Definite integrals and operational methods

An operational method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various types. This technique provides a very flexible and powerful tool yielding new results encompassing different aspects of the special function theory. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.

A model of road effect using line integrals and a test of the performance of two new road indices using the distribution of small mammals in an Atlantic Forest landscape

Effects of roads on wildlife and its habitat have been measured using metrics, such as the nearest road distance, road density, and effective mesh size. In this work we introduce two new indices: (1) Integral Road Effect (IRE), which measured the sum effects of points in a road at a fixed point in the forest; and (2) Average Value of the Infinitesimal Road Effect (AVIRE), which measured the average of the effects of roads at this point. IRE is formally defined as the line integral of a special function (the infinitesimal road effect) along the curves that model the roads, whereas AVIRE is the quotient of IRE by the length of the roads. Combining tools of ArcGIS software with a numerical algorithm, we calculated these and other road and habitat cover indices in a sample of points in a human-modified landscape in the Brazilian Atlantic Forest, where data on the abundance of two groups of small mammals (forest specialists and habitat generalists) were collected in the field. We then compared through the Akaike Information Criterion (AIC) a set of candidate regression models to explain the variation in small mammal abundance, including models with our two new road indices (AVIRE and IRE) or models with other road effect indices (nearest road distance, mesh size, and road density), and reference models (containing only habitat indices, or only the intercept without the effect of any variable). Compared to other road effect indices, AVIRE showed the best performance to explain abundance of forest specialist species, whereas the nearest road distance obtained the best performance to generalist species. AVIRE and habitat together were included in the best model for both small mammal groups, that is, higher abundance of specialist and generalist small mammals occurred where there is lower average road effect (less AVIRE) and more habitat. Moreover, AVIRE was not significantly correlated with habitat cover of specialists and generalists differing from the other road effect indices, except mesh size, which allows for separating the effect of roads from the effect of habitat on small mammal communities. We suggest that the proposed indices and GIS procedures could also be useful to describe other spatial ecological phenomena, such as edge effect in habitat fragments. (C) 2012 Elsevier B.V. All rights reserved.

Differentiability of bizonal positive definite kernels on complex spheres

We prove that any continuous function with domain {z ∈ C: |z| ≤ 1} that generates a bizonal positive definite kernel on the unit sphere in 'C POT.Q' , q ⩾ 3, is continuously differentiable in {z ∈ C: |z| < 1} up to order q − 2, with respect to both z and 'Z BARRA'. In particular, the partial derivatives of the function with respect to x = Re z and y = Im z exist and are continuous in {z ∈ C: |z| < 1} up to the same order.

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.

Causes of pulmonary granulomas: a retrospective study of 500 cases from seven countries

Background The frequencies of various causes of pulmonary granulomas in pathological material are unknown, as is the influence of geographical location on aetiology. The aim of this study was to identify the causes of pulmonary granulomas in pathological specimens, to define their frequencies, and to determine whether these causes vary by geographical location. Methods 500 lung biopsies and resections containing granulomas were reviewed retrospectively by expert pulmonary pathologists from 10 institutions in seven countries. Fifty consecutive cases from each location were assigned a diagnosis based on histological features and available clinical/microbiological data. Results A specific cause was identified in 58% of cases (290/500), most commonly sarcoidosis (136, 27%) and mycobacterial or fungal infections (125, 25%). Mycobacteria were identified in 19% of cases outside the USA versus 8% within the USA. In contrast, fungi accounted for 19% cases in the USA versus 4% in other locations. Fungi were mostly detected by histology, whereas most mycobacteria were identified in cultures. In 42% of cases (210/500) an aetiology could not be determined. Conclusions Across several geographical settings, sarcoidosis and infections are the most common causes of pulmonary granulomas diagnosed in pathological specimens. Fungi are more commonly identified than mycobacteria in the USA, whereas the reverse is true in other countries. A definite aetiology cannot be demonstrated in more than a third of all cases of pulmonary granulomas, even after histological examination. These findings highlight the need to submit material for histology as well as cultures in all cases in which granulomatous disease enters the differential diagnosis.

Twelve-month clinical outcomes after coronary stenting with the Genous Bio-engineered R Stent in patients with a bifurcation lesion: from the e-HEALING (Healthy Endothelial Accelerated Lining Inhibits Neointimal Growth) registry

Background The e-Healthy Endothelial Accelerated Lining Inhibits Neointimal Growth (e-HEALING) registry was designed to capture clinical data on the use of the endothelial progenitor cell capture stent (ECS) in routine clinical practice. In this analysis, we investigated the 12-month clinical outcomes in patients treated with an ECS for a bifurcation lesion. Methods The worldwide, prospective, nonrandomized e-HEALING registry aimed to enrol 5000 patients treated for coronary artery disease with one or more ECS between October 2005 and October 2007. Clinical follow-up was obtained at 1, 6, and 12 months. The primary endpoint was target vessel failure (TVF), defined as the composite of cardiac death, myocardial infarction, and target vessel revascularization at 12 months. Results A total of 573 patients were treated for at least one bifurcation lesion and were assessed in the current analysis. Baseline characteristics showed a median age of 65 years; 21% were diabetic patients and 36% had unstable angina. A total of 63% of the bifurcation lesions were located in the left artery descending and the mean stent length was 20.7 +/- 12.6 mm. At 12 months, TVF was 12.7% and target lesion revascularization was 7.5%. Definite or probable stent thrombosis occurred in 1.7% of the patients. Moreover, one or more stents per lesion [hazard ratio (HR): 2.79, 95% confidence interval (CI): 1.60-4.86, P < 0.001], predilatation (HR: 0.39, 95% CI: 0.17-0.87, P = 0.023), and lesions located in the right coronary artery (HR: 4.56, 95% CI: 1.07-19.5, P = 0.041) were independent predictors of TVF. Conclusion In the e-HEALING registry, coronary bifurcation stenting with the ECS results in favorable clinical outcomes and low incidences of repeat revascularization and stent thrombosis. Coron Artery Dis 23:201-207 (C) 2012 Wolters Kluwer Health vertical bar Lippincott Williams & Wilkins.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

Endoscopic Laser Thyroarytenoid Myoneurectomy in Patients with Adductor Spasmodic Dysphonia: A Pilot Study on Long-Term Outcome on Voice Quality

Objectives. Adductor spasmodic dysphonia (ADSD) is a focal laryngeal dystonia, which compromises greatly the quality of life of the patients involved. It is a severe vocal disorder characterized by spasms of laryngeal muscles during speech, producing phonatory breaks, forced, strained and strangled voice. Its symptoms result from involuntary and intermittent contractions of thyroarytenoid muscle during speech, which causes vocal fold to strain, pressing each vocal fold against the other and increasing glottic resistance. Botulinum toxin injection remains the gold-standard treatment. However, as injections should be repeated periodically leading to voice quality instability, a more definitive procedure would be desirable. In this pilot study we report the long-term vocal quality results of endoscopic laser thyroarytenoid myoneurectomy. Study Design. Prospective study. Methods. Surgery was performed in 15 patients (11 females and four males), aged between 29 and 73 years, diagnosed with ADSD. Voice Handicap Index (VHI) was obtained before and after surgery (median 31 months postoperatively). Results. A significant improvement in VHI was observed after surgery, as compared with baseline values (P = 0.001). The median and interquartile range for preoperative VHI was 99 and 13, respectively and 24 and 42, for postoperative VHI. Subjective improvement of voice as assessed by the patients showed median improvement of 80%. Conclusions. Because long-term follow-up showed significant improvement of voice quality, this innovative surgical technique seems a satisfactory alternative treatment of ADSD patients who seek a definite improvement of their condition.

Tunnel excavation triggering pulmonary sarcoidosis

Context A definite cause of sarcoidosis has not been identified, however past research suggests that environmental factors may be triggers of the granulomatous response in genetically susceptible individuals. Case Presentation A 22-year-old male non-smoker, presented with progressive exertional dyspnea and cough of 3 months duration. One year before, when he started working in tunnel excavation, he had a normal chest radiograph. Chest imaging revealed bilateral nodules and masses of peribronchovascular distribution plus mediastinal lymphadenomegaly. Histologic lymph node analysis revealed non-caseating confluent granulomas. Sarcoidosis was diagnosed. The patient was treated with corticosteroids and advised to change jobs. Complete remission of the disease was achieved and persisted for at least one year without steroid treatment. Discussion Sarcoidosis is believed to have environmental triggers. The timing of the onset of sarcoidosis in this patient following intensive exposure to tunnel dust suggests an environmental contribution. The recognition that sarcoidosis may have occupational triggers have medical, employment, and legal implications. Am. J. Ind. Med. 55: 390-394, 2012. (C) 2011 Wiley Periodicals, Inc.

Cross-national differences in questionnaires do not necessarily reflect comparable differences in disorder prevalence

To examine whether the widely used Strengths and Difficulties Questionnaire (SDQ) can validly be used to compare the prevalence of child mental health problems cross nationally. We used data on 29,225 5- to 16-year olds in eight population-based studies from seven countries: Bangladesh, Brazil, Britain, India, Norway, Russia and Yemen. Parents completed the SDQ in all eight studies, teachers in seven studies and youth in five studies. We used these SDQ data to calculate three different sorts of "caseness indicators" based on (1) SDQ symptoms, (2) SDQ symptoms plus impact and (3) an overall respondent judgement of 'definite' or 'severe' difficulties. Respondents also completed structured diagnostic interviews including extensive open-ended questions (the Development and Well-Being Assessment, DAWBA). Diagnostic ratings were all carried out or supervised by the DAWBA's creator, working in conjunction with experienced local professionals. As judged by the DAWBA, the prevalence of any mental disorder ranged from 2.2% in India to 17.1% in Russia. The nine SDQ caseness indicators (three indicators times three informants) explained 8-56% of the cross-national variation in disorder prevalence. This was insufficient to make meaningful prevalence estimates since populations with a similar measured prevalence of disorder on the DAWBA showed large variations across the various SDQ caseness indicators. The relationship between SDQ caseness indicators and disorder rates varies substantially between populations: cross-national differences in SDQ indicators do not necessarily reflect comparable differences in disorder rates. More generally, considerable caution is required when interpreting cross-cultural comparisons of mental health, particularly when these rely on brief questionnaires.

Lupus anticoagulant: a marker for stroke and venous thrombosis in primary Sjogren's syndrome

Antiphospholipid antibodies (aPL) and antiphospholipid syndrome (APS) have been described in primary Sjogren's syndrome (pSS) with controversial findings regarding aPL prevalence and their association with thrombotic events. We evaluated 100 consecutive pSS patients (American-European criteria) and 89 age-gender-ethnicity-matched healthy controls for IgG/IgM anticardiolipin (aCL), IgG/IgM anti-beta2-glycoprotein-I (a beta 2GPI), and lupus anticoagulant (LA) (positivity according to APS Sydney's criteria). Clinical analysis followed standardized interview and physical examination assessing thrombotic and nonthrombotic APS manifestations and thrombosis risk factors. aPLs were detected in 16 % patients and 5.6 % controls (p = 0.035). LA was the most common aPL in patients (9 %), followed by a beta 2GPI (5 %) and aCL (4 %). Thrombotic events occurred in five patients [stroke in two, myocardial infarction in one and deep-vein thrombosis (DVT) in four], but in none of controls (p = 0.061). Mean age at time of stroke was 35 years. Three patients with thrombotic events (including the two with stroke) had APS (Sydney's criteria) and were positive exclusively for LA. Comparison of patients with (n = 16) and without (n = 84) aPL revealed similar mean age, female predominance, and ethnicity (p > =0.387). Frequencies of livedo reticularis (25 vs. 4.8 %, p = 0.021), stroke (12.5 vs. 0 %, p = 0.024), and DVT (18.8 vs. 1.2 %, p = 0.013) were significantly higher in APL + patients. Conversely, frequencies of hypertension, dyslipidemia, diabetes, obesity, smoking, sedentarism, and hormonal contraception were similar in patients with or without aPL (p a parts per thousand yenaEuro parts per thousand 0.253). Our study identified LA as an important marker for APS in pSS, particularly for stroke in young patients, warranting routine evaluation of these antibodies and rigorous intervention in modifiable risk factors.

Levy stable distributions via associated integral transform

We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g(alpha)(x), 0 <= x < infinity, 0 < alpha < 1. We demonstrate that the knowledge of one such a distribution g a ( x) suffices to obtain exactly g(alpha)p ( x), p = 2, 3, .... Similarly, from known g(alpha)(x) and g(beta)(x), 0 < alpha, beta < 1, we obtain g(alpha beta)( x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For a rational, alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g(l/k)(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4709443]

High temperature limit in static backgrounds

We prove that the hard thermal loop contribution to static thermal amplitudes can be obtained by setting all the external four-momenta to zero before performing the Matsubara sums and loop integrals. At the one-loop order we do an iterative procedure for all the one-particle irreducible one-loop diagrams, and at the two-loop order we consider the self-energy. Our approach is sufficiently general to the extent that it includes theories with any kind of interaction vertices, such as gravity in the weak field approximation, for d space-time dimensions. This result is valid whenever the external fields are all bosonic.

Kurzweil integral for Riesz space-valued functions: Uniform convergence theorem

Our objective here is to prove that the uniform convergence of a sequence of Kurzweil integrable functions implies the convergence of the sequence formed by its corresponding integrals.

BEM modeling of saturated porous media susceptible to damage

This paper deals with the numerical analysis of saturated porous media, taking into account the damage phenomena on the solid skeleton. The porous media is taken into poro-elastic framework, in full-saturated condition, based on Biot's Theory. A scalar damage model is assumed for this analysis. An implicit boundary element method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and two-dimensional elastostatic problems. The integration over boundary elements is evaluated using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear problem is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficacy. (C) 2011 Elsevier Ltd. All rights reserved.