Spectral method for the unsteady incompressible Navier-Stokes equations in gauge formulation

A spectral method which uses a gauge method, as opposed to a projection method, to decouple the computation of velocity and pressure in the unsteady incompressible Navier-Stokes equations, is presented. Gauge methods decompose velocity into the sum of an auxilary field and the gradient of a gauge variable, which may, in principle, be assigned arbitrary boundary conditions, thus overcoming the issue of artificial pressure boundary conditions in projection methods. A lid-driven cavity flow is used as a test problem. A subtraction method is used to reduce the pollution effect of singularities at the top corners of the cavity. A Chebyshev spectral collocation method is used to discretize spatially. An exponential time differencing method is used to discretize temporally. Matrix diagonalization procedures are used to compute solutions directly and efficiently. Numerical results for the flow at Reynolds number Re = 1000 are presented, and compared to benchmark results. It is shown that the method, called the spectral gauge method, is straightforward to implement, and yields accurate solutions if Neumann boundary conditions are imposed on the gauge variable, but suffers from reduced convergence rates if Dirichlet boundary conditions are imposed on the gauge variable

Conformal Maps to Multiply-Slit Domains and Applications

By exploiting conformal maps to vertically slit regions in the complex plane, a recently developed rational spectral method [Tee and Trefethen, 2006] is able to solve PDEs with interior layer-like behaviour using significantly fewer collocation points than traditional spectral methods. The conformal maps are chosen to 'enlarge the region of analyticity' in the solution: an idea which can be extended to other numerical methods based upon global polynomial interpolation. Here we show how such maps can be rapidly computed in both periodic and nonperiodic geometries, and apply them to some challenging differential equations

A rational spectral collocation method with adaptively transformed Chebyshev grid points

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are approximated by the locations of poles of Chebyshev-Padé approximants. Numerical experiments on two time-dependent problems, one with finite time blow-up and one with a moving front, indicate that the method far outperforms the standard Chebyshev spectral collocation method for problems whose solutions have singularities in the complex plan close to [-1,1]

Prognostic value of serum levels of immunoglobulins (IgG, IgA, IgM and IgE) in breast cancer: a preliminary study.

One hundred and sixty women admitted for breast tumour biopsy to the King's College Hospital group have been followed sequentially for 2 years. Sixty-nine women had early operable breast cancer and 91 had benign breast disease. All these women had serum immunoglobulin IgG, IgA, IgM and IgE levels measured preoperatively and postoperatively at 3 months, 1 year and 2 years. No differences were found in any of the serum immunoglobulin levels between the two groups at any time. There was, however, a positive correlation between the extent of metastatic breast cancer and the serum level of various immunoglobulins, particularly IgA. There was no evidence that routine postoperative radiotherapy influenced the levels of serum immunoglobulins. The findings suggest a secondary defence reaction against increasing tumour load, and do not support the theory of an early immune defect in immunoglobulin metabolism which could play a part in the pathogenesis of breast cancer. Although there is no diagnostic value in measuring the levels of serum immunoglobulins in patients with breast tumours, there may be some value in following the levels in cancer patients, as a guide to subclinical spread of the disease

Self-cleaning and colour-preserving efficiency of photocatalytic concrete: case study of the Jubilee Church in Rome

The Jubilee Church in the south-eastern outskirts of Rome is one of the first buildings constructed with super white reinforced concrete with self-cleaning photocatalytic cement. However, 16 years after the opening of the building, the self-cleaning and colour-preserving properties arising from the titania particles (TiO2) within the concrete mix are not meeting the design requirements and the concrete is showing premature evidence of decay. While the form of the decay is affecting the appearance of the building and not its structural soundness, the ageing pattern of the building's components is resulting in a high maintenance cost, one not easily affordable within the ordinary budget supported by a small parish. This study comprises the first comprehensive step in understanding the causes of the accelerated ageing pattern of the concrete, highlighting methods to improve the long-term durability of the concrete and therefore reduce the cost of its maintenance. Moreover, this research offered the opportunity to test the durability and the effectiveness of the TiO2 in the real conditions on an actual building featuring non-standard geometries. The findings highlight how the ageing pattern directly connects with the geometry of the building and inadequate consideration of the local weathering at the design stage

Decline in Clostridium difficile-associated disease rates in Singapore public hospitals, 2006 to 2008

<p>Abstract</p> <p>Background</p> <p><it>Clostridium difficile </it>is the major cause of pseudomembranous colitis associated with antibiotic use, and the spread of the hypervirulent epidemic ribotype 027/NAP-1 strain across hospitals worldwide has re-focused attention on this nosocomial pathogen. The overall incidence and trend of <it>C. difficile</it>-associated disease (CDAD) in Singapore is unknown, and a surveillance program to determine these via formal laboratory-based reporting was established.</p> <p>Findings</p> <p>Laboratory and pharmacy data were collated from one tertiary and two secondary hospitals on a quarterly basis between 2006 and 2008. All hospitals tested for <it>C. difficile </it>using Immunocard Toxins A&B (Meridian Bioscience Inc., Cincinnati, OH) during this period. Duplicate positive <it>C. difficile </it>results within a 14-day period were removed. The CDAD results were compared with trends in hospital-based prescription of major classes of antibiotics.</p> <p>Overall CDAD incidence-density decreased from 5.16 (95%CI: 4.73 - 5.62) cases per 10,000 inpatient-days in 2006 to 2.99 (95%CI: 2.67 to 3.33) cases per 10,000 inpatient-days in 2008 (<it>p </it>< 0.001), while overall rates for <it>C. difficile </it>testing increased significantly (<it>p </it>< 0.001) within the same period. These trends were mirrored at the individual hospital level. Evaluation of antibiotic prescription data at all hospitals showed increasing use of carbapenems and fluoroquinolones, while cephalosporin and clindamycin prescription remained stable.</p> <p>Conclusions</p> <p>Our results demonstrate a real decline of CDAD rates in three large local hospitals. The cause is unclear and is not associated with improved infection control measures or reduction in antibiotic prescription. Lack of <it>C. difficile </it>stool cultures as part of routine testing precluded determination of the decline of a major clone as a potential explanation. For more accurate epidemiological trending of CDAD and early detection of epidemic clones, data collection will have to be expanded and resources set in place for reference laboratory culture and typing.</p

Interaction design for supporting communication between Chinese sojourners

In our global village, distance is not a barrier anymore for traveling. People experience new cultures and face accompanying difficulties in order to live anywhere. Social support can help these sojourners to cope with difficulties, such as culture shock. In this paper, we investigate how computer-mediated communication (CMC) tools can facilitate social support when living physically separated from loved-ones in different cultures. The goal is to understand the design considerations necessary to design new CMC tools. We studied communication practices of Chinese sojourners living in the Netherlands and the use of a technology probe with a novel video communication system. These results led to recommendations which can help designers to design interactive communication tools that facilitate communication across cultures. We conclude the paper with an interactive communication device called Circadian, which was designed based on these recommendations. We experienced the design recommendations to be abstract enough to leave space for creativity while providing a set of clear requirements which we used to base design decisions upon

Disparity between skin perfusion and sublingual microcirculatory alterations in severe sepsis and septic shock: a prospective observational study

Objective: Measurement of central-to-toe temperature difference has been advocated as an index of severity of shock and as a guide for circulatory therapy in critically ill patients. However, septic shock, in contrast to other forms of shock, is associated with a distributive malfunction resulting in a disparity between vascular compartments. Although this disparity has been established between systemic and microcirculatory parameters, it is unclear whether such disparity exists between skin perfusion and microcirculation. To test this hypothesis of disparity, we simultaneously measured parameters of the two vascular compartments, in the early phase of sepsis. Design: Prospective observational study in patients with severe sepsis/septic shock in the first 6 h of ICU admission. Simultaneous measurements of central-to-toe temperature difference and sublingual microcirculatory orthogonal polarization spectral imaging, together with parameters of systemic hemodynamics. Setting: 22 bed mixed-ICU in a tertiary teaching hospital. Patients: 35 consecutive patients in a 12-month period. Measurements and results: In 35 septic patients and a median APACHE II score of 20, no correlation between central-to-toe temperature gradient and microvascular flow index was observed (r(s) =-0.08, p = 0.65). Also no significant correlation between temperature gradient/microvascular flow index and systemic hemodynamic parameters could be demonstrated. Conclusions: During the early phase of resuscitated severe sepsis and septic shock there appears to be no correlation between sublingual microcirculatory alterations and the central-to-toe temperature difference. This finding adds to the concept of a dispersive nature of blood flow under conditions of sepsis between microcirculatory and systemic hemodynamic

BTK inhibition sensitizes acute lymphoblastic leukemia to asparaginase by suppressing the amino acid response pathway

Asparaginase (ASNase) therapy has been a mainstay of acute lymphoblastic leukemia (ALL) protocols for decades and shows promise in the treatment of a variety of other cancers. To improve the efficacy of ASNase treatment, we used a CRISPR/Cas9-based screen to identify actionable signaling intermediates that improve the response to ASNase. Both genetic inactivation of Bruton’s tyrosine kinase (BTK) and pharmacological inhibition by the BTK inhibitor ibrutinib strongly synergize with ASNase by inhibiting the amino acid response pathway, a mechanism involving c-Myc–mediated suppression of GCN2 activity. This synthetic lethal interaction was observed in 90% of patient-derived xenografts, regardless of the genomic subtype. Moreover, ibrutinib substantially improved ASNase treatment response in a murine PDX model. Hence, ibrutinib may be used to enhance the clinical efficacy of ASNase in ALL. This trial was registered at www.clinicaltrials.gov as # NCT02884453

A robust spectral method for solving Heston’s model

In this paper, we consider the Heston’s volatility model (Heston in Rev. Financ. Stud. 6: 327–343, 1993]. We simulate this model using a combination of the spectral collocation method and the Laplace transforms method. To approximate the two dimensional PDE, we construct a grid which is the tensor product of the two grids, each of which is based on the Chebyshev points in the two spacial directions. The resulting semi-discrete problem is then solved by applying the Laplace transform method based on Talbot’s idea of deformation of the contour integral (Talbot in IMA J. Appl. Math. 23(1): 97–120, 1979)