On the efficiency of estimating penetrating rank on large graphs

P-Rank (Penetrating Rank) has been suggested as a useful measure of structural similarity that takes account of both incoming and outgoing edges in ubiquitous networks. Existing work often utilizes memoization to compute P-Rank similarity in an iterative fashion, which requires cubic time in the worst case. Besides, previous methods mainly focus on the deterministic computation of P-Rank, but lack the probabilistic framework that scales well for large graphs. In this paper, we propose two efficient algorithms for computing P-Rank on large graphs. The first observation is that a large body of objects in a real graph usually share similar neighborhood structures. By merging such objects with an explicit low-rank factorization, we devise a deterministic algorithm to compute P-Rank in quadratic time. The second observation is that by converting the iterative form of P-Rank into a matrix power series form, we can leverage the random sampling approach to probabilistically compute P-Rank in linear time with provable accuracy guarantees. The empirical results on both real and synthetic datasets show that our approaches achieve high time efficiency with controlled error and outperform the baseline algorithms by at least one order of magnitude

Dielectric behavior of oblate spheroidal particles: Application to erythrocytes suspensions

We have investigated the effect of particle shape on the eletrorotation (ER) spectrum of living cells suspensions. In particular, we consider coated oblate spheroidal particles and present a theoretical study of ER based on the spectral representation theory. Analytic expressions for the characteristic frequency as well as the dispersion strength can be obtained, thus simplifying the fitting of experimental data on oblate spheroidal cells that abound in the literature. From the theoretical analysis, we find that the cell shape, coating as well as material parameters can change the ER spectrum. We demonstrate good agreement between our theoretical predictions and experimental data on human erthrocytes suspensions.Comment: RevTex; 5 eps figure

Many-body dipole-induced dipole model for electrorheological fluids

Theoretical investigations on electrorheological (ER) fluids usually rely on computer simulations. An initial approach for these studies would be the point-dipole (PD) approximation, which is known to err considerably when the particles approach and finally touch due to many-body and multipolar interactions. Thus various work attempted to go beyond the PD model. Being beyond the PD model, previous attempts have been restricted to either local-field effects only or multipolar effects only, but not both. For instance, we recently proposed a dipole-induced-dipole (DID) model which is shown to be both more accurate than the PD model and easy to use. This work is necessary because the many-body (local-field) effect is included to put forth the many-body DID model. The results show that the multipolar interactions can indeed be dominant over the dipole interaction, while the local-field effect may yield an important correction.Comment: RevTeX, 3 eps figure

Nonlinear ac responses of electro-magnetorheological fluids

We apply a Langevin model to investigate the nonlinear ac responses of electro-magnetorheological (ERMR) fluids under the application of two crossed dc magnetic (z axis) and electric (x axis) fields and a probing ac sinusoidal magnetic field. We focus on the influence of the magnetic fields which can yield nonlinear behaviors inside the system due to the particles with a permanent magnetic dipole moment. Based on a perturbation approach, we extract the harmonics of the magnetic field and orientational magnetization analytically. To this end, we find that the harmonics are sensitive to the degree of anisotropy of the structure as well as the field frequency. Thus, it is possible to real-time monitor the structure transformation of ERMR fluids by detecting the nonlinear ac responses.Comment: 21 pages, 4 figure

Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry

We study topological phases of time-reversal invariant singlet superconductors in three spatial dimensions. In these particle-hole symmetric systems the topological phases are characterized by an even-numbered winding number $\nu$. At a two-dimensional (2D) surface the topological properties of this quantum state manifest themselves through the presence of $\nu$ flavors of gapless Dirac fermion surface states, which are robust against localization from random impurities. We construct a tight-binding model on the diamond lattice that realizes a topologically nontrivial phase, in which the winding number takes the value $\nu =\pm 2$. Disorder corresponds to a (non-localizing) random SU(2) gauge potential for the surface Dirac fermions, leading to a power-law density of states $\rho(\epsilon) \sim \epsilon^{1/7}$. The bulk effective field theory is proposed to be the (3+1) dimensional SU(2) Yang-Mills theory with a theta-term at $\theta=\pi$.Comment: 5 pages, 3 figure

Theory of the Stark Effect for P donors in Si

We develop a multi-valley effective mass theory for substitutional donors in silicon in an inhomogeneous environment. Valley-orbit coupling is treated perturbatively. We apply the theory to the Stark effect in Si:P. The method becomes more accurate at high fields, and it is designed to give correct experimental binding energies at zero field. Unexpectedly, the ground state energy for the donor electron is found to increase with electric field as a consequence of spectrum narrowing of the 1s manifold. Our results are of particular importance for the Kane quantum computer.Comment: published versio

Magneto-controlled nonlinear optical materials

We exploit theoretically a magneto-controlled nonlinear optical material which contains ferromagnetic nanoparticles with a non-magnetic metallic nonlinear shell in a host fluid. Such an optical material can have anisotropic linear and nonlinear optical properties and a giant enhancement of nonlinearity, as well as an attractive figure of merit.Comment: 11 pages, 2 figures. To be published in Appl. Phys. Let