Analysis of Crowdsourced Sampling Strategies for HodgeRank with Sparse Random Graphs

Crowdsourcing platforms are now extensively used for conducting subjective pairwise comparison studies. In this setting, a pairwise comparison dataset is typically gathered via random sampling, either \emph{with} or \emph{without} replacement. In this paper, we use tools from random graph theory to analyze these two random sampling methods for the HodgeRank estimator. Using the Fiedler value of the graph as a measurement for estimator stability (informativeness), we provide a new estimate of the Fiedler value for these two random graph models. In the asymptotic limit as the number of vertices tends to infinity, we prove the validity of the estimate. Based on our findings, for a small number of items to be compared, we recommend a two-stage sampling strategy where a greedy sampling method is used initially and random sampling \emph{without} replacement is used in the second stage. When a large number of items is to be compared, we recommend random sampling with replacement as this is computationally inexpensive and trivially parallelizable. Experiments on synthetic and real-world datasets support our analysis

Total syntheses of sanggenon-type natural products and rearrangements of 3-substituted flavone ethers

An efficient approach to the hydrobenzofuro[3,2-b]chromenone core of sanggenon-type natural products has been developed. The key transformation involves a protecting group-free double rearrangement of a bis-allyloxyflavone ether substrate. A sequence involving asymmetric 3-allyl rearrangement followed by aromatic Claisen rearrangement has been established for the asymmetric synthesis of the hydrobenzofuro[3,2-b]chromenone core structure. This methodology has been successfully applied to asymmetric syntheses of both sanggenol F and sanggenon A. Efficient chiral, racemic syntheses for sanggenons C and O have been achieved. The key transformation entails a biomimetic Diels-Alder cycloaddition between a flavonoid diene and a 2'-hydroxychalcone. The flavonoid diene was produced from a protected flavonoid chromene via isomerization. Metal-catalyzed alkynyl Claisen (Saucy-Marbet) rearrangements of 3-alkynyl flavone ethers have been evaluated, and a 1,2-acyl migration cascade which afforded novel furanyl benzofuranone scaffolds was discovered. Mechanistic studies have revealed that the rearrangement is likely initiated by 5-endo enyne cyclization to a platinum-containing spiro-oxocarbenium intermediate, which may be intercepted by methanol to produce a spirodihydrofuran or further rearranged to afford allenyl chromanediones and benzofuranones at higher reaction temperature. Lewis acid-catalyzed [1,3]-rearrangements of 3-aryl substituted flavone ethers have also been developed

Proton Spin Structure from Measurable Parton Distributions

We present a systematic study of the proton spin structure in terms of measurable parton distributions. For a transversely-polarizedproton, we derive a polarization sum rule from the leading generalized parton distributions appearing in hard exclusive processes. For a longitudinally-polarized proton, we obtain a helicity decomposition from well-known quark and gluon helicity distributions and orbital angular-momentum contributions. The latter is shown to be related to measurable subleading generalized parton distributions and quantum-phase space Wigner distributions.Comment: 7 pages, title change

Probing Parton Orbital Angular Momentum in Longitudinally Polarized Nucleon

While the total orbital angular momentum (OAM) of a definite quark flavor in a longitudinally-polarized nucleon can be obtained through a sum rule involving twist-two generalized parton distribution (GPDs), its distribution as a function of parton momentum in light-front coordinates is more complicated to define and measure because it involves intrinsically twist-three effects. In this paper, we consider two different parton OAM distributions. The first is manifestly gauge invariant, and its moments are local operators and calculable in lattice QCD. We show that it can potentially be measured through twist-three GPDs. The second is the much-debated canonical OAM distribution natural in free-field theory and light-cone gauge. We show the latter in light-cone gauge can also be related to twist-three GPDs as well as quantum phase-space Wigner distributions, both being measurable in high-energy experiments.Comment: 14 pages, no figur