Tight local approximation results for max-min linear programs

In a bipartite max-min LP, we are given a bipartite graph \myG = (V \cup I \cup K, E), where each agent $v \in V$ is adjacent to exactly one constraint $i \in I$ and exactly one objective $k \in K$. Each agent $v$ controls a variable $x_v$. For each $i \in I$ we have a nonnegative linear constraint on the variables of adjacent agents. For each $k \in K$ we have a nonnegative linear objective function of the variables of adjacent agents. The task is to maximise the minimum of the objective functions. We study local algorithms where each agent $v$ must choose $x_v$ based on input within its constant-radius neighbourhood in \myG. We show that for every $\epsilon>0$ there exists a local algorithm achieving the approximation ratio ${\Delta_I (1 - 1/\Delta_K)} + \epsilon$. We also show that this result is the best possible -- no local algorithm can achieve the approximation ratio ${\Delta_I (1 - 1/\Delta_K)}$. Here $\Delta_I$ is the maximum degree of a vertex $i \in I$, and $\Delta_K$ is the maximum degree of a vertex $k \in K$. As a methodological contribution, we introduce the technique of graph unfolding for the design of local approximation algorithms.Comment: 16 page

Localization of Matter Waves in 2D-Disordered Optical Potentials

We consider ultracold atoms in 2D-disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the non-interacting regime. We derive the diffusion constant as function of all relevant microscopic parameters and show that coherent multiple scattering induces significant weak localization effects. In particular, we find that even the strong localization regime is accessible with current experimental techniques and calculate the corresponding localization length.Comment: 4 pages, 3 figures, figures changed, references update

Neutron spin structure with polarized deuterons and spectator proton tagging at EIC

The neutron's deep-inelastic structure functions provide essential information for the flavor separation of the nucleon parton densities, the nucleon spin decomposition, and precision studies of QCD phenomena in the flavor-singlet and nonsinglet sectors. Traditional inclusive measurements on nuclear targets are limited by dilution from scattering on protons, Fermi motion and binding effects, final-state interactions, and nuclear shadowing at x << 0.1. An Electron-Ion Collider (EIC) would enable next-generation measurements of neutron structure with polarized deuteron beams and detection of forward-moving spectator protons over a wide range of recoil momenta (0 < p_R < several 100 MeV in the nucleus rest frame). The free neutron structure functions could be obtained by extrapolating the measured recoil momentum distributions to the on-shell point. The method eliminates nuclear modifications and can be applied to polarized scattering, as well as to semi-inclusive and exclusive final states. We review the prospects for neutron structure measurements with spectator tagging at EIC, the status of R&D efforts, and the accelerator and detector requirements.Comment: 11 pages, 3 figures. To appear in proceedings of Tensor Polarized Solid Target Workshop, Jefferson Lab, March 10-12, 201

The Role of Source Coherence in Atom Interferometery

The role of source cloud spatial coherence in a Mach-Zehnder type atom interferometer is experimentally investigated. The visibility and contrast of a Bose-Einstein condensate (BEC) and three thermal sources with varying spatial coherence are compared as a function of interferometer time. At short times, the fringe visibility of a BEC source approaches 100 % nearly independent of pi pulse efficiency, while thermal sources have fringe visibilities limited to the mirror efficiency. More importantly for precision measurement systems, the BEC source maintains interference at interferometer times significantly beyond the thermal source

A Bose-condensed, simultaneous dual species Mach-Zehnder atom interferometer

This paper presents the first realisation of a simultaneous $^{87}$Rb -$^{85}$Rb Mach-Zehnder atom interferometer with Bose-condensed atoms. A number of ambitious proposals for precise terrestrial and space based tests of the Weak Equivalence Principle rely on such a system. This implementation utilises hybrid magnetic-optical trapping to produce spatially overlapped condensates with a duty cycle of 20s. A horizontal optical waveguide with co-linear Bragg beamsplitters and mirrors is used to simultaneously address both isotopes in the interferometer. We observe a non-linear phase shift on a non-interacting $^{85}$Rb interferometer as a function of interferometer time, $T$, which we show arises from inter-isotope scattering with the co-incident $^{87}$Rb interferometer. A discussion of implications for future experiments is given.Comment: 7 pages, 5 figures. The authors welcome comments and feedback on this manuscrip

80hk Momentum Separation with Bloch Oscillations in an Optically Guided Atom Interferometer

We demonstrate phase sensitivity in a horizontally guided, acceleration-sensitive atom interferometer with a momentum separation of 80hk between its arms. A fringe visibility of 7% is observed. Our coherent pulse sequence accelerates the cold cloud in an optical waveguide, an inherently scalable route to large momentum separation and high sensitivity. We maintain coherence at high momentum separation due to both the transverse confinement provided by the guide, and our use of optical delta-kick cooling on our cold-atom cloud. We also construct a horizontal interferometric gradiometer to measure the longitudinal curvature of our optical waveguide.Comment: 6 pages, 6 figure

Reducing decoherence of the confined exciton state in a quantum dot by pulse-sequence control

We study the phonon-induced dephasing of the exciton state in a quantum dot excited by a sequence of ultra-short pulses. We show that the multiple-pulse control leads to a considerable improvement of the coherence of the optically excited state. For a fixed control time window, the optimized pulsed control often leads to a higher degree of coherence than the control by a smooth single Gaussian pulse. The reduction of dephasing is considerable already for 2-3 pulses.Comment: Final version (moderate changes

Measuring Global Similarity between Texts

We propose a new similarity measure between texts which, contrary to the current state-of-the-art approaches, takes a global view of the texts to be compared. We have implemented a tool to compute our textual distance and conducted experiments on several corpuses of texts. The experiments show that our methods can reliably identify different global types of texts.Comment: Submitted to SLSP 201