Combining Traditional Marketing and Viral Marketing with Amphibious Influence Maximization

In this paper, we propose the amphibious influence maximization (AIM) model that combines traditional marketing via content providers and viral marketing to consumers in social networks in a single framework. In AIM, a set of content providers and consumers form a bipartite network while consumers also form their social network, and influence propagates from the content providers to consumers and among consumers in the social network following the independent cascade model. An advertiser needs to select a subset of seed content providers and a subset of seed consumers, such that the influence from the seed providers passing through the seed consumers could reach a large number of consumers in the social network in expectation. We prove that the AIM problem is NP-hard to approximate to within any constant factor via a reduction from Feige's k-prover proof system for 3-SAT5. We also give evidence that even when the social network graph is trivial (i.e. has no edges), a polynomial time constant factor approximation for AIM is unlikely. However, when we assume that the weighted bi-adjacency matrix that describes the influence of content providers on consumers is of constant rank, a common assumption often used in recommender systems, we provide a polynomial-time algorithm that achieves approximation ratio of $(1-1/e-\epsilon)^3$ for any (polynomially small) $\epsilon > 0$. Our algorithmic results still hold for a more general model where cascades in social network follow a general monotone and submodular function.Comment: An extended abstract appeared in the Proceedings of the 16th ACM Conference on Economics and Computation (EC), 201

Strongly nonlinear waves in capillary electrophoresis

In capillary electrophoresis, sample ions migrate along a micro-capillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity in the sample zone could differ significantly from the background.Under such conditions, the local migration velocity of sample ions becomes concentration dependent resulting in a nonlinear wave that exhibits shock like features. If the nonlinearity is weak, the sample concentration profile, under certain simplifying assumptions, can be shown to obey Burgers' equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, 72(8), pg. 2047) which has an exact analytical solution for arbitrary initial condition.In this paper, we use a numerical method to study the problem in the more general case where the sample concentration is not small in comparison to the concentration of background ions. In the case of low concentrations, the numerical results agree with the weakly nonlinear theory presented earlier, but at high concentrations, the wave evolves in a way that is qualitatively different.Comment: 7 pages, 5 figures, 1 Appendix, 2 videos (supplementary material

Direct Numerical Simulations of the Navier-Stokes Alpha Model

We explore the utility of the recently proposed alpha equations in providing a subgrid model for fluid turbulence. Our principal results are comparisons of direct numerical simulations of fluid turbulence using several values of the parameter alpha, including the limiting case where the Navier-Stokes equations are recovered. Our studies show that the large scale features, including statistics and structures, are preserved by the alpha models, even at coarser resolutions where the fine scales are not fully resolved. We also describe the differences that appear in simulations. We provide a summary of the principal features of the alpha equations, and offer some explanation of the effectiveness of these equations used as a subgrid model for three-dimensional fluid turbulence

Profile of bubbling solutions to a Liouville system

In several fields of Physics, Chemistry and Ecology, some models are described by Liouville systems. In this article we first prove a uniqueness result for a Liouville system in $\mathbb R^2$. Then we establish an uniform estimate for bubbling solutions of a locally defined Liouville system near an isolated blowup point. The uniqueness result, as well as the local uniform estimates are crucial ingredients for obtaining a priori estimate, degree counting formulas and existence results for Liouville systems defined on Riemann surfaces.Comment: 32 page

The Navier-Stokes-alpha model of fluid turbulence

We review the properties of the nonlinearly dispersive Navier-Stokes-alpha (NS-alpha) model of incompressible fluid turbulence -- also called the viscous Camassa-Holm equations and the LANS equations in the literature. We first re-derive the NS-alpha model by filtering the velocity of the fluid loop in Kelvin's circulation theorem for the Navier-Stokes equations. Then we show that this filtering causes the wavenumber spectrum of the translational kinetic energy for the NS-alpha model to roll off as k^{-3} for k \alpha > 1 in three dimensions, instead of continuing along the slower Kolmogorov scaling law, k^{-5/3}, that it follows for k \alpha < 1. This rolloff at higher wavenumbers shortens the inertial range for the NS-alpha model and thereby makes it more computable. We also explain how the NS-alpha model is related to large eddy simulation (LES) turbulence modeling and to the stress tensor for second-grade fluids. We close by surveying recent results in the literature for the NS-alpha model and its inviscid limit (the Euler-alpha model).Comment: 22 pages, 1 figure. Dedicated to V. E. Zakharov on the occasion of his 60th birthday. To appear in Physica

Thermopower peak in phase transition region of (1-x)La2/3_{2/3}Ca1/3_{1/3}MnO3_{3}/xYSZ

The thermoelectric power (TEP) and the electrical resistivity of the intergranular magnetoresistance (IGMR) composite, (1-x)La$_{2/3}$Ca$_{1/3}$MnO$_{3}$/xYSZ (LCMO/YSZ) with x = 0, 0.75%, 1.25%, 4.5%, 13% 15% and 80% of the yttria-stabalized zirconia (YSZ), have been measured from 300 K down to 77 K. Pronounced TEP peak appears during the phase transition for the samples of x $>$ 0, while not observed for x = 0. We suggest that this is due to the magnetic structure variation induced by the lattice strain which is resulting from the LCMO/YSZ boundary layers. The transition width in temperature derived from $d\chi/dT$, with $\chi$ being the AC magnetic susceptibility, supports this interpretation.Comment: 4 pages, 4 eps figures, Latex, J. Appl. Phys 94, 7206 (2003

Polymer translocation out of confined environments

We consider the dynamics of polymer translocation out of confined environments. Analytic scaling arguments lead to the prediction that the translocation time scales like $\tau\sim N^{\beta+\nu_{2D}}R^{1+(1-\nu_{2D})/\nu}$ for translocation out of a planar confinement between two walls with separation $R$ into a 3D environment, and $\tau \sim N^{\beta+1}R$ for translocation out of two strips with separation $R$ into a 2D environment. Here, $N$ is the chain length, $\nu$ and $\nu_{2D}$ are the Flory exponents in 3D and 2D, and $\beta$ is the scaling exponent of translocation velocity with $N$, whose value for the present choice of parameters is $\beta \approx 0.8$ based on Langevin dynamics simulations. These scaling exponents improve on earlier predictions.Comment: 5 pages, 5 figures. To appear in Phys. Rev.

Electroweak Matrix Elements in the Two-Nucleon Sector from Lattice QCD

We demonstrate how to make rigorous predictions for electroweak matrix elements in nuclear systems directly from QCD. More precisely, we show how to determine the short-distance contributions to low-momentum transfer electroweak matrix elements in the two-nucleon sector from lattice QCD. In potential model descriptions of multi-nucleon systems, this is equivalent to uniquely determining the meson-exchange currents, while in the context of nuclear effective field theory, this translates into determining the coefficients of local, gauge-invariant, multi-nucleon-electroweak current operators. The energies of the lowest-lying states of two nucleons on a finite volume lattice with periodic boundary conditions in the presence of a background magnetic field are sufficient to determine the local four-nucleon operators that contribute to the deuteron magnetic moment and to the threshold cross-section of n + p -> d + gamma. Similarly, the energy-levels of two nucleons immersed in a background isovector axial weak field can be used to determine the coefficient of the leading local four-nucleon operator contributing to the neutral- and charged-current break-up of the deuteron. This is required for the extraction of solar neutrino fluxes at SNO and future neutrino experiments.Comment: 22 pages, 4 figure

Fine-grained Complexity Meets IP = PSPACE

In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable) example, we show that the Closest-LCS-Pair problem (Given two sets of strings $A$ and $B$, compute exactly the maximum $\textsf{LCS}(a, b)$ with $(a, b) \in A \times B$) is equivalent to its approximation version (under near-linear time reductions, and with a constant approximation factor). More generally, we identify a class of problems, which we call BP-Pair-Class, comprising both exact and approximate solutions, and show that they are all equivalent under near-linear time reductions. Exploring this class and its properties, we also show: $\bullet$ Under the NC-SETH assumption (a significantly more relaxed assumption than SETH), solving any of the problems in this class requires essentially quadratic time. $\bullet$ Modest improvements on the running time of known algorithms (shaving log factors) would imply that NEXP is not in non-uniform $\textsf{NC}^1$. $\bullet$ Finally, we leverage our techniques to show new barriers for deterministic approximation algorithms for LCS. At the heart of these new results is a deep connection between interactive proof systems for bounded-space computations and the fine-grained complexity of exact and approximate solutions to problems in P. In particular, our results build on the proof techniques from the classical IP = PSPACE result

Emerging applications for OCT in the head and neck

Objectives: To describe the current and promising new applications of Optical Coherence Tomography (OCT) as a helpful tool when imaging the different sites in the head and neck. We used the OCT Niris system, which is the first commercially available OCT device for applications outside the field of ophthalmology. Methods: OCT images were obtained of normal, benign, premalignant and malignant lesions in different areas of the head and neck. The OCT imaging system has a tissue penetration depth of approximately 1-2mm, a scanning range of 2mm and a spatial depth resolution of approximately 10-20μm. Imaging was performed using a flexible probe in two different settings, the outpatient clinic and the operating room. Results: High-resolution cross-sectional images from the larynx were obtained with the patient awake, without the need for general anesthesia, under direct visualization with a flexible fiberoptic endoscope. The OCT probe was inserted through the nasal cavity and placed in slight contact with the laryngeal tissue. In the ears, cholesteatoma was differentiated from inflamed middle ear mucosa by the different hyperintensity. In the neck, normal as well as different pathologies of the thyroid were identified. Conclusions: This system is non invasive and easy to incorporate into the operating room setting as well as the outpatient clinic. It requires minimal set-up and only one person is required to operate the system. OCT has the distinctive capability to obtain highresolution images, and the microanatomy of different sites can be observed. OCT technology has the potential to offer a quick, efficient and reliable imaging method to help the surgeon not only in the operating room but also in the clinical setting to guide surgical biopsies and aid in clinical decision making of different head and neck pathologies, especially those arising form the larynx. © 2010 Copyright SPIE - The International Society for Optical Engineering