Improved Approximation Algorithms for Stochastic Matching

In this paper we consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. We are given an undirected graph in which every edge is assigned a probability of existence and a positive profit, and each node is assigned a positive integer called timeout. We know whether an edge exists or not only after probing it. On this random graph we are executing a process, which one-by-one probes the edges and gradually constructs a matching. The process is constrained in two ways: once an edge is taken it cannot be removed from the matching, and the timeout of node $v$ upper-bounds the number of edges incident to $v$ that can be probed. The goal is to maximize the expected profit of the constructed matching. For this problem Bansal et al. (Algorithmica 2012) provided a $3$-approximation algorithm for bipartite graphs, and a $4$-approximation for general graphs. In this work we improve the approximation factors to $2.845$ and $3.709$, respectively. We also consider an online version of the bipartite case, where one side of the partition arrives node by node, and each time a node $b$ arrives we have to decide which edges incident to $b$ we want to probe, and in which order. Here we present a $4.07$-approximation, improving on the $7.92$-approximation of Bansal et al. The main technical ingredient in our result is a novel way of probing edges according to a random but non-uniform permutation. Patching this method with an algorithm that works best for large probability edges (plus some additional ideas) leads to our improved approximation factors

SNO+: predictions from standard solar models and spin flavour precession

Time variability of the solar neutrino flux especially in the low and intermediate energy sector remains an open question and, if it exists, it is likely to be originated from the magnetic moment transition from active to light sterile neutrinos at times of intense solar activity and magnetic field. We examine the prospects for the SNO+ experiment to address this important issue and to distinguish between the two classes of solar models which are currently identified as corresponding to a high (SSM I) and a low (SSM II) heavy element abundance. We also evaluate the predictions from these two models for the Chlorine experiment event rate in the standard LMA and LMA+Spin Flavour Precession (SFP) scenarios. It is found that after three years of SNO+ data taking, the pep flux measurement will be able to discriminate between the standard LMA and LMA+SFP scenarios, independently of which is the correct solar model. If the LMA rate is measured, SFP with $B_0 \sim 280kG$ for the resonant $\Delta m^2_{01}$ can be excluded at more than $4\sigma$. A low rate would signal new physics, excluding all the 90% allowed range of the standard LMA solution at 3$\sigma$, and a time variability would be a strong signature of the SFP model. The CNO fluxes are the ones for which the two SSM predictions exhibit the largest differences, so their measurement at SNO+ will be important to favour one or the other. The distinction will be clearer after LMA or SFP are confirmed with pep, but still, a CNO measurement at the level of SSM I/LMA will disfavour SSM II at about $3 \sigma$. We conclude that consistency between future pep and CNO flux measurements at SNO+ and Chlorine would either favour an LMA+SFP scenario or favour SSM II over SSM I.Comment: 20 pages. Sections 1 and 2 extended, section 4.4 added, references added and updated. Final version to be published in JHE

Synthetic sequence generator for recommender systems - memory biased random walk on sequence multilayer network

Personalized recommender systems rely on each user's personal usage data in the system, in order to assist in decision making. However, privacy policies protecting users' rights prevent these highly personal data from being publicly available to a wider researcher audience. In this work, we propose a memory biased random walk model on multilayer sequence network, as a generator of synthetic sequential data for recommender systems. We demonstrate the applicability of the synthetic data in training recommender system models for cases when privacy policies restrict clickstream publishing.Comment: The new updated version of the pape

Contact-induced spin polarization in carbon nanotubes

Motivated by the possibility of combining spintronics with molecular structures, we investigate the conditions for the appearance of spin-polarization in low-dimensional tubular systems by contacting them to a magnetic substrate. We derive a set of general expressions describing the charge transfer between the tube and the substrate and the relative energy costs. The mean-field solution of the general expressions provides an insightful formula for the induced spin-polarization. Using a tight-binding model for the electronic structure we are able to estimate the magnitude and the stability of the induced moment. This indicates that a significant magnetic moment in carbon nanotubes can be observed.Comment: To appear in Phys. Rev. B (2003

Simulating EGFR-ERK signaling control by scaffold proteins KSR and MP1 reveals differential Ligand-Sensitivity Co-Regulated by CBL-CIN85 and Endophilin

10.1371/journal.pone.0022933PLoS ONE68

The Abundance of New Kind of Dark Matter Structures

A new kind of dark matter structures, ultracompact minihalos (UCMHs) was proposed recently. They would be formed during the radiation dominated epoch if the large density perturbations are existent. Moreover, if the dark matter is made up of weakly interacting massive particles, the UCMHs can have effect on cosmological evolution because of the high density and dark matter annihilation within them. In this paper, one new parameter is introduced to consider the contributions of UCMHs due to the dark matter annihilation to the evolution of cosmology, and we use the current and future CMB observations to obtain the constraint on the new parameter and then the abundance of UCMHs. The final results are applicable for a wider range of dark matter parametersComment: 4 pages, 1 tabl

Is the `Finite Bias Anomaly' in planar GaAs-Superconductor junctons caused by point-contact like structures?

We correlate transmission electron microscope (TEM) pictures of superconducting In contacts to an AlGaAs/GaAs heterojunction with differential conductance spectroscopy performed on the same heterojunction. Metals deposited onto a (100) AlGaAs/GaAs heterostructure do not form planar contacts but, during thermal annealing, grow down into the heterostructure along crystallographic planes in pyramid-like `point contacts'. Random surface nucleation and growth gives rise to a different interface transmission for each superconducting point contact. Samples annealed for different times, and therefore having different contact geometry, show variations in $dI/dV$ characteristic of ballistic transport of Cooper pairs, wave interference between different point emitters, and different types of weak localization corrections to Giaever tunneling. We give a possible mechanism whereby the `finite bias anomaly' of Poirier et al. (Phys. Rev. Lett., {\bf 79}, 2105 (1997)), also observed in these samples, can arise by adding the conductance of independent superconducting point emitters in parallel

Theory of Current and Shot Noise Spectroscopy in Single-Molecular Quantum Dots with Phonon Mode

Using the Keldysh nonequilibrium Green function technique, we study the current and shot noise spectroscopy of a single molecular quantum dot coupled to a local phonon mode. It is found that in the presence of electron-phonon coupling, in addition to the resonant peak associated with the single level of the dot, satellite peaks with the separation set by the frequency of phonon mode appear in the differential conductance. In the ``single level'' resonant tunneling region, the differential shot noise power exhibit two split peaks. However, only single peaks show up in the ``phonon assisted'' resonant-tunneling region. An experimental setup to test these predictions is also proposed.Comment: 5 pages, 3 eps figures embedde