Flaporhexis, a technique to make the femtosecond laser corneal flap was developed primarily to reduce the mechanical trauma associated with separating the corneal tissue by taking advantage of the cornea’s natural anatomy and was first described in a peer reviewed artice in 2008. The anterior part of the cornea tends to be stronger, thereby allowing tearing (Greek “rhexis”) along the preformed cuts of the femtosecond photo disruption. Flaporhexis differs from Binder’s technique of “hinge opening” as published in 2006 by opening the flap from the opposite side. If a femtosecond flap lift is performed correctly, the surgeon will find a virgin, uniform, dry stromal bed, which had not been manipulated by any surgical instrument and is therefore perfect for wavefront guided laser surgery as “Sub-Bowman’s Keratomileusis”.

Abstract:
Analyses of DNA methylation in human cancers have identified hypermethylation of individual genes and diminished methylation at repeat elements as common alterations, and have thereby provided important mechanistic insights into cancer biology as well as biomarkers for cancer detection, prognosis and prediction of therapy responses. The techniques available in the past were best suited for investigations of individual candidate genes and sequences, whereas recently developed high-throughput techniques promise to generate unbiased and comprehensive surveys of DNA methylation states across entire genomes. In this minireview we give a short overview of established and novel techniques and outline some major questions that can now be addressed to develop further cancer biomarkers and therapies based on DNA methylation.

Abstract:
Changes in DNA methylation frequently accompany cancer development. One prominent change is an apparently genome-wide decrease in methylcytosine that is often ascribed to DNA hypomethylation at retroelements comprising nearly half the genome. DNA hypomethylation may allow reactivation of retroelements, enabling retrotransposition, and causing gene expression disturbances favoring tumor development. However, neither the extent of hypomethylation nor of retroelement reactivation are precisely known. We therefore assessed DNA methylation and expression of three major classes of retroelements (LINE-1, HERV-K, and AluY) in human urinary bladder cancer tissues and cell lines by pyrosequencing and quantitative reverse transcription–polymerase chain reaction, respectively. We found substantial global LINE-1 DNA hypomethylation in bladder cancer going along with a shift toward full-length LINE-1 expression. Thus, pronounced differences in LINE-1 expression were observed, which may be promoted, among others, by LINE-1 hypomethylation. Significant DNA hypomethylation was found at the HERV-K_22q11.23 proviral long terminal repeat (LTR) in bladder cancer tissues but without reactivation of its expression. DNA methylation of HERVK17, essentially absent from normal urothelial cells, was elevated in cell lines from invasive bladder cancers. Accordingly, the faint expression of HERVK17 in normal urothelial cells disappeared in such cancer cell lines. Of 16 additional HERV-Ks, expression of 7 could be detected in the bladder, albeit generally at low levels. Unlike in prostate cancers, none of these showed significant expression changes in bladder cancer. In contrast, expression of the AluYb8 but not of the AluYa5 family was significantly increased in bladder cancer tissues. Collectively, our findings demonstrate a remarkable specificity of changes in expression and DNA methylation of retroelements in bladder cancer with a significantly different pattern from that in prostate cancer.

Abstract:
Retrotransposons like L1 are silenced in somatic cells by a variety of mechanisms acting at different levels. Protective mechanisms include DNA methylation and packaging into inactive chromatin to suppress transcription and prevent recombination, potentially supported by cytidine deaminase editing of RNA. Furthermore, DNA strand breaks arising during attempted retrotranspositions ought to activate cellular checkpoints, and L1 activation outside immunoprivileged sites may elicit immune responses. A number of observations indicate that L1 sequences nevertheless become reactivated in human cancer. Prominently, methylation of L1 sequences is diminished in many cancer types and full-length L1 RNAs become detectable, although strong expression is restricted to germ cell cancers. L1 elements have been found to be enriched at sites of illegitimate recombination in many cancers. In theory, lack of L1 repression in cancer might cause transcriptional deregulation, insertional mutations, DNA breaks, and an increased frequency of recombinations, contributing to genome disorganization, expression changes, and chromosomal instability. There is however little evidence that such effects occur at a gross scale in human cancers. Rather, as a rule, L1 repression is only partly alleviated. Unfortunately, many techniques commonly used to investigate genetic and epigenetic alterations in cancer cells are not well suited to detect subtle effects elicited by partial reactivation of retroelements like L1 which are present as abundant, but heterogeneous copies. Therefore, effects of L1 sequences exerted on the local chromatin structure, on the transcriptional regulation of individual genes, and on chromosome fragility need to be more closely investigated in normal and cancer cells.

Abstract:
Representations of Quantum Groups U_q (g_n), g_n any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n-1 quantum groups for q a root of unity. Representations which have the maximal dimension and number of free parameters for irreducible representations arise as special cases.

Abstract:
The ongoing High Accuracy Radial velocity Planet Search (HARPS) has found that 30-50% of GK dwarfs in the solar neighborhood host planets with sub-Neptune masses in orbits of P < 50 days. At first glance, this overall occurrence rate seems inconsistent with the planet frequency measured during Q0-Q2 of the Kepler Mission, whose 1,235 detected planetary candidates imply that ~ 15% of main sequence dwarfs harbor short-period planets with R_pl < 4 R_Earth. A rigorous comparison between the two surveys is difficult, however, as they observe different stellar populations and measure different planetary properties. Here we report the results of a Monte Carlo study that can account for this discrepancy via plausible distributions of planetary compositions. We find that a population concurrently consisting of (1) dense silicate-iron planets and (2) low-density gas-dominated worlds provides a natural fit to the current data. In this scenario, the fraction of dense planets decreases with increasing mass, from f_rocky = 90% at M = 1 M_Earth to f_rocky = 10% at M = 17 M_Earth. Our best fit population has a total occurrence rate of 40% for 2 < P < 50 days and 1 < M < 17 M_Earth, and is characterized by simple power-law indices of the form N(M)dM ~ M^alpha dM and N(P)dP ~ P^beta dP with alpha = -1.0 and beta = 0.0. Our model population therefore contains four free parameters and is readily testable with future observations. Furthermore, our model's insistence that at least two distinct types of planets must exist in the survey data indicates that multiple formation mechanisms are at work to produce the population of planets commonly referred to as "super-Earths".

Abstract:
Let $G$ be an additive finite abelian group. A sequence over $G$ is called a minimal zero-sum sequence if the sum of its terms is zero and no proper subsequence has this property. Davenport's constant of $G$ is the maximum of the lengths of the minimal zero-sum sequences over $G$. Its value is well-known for groups of rank two. We investigate the structure of minimal zero-sum sequences of maximal length for groups of rank two. Assuming a well-supported conjecture on this problem for groups of the form $C_m \oplus C_m$, we determine the structure of these sequences for groups of rank two. Combining our result and partial results on this conjecture, yields unconditional results for certain groups of rank two.

Abstract:
Let $(G,+)$ be a finite abelian group. Then, $\so(G)$ and $\eta(G)$ denote the smallest integer $\ell$ such that each sequence over $G$ of length at least $\ell$ has a subsequence whose terms sum to $0$ and whose length is equal to and at most, resp., the exponent of the group. For groups of rank two, we study the inverse problems associated to these constants, i.e., we investigate the structure of sequences of length $\so(G)-1$ and $\eta(G)-1$ that do not have such a subsequence. On the one hand, we show that the structure of these sequences is in general richer than expected. On the other hand, assuming a well-supported conjecture on this problem for groups of the form $C_m \oplus C_m$, we give a complete characterization of all these sequences for general finite abelian groups of rank two. In combination with partial results towards this conjecture, we get unconditional characterizations in special cases.

Abstract:
We study the frequentist properties of confidence intervals for the On-Off problem. The methods include all those in common use today. We derive explicit formulas for the limits and calculate the true coverage and the expected lengths of these methods.