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.

Redox-Active Metal-Organic Frameworks: Highly Stable Charge-Separated States through Strut/Guest-to-Strut Electron Transfer

Molecular organization of donor and acceptor chromophores in self-assembled materials is of paramount interest in the field of photovoltaics or mimicry of natural light-harvesting systems. With this in mind, a redox-active porous interpenetrated metal-organic framework (MOF), {Cd(bpdc)(bpNDI)]4.5H(2)ODMF}(n) (1) has been constructed from a mixed chromophoric system. The -oxo-bridged secondary building unit, {Cd-2(-OCO)(2)}, guides the parallel alignment of bpNDI (N,N-di(4-pyridyl)-1,4,5,8-naphthalenediimide) acceptor linkers, which are tethered with bpdc (bpdcH(2)=4,4-biphenyldicarboxylic acid) linkers of another entangled net in the framework, resulting in photochromic behaviour through inter-net electron transfer. Encapsulation of electron-donating aromatic molecules in the electron-deficient channels of 1 leads to a perfect donor-acceptor co-facial organization, resulting in long-lived charge-separated states of bpNDI. Furthermore, 1 and guest encapsulated species are characterised through electrochemical studies for understanding of their redox properties.

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.

Fermionic edge states and new physics

We investigate the properties of the Dirac operator on manifolds with boundaries in the presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given. We show that the problem with the above boundary condition can be mapped to one where the manifold is extended beyond the boundary and the boundary condition is replaced by a delta function potential of suitable strength. We also briefly highlight how the problem of the self-adjointness of the operators in the presence of moving boundaries can be simplified by suitable transformations which render the boundary fixed and modify the Hamiltonian and the boundary condition to reflect the effect of moving boundary.

Lower-Bound Axisymmetric Formulation for Geomechanics Problems Using Nonlinear Optimization

A lower-bound limit analysis formulation, by using two-dimensional finite elements, the three-dimensional Mohr-Coulomb yield criterion, and nonlinear optimization, has been given to deal with an axisymmetric geomechanics stability problem. The optimization was performed using an interior point method based on the logarithmic barrier function. The yield surface was smoothened (1) by removing the tip singularity at the apex of the pyramid in the meridian plane and (2) by eliminating the stress discontinuities at the corners of the yield hexagon in the pi-plane. The circumferential stress (sigma(theta)) need not be assumed. With the proposed methodology, for a circular footing, the bearing-capacity factors N-c, N-q, and N-gamma for different values of phi have been computed. For phi = 0, the variation of N-c with changes in the factor m, which accounts for a linear increase of cohesion with depth, has been evaluated. Failure patterns for a few cases have also been drawn. The results from the formulation provide a good match with the solutions available from the literature. (C) 2014 American Society of Civil Engineers.

Turbulent states and their transitions in mathematical models for ventricular tissue: The effects of random interstitial fibroblasts

We study the dynamical behaviors of two types of spiral-and scroll-wave turbulence states, respectively, in two-dimensional (2D) and three-dimensional (3D) mathematical models, of human, ventricular, myocyte cells that are attached to randomly distributed interstitial fibroblasts; these turbulence states are promoted by (a) the steep slope of the action-potential-duration-restitution (APDR) plot or (b) early afterdepolarizations (EADs). Our single-cell study shows that (1) the myocyte-fibroblast (MF) coupling G(j) and (2) the number N-f of fibroblasts in an MF unit lower the steepness of the APDR slope and eliminate the EAD behaviors of myocytes; we explore the pacing dependence of such EAD suppression. In our 2D simulations, we observe that a spiral-turbulence (ST) state evolves into a state with a single, rotating spiral (RS) if either (a) G(j) is large or (b) the maximum possible number of fibroblasts per myocyte N-f(max) is large. We also observe that the minimum value of G(j), for the transition from the ST to the RS state, decreases as N-f(max) increases. We find that, for the steep-APDR-induced ST state, once the MF coupling suppresses ST, the rotation period of a spiral in the RS state increases as (1) G(j) increases, with fixed N-f(max), and (2) N-f(max) increases, with fixed G(j). We obtain the boundary between ST and RS stability regions in the N-f(max)-G(j) plane. In particular, for low values of N-f(max), the value of G(j), at the ST-RS boundary, depends on the realization of the randomly distributed fibroblasts; this dependence decreases as N-f(max) increases. Our 3D studies show a similar transition from scroll-wave turbulence to a single, rotating, scroll-wave state because of the MF coupling. We examine the experimental implications of our study and propose that the suppression (a) of the steep slope of the APDR or (b) EADs can eliminate spiral-and scroll-wave turbulence in heterogeneous cardiac tissue, which has randomly distributed fibroblasts.

Cell-Membrane-Mimicking Lipid-Coated Nanoparticles Confer Raman Enhancement to Membrane Proteins and Reveal Membrane-Attached Amyloid-beta Conformation

Identifying the structures of membrane bound proteins is critical to understanding their function in healthy and diseased states. We introduce a surface enhanced Raman spectroscopy technique which can determine the conformation of membrane-bound proteins, at low micromolar concentrations, and also in the presence of a substantial membrane-free fraction. Unlike conventional surface enhanced Raman spectroscopy, our approach does not require immobilization of molecules, as it uses spontaneous binding of proteins to lipid bilayer-encapsulated Ag nanoparticles. We apply this technique to probe membrane-attached oligomers of Amyloid-beta(40) (A beta(40)), whose conformation is keenly sought in the context of Alzheimer's disease. Isotope-shifts in the Raman spectra help us obtain secondary structure information at the level of individual residues. Our results show the presence of a beta-turn, flanked by two beta-sheet regions. We use solid-state NMR data to confirm the presence of the beta-sheets in these regions. In the membrane-attached oligomer, we find a strongly contrasting and near-orthogonal orientation of the backbone H-bonds compared to what is found in the mature, less-toxic A beta fibrils. Significantly, this allows a ``porin'' like beta-barrel structure, providing a structural basis for proposed mechanisms of A beta oligomer toxicity.

Direct Observation of Thermal Equilibrium of Excited Triplet States of 9,10-Phenanthrenequinone. A Time-Resolved Resonance Raman Study

The photochemistry of aromatic ketones plays a key role in various physicochemical and biological processes, and solvent polarity can be used to tune their triplet state properties. Therefore, a comprehensive analysis of the conformational structure and the solvent polarity induced energy level reordering of the two lowest triplet states of 9,10-phenanthrenequinone (PQ) was carried out using nanosecond-time-resolved absorption (ns-TRA), time-resolved resonance Raman (TR3) spectroscopy, and time dependent-density functional theory (TD-DFT) studies. The ns-TRA of PQ in acetonitrile displays two bands in the visible range, and these two bands decay with similar lifetime at least at longer time scales (mu s). Interestingly, TR3 spectra of these two bands indicate that the kinetics are different at shorter time scales (ns), while at longer time scales they followed the kinetics of ns-TRA spectra. Therefore, we report a real-time observation of the thermal equilibrium between the two lowest triplet excited states of PQ assigned to n pi* and pi pi* of which the pi pi* triplet state is formed first through intersystem crossing. Despite the fact that these two states are energetically close and have a similar conformational structure supported by TD-DFT studies, the slow internal conversion (similar to 2 ns) between the T-2(1(3)n pi*) and T-1(1(3)pi pi*) triplet states indicates a barrier. Insights from the singlet excited states of PQ in protic solvents J. Chem. Phys. 2015, 142, 24305] suggest that the lowest n pi* and pi pi* triplet states should undergo hydrogen bond weakening and strengthening, respectively, relative to the ground state, and these mechanisms are substantiated by TD-DFT calculations. We also hypothesize that the different hydrogen bonding mechanisms exhibited by the two lowest singlet and triplet excited states of PQ could influence its ISC mechanism.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.

Lower Bound Axisymmetric Limit Analysis Using Drucker-Prager Yield Cone and Simulation with Mohr-Coulomb Pyramid

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker-Prager (D-P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D-P yield cone with the Mohr-Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors N-c, N-q and N-gamma have been computed, as a function of phi, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.

Supersymmetry: Boundary conditions and edge states

When spatial boundaries are inserted, supersymmetry (SUSY) can be broken. We have shown that in an N = 2 supersymmetric theory, all local boundary conditions allowed by self-adjointness of the Hamiltonian break N = 2 SUSY, while only a few of these boundary conditions preserve N = 1 SUSY. We have also shown that for a subset of the boundary conditions compatible with N = 1 SUSY, there exist fermionic ground states which are localized near the boundary. We also show that only very few nonlocal boundary conditions like periodic boundary conditions preserve full N = 2 supersymmetry, but none of them exhibits edge states.

Bearing capacity factors for a conical footing using lower- and upper-bound finite elements limit analysis

Bearing capacity factors, N-c, N-q, and N-gamma, for a conical footing are determined by using the lower and upper bound axisymmetric formulation of the limit analysis in combination with finite elements and optimization. These factors are obtained in a bound form for a wide range of the values of cone apex angle (beta) and phi with delta = 0, 0.5 phi, and phi. The bearing capacity factors for a perfectly rough (delta = phi) conical footing generally increase with a decrease in beta. On the contrary, for delta = 0 degrees, the factors N-c and N-q reduce gradually with a decrease in beta. For delta = 0 degrees, the factor N-gamma for phi >= 35 degrees becomes a minimum for beta approximate to 90 degrees. For delta = 0 degrees, N-gamma for phi <= 30 degrees, as in the case of delta = phi, generally reduces with an increase in beta. The failure and nodal velocity patterns are also examined. The results compare well with different numerical solutions and centrifuge tests' data available from the literature.

An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas

We show here a 2(Omega(root d.log N)) size lower bound for homogeneous depth four arithmetic formulas. That is, we give an explicit family of polynomials of degree d on N variables (with N = d(3) in our case) with 0, 1-coefficients such that for any representation of a polynomial f in this family of the form f = Sigma(i) Pi(j) Q(ij), where the Q(ij)'s are homogeneous polynomials (recall that a polynomial is said to be homogeneous if all its monomials have the same degree), it must hold that Sigma(i,j) (Number of monomials of Q(ij)) >= 2(Omega(root d.log N)). The above mentioned family, which we refer to as the Nisan-Wigderson design-based family of polynomials, is in the complexity class VNP. Our work builds on the recent lower bound results 1], 2], 3], 4], 5] and yields an improved quantitative bound as compared to the quasi-polynomial lower bound of 6] and the N-Omega(log log (N)) lower bound in the independent work of 7].

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.

Edge states, spin transport, and impurity-induced local density of states in spin-orbit coupled graphene

We study graphene, which has both spin-orbit coupling (SOC), taken to be of the Kane-Mele form, and a Zeeman field induced due to proximity to a ferromagnetic material. We show that a zigzag interface of graphene having SOC with its pristine counterpart hosts robust chiral edge modes in spite of the gapless nature of the pristine graphene; such modes do not occur for armchair interfaces. Next we study the change in the local density of states (LDOS) due to the presence of an impurity in graphene with SOC and Zeeman field, and demonstrate that the Fourier transform of the LDOS close to the Dirac points can act as a measure of the strength of the spin-orbit coupling; in addition, for a specific distribution of impurity atoms, the LDOS is controlled by a destructive interference effect of graphene electrons which is a direct consequence of their Dirac nature. Finally, we study transport across junctions, which separates spin-orbit coupled graphene with Kane-Mele and Rashba terms from pristine graphene both in the presence and absence of a Zeeman field. We demonstrate that such junctions are generally spin active, namely, they can rotate the spin so that an incident electron that is spin polarized along some direction has a finite probability of being transmitted with the opposite spin. This leads to a finite, electrically controllable, spin current in such graphene junctions. We discuss possible experiments that can probe our theoretical predictions.