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

Time-dependent simulation of particle and displacement currents in THz graphene transistors

Although time-independent models provide very useful dynamical information with a reduced computational burden, going beyond the quasi-static approximation provides enriched information when dealing with TeraHertz (THz) frequencies. In this work, the THz noise of dual-gate graphene transistors with DC polarization is analyzed from a careful simulation of the time-dependent particle and displacement currents. From such currents, the power spectral density (PSD) of the total current fluctuations are computed at the source, drain and gate contacts. The role of the lateral dimensions of the transistors, the Klein tunneling and the positive-negative energy injection on the PSD are analyzed carefully. Through the comparison of the PSD with and without Band-to-Band tunneling and graphene injection, it is shown that the unavoidable Klein tunneling and positive-negative energy injection in graphene structures imply an increment of noise without similar increment on the current, degrading the (either low or high frequency) signal-to-noise ratio. Finally, it is shown that the shorter the vertical height (in comparison with the length of the active region in the transport direction), the larger the maximum frequency of the PSD. As a byproduct of this result, an alternative strategy (without length scaling) to optimize the intrinsic cut-off frequency of graphene transistors is envisioned.Comment: 22 pages, 9 figures, proceeding of UPoN201

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

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

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

On the generalized drift Skorokhod problem in one dimension

We show how to write the solution to the generalized drift Skorokhod problem in one-dimension in terms of the supremum of the solution of a tractable unrestricted integral equation (that is, an integral equation with no boundaries). As an application of our result, we equate the transient distribution of a reflected Ornstein–Uhlenbeck (OU) process to the first hitting time distribution of an OU process (that is not reflected). Then, we use this relationship to approximate the transient distribution of the GI/GI/1 + GI queue in conventional heavy traffic and the M/M/N/N queue in a many-server heavy traffic regime