Distributed Function Computation over Fields and Rings via Linear Compression of Sources

The setting considered in this paper is one of distributed function computation. More specifically, there is a collection of N sources possessing correlated information and a destination that would like to acquire a specific linear combination of the N sources. We address both the case when the common alphabet of the sources is a finite field and the case when it is a finite, commutative principal ideal ring with identity. The goal is to minimize the total amount of information needed to be transmitted by the N sources while enabling reliable recovery at the destination of the linear combination sought. One means of achieving this goal is for each of the sources to compress all the information it possesses and transmit this to the receiver. The Slepian-Wolf theorem of information theory governs the minimum rate at which each source must transmit while enabling all data to be reliably recovered at the receiver. However, recovering all the data at the destination is often wasteful of resources since the destination is only interested in computing a specific linear combination. An alternative explored here is one in which each source is compressed using a common linear mapping and then transmitted to the destination which then proceeds to use linearity to directly recover the needed linear combination. The article is part review and presents in part, new results. The portion of the paper that deals with finite fields is previously known material, while that dealing with rings is mostly new.Attempting to find the best linear map that will enable function computation forces us to consider the linear compression of source. While in the finite field case, it is known that a source can be linearly compressed down to its entropy, it turns out that the same does not hold in the case of rings. An explanation for this curious interplay between algebra and information theory is also provided in this paper.

Development of novel multiple quantummethodologies for the analyses of complex protonNMR spectra of scalar coupled spins

One of the significant advancements in Nuclear Magnetic Resonance spectroscopy (NMR) in combating the problem of spectral complexity for deriving the structure and conformational information is the incorporation of additional dimension and to spread the information content in a two dimensional space. This approach together with the manipulation of the dynamics of nuclear spins permitted the designing of appropriate pulse sequences leading to the evolution of diverse multidimensional NMR experiments. The desired spectral information can now be extracted in a simplified and an orchestrated manner. The indirect detection of multiple quantum (MQ) NMR frequencies is a step in this direction. The MQ technique has been extensively used in the study of molecules aligned in liquid crystalline media to reduce spectral complexity and to determine molecular geometries. Unlike in dipolar coupled systems, the size of the network of scalar coupled spins is not big in isotropic solutions and the MQ 1H detection is not routinely employed,although there are specific examples of spin topology filtering. In this brief review, we discuss our recent studies on the development and application of multiple quantum correlation and resolved techniques for the analyses of proton NMR spectra of scalar coupled spins.

High emission currents and low threshold fields in multi-wall carbon nanotube-polymer composites in the vertical configuration

In this work, we present field emission characteristics of multi-wall carbon nanotube (MWCNT)-polystyrene composites at various weight fractions along the cross-section of sample. Scanning electron microscope images in cross-sectional view reveal that MWCNTs are homogeneously distributed across the thickness and the density of protruding tubes can be scaled with weight fraction of the composite film. Field emission from composites has been observed to vary considerably with density of MWCNTs in the polymer matrix. High current density of 100 mA/cm(2) was achieved at a field of 2.2 V/lm for 0.15 weight fraction. The field emission is observed to follow the Fowler-Nordheim tunneling mechanism, however, electrostatic screening is observed to play a role in limiting the current density at higher weight fractions. (C) 2012 American Institute of Physics. [doi:10.1063/1.3685754]

A pseudo-time EnKF incorporating shape based reconstruction for diffuse optical tomography

Purpose: The authors aim at developing a pseudo-time, sub-optimal stochastic filtering approach based on a derivative free variant of the ensemble Kalman filter (EnKF) for solving the inverse problem of diffuse optical tomography (DOT) while making use of a shape based reconstruction strategy that enables representing a cross section of an inhomogeneous tumor boundary by a general closed curve. Methods: The optical parameter fields to be recovered are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions) and the EnKF is used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the pseudo-dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ``measurement'' equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. Results: In our numerical simulations, we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes (such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as mu(b)(a)=0.01mm(-1) and mu('b)(s)=1.0mm(-1), respectively. We also assume mu(a) = 0.02 mm(-1) within the inhomogeneity (for the single inhomogeneity case) and mu(a) = 0.02 and 0.03 mm(-1) (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown mu(a) from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. Conclusions: The PD-EnKF, which exhibits little sensitivity against variations in the fictitiously introduced noise processes, is also proven to be accurate and robust in recovering a spatial map of the absorption coefficient from DOT data. With the help of shape based representation of the inhomogeneities and an appropriate scaling of the CH expansion coefficients representing the boundary, we have been able to recover inhomogeneities representative of the shape of malignancies in medical diagnostic imaging. (C) 2012 American Association of Physicists in Medicine. [DOI: 10.1118/1.3679855]

Measurement and Applications of Long-Range Heteronuclear Scalar Couplings: Recent Experimental and Theoretical Developments

The use of long-range heteronuclear couplings, in association with 1H1H scalar couplings and NOE restraints, has acquired growing importance for the determination of the relative stereochemistry, and structural and conformational information of organic and biological molecules. However, the routine use of such couplings is hindered by the inherent difficulties in their measurement. Prior to the advancement in experimental techniques, both long-range homo- and heteronuclear scalar couplings were not easily accessible, especially for very large molecules. The development of a large number of multidimensional NMR experimental methodologies has alleviated the complications associated with the measurement of couplings of smaller strengths. Subsequent application of these methods and the utilization of determined J-couplings for structure calculations have revolutionized this area of research. Problems in organic, inorganic and biophysical chemistry have also been solved by utilizing the short- and long-range heteronuclear couplings. In this minireview, we discuss the advantages and limitations of a number of experimental techniques reported in recent times for the measurement of long-range heteronuclear couplings and a few selected applications of such couplings. This includes the study of medium- to larger-sized molecules in a variety of applications, especially in the study of hydrogen bonding in biological systems. The utilization of these couplings in conjunction with theoretical calculations to arrive at conclusions on the hyperconjugation, configurational analysis and the effect of the electronegativity of the substituents is also discussed.

Quasi-static crack tip fields in rate-sensitive FCC single crystals

In this work, the effects of loading rate, material rate sensitivity and constraint level on quasi-static crack tip fields in a FCC single crystal are studied. Finite element simulations are performed within a mode I, plane strain modified boundary layer framework by prescribing the two term (K-T) elastic crack tip field as remote boundary conditions. The material is assumed to obey a rate-dependent crystal plasticity theory. The orientation of the single crystal is chosen so that the crack surface coincides with the crystallographic (010) plane and the crack front lies along 101] direction. Solutions corresponding to different stress intensity rates K., T-stress values and strain rate exponents m are obtained. The results show that the stress levels ahead of the crack tip increase with K. which is accompanied by gradual shrinking of the plastic zone size. However, the nature of the shear band patterns around the crack tip is not affected by the loading rate. Further, it is found that while positive T-stress enhances the opening and hydrostatic stress levels ahead of crack tip, they are considerably reduced with imposition of negative T-stress. Also, negative T-stress promotes formation of shear bands in the forward sector ahead of the crack tip and suppresses them behind the tip.

Influence fields: a quantitative framework for representation and analysis of active dendrites

Rathour RK, Narayanan R. Influence fields: a quantitative framework for representation and analysis of active dendrites. J Neurophysiol 107: 2313-2334, 2012. First published January 18, 2012; doi:10.1152/jn.00846.2011.-Neuronal dendrites express numerous voltage-gated ion channels (VGICs), typically with spatial gradients in their densities and properties. Dendritic VGICs, their gradients, and their plasticity endow neurons with information processing capabilities that are higher than those of neurons with passive dendrites. Despite this, frameworks that incorporate dendritic VGICs and their plasticity into neurophysiological and learning theory models have been far and few. Here, we develop a generalized quantitative framework to analyze the extent of influence of a spatially localized VGIC conductance on different physiological properties along the entire stretch of a neuron. Employing this framework, we show that the extent of influence of a VGIC conductance is largely independent of the conductance magnitude but is heavily dependent on the specific physiological property and background conductances. Morphologically, our analyses demonstrate that the influences of different VGIC conductances located on an oblique dendrite are confined within that oblique dendrite, thus providing further credence to the postulate that dendritic branches act as independent computational units. Furthermore, distinguishing between active and passive propagation of signals within a neuron, we demonstrate that the influence of a VGIC conductance is spatially confined only when propagation is active. Finally, we reconstruct functional gradients from VGIC conductance gradients using influence fields and demonstrate that the cumulative contribution of VGIC conductances in adjacent compartments plays a critical role in determining physiological properties at a given location. We suggest that our framework provides a quantitative basis for unraveling the roles of dendritic VGICs and their plasticity in neural coding, learning, and homeostasis.

Thermoelectricity in graphene: Effects of a gap and magnetic fields

We calculate the thermopower of monolayer graphene in various circumstances. We consider acoustic phonon scattering which might be the operative scattering mechanism in freestanding films and predict that the thermopower will be linear in any induced gap in the system. Further, the thermopower peaks at the same value of chemical potential (tunable by gate voltage) independent of the gap. We show that in the semiclassical approximation, the thermopower in a magnetic field saturates at high field to a value which can be calculated exactly and is independent of the details of the scattering. This effect might be observable experimentally. We also note that a Yukawa scattering potential can be used to fit experimental data for the thermopower for reasonable values of the screening length parameter.

Conformational dynamics of HIV-1 protease: a comparative molecular dynamics simulation study with multiple amber force fields

Flap dynamics of HIV-1 protease (HIV-pr) controls the entry of inhibitors and substrates to the active site. Dynamical models from previous simulations are not all consistent with each other and not all are supported by the NMR results. In the present work, the er effect of force field on the dynamics of HIV-pr is investigated by MD simulations using three AMBER force fields ff99, ff99SB, and ff03. The generalized order parameters for amide backbone are calculated from the three force fields and compared with the NMR S2 values. We found that the ff99SB and ff03 force field calculated order parameters agree reasonably well with the NMR S2 values, whereas ff99 calculated values deviate most from the NMR order parameters. Stereochemical geometry of protein models from each force field also agrees well with the remarks from NMR S2 values. However, between ff99SB and ff03, there are several differences, most notably in the loop regions. It is found that these loops are, in general, more flexible in the ff03 force field. This results in a larger active site cavity in the simulation with the ff03 force field. The effect of this difference in computer-aided drug design against flexible receptors is discussed.

Interacting fermions in synthetic non-Abelian gauge fields

Generation and study of synthetic gauge fields has enhanced the possibility of using cold atom systems as quantum emulators of condensed matter Hamiltonians. In this article we describe the physics of interacting spin -1/2 fermions in synthetic non-Abelian gauge fields which induce a Rashba spin-orbit interaction on the motion of the fermions. We show that the fermion system can evolve to a Bose-Einstein condensate of a novel boson which we call rashbon. The rashbon-rashbon interaction is shown to be independent of the interaction between the constituent fermions. We also show that spin-orbit coupling can help enhancing superfluid transition temperature of weak superfluids to the order of Fermi temperature. A non-Abelian gauge field, when used in conjunction with another potential, can generate interesting Hamiltonians such as that of a magnetic monopole.

Postcards from oases in the desert: phenomenology of SUSY with intermediate scales

The presence of new matter fields charged under the Standard Model gauge group at intermediate scales below the Grand Unification scale modifies the renormalization group evolution of the gauge couplings. This can in turn significantly change the running of the Minimal Supersymmetric Standard Model parameters, in particular the gaugino and the scalar masses. In the absence of new large Yukawa couplings we can parameterise all the intermediate scale models in terms of only two parameters controlling the size of the unified gauge coupling. As a consequence of the modified running, the low energy spectrum can be strongly affected with interesting phenomenological consequences. In particular, we show that scalar over gaugino mass ratios tend to increase and the regions of the parameter space with neutralino Dark Matter compatible with cosmological observations get drastically modified. Moreover, we discuss some observables that can be used to test the intermediate scale physics at the LHC in a wide class of models.

Top-spin analysis of new scalar and tensor interactions in e(+) e (-) collisions with transverse beam polarization

The top polarization at the International Linear Collider (ILC) with transverse beam polarization is utilized in the process to probe interactions of the scalar and tensor type beyond the Standard Model and to disentangle their individual contributions. Confidence level limits of 90% are presented on the interactions with realistic integrated luminosity and are found to improve by an order of magnitude compared to the case when the spin of the top quark is not measured. Sensitivities of the order of a few times 10 (-aEuro parts per thousand 3) TeV (-aEuro parts per thousand 2) for real and imaginary parts of both scalar and tensor couplings at and 800 GeV with an integrated luminosity of 500 fb (-aEuro parts per thousand 1) and completely polarized beams are shown to be possible.

Selective excitation and detection of maximum quantum coherence of a group of scalar coupled protons in chiral molecules: an NMR experiment for enantiodiscrimination

The H-1 NMR spectroscopic discrimination of enantiomers in the solution state and the measurement of enantiomeric composition is most often hindered due to either very small chemical shift differences between the discriminated peaks or severe overlap of transitions from other chemically non-equivalent protons. In addition the use of chiral auxiliaries such as, crown ether and chiral lanthanide shift reagent may often cause enormous line broadening or give little degree of discrimination beyond the crown ether substrate ratio, hampering the discrimination. In circumventing such problems we are proposing the utilization of the difference in the additive values of all the chemical shifts of a scalar coupled spin system. The excitation and detection of appropriate highest quantum coherence yields the measurable difference in the frequencies between two transitions, one pertaining to each enantiomer in the maximum quantum dimension permitting their discrimination and the F-2 cross section at each of these frequencies yields an enantiopure spectrum. The advantage of the utility of the proposed method is demonstrated on several chiral compounds where the conventional one dimensional H-1 NMR spectra fail to differentiate the enantiomers.