Loop-Erasure of Plane Brownian Motion

We use the coupling technique to prove that there exists a loop-erasure of a plane Brownian motion stopped on exiting a simply connected domain, and the loop-erased curve is the reversal of a radial SLE$_2$ curve.Comment: 10 page

Restriction Properties of Annulus SLE

For $\kappa\in(0,4]$, a family of annulus SLE$(\kappa;\Lambda)$ processes were introduced in [14] to prove the reversibility of whole-plane SLE$(\kappa)$. In this paper we prove that those annulus SLE$(\kappa;\Lambda)$ processes satisfy a restriction property, which is similar to that for chordal SLE$(\kappa)$. Using this property, we construct $n\ge 2$ curves crossing an annulus such that, when any $n-1$ curves are given, the last curve is a chordal SLE$(\kappa)$ trace.Comment: 37 page

Baryon Oscillations and Consistency Tests for Photometrically-Determined Redshifts of Very Faint Galaxies

Weak lensing surveys that can potentially place strong constraints on dark energy parameters can only do so if the source redshift means and error distributions are very well known. We investigate prospects for controlling errors in these quantities by exploiting their influence on the power spectra of the galaxies. Although, from the galaxy power spectra alone, sufficiently precise and simultaneous determination of redshift biases and variances is not possible, a strong consistency test is. Given the redshift error rms, galaxy power spectra can be used to determine the mean redshift of a group of galaxies to subpercent accuracy. Although galaxy power spectra cannot be used to determine the redshift error rms, they can be used to determine this rms divided by the Hubble parameter, a quantity that may be even more valuable for interpretation of cosmic shear data than the rms itself. We also show that galaxy power spectra, due to the baryonic acoustic oscillations, can potentially lead to constraints on dark energy that are competitive with those due to the cosmic shear power spectra from the same survey.Comment: 8 pages, 6 figures, submitted to Ap

Probing Dark Energy with the Kunlun Dark Universe Survey Telescope

Dark energy is an important science driver of many upcoming large-scale surveys. With small, stable seeing and low thermal infrared background, Dome A, Antarctica, offers a unique opportunity for shedding light on fundamental questions about the universe. We show that a deep, high-resolution imaging survey of 10,000 square degrees in \emph{ugrizyJH} bands can provide competitive constraints on dark energy equation of state parameters using type Ia supernovae, baryon acoustic oscillations, and weak lensing techniques. Such a survey may be partially achieved with a coordinated effort of the Kunlun Dark Universe Survey Telescope (KDUST) in \emph{yJH} bands over 5000--10,000 deg$^2$ and the Large Synoptic Survey Telescope in \emph{ugrizy} bands over the same area. Moreover, the joint survey can take advantage of the high-resolution imaging at Dome A to further tighten the constraints on dark energy and to measure dark matter properties with strong lensing as well as galaxy--galaxy weak lensing.Comment: 9 pages, 6 figure

Comprehensive profiling of zebrafish hepatic proximal promoter CpG island methylation and its modification during chemical carcinogenesis

Background\ud DNA methylation is an epigenetic mechanism associated with regulation of gene expression and it is modulated during chemical carcinogenesis. The zebrafish is increasingly employed as a human disease model; however there is a lack of information on DNA methylation in zebrafish and during fish tumorigenesis. \ud \ud Results\ud A novel CpG island tiling array containing 44,000 probes, in combination with immunoprecipitation of methylated DNA, was used to achieve the first comprehensive methylation profiling of normal adult zebrafish liver. DNA methylation alterations were detected in zebrafish liver tumors induced by the environmental carcinogen 7, 12-dimethylbenz(a)anthracene. Genes significantly hypomethylated in tumors were associated particularly with proliferation, glycolysis, transcription, cell cycle, apoptosis, growth and metastasis. Hypermethylated genes included those associated with anti-angiogenesis and cellular adhesion. Of 49 genes that were altered in expression within tumors, and which also had appropriate CpG islands and were co-represented on the tiling array, approximately 45% showed significant changes in both gene expression and methylation. \ud \ud Conclusion\ud The functional pathways containing differentially methylated genes in zebrafish hepatocellular carcinoma have also been reported to be aberrantly methylated during tumorigenesis in humans. These findings increase the confidence in the use of zebrafish as a model for human cancer in addition to providing the first comprehensive mapping of DNA methylation in the normal adult zebrafish liver. \ud \u

Economic behavior of information acquisition: Impact of peer grading in MOOCs

A critical issue in operating massive open online courses (MOOCs) is the scalability of providing feedback. Because it is not feasible for instructors to grade a large number of students’ assignments, MOOCs use peer grading systems. This study investigates the efficacy of that practice when student graders are rational economic agents. We characterize grading as a process of (a) acquiring information to assess an assignment’s quality and (b) reporting a score. This process entails a tradeoff between the cost of acquiring information and the benefits of accurate grading. Because the true quality is not observable, any measure of inaccuracy must reference the actions of other graders, which motivates student graders to behave strategically. We present the unique equilibrium information level and reporting strategy of a homogeneous group of student graders and then examine the outcome of peer grading. We show how both the peer grading structure and the nature of MOOC courses affect peer grading accuracy, and we identify conditions under which the process fails. There is a systematic grading bias toward the mean, which discourages students from learning. To improve current practice, we introduce a scale-shift grading scheme, theoretically examine how it can improve grading accuracy and adjust grading bias and discuss how it can be practically implemented

Multiparty Quantum Secret Sharing Based on Entanglement Swapping

A multiparty quantum secret sharing (QSS) protocol is proposed by using swapping quantum entanglement of Bell states. The secret messages are imposed on Bell states by local unitary operations. The secret messages are split into several parts and each part is distributed to a party so that no action of a subset of all the parties but their entire cooperation is able to read out the secret messages. In addition, the dense coding is used in this protocol to achieve a high efficiency. The security of the present multiparty QSS against eavesdropping has been analyzed and confirmed even in a noisy quantum channel.Comment: 5 page