Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Pharmacokinetics and safety of panobacumab: specific adjunctive immunotherapy in critical patients with nosocomial Pseudomonas aeruginosa O11 pneumonia.

Objectives Nosocomial Pseudomonas aeruginosa pneumonia remains a major concern in critically ill patients. We explored the potential impact of microorganism-targeted adjunctive immunotherapy in such patients. Patients and methods This multicentre, open pilot Phase 2a clinical trial (NCT00851435) prospectively evaluated the safety, pharmacokinetics and potential efficacy of three doses of 1.2 mg/kg panobacumab, a fully human monoclonal anti-lipopolysaccharide IgM, given every 72 h in 18 patients developing nosocomial P. aeruginosa (serotype O11) pneumonia. Results Seventeen out of 18 patients were included in the pharmacokinetic analysis. In 13 patients receiving three doses, the maximal concentration after the third infusion was 33.9 ± 8.0 μg/mL, total area under the serum concentration-time curve was 5397 ± 1993 μg h/mL and elimination half-life was 102.3 ± 47.8 h. Panobacumab was well tolerated, induced no immunogenicity and was detected in respiratory samples. In contrast to Acute Physiology and Chronic Health Evaluation II (APACHE II) prediction, all 13 patients receiving three doses survived, with a mean clinical resolution in 9.0 ± 2.7 days. Two patients suffered a recurrence at days 17 and 20. Conclusions These data suggest that panobacumab is safe, with a pharmacokinetic profile similar to that in healthy volunteers. It was associated with high clinical cure and survival rates in patients developing nosocomial P. aeruginosa O11 pneumonia. We concluded that these promising results warrant further trials.

Relationships between imatinib plasma levels and efficacy

Purpose: While imatinib has revolutionized the treatment of chronic myeloid leukaemia (CML) and gastrointestinal stromal tumors (GIST), its pharmacokinetic-pharmacodynamic relationships have been poorly studied. This study aimed to explore the issue in oncologic patients, and to evaluate the specific influence of the target genotype in a GIST subpopulation. Patients and methods: Data from 59 patients (321 plasma samples) were collected during a previous pharmacokinetic study. Based on a population model purposely developed, individual post-hoc Bayesian estimates of pharmacokinetic parameters were derived, and used to estimate drug exposure (AUC; area under curve). Free fraction parameters were deduced from a model incorporating plasma alpha1-acid glycoprotein levels. Associations between AUC (or clearance) and therapeutic response (coded on a 3-point scale), or tolerability (4-point scale), were explored by ordered logistic regression. Influence of KIT genotype on response was also assessed in GIST patients. Results: Total and free drug exposure correlated with the number of side effects (p < 0.005). A relationship with response was not evident in the whole patient set (with good-responders tending to receive lower doses and bad-responders higher doses). In GIST patients however, higher free drug exposure predicted better responses. A strong association was notably observed in patients harboring an exon 9 mutation or a wild type KIT, known to decrease tumor sensitivity towards imatinib (p < 0.005). Conclusions: Our results are arguments to further evaluate the potential benefit of a therapeutic monitoring program for imatinib. Our data also suggest that stratification by genotype will be important in future trials.

Immuno-reactive proteins from Mycobacterium immunogenum useful for serodiagnosis of metalworking fluid hypersensitivity pneumonitis.

Metalworking fluid-associated hypersensitivity pneumonitis (MWF-HP) is a pulmonary disease caused by inhaling microorganisms present in the metalworking fluids used in the industrial sector. Mycobacterium immunogenum is the main etiological agent. Among the clinical, radiological and biological tools used for diagnosis, serological tests are important. The aim of this study was to identify immunogenic proteins in M. immunogenum and to use recombinant antigens for serological diagnosis of MWF-HP. Immunogenic proteins were detected by two-dimensional Western blot and candidate proteins were identified by mass spectrometry. Recombinant antigens were expressed in Escherichia coli and tested by enzyme-linked immunosorbent assay (ELISA) with the sera of 14 subjects with MWF-HP and 12 asymptomatic controls exposed to M. immunogenum. From the 350 spots visualized by two-dimensional gel electrophoresis with M. immunogenum extract, 6 immunogenic proteins were selected to be expressed as recombinant antigens. Acyl-CoA dehydrogenase antigen allowed for the best discrimination of MWF-HP cases against controls with an area under the receiver operating characteristics (ROC) curve of 0.930 (95% CI=0.820-1), a sensitivity of 100% and a specificity of 83% for the optimum threshold. Other recombinant antigens correspond to acyl-CoA dehydrogenase FadE, cytosol aminopeptidase, dihydrolipoyl dehydrogenase, serine hydroxymethyltransferase and superoxide dismutase. This is the first time that recombinant antigens have been used for the serodiagnosis of hypersensitivity pneumonitis. The availability of recombinant antigens makes it possible to develop standardized serological tests which in turn could simplify diagnosis, thus making it less invasive.

Pharmacokinetic aspects of Tert-Butylaminoethyl disulfide, an experimental drug against schistosomiasis in mice

A preliminary study of the pharmacokinetic parameters of t-Butylaminoethyl disulfide was performed after administration of two different single doses (35 and 300 mg/kg) of either the cold or labelled drug. Plasma or blood samples were treated with dithiothreitol, perchloric acid, and, after filtration, submitted to further purification with anionic resein. In the final step, the drug was retained on a cationic resin column, eluted with NaCl 1M and detected according to the method of Ellman (1958). Alternatively, radioactive drug was detected by liquid scintillation counting. The results corresponding to the smaller dose of total drug suggested a pharmacokinetic behavior related to a one open compartment model with the following parameters: area under the intravenous curve (AUC i.v.):671 ± 14; AUC oral: 150 ± 40 µg.min. ml [raised to the power of -1]; elimination rate constant: 0.071 min [raised to the power of -1]; biological half life: 9.8 min; distribution volume: 0.74 ml/g. For the higher dose, the results seemed to obey a more complex undertermined model. Combining the results, the occurence of a dose-dependent pharmacokinetic behavior is suggested, the drug being rapidly absorbed and rapidly eliminated; the elimination process being related mainly to metabolization. The drug seems to be more toxic when administered I.V. because by this route it escapes first pass metabolism, while being quickly distributed to tissues. The maximum tolerated blood level seems to be around 16 µg/ml.

Device-specific weighted T-score for two quantitative ultrasounds: operational propositions for the management of osteoporosis for 65 years and older women in Switzerland.

The World Health Organization (WHO) criteria for the diagnosis of osteoporosis are mainly applicable for dual X-ray absorptiometry (DXA) measurements at the spine and hip levels. There is a growing demand for cheaper devices, free of ionizing radiation such as promising quantitative ultrasound (QUS). In common with many other countries, QUS measurements are increasingly used in Switzerland without adequate clinical guidelines. The T-score approach developed for DXA cannot be applied to QUS, although well-conducted prospective studies have shown that ultrasound could be a valuable predictor of fracture risk. As a consequence, an expert committee named the Swiss Quality Assurance Project (SQAP, for which the main mission is the establishment of quality assurance procedures for DXA and QUS in Switzerland) was mandated by the Swiss Association Against Osteoporosis (ASCO) in 2000 to propose operational clinical recommendations for the use of QUS in the management of osteoporosis for two QUS devices sold in Switzerland. Device-specific weighted "T-score" based on the risk of osteoporotic hip fractures as well as on the prediction of DXA osteoporosis at the hip, according to the WHO definition of osteoporosis, were calculated for the Achilles (Lunar, General Electric, Madison, Wis.) and Sahara (Hologic, Waltham, Mass.) ultrasound devices. Several studies (totaling a few thousand subjects) were used to calculate age-adjusted odd ratios (OR) and area under the receiver operating curve (AUC) for the prediction of osteoporotic fracture (taking into account a weighting score depending on the design of the study involved in the calculation). The ORs were 2.4 (1.9-3.2) and AUC 0.72 (0.66-0.77), respectively, for the Achilles, and 2.3 (1.7-3.1) and 0.75 (0.68-0.82), respectively, for the Sahara device. To translate risk estimates into thresholds for clinical application, 90% sensitivity was used to define low fracture and low osteoporosis risk, and a specificity of 80% was used to define subjects as being at high risk of fracture or having osteoporosis at the hip. From the combination of the fracture model with the hip DXA osteoporotic model, we found a T-score threshold of -1.2 and -2.5 for the stiffness (Achilles) determining, respectively, the low- and high-risk subjects. Similarly, we found a T-score at -1.0 and -2.2 for the QUI index (Sahara). Then a screening strategy combining QUS, DXA, and clinical factors for the identification of women needing treatment was proposed. The application of this approach will help to minimize the inappropriate use of QUS from which the whole field currently suffers.

Study of a population of Biomphalaria tenagophila (Orbigny, 1835) and of schistosomiasis transmission in "Alto da Boa Vista", Rio de Janeiro

The present study was performed using data from a Biomphalaria tenagophila population located in a water cress garden in the Alto da Boa Vista region representing an isolated focal point of schistosomiasis in the city of Rio de Janeiro. The density and age structure of this B. tenagophila population and its rate of intection by Schistosoma mansoni were studied for a period of 15 months. The snail population showed seasonal variation in density, with a decrease in number of individual at the begining of the rainy season. At the end of this season, the population consisted mainly of adults (92.8% in May 1985 and 82.8% in April 1986). The population growth curve was logistic and of sigmoidal configuration. Shiscotoma mansoni cercariae were eliminated over a short period of time (March, April and May 1986). The release of cercariae of S. mansoni and of birds seems to depend on environmental temperature, which during certain months would show a daily variation of up to 13ºC, with the lower thermal limit approaching the limit value for sporocyte development.

Routine use of point-of-care tests: usefulness and application in clinical microbiology.

Point-of-care (POC) tests offer potentially substantial benefits for the management of infectious diseases, mainly by shortening the time to result and by making the test available at the bedside or at remote care centres. Commercial POC tests are already widely available for the diagnosis of bacterial and viral infections and for parasitic diseases, including malaria. Infectious diseases specialists and clinical microbiologists should be aware of the indications and limitations of each rapid test, so that they can use them appropriately and correctly interpret their results. The clinical applications and performance of the most relevant and commonly used POC tests are reviewed. Some of these tests exhibit insufficient sensitivity, and should therefore be coupled to confirmatory tests when the results are negative (e.g. Streptococcus pyogenes rapid antigen detection test), whereas the results of others need to be confirmed when positive (e.g. malaria). New molecular-based tests exhibit better sensitivity and specificity than former immunochromatographic assays (e.g. Streptococcus agalactiae detection). In the coming years, further evolution of POC tests may lead to new diagnostic approaches, such as panel testing, targeting not just a single pathogen, but all possible agents suspected in a specific clinical setting. To reach this goal, the development of serology-based and/or molecular-based microarrays/multiplexed tests will be needed. The availability of modern technology and new microfluidic devices will provide clinical microbiologists with the opportunity to be back at the bedside, proposing a large variety of POC tests that will allow quicker diagnosis and improved patient care.

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities (Draft 1)

We extend a reduced form model for pricing pass-through mortgage backed securities (MBS) and provide a novel hedging tool for investors in this market. To calculate the price of an MBS, traders use what is known as option-adjusted spread (OAS). The resulting OAS value represents the required basis points adjustment to reference curve discounting rates needed to match an observed market price. The OAS suffers from some drawbacks. For example, it remains constant until the maturity of the bond (thirty years in mortgage-backed securities), and does not incorporate interest rate volatility. We suggest instead what we call dynamic option adjusted spread (DOAS). The latter allows investors in the mortgage market to account for both prepayment risk and changes of the yield curve.

Effect of rufinamide on gating properties of voltage-gated sodium channel Na(v)1.7

Background: Voltage-gated sodium channels (Nav1.x) are important players in chronic pain. A particular interest has grown in Nav1.7, expressed in nociceptors, since mutations in its gene are associated to two inherited pain syndromes or insensitivity to pain. Rufinamide, a drug used to treat refractory epilepsy such as the Lennox-Gastaut syndrome, has been shown to reduce the number of action potentials in cortical neurons without completely blocking Na channels. Aim: The goal of this study was to investigate the effect of rufinamide on Nav1.7 current. Methods and results: Whole-cell patch clamp experiments were performed using HEK293 cells stably expressing Nav1.7. Rufinamide significantly decreased peak sodium current by 28.3, 21.2 and 12.5% at concentrations of 500, 100 and 50μM respectively (precise EC50 could not be calculated since higher rufinamide concentrations could not be achieved in physiological buffer solution). No significant difference on the V1/2 of voltage-dependence of activation was seen; however a shift in the steady-state inactivation curve was observed (-82.6 mV to -88.8 mV and -81.8 to -87.6 mV for 50 and 100 μM rufinamide respectively, p <0.005). Frequency-dependent inhibition of Nav1.7 was also influenced by the drug. One hundred μM rufinamide reduced the peak sodium current (in % of the peak current taken at the first sweep of a train of 50) from 90.8 to 80.8% (5Hz), 88.7 to 71.8% (10 Hz), 69.1 to 49.2% (25 Hz) and 22.3 to 9.8% (50 Hz) (all p <0.05). Onset of fast inactivation was not influenced by the drug since no difference in the time constant of current decay was observed. Conclusion: In the concentration range of plasma level in human treated for epilepsy, 15 μM, rufinamide only minimally blocks Nav1.7. However, it stabilizes the inactivated state and exerts frequencydependent inhibition of Nav1.7. These pharmacological properties may be of use in reducing ectopic discharges as a causal and symptom related contributor of neuropathic pain syndrome.

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities (Draft 2)

We extend a reduced form model for pricing pass-through mortgage backed securities (MBS) and provide a novel hedging tool for investors in this market. To calculate the price of an MBS, traders use what is known as option-adjusted spread (OAS). The resulting OAS value represents the required basis points adjustment to reference curve discounting rates needed to match an observed market price. The OAS suffers from some drawbacks. For example, it remains constant until the maturity of the bond (thirty years in mortgage-backed securities), and does not incorporate interest rate volatility. We suggest instead what we call dynamic option adjusted spread (DOAS), which allows investors in the mortgage market to account for both prepayment risk and changes of the yield curve.

Indicators for the total number of melanocytic naevi : an adjunct for screening campaigns. Observational study on 292 patients.

BACKGROUND: The presence of multiple melanocytic naevi is a strong risk factor for melanoma. Use of the whole body naevus count to identify at-risk patients is impractical. OBJECTIVES: To (i) identify a valid anatomical predictor of total naevus count; (ii) determine the number of naevi that most accurately predict total naevus count above 25, 50 and 100; and (iii) evaluate determinants of multiple melanocytic naevi and atypical naevi. METHODS: Clinical data from 292 consecutive Spanish patients consulting for skin lesions requiring debriding were collected throughout 2009 and 2010. Correlations between site-specific and whole body naevus counts were analysed. Cut-offs to predict total naevus counts were determined using the area under the receiver operating characteristic curve. RESULTS: The studied population was young (median age 31 years, interquartile range 28-43). The naevus count on the right arm correlated best with the total nevus count (R(2) 0·80 for men, 0·86 for women). Presence of at least five naevi on the right arm was the strongest determinant of a total naevus count above 50 [odds ratio (OR) 34·4, 95% confidence interval (CI) 13·9-85·0] and of having at least one atypical naevus (OR 5·7, 95% CI 2·4-13·5). Cut-off values of 6, 8 and 11 naevi on the right arm best predicted total naevus count above 25, 50 and 100, respectively. CONCLUSIONS: Our results support the arm as a practical and reliable site to estimate the total naevus count when screening or phenotyping large populations. Threshold values for the number of naevi on the arm are proposed to help identify patients for melanoma screening.