On the biparametric quantum deformation of GL(2) x GL(1)

We study the biparametric quantum deformation of GL(2) x GL(1) and exhibit its cross-product structure. We derive explictly the associated dual algebra, i.e., the quantised universal enveloping algebra employing the R-matrix procedure. This facilitates construction of a bicovariant differential calculus which is also shown to have a cross-product structure. Finally, a Jordanian analogue of the deformation is presented as a cross-product algebra.Comment: 16 pages LaTeX, published in JM

Coloured extension of GL_q(2) and its dual algebra

We address the problem of duality between the coloured extension of the quantised algebra of functions on a group and that of its quantised universal enveloping algebra i.e. its dual. In particular, we derive explicitly the algebra dual to the coloured extension of GL_q(2) using the coloured RLL relations and exhibit its Hopf structure. This leads to a coloured generalisation of the R-matrix procedure to construct a bicovariant differential calculus on the coloured version of GL_q(2). In addition, we also propose a coloured generalisation of the geometric approach to quantum group duality given by Sudbery and Dobrev.Comment: 10 pages LaTeX. Talk given at the "XXIII International Colloquium on Group Theoretical Methods in Physics", July 31 - August 05, 2000, Dubna (Russia); to appear in the proceeding

Type I error control in biomarker-stratified clinical trials

Biomarker-stratified clinical trials assess the biomarker signature of subjects and split them into subgroups so that treatment is of benefit to those who are likely to respond. Since multiple hypotheses are tested, it becomes important to control the type I error. Current methods control the false positive rate where one rejects the null hypothesis while in reality that was true. For two subgroups, the false positive rate is controlled across the two hypotheses as a Family Wise Error Rate (FWER) to an overall predetermined significance level

Adaptive enrichment in biomarker-stratified clinical trial design

In Phase II oncology trials, targeted therapies are being constantly evaluated for their efficacy in specific populations of interest. Such trials require designs that allow for stratification based on the participants' biomarker signature. One of the disadvantages of a targeted design (defined as enrichment in biomarker-positive sub-population) is that if the drug has at least some activity in the biomarker-negative subjects, then their effect in the biomarker-negative population may never be known. Jones and Holmgren (JH) have proposed a design to determine whether drug has activity only in target population or the general population. Their design is an enrichment adaptation based on two parallel Simon two-stage designs. Unfortunately, there are several pitfalls in the JH design: the issue of hypothesis testing is not properly addressed and the type I error, power calculations and expected sample size formulae are wrong too. We study the JH design in detail, appropriately control the type I and type II error probabilities that yield novel optimal designs. We also discuss various alternative Family Wise Error Rates (FWER) and the Individual Hypothesis (IH) error rates in the weak sense as well as the strong sense. For each option of the error controls, we search for designs over a 10 trillion search space and obtain optimal designs that minimise the expected sample size. For the particular example trial that JH consider, our optimal design requires 38% fewer subjects in comparison with the two parallel Simon two-stage design thereby offering substantial efficiency in terms of the expected sample size. In conclusion, our rectified design provides a robust framework for adaptive enrichment in biomarker-stratified Phase II trial design

Real-Time Data Processing in the Muon System of the D0 Detector

This paper presents a real-time application of the 16-bit fixed point Digital Signal Processors (DSPs), in the Muon System of the D0 detector located at the Fermilab Tevatron, presently the world's highest-energy hadron collider. As part of the Upgrade for a run beginning in the year 2000, the system is required to process data at an input event rate of 10 KHz without incurring significant deadtime in readout. The ADSP21csp01 processor has high I/O bandwidth, single cycle instruction execution and fast task switching support to provide efficient multisignal processing. The processor's internal memory consists of 4K words of Program Memory and 4K words of Data Memory. In addition there is an external memory of 32K words for general event buffering and 16K words of Dual Port Memory for input data queuing. This DSP fulfills the requirement of the Muon subdetector systems for data readout. All error handling, buffering, formatting and transferring of the data to the various trigger levels of the data acquisition system is done in software. The algorithms developed for the system complete these tasks in about 20 microseconds per event.Comment: 4 pages, Presented and published at the 11th IEEE NPSS Real Time Conference, held at Santa Fe, New Mexico, USA, from June 14-18, 199

A (p,q) Deformation of the Universal Enveloping Superalgebra U(osp(2/2))

We investigate a two parameter quantum deformation of the universal enveloping orthosymplectic superalgebra U(osp(2/2)) by extending the Faddeev-Reshetikhin-Takhtajan formalism to the supersymetric case. It is shown that $U_{p,q}(osp(2/2))$ possesses a non-commutative, non-cocommutative Hopf algebra structure. All the results are expressed in the standard form using quantum Chevalley basis.Comment: 8 pages; IC/93/41

Casimir energy, dispersion, and the Lifshitz formula

Despite suggestions to the contrary, we show in this paper that the usual dispersive form of the electromagnetic energy must be used to derive the Lifshitz force between parallel dielectric media. This conclusion follows from the general form of the quantum vacuum energy, which is the basis of the multiple-scattering formalism. As an illustration, we explicitly derive the Lifshitz formula for the interaction between parallel dielectric semispaces, including dispersion, starting from the expression for the total energy of the system. The issues of constancy of the energy between parallel plates and of the observability of electrostrictive forces are briefly addressed.Comment: 11 pages, no figure

Household Transmission of Rotavirus in a Community with Rotavirus Vaccination in Quininde, Ecuador

Background: We studied the transmission of rotavirus infection in households in peri-urban Ecuador in the vaccination era. Methods: Stool samples were collected from household contacts of child rotavirus cases, diarrhea controls and healthy controls following presentation of the index child to health facilities. Rotavirus infection status of contacts was determined by RT-qPCR. We examined factors associated with transmissibility (index-case characteristics) and susceptibility (householdcontact characteristics). Results: Amongst cases, diarrhea controls and healthy control household contacts, infection attack rates (iAR) were 55%, 8% and 2%, (n = 137, 130, 137) respectively. iARs were higher from index cases with vomiting, and amongst siblings. Disease ARs were higher when the index child was ,18 months and had vomiting, with household contact ,10 years and those sharing a room with the index case being more susceptible. We found no evidence of asymptomatic infections leading to disease transmission. Conclusion: Transmission rates of rotavirus are high in households with an infected child, while background infections are rare. We have identified factors associated with transmission (vomiting/young age of index case) and susceptibility (young age/sharing a room/being a sibling of the index case). Vaccination may lead to indirect benefits by averting episodes or reducing symptoms in vaccinees