Sharp Bounds on Heterogeneous Individual Treatment Responses

This paper discusses how to identify individual-specific causal effects of an ordered discrete endogenous variable. The counterfactual heterogeneous causal information is recovered by identifying the partial differences of a structural relation. The proposed refutable nonparametric local restrictions exploit the fact that the pattern of endogeneity may vary across the level of the unobserved variable. The restrictions adopted in this paper impose a sense of order to an unordered binary endogeneous variable. This allows for a uni.ed structural approach to studying various treatment effects when self-selection on unobservables is present. The usefulness of the identi.cation results is illustrated using the data on the Vietnam-era veterans. The empirical findings reveal that when other observable characteristics are identical, military service had positive impacts for individuals with low (unobservable) earnings potential, while it had negative impacts for those with high earnings potential. This heterogeneity would not be detected by average effects which would underestimate the actual effects because different signs would be cancelled out. This partial identification result can be used to test homogeneity in response. When homogeneity is rejected, many parameters based on averages may deliver misleading information.

Integer Programming on Domains Containing Inseparable Ordered Paris

Using the integer programming approach introduced by Sethuraman, Teo, and Vohra (2003), we extend the analysis of the preference domains containing an inseparable ordered pair, initiated by Kalai and Ritz (1978). We show that these domains admit not only Arrovian social welfare functions \without ties," but also Arrovian social welfare functions \with ties," since they satisfy the strictly decomposability condition introduced by Busetto, Codognato, and Tonin (2012). Moreover, we go further in the comparison between Kalai and Ritz (1978)'s inseparability and Arrow (1963)'s single-peak restrictions, showing that the former condition is more \respectable," in the sense of Muller and Satterthwaite (1985).

Conjugacy of piecewise linear Lorenz map that expand on average

For piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a ß-transformation.

T1-weighted MRI as a substitute to CT for refocusing planning in MR-guided focused ultrasound.

Precise focusing is essential for transcranial MRI-guided focused ultrasound (TcMRgFUS) to minimize collateral damage to non-diseased tissues and to achieve temperatures capable of inducing coagulative necrosis at acceptable power deposition levels. CT is usually used for this refocusing but requires a separate study (CT) ahead of the TcMRgFUS procedure. The goal of this study was to determine whether MRI using an appropriate sequence would be a viable alternative to CT for planning ultrasound refocusing in TcMRgFUS. We tested three MRI pulse sequences (3D T1 weighted 3D volume interpolated breath hold examination (VIBE), proton density weighted 3D sampling perfection with applications optimized contrasts using different flip angle evolution and 3D true fast imaging with steady state precision T2-weighted imaging) on patients who have already had a CT scan performed. We made detailed measurements of the calvarial structure based on the MRI data and compared those so-called 'virtual CT' to detailed measurements of the calvarial structure based on the CT data, used as a reference standard. We then loaded both standard and virtual CT in a TcMRgFUS device and compared the calculated phase correction values, as well as the temperature elevation in a phantom. A series of Bland-Altman measurement agreement analyses showed T1 3D VIBE as the optimal MRI sequence, with respect to minimizing the measurement discrepancy between the MRI derived total skull thickness measurement and the CT derived total skull thickness measurement (mean measurement discrepancy: 0.025; 95% CL (-0.22-0.27); p = 0.825). The T1-weighted sequence was also optimal in estimating skull CT density and skull layer thickness. The mean difference between the phase shifts calculated with the standard CT and the virtual CT reconstructed from the T1 dataset was 0.08 ± 1.2 rad on patients and 0.1 ± 0.9 rad on phantom. Compared to the real CT, the MR-based correction showed a 1 °C drop on the maximum temperature elevation in the phantom (7% relative drop). Without any correction, the maximum temperature was down 6 °C (43% relative drop). We have developed an approach that allows for a reconstruction of a virtual CT dataset from MRI to perform phase correction in TcMRgFUS.

Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Investigation of field and diffusion time dependence of the diffusion-weighted signal at ultrahigh magnetic fields.

Over the last decade, there has been a significant increase in the number of high-magnetic-field MRI magnets. However, the exact effect of a high magnetic field strength (B0 ) on diffusion-weighted MR signals is not yet fully understood. The goal of this study was to investigate the influence of different high magnetic field strengths (9.4 T and 14.1 T) and diffusion times (9, 11, 13, 15, 17 and 24 ms) on the diffusion-weighted signal in rat brain white matter. At a short diffusion time (9 ms), fractional anisotropy values were found to be lower at 14.1 T than at 9.4 T, but this difference disappeared at longer diffusion times. A simple two-pool model was used to explain these findings. The model describes the white matter as a first hindered compartment (often associated with the extra-axonal space), characterized by a faster orthogonal diffusion and a lower fractional anisotropy, and a second restricted compartment (often associated with the intra-axonal space), characterized by a slower orthogonal diffusion (i.e. orthogonal to the axon direction) and a higher fractional anisotropy. Apparent T2 relaxation time measurements of the hindered and restricted pools were performed. The shortening of the pseudo-T2 value from the restricted compartment with B0 is likely to be more pronounced than the apparent T2 changes in the hindered compartment. This study suggests that the observed differences in diffusion tensor imaging parameters between the two magnetic field strengths at short diffusion time may be related to differences in the apparent T2 values between the pools. Copyright © 2013 John Wiley & Sons, Ltd.

Diffusion-weighted MR imaging of the spine at 3-T: feasibility, optimization of b-value and utility to differentiate benign from pathological vertebral compression fractures

Purpose: To evaluate the feasibility, determine the optimal b-value, and assess the utility of 3-T diffusion-weighted MR imaging (DWI) of the spine in differentiating benign from pathologic vertebral compression fractures.Methods and Materials: Twenty patients with 38 vertebral compression fractures (24 benign, 14 pathologic) and 20 controls (total: 23 men, 17 women, mean age 56.2years) were included from December 2010 to May 2011 in this IRB-approved prospective study. MR imaging of the spine was performed on a 3-T unit with T1-w, fat-suppressed T2-w, gadolinium-enhanced fat-suppressed T1-w and zoomed-EPI (2D RF excitation pulse combined with reduced field-of-view single-shot echo-planar readout) diffusion-w (b-values: 0, 300, 500 and 700s/mm2) sequences. Two radiologists independently assessed zoomed-EPI image quality in random order using a 4-point scale: 1=excellent to 4=poor. They subsequently measured apparent diffusion coefficients (ADCs) in normal vertebral bodies and compression fractures, in consensus.Results: Lower b-values correlated with better image quality scores, with significant differences between b=300 (mean±SD=2.6±0.8), b=500 (3.0±0.7) and b=700 (3.6±0.6) (all p<0.001). Mean ADCs of normal vertebral bodies (n=162) were 0.23, 0.17 and 0.11×10-3mm2/s with b=300, 500 and 700s/mm2, respectively. In contrast, mean ADCs were 0.89, 0.70 and 0.59×10-3mm2/s for benign vertebral compression fractures and 0.79, 0.66 and 0.51×10-3mm2/s for pathologic fractures with b=300, 500 and 700s/mm2, respectively. No significant difference was found between ADCs of benign and pathologic fractures.Conclusion: 3-T DWI of the spine is feasible and lower b-values (300s/mm2) are recommended. However, our preliminary results show no advantage of DWI in differentiating benign from pathologic vertebral compression fractures.

Weighted norm inequalities for Fourier transforms of radial functions

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Individual versus standard quality of life assessment in a phase II clinical trial in mesothelioma patients: feasibility and responsiveness to clinical changes.

BACKGROUND: In patients with malignant pleural mesothelioma undergoing a multimodality therapy, treatment toxicity may outweigh the benefit of progression-free survival. The subjective experience across different treatment phases is an important clinical outcome. This study compares a standard with an individual quality of life (QoL) measure used in a multi-center phase II trial. PATIENTS AND METHODS: Sixty-one patients with stage I-III technically operable pleural mesothelioma were treated with preoperative chemotherapy, followed by pleuropneumonectomy and subsequent radiotherapy. QoL was assessed at baseline, at day 1 of cycle 3, and 1, 3 and 6 months post-surgery by using the Rotterdam Symptom Checklist (RSCL) and the Schedule for the Evaluation of Quality of Life-Direct Weighting (SEIQoL-DW), a measure that is based on five individually nominated and weighted QoL-domains. RESULTS: Completion rates were 98% (RSCL) and 92% (SEIQoL) at baseline and 98%/89% at cycle 3, respectively. Of the operated patients (N=45) RSCL and SEIQoL were available from 86%/72%, 93%/74%, and 94%/76% at months 1, 3, and 6 post-surgery. Average assessment time for the SEIQoL was 24min compared to 8min needed for the RSCL. Median changes from baseline indicate that both RSCL QoL overall score and SEIQoL index remained stable during chemotherapy with a clinically significant deterioration (change>or=8 points) 1 month after surgery (median change of -66 and -14 for RSCL and SEIQoL, respectively). RSCL QoL overall scores improved thereafter, but remained beneath baseline level until 6 months after surgery. SEIQoL scores improved to baseline-level at month 3 after surgery, but worsened again at month 6. RSCL QoL overall score and SEIQoL index were moderately correlated at baseline (r=.30; p<or=.05) and at 6-month follow-up (r=.42; p<or=.05) but not at the other time points. CONCLUSION: The SEIQoL assessment seems to be feasible within a phase II clinical trial, but may require more effort from staff. More distinctive QoL changes in accordance with clinical changes were measured with the RSCL. Our findings suggest that the two measures are not interchangeable: the RSCL is to favor when mainly information related to the course of disease- and treatment is of interest.

Comparing Multilevel Clustering Methods on Weighted Graphs : The Case of Worldwide Air Passenger Traffic 2000-2004

Specific properties emerge from the structure of large networks, such as that of worldwide air traffic, including a highly hierarchical node structure and multi-level small world sub-groups that strongly influence future dynamics. We have developed clustering methods to understand the form of these structures, to identify structural properties, and to evaluate the effects of these properties. Graph clustering methods are often constructed from different components: a metric, a clustering index, and a modularity measure to assess the quality of a clustering method. To understand the impact of each of these components on the clustering method, we explore and compare different combinations. These different combinations are used to compare multilevel clustering methods to delineate the effects of geographical distance, hubs, network densities, and bridges on worldwide air passenger traffic. The ultimate goal of this methodological research is to demonstrate evidence of combined effects in the development of an air traffic network. In fact, the network can be divided into different levels of âeurooecohesionâeuro, which can be qualified and measured by comparative studies (Newman, 2002; Guimera et al., 2005; Sales-Pardo et al., 2007).

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

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Allocating Resources to HSS Boards: Proposed Changes to the Weighted Capitation Formula - Final Consultation Summary (PDF 167 KB)

Allocating Resources to HSS Boards: Proposed Changes to the Weighted Capitation Formula - Final Consultation Summary

Optimal 3-T MRI for depiction of the finger A2 pulley: comparison between T1-weighted, fat-saturated T2-weighted and gadolinium-enhanced fat-saturated T1-weighted sequences

OBJECTIVE: To compare three spin-echo sequences, transverse T1-weighted (T1WI), transverse fat-saturated (FS) T2-weighted (T2WI), and transverse gadolinium-enhanced (Gd) FS T1WI, for the visualisation of normal and abnormal finger A2 pulley with magnetic resonance (MR) imaging at 3 tesla (T). MATERIALS AND METHODS: Sixty-three fingers from 21 patients were consecutively investigated. Two musculoskeletal radiologists retrospectively compared all sequences to assess the visibility of normal and abnormal A2 pulleys and the presence of motion or ghost artefacts. RESULTS: Normal and abnormal A2 pulleys were visible in 94% (59/63) and 95% (60/63) on T1WI sequences, in 63% (40/63) and 60% (38/63) on FS T2WI sequences, and in 87% (55/63) and 73% (46/63) on Gd FS T1WI sequences when read by the first and second observer, respectively. Motion and ghost artefacts were higher on FS T2WI sequences. Seven among eight abnormal A2 pulleys were detected, and were best depicted with Gd FS T1WI sequences in 71% (5/7) and 86% (6/7) by the first and the second observer, respectively. CONCLUSION: In 3-T MRI, the comparison between transverse T1WI, FS T2WI, and Gd FS T1WI sequences shows that transverse T1WI allows excellent depiction of the A2 pulley, that FS T2WI suffers from a higher rate of motion and ghost artefacts, and transverse Gd FS T1WI is the best sequence for the depiction of abnormal A2 pulley.