Using The t Test With Uncommon Sample Sizes

Monte Carlo techniques were used to determine the effect of using common critical values as an approximation for uncommon sample sizes. Results indicate there can be a significant loss in statistical power. Therefore, even though many instructors now rely on computer statistics packages, the recommendation is made to provide more specificity (i.e., values between 30 and 60) in tables of critical values published in textbooks

Treating cisplatin-resistant cancer: a systematic analysis of oxaliplatin or paclitaxel salvage chemotherapy

Objective: To examine the pre-clinical and clinical evidence for the use of oxaliplatin or paclitaxel salvage chemotherapy in patients with cisplatin-resistant cancer. Methods: Medline was searched for 1) Cell models of acquired resistance reporting cisplatin, oxaliplatin and paclitaxel sensitivities and 2) Clinical trials of single agent oxaliplatin or paclitaxel salvage therapy for cisplatin/carboplatin-resistant ovarian cancer. Results: Oxaliplatin - Oxaliplatin is widely regarded as being active in cisplatin-resistant cancer. In contrast, data in cell models suggests that there is cross-resistance between cisplatin and oxaliplatin in cellular models with resistance levels which reflect clinical resistance (<10 fold). Oxaliplatin as a single agent had a poor response rate in patients with cisplatin-resistant ovarian cancer (8%, n=91). Oxaliplatin performed better in combination with other agents for the treatment of platinum-resistant cancer suggesting that the benefit of oxaliplatin may lie in its more favourable toxicity and ability to be combined with other drugs rather than an underlying activity in cisplatin resistance. Oxaliplatin therefore should not be considered broadly active in cisplatin-resistant cancer. Paclitaxel – Cellular data suggests that paclitaxel is active in cisplatin-resistant cancer. 68.1% of cisplatin-resistant cells were sensitive to paclitaxel. Paclitaxel as a single agent had a response rate of 22% in patients with platinum-resistant ovarian cancer (n = 1918), a significant increase from the response of oxaliplatin (p<0.01). Paclitaxel-resistant cells were also sensitive to cisplatin, suggesting that alternating between agents may be beneficial. Studies of single agent paclitaxel in platinum-resistant ovarian cancer where patients had previously received paclitaxel had an improved response rate of 35.3% n=232 (p<0.01), suggesting that pre-treatment with paclitaxel improves the response of salvage paclitaxel therapy. Conclusions: Cellular models reflect the resistance observed in the clinic as the cross resistant agent oxaliplatin has a lower response rate compared to the non-cross resistant agent paclitaxel in cisplatin-resistant ovarian cancer. Alternating therapy with cisplatin and paclitaxel may therefore lead to an improved response rate in ovarian cancer

Lagrangian fibrations of holomorphic-symplectic varieties of K3^[n]-type

Let X be a compact Kahler holomorphic-symplectic manifold, which is deformation equivalent to the Hilbert scheme of length n subschemes of a K3 surface. Let L be a nef line-bundle on X, such that the 2n-th power of c_1(L) vanishes and c_1(L) is primitive. Assume that the two dimensional subspace H^{2,0}(X) + H^{0,2}(X), of the second cohomology of X with complex coefficients, intersects trivially the integral cohomology. We prove that the linear system of L is base point free and it induces a Lagrangian fibration on X. In particular, the line-bundle L is effective. A determination of the semi-group of effective divisor classes on X follows, when X is projective. For a generic such pair (X,L), not necessarily projective, we show that X is bimeromorphic to a Tate-Shafarevich twist of a moduli space of stable torsion sheaves, each with pure one dimensional support, on a projective K3 surface.Comment: 34 pages. v3: Reference [Mat5] and Remark 1.8 added. Incorporated improvement to the exposition and corrected typos according to the referees suggestions. To appear in the proceedings of the conference Algebraic and Complex Geometry, Hannover 201

Using serum CA125 to assess the activity of potential cytostatic agents in ovarian cancer

Objective: New strategies are required to rapidly identify novel cytostatic agents before embarking on large randomized trials. This study investigates whether a change in rate of rise (slope) of serum CA125 from before to after starting a novel agent could be used to identify cytostatic agents. Tamoxifen was used to validate this hypothesis. Methods: Asymptomatic patients with relapsed ovarian cancer who had responded to chemotherapy were enrolled and had CA125 measurements taken every 4 weeks, then more frequently when rising. Once levels reached 4 times the upper limit of normal or nadir, they started continuous tamoxifen 20 mg daily, as well as fortnightly CA125 measurements until symptomatic progression. Because of the potentially nonlinear relationship of CA125 over time, it was felt that to enable normal approximations to be utilized a natural logarithmic standard transformation [ln(CA125)] was the most suitable to improve linearity above the common logarithmic transformation to base 10. Results: From 235 recruited patients, 81 started tamoxifen and had at least 4 CA125 measurements taken before and 4 CA125 measurements taken after starting tamoxifen, respectively. The mean regression slopes from using at least 4 1n(CA125) measurements immediately before and after starting tamoxifen were 0I0149 and 0I0093 [ln(CA125)/d], respectively. This difference is statistically significant, P = 0I001. Therefore, in a future trial with a novel agent, at least as effective as tamoxifen, using this effect size, the number of evaluable patients needed, at significance level of 5% and power of 80%, is 56. Conclusions: Further validation of this methodology is required, but there is potential to use comparison of mean regression slopes of ln(CA125) as an interim analysis measure of efficacy for novel cytostatic agents in relapsed ovarian cancer.Peer reviewedFinal Accepted Versio

Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant.Comment: v2: added due credits to the work of Burger, Iozzi and Wienhard. v3: corrected count of connected components for G=SU(p,q) (p \neq q); added due credits to the work of Xia and Markman-Xia; minor corrections and clarifications. 31 page

On Integrable Systems and Supersymmetric Gauge Theories

The properties of the N=2 SUSY gauge theories underlying the Seiberg-Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential are presented, the invariant sense of these definitions is illustrated. Recently found exact nonperturbative solutions to N=2 SUSY gauge theories are formulated using the methods of the theory of integrable systems and where possible the parallels between standard quantum field theory results and solutions to integrable systems are discussed.Comment: LaTeX, 38 pages, no figures; based on the lecture given at INTAS School on Advances in Quantum Field Theory and Statistical Mechanics, Como, Italy, 1996; minor changes, few references adde

Semantic memory redux: an experimental test of hierarchical category representation

Four experiments investigated the classic issue in semantic memory of whether people organize categorical information in hierarchies and use inference to retrieve information from them, as proposed by Collins & Quillian (1969). Past evidence has focused on RT to confirm sentences such as “All birds are animals” or “Canaries breathe.” However, confounding variables such as familiarity and associations between the terms have led to contradictory results. Our experiments avoided such problems by teaching subjects novel materials. Experiment 1 tested an implicit hierarchical structure in the features of a set of studied objects (e.g., all brown objects were large). Experiment 2 taught subjects nested categories of artificial bugs. In Experiment 3, subjects learned a tree structure of novel category hierarchies. In all three, the results differed from the predictions of the hierarchical inference model. In Experiment 4, subjects learned a hierarchy by means of paired associates of novel category names. Here we finally found the RT signature of hierarchical inference. We conclude that it is possible to store information in a hierarchy and retrieve it via inference, but it is difficult and avoided whenever possible. The results are more consistent with feature comparison models than hierarchical models of semantic memory

Stable isotope analysis provides new information on winter habitat use of declining avian migrants that is relevant to their conservation

Winter habitat use and the magnitude of migratory connectivity are important parameters when assessing drivers of the marked declines in avian migrants. Such information is unavailable for most species. We use a stable isotope approach to assess these factors for three declining African-Eurasian migrants whose winter ecology is poorly known: wood warbler Phylloscopus sibilatrix, house martin Delichon urbicum and common swift Apus apus. Spatially segregated breeding wood warbler populations (sampled across a 800 km transect), house martins and common swifts (sampled across a 3,500 km transect) exhibited statistically identical intra-specific carbon and nitrogen isotope ratios in winter grown feathers. Such patterns are compatible with a high degree of migratory connectivity, but could arise if species use isotopically similar resources at different locations. Wood warbler carbon isotope ratios are more depleted than typical for African-Eurasian migrants and are compatible with use of moist lowland forest. The very limited variance in these ratios indicates specialisation on isotopically restricted resources, which may drive the similarity in wood warbler populations' stable isotope ratios and increase susceptibility to environmental change within its wintering grounds. House martins were previously considered to primarily use moist montane forest during the winter, but this seems unlikely given the enriched nature of their carbon isotope ratios. House martins use a narrower isotopic range of resources than the common swift, indicative of increased specialisation or a relatively limited wintering range; both factors could increase house martins' vulnerability to environmental change. The marked variance in isotope ratios within each common swift population contributes to the lack of population specific signatures and indicates that the species is less vulnerable to environmental change in sub-Saharan Africa than our other focal species. Our findings demonstrate how stable isotope research can contribute to understanding avian migrants' winter ecology and conservation status

Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatio-temporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatio-temporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive part, then crosstalk among encoded patterns vanishes. Phase transition due to the loss of the stability of periodic solution is observed when we assume fast alpha-function for direct interaction among neurons. In order to evaluate the critical point of this phase transition, we employ Floquet theory in which the stability problem of the infinite number of spiking neurons interacting with alpha-function is reduced into the eigenvalue problem with the finite size of matrix. Numerical integration of the single-body dynamics yields the explicit value of the matrix, which enables us to determine the critical point of the phase transition with a high degree of precision.Comment: Accepted for publication in Phys. Rev.