Construction of scaling partitions of unity

Partitions of unity in ${\mathbf R}^d$ formed by (matrix) scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the functions and matrices yielding such a partition of unity. For invertible expanding matrices, the characterization leads to easy ways of constructing appropriate functions with attractive properties like high regularity and small support. We also discuss a class of integral transforms that map functions having the partition of unity property to functions with the same property. The one-dimensional version of the transform allows a direct definition of a class of nonuniform splines with properties that are parallel to those of the classical B-splines. The results are illustrated with the construction of dual pairs of wavelet frames

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Taha Toros Arşivi, Dosya No: 204-İlhan Usmanba

Mri-Ultrasound Fusion Targeted Biopsy In Men With Prior Negative Prostate Biopsy For Prostate Cancer

A particularly challenging subpopulation of prostate cancer patients are those who present with a persistently elevated PSA and suspicion of prostate cancer despite having had one or more prior negative prostate biopsies. These patients may benefit from the improvements made in prostate imaging through multiparametric MRI (mpMRI) and MRI-guided prostate biopsy techniques. In this study, we evaluate mpMRI and MRI-US fusion biopsy as a means of detecting clinically significant cancer as well as a potential indicator for avoiding repeat biopsies. We performed a retrospective study of 374 men seen between 12/2012 and 06/2015. All patients underwent pre-biopsy mpMRI to identify regions of interest (ROIs) within the prostate and each was assigned an MRI suspicion score. All patients then underwent a 12-core standard trans-rectal mapping biopsy, and all patients with ROIs identified on mpMRI underwent MRI-US fusion targeted biopsy. We defined cancer as any Gleason score ≥ 6, and we defined clinically significant cancer as Gleason score ≥ 3+4. Statistical analysis was performed using chi squared, Fisher’s exact, student’s t- test, one-way ANOVA, and multivariate logistic regression. All test results were considered statistically significant if p \u3c 0.05. 143 patients were included in our analysis. Overall cancer detection rate was 42.66%, and the clinically significant cancer detection rate was 27.27%. For standard 12-core mapping biopsy, the cancer detection rate was 34.97%, and the clinically significant cancer detection rate was 18.18%. For men who underwent targeted biopsies, the cancer detection rate of the targeted biopsies was 40.5%, and the clinically significant cancer detection rate was 27.27%. In total, 21.50% of patients were upgraded by inclusion of targeted biopsy. For the 72 patients with no cancer on targeted biopsy, only 2 were found to have clinically significant cancer on mapping biopsy. A total of 213 ROIs were identified following mpMRI. Cancer was found in 32.86% of the ROIs and clinically significant cancer was found in 22.54%. For the 22 patients with no target identified on MRI, none were found to have clinically significant cancer. Age, PSA, MRI suspicion score, and PSA density were correlated with clinically significant. Anterior location of ROI was significantly correlated with presence of cancer and higher grade cancer, particularly on targeted biopsy. For clinically significant cancer detected on targeted biopsy, multivariate logistic regression revealed that the only significant independent predictor of disease was the presence of an anteriorly located ROI on mpMRI (OR 4.50, p \u3c 0.01). In men with one or more previous negative biopsies and continued suspicion for prostate cancer, mpMRI and MRI-US fusion targeted biopsy provide greater detection rate of clinically significant disease compared to standard 12-core TRUS biopsy. Men with negative MRI findings may be able to avoid or delay biopsy. Patients with high MRI suspicion score lesions and those with anterior lesions are at increased risk for significant disease and should be treated with the necessary diligence

Hands of Another

I believe that our biggest battles in the Disabled Community are battles we face with our personal care attendants. This poem was experienced and written during an intense three week period in which I fired and then hired a new attendant. “Hands of Another” are his hands, and are symbolic of any personal care attendant

Comparative Study on Academia, Local Government, and International Organization’s Work Interest with the Local Community Tourism Development.

Community-based tourism (CBT) is a strategy that can be used by a community to manage its resources and control its development through the use of tourism [1,2]. Often there are cases where CBT experts are requested to help community to improve its livelihood while sustaining its resources [3,4]. But during the transformation process, at times the local community would consider the external assistance as a problem than a solution to their development process, causing undesirable conflict. This research investigate the work interest of the following CBT developers: academia, non-government organization (NGO), local government, and international organization with the local community. This article helps compare and measure developers’ understanding of the local community, their collaboration and assistance to that community, each group’s evaluation of other developers’ work productivity, and the possible benefits for developers from their taking part in CBT development

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Taha Toros Arşivi, Dosya No: 13-Berat Zeki-Zeki-Ekrem Zeki-Vedat Üngö