Time-Symmetrized Kustaanheimo-Stiefel Regularization

In this paper we describe a new algorithm for the long-term numerical integration of the two-body problem, in which two particles interact under a Newtonian gravitational potential. Although analytical solutions exist in the unperturbed and weakly perturbed cases, numerical integration is necessary in situations where the perturbation is relatively strong. Kustaanheimo--Stiefel (KS) regularization is widely used to remove the singularity in the equations of motion, making it possible to integrate orbits having very high eccentricity. However, even with KS regularization, long-term integration is difficult, simply because the required accuracy is usually very high. We present a new time-integration algorithm which has no secular error in either the binding energy or the eccentricity, while allowing variable stepsize. The basic approach is to take a time-symmetric algorithm, then apply an implicit criterion for the stepsize to ensure strict time reversibility. We describe the algorithm in detail and present the results of numerical tests involving long-term integration of binaries and hierarchical triples. In all cases studied, we found no systematic error in either the energy or the angular momentum. We also found that its calculation cost does not become higher than those of existing algorithms. By contrast, the stabilization technique, which has been widely used in the field of collisional stellar dynamics, conserves energy very well but does not conserve angular momentum.Comment: figures are available at http://grape.c.u-tokyo.ac.jp/~funato/; To appear in Astronomical Journal (July, 1996

Structural changes in cartilage and collagen studied by high temperature Raman spectroscopy

Understanding the high temperature behavior of collagen and collagenous tissue is important for surgical procedures and biomaterials processing for the food, pharmaceutical, and cosmetics industries. One primary event for proteins is thermal denaturation that involves unfolding the polypeptide chains while maintaining the primary structure intact. Collagen in the extracellular matrix of cartilage and other connective tissue is a hierarchical material containing bundles of triple-helical fibers associated with water and proteoglycan components. Thermal analysis of dehydrated collagen indicates irreversible denaturation at high temperature between 135°C and 200°C, with another reversible event at ∼60-80°C for hydrated samples. We report high temperature Raman spectra for freeze-dried cartilage samples that show an increase in laser-excited fluorescence interpreted as conformational changes associated with denaturation above 140°C. Spectra for separated collagen and proteoglycan fractions extracted from cartilage indicate the changes are associated with collagen. The Raman data also show appearance of new features indicating peptide bond hydrolysis at high temperature implying that molecular H2O is retained within the freeze-dried tissue. This is confirmed by thermogravimetric analysis that show 5-7 wt% H2O remaining within freeze-dried cartilage that is released progressively upon heating up to 200°C. Spectra obtained after exposure to high temperature and re-hydration following recovery indicate that the capacity of the denatured collagen to re-absorb water is reduced. Our results are important for revealing the presence of bound H2O within the collagen component of connective tissue even after freeze-drying and its role in denaturation that is accompanied by or perhaps preceded by breakdown of the primary polypeptide structure

Comparison of the prognostic value of measures of the tumor inflammatory cell infiltrate and tumor-associated stroma in patients with primary operable colorectal cancer

The aim of the present study was to compare the clinical utility of two measures of the inflammatory cell infiltrate - a H&E-based assessment of the generalised inflammatory cell infiltrate (the Klintrup-Mäkinen (KM) grade), and an immunohistochemistry-based assessment of combined CD3+ and CD8+ T-cell density (the “Immunoscore”), in conjunction with assessment of the tumor stroma percentage (TSP) in patients undergoing resection of stage I-III colorectal cancer (CRC). 246 patients were identified from a prospectively maintained database of CRC resections in a single surgical unit. Assessment of KM grade and TSP was performed using full H&E sections. CD3+ and CD8+ T-cell density was assessed on full sections and the Immunoscore calculated. KM grade and Immunoscore were strongly associated (P<0.001). KM grade stratified cancer-specific survival (CSS) from 88% to 66% (P=0.002) and Immunoscore from 93% to 61% (P<0.001). Immunoscore further stratified survival of patients independent of KM grade from 94% (high KM, Im4) to 60% (low KM, Im0/1). Furthermore, TSP stratified survival of patients with a weak inflammatory cell infiltrate (low KM: from 75% to 47%; Im0/1: from 71% to 38%, both P<0.001) but not those with a strong inflammatory infiltrate. On multivariate analysis, only Immunoscore (HR 0.44, P<0.001) and TSP (HR 2.04, P<0.001) were independently associated with CSS. These results suggest that the prognostic value of an immunohistochemistry-based assessment of the inflammatory cell infiltrate is superior to H&E-based assessment in patients undergoing resection of stage I-III CRC. Furthermore, assessment of the tumor-associated stroma, using TSP, further improves prediction of outcome

Interpolation Properties and SAT-based Model Checking

Craig interpolation is a widespread method in verification, with important applications such as Predicate Abstraction, CounterExample Guided Abstraction Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model checking techniques based on interpolation require collections of interpolants to satisfy particular properties, to which we refer as "collectives"; they do not hold in general for all interpolation systems and have to be established for each particular system and verification environment. Nevertheless, no systematic approach exists that correlates the individual interpolation systems and compares the necessary collectives. This paper proposes a uniform framework, which encompasses (and generalizes) the most common collectives exploited in verification. We use it for a systematic study of the collectives and of the constraints they pose on propositional interpolation systems used in SAT-based model checking

Long-term health outcomes after exposure to repeated concussion in elite level: rugby union players

Background: There is continuing concern about effects of concussion in athletes, including risk of the neurodegenerative disease chronic traumatic encephalopathy. However, information on long-term health and wellbeing in former athletes is limited. Method: Outcome after exposure to repeated brain injury was investigated in 52 retired male Scottish international rugby players (RIRP) and 29 male controls who were similar in age and social deprivation. Assessment included history of playing rugby and traumatic brain injury, general and mental health, life stress, concussion symptoms, cognitive function, disability and markers of chronic stress (allostatic load). Results: The estimated number of concussions in RIRP averaged 14 (median=7; IQR 5-40). Performance was poorer in RIRP than controls on a test of verbal learning (p=0.022) and of fine co-ordination of the dominant hand (p=0.038) and not significantly different on other cognitive tests (p>0.05). There were no significant associations between number of concussions and performance on cognitive tests. Other than a higher incidence of cardiovascular disease in controls, no group differences were detected in general or mental health or estimates of allostatic load. In RIRP, persisting symptoms attributed to concussion were more common if reporting more than nine concussions (p=0.028), although these symptoms were not perceived to affect social or work functioning. Conclusions: Despite a high number of concussions in RIRP, differences in mental health, social or work functioning were not found late after injury. Subtle group differences were detected on two cognitive tests, the cause of which is uncertain. Prospective group comparison studies on representative cohorts are required

Preoperative systemic inflammation predicts postoperative infectious complications in patients undergoing curative resection for colorectal cancer

The presence of systemic inflammation before surgery, as evidenced by the glasgow prognostic score (mGPS), predicts poor long-term survival in colorectal cancer. The aim was to examine the relationship between the preoperative mGPS and the development of postoperative complications in patients undergoing potentially curative resection for colorectal cancer. Patients (n=455) who underwent potentially curative resections between 2003 and 2007 were assessed consecutively, and details were recorded in a database. The majority of patients presented for elective surgery (85%) were over the age of 65 years (70%), were male (58%), were deprived (53%), and had TNM stage I/II disease (61%), had preoperative haemoglobin (56%), white cell count (87%) and mGPS 0 (58%) in the normal range. After surgery, 86 (19%) patients developed a postoperative complication; 70 (81%) of which were infectious complications. On multivariate analysis, peritoneal soiling (P<0.01), elevated preoperative white cell count (P<0.05) and mGPS (P<0.01) were independently associated with increased risk of developing a postoperative infection. In elective patients, only the mGPS (OR=1.75, 95% CI=1.17-2.63, P=0.007) was significantly associated with increased risk of developing a postoperative infection. Preoperative elevated mGPS predicts increased postoperative infectious complications in patients undergoing potentially curative resection for colorectal cancer

Properties of the superconducting state in a two-band model

Eliashberg theory is used to investigate the range of thermodynamic properties possible within a two-band model for s-wave superconductivity and to identify signatures of its two-band nature. We emphasize dimensionless BCS ratios (those for the energy gaps, the specific heat jump and the negative of its slope near Tc, the thermodynamic critical field Hc(0), and the normalized slopes of the critical field and the penetration depth near Tc), which are no longer universal even in weak coupling. We also give results for temperature-dependent quantities, such as the penetration depth and the energy gap. Results are presented both for microscopic parameters appropriate to MgB2 and for variations away from these. Strong coupling corrections are identified and found to be significant. Analytic formulas are provided which show the role played by the anisotropy in coupling in some special limits. Particular emphasis is placed on small interband coupling and on the opposite limit of no diagonal coupling. The effect of impurity scattering is considered, particularly for the interband case.Comment: 20 pages, 14 figures, final version accepted in PR