Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

Quantum Iterated Function Systems

Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting a QIFS consists of completely positive maps acting in the space of density operators. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant states.Comment: 12 pages, 1 figure include

Birth Size and Breast Cancer Risk: Re-analysis of Individual Participant Data from 32 Studies

BACKGROUND: Birth size, perhaps a proxy for prenatal environment, might be a correlate of subsequent breast cancer risk, but findings from epidemiological studies have been inconsistent. We re-analysed individual participant data from published and unpublished studies to obtain more precise estimates of the magnitude and shape of the birth size-breast cancer association. METHODS AND FINDINGS: Studies were identified through computer-assisted and manual searches, and personal communication with investigators. Individual participant data from 32 studies, comprising 22,058 breast cancer cases, were obtained. Random effect models were used, if appropriate, to combine study-specific estimates of effect. Birth weight was positively associated with breast cancer risk in studies based on birth records (pooled relative risk [RR] per one standard deviation [SD] [= 0.5 kg] increment in birth weight: 1.06; 95% confidence interval [CI] 1.02-1.09) and parental recall when the participants were children (1.02; 95% CI 0.99-1.05), but not in those based on adult self-reports, or maternal recall during the woman's adulthood (0.98; 95% CI 0.95-1.01) (p for heterogeneity between data sources = 0.003). Relative to women who weighed 3.000-3.499 kg, the risk was 0.96 (CI 0.80-1.16) in those who weighed or = 4.000 kg (p for linear trend = 0.001) in birth record data. Birth length and head circumference from birth records were also positively associated with breast cancer risk (pooled RR per one SD increment: 1.06 [95% CI 1.03-1.10] and 1.09 [95% CI 1.03-1.15], respectively). Simultaneous adjustment for these three birth size variables showed that length was the strongest independent predictor of risk. The birth size effects did not appear to be confounded or mediated by established breast cancer risk factors and were not modified by age or menopausal status. The cumulative incidence of breast cancer per 100 women by age 80 y in the study populations was estimated to be 10.0, 10.0, 10.4, and 11.5 in those who were, respectively, in the bottom, second, third, and top fourths of the birth length distribution. CONCLUSIONS: This pooled analysis of individual participant data is consistent with birth size, and in particular birth length, being an independent correlate of breast cancer risk in adulthood

Cerebrospinal Fluid Metals and the Association with Cerebral Small Vessel Disease

BACKGROUND: Brain metal homeostasis is essential for brain health, and deregulation can result in oxidative stress on the brain parenchyma. OBJECTIVE: Our objective in this study was to focus on two hemorrhagic MRI manifestations of small vessel disease [cerebral microbleeds (CMBs) and cortical superficial siderosis (cSS)] and associations with cerebrospinal fluid (CSF) iron levels. In addition, we aimed to analyze CSF biomarkers for dementia and associations with CSF metal levels. METHODS: This is a cross-sectional study of 196 patients who underwent memory clinic investigation, including brain MRI. CSF was collected and analyzed for metals, amyloid-β (Aβ) 42, total tau (T-tau), and phosphorylated tau (P-tau), and CSF/serum albumin ratios. Statistical analyses were performed using generalized linear models. RESULTS: No significant difference was found between CSF metal levels across diagnostic groups. Higher iron and copper levels were associated with higher CSF levels of Aβ42, T-tau, P-tau, and CSF/serum albumin ratios (p < 0.05). Zinc was associated with higher CSF/serum albumin ratios. There was no significant association between CMBs or cSS and CSF iron levels. An increase in CSF iron with the number of CMBs was seen in APOEɛ4 carriers. CONCLUSION: CSF iron levels are elevated with cerebral microbleeds in APOEɛ4 carriers, with no other association seen with hemorrhagic markers of small vessel disease. The association of elevated CSF iron and copper with tau could represent findings of increased neurodegeneration in these patients

Evaluating the risk of ovarian cancer before surgery using the ADNEX model to differentiate between benign, borderline, early and advanced stage invasive, and secondary metastatic tumours: prospective multicentre diagnostic study

Objectives To develop a risk prediction model to preoperatively discriminate between benign, borderline, stage I invasive, stage II-IV invasive, and secondary metastatic ovarian tumours. Design Observational diagnostic study using prospectively collected clinical and ultrasound data. Setting 24 ultrasound centres in 10 countries. Participants Women with an ovarian (including para-ovarian and tubal) mass and who underwent a standardised ultrasound examination before surgery. The model was developed on 3506 patients recruited between 1999 and 2007, temporally validated on 2403 patients recruited between 2009 and 2012, and then updated on all 5909 patients. Main outcome measures Histological classification and surgical staging of the mass. Results The Assessment of Different NEoplasias in the adneXa (ADNEX) model contains three clinical and six ultrasound predictors: age, serum CA-125 level, type of centre (oncology centres v other hospitals), maximum diameter of lesion, proportion of solid tissue, more than 10 cyst locules, number of papillary projections, acoustic shadows, and ascites. The area under the receiver operating characteristic curve (AUC) for the classic discrimination between benign and malignant tumours was 0.94 (0.93 to 0.95) on temporal validation. The AUC was 0.85 for benign versus borderline, 0.92 for benign versus stage I cancer, 0.99 for benign versus stage II-IV cancer, and 0.95 for benign versus secondary metastatic. AUCs between malignant subtypes varied between 0.71 and 0.95, with an AUC of 0.75 for borderline versus stage I cancer and 0.82 for stage II-IV versus secondary metastatic. Calibration curves showed that the estimated risks were accurate. Conclusions The ADNEX model discriminates well between benign and malignant tumours and offers fair to excellent discrimination between four types of ovarian malignancy. The use of ADNEX has the potential to improve triage and management decisions and so reduce morbidity and mortality associated with adnexal pathology

Predicting the risk of malignancy in adnexal masses based on the Simple Rules from the International Ovarian Tumor Analysis group

BACKGROUND: Accurate methods to preoperatively characterize adnexal tumors are pivotal for optimal patient management. A recent metaanalysis concluded that the International Ovarian Tumor Analysis algorithms such as the Simple Rules are the best approaches to preoperatively classify adnexal masses as benign or malignant. OBJECTIVE: We sought to develop and validate a model to predict the risk of malignancy in adnexal masses using the ultrasound features in the Simple Rules. STUDY DESIGN: This was an international cross-sectional cohort study involving 22 oncology centers, referral centers for ultrasonography, and general hospitals. We included consecutive patients with an adnexal tumor who underwent a standardized transvaginal ultrasound examination and were selected for surgery. Data on 5020 patients were recorded in 3 phases from 2002 through 2012. The 5 Simple Rules features indicative of a benign tumor (B-features) and the 5 features indicative of malignancy (M-features) are based on the presence of ascites, tumor morphology, and degree of vascularity at ultrasonography. Gold standard was the histopathologic diagnosis of the adnexal mass (pathologist blinded to ultrasound findings). Logistic regression analysis was used to estimate the risk of malignancy based on the 10 ultrasound features and type of center. The diagnostic performance was evaluated by area under the receiver operating characteristic curve, sensitivity, specificity, positive likelihood ratio (LR+), negative likelihood ratio (LR-), positive predictive value (PPV), negative predictive value (NPV), and calibration curves. RESULTS: Data on 4848 patients were analyzed. The malignancy rate was 43% (1402/3263) in oncology centers and 17% (263/1585) in other centers. The area under the receiver operating characteristic curve on validation data was very similar in oncology centers (0.917; 95% confidence interval, 0.901-0.931) and other centers (0.916; 95% confidence interval, 0.873-0.945). Risk estimates showed good calibration. In all, 23% of patients in the validation data set had a very low estimated risk (<1%) and 48% had a high estimated risk (≥30%). For the 1% risk cutoff, sensitivity was 99.7%, specificity 33.7%, LR+ 1.5, LR- 0.010, PPV 44.8%, and NPV 98.9%. For the 30% risk cutoff, sensitivity was 89.0%, specificity 84.7%, LR+ 5.8, LR- 0.13, PPV 75.4%, and NPV 93.9%. CONCLUSION: Quantification of the risk of malignancy based on the Simple Rules has good diagnostic performance both in oncology centers and other centers. A simple classification based on these risk estimates may form the basis of a clinical management system. Patients with a high risk may benefit from surgery by a gynecological oncologist, while patients with a lower risk may be managed locally

Coherent States Measurement Entropy

Coherent states (CS) quantum entropy can be split into two components. The dynamical entropy is linked with the dynamical properties of a quantum system. The measurement entropy, which tends to zero in the semiclassical limit, describes the unpredictability induced by the process of a quantum approximate measurement. We study the CS--measurement entropy for spin coherent states defined on the sphere discussing different methods dealing with the time limit $n \to \infty$. In particular we propose an effective technique of computing the entropy by iterated function systems. The dependence of CS--measurement entropy on the character of the partition of the phase space is analysed.Comment: revtex, 22 pages, 14 figures available upon request (e-mail: [email protected]). Submitted to J.Phys.

Perinatal Risk Factors for Diabetes in Later Life

OBJECTIVE—Low birth weight is consistently associated with an increased risk of type 2 diabetes in adulthood, but the individual contributions from poor fetal growth and preterm birth are not known. We therefore investigated the significance of these two factors separately