LP-Based Algorithms for Capacitated Facility Location

Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of algorithmic methodologies, such as LP-rounding and primal-dual method, have been applied to and evolved from algorithms for this problem. Unfortunately, this collection of powerful algorithmic techniques had not yet been applicable to the more general capacitated facility location problem. In fact, all of the known algorithms with good performance guarantees were based on a single technique, local search, and no linear programming relaxation was known to efficiently approximate the problem. In this paper, we present a linear programming relaxation with constant integrality gap for capacitated facility location. We demonstrate that the fundamental theories of multi-commodity flows and matchings provide key insights that lead to the strong relaxation. Our algorithmic proof of integrality gap is obtained by finally accessing the rich toolbox of LP-based methodologies: we present a constant factor approximation algorithm based on LP-rounding.Comment: 25 pages, 6 figures; minor revision

Electronic structure and Magnetism in BaMn2_2As2_2 and BaMn2_2Sb2_2

We study the properties of ThCr$_2$Si$_2$ structure BaMn$_2$As$_2$ and BaMn$_2$Sb$_2$ using density functional calculations of the electronic and magnetic as well experimental measurements on single crystal samples of BaMn$_2$As$_2$. These materials are local moment magnets with moderate band gap antiferromagnetic semiconducting ground states. The electronic structures show substantial Mn - pnictogen hybridization, which stabilizes an intermediate spin configuration for the nominally $d^5$ Mn. The results are discussed in the context of possible thermoelectric applications and the relationship with the corresponding iron / cobalt / nickel compounds Ba(Fe,Co,Ni)$_2$As$_2$

Hole-doped, High-Temperature Superconductors Li_{x}BC, Na_{x}BC and C_{x} : A Coherent-Potential-Based Prediction

Using density-functional-based methods, we show that the hole-doped Li_{x}BC and Na_{x}BC in P6_{3}/mmc crystal structure and C_{x} in graphite structure are capable of showing superconductivity, possibly with a T_{c} much higher than that of MgB_{2}. We use full-potential methods to obtain the optimized lattice constants a and c, coherent-potential approximation to describe the effects of disorder, Gaspari-Gyorffy formalism to obtain the electron-phonon coupling constant $\lambda$, and Allen-Dynes equation to calculate T_{c} as a function of hole concentration in these alloys.Comment: 4 pages, 5 figure

Eigenvalue hypothesis for multi-strand braids

Computing polynomial form of the colored HOMFLY-PT for non-arborescent knots obtained from three or more strand braids is still an open problem. One of the efficient methods suggested for the three-strand braids relies on the eigenvalue hypothesis which uses the Yang-Baxter equation to express the answer through the eigenvalues of the ${\cal R}$-matrix. In this paper, we generalize the hypothesis to higher number of strands in the braid where commuting relations of non-neighbouring $\mathcal{R}$ matrices are also incorporated. By solving these equations, we determine the explicit form for $\mathcal{R}$-matrices and the inclusive Racah matrices in terms of braiding eigenvalues (for matrices of size up to 6 by 6). For comparison, we briefly discuss the highest weight method for four-strand braids carrying fundamental and symmetric rank two $SU_q(N)$ representation. Specifically, we present all the inclusive Racah matrices for representation $[2]$ and compare with the matrices obtained from eigenvalue hypothesis.Comment: 23 page

Role of differentially expressed microRNA-139-5p in the regulation of phenotypic internal anal sphincter smooth muscle tone.

The present study focused on the role of microRNA-139-5p (miRNA-139-5p) in the regulation of basal tone in internal anal sphincter (IAS). Applying genome-wide miRNA microarrays on the phenotypically distinct smooth muscle cells (SMCs) within the rat anorectrum, we identified miRNA-139-5p as differentially expressed RNA repressor with highest expression in the purely phasic smooth muscle of anococcygeus (ASM) vs. the truly tonic smooth muscle of IAS. This pattern of miRNA-139-5p expression, previously shown to target ROCK2, was validated by target prediction using ingenuity pathway (IPA) and by qPCR analyses. Immunoblotting, immunocytochemistry (ICC), and functional assays using IAS tissues and cells subjected to overexpression/knockdown of miRNA-139-5p confirmed the inverse relationship between miRNA-139-5p and ROCK2 expressions/IAS tone. Overexpression of miRNA-139-5p caused a decrease, while knockdown by anti-miRNA-139-5p caused an increase in the IAS tone; these tissue contractile responses were confirmed by single-cell contraction using magnetic twisting cytometry (MTC). These findings suggest miRNA-139-5p is capable of significantly influencing the phenotypic tonicity in smooth muscle via ROCK2: a lack of tone in ASM may be associated with the suppression of ROCK2 by high expression of miRNA-139-5p, whereas basal IAS tone may be associated with the persistence of ROCK2 due to low expression of miRNA-139-5p

BaT2As2 Single Crystals (T = Fe, Co, Ni) and Superconductivity upon Co-doping

The crystal structure and physical properties of BaFe2As2, BaCo2As2, and BaNi2As2 single crystals are surveyed. BaFe2As2 gives a magnetic and structural transition at TN = 132(1) K, BaCo2As2 is a paramagnetic metal, while BaNi2As2 has a structural phase transition at T0 = 131 K, followed by superconductivity below Tc = 0.69 K. The bulk superconductivity in Co-doped BaFe2As2 below Tc = 22 K is demonstrated by resistivity, magnetic susceptibility, and specific heat data. In contrast to the cuprates, the Fe-based system appears to tolerate considerable disorder in the transition metal layers. First principles calculations for BaFe1.84Co0.16As2 indicate the inter-band scattering due to Co is weak.Comment: Accepted to Physica