Observability and nonlinear filtering

This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a model observable if no two initial measures of the signal process give rise to the same law of the observation process. We demonstrate that observability implies stability of the filter, i.e., the filtered estimates become insensitive to the initial measure at large times. For the special case where the signal is a finite-state Markov process and the observations are of the white noise type, a complete (necessary and sufficient) characterization of filter stability is obtained in terms of a slightly weaker detectability condition. In addition to observability, the role of controllability in filter stability is explored. Finally, the results are partially extended to non-compact signal state spaces

Applying an Anti-reflux Suture in the One Anastomosis Gastric Bypass to Prevent Biliary Reflux:a Long-Term Observational Study

INTRODUCTION: The one anastomosis gastric bypass (OAGB) is an effective treatment to induce sustained weight loss in morbidly obese patients. Concerns remain regarding the development of reflux. The aim of this study was to investigate the effect of an "anti-reflux suture" as anti-reflux modification to prevent reflux. METHOD: This is a single-center retrospective cohort study of patients who underwent a primary OAGB at the Center Obesity North-Netherlands (CON) between January 2015 and December 2016. Reflux was defined as symptoms of acid/bilious regurgitation or pyrosis. This was consequently asked and reported at each follow-up visit. Outcomes of patients with an anti-reflux suture were compared to those without. RESULTS: In 414 (59%) of the 703 included patients, an anti-reflux suture was applied. Follow-up at 3 years was 74%. The incidence of reflux did not differ between patients with or without an anti-reflux suture (57 versus 56%, respectively; P = 0.9). The presence of an anti-reflux suture was significantly associated with a lower incidence of conversion to Roux-en-Y gastric bypass (RYGB) for reflux (OR 0.56, 95%CI 0.34-0.91). Patients preoperatively diagnosed with gastroesophageal reflux disease (GERD) were 5.2 times more likely to need a conversion to RYGB for reflux (95%CI 2.7-10.1). CONCLUSION: The presence of preoperative GERD should be weighted heavily in the decision to perform an OAGB as this is a major risk factor for conversion surgery due to reflux. The anti-reflux suture might be a valuable addition to the procedure of the OAGB because it results in fewer conversion surgeries for reflux

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.

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

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>

Birth weight is associated with postmenopausal breast cancer risk in Swedish women

There is some evidence that birth weight is associated with breast cancer. Whether this association differs between premenopausal and postmenopausal ages is still unclear. The results from this study suggest that higher birth weight is a risk factor for postmenopausal breast cancer (OR 1.06, CI 1.00-1.12, per 100 g), independent of selected early-life and adult factors

Birth characteristics and risk of colorectal cancer: a study among Swedish twins

Type-2 diabetes increases the risk of colorectal cancer, and is also associated with low birth weight. However, we found no evidence of associations between birth characteristics and risk of colorectal cancer (m=248) among Swedish twins

Strategies to diagnose ovarian cancer: new evidence from phase 3 of the multicentre international IOTA study

Background: To compare different ultrasound-based international ovarian tumour analysis (IOTA) strategies and risk of malignancy index (RMI) for ovarian cancer diagnosis using a meta-analysis approach of centre-specific data from IOTA3. Methods: This prospective multicentre diagnostic accuracy study included 2403 patients with 1423 benign and 980 malignant adnexal masses from 2009 until 2012. All patients underwent standardised transvaginal ultrasonography. Test performance of RMI, subjective assessment (SA) of ultrasound findings, two IOTA risk models (LR1 and LR2), and strategies involving combinations of IOTA simple rules (SRs), simple descriptors (SDs) and LR2 with and without SA was estimated using a meta-analysis approach. Reference standard was histology after surgery. Results: The areas under the receiver operator characteristic curves of LR1, LR2, SA and RMI were 0.930 (0.917–0.942), 0.918 (0.905–0.930), 0.914 (0.886–0.936) and 0.875 (0.853–0.894). Diagnostic one-step and two-step strategies using LR1, LR2, SR and SD achieved summary estimates for sensitivity 90–96%, specificity 74–79% and diagnostic odds ratio (DOR) 32.8–50.5. Adding SA when IOTA methods yielded equivocal results improved performance (DOR 57.6–75.7). Risk of Malignancy Index had sensitivity 67%, specificity 91% and DOR 17.5. Conclusions: This study shows all IOTA strategies had excellent diagnostic performance in comparison with RMI. The IOTA strategy chosen may be determined by clinical preference

External validation of the ovarian-adnexal reporting and data system (O-RADS) lexicon and the international ovarian tumor analysis 2-step strategy to stratify ovarian tumors into O-RADS risk groups.

IMPORTANCE: Correct diagnosis of ovarian cancer results in better prognosis. Adnexal lesions can be stratified into the Ovarian-Adnexal Reporting and Data System (O-RADS) risk of malignancy categories with either the O-RADS lexicon, proposed by the American College of Radiology, or the International Ovarian Tumor Analysis (IOTA) 2-step strategy. OBJECTIVE: To investigate the diagnostic performance of the O-RADS lexicon and the IOTA 2-step strategy. DESIGN, SETTING, AND PARTICIPANTS: Retrospective external diagnostic validation study based on interim data of IOTA5, a prospective international multicenter cohort study, in 36 oncology referral centers or other types of centers. A total of 8519 consecutive adult patients presenting with an adnexal mass between January 1, 2012, and March 1, 2015, and treated either with surgery or conservatively were included in this diagnostic study. Twenty-five patients were excluded for withdrawal of consent, 2777 were excluded from 19 centers that did not meet predefined data quality criteria, and 812 were excluded because they were already in follow-up at recruitment. The analysis included 4905 patients with a newly detected adnexal mass in 17 centers that met predefined data quality criteria. Data were analyzed from January 31 to March 1, 2022. EXPOSURES: Stratification into O-RADS categories (malignancy risk <1%, 1% to <10%, 10% to <50%, and ≥50%). For the IOTA 2-step strategy, the stratification is based on the individual risk of malignancy calculated with the IOTA 2-step strategy. MAIN OUTCOMES AND MEASURES: Observed prevalence of malignancy in each O-RADS risk category, as well as sensitivity and specificity. The reference standard was the status of the tumor at inclusion, determined by histology or clinical and ultrasonographic follow-up for 1 year. Multiple imputation was used for uncertain outcomes owing to inconclusive follow-up information. RESULTS: Median age of the 4905 patients was 48 years (IQR, 36-62 years). Data on race and ethnicity were not collected. A total of 3441 tumors (70%) were benign, 978 (20%) were malignant, and 486 (10%) had uncertain classification. Using the O-RADS lexicon resulted in 1.1% (24 of 2196) observed prevalence of malignancy in O-RADS 2, 4% (34 of 857) in O-RADS 3, 27% (246 of 904) in O-RADS 4, and 78% (732 of 939) in O-RADS 5; the corresponding results for the IOTA 2-step strategy were 0.9% (18 of 1984), 4% (58 of 1304), 30% (206 of 690), and 82% (756 of 927). At the 10% risk threshold (O-RADS 4-5), the O-RADS lexicon had 92% sensitivity (95% CI, 87%-96%) and 80% specificity (95% CI, 74%-85%), and the IOTA 2-step strategy had 91% sensitivity (95% CI, 84%-95%) and 85% specificity (95% CI, 80%-88%). CONCLUSIONS AND RELEVANCE: The findings of this external diagnostic validation study suggest that both the O-RADS lexicon and the IOTA 2-step strategy can be used to stratify patients into risk groups. However, the observed malignancy rate in O-RADS 2 was not clearly below 1%