Linear models for control of cavity flow oscillations

Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes are limited by nonlinearities. We present experimental data which suggests that in some regimes, the oscillations may not be self-sustained, but lightly damped: oscillations are sustained by external forcing, such as boundary-layer turbulence. In these regimes, linear models suffice to describe the behaviour, and the final amplitude of oscillations depends on the characteristics of the external disturbances. These linear models are particularly appropriate for describing cavities in which feedback has been used for noise suppression, as the oscillations are small and nonlinearities are less likely to be important. It is shown that increasing the gain too much in such feedback control experiments can lead to a peak-splitting phenomenon, which is explained by the linear models. Fundamental performance limits indicate that peak splitting is likely to occur for narrow-bandwidth actuators and controllers

Management of leiomyosarcomas of the spermatic cord: the role of reconstructive surgery

BACKGROUND: Leiomyosarcomas (LMS) of the spermatic cord are extremely rare. Radical inguinal orchiectomy and high ligation of the cord is the standard primary surgical procedure. The extent of surrounding soft tissue excision required and the precise role of adjuvant radiotherapy, however, remains unclear. In addition, recurrence is a commonly encountered problem which might necessitate further radical excision of adjacent soft tissues. METHODS: This article reviews the pathophysiology of spermatic cord leiomyosarcomas (LMS), and discusses the various reconstructive surgical options available to repair the inguinal region and the lower anterior abdominal wall after excision of the tumour and the adjacent soft tissues. RESULTS: There is paucity of literature on LMS of spermatic cord. The majority of paratesticular neoplasms are of mesenchymal origin and up to 30% of these are malignant. In adults, approximately 10% of spermatic cord sarcomas are LMS. Approximately 50% of these tumours recur loco-regionally following definitive surgery; however, the incidence decreases if resection is followed by adjuvant radiotherapy. CONCLUSION: It is therefore important to achieve negative histological margins during the primary surgical procedure, even if adjuvant radiotherapy is instituted. If extensive resection is required, either during the primary procedure or following recurrence, reconstructive surgery may become necessary. This article reviews the pathophysiology of spermatic cord LMS, the reasons for recurrence, and discusses the management options including the role of reconstructive surgery

Ejection of Supernova-Enriched Gas From Dwarf Disk Galaxies

We examine the efficiency with which supernova-enriched gas may be ejected from dwarf disk galaxies, using a methodology previously employed to study the self-enrichment efficiency of dwarf spheroidal systems. Unlike previous studies that focused on highly concentrated starbursts, in the current work we consider discrete supernova events spread throughout various fractions of the disk. We model disk systems having gas masses of 10^8 and 10^9 solar masses with supernova rates of 30, 300, and 3000 per Myr. The supernova events are confined to the midplane of the disk, but distributed over radii of 0, 30, and 80% of the disk radius, consistent with expectations for Type II supernovae. In agreement with earlier studies, we find that the enriched material from supernovae is largely lost when the supernovae are concentrated near the nucleus, as expected for a starburst event. In contrast, however, we find the loss of enriched material to be much less efficient when the supernovae occur over even a relatively small fraction of the disk. The difference is due to the ability of the system to relax following supernova events that occur over more extended regions. Larger physical separations also reduce the likelihood of supernovae going off within low-density "chimneys" swept out by previous supernovae. We also find that, for the most distributed systems, significant metal loss is more likely to be accompanied by significant mass loss. A comparison with theoretical predications indicates that, when undergoing self-regulated star formation, galaxies in the mass range considered shall efficiently retain the products of Type II supernovae.Comment: 16 pages, 14 figures, to appear in Astrophysical Journal; higher resolution figures available through Ap

Referral for menstrual problems:cross sectional survey of symptoms, reasons for referral, and management

OBJECTIVES: To describe the menstrual experience of women referred for menstrual problems, in particular menorrhagia (excessive menstrual loss), and to assess associations with reasons for referral given by their general practitioners, the women's understanding of the reasons for their attendance at the hospital clinics, and clinic outcome. DESIGN: Questionnaire survey, with partial review of case notes after 8 months. SETTING: Three hospital gynaecology clinics in Glasgow and Edinburgh. PARTICIPANTS: 952 women completed the questionnaire, and the first 665 were reviewed. OUTCOME MEASURES: Reason for referral, women's reported menstrual problems and reason for clinic attendance, diagnosis, and treatment. RESULTS: Only 38% (95% confidence interval 34% to 41%) of women reported excessive menstrual loss as a severe problem. However 60% (57-63%) gave it as reason for attending a clinic, and 76% (73-79%) of general practitioners gave it as reason for referral. Reason for referral was significantly biased towards bleeding (McNemar odds ratio 4.01, 3.0 to 5.3, P<0.001) and against pain (0.54, 0.4 to 0.7, P<0.001). Dysfunctional uterine bleeding was diagnosed in 37% (31-42%) of the 259 women who gave as reason for attendance something other than bleeding. Women who were economically disadvantaged differed in prevalence of the main diagnoses and were more likely to fail to reattend. Hysterectomy was associated with referral for bleeding (relative risk 4.9, 1.6 to 15.6, P<0.001) but not with the patient stating bleeding as the reason for clinic attendance. CONCLUSIONS: Intolerance of the volume of their bleeding is not a key feature among women attending clinics for bleeding problems. Broad menstrual complaint tends to be reframed as excessive bleeding at referral and during management. This may result in women receiving inappropriate care. Conceptualisation and assessment of menorrhagia requires reconsideration

Roche Lobe Overflow from Dwarf Stellar Systems

We use both analytical analyses and numerical simulations to examine the evolution of residual gas within tidally-limited dwarf galaxies and globular clusters. If the gas sound speed exceeds about 10% of the central velocity dispersion, as is the case for ionized gas within small stellar systems, the gas shall have significant density at the tidal radius, and the gas may be lost on timescales as short as a few times the sound crossing time of the system. In colder systems, the density at the tidal radius is much lower, greatly reducing the mass loss rate, and the system may retain its gas for a Hubble time. The tidally removed gas shall follow an orbit close to that of the original host system, forming an extended stream of ionized, gaseous debris. Tidal mass loss severely limits the ability of dwarf systems to continuously form stars. The ordinary gas content in many dwarf galaxies is fully ionized during high red-shift epochs, possibly preventing star formation in some systems, leading to the formation of starless, dark-matter concentrations. In either the field or in the center of galaxy clusters, ionized gas may be retained by dwarf galaxies, even though its sound speed may be comparable to or even exceed the velocity dispersion. These processes may help to explain some observed differences among dwarf galaxy types, as well as observations of the haloes of massive galaxies.Comment: 28 pages, LaTeX, AASTex macro

The structure of HI in galactic disks: Simulations vs observations

We generate synthetic HI Galactic plane surveys from spiral galaxy simulations which include stellar feedback processes. Compared to a model without feedback we find an increased scale height of HI emission (in better agreement with observations) and more realistic spatial structure (including supernova blown bubbles). The synthetic data show HI self-absorption with a morphology similar to that seen in observations. The density and temperature of the material responsible for HI self-absorption is consistent with observationally determined values, and is found to be only weakly dependent on absorption strength and star formation efficiency.Comment: 12 pages, 7 figures. Accepted for publication in MNRA

Composition Operators and Endomorphisms

If $b$ is an inner function, then composition with $b$ induces an endomorphism, $\beta$, of $L^\infty(\mathbb{T})$ that leaves $H^\infty(\mathbb{T})$ invariant. We investigate the structure of the endomorphisms of $B(L^2(\mathbb{T}))$ and $B(H^2(\mathbb{T}))$ that implement $\beta$ through the representations of $L^\infty(\mathbb{T})$ and $H^\infty(\mathbb{T})$ in terms of multiplication operators on $L^2(\mathbb{T})$ and $H^2(\mathbb{T})$. Our analysis, which is based on work of R. Rochberg and J. McDonald, will wind its way through the theory of composition operators on spaces of analytic functions to recent work on Cuntz families of isometries and Hilbert $C^*$-modules

Weighted Consensus Segmentations

The problem of segmenting linearly ordered data is frequently encountered in time-series analysis, computational biology, and natural language processing. Segmentations obtained independently from replicate data sets or from the same data with different methods or parameter settings pose the problem of computing an aggregate or consensus segmentation. This Segmentation Aggregation problem amounts to finding a segmentation that minimizes the sum of distances to the input segmentations. It is again a segmentation problem and can be solved by dynamic programming. The aim of this contribution is (1) to gain a better mathematical understanding of the Segmentation Aggregation problem and its solutions and (2) to demonstrate that consensus segmentations have useful applications. Extending previously known results we show that for a large class of distance functions only breakpoints present in at least one input segmentation appear in the consensus segmentation. Furthermore, we derive a bound on the size of consensus segments. As show-case applications, we investigate a yeast transcriptome and show that consensus segments provide a robust means of identifying transcriptomic units. This approach is particularly suited for dense transcriptomes with polycistronic transcripts, operons, or a lack of separation between transcripts. As a second application, we demonstrate that consensus segmentations can be used to robustly identify growth regimes from sets of replicate growth curves