Improved Probability Method for Estimating Signal in the Presence of Background

A suggestion is made for improving the Feldman Cousins method of estimating signal counts in the presence of background. The method concentrates on finding essential information about the signal and ignoring extraneous information about background. An appropriate method is found which uses the condition that the number of background events obtained does not exceed the total number of events obtained. Several alternative approaches are explored.Comment: Modified 12/21 for singlespace to save trees, 9 pages, 1 figure. Modified 8/11/99 to add small modifications made for the Phys. Rev. articl

On unbounded p-summable Fredholm modules

We prove that odd unbounded p-summable Fredholm modules are also bounded p-summable Fredholm modules (this is the odd counterpart of a result of A. Connes for the case of even Fredholm modules)

Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation in meta-analysis of single proportions.

Standard generic inverse variance methods for the combination of single proportions are based on transformed proportions using the logit, arcsine, and Freeman-Tukey double arcsine transformations. Generalized linear mixed models are another more elaborate approach. Irrespective of the approach, meta-analysis results are typically back-transformed to the original scale in order to ease interpretation. Whereas the back-transformation of meta-analysis results is straightforward for most transformations, this is not the case for the Freeman-Tukey double arcsine transformation, albeit possible. In this case study with five studies, we demonstrate how seriously misleading the back-transformation of the Freeman-Tukey double arcsine transformation can be. We conclude that this transformation should only be used with special caution for the meta-analysis of single proportions due to potential problems with the back-transformation. Generalized linear mixed models seem to be a promising alternative

Classifying and Understanding the Reactivities of Mo-Based Alkyne Metathesis Catalysts from ⁹⁵Mo NMR Chemical Shift Descriptors

The most active alkyne metathesis catalysts rely on well-defined Mo alkylidynes, X3Mo≡CR (X = OR), in particular the recently developed canopy catalyst family bearing silanolate ligand sets. Recent efforts to understand catalyst reactivity patterns have shown that NMR chemical shifts are powerful descriptors, though previous studies have mostly focused on ligand-based NMR descriptors. Here, we show in the context of alkyne metathesis that 95Mo chemical shift tensors encode detailed information on the electronic structure of these catalysts. Analysis by first-principles calculations of 95Mo chemical shift tensors extracted from solid-state 95Mo NMR spectra shows a direct link of chemical shift values with the energies of the HOMO and LUMO, two molecular orbitals involved in the key [2 + 2]-cycloaddition step, thus linking 95Mo chemical shifts to reactivity. In particular, the 95Mo chemical shifts are driven by ligand electronegativity (σ-donation) and electron delocalization through Mo–O π interactions, thus explaining the reactivity patterns of the silanolate canopy catalysts. These results further motivate exploration of transition metal NMR signatures and their relationships to electronic structure and reactivity

In Vivo Length Changes Between the Attachments of the Medial Patellofemoral Complex Fibers in Knees With Anatomic Risk Factors for Patellar Instability

Background: Medial patellofemoral complex (MPFC) reconstruction plays an important role in the surgical treatment of patellar instability. Anatomic reconstruction is critical in re-creating the native function of the ligament, which includes minimizing length changes that occur in early flexion. Anatomic risk factors for patellar instability such as trochlear dysplasia, patella alta, and increased tibial tuberosity to trochlear groove (TT-TG) distance have been shown to influence the function of the MPFC graft in cadaveric studies, but the native length change patterns of the MPFC fibers in knees with anatomic risk factors have not been described. Purpose: To describe the in vivo length changes of the MPFC fibers in knees with anatomic risk factors for patellar instability and identify the optimal attachment sites for MPFC reconstruction. Study Design: Controlled laboratory study. Methods: Dynamic computed tomography imaging was performed on the asymptomatic knee in patients with contralateral patellar instability. Three-dimensional digital knee models were created to assess knees between 0° and 50° of flexion in 10° increments. MPFC fiber lengths were calculated at each flexion angle between known anatomic attachment points on the extensor mechanism (quadriceps tendon, MPFC midpoint [M], and patella) and femur (1, 2, and 3, representing the proximal to distal femoral footprint). Changes in MPFC fiber length were compared for each condition and assessed for their relationships to morphologic risk factors (trochlear depth, Caton Deschamps Index [CDI], and TT-TG distance). Results: In 22 knees, native MPFC fibers were found to be longer at 0° than at 20° to 50° of flexion. Length changes observed between 0° and 50° increased with the number of risk factors present. In the central fibers of the MPFC (M-2), 1.7% ± 3.1% length change was noted in knees with no anatomic risk factors, which increased to 5.6% ± 4.6%, 17.0% ± 6.4%, and 26.7% ± 6.8% in the setting of 1, 2, and 3 risk factors, respectively. Nonanatomic patella-based attachments were more likely to demonstrate unfavorable length change patterns, in which length was greater at 50° than 0°. In patellar attachments, an independent relationship was found between increasing length changes and TT-TG distance, while in quadriceps tendon attachments, a trend toward a negative relationship between length changes and CDI was noted. All configurations demonstrated a strong relationship between percentage change in length and number of morphologic risk factors present, with the greatest influence found in patella-based attachments. Conclusion: The MPFC fibers demonstrated increased length changes in knees when a greater number of morphological risk factors for patellar instability were present, which worsened in the setting of nonanatomic configurations. This suggests that the function of the intact MPFC in patients with anatomic risk factors may not reflect previously described findings in anatomically normal knees. Further studies are needed to understand the pathoanatomy related to these changes, as well as the implications for graft placement and assessment of length changes during MPFC reconstruction techniques. Clinical Relevance: MPFC length change patterns vary based on the number of morphologic risk factors for patellar instability present and should be considered during reconstructive procedures.</p

Smoking and Lung Cancer: Some Observations on Two Recent Reports,

EXPRESSING THE TREATMENT EFFECT of local recurrence of malignancy after the surgery. Patients were divided into two groups, depending upon the stage of the disease prior to surgery. Since both the risk and outcome variables are categorical, three measures of treatment effect-difference in recurrence rates, relative risk, and odds ratio-may be computed for each stage (see the calculations in Since the logarithm of the relative risk is equal to the difference of the log rates (log 19 = log r l -log r2), this is an example where an analysis in the original units (recurrence rates) show an interaction, whereas an analysis in a different scale (log -recurrence rates) does not. Often, however, interactions cannot be removed by changing the scale. If in the previous example, stage 1 patients had fewer recurrences with tylectomy than with mastectomy but the opposite had been true for stage 2 patients, there would be no way of avoiding interaction. Although it is desirable to avoid interaction since a single measure can then completely describe the treatment effect, sometimes, as we discussed in Section 3.1, because one measure of treatment effect is more useful than others, t p measure should be used even if it does result in interaction. Estimating a treatment effect requires the construction of a standard of comparison. As we have seen in Chapter 1, this involves a comparison group which does not receive the treatment of interest. In this chapter we will explore several ways of establishing such a comparison group, emphasizing the difference between randomization and other methods. It will be seen that a randomized allocation of subjects to a treatment and control group generally ensures that the latter is an adequate standard of comparison for the former. We will start by defining randomization and discussing the properties that make this method particularly attractive. We will then give reasons for doing nonrandomized studies, and distinguish the different types of studies involving a comparison group. For simplicity of presentation, this chapter will be confined mainly to studies with a dichotomous risk factor. 31 REFERENCE

Loop Representations

The loop representation plays an important role in canonical quantum gravity because loop variables allow a natural treatment of the constraints. In these lectures we give an elementary introduction to (i) the relevant history of loops in knot theory and gauge theory, (ii) the loop representation of Maxwell theory, and (iii) the loop representation of canonical quantum gravity. (Based on lectures given at the 117. Heraeus Seminar, Bad Honnef, Sept. 1993)Comment: 38 pages, MPI-Ph/93-9

Hardness as a Spectral Peak Estimator for Gamma-Ray Bursts

Simple hardness ratios are found to be a good estimator for the spectral peak energy in Gamma-Ray Bursts (GRBs). Specifically, a high correlation strength is found between the $\nu F_{\nu}$ peak in the spectrum of BATSE GRBs, \epo, and the hardness of GRBs, \hr, as defined by the fluences in channels 3 and 4, divided by the combined fluences in channels 1 and 2 of the BATSE Large Area Detectors. The correlation is independent of the type of the burst, whether Long-duration GRB (LGRB) or Short-duration (SGRB) and remains almost linear over the wide range of the BATSE energy window (20-2000 KeV). Based on Bayes theorem and Markov Chain Monte Carlo techniques, we also present multivariate analyses of the observational data while accounting for data truncation and sample-incompleteness. Prediction intervals for the proposed \hrep ~relation are derived. Results and further simulations are used to compute \epo estimates for nearly the entire BATSE catalog: 2130 GRBs. These results may be useful for investigating the cosmological utility of the spectral peak in GRBs intrinsic luminosity estimates.Comment: MNRAS submitted, Some technical side analyses removed or reduced following the referee's review, 68 pages, 13 figure