Graph theory, irreducibility, and structural analysis of differential-algebraic equation systems

The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of a system Jacobian is derived. This pattern implies a block-triangular form (BTF) of the DAE that can be exploited to speed up numerical solution. The paper compares this fine BTF with the usually coarser BTF derived from the sparsity pattern of the \sigmx. It defines a Fine-Block Graph with weighted edges, which gives insight into the relation between coarse and fine blocks, and the permitted ordering of blocks to achieve BTF. It also illuminates the structure of the set of normalised offset vectors of the DAE, e.g.\ this set is finite if and only if there is just one coarse block

How AD Can Help Solve Differential-Algebraic Equations

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical solution. This is often done with the help of a computer algebra system. We show in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the Dummy Derivatives method, here we give a mainly theoretical description, with tutorial examples. The second is the solution of a mechanical system directly from its Lagrangian formulation. Here we outline the theory and show several non-trivial examples of using the "Lagrangian facility" of the Nedialkov-Pryce initial-value solver DAETS, namely: a spring-mass-multipendulum system, a prescribed-trajectory control problem, and long-time integration of a model of the outer planets of the solar system, taken from the DETEST testing package for ODE solvers

In-depth critical analysis of complications following robot-assisted radical cystectomy with intracorporeal urinary diversion

Background: Robot-assisted radical cystectomy with intracorporeal urinary diversion (iRARC) is an attractive option to open cystectomy, but the benefit in terms of improved outcomes is not established. Objective: To evaluate the early postoperative morbidity and mortality of patients undergoing iRARC and conduct a critical analysis of complications using standardised reporting criteria as stratified according to urinary diversion. Design, setting, and participants: A total of 134 patients underwent iRARC for bladder cancer at a single centre between June 2011 and July 2015. Intervention: Radical cystectomy with iRARC. Outcome measurements and statistical analysis: Patient demographics, pathologic data, and 90-d perioperative mortality and complications were recorded. Complications were reported according to the Clavien-Dindo (CD) classification and stratified according to urinary diversion type and either surgical or medical complications. The chi-square test and t test were used for categorical and continuous variables respectively. Multivariable logistic regression was performed on variables with significance in univariate analysis. Results and limitations: The 90-d all complication rate following ileal conduit and continent diversion was 68% and 82.4%, and major complications were 21.0% and 20.6% respectively. The 90-d mortality was 3% and 2.9% for ileal conduit and continent diversion patients, respectively. On multivariate analysis, the blood transfusion requirement was independently associated with major complications (p = 0.002) and all 30-d (p = 0.002) and 90-d (p = 0.012) major complications. Male patients were associated with 90-d major complications (p = 0.015). Critical analysis identified that surgical complications were responsible for 39.4% of all 90-d major complications. The incidence of surgical complications did not decline with increasing number of iRARC cases performed (p = 0.742, r = 0.31). Limitations of this study include its retrospective nature, limited sample size, and limited multivariate analysis due to the low number of major complications events. Conclusions: Although complications following iRARC are common, most are low grade. A critical analysis identified surgical complications as a cause of major complications. Addressing this issue could have a significant impact on lowering the morbidity associated with iRARC. Patient summary: We looked at the surgical outcomes in bladder cancer patients treated with minimally invasive robotic surgery. We found that surgical complications account for most major complications and previous surgical experience may be a confounding factor when interpreting results from a different centre even in a randomised trial setting

Shock temperature measurements in metals: New results for an Fe alloy

The temperature of a Fe-Cr-Ni alloy (304 stainless steel) has been measured during shock compression using a high-speed radiometric technique. Experiments were performed on high-quality thick films deposited on sapphire and LiF windows. The samples had no observable porosity or defects and closely meet the ideal criteria for shock temperature measurements. Data obtained with both Al_2O_3 and LiF windows are internally consistent, indicating that they remain transparent to high pressures and are thus suitable windows for shock temperature measurements. Our data yield stainless steel melting temperatures ranging from 4570±310K at 138 GPa to 5710±340 K at 215 GPa, and additionally provide bounds on the initial Hugoniot temperatures of the sample between 5600±340 K at 234 GPa (near the solidus) and 6580±440 K at 283 (in the liquid field). Taken together, these data define a smooth curve for melting of the alloy up to 271 GPa and 5860 K, which should represent a point on the Iiquidus. Melting along the Hugoniot begins at approximately 234 GPa and 5600 K, as compared with 242 GPa and 6400 K for pure Fe. At the pressure of the inner core-outer core boundary, the melting point of 304 stainless steel is lower than that of pure Fe by ≈ 1450 K, as compared with only 110 K at 1 atm. These results demonstrate that upon alloying with Ni and Cr the melting point depression of Fe and thus material likely to comprise the inner core increases with increasing pressure

Benefits of robotic cystectomy with intracorporeal diversion for patients with low cardiorespiratory fitness: a prospective cohort study

Background: Patients undergoing radical cystectomy have associated comorbidities resulting in reduced cardiorespiratory fitness. Preoperative cardiopulmonary exercise testing (CPET) measures including anaerobic threshold (AT) can predict major adverse events (MAE) and hospital length of stay (LOS) for patients undergoing open and robotic cystectomy with extracorporeal diversion. Our objective was to determine the relationship between CPET measures and outcome in patients undergoing robotic radical cystectomy and intracorporeal diversion (intracorporeal robotic assisted radical cystectomy [iRARC]). Methods: A single institution prospective cohort study in patients undergoing iRARC for muscle invasive and high-grade bladder cancer. Inclusion: patients undergoing standardised CPET before iRARC. Exclusions: patients not consenting to data collection. Data on CPET measures (AT, ventilatory equivalent for carbon dioxide [VE/VCO2] at AT, peak oxygen uptake [VO2]), and patient demographics prospectively collected. Outcome measurements included hospital LOS; 30-day MAE and 90-day mortality data, which were prospectively recorded. Descriptive and regression analyses were used to assess whether CPET measures were associated with or predicted outcomes. Results: From June 2011 to March 2015, 128 patients underwent radical cystectomy (open cystectomy, n = 17; iRARC, n = 111). A total of 82 patients who underwent iRARC and CPET and consented to participation were included. Median (interquartile range): age = 65 (58–73); body mass index = 27 (23–30); AT = 10.0 (9–11), Peak VO2 = 15.0 (13–18.5), VE/VCO2 (AT) = 33.0 (30–38). 30-day MAE = 14/111 (12.6%): death = 2, multiorgan failure = 2, abscess = 2, gastrointestinal = 2, renal = 6; 90-day mortality = 3/111 (2.7%). AT, peak VO2, and VE/VCO2 (at AT) were not significant predictors of 30-day MAE or LOS. The results are limited by the absence of control group undergoing open surgery. Conclusions: Poor cardiorespiratory fitness does not predict increased hospital LOS or MAEs in patients undergoing iRARC. Overall, MAE and LOS comparable with other series

Water Table Management Reduces Tile Nitrate Loss in Continuous Corn and in a Soybean-Corn Rotation

Water table management systems can be designed to alleviate soil water excesses and deficits, as well as reduce nitrate leaching losses in tile discharge. With this in mind, a standard tile drainage (DR) system was compared over 8 years (1991 to 1999) to a controlled tile drainage/subirrigation (CDS) system on a low-slope (0.05 to 0.1%) Brookston clay loam soil (Typic Argiaquoll) in southwestern Ontario, Canada. In the CDS system, tile discharge was controlled to prevent excessive drainage, and water was pumped back up the tile lines (subirrigation) to replenish the crop root zone during water deficit periods. In the first phase of the study (1991 to 1994), continuous corn (Zea mays, L.) was grown with annual nitrogen (N) fertilizer inputs as per local soil test recommendations. In the second phase (1995 to 1999), a soybean (Glycine max L., Merr.)-corn rotation was used with N fertilizer added only during the two corn years. In Phase 1 when continuous corn was grown, CDS reduced total tile discharge by 26% and total nitrate loss in tile discharge by 55%, compared to DR. In addition, the 4-year flow weighted mean (FWM) nitrate concentration in tile discharge exceeded the Canadian drinking water guideline (10 mg N l–1) under DR (11.4 mg N l–1), but not under CDS (7.0 mg N l–1). In Phase 2 during the soybean-corn rotation, CDS reduced total tile discharge by 38% and total nitrate loss in tile discharge by 66%, relative to DR. The 4-year FWM nitrate concentration during Phase 2 in tile discharge was below the drinking water guideline for both DR (7.3 mg N l–1) and CDS (4.0 mg N l–1). During both phases of the experiment, the CDS treatment caused only minor increases in nitrate loss in surface runoff relative to DR. Hence CDS decreased FWM nitrate concentrations, total drainage water loss, and total nitrate loss in tile discharge relative to DR. In addition, soybean-corn rotation reduced FWM nitrate concentrations and total nitrate loss in tile discharge relative to continuous corn. CDS and crop rotations with reduced N fertilizer inputs can thus improve the quality of tile discharge water substantially