Tractable theories for the synthesis of neural networks

The Radius of Direct attraction of a discrete neural network is a measure of stability of the network. it is known that Hopfield networks designed using Hebb's Rule have a radius of direct attraction of Omega(n/p) where n is the size of the input patterns and p is the number of them. This lower bound is tight if p is no larger than 4. We construct a family of such networks with radius of direct attraction Omega(n/root plog p), for any p greater than or equal to 5. The techniques used to prove the result led us to the first polynomial-time algorithm for designing a neural network with maximum radius of direct attraction around arbitrary input patterns. The optimal synaptic matrix is computed using the ellipsoid method of linear programming in conjunction with an efficient separation oracle. Restrictions of symmetry and non-negative diagonal entries in the synaptic matrix can be accommodated within this scheme.

Excess dissipation in dense emulsions

A new model for the structure, elastic properties and dynamics of foams and concentrated emulsions is presented, based on the idea of local regions lacking shear-rigidity in one or more directions which vary randomly through the medium. It is shown to lead naturally to slow (t(-1/2)) stress-relaxation, implying a piece of the dynamic modulus scaling with frequency omega as omega(1/2). Striking experimental confirmation of this prediction using a novel experimental technique is reported, and challenges for the theoretician are offered. This work was done in collaboration with Andrea Liu, Tom Mason, Hu Gang, and David Weitz [1].

Boxicity and Poset Dimension

Let G be a simple, undirected, finite graph with vertex set V (G) and edge set E(G). A k-dimensional box is a Cartesian product of closed intervals [a(1), b(1)] x [a(2), b(2)] x ... x [a(k), b(k)]. The boxicity of G, box(G), is the minimum integer k such that G can be represented as the intersection graph of k-dimensional boxes; i.e., each vertex is mapped to a k-dimensional box and two vertices are adjacent in G if and only if their corresponding boxes intersect. Let P = (S, P) be a poset, where S is the ground set and P is a reflexive, antisymmetric and transitive binary relation on S. The dimension of P, dim(P), is the minimum integer t such that P can be expressed as the intersection of t total orders. Let G(P) be the underlying comparability graph of P; i.e., S is the vertex set and two vertices are adjacent if and only if they are comparable in P. It is a well-known fact that posets with the same underlying comparability graph have the same dimension. The first result of this paper links the dimension of a poset to the boxicity of its underlying comparability graph. In particular, we show that for any poset P, box(G(P))/(chi(G(P)) - 1) <= dim(P) <= 2box(G(P)), where chi(G(P)) is the chromatic number of G(P) and chi(G(P)) not equal 1. It immediately follows that if P is a height-2 poset, then box(G(P)) <= dim(P) <= 2box(G(P)) since the underlying comparability graph of a height-2 poset is a bipartite graph. The second result of the paper relates the boxicity of a graph G with a natural partial order associated with the extended double cover of G, denoted as G(c): Note that G(c) is a bipartite graph with partite sets A and B which are copies of V (G) such that, corresponding to every u is an element of V (G), there are two vertices u(A) is an element of A and u(B) is an element of B and {u(A), v(B)} is an edge in G(c) if and only if either u = v or u is adjacent to v in G. Let P(c) be the natural height-2 poset associated with G(c) by making A the set of minimal elements and B the set of maximal elements. We show that box(G)/2 <= dim(P(c)) <= 2box(G) + 4. These results have some immediate and significant consequences. The upper bound dim(P) <= 2box(G(P)) allows us to derive hitherto unknown upper bounds for poset dimension such as dim(P) = 2 tree width (G(P)) + 4, since boxicity of any graph is known to be at most its tree width + 2. In the other direction, using the already known bounds for partial order dimension we get the following: (1) The boxicity of any graph with maximum degree Delta is O(Delta log(2) Delta), which is an improvement over the best-known upper bound of Delta(2) + 2. (2) There exist graphs with boxicity Omega(Delta log Delta). This disproves a conjecture that the boxicity of a graph is O(Delta). (3) There exists no polynomial-time algorithm to approximate the boxicity of a bipartite graph on n vertices with a factor of O(n(0.5-is an element of)) for any is an element of > 0 unless NP = ZPP.

Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance

We present two online algorithms for maintaining a topological order of a directed n-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles m arc additions in O(m(3/2)) time. For sparse graphs (m/n = O(1)), this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural locality property. Our second algorithm handles an arbitrary sequence of arc additions in O(n(5/2)) time. For sufficiently dense graphs, this bound improves the best previous bound by a polynomial factor. Our bound may be far from tight: we show that the algorithm can take Omega(n(2)2 root(2lgn)) time by relating its performance to a generalization of the k-levels problem of combinatorial geometry. A completely different algorithm running in Theta (n(2) log n) time was given recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to the maintenance of strong components, without affecting the asymptotic time bounds.

Excitation energy transfer from dye molecules to doped graphene

Recently, we have reported theoretical studies on the rate of energy transfer from an electronically excited molecule to graphene. It was found that graphene is a very efficient quencher of the electronically excited states and that the rate infinity z(-4). The process was found to be effective up to 30 nm which is well beyond the traditional FRET limit. In this report, we study the transfer of an amount of energy (h) over bar Omega from a dye molecule to doped graphene. We find a crossover of the distance dependence of the rate from z(-4) to exponential as the Fermi level is increasingly shifted into the conduction band, with the crossover occurring at a shift of the Fermi level by an amount (h) over bar Omega/2.

Electrical Resistance and Seebeck Coefficient in PbTe Nanowires

We address a physics-based simplified analytical formulation of the diffusive electrical resistance ( (Omega)) and Seebeck coefficient () in a PbTe nanowire dominated by acoustic phonon scattering under the presence of a low static longitudinal electric field. The use of a second-order nonparabolic electron energy band structure involving a geometry-dependent band gap has been selected in principle to demonstrate that the electron mean free path (MFP) in such a system can reach as low as about 8 nm at room temperature for a 10-nm-wide PbTe nanowire. This is followed by the formulation of the carrier back-scattering coefficient for determination of (Omega) and as functions of wire dimensions, temperature, and the field, respectively. The present analytical formulation agrees well with the available experimental data and may find extensive use in determination of various electrothermal transport phenomena in PbTe-based one-dimensional electron devices.

The effect of potential on electrodeposited CdSe thin films

Cadmium selenide (CdSe) thin films have been successfully prepared by the electrodeposition technique on indium doped tin oxide (ITO) substrates with aqueous solutions of cadmium sulphate and selenium dioxide. The deposited films were characterized with X-ray diffraction (XRD), scanning electron microscope (SEM), energy dispersive analysis by X-rays (EDAX), photoluminescence (PL), UV spectrometry and electrical resistivity measurements. XRD analysis shows that the films are polycrystalline in nature with hexagonal crystalline structure. The various parameters such as crystallite size, micro strain, dislocation density and texture coefficients were evaluated. SEM study shows that the total substrate surface is well covered with uniformly distributed spherical shaped grains. Photoluminescence spectra of films were recorded to understand the emission properties of the films. The presence of direct transition with band gap energy 1.75 eV is established from optical studies. The electrical resistivity of the thin films is found to be 10(6) Omega cm and the results are discussed. (c) 2011 Elsevier Ltd. All rights reserved.

Effect of doping concentration on the structural and optical properties of pure and tin doped zinc oxide thin films by nebulizer spray pyrolysis (NSP) technique

Pure and tin doped zinc oxide (Sn:ZnO) thin films were prepared for the first time by NSP technique using aqueous solutions of zinc acetate dehydrate, tin (IV) chloride fendahydrate and methanol. X-ray diffraction patterns confirm that the films are polycrystalline in nature exhibiting hexagonal wurtzite type, with (0 0 2) as preferred orientation. The structural parameters such as lattice constant ('a' and `c'), crystallite size, dislocation density, micro strain, stress and texture coefficient were calculated from X-ray diffraction studies. Surface morphology was found to be modified with increasing Sn doping concentration. The ZnO films have high transmittance 85% in the visible region, and the transmittance is found to be decreased with the increase of Sn doping concentration. The corresponding optical band gap decreases from 3.25 to 3.08 eV. Room temperature photoluminescence reveals the sharp emission of strong UV peak at 400 nm (3.10 eV) and a strong sharp green luminescence at 528 nm (2.34 eV) in the Sn doped ZnO films. The electrical resistivity is found to be 10(6) Omega-cm at higher temperature and 10(5) Omega-cm at lower temperature. (C) 2012 Elsevier Ltd. All rights reserved.

A Comparative Kinetic and Thermodynamic Perspective of the sigma-Competition Model in Escherichia coli

Transcription is the most fundamental step in gene expression in any living organism. Various environmental cues help in the maturation of core RNA polymerase (RNAP; alpha(2)beta beta'omega) with different sigma-factors, leading to the directed recruitment of RNAP to different promoter DNA sequences. Thus it is essential to determine the sigma-factors that affect the preferential partitioning of core RNAP among various a-actors, and the role of sigma-switching in transcriptional gene regulation. Further, the macromolecular assembly of holo RNAP takes place in an extremely crowded environment within a cell, and thus far the kinetics and thermodynamics of this molecular recognition process have not been well addressed. In this study we used a site-directed bioaffinity immobilization method to evaluate the relative binding affinities of three different Escherichia coli sigma-factors to the same core RNAP with variations in temperature and ionic strength while emulating the crowded cellular milieu. Our data indicate that the interaction of core RNAP-sigma is susceptible to changes in external stimuli such as osmolytic and thermal stress, and the degree of susceptibility varies among different sigma-factors. This allows for a reversible sigma-switching from housekeeping factors to alternate sigma-factors when the organism senses a change in its physiological conditions.

Quantitative estimation of mechanical and optical properties from ultrasound assisted optical tomography data

We demonstrate quantitative optical property and elastic property imaging from ultrasound assisted optical tomography data. The measurements, which are modulation depth M and phase phi of the speckle pattern, are shown to be sensitively dependent on these properties of the object in the insonified focal region of the ultrasound (US) transducer. We demonstrate that Young's modulus (E) can be recovered from the resonance observed in M versus omega (the US frequency) plots and optical absorption (mu(a)) and scattering (mu(s)) coefficients from the measured differential phase changes. All experimental observations are verified also using Monte Carlo simulations. (c) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). DOI: 10.1117/1.JBO.17.10.101507]

Thermodynamics of Congruent Oxidation

Congruent oxidation occurs when an alloy oxidizes at constant oxygen chemical potential and temperature to an oxide in which the ratio of metallic components is the same as in the alloy. In alloys that undergo congruent oxidation concentration gradients near the surface are minimized. In this work thermodynamic conditions for congruent oxidation of binary and ternary alloys are formulated using the regular solution model to describe thermodynamic mixing properties. The conditions under which congruent oxidation can occur are identified. Congruent oxidation of a binary alloy X-Y will occur only if difference in oxygen potential for the oxidation of the two pure metals is less than twice the difference in regular solution parameters for the oxide and alloy phases (Omega(O)-Omega(A)). In the case of ternary alloys, congruency requirements for both two-phase and three-phase equilibria are discussed. Since the conditions for congruent oxidation of ternary alloy X-Y-Z depends on many parameters, the effect of systematic variation of the binary sets of regular solution parameters on the congruent composition is explored by numerical solution of the governing equations.

Model Pseudoconvex Domains and Bumping

The Levi geometry at weakly pseudoconvex boundary points of domains in C-n, n >= 3, is sufficiently complicated that there are no universal model domains with which to compare a general domain. Good models may be constructed by bumping outward a pseudoconvex, finite- type Omega subset of C-3 in such a way that: (i) pseudoconvexity is preserved, (ii) the (locally) larger domain has a simpler defining function, and (iii) the lowest possible orders of contact of the bumped domain with partial derivative Omega, at the site of the bumping, are realized. When Omega subset of C-n, n >= 3, it is, in general, hard to meet the last two requirements. Such well-controlled bumping is possible when Omega is h-extendible/semiregular. We examine a family of domains in C-3 that is strictly larger than the family of h-extendible/semiregular domains and construct explicit models for these domains by bumping.

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.

Observation of the nuclear magnetic octupole moment of Yb-173 from precise measurements of the hyperfine structure in the P-3(2) state

We measure hyperfine structure in the metastable P-3(2) state of Yb-173 and extract the nuclear magnetic octupole moment. We populate the state using dipole-allowed transitions through the P-3(1) and S-3(1) states. We measure frequencies of hyperfine transitions of the P-3(2) -> S-3(1) line at 770 nm using a Rb-stabilized ring cavity resonator with a precision of 200 kHz. Second-order corrections due to perturbations from the nearby P-3(1) and P-1(1) states are below 30 kHz. We obtain the hyperfine coefficients as A = -742.11(2) MHz and B = 1339.2(2) MHz, which represent a two orders-of-magnitude improvement in precision, and C = 0.54(2) MHz. From atomic structure calculations, we obtain the nuclear moments quadrupole Q = 2.46(12) b and octupole Omega = -34.4(21) b x mu(N). DOI: 10.1103/PhysRevA.87.012512

Effect of iodine concentration on the photovoltaic properties of dye sensitized solar cells for various I-2/LiI ratios

In the present study, the effect of iodine concentration on the photovoltaic properties of dye sensitized solar cells (DSSC) based on TiO2 nanoparticles for three different ratios of lithium iodide (LiI) and iodine (I-2) has been investigated. The electron transport properties and interfacial recombination kinetics have been evaluated by electrochemical impedance spectroscopy (EIS). It is found that increasing the concentration of lithium iodide for all ratios of iodine and lithium iodide decreases the open-circuit voltage (V-oc) whereas short circuit current density (J(sc)) and fill factor (FF) shows improvement. The reduction in V-oc and increment in J(sc) is ascribed to the higher concentration of absorptive Li+ cations which shifts the conduction band edge of TiO2 positively. The increase in FF is due to the reduction in electron transport resistance (R-omega) of the cell. In addition for all the ratios of LiI/I-2 increasing the concentration of I-2 decreases the V-oc which is attributed to the increased recombination with tri-iodide ions (I-3(-)) as verified from the low recombination resistance (R-k) and electron lifetime (tau) values obtained by EIS analysis. (C) 2012 Elsevier Ltd. All rights reserved.