KAM-tori near an analytic elliptic fixed point

We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector \o_0 is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a R\"ussmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that \o_0 has rationally independent coordinates). If the Birkhoff normal form is degenerate, there exists an analytic subvariety of complex dimension at least $d+1$ passing through 0 that is foliated by complex analytic KAM-tori with frequency $\omega_0$. This is an extension of previous results obtained in \cite{EFK} to the case of an elliptic fixed point

Educational Intervention Improves Proton Pump Inhibitor Stewardship in Outpatient Gastroenterology Clinics

Background Improper chronic proton pump inhibitor (PPI) use has risen significantly in the last few decades. In our gastroenterology trainees’ clinics, we aimed to optimize PPI usage. Methods We collected baseline data on patients’ PPI use for 8 weeks. Based on gastroenterology society guidelines, we determined conditions for appropriate PPI use. If the indication could not be determined, it was categorized as “unknown”. Generated from the three most frequent causes for inappropriate PPI use, interventions were developed to correct each issue. Following a brief educational session, trainees implemented these interventions over a subsequent 8-week interval. Results During our pre-intervention period, trainees evaluated 263 patients who were prescribed a PPI. In 49% of the cases, the use of PPI was deemed inappropriate. The most common reasons were: gastroesophageal reflux disease (GERD) which was never titrated to the lowest effective dose, twice daily dosing for Barrett’s esophagus (BE) chemoprevention and unknown indication. During our intervention period, trainees evaluated 145 patients prescribed a PPI for GERD with well-controlled symptoms in 101 cases. PPI had not been titrated to lowest effective dose in 37 cases prompting intervention which was successful in 23 cases. PPI indication was unknown in 17 cases prompting a message to the prescribing provider to review appropriateness. Two cases of BE chemoprevention with twice daily dosing were appropriately reduced to daily dosing. Ultimately, after intervention, PPI use was deemed appropriate after intervention in 172 (77%) cases. Conclusions Improper chronic PPI use was significant. Focusing intervention efforts on PPI use for GERD, BE and unknown indications substantially increased appropriateness of PPI use

Network Mutual Information and Synchronization under Time Transformations

We investigate the effect of general time transformations on the phase synchronization (PS) phenomenon and the mutual information rate (MIR) between pairs of nodes in dynamical networks. We demonstrate two important results concerning the invariance of both PS and the MIR. Under time transformations PS can neither be introduced nor destroyed and the MIR cannot be raised from zero. On the other hand, for proper time transformations the timing between the cycles of the coupled oscillators can be largely improved. Finally, we discuss the relevance of our findings for communication in dynamical networks.Comment: 15 p

Towards a method for rigorous development of generic requirements patterns

We present work in progress on a method for the engineering, validation and verification of generic requirements using domain engineering and formal methods. The need to develop a generic requirement set for subsequent system instantiation is complicated by the addition of the high levels of verification demanded by safety-critical domains such as avionics. Our chosen application domain is the failure detection and management function for engine control systems: here generic requirements drive a software product line of target systems. A pilot formal specification and design exercise is undertaken on a small (twosensor) system element. This exercise has a number of aims: to support the domain analysis, to gain a view of appropriate design abstractions, for a B novice to gain experience in the B method and tools, and to evaluate the usability and utility of that method.We also present a prototype method for the production and verification of a generic requirement set in our UML-based formal notation, UML-B, and tooling developed in support. The formal verification both of the structural generic requirement set, and of a particular application, is achieved via translation to the formal specification language, B, using our U2B and ProB tools

Simulation of the effect of microstructure on electromigration induced failure of interconnects

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1997.Includes bibliographical references (leaves 85-87).by Walid R. Fayad.M.S

Microstructure evolution and interconnect realiability

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2000.Includes bibliographical references (leaves 207-213).In the context of predicting the effects of geometry, microstructure, and processing conditions on electromigration (EM) induced interconnect failure, normal grain growth in thin films was studied, analytic models were built for the grain structure statistics in 2D and 3D interconnects, and simulation programs were developed for generation of process and complex-geometry-sensitive interconnect structures. The models were validated through simulations and experiments and were integrated into tools for circuit-design level interconnect reliability predictions. The universal scaling behavior of 2D normal grain growth was demonstrated and characterized using a simulation of 2D grain growth (GGSim). We showed that the constant rate of change of the average grain area is equal to the grain boundary mobility constant pt. We also found that the steady state grain size distribution obtained using our simulation technique, as well as those reported in experiments on simple model systems and those reported for very different simulation techniques, are all very well fit by a Weibull distribution function with the dimensionless parameter p = 5/2, and are better fit by this function than the log normal, Gamma or Rayleigh functions. The 2D simulation was used to simulate the development of film structures with drag induced lognormal grain size distributions from which interconnect strips were etched and then annealed, in order to analyze the statistics of as-patterned, as well as post-pattern annealed, interconnect grain structures. These statistics were characterized as a function of the ratios of the line-widths to the initial-grain-sizes. Among the important findings is that polygranular cluster and bamboo segment length distributions for as-patterned lines are best fit by Weibull distribution functions. Analytic formulae describing grain structure statistics were reported, for usage in EM simulations and reliability predictions. A differential model predicting the evolution of the polygranular cluster length distribution during post-patterning annealing was developed. It was shown that the rate of bamboo-segment nucleation per unit time and unit of untransformed length is proportional to [mu]/w 3 , and is negligible in the growth-dominated steady-state. The cluster shrinkage velocity was demonstrated to reach a constant steady-state value proportional to [mu]/w (assuming constant and uniform [mu]). This was shown to lead to a time-invariant, steady-state exponential cluster length distribution with an average cluster length proportional to the strip width, and a cluster length fraction decaying exponentially with U=[mu]/w2 . The distribution of grain lengths in the resulting final bamboo grain structure is well fit by a log normal distribution, with a median grain length scaling with the line width, and a line-width-independent normalized deviation in the grain length. This result was used to show, using an EM simulation, that grain-orientation-dependent variations in surface diffusivities constitute a likely cause for the variabilities in lifetimes observed experimentally. The 2D simulation GGSim was also substantially modified to simulate the patterning of interconnect features of general shapes from polygranular thin film structures, as well as to simulate further grain structure evolution due to post-patterning annealing in these complex shapes. A grain structure extraction tool, PolySeg, was developed to allow extraction of the atomic transport details in the case of complex interconnect trees for EM reliability predictions using EM simulations. To assess the 3D effects on grain structure evolution, and therefore on interconnect reliability, a soap froth experiment was used to study 3D normal grain growth in long rectangular prisms. The kinetics were found to scale with the normalized time [mu]/w 2 (with w being the largest of the two prism cross-sectional dimensions). It was found that the normalized duration of the conversion from 3D (non-columnar) to 2D (columnar) structures and the normalized duration of the initial phase during which the structure was polygranular became longer as w/h approached 1. The same results obtained in the 2D case for the scaling behaviors of the bamboo nucleation rate and the polygranular cluster shrinkage rate were demonstrated. Based on a 2D approach, a prism-geometry-sensitive analytic model was developed for the transformation to fully-bamboo structures. These results were compared with preliminary results obtained using a 3D grain growth simulation and qualitative agreement was demonstrated. We have successfully captured with simple analytic models as well as elaborate simulations the physics of microstructure evolution in complex patterned thin-film structures. In particular, we have developed an array of models and simulations that can be used to investigate the impact of geometry and process history on microstructure evolution, and ultimately on EM-induced failure statistics.by Walid R. Fayad.Ph.D

Should We Measure Adenoma Detection Rate for Gastroenterology Fellows in Training?

Background: Adenoma detection rate (ADR) is a proven quality metric for colonoscopy. The value of ADR for the evaluation of gastroenterology fellows is not well established. The aim of this study is to calculate and evaluate the utility of ADR as a measure of competency for gastroenterology fellows. Methods: Colonoscopies for the purposes of screening and surveillance, on which gastroenterology fellows participated at the Richard L. Roudebush VAMC (one of the primary training sites at Indiana University), during a 9-month period, were included. ADR, cecal intubation rate, and indirect withdrawal time were measured. These metrics were compared between the levels of training. Results: A total of 591 screening and surveillance colonoscopies were performed by 14 fellows. This included six, four and four fellows, in the first, second and third year of clinical training, respectively. Fellows were on rotation at the VAMC for a mean of 1.9 months (range 1 to 3 months) during the study period. The average ADR was 68.8% (95% CI 65.37 - 72.24). The average withdrawal time was 27.59 min (95% CI 23.45 - 31.73). The average cecal intubation rate was 99% (95% CI 98-100%). There was no significant difference between ADRs, cecal intubation rates, and withdrawal times at different levels of training; however, a trend toward swifter withdrawal times with advancing training was noted. Conclusions: ADR appears not to be a useful measure of competency for gastroenterology fellows. Consideration should be given to alternative metrics that could avoid bias and confounders

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie

Improving Colorectal Cancer Screening Rates in Patients Referred to a Gastroenterology Clinic

Colorectal cancer (CRC) is the third most common cancer and the second leading cause of cancer-related death in the United States. Colonoscopy and fecal immunochemistry testing (FIT) are the primary recommended CRC screening modalities. The purpose of this study is to improve rates of CRC screening in Veterans and County hospital patients referred to gastroenterology fellow's clinics. A total of 717 patients between ages of 49 and 75 years were seen. Previous CRC screening was not performed in 109 patients (15.2%) because of not being offered (73.4%) or declining (26.6%) screening. Patients who received previous CRC screening compared with no previous screening were older (mean age 62.3 years vs. 60.3 years, p < .003), white (88.6% vs. 78.3%, p < .027), and more likely to be Veterans patients (90.8% vs. 77.5%, p < .001). After systematically discussing options for screening with 78 of the 109 unscreened patients, 56 of them (71.8%) underwent screening with either colonoscopy (32) or FIT (24). Patients seen by fellows in their last year of training agreed to undergo screening more often than those seen by other fellows (100% vs. 66.2%, p < .033). Systematic discussions about both colonoscopy and FIT can improve the overall rates of CRC screening