Semi-leptonic Decays of Heavy Quarks in Dijet Photoproduction at HERA

The production of heavy quarks has been studied in photoproduction processes with the ZEUS detector at HERA using an integrated luminosity of $36.9 pb^{-1}$. Events with a photon virtuality, $Q^2<1 GeV^2$, were selected with two jets of high transverse energy and an electron in the final state. Consideration of the distribution in $p_T^{rel}$ - the momentum of the electron transverse to the axis of the jet to which the electron is closest - allows a measurement of the beauty cross-section in a restricted region of phase space.Comment: 3 pages, 3 figures. To appear in DIS99 conference proceeding

The Loewner driving function of trajectory arcs of quadratic differentials

We obtain a first order differential equation for the driving function of the chordal Loewner differential equation in the case where the domain is slit by a curve which is a trajectory arc of certain quadratic differentials. In particular this includes the case when the curve is a path on the square, triangle or hexagonal lattice in the upper halfplane or, indeed, in any domain with boundary on the lattice. We also demonstrate how we use this to calculate the driving function numerically. Equivalent results for other variants of the Loewner differential equation are also obtained: Multiple slits in the chordal Loewner differential equation and the radial Loewner differential equation. The method also works for other versions of the Loewner differential equation. The proof of our formula uses a generalization of Schwarz-Christoffel mapping to domains bounded by trajectory arcs of rotations of a given quadratic differential that is of interest in its own right.Comment: 22 pages, 4 figures Changes in v2: Changed some definitions and exchanged ordering of theorems for clarity purposes. Typos corrected. Changes in v3: Mistakes corrected. Added new Lemma 2.2. Overall clarity improve

RGC1/RGC2 deletions cause increased sensitivity to oxidative stress in Saccharomyces cerevisiae, which can be overcome by constitutive nuclear Yap1 expression

Oxidative stress mechanism in yeast presents an innovative pathway to understand in creating the next generation of antifungal drugs. Rgc1 and Rgc2 are paralogous proteins that regulate the Fps1 glycerol channel in hyperosmotic stress. Hyperosmotic conditions lead Hog1 MAP kinase to phosphorylate Rgc2 and cause its dissociation from Fps1, allowing the channel to close and protect the cell from damage. Rgc2 contains pleckstrin homology (PH) domains broken up by long insertions and more phosphorylation sites than targeted by Hog1 in response to hyperosmotic stress. Since none of the other MAP kinases in yeast were seen to phosphorylate Rgc2 during oxidative stress, it is thought that Rgc2 may bind to other proteins. In this study, the sensitivity of a strain deleted for both RGC1 and RGC2 was compared to strains with single deletions in either gene in response to oxidative stress. Having deletions in both RGC1 and RGC2 caused increased sensitivity to hydrogen peroxide whereas strains with deletions in either gene seemed unaffected, correlating with the fact that Rgc1 and Rgc2 are paralogous proteins, able to recover each other's functions. A second analysis compared mutated Fps1 (fps1∆-FKSV) and a strain with deletions for both RGC1 and RGC2 (rgc1/2∆). The fps1∆-FKSV strain has four amino acid substitutions in the C-terminal region where Rgc2 binds to Fps1. While both strains grew less than wild-type in hydrogen peroxide, the rgc1/2∆ strain was more sensitive suggesting that Rgc1/2 has an additional role in oxidative stress. To identify the oxidative stress function of Rgc1/2, a genomic overexpression library was transformed into the rgc1/2∆ strain and used for a suppressor screen in the presence of hydrogen peroxide. Although the screen revealed a manageable amount of 49 candidates, only four produced sequences that spanned a protein-encoding region. The candidate plasmids were transformed back into the rgc1/2∆ strain for preparation of a sensitivity assay which showed that the colonies did not survive any better than the starting rgc1/2∆ strain. Without a plausible plasmid candidate, we decided to look into the effect of YAP1 on the rgc1/2∆ strain. Yap1 is a transcription factor known to activate many genes in oxidative stress. Two forms of YAP1 were transformed into rgc1/2∆: wild-type YAP1 and YAP1-A627E which contains a mutation in the nuclear export signal. Compared to the controls, YAP1-A627E allowed the rgc1/2∆ strain to grow at 1.5mM H2O2 while wild-type YAP1 did not. This result showed that a constitutively nuclear Yap1 can overcome deletions in RGC1 and RGC2. It also suggested that an increased activity in the nucleus was important in hydrogen peroxide resistance and another suppressor screen of rgc1/2∆ was performed looking for spontaneous mutations in the genomic DNA. The screened colonies were tested for their survival on hydrogen peroxide but their resistance appeared to be transient. We have shown Rgc1 and Rgc2 to be important cellular components in oxidative stress in addition to hyperosmotic stress. Further research on Rgc1/2 would provide invaluable knowledge on oxidative stress protection in yeast and a better foundation on which to build antifungal drugs

Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form [{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}], where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all $a_j$'s are nonzero and $B$ is an $n$-by-$n$ weighted shift matrix with weights $b_1,..., b_n$. We show that $B$ is unitarily equivalent to $A$ if and only if $b_1... b_n=a_1...a_n$ and, for some fixed $k$, $1\le k \le n$, $|b_j| = |a_{k+j}|$ ($a_{n+j}\equiv a_j$) for all $j$. Next, we show that $A$ is reducible if and only if $A$ has periodic weights, that is, for some fixed $k$, $1\le k \le \lfloor n/2\rfloor$, $n$ is divisible by $k$, and $|a_j|=|a_{k+j}|$ for all $1\le j\le n-k$. Finally, we prove that $A$ and $B$ have the same numerical range if and only if $a_1...a_n=b_1...b_n$ and $S_r(|a_1|^2,..., |a_n|^2)=S_r(|b_1|^2,..., |b_n|^2)$ for all $1\le r\le \lfloor n/2\rfloor$, where $S_r$'s are the circularly symmetric functions.Comment: 27 page

Large-q series expansion for the ground state degeneracy of the q-state Potts antiferromagnet on the (3.12^2) lattice

We calculate the large-$q$ series expansion for the ground state degeneracy (= exponent of the ground state entropy) per site of the $q$-state Potts antiferromagnet on the $(3 \cdot 12^2)$ lattice, to order $O(y^{19})$, where $y=1/(q-1)$. We note a remarkable agreement, to $O(y^{18})$, between this series and a rigorous lower bound derived recently.Comment: 10 pages, Latex, 3 encapsulated postscript figures, to appear in Phys. Rev.