Combinatorial Assortment Optimization

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a model of consumer choice where the relative value of different bundles is described by a valuation function, while individual customers may differ in their absolute willingness to pay, and study the complexity of the resulting optimization problem. We show that any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS, and that no FPTAS exists even for succinctly-representable submodular valuations. On the positive side, we show how to obtain constant approximations under a "well-priced" condition, where each product's price is sufficiently high. We also provide an exact algorithm for $k$-additive valuations, and show how to extend our results to a learning setting where the seller must infer the customers' preferences from their purchasing behavior

On the galactic rotation curves problem within an axisymmetric approach

In U. Nucamendi et al. Phys. Rev. D63 (2001) 125016 and K. Lake, Phys. Rev. Lett. 92 (2004) 051101 it has been shown that galactic potentials can be kinematically linked to the observed red/blue shifts of the corresponding galactic rotation curves under a minimal set of assumptions: the emitted photons come from stable timelike circular geodesic orbits of stars in a static spherically symmetric gravitational field, and propagate to us along null geodesics. It is remarkable that this relation can be established without appealing at all to a concrete theory of gravitational interaction. Here we generalize this kinematical spherically symmetric approach to the galactic rotation curves problem to the stationary axisymmetric realm since this is precisely the symmetry that spiral galaxies possess. Thus, by making use of the most general stationary axisymmetric metric, we also consider stable circular orbits of stars that emit signals which travel to a distant observer along null geodesics and express the galactic red/blue shifts in terms of three arbitrary metric functions, clarifying the contribution of the rotation as well as the dragging of the gravitational field. This stationary axisymmetric approach distinguishes between red and blue shifts emitted by circularly orbiting receding and approaching stars, respectively, even when they are considered with respect to the center of a spiral galaxy, indicating the need of precise measurements in order to confront predictions with observations. We also point out the difficulties one encounters in the attempt of determining the metric functions from observations and list some possible strategies to overcome them.Comment: 7 pages in latex (MNRAS format), no figures, discussion and references adde

S=−1S=-1 Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory and the S01−S_{01}- Λ\Lambda(1405) and −Λ- \Lambda(1670) Resonances

The $s-$wave meson-baryon scattering is analyzed for the strangeness $S=-1$ and isospin I=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four channels have been considered: $\pi \Sigma$, $\bar K N$, $\eta \Lambda$ and $K \Xi$. The required input to solve the Bethe-Salpeter equation is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. There appear undetermined low energy constants, as a consequence of the renormalization of the amplitudes, which are obtained from fits to the $\pi\Sigma\to\pi\Sigma$ mass-spectrum, to the elastic $\bar K N \to \bar K N$ and $\bar K N\to \pi \Sigma$ $t$--matrices and to the $K^- p \to \eta \Lambda$ cross section data. The position and residues of the complex poles in the second Riemann Sheet of the scattering amplitude determine masses, widths and branching ratios of the $S_{01}-$ $\Lambda$(1405) and $-\Lambda$(1670) resonances, in reasonable agreement with experiment. A good overall description of data, from $\pi \Sigma$ threshold up to 1.75 GeV, is achieved despite the fact that three-body channels have not been explicitly included.Comment: 23 pages, Latex, 10 Figures. In this revised version a new subsection 3.6 on Heavy Baryon Expansion and new references have been adde

CP Violation in Hyperon Nonleptonic Decays within the Standard Model

We calculate the CP-violating asymmetries A(Lambda_-^0) and A(Xi_-^-) in nonleptonic hyperon decay within the Standard Model using the framework of heavy-baryon chiral perturbation theory (chiPT). We identify those terms that correspond to previous calculations and discover several errors in the existing literature. We present a new result for the lowest-order (in chiPT) contribution of the penguin operator to these asymmetries, as well as an estimate for the uncertainty of our result that is based on the calculation of the leading nonanalytic corrections.Comment: 21 pages, 2 figures; discussion clarified, results & conclusions unchanged, to appear in Phys. Rev.

New Physics and CP Violation in Hyperon Nonleptonic Decays

The sum of the CP-violating asymmetries A(Lambda_-^0) and A(Xi_-^-) in hyperon nonleptonic decays is presently being measured by the E871 experiment. We evaluate contributions to the asymmetries induced by chromomagnetic-penguin operators, whose coefficients can be enhanced in certain models of new physics. Incorporating recent information on the strong phases in Xi->Lambda pi decay, we show that new-physics contributions to the two asymmetries can be comparable. We explore how the upcoming results of E871 may constrain the coefficients of the operators. We find that its preliminary measurement is already better than the epsilon parameter of K-Kbar mixing in bounding the parity-conserving contributions.Comment: 12 pages, 2 figure

The abundance of C18O and HDO in the envelope and hot core of the intermediate mass protostar NGC 7129 FIRS 2

NGC 7129 FIRS 2 is a young intermediate-mass (IM) protostar, which is associated with two energetic bipolar outflows and displays clear signs of the presence of a hot core. It has been extensively observed with ground based telescopes and within the WISH Guaranteed Time Herschel Key Program. We present new observations of the C18O 3-2 and the HDO 3_{12}-2_{21} lines towards NGC 7129 FIRS 2. Combining these observations with Herschel data and modeling their emissions, we constrain the C18O and HDO abundance profiles across the protostellar envelope. In particular, we derive the abundance of C18O and HDO in the hot core. The intensities of the C18O lines are well reproduced assuming that the C18O abundance decreases through the protostellar envelope from the outer edge towards the centre until the point where the gas and dust reach the CO evaporation temperature (~20-25 K) where the C18O is released back to the gas phase. Once the C18O is released to the gas phase, the modelled C18O abundance is found to be ~1.6x10^{-8}, which is a factor of 10 lower than the reference abundance. This result is supported by the non-detection of C18O 9-8, which proves that even in the hot core (T_k>100 K) the CO abundance must be 10 times lower than the reference value. Several scenarios are discussed to explain this C18O deficiency. One possible explanation is that during the pre-stellar and protostellar phase, the CO is removed from the grain mantles by reactions to form more complex molecules. Our HDO modeling shows that the emission of HDO 3_{12}-2_{21} line is maser and comes from the hot core (T_k>100 K). Assuming the physical structure derived by Crimier et al. (2010), we determine a HDO abundance of ~0.4 - 1x10^{-7} in the hot core of this IM protostar, similar to that found in the hot corinos NGC 1333 IRAS 2A and IRAS 16293-2422.Comment: 10 pages, 7 figure

Haemodynamics and flow modification stents for peripheral arterial disease:a review

Endovascular stents are widely used for the treatment of peripheral arterial disease (PAD). However, the development of in-stent restenosis and downstream PAD progression remain a challenge. Stent revascularisation of PAD causes arterial trauma and introduces abnormal haemodynamics, which initiate complicated biological processes detrimental to the arterial wall. The interaction between stent struts and arterial cells in contact, and the blood flow field created in a stented region, are highly affected by stent design. Spiral flow is known as a normal physiologic characteristic of arterial circulation and is believed to prevent the development of flow disturbances. This secondary flow motion is lost in atheromatous disease and its re-introduction after endovascular treatment of PAD has been suggested as a method to induce stabilised and coherent haemodynamics. Stent designs able to generate spiral flow may support endothelial function and therefore increase patency rates. This review is focused on secondary flow phenomena in arteries and the development of flow modification stent technologies for the treatment of PAD

Initial experience with a synthetic sealant PleuraSeal™ after pulmonary resections: a prospective study with retrospective case matched controls

The objective of this study was to evaluate postoperative outcome and efficacy of a hydrogel tissue sealant for prevention of alveolar leakage after open lung resections

The ionizing photon production efficiency of bright z∼\sim2-5 galaxies

We investigate the production efficiency of ionizing photons ($\xi_{ion}^*$) of 1174 galaxies with secure redshift at z=2-5 from the VANDELS survey to determine the relation between ionizing emission and physical properties of bright and massive sources. We constrain $\xi_{ion}^*$ and galaxy physical parameters by means of spectro-photometric fits performed with the BEAGLE code. The analysis exploits the multi-band photometry in the VANDELS fields, and the measurement of UV rest-frame emission lines (CIII]$\lambda 1909$, HeII$\lambda 1640$, OIII]$\lambda 1666$) from deep VIMOS spectra. We find no clear evolution of $\xi_{ion}^*$ with redshift within the probed range. The ionizing efficiency slightly increases at fainter $M_{UV}$, and bluer UV slopes, but these trends are less evident when restricting the analysis to a complete subsample at log(M$_{star}$/M$_{\odot}$)$>$9.5. We find a significant trend of increasing $\xi_{ion}^*$ with increasing EW(Ly$\alpha$), with an average log($\xi_{ion}^*$/Hz erg$^{-1}$)$>$25 at EW$>$50\AA, and a higher ionizing efficiency for high-EW CIII]$\lambda 1909$ and OIII]$\lambda 1666$ emitters. The most significant correlations are found with respect to stellar mass, specific star-formation rate (sSFR) and SFR surface density ($\Sigma_{SFR}$). The relation between $\xi_{ion}^*$ and sSFR shows a monotonic increase from log($\xi_{ion}^*$/Hz erg$^{-1}$) $\sim$24.5 at log(sSFR)$\sim$-9.5$yr^{-1}$ to $\sim$25.5 at log(sSFR)$\sim$-7.5$yr^{-1}$, a low scatter and little dependence on mass. The objects above the main-sequence of star-formation consistently have higher-than-average $\xi_{ion}^*$. A clear increase of $\xi_{ion}^*$ with $\Sigma_{SFR}$ is also found, with log($\xi_{ion}^*$/Hz erg$^{-1}$)$>$25 for objects at $\Sigma_{SFR}>$10 M$_{\odot}/yr/kpc^2$.(Abridged)Comment: 11 pages, 9 figures, accepted for publication in A&