Pseudo-High-Order Symplectic Integrators

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa

On the relationship between instability and Lyapunov times for the 3-body problem

In this study we consider the relationship between the survival time and the Lyapunov time for 3-body systems. It is shown that the Sitnikov problem exhibits a two-part power law relationship as demonstrated previously for the general 3-body problem. Using an approximate Poincare map on an appropriate surface of section, we delineate escape regions in a domain of initial conditions and use these regions to analytically obtain a new functional relationship between the Lyapunov time and the survival time for the 3-body problem. The marginal probability distributions of the Lyapunov and survival times are discussed and we show that the probability density function of Lyapunov times for the Sitnikov problem is similar to that for the general 3-body problem.Comment: 9 pages, 19 figures, accepted for publication in MNRA

Basal cell carcinoma treated successfully with combined CO2 laser and photodynamic therapy in a renal transplant patient: a case report

Renal transplant recipients are at significantly greater risk of developing skin malignancies due to combination immunosuppressive therapy. A significant number of patients present with lesions needing excision at multiple outpatient follow-up visits. For basal cell carcinoma, we have recently described how combining CO2 laser with Photodynamic therapy greatly increases the efficacy of long-term tumour clearance compared with each modality alone. We present a case of a 66-year-old renal transplant therapy patient who repeatedly presents with new skin malignancies, in whom we treated successfully with Laser-Photodynamic therapy in a see-and-treat setting. This therapy offers patients the possibility of better cosmetic and functional results whilst obviating the need for repeated surgery. Other pre-cancerous lesions such as solar keratoses are prevalent in this patient group and respond extremely well to Photodynamic therapy monotherapy. We propose a regular clinic for renal transplant patients in a laser facility equipped with CO2 laser and Photodynamic therapy, histopathology and punch-biopsy materials. This strategy allows simple and effective treatment of multiple lesions simultaneously, avoidance of numerous operations, avoidance of non-essential outpatient appointments that result in booking furthers visits for treatment, whilst facilitating diagnostic biopsies of potentially malignant lesions. We outline a care pathway for a see-and-treat clinic that implements this novel treatment modality improving the care of this unique patient population

Intestinal permeability and faecal Granulocyte Marker Protein in Dextran Sulphate Sodium - induced colitis in rats

The aims of this preliminary study were to foster the development of an animal model of inflammatory bowel disease (IBD). We hereby studied the effects of dextran sulphate sodium (DSS) in drinking water on (a) intestinal permeability and (b) faecal levels of granulocyte marker protein (GMP) in rats. Methods were adopted to keep stress at a minimum. The animals had free access to DSS for 36 or 96 hrs. Controls received only water. Oral administration of 51Cr-labelled ethylenediaminetetraacetic acid (51CrEDTA) is used for clinical evaluation of intestinal permeability in IBD. 51CrEDTA was administered by training the animals to drink a given quantity of fluid within 5 minutes in a specific environment. On the test day, they voluntarily consumed 1 ml water containing 2 μCi 51CrEDTA. Urine samples were taken from filter paper in their home-cages for 6 hrs and radioactivity measured in a gamma counter. Faecal samples were collected after 36 and 96 hrs on DSS or water for GMP analysis. RESULTS: GMP was elevated in the DSSinduced animals after both 36 hrs (p<.05) and 96 hrs (p<.01), the elevation being greater after 96 hrs. Consumption of DSS increased the urinary excretion of 51CrEDTA after 36 hrs, but not after 96 hrs. Only DSS consumption for 96 hrs resulted in visible colonic erosions in either the proximal, mid or distal part of the colon. CONCLUSION: DSS has an acute effect upon urinary excretion of 51CrEDTA, and 96 hrs of access to DSS is sufficient to induce elevated GMP levels and colonic erosions in adult rats

Retrospective computed tomography analysis of endotracheal tube constriction & mispositioning in cats & dogs

Objectives: To discover the prevalence of endotracheal tube (ETT) constriction and rostral and caudal mispositioning in anaesthetised cats and dogs, and to identify associated risk factors. Study Design: Retrospective analysis. Animal population: A total of 146 cats, 670 dogs. Methods: Computed tomography images of the head/neck/thorax from orotracheally intubated cats and dogs were visually assessed for constriction or mispositioning of the ETT. If constriction was present, measurements of the cross-sectional area (CSA) of the ETT lumen at constricted and un-constricted locations were compared. Location and cause of constriction were noted and the expected increase in resistance to gas flow was calculated. Animal information was collected from clinical records. Normality of continuous variables was assessed via the Shapiro-Wilk test. Chi square tests examined associations between variables. Kendall’s tau-b test was performed between measured ETT size and degree of constriction. Results: The ETT extended rostrally beyond incisors in 52% of cases; the connector was within the oral cavity in 19% of cases. The ETT extended beyond the first rib in 25.5% of cases. The prevalence of ETT constriction was 22.7%. Median reduction in CSA was 7.68% (0.14–64.19%). Median increase in resistance assuming laminar and turbulent flow was 16.5% (0.3–680%) and 21% (0.3–1200%), respectively. The most common cause of constriction was the presence of a radiotherapy mouth gag. Significant associations existed between presence of constriction and rostral mispositioning, and caudal mispositioning and extreme brachycephaly. Increased severity of constriction was more likely in smaller ETT. Conclusions: And clinical relevance Constriction and mispositioning of ETT occurred very commonly in this population. Checking the ETT within the oral cavity for constriction and mispositioning is recommended. Radiotherapy mouth gags increase the risk of ETT compression. Smaller ETT are at greater risk of severe constriction. Brachycephalic dogs are at particular risk of caudal mispositioning

The Full-sky Astrometric Mapping Explorer -- Astrometry for the New Millennium

FAME is designed to perform an all-sky, astrometric survey with unprecedented accuracy. It will create a rigid astrometric catalog of 4x10^7 stars with 5 < m_V < 15. For bright stars, 5 < m_V < 9, FAME will determine positions and parallaxes accurate to < 50 microarcseconds, with proper motion errors < 50 microarcseconds/year. For fainter stars, 9 < m_V < 15, FAME will determine positions and parallaxes accurate to < 500 microarcseconds, with proper motion errors < 500 microarcseconds/year. It will also collect photometric data on these 4 x 10^7 stars in four Sloan DSS colors.Comment: 6 pages, 4 figures, to appear in "Working on the Fringe

Laryngeal transplantation in minipigs: vascular, myologic and functional outcomes

There is no effective way of replacing all the functions of the larynx in those requiring laryngectomy. Regenerative medicine offers promise, but cannot presently deliver implants with functioning neuromuscular units. A single well-documented laryngeal transplant in man was a qualified success, but more information is required before clinical trials may be proposed. We studied the early response of the larynx to laryngeal transplantation between 17 pairs of NIH minipigs full matched at the MHC2 locus. Following iterative technical improvements, pigs had good swallowing and a patent airway at 1 week. No significant changes in mucosal blood flux were observed compared with pre-operative measurements. Changes in muscle morphology and fibre phenotype were observed in transplant muscles retrieved after 7 days: the levels of fast and slow myosin heavy chain (MyHC) protein were reduced and embryonic MyHC was up regulated consistent with denervation induced atrophy. At 1 week laryngeal transplantation can result in good swallowing, and is not associated with clinical evidence of ischemia-reperfusion injury in MHC-matched pigs