New Approximability Results for the Robust k-Median Problem

We consider a robust variant of the classical $k$-median problem, introduced by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust $k$-Median problem}, we are given an $n$-vertex metric space $(V,d)$ and $m$ client sets $\set{S_i \subseteq V}_{i=1}^m$. The objective is to open a set $F \subseteq V$ of $k$ facilities such that the worst case connection cost over all client sets is minimized; in other words, minimize $\max_{i} \sum_{v \in S_i} d(F,v)$. Anthony et al.\ showed an $O(\log m)$ approximation algorithm for any metric and APX-hardness even in the case of uniform metric. In this paper, we show that their algorithm is nearly tight by providing $\Omega(\log m/ \log \log m)$ approximation hardness, unless ${\sf NP} \subseteq \bigcap_{\delta >0} {\sf DTIME}(2^{n^{\delta}})$. This hardness result holds even for uniform and line metrics. To our knowledge, this is one of the rare cases in which a problem on a line metric is hard to approximate to within logarithmic factor. We complement the hardness result by an experimental evaluation of different heuristics that shows that very simple heuristics achieve good approximations for realistic classes of instances.Comment: 19 page

Mesomorphic properties of alkoxybenzylidene- aminoacetophenones

Liquid crystal phase transitions in compounds of alkoxybenzylidene-aminoacetophene serie

The pressure-amorphized state in zirconium tungstate: a precursor to decomposition

In contrast to widely accepted view that pressure-induced amorphization arises due to kinetic hindrance of equilibrium phase transitions, here we provide evidence that the metastable pressure-amorphized state in zirconium tungstate is a precursor to decomposition of the compound into a mixture of simple oxides. This is from the volume collapse ΔV across amorphization, which is obtained for the first time by measuring linear dimensions of irreversibly amorphized samples during their recovery to the original cubic phase upon isochronal annealing up to 1000 K. The anomalously large ΔV of 25.7 ± 1.2% being the same as that expected for the decomposition indicates that this amorphous state is probably a precursor to kinetically hindered decomposition. A P–T diagram of the compound is also proposed

Altered membrane permeability in multidrug resistant Escherichia coli isolated from extra-intestinal infections

The study was conducted with the objective of examining the outer membrane proteins and their involvement during the transport of &#946 - lactams in multidrug resistant Escherichia coli isolated from extra-intestinal infections. Also, the response of gram negative bacterial biomembrane alteration wasstudied using extended spectrum &#946-Lactamase (ESBL) positive strains of E.coli in the presence and absence of stress. Outer membrane protein  analysis revealed that multidrug resistance was mediated by loss of porins in the ESBL isolates of E. coli. Parallel to this, the level of outer membrane proteins decreased dramatically with increased antibiotic stress in the isolates. In non-ESBL isolates of E. coli, porins seems to have no influence in co-modulation of resistance

Semiclassical Moser--Trudinger inequalities

We extend the Moser--Trudinger inequality of one function to systems of orthogonal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfunctions of Schr\"odinger operators on bounded domains.Comment: 18 page

Separation of Circulating Tokens

Self-stabilizing distributed control is often modeled by token abstractions. A system with a single token may implement mutual exclusion; a system with multiple tokens may ensure that immediate neighbors do not simultaneously enjoy a privilege. For a cyber-physical system, tokens may represent physical objects whose movement is controlled. The problem studied in this paper is to ensure that a synchronous system with m circulating tokens has at least d distance between tokens. This problem is first considered in a ring where d is given whilst m and the ring size n are unknown. The protocol solving this problem can be uniform, with all processes running the same program, or it can be non-uniform, with some processes acting only as token relays. The protocol for this first problem is simple, and can be expressed with Petri net formalism. A second problem is to maximize d when m is given, and n is unknown. For the second problem, the paper presents a non-uniform protocol with a single corrective process.Comment: 22 pages, 7 figures, epsf and pstricks in LaTe

Magic wavelengths for the np-ns transitions in alkali-metal atoms

Extensive calculations of the electric-dipole matrix elements in alkali-metal atoms are conducted using the relativistic all-order method. This approach is a linearized version of the coupled-cluster method, which sums infinite sets of many-body perturbation theory terms. All allowed transitions between the lowest ns, np_1/2, np_3/2 states and a large number of excited states are considered in these calculations and their accuracy is evaluated. The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of the excited states of alkali-metal atoms. We find magic wavelengths in alkali-metal atoms for which the ns and np_1/2 and np_3/2 atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.Comment: 12 pages, 8 figure

Surface optical Raman modes in InN nanostructures

Raman spectroscopic investigations are carried out on one-dimensional nanostructures of InN,such as nanowires and nanobelts synthesized by chemical vapor deposition. In addition to the optical phonons allowed by symmetry; A1, E1 and E2(high) modes, two additional Raman peaks are observed around 528 cm-1 and 560 cm-1 for these nanostructures. Calculations for the frequencies of surface optical (SO) phonon modes in InN nanostructures yield values close to those of the new Raman modes. A possible reason for large intensities for SO modes in these nanostructures is also discussed.Comment: 13 pages, 4 figures, Submitted in Journa

A Hypergraph Dictatorship Test with Perfect Completeness

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based \PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.Comment: Some minor correction

Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing

We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to the question of tripartite to bipartite entanglement transformations