Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence

In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection.

Characterizing graph symmetries through quantum Jensen-Shannon divergence

In this paper we investigate the connection between quantum walks and graph symmetries. We begin by designing an experiment that allows us to analyze the behavior of the quantum walks on the graph without causing the wave function collapse. To achieve this, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the quantum Jensen-Shannon divergence between the evolution of two quantum walks with suitably defined initial states is maximum when the graph presents symmetries. Hence, we assign to each pair of nodes of the graph a value of the divergence, and we average over all pairs of nodes to characterize the degree of symmetry possessed by a graph. © 2013 American Physical Society.

Cognitive dissonance and the effect of acceptance of methodology, beliefs about religion, religious orientation, and dogmatism on the success of university students in a religious studies course

The problem investigated was negative effects on the ability of a university student to successfully complete a course in religious studies resulting from conflict between the methodologies and objectives of religious studies and the student's system of beliefs. Using Festinger's theory of cognitive dissonance as a theoretical framework, it was hypothesized that completing a course with a high level of success would be negatively affected by (1) failure to accept the methodologies and objectives of religious studies (methodology), (2) holding beliefs about religion that had potential conflicts with the methodologies and objectives (beliefs), (3) extrinsic religiousness, and (4) dogmatism. The causal comparative method was used. The independent variables were measured with four scales employing Likert-type items. An 8-item scale to measure acceptance of the methodologies and objectives of religious studies and a 16-item scale to measure holding of beliefs about religion having potential conflict with the methodologies were developed for this study. These scales together with a 20-item form of Rokeach's Dogmatism Scale and Feagin's 12-item Religious Orientation Scale to measure extrinsic religiousness were administered to 144 undergraduate students enrolled in randomly selected religious studies courses at Florida International University. Level of success was determined by course grade with the 27% of students receiving the highest grades classified as highly successful and the 27% receiving the lowest grades classified as not highly successful. A stepwise discriminant analysis produced a single significant function with methodology and dogmatism as the discriminants. Methodology was the principal discriminating variable. Beliefs and extrinsic religiousness failed to discriminate significantly. It was concluded that failing to accept the methodologies and objectives of religious studies and being highly dogmatic have significant negative effects on a student's success in a religious studies course. Recommendations were made for teaching to diminish these negative effects.

Experimental deuteron momentum distributions with reduced final state interactions

This dissertation presents a study of the D( e, e′p)n reaction carried out at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) for a set of fixed values of four-momentum transfer Q 2 = 2.1 and 0.8 (GeV/c)2 and for missing momenta pm ranging from pm = 0.03 to pm = 0.65 GeV/c. The analysis resulted in the determination of absolute D(e,e′ p)n cross sections as a function of the recoiling neutron momentum and it's scattering angle with respect to the momentum transfer [vector] q. The angular distribution was compared to various modern theoretical predictions that also included final state interactions. The data confirmed the theoretical prediction of a strong anisotropy of final state interaction contributions at Q2 of 2.1 (GeV/c)2 while at the lower Q2 value, the anisotropy was much less pronounced. At Q2 of 0.8 (GeV/c)2, theories show a large disagreement with the experimental results. The experimental momentum distribution of the bound proton inside the deuteron has been determined for the first time at a set of fixed neutron recoil angles. The momentum distribution is directly related to the ground state wave function of the deuteron in momentum space. The high momentum part of this wave function plays a crucial role in understanding the short-range part of the nucleon-nucleon force. At Q2 = 2.1 (GeV/c)2, the momentum distribution determined at small neutron recoil angles is much less affected by FSI compared to a recoil angle of 75°. In contrast, at Q2 = 0.8 (GeV/c)2 there seems to be no region with reduced FSI for larger missing momenta. Besides the statistical errors, systematic errors of about 5–6 % were included in the final results in order to account for normalization uncertainties and uncertainties in the determi- nation of kinematic veriables. The measurements were carried out using an electron beam energy of 2.8 and 4.7 GeV with beam currents between 10 to 100 &mgr; A. The scattered electrons and the ejected protons originated from a 15cm long liquid deuterium target, and were detected in conicidence with the two high resolution spectrometers of Hall A at Jefferson Lab.^

Exclusive electrodisintegration of three-nucleon systems

The purpose of this research was to develop a theory of high-energy exclusive electrodisintegration of three-nucleon systems on the example of 3He(e, e'NN)N reaction with knocked-out nucleon in the final state. The scattering amplitudes and differential cross section of the reaction were calculated in details within the Generalized Eikonal Approximation(GEA). The manifestly covariant nature of Feynman diagrams derived in GEA allowed us to preserve both the relativistic dynamics and kinematics of the scattering while identifying the low momentum nuclear part of the amplitude with a nonrelativistic nuclear wave function. Numerical calculations of the residual system's total and relative momentum distribution were performed which show reasonable agreement with available experimental data. The theoretical framework of GEA, which was applied previously only for the case of two-body (deuteron) high energy break up reactions, has been practically implemented and shown to provide a valid description for more complex A = 3 systems.

Electrical and dielectric properties of uncoated and coated wood-free paper for electrophotography

The print substrate influences the print result in dry toner electrophotography, which is a widely used digital printing method. The influence of the substrate can be seen more easily in color printing, as that is a more complex process compared to monochrome printing. However, the print quality is also affected by the print substrate in grayscale printing. It is thus in the interests of both substrate producers and printing equipment manufacturers to understand the substrate properties that influence the quality of printed images in more detail. In dry toner electrophotography, the image is printed by transferring charged toner particles to the print substrate in the toner transfer nip, utilizing an electric field, in addition to the forces linked to the contact between toner particles and substrate in the nip. The toner transfer and the resulting image quality are thus influenced by the surface texture and the electrical and dielectric properties of the print substrate. In the investigation of the electrical and dielectric properties of the papers and the effects of substrate roughness, in addition to commercial papers, controlled sample sets were made on pilot paper machines and coating machines to exclude uncontrolled variables from the experiments. The electrical and dielectric properties of the papers investigated were electrical resistivity and conductivity, charge acceptance, charge decay, and the dielectric permittivity and losses at different frequencies, including the effect of temperature. The objective was to gain an understanding of how the electrical and dielectric properties are affected by normal variables in papermaking, including basis weight, material density, filler content, ion and moisture contents, and coating. In addition, the dependency of substrate resistivity on the electric field applied was investigated. Local discharging did not inhibit transfer with the paper roughness levels that are normal in electrophotographic color printing. The potential decay of paper revealed that the charge decay cannot be accurately described with a single exponential function, since in charge decay there are overlapping mechanisms of conduction and depolarization of paper. The resistivity of the paper depends on the NaCl content and exponentially on moisture content although it is also strongly dependent on the electric field applied. This dependency is influenced by the thickness, density, and filler contents of the paper. Furthermore, the Poole-Frenkel model can be applied to the resistivity of uncoated paper. The real part of the dielectric constant ε’ increases with NaCl content and relative humidity, but when these materials cannot polarize freely, the increase cannot be explained by summing the effects of their dielectric constants. Dependencies between the dielectric constant and dielectric loss factor and NaCl content, temperature, and frequency show that in the presence of a sufficient amount of moisture and NaCl, new structures with a relaxation time of the order of 10-3 s are formed in paper. The ε’ of coated papers is influenced by the addition of pigments and other coating additives with polarizable groups and due to the increase in density. The charging potential decreases and the electrical conductivity, potential decay rate, and dielectric constant of paper increase with increasing temperature. The dependencies are exponential and the temperature dependencies and their activation energies are altered by the ion content. The results have been utilized in manufacturing substrates for electrophotographic color printing.

Symmetry properties of one- and two- electron molecular integrals

The maximum numbers of distinct one- and two-electron integrals that arise in calculating the electronic energy of a molecule are discussed. It is shown that these may be calculated easily using the character table of the symmetry group of the set of basis functions used to express the wave function. Complications arising from complex group representations and from a conflict of symmetry between the basis set and the nuclear configuration are considered and illustrated by examples.

High-temperature superconductivity in the two-dimensional t-J model: Gutzwiller wavefunction solution

A systematic diagrammatic expansion for Gutzwiller wavefunctions (DE-GWFs) proposed very recently is used for the description of the superconducting (SC) ground state in the two-dimensional square-lattice t-J model with the hopping electron amplitudes t (and t') between nearest (and next-nearest) neighbors. For the example of the SC state analysis we provide a detailed comparison of the method's results with those of other approaches. Namely, (i) the truncated DE-GWF method reproduces the variational Monte Carlo (VMC) results and (ii) in the lowest (zeroth) order of the expansion the method can reproduce the analytical results of the standard Gutzwiller approximation (GA), as well as of the recently proposed 'grand-canonical Gutzwiller approximation' (called either GCGA or SGA). We obtain important features of the SC state. First, the SC gap at the Fermi surface resembles a d(x2-y2) wave only for optimally and overdoped systems, being diminished in the antinodal regions for the underdoped case in a qualitative agreement with experiment. Corrections to the gap structure are shown to arise from the longer range of the real-space pairing. Second, the nodal Fermi velocity is almost constant as a function of doping and agrees semi-quantitatively with experimental results. Third, we compare the

A novel methodology for simulating contact-line behavior in capillary-driven flows

Despite the wide swath of applications where multiphase fluid contact lines exist, there is still no consensus on an accurate and general simulation methodology. Most prior numerical work has imposed one of the many dynamic contact-angle theories at solid walls. Such approaches are inherently limited by the theory accuracy. In fact, when inertial effects are important, the contact angle may be history dependent and, thus, any single mathematical function is inappropriate. Given these limitations, the present work has two primary goals: 1) create a numerical framework that allows the contact angle to evolve naturally with appropriate contact-line physics and 2) develop equations and numerical methods such that contact-line simulations may be performed on coarse computational meshes.

Fluid flows affected by contact lines are dominated by capillary stresses and require accurate curvature calculations. The level set method was chosen to track the fluid interfaces because it is easy to calculate interface curvature accurately. Unfortunately, the level set reinitialization suffers from an ill-posed mathematical problem at contact lines: a ``blind spot'' exists. Standard techniques to handle this deficiency are shown to introduce parasitic velocity currents that artificially deform freely floating (non-prescribed) contact angles. As an alternative, a new relaxation equation reinitialization is proposed to remove these spurious velocity currents and its concept is further explored with level-set extension velocities.

To capture contact-line physics, two classical boundary conditions, the Navier-slip velocity boundary condition and a fixed contact angle, are implemented in direct numerical simulations (DNS). DNS are found to converge only if the slip length is well resolved by the computational mesh. Unfortunately, since the slip length is often very small compared to fluid structures, these simulations are not computationally feasible for large systems. To address the second goal, a new methodology is proposed which relies on the volumetric-filtered Navier-Stokes equations. Two unclosed terms, an average curvature and a viscous shear VS, are proposed to represent the missing microscale physics on a coarse mesh.

All of these components are then combined into a single framework and tested for a water droplet impacting a partially-wetting substrate. Very good agreement is found for the evolution of the contact diameter in time between the experimental measurements and the numerical simulation. Such comparison would not be possible with prior methods, since the Reynolds number Re and capillary number Ca are large. Furthermore, the experimentally approximated slip length ratio is well outside of the range currently achievable by DNS. This framework is a promising first step towards simulating complex physics in capillary-dominated flows at a reasonable computational expense.

Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation

Atomic vibration in the Carbon Nanotubes (CNTs) gives rise to non-local interactions. In this paper, an expression for the non-local scaling parameter is derived as a function of the geometric and electronic properties of the rolled graphene sheet in single-walled CNTs. A self-consistent method is developed for the linearization of the problem of ultrasonic wave propagation in CNTs. We show that (i) the general three-dimensional elastic problem leads to a single non-local scaling parameter (e(0)), (ii) e(0) is almost constant irrespective of chirality of CNT in the case of longitudinal wave propagation, (iii) e(0) is a linear function of diameter of CNT for the case of torsional mode of wave propagation, (iv) e(0) in the case of coupled longitudinal-torsional modes of wave propagation, is a function which exponentially converges to that of axial mode at large diameters and to torsional mode at smaller diameters. These results are valid in the long-wavelength limit. (C) 2011 Elsevier Ltd. All rights reserved.

Multiple human single-stranded DNA binding proteins function in genome maintenance : structural, biochemical and functional analysis

DNA exists predominantly in a duplex form that is preserved via specific base pairing. This base pairing affords a considerable degree of protection against chemical or physical damage and preserves coding potential. However, there are many situations, e.g. during DNA damage and programmed cellular processes such as DNA replication and transcription, in which the DNA duplex is separated into two singlestranded DNA (ssDNA) strands. This ssDNA is vulnerable to attack by nucleases, binding by inappropriate proteins and chemical attack. It is very important to control the generation of ssDNA and protect it when it forms, and for this reason all cellular organisms and many viruses encode a ssDNA binding protein (SSB). All known SSBs use an oligosaccharide/oligonucleotide binding (OB)-fold domain for DNA binding. SSBs have multiple roles in binding and sequestering ssDNA, detecting DNA damage, stimulating strand-exchange proteins and helicases, and mediation of protein–protein interactions. Recently two additional human SSBs have been identified that are more closely related to bacterial and archaeal SSBs. Prior to this it was believed that replication protein A, RPA, was the only human equivalent of bacterial SSB. RPA is thought to be required for most aspects of DNA metabolism including DNA replication, recombination and repair. This review will discuss in further detail the biological pathways in which human SSBs function.

Wave propagation in multi-walled carbon nanotube

In this paper, wave propagation in multi-walled carbon nanotubes (MWNTs) are studied by modeling them as continuum multiple shell coupled through van der Waals force of interaction. The displacements, namely, axial, radial and circumferential displacements vary along the circumferential direction. The wave propagation are simulated using the wavelet based spectral finite element (WSFE) method. This technique involves Daubechies scaling function approximation in time and spectral element approach. The WSFE Method allows the study of wave properties in both time and frequency domains. This is in contrast to the conventional Fourier transform based analysis which are restricted to frequency domain analysis. Here, first, the wavenumbers and wave speeds of carbon nanotubes (CNTs) are Studied to obtain the characteristics of the waves. These group speeds have been compared with those reported in literature. Next, the natural frequencies of a single-walled carbon nanotube (SWNT) are studied for different values of the radius. The frequencies of the first five modes vary linearly with the radius of the SWNT. Finally, the time domain responses are simulated for SWNT and three-walled carbon nanotubes.

Terahertz wave characteristics of a single-walled carbon nanotube containing a fluid flow using the nonlocal Timoshenko beam model

This paper presents the effect of nonlocal scaling parameter on the terahertz wave propagation in fluid filled single walled carbon nanotubes (SWCNTs). The SWCNT is modeled as a Timoshenko beam,including rotary inertia and transverse shear deformation by considering the nonlocal scale effects. A uniform fluid velocity of 1000 m/s is assumed. The analysis shows that, for a fluid filled SWCNT, the wavenumbers of flexural and shear waves will increase and the corresponding wave speeds will decrease as compared to an empty SWCNT. The nonlocal scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or wave speed tends to zero). The frequency at which this phenomenon occurs is called the ``escape frequency''. The effect of fluid density on the terahertz wave propagation in SWCNT is also studied and the analysis shows that as the fluid becomes denser, the wave speeds will decrease. The escape frequency decreases with increase in nonlocal scaling parameter, for both wave modes. We also show that the effect of fluid density and velocity are negligible on the escape frequencies of flexural and shear wave modes. (C) 2010 Elsevier B.V. All rights reserved.

Note: Dynamic point spread function for single and multiphoton fluorescence microscopy

We propose and demonstrate a dynamic point spread function (PSF) for single and multiphoton fluorescence microscopy. The goal is to generate a PSF whose shape and size can be maneuvered from highly localized to elongated one, thereby allowing shallow-to-depth excitation capability during active imaging. The PSF is obtained by utilizing specially designed spatial filter and dynamically altering the filter parameters. We predict potential applications in nanobioimaging and fluorescence microscopy.

Note: Dynamic point spread function for single and multiphoton fluorescence microscopy

We propose and demonstrate a dynamic point spread function (PSF) for single and multiphoton fluorescence microscopy. The goal is to generate a PSF whose shape and size can be maneuvered from highly localized to elongated one, thereby allowing shallow-to-depth excitation capability during active imaging. The PSF is obtained by utilizing specially designed spatial filter and dynamically altering the filter parameters. We predict potential applications in nanobioimaging and fluorescence microscopy.