Improved Approximation Algorithms for (Budgeted) Node-weighted Steiner Problems

Moss and Rabani[12] study constrained node-weighted Steiner tree problems with two independent weight values associated with each node, namely, cost and prize (or penalty). They give an O(log n)-approximation algorithm for the prize-collecting node-weighted Steiner tree problem (PCST). They use the algorithm for PCST to obtain a bicriteria (2, O(log n))-approximation algorithm for the Budgeted node-weighted Steiner tree problem. Their solution may cost up to twice the budget, but collects a factor Omega(1/log n) of the optimal prize. We improve these results from at least two aspects. Our first main result is a primal-dual O(log h)-approximation algorithm for a more general problem, prize-collecting node-weighted Steiner forest, where we have (h) demands each requesting the connectivity of a pair of vertices. Our algorithm can be seen as a greedy algorithm which reduces the number of demands by choosing a structure with minimum cost-to-reduction ratio. This natural style of argument (also used by Klein and Ravi[10] and Guha et al.[8]) leads to a much simpler algorithm than that of Moss and Rabani[12] for PCST. Our second main contribution is for the Budgeted node-weighted Steiner tree problem, which is also an improvement to [12] and [8]. In the unrooted case, we improve upon an O(log^2(n))-approximation of [8], and present an O(log n)-approximation algorithm without any budget violation. For the rooted case, where a specified vertex has to appear in the solution tree, we improve the bicriteria result of [12] to a bicriteria approximation ratio of (1+eps, O(log n)/(eps^2)) for any positive (possibly subconstant) (eps). That is, for any permissible budget violation (1+eps), we present an algorithm achieving a tradeoff in the guarantee for prize. Indeed, we show that this is almost tight for the natural linear-programming relaxation used by us as well as in [12].Comment: To appear in ICALP 201

White-light toxicity, resulting from systemically administered 5-aminolevulinic acid, under normal operating conditions

This study has investigated damage to the intraperitoneal organs of the rat after systemic (intraperitoneal and intravenous) administration of low doses of 5-aminolevulinic acid (ALA) and illumination with a standard white-light operating-room (o.r.) lamp. The study has been done within the framework of a larger study in which the possibility of using ALA for localization of small-volume macroscopically non-visible peritoneal metastasis of ovarian tumors is being investigated. Fluorescence diagnostics are done in addition to the standard staging and localization procedures, either through a laparoscope or during laparotomy. In these circumstances, fluorescence diagnostics involve some risk of photosensitization of critical organs since a broad-band (o.r.) light source is used during the surgical procedures for illumination of the operating area. The drug dose and the time interval between administration of ALA and illumination are varied and normal tissues are examined both macroscopically and microscopically for damage. A relationship is demonstrated between the maximum tolerable dose (MTD) of ALA (defined as the dose that does not cause any tissue damage) and the time interval between administration and illumination. The white light that is used for illumination of the operating area is sufficient to induce damage to the peritoneal organs at relatively low ALA doses. The MDTs for 2, 6 and 16 h intervals are found to be respectively 1, 10 and 100 mg kg-1. The results are similar for both intraperitoneal and intravenous administration

Study of Effect on Teeth of Intermittent Fluoridation of a Community Water Supply

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67913/2/10.1177_00220345530320011601.pd

A New Histogram-based Descriptor for Images Retrieval from databases

International audienceIn this paper, we propose a new approach for designing histogram-based descriptors. For demonstration purpose, we generate a descriptor based on the histogram of differential-turning angle scale space (d-TASS) function and its derived data. We then compare the proposed histogram-based descriptor with the traditional histogram descriptors in terms of retrieval performance from image databases. Experiments on three shapes databases demonstrate the efficiency and the effectiveness of the new technique: the proposed technique of histogram-based descriptor outperforms the traditional one. These experiments showed also that the proposed histogram-based descriptor using d-TASS function and the derived features performs well compared with the state-of-the-art. When applied to texture images retrieval, the proposed approach yields higher performance than the traditional histogram-based descriptors. From these results, we believe that the proposed histogram-based descriptor should perform efficiently for medical images retrieval so we will focus on this aspect in the future work

Thomae type formulae for singular Z_N curves

We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs.Comment: 22 page

Schroedingers equation with gauge coupling derived from a continuity equation

We consider a statistical ensemble of particles of mass m, which can be described by a probability density \rho and a probability current \vec{j} of the form \rho \nabla S/m. The continuity equation for \rho and \vec{j} implies a first differential equation for the basic variables \rho and S. We further assume that this system may be described by a linear differential equation for a complex state variable \chi. Using this assumptions and the simplest possible Ansatz \chi(\rho,S) Schroedingers equation for a particle of mass m in an external potential V(q,t) is deduced. All calculations are performed for a single spatial dimension (variable q) Using a second Ansatz \chi(\rho,S,q,t) which allows for an explict q,t-dependence of \chi, one obtains a generalized Schroedinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schroeodingers equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for an non-unique external q,t-dependence of \chi, one obtains Schroedingers equation with electromagnetic potentials \vec{A}, \phi in the familiar gauge coupling form. A possible source of the non-uniqueness is pointed out.Comment: 25 pages, no figure

Tomonaga-Luttinger features in the resonant Raman spectra of quantum wires

The differential cross section for resonant Raman scattering from the collective modes in a one dimensional system of interacting electrons is calculated non-perturbatively using the bosonization method. The results indicate that resonant Raman spectroscopy is a powerful tool for studying Tomonaga-Luttinger liquid behaviour in quasi-one dimensional electron systems.Comment: 4 pages, no figur

Seminal magnetic fields from Inflato-electromagnetic Inflation

We extend some previous attempts to explain the origin and evolution of primordial magnetic fields during inflation induced from a 5D vacuum. We show that the usual quantum fluctuations of a generalized 5D electromagnetic field cannot provide us with the desired magnetic seeds. We show that special fields without propagation on the extra non-compact dimension are needed to arrive to appreciable magnetic strengths. We also identify a new magnetic tensor field $B_{ij}$ in this kind of extra dimensional theories. Our results are in very good agreement with observational requirements, in particular from TeV Blazars and CMB radiation limits we obtain that primordial cosmological magnetic fields should be close scale invariance.Comment: Improved version. arXiv admin note: text overlap with arXiv:1007.3891 by other author

Coherent quantum transport in narrow constrictions in the presence of a finite-range longitudinally polarized time-dependent field

We have studied the quantum transport in a narrow constriction acted upon by a finite-range longitudinally polarized time-dependent electric field. The electric field induces coherent inelastic scatterings which involve both intra-subband and inter-sideband transitions. Subsequently, the dc conductance G is found to exhibit suppressed features. These features are recognized as the quasi-bound-state (QBS) features which are associated with electrons making transitions to the vicinity of a subband bottom, of which the density of states is singular. Having valley-like instead of dip-like structures, these QBS features are different from the G characteristics for constrictions acted upon by a finite-range time-modulated potential. In addition, the subband bottoms in the time-dependent electric field region are shifted upward by an energy proportional to the square of the electric field and inversely proportional to the square of the frequency. This effective potential barrier is originated from the square of the vector potential and it leads to the interesting field-sensitive QBS features. An experimental set-up is proposed for the observation of these features.Comment: 8 pages, 4 figure

A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear Programs

We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual solutions whose costs are within a factor of 1+eps of the optimal cost in time O((r+c)log(n)/eps^2 + n).Comment: corrected version of FOCS 2007 paper: 10.1109/FOCS.2007.62. Accepted to Algorithmica, 201