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.

Isolating CP-violating gamma ZZ coupling in e(+)e(-) -> gamma Z with transverse beam polarizations

We revisit the process e(+)e(-) -> gamma Z at the ILC with transverse beam polarization in the presence of anomalous CP- violating gamma ZZ coupling lambda(1) and gamma gamma Z coupling lambda(2). We point out that if the final- state spins are resolved, then it becomes possible to fingerprint the anomalous coupling Re lambda(1). 90% confidence level limit on Re lambda(1) achievable at ILC with center- of- mass energy of 500 GeVor 800 GeV with realistic initial beam polarization and integrated luminosity is of the order of few times of 10(-2) when the helicity of Z is used and 10(-3) when the helicity of gamma is used. The resulting corrections at quadratic order to the cross section and its influence on these limits are also evaluated and are shown to be small. The benefits of such polarization programmes at the ILC are compared and contrasted for the process at hand. We also discuss possible methods by which one can isolate events with a definite helicity for one of the final- state particles.

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]

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.

Influence of anion on the quadratic nonlinearity and depolarization ratios of scattered second harmonic light from cation-pi complexes

We have investigated quadratic nonlinearity (beta(HRS)) and linear and circular depolarization ratios (D and D', respectively) of a series of 1:1 complexes of tropyliumtetrafluoroborate as a cation and methyl-substituted benzenes as pi-donors by making polarization resolved hyper-Rayleigh scattering measurements in solution. The measured D and D' values are much lower than the values expected from a typical sandwich or a T-shaped geometry of a complex. In the cation-pi complexes studied here, the D value varies from 1.36 to 1.46 and D' from 1.62 to 1.72 depending on the number of methyl substitutions on the benzene ring. In order to probe it further, beta, D and D' were computed using the Zerner intermediate neglect of differential overlap-correction vector self-consistent reaction field technique including single and double configuration interactions in the absence and presence of BF4- anion. In the absence of the anion, the calculated value of D varies from 4.20 to 4.60 and that of D' from 2.45 to 2.72 which disagree with experimental values. However, by arranging three cation-pi BF4- complexes in a trigonal symmetry, the computed values are brought to agreement with experiments. When such an arrangement was not considered, the calculated beta values were lower than the experimental values by more than a factor of two. This unprecedented influence of the otherwise ``unimportant'' anion in solution on the beta value and depolarization ratios of these cation-pi complexes is highlighted and emphasized in this paper. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4716020]

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.

Decentralized linear quadratic power system stabilizers for multi-machine power systems

Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead-lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not available in most of the power plants. Full state feedback controllers require feedback of other machine states in a multi-machine power system and necessitate block diagonal structure constraints for decentralized implementation. This paper investigates the design of Linear Quadratic Power System Stabilizers using a recently proposed modified Heffron-Phillip's model. This model is derived by taking the secondary bus voltage of the step-up transformer as reference instead of the infinite bus. The state variables of this model can be obtained by local measurements. This model allows a coordinated linear quadratic control design in multi machine systems. The performance of the proposed controller has been evaluated on two widely used multi-machine power systems, 4 generator 10 bus and 10 generator 39 bus systems. It has been observed that the performance of the proposed controller is superior to that of the conventional Power System Stabilizers (PSS) over a wide range of operating and system conditions.

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.

A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

Network-error correcting codes using small fields

Recently, Ebrahimi and Fragouli proposed an algorithm to construct scalar network codes using small fields (and vector network codes of small lengths) satisfying multicast constraints in a given single-source, acyclic network. The contribution of this paper is two fold. Primarily, we extend the scalar network coding algorithm of Ebrahimi and Fragouli (henceforth referred to as the EF algorithm) to block network-error correction. Existing construction algorithms of block network-error correcting codes require a rather large field size, which grows with the size of the network and the number of sinks, and thereby can be prohibitive in large networks. We give an algorithm which, starting from a given network-error correcting code, can obtain another network code using a small field, with the same error correcting capability as the original code. Our secondary contribution is to improve the EF Algorithm itself. The major step in the EF algorithm is to find a least degree irreducible polynomial which is coprime to another large degree polynomial. We suggest an alternate method to compute this coprime polynomial, which is faster than the brute force method in the work of Ebrahimi and Fragouli.

An inquisitive analysis on the temporal variation of return stroke current essential for producing observed remote electro-magnetic fields

The gross characteristics of spatio-temporal current evolution in the return stroke phase of a cloud-to-ground lightning are rather well defined. However, they by themselves do not ensure the salient features for the resulting remote Electro- Magnetic Fields (EMFs). In spite of significant efforts in the engineering models wherein, the spatio-temporal current distribution all along the channel is specified by the design, all the salient features of remote EMFs could not be achieved. Only the current evolution that ensures the basic characteristics along with its ability to reproduce all the salient features of remote EMFs ranging from 50 m – 200 km from the lightning channel, can be considered as a realistic return stroke channel current. In view of this, the present work intends to investigate on the required fine features of the return stroke current evolution that yields all the desired features. To ensure that the current evolution is not arbitrary but obeys the involved basic physical processes, a recently developed physical model will be employed for the analysis.