Susan C. Geller

Transformation and normalization of oligonucleotide microarray data

MOTIVATION Most methods of analyzing microarray data or doing power calculations have an underlying assumption of constant variance across all levels of gene expression. The most common transformation, the logarithm, results in data that have constant variance at high levels but not at low levels. Rocke and Durbin showed that data from spotted arrays fit a two-component model and Durbin, Hardin, Hawkins, and Rocke, Huber et al. and Munson provided a transformation that stabilizes the variance as well as symmetrizes and normalizes the error structure. We wish to evaluate the applicability of this transformation to the error structure of GeneChip microarrays. RESULTS We demonstrate in an example study a simple way to use the two-component model of Rocke and Durbin and the data transformation of Durbin, Hardin, Hawkins and Rocke, Huber et al. and Munson on Affymetrix GeneChip data. In addition we provide a method for normalization of Affymetrix GeneChips simultaneous with the determination of the transformation, producing a data set without chip or slide effects but with constant variance and with symmetric errors. This transformation/normalization process can be thought of as a machine calibration in that it requires a few biologically constant replicates of one sample to determine the constant needed to specify the transformation and normalize. It is hypothesized that this constant needs to be found only once for a given technology in a lab, perhaps with periodic updates. It does not require extensive replication in each study. Furthermore, the variance of the transformed pilot data can be used to do power calculations using standard power analysis programs. AVAILABILITY SPLUS code for the transformation/normalization for four replicates is available from the first author upon request. A program written in C is available from the last author.

Étale descent for hochschild and cyclic homology

AbstractIfB is an étale extension of ak-algebraA, we prove for Hochschild homology thatHH*(B)≅HH*(A)⊗AB. For Galois descent with groupG there is a similar result for cyclic homology:HC*≅HC*(B)G if

Pharmacokinetics and selected behavioral responses to butorphanol and its metabolites in goats following intravenous and intramuscular administration

\mathbb{Q} \subseteq A

K

. In the process of proving these results we give a localization result for Hochschild homology without any flatness assumption. We then extend the definition of Hochschild homology to all schemes and show that Hochschild homology satisfies cohomological descent for the Zariski, Nisnevich and étale topologies. We extend the definition of cyclic homology to finite-dimensional noetherian schemes and show that cyclic homology satisfies cohomological descent for the Zariski and Nisnevich topologies, as well as for the étale topology overQ. Finally we apply these results to complete the computation of the algebraicK-theory of seminormal curves in characteristic zero.

-theory of curves

In this paper we continue the study of excision for K1 of algebraic curves begun in [4]. If A c B are commutative rings and I is a B-ideal contained in A, then excision holds if the natural map K1(A, I) + K1(B, I) is an isomorphism. By “curve” we mean an algebra A of finite type over a field k, such that if P is a minimal prime ideal of A, then A/P is of Krull dimension 1. This is an abuse of notation, but is shorter than “co-ordinate ring of an affine curve.” All the curves that we consider in the paper are reduced and irreducible, i.e. A is already a domain. We have not thought about non-reduced curves. For reduced curves the additional assumption of irreducibility involves no loss of generality, as can be seen from the proof of Theorem 9 in [4]. The methods we use in the curve case sometimes work for subrings of R[t], R a commutative ring. This paper is a revision and extension of the unpublished manuscript [S]. In order to prove that excision holds we use the exact sequence of Swan (see Section 1) or its improvement due to Vorst (see Section 2). Usually we find explicit generators of R *,,., &I/I2 and then show that these generators map to 1 in K1(A, I). However in Section 4 we use a trick of Swan [15, p. 2381. Using these methods we show that excision holds if enough integers are invertible (Theorem 3.1, Theorem 3.3) or if the ground field is perfect (Theorem 4.2). We also give counterexamples to excision in all characteristics. In order to prove that elements in the kernel of the excision homomorphism are non-zero we use in this paper only one method, the “12-trick” (see proof of Theorem 6.3). However we have

Subgroups of the elementary and Steinberg groups of congruence level I2

OBJECTIVE To evaluate disposition of a single dose of butorphanol in goats after intravenous (IV) and intramuscular (IM) administration and to relate behavioral changes after butorphanol administration with plasma concentrations. DESIGN Randomized experimental study. ANIMALS Six healthy 3-year-old neutered goats (one male and five female) weighing 46.5 ± 10.5 kg (mean ± D). METHODS Goats were given IV and IM butorphanol (0.1 mg kg-1) using a randomized cross-over design with a 1-week interval between treatments. Heparinized blood samples were collected at fixed intervals for subsequent determination of plasma butorphanol concentrations using an enzyme linked immunosorbent assay (ELISA). Pharmacokinetic values (volume of distribution at steady state [VdSS], systemic clearance [ClTB], extrapolated peak plasma concentration [C0] or estimated peak plasma concentration [CMAX], time to estimated peak plasma concentration [TMAX], distribution and elimination half-lives [t1/2], and bioavailability) were calculated. Behavior was subjectively scored. A two-tailed paired t-test was used to compare the elimination half-lives after IV and IM administration. Behavioral scores are reported as median (range). A Friedman Rank Sums test adjusted for ties was used to analyze the behavioral scores. A logit model was used to determine the effect of time and concentration on behavior. A value of p < 0.05 was considered significant. RESULTS Volume of distribution at steady state after IV administration of butorphanol was 1.27 ± 0.73 L kg-1, and ClTB was 0.0096 ± 0.0024 L kg-1 minute-1. Extrapolated C0 of butorphanol after IV administration was 146.5 ± 49.8 ng mL-1. Estimated CMAX after IM administration of butorphanol was 54.98 ± 14.60 ng mL-1, and TMAX was 16.2 ± 5.2 minutes; bioavailability was 82 ± 41%. Elimination half-life of butorphanol was 1.87 ± 1.49 and 2.75 ± 1.93 hours for IV and IM administration, respectively. Goats became hyperactive after butorphanol administration within the first 5 minutes after administration. Behavioral scores for goats were significantly different from baseline at 15 minutes after IV administration and at 15 and 30 minutes after IM administration. Both time and plasma butorphanol concentration were predictors of behavior. Behavioral scores of all goats had returned to baseline by 120 minutes after IV administration and by 240 minutes after IM administration. Conclusions and Clinical Relevance  The dose of butorphanol (0.1 mg kg-1, IV or IM) being used clinically to treat postoperative pain in goats has an elimination half-life of 1.87 and 2.75 hours, respectively. Nonpainful goats become transiently excited after IV and IM administration of butorphanol. Clinical trials to validate the efficacy of butorphanol as an analgesic in goats are needed.

Acculturation and depressive symptoms in latino caregivers of cognitively impaired older adults.

An electromagnetic plunger valve which does not require an electromagnetic valve, and at the same time, which is low in cost, and in which the discharge passage is closed automatically as soon as the pump is stopped, and opened as soon as the pump is started, and the movable valve is actuated by the electromagnetic coil provided for the actuation of the electromagnetic plunger.

Using Humor to Combat Inequities

Abstract There are several subgroups of the Elementary group E ( B , I ) and of the Steinberg group St( B , I ) which lie at the congruence level I 2 . We describe their interrelationships and give examples to show that they can be distinct. Our main result is that, although the group E ( B , I ) depends on the choice of the ambient ring B , its commutator subgroup does not. In fact, the commutator subgroup is the intersection of Gl( I 2 ) with E ( Z ⊕ I , I ).