Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality

Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality.

Aleatory Sovereignty and the Rule of Sensitive Spaces

Addressing life in borders and refugee camps requires understanding the way these spaces are ruled, the kinds of problems rule poses for the people who live there, and the abilities of inhabitants to remake their own lives. Recent literature on such spaces has been influenced by Agamben's notion of sovereignty, which reduces these spaces and their residents to abstractions. We propose an alternate framework focused on what we call aleatory sovereignty, or rule by chance. This allows us to see camps and borders not only as the outcomes of humanitarian projects but also of anxieties about governance and rule; to see their inhabitants not only as abject recipients of aid, but also as individuals who make decisions and choices in complex conditions; and to show that while the outcome of projects within such spaces is often unpredictable, the assumptions that undergird such projects create regular cycles of implementation and failure.

Tridiagonal Reproducing Kernels and Subnormality

We consider analytic reproducing kernel Hilbert spaces H with orthonormal bases of the form {(a(n) + b(n)z)z(n) : n >= 0}. If b(n) = 0 for all n, then H is a diagonal space and multiplication by z, M-z, is a weighted shift. Our focus is on providing extensive classes of examples for which M-z is a bounded subnormal operator on a tridiagonal space H where b(n) not equal 0. The Aronszajn sum of H and (1 - z)H where H is either the Hardy space or the Bergman space on the disk are two such examples.

Detecting subarachnoid hemorrhage: Comparison of combined FLAIR/SWI versus CT

OBJECTIVES: Aim of this study was to compare the utility of susceptibility weighted imaging (SWI) with the established diagnostic techniques CT and fluid attenuated inversion recovery (FLAIR) in their detecting capacity of subarachnoid hemorrhage (SAH), and further to compare the combined SWI/FLAIR MRI data with CT to evaluate whether MRI is more accurate than CT. METHODS: Twenty-five patients with acute SAH underwent CT and MRI within 6 days after symptom onset. Underlying pathology for SAH was head trauma (n=9), ruptured aneurysm (n=6), ruptured arteriovenous malformation (n=2), and spontaneous bleeding (n=8). SWI, FLAIR, and CT data were analyzed. The anatomical distribution of SAH was subdivided into 8 subarachnoid regions with three peripheral cisterns (frontal-parietal, temporal-occipital, sylvian), two central cisterns and spaces (interhemispheric, intraventricular), and the perimesencephalic, posterior fossa, superior cerebellar cisterns. RESULTS: SAH was detected in a total of 146 subarachnoid regions. CT identified 110 (75.3%), FLAIR 127 (87%), and SWI 129 (88.4%) involved regions. Combined FLAIR and SWI identified all 146 detectable regions (100%). FLAIR was sensitive for frontal-parietal, temporal-occipital and Sylvian cistern SAH, while SWI was particularly sensitive for interhemispheric and intraventricular hemorrhage. CONCLUSIONS: By combining SWI and FLAIR, MRI yields a distinctly higher detection rate for SAH than CT alone, particularly due to their complementary detection characteristics in different anatomical regions. Detection strength of SWI is high in central areas, whereas FLAIR shows a better detection rate in peripheral areas.

Comparison of inversion recovery and contrast-enhanced T1-weighted fat-suppressed sequences for the staging of cervical lymphoma

In a retrospective analysis with two readers blinded to the clinical information, coronal short tau inversion recovery (STIR) images were compared to contrast-enhanced fat-saturated T1-weighted imaging (T1 CEfs) in 51 cases of cervical lymphoma. Interrater reliability was good to excellent. Although sensitivity and subjective quality of the STIR sequence were higher than those of the T1 CEfs sequence (sensitivity 85%/72%, respectively), specificity (82%/95%) as well as positive likelihood ratio (4.65/15.93) was much lower. Therefore, contrast-enhanced sequences should be included in the primary staging of lymphoma.

Genitourinary applications of diffusion-weighted MR imaging in the pelvis

Diffusion-weighted (DW) magnetic resonance (MR) imaging has a large number of potential clinical applications in the female and male pelvis and can easily be added to any routine MR protocol. In the female pelvis, DW imaging allows improvement of staging in endometrial and cervical cancer, especially in locally advanced disease and in patients in whom contrast medium administration should be avoided. It can also be helpful in characterizing complex adnexal masses and in depicting recurrent tumor after treatment of various gynecologic malignancies. DW imaging shows promising results in monitoring treatment response in patients undergoing radiation therapy of cervical cancer. An increase in apparent diffusion coefficient (ADC) values of responders precedes changes in size and may therefore allow early assessment of treatment success. In the male pelvis, the detection of prostate cancer in the peripheral zone is relatively easier than in the central gland based on the underlying ADC values, whereas overlapping values reported in the central gland still need further research. DW imaging might also be applied in the noninvasive evaluation of bladder cancer to differentiate between superficial and muscle-invasive tumors. Initial promising results have been reported in differentiating benign from malignant pelvic lymph nodes based on the ADC values; however, larger-scale studies will be needed to allow the detection of lymph node metastases in an individual patient. Prerequisites for successfully performing DW imaging of the female and male pelvis are standardization of the DW imaging technique, including the choice of b values, administration of an antiperistaltic drug, and comparison of DW findings with those of morphologic MR imaging.

Diffusion-weighted MR imaging in the head and neck

Extracranial applications of diffusion-weighted (DW) magnetic resonance (MR) imaging are gaining increasing importance, including in head and neck radiology. The main indications for performing DW imaging in this relatively small but challenging region of the body are tissue characterization, nodal staging, therapy monitoring, and early detection of treatment failure by differentiating recurrence from posttherapeutic changes. Lower apparent diffusion coefficients (ADCs) have been reported in the head and neck region of adults and children for most malignant lesions, as compared with ADCs of benign lesions. For nodal staging, DW imaging has shown promise in helping detect lymph node metastases, even in small (subcentimeter) nodes with lower ADCs, as compared with normal or reactive nodes. Follow-up of early response to treatment is reflected in an ADC increase in the primary tumor and nodal metastases; whereas nonresponding lesions tend to reveal only a slight increase or even a decrease in ADC during follow-up. Optimization and standardization of DW imaging technical parameters, comparison of DW images with morphologic images, and increasing experience, however, are prerequisites for successful application of this challenging technique in the evaluation of various head and neck pathologic conditions.