotoxicity

A new benzoyl hydrazone based chemosensor R is synthesized by Schiff base condensation of 2,6-diformyl-4-methylphenol and phenyl carbohydrazide and acts as a highly selective fluorescence sensor for Cu2+ and Zn2+ ions in aqueous media. The reaction of R with CuCl2 or ZnCl2 forms the corresponding dimeric dicopper(II) Cu-2(R)(CH3O)-(NO3)](2)(CH3O)(2) (R-Cu2+) and dizinc(1) Zn-2(R)(2)](NO3)(2) (R-Zn2+) complexes, which are characterized, as R, by conventional techniques including single-crystal X-ray analysis. Electronic absorption and fluorescence titration studies of R with different metal cations in a CH3CN/0.02 M HEPES buffer medium (pH = 7.3) show a highly selective binding affinity only toward Cu(2+)and Zn2+ ions even in the presence of other commonly coexisting ions such as Ne+, K+, Mg2+, Ca2+, Mn2+, Fe2+, Fe3+, Co2+, Ni2+, Cd2+, and Hg2+. Quantification of the fluorescence titration analysis shows that the chemosensor R can indicate the presence of Cu2+ and Zn2+ even at very low concentrations of 17.3 and 16.5 ppb, respectively. R-Zn2+ acts as a selective metal-based fluorescent sensor for inorganic pyrophosphate ion (PPi) even in the presence of other common anions such as F-, Cl-, Br-, I-, CH3COO-, CO32-, HCO3-, N-3(-), SO42-, PPi, AMP, ADP, and ATP in an aqueous medium. The propensity of R as a bioimaging fluorescent probe to detect Cu2+ and Zn2+ ions in human cervical HeLa cancer cell lines and their cytotoxicity against human cervical (HeLa), breast cancer (MCF7), and noncancer breast epithelial (MCF10a) cells have also been investigated. R-Cu2+ shows better cytotoxicity and sensitivity toward cancer cells over noncancer cells than R and R-Zn2+ under identical conditions, with the appearance of apoptotic bodies.

Small strong epsilon nets

Let P be a set of n points in R-d. A point x is said to be a centerpoint of P if x is contained in every convex object that contains more than dn/d+1 points of P. We call a point x a strong centerpoint for a family of objects C if x is an element of P is contained in every object C is an element of C that contains more than a constant fraction of points of P. A strong centerpoint does not exist even for halfspaces in R-2. We prove that a strong centerpoint exists for axis-parallel boxes in Rd and give exact bounds. We then extend this to small strong epsilon-nets in the plane. Let epsilon(S)(i) represent the smallest real number in 0, 1] such that there exists an epsilon(S)(i)-net of size i with respect to S. We prove upper and lower bounds for epsilon(S)(i) where S is the family of axis-parallel rectangles, halfspaces and disks. (C) 2014 Elsevier B.V. All rights reserved.

The generalized Onsager model for a binary gas mixture

The Onsager model for the secondary flow field in a high-speed rotating cylinder is extended to incorporate the difference in mass of the two species in a binary gas mixture. The base flow is an isothermal solid-body rotation in which there is a balance between the radial pressure gradient and the centrifugal force density for each species. Explicit expressions for the radial variation of the pressure, mass/mole fractions, and from these the radial variation of the viscosity, thermal conductivity and diffusion coefficient, are derived, and these are used in the computation of the secondary flow. For the secondary flow, the mass, momentum and energy equations in axisymmetric coordinates are expanded in an asymptotic series in a parameter epsilon = (Delta m/m(av)), where Delta m is the difference in the molecular masses of the two species, and the average molecular mass m(av) is defined as m(av) = (rho(w1)m(1) + rho(w2)m(2))/rho(w), where rho(w1) and rho(w2) are the mass densities of the two species at the wall, and rho(w) = rho(w1) + rho(w2). The equation for the master potential and the boundary conditions are derived correct to O(epsilon(2)). The leading-order equation for the master potential contains a self-adjoint sixth-order operator in the radial direction, which is different from the generalized Onsager model (Pradhan & Kumaran, J. Fluid Mech., vol. 686, 2011, pp. 109-159), since the species mass difference is included in the computation of the density, viscosity and thermal conductivity in the base state. This is solved, subject to boundary conditions, to obtain the leading approximation for the secondary flow, followed by a solution of the diffusion equation for the leading correction to the species mole fractions. The O(epsilon) and O(epsilon(2)) equations contain inhomogeneous terms that depend on the lower-order solutions, and these are solved in a hierarchical manner to obtain the O(epsilon) and O(epsilon(2)) corrections to the master potential. A similar hierarchical procedure is used for the Carrier-Maslen model for the end-cap secondary flow. The results of the Onsager hierarchy, up to O(epsilon(2)), are compared with the results of direct simulation Monte Carlo simulations for a binary hard-sphere gas mixture for secondary flow due to a wall temperature gradient, inflow/outflow of gas along the axis, as well as mass and momentum sources in the flow. There is excellent agreement between the solutions for the secondary flow correct to O(epsilon(2)) and the simulations, to within 15 %, even at a Reynolds number as low as 100, and length/diameter ratio as low as 2, for a low stratification parameter A of 0.707, and when the secondary flow velocity is as high as 0.2 times the maximum base flow velocity, and the ratio 2 Delta m/(m(1) + m(2)) is as high as 0.5. Here, the Reynolds number Re = rho(w)Omega R-2/mu, the stratification parameter A = root m Omega R-2(2)/(2k(B)T), R and Omega are the cylinder radius and angular velocity, m is the molecular mass, rho(w) is the wall density, mu is the viscosity and T is the temperature. The leading-order solutions do capture the qualitative trends, but are not in quantitative agreement.

Hall viscosity to entropy ratio in higher derivative theories

In this paper based on the basic principles of gauge/gravity duality we compute the hall viscosity to entropy ratio in the presence of various higher derivative corrections to the dual gravitational description embedded in an asymptotically AdS(4) space time. As the first step of our analysis, considering the back reaction we impose higher derivative corrections to the abelian gauge sector of the theory where we notice that the ratio indeed gets corrected at the leading order in the coupling. Considering the probe limit as a special case we compute this leading order correction over the fixed background of the charged black brane solution. Finally we consider higher derivative (R-2) correction to the gravity sector of the theory where we notice that the above ratio might get corrected at the sixth derivative level.

On entanglement entropy functionals in higher-derivative gravity theories

In arXiv:1310.5713 1] and arXiv:1310.6659 2] a formula was proposed as the entanglement entropy functional for a general higher-derivative theory of gravity, whose lagrangian consists of terms containing contractions of the Riemann tensor. In this paper, we carry out some tests of this proposal. First, we find the surface equation of motion for general four-derivative gravity theory by minimizing the holographic entanglement entropy functional resulting from this proposed formula. Then we calculate the surface equation for the same theory using the generalized gravitational entropy method of arXiv:1304.4926 3]. We find that the two do not match in their entirety. We also construct the holographic entropy functional for quasi-topological gravity, which is a six-derivative gravity theory. We find that this functional gives the correct universal terms. However, as in the R-2 case, the generalized gravitational entropy method applied to this theory does not give exactly the surface equation of motion coming from minimizing the entropy functional.

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).