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

Outcomes of the One Anastomosis Gastric Bypass with Various Biliopancreatic Limb Lengths:a Retrospective Single-Center Cohort Study

Introduction: One anastomosis gastric bypass (OAGB) is an effective and safe treatment for morbidly obese patients. Longer biliopancreatic (BP) limb length is suggested to result in better weight loss outcomes, but to date, no data are available for the OAGB to substantiate this. We hypothesized that applying a longer BP-limb length in the higher BMI classes would result in more weight reduction so that the attained BMI would be comparable to patients with a lower BMI, thereby compensating for differences in baseline BMI. Method: A retrospective cohort study in patients who underwent a primary OAGB at a teaching hospital in the Netherlands between January 2015 and December 2016. BP-limb length was tailored based on preoperative BMI. Patients were divided into three different groups depending on the length of the BP-limb: 150, 180, and 200 cm. Weight loss outcomes after 1 and 3 years and resolution of comorbidities were compared between these groups. Results: Of the 632 included patients, a BP-limb length of 150 cm was used in 172 (27.2%), 180 cm in 388 (61.4%), and 200 cm in 72 (11.4%) patients. Despite more BMI loss, %EWL was lower and attained BMI remained higher in the groups with longer BP-limb lengths. After adjustment for the confounder preoperative BMI, longer BP-limb lengths were not associated with higher BMI loss. There was no difference in remission rates of comorbidities. Conclusion: Attained BMI remained higher in spite of tailoring BP-limb length according to baseline BMI with no differences in remission rates of comorbidities

Tailoring limb length based on total small bowel length in one anastomosis gastric bypass surgery (TAILOR study):study protocol for a randomized controlled trial

Background: The one anastomosis gastric bypass (OAGB) is being performed by an increasing number of bariatric centers over the world. However, the optimal length of the biliopancreatic (BP) limb remains a topic of discussion. Retrospective studies suggest the benefit of tailoring BP-limb length; however, randomized trials are lacking. The aim of this study is to investigate whether tailoring the length of the BP-limb based on total small bowel length (TSBL) leads to better results in terms of weight loss, vitamin deficiencies, and bowel movements compared to a fixed BP-limb length. Methods: The TAILOR study is a double-blind single-center randomized controlled trial. Patients scheduled for primary OAGB surgery will be randomly allocated either to a standard BP-limb of 150 cm or to a BP-limb length based on their TSBL: TSBL 700 cm, BP-limb 210 cm. The primary outcome is to compare the percent total weight loss (%TWL) at 5 years between the two groups. Secondary outcomes include nutritional deficiencies, remission of comorbidities, symptoms of dumping, quality of life, and daily bowel movements. The study includes a total of 212 patients and is designed to detect a 5% difference in the primary endpoint. Discussion: The TAILOR study will provide new insights into the effect of different BP-limb lengths and the role of the TSBL in the OAGB. The study is designed to provide guidance for bariatric surgeons to determine the optimal BP-limb length in the OAGB

Laparoscopic Small Bowel Length Measurement in Bariatric Surgery Using a Hand-Over-Hand Technique with Marked Graspers:an Ex Vivo Experiment

Introduction Tailoring limb length in bariatric surgery is a subject of many studies. To acquire the optimal limb length, accurate measurement of the small bowel length is essential. Objective To assess the intra- and inter-individual variability of laparoscopic bowel length measurement using a hand-over-hand technique with marked graspers. Method Four bariatric surgeons and four surgical residents performed measurements on cadaver porcine intestine in a laparoscopic box using marked graspers. Each participant performed 10 times a measurement of three different lengths: 150, 180, and 210 cm. Acceptable percentage deviation from the goal lengths was defined as less than 10%, while unacceptable deviations were defined as more than 15%. Results The bariatric surgeons measured the 150-, 180-, and 210-cm tasks with 4% (CI 0.4, 9), - 6% (CI - 11, - 0.8), and 1% (CI - 4, 6) deviation, respectively. In total, the bariatric surgeons estimated 58 out of 119 times (49%) between the margins of 10% deviation and 36 times (30%) outside the 15% margin. Considerable inter-individual differences were found between the surgeons. The surgical residents underestimated the tasks with 12% (CI - 18, - 6), 16% (CI - 19, - 13), and 18% (CI - 22, - 13), respectively. Conclusion Bariatric surgeons estimated bowel length with on average less than 10% deviation. However, this still resulted in 30% of the measurements with more than 15% deviation. There were considerable inter-individual differences between the surgeons and residents structurally underestimated the bowel length. Ascertainment of measurement accuracy and adequate training is essential for bariatric procedures in which limb length is of importance

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.

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