Independent Range Sampling, Revisited Again

We revisit the range sampling problem: the input is a set of points where each point is associated with a real-valued weight. The goal is to store them in a structure such that given a query range and an integer k, we can extract k independent random samples from the points inside the query range, where the probability of sampling a point is proportional to its weight. This line of work was initiated in 2014 by Hu, Qiao, and Tao and it was later followed up by Afshani and Wei. The first line of work mostly studied unweighted but dynamic version of the problem in one dimension whereas the second result considered the static weighted problem in one dimension as well as the unweighted problem in 3D for halfspace queries. We offer three main results and some interesting insights that were missed by the previous work: We show that it is possible to build efficient data structures for range sampling queries if we allow the query time to hold in expectation (the first result), or obtain efficient worst-case query bounds by allowing the sampling probability to be approximately proportional to the weight (the second result). The third result is a conditional lower bound that shows essentially one of the previous two concessions is needed. For instance, for the 3D range sampling queries, the first two results give efficient data structures with near-linear space and polylogarithmic query time whereas the lower bound shows with near-linear space the worst-case query time must be close to n^{2/3}, ignoring polylogarithmic factors. Up to our knowledge, this is the first such major gap between the expected and worst-case query time of a range searching problem

High visibility two photon interference of frequency time entangled photons generated in a quasi phase matched AlGaAs waveguide

We demonstrate experimentally the frequency time entanglement of photon pairs produced in a CW pumped quasi phased matched AlGaAs superlattice waveguide. A visibility of 96.0+-0.7% without background subtraction has been achieved, which corresponds the violation of Bell inequality by 52 standard deviations

Airborne bacterial populations above desert soils of the McMurdo Dry Valleys, Antarctica

Bacteria are assumed to disperse widely via aerosolized transport due to their small size and resilience. The question of microbial endemicity in isolated populations is directly related to the level of airborne exogenous inputs, yet this has proven hard to identify. The ice-free terrestrial ecosystem of Antarctica, a geographically and climatically isolated continent, was used to interrogate microbial bio-aerosols in relation to the surrounding ecology and climate. High-throughput sequencing of bacterial ribosomal RNA (rRNA) genes was combined with analyses of climate patterns during an austral summer. In general terms, the aerosols were dominated by Firmicutes, whereas surrounding soils supported Actinobacteria-dominated communities. The most abundant taxa were also common to aerosols from other continents, suggesting that a distinct bio-aerosol community is widely dispersed. No evidence for significant marine input to bio-aerosols was found at this maritime valley site, instead local influence was largely from nearby volcanic sources. Back trajectory analysis revealed transport of incoming regional air masses across the Antarctic Plateau, and this is envisaged as a strong selective force. It is postulated that local soil microbial dispersal occurs largely via stochastic mobilization of mineral soil particulates

Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity

Using bosonization-fermionization transformation we map the Tomonaga-Luttinger model of spinless fermions with non-linear dispersion on the model of fermionic quasiparticles whose interaction is irrelevant in the renormalization group sense. Such mapping allows us to set up an expansion for the density-density propagator of the original Tomonaga-Luttinger Hamiltonian in orders of the (irrelevant) quasiparticle interaction. The lowest order term in such an expansion is proportional to the propagator for free fermions. The next term is also evaluated. The propagator found is used for calculation of the Coulomb drug resistivity $r$ in a system of two capacitively coupled one-dimensional conductors. It is shown that $r$ is proportional to $T^2$ for both free and interacting fermions. The marginal repulsive in-chain interaction acts to reduce $r$ as compared to the non-interacting result. The correction to $r$ due to the quasiparticle interaction is found as well. It scales as $T^4$ at low temperature.Comment: 5 pages, 1 eps figure; the new version of the e-print corrects an error, which exists in the original submission; fortunately, all important conclusions of the study remain vali

The generation of multi-laminar reagent streams for rapid, sequential (bio)chemical reactions on magnetic particles in a continuous flow microreactor

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.We demonstrate a versatile microfluidic system for performing rapid, consecutive (bio)chemical reactions in continuous flow. Surface-functionalised magnetic microparticles are introduced into a chamber and pulled, via a magnet, across a series of laminar flow streams containing different reagents, thus performing multiple sequential reactions on the particles’ surface. Such a continuous flow method eliminates many of the inefficiencies associated with batch techniques, such as the time-consuming, laborious sequential reaction and washing steps, to yield a system that can perform analyses far more rapidly and with less reagent volume than conventional methods. This innovative device has been applied to a two-reaction step mouse IgG sandwich immunoassay and one- and two-reaction step DNA hybridisation assays, all of which were completed within one minute. These results pave the way for a multi-purpose microreactor that can perform a variety of analytical and synthetic processes.This study is funded by the Engineering and Physical Sciences Research Council (EPSRC)

The TGFβ type I receptor TGFβRI functions as an inhibitor of BMP signaling in cartilage.

The type I TGFβ receptor TGFβRI (encoded by Tgfbr1) was ablated in cartilage. The resulting Tgfbr1 Col2 mice exhibited lethal chondrodysplasia. Similar defects were not seen in mice lacking the type II TGFβ receptor or SMADs 2 and 3, the intracellular mediators of canonical TGFβ signaling. However, we detected elevated BMP activity in Tgfbr1 Col2 mice. As previous studies showed that TGFβRI can physically interact with ACVRL1, a type I BMP receptor, we generated cartilage-specific Acvrl1 (Acvrl1 Col2 ) and Acvrl1/Tgfbr1 (Acvrl1/Tgfbr1 Col2 ) knockouts. Loss of ACVRL1 alone had no effect, but Acvrl1/Tgfbr1 Col2 mice exhibited a striking reversal of the chondrodysplasia seen in Tgfbr1 Col2 mice. Loss of TGFβRI led to a redistribution of the type II receptor ACTRIIB into ACVRL1/ACTRIIB complexes, which have high affinity for BMP9. Although BMP9 is not produced in cartilage, we detected BMP9 in the growth plate, most likely derived from the circulation. These findings demonstrate that the major function of TGFβRI in cartilage is not to transduce TGFβ signaling, but rather to antagonize BMP signaling mediated by ACVRL1

PSEUDOSPECTRAL LEAST SQUARES METHOD FOR STOKES-DARCY EQUATIONS

We investigate the first order system least squares Legendre and Chebyshev pseudospectral method for coupled Stokes-Darcy equations. A least squares functional is defined by summing up the weighted L-2-norm of residuals of the first order system for coupled Stokes-Darcy equations and that of Beavers-Joseph-Saffman interface conditions. Continuous and discrete homogeneous functionals are shown to be equivalent to a combination of weighted H(div) and H-1-norms for Stokes and Darcy equations. The spectral convergence for the Legendre and Chebyshev methods is derived. Some numerical experiments are demonstrated to validate our analysisopen0