A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Multiple Dynamic Processes Contribute to the Complex Steady Shear Behavior of Cross-Linked Supramolecular Networks of Semidilute Entangled Polymer Solutions.

Molecular theories of shear thickening and shear thinning in associative polymer networks are typically united in that they involve a single kinetic parameter that describes the network -- a relaxation time that is related to the lifetime of the associative bonds. Here we report the steady-shear behavior of two structurally identical metallo-supramolecular polymer networks, for which single-relaxation parameter models break down in dramatic fashion. The networks are formed by the addition of reversible cross-linkers to semidilute entangled solutions of PVP in DMSO, and they differ only in the lifetime of the reversible cross-links. Shear thickening is observed for cross-linkers that have a slower dissociation rate (17 s(-1)), while shear thinning is observed for samples that have a faster dissociation rate (ca. 1400 s(-1)). The difference in the steady shear behavior of the unentangled vs. entangled regime reveals an unexpected, additional competing relaxation, ascribed to topological disentanglement in the semidilute entangled regime that contributes to the rheological properties.

Mechanism of Shear Thickening in Reversibly Cross-linked Supramolecular Polymer Networks.

We report here the nonlinear rheological properties of metallo-supramolecular networks formed by the reversible cross-linking of semi-dilute unentangled solutions of poly(4-vinylpyridine) (PVP) in dimethyl sulfoxide (DMSO). The reversible cross-linkers are bis-Pd(II) or bis-Pt(II) complexes that coordinate to the pyridine functional groups on the PVP. Under steady shear, shear thickening is observed above a critical shear rate, and that critical shear rate is experimentally correlated with the lifetime of the metal-ligand bond. The onset and magnitude of the shear thickening depend on the amount of cross-linkers added. In contrast to the behavior observed in most transient networks, the time scale of network relaxation is found to increase during shear thickening. The primary mechanism of shear thickening is ascribed to the shear-induced transformation of intrachain cross-linking to interchain cross-linking, rather than nonlinear high tension along polymer chains that are stretched beyond the Gaussian range.

Who tests, who doesn't, and why? Uptake of mobile HIV counseling and testing in the Kilimanjaro Region of Tanzania.

BACKGROUND: Optimally, expanded HIV testing programs should reduce barriers to testing while attracting new and high-risk testers. We assessed barriers to testing and HIV risk among clients participating in mobile voluntary counseling and testing (MVCT) campaigns in four rural villages in the Kilimanjaro Region of Tanzania. METHODS: Between December 2007 and April 2008, 878 MVCT participants and 506 randomly selected community residents who did not access MVCT were surveyed. Gender-specific logistic regression models were used to describe differences in socioeconomic characteristics, HIV exposure risk, testing histories, HIV related stigma, and attitudes toward testing between MVCT participants and community residents who did not access MVCT. Gender-specific logistic regression models were used to describe differences in socioeconomic characteristics, HIV exposure risk, testing histories, HIV related stigma, and attitudes toward testing, between the two groups. RESULTS: MVCT clients reported greater HIV exposure risk (OR 1.20 [1.04 to 1.38] for males; OR 1.11 [1.03 to 1.19] for females). Female MVCT clients were more likely to report low household expenditures (OR 1.47 [1.04 to 2.05]), male clients reported higher rates of unstable income sources (OR 1.99 [1.22 to 3.24]). First-time testers were more likely than non-testers to cite distance to testing sites as a reason for not having previously tested (OR 2.17 [1.05 to 4.48] for males; OR 5.95 [2.85 to 12.45] for females). HIV-related stigma, fears of testing or test disclosure, and not being able to leave work were strongly associated with non-participation in MVCT (ORs from 0.11 to 0.84). CONCLUSIONS: MVCT attracted clients with increased exposure risk and fewer economic resources; HIV related stigma and testing-related fears remained barriers to testing. MVCT did not disproportionately attract either first-time or frequent repeat testers. Educational campaigns to reduce stigma and fears of testing could improve the effectiveness of MVCT in attracting new and high-risk populations.

Intracardiac acoustic radiation force impulse (ARFI) and shear wave imaging in pigs with focal infarctions.

Four pigs, three with focal infarctions in the apical intraventricular septum (IVS) and/or left ventricular free wall (LVFW), were imaged with an intracardiac echocardiography (ICE) transducer. Custom beam sequences were used to excite the myocardium with focused acoustic radiation force (ARF) impulses and image the subsequent tissue response. Tissue displacement in response to the ARF excitation was calculated with a phase-based estimator, and transverse wave magnitude and velocity were each estimated at every depth. The excitation sequence was repeated rapidly, either in the same location to generate 40 Hz M-modes at a single steering angle, or with a modulated steering angle to synthesize 2-D displacement magnitude and shear wave velocity images at 17 points in the cardiac cycle. Both types of images were acquired from various views in the right and left ventricles, in and out of infarcted regions. In all animals, acoustic radiation force impulse (ARFI) and shear wave elasticity imaging (SWEI) estimates indicated diastolic relaxation and systolic contraction in noninfarcted tissues. The M-mode sequences showed high beat-to-beat spatio-temporal repeatability of the measurements for each imaging plane. In views of noninfarcted tissue in the diseased animals, no significant elastic remodeling was indicated when compared with the control. Where available, views of infarcted tissue were compared with similar views from the control animal. In views of the LVFW, the infarcted tissue presented as stiff and non-contractile compared with the control. In a view of the IVS, no significant difference was seen between infarcted and healthy tissue, whereas in another view, a heterogeneous infarction was seen to be presenting itself as non-contractile in systole.

Do You Want to Hear the Bad News? The Value of Diagnostic Tests for Alzheimer's Disease.

OBJECTIVE: The diagnosis of Alzheimer's disease (AD) remains difficult. Lack of diagnostic certainty or possible distress related to a positive result from diagnostic testing could limit the application of new testing technologies. The objective of this paper is to quantify respondents' preferences for obtaining AD diagnostic tests and to estimate the perceived value of AD test information. METHODS: Discrete-choice experiment and contingent-valuation questions were administered to respondents in Germany and the United Kingdom. Choice data were analyzed by using random-parameters logit. A probit model characterized respondents who were not willing to take a test. RESULTS: Most respondents indicated a positive value for AD diagnostic test information. Respondents who indicated an interest in testing preferred brain imaging without the use of radioactive markers. German respondents had relatively lower money-equivalent values for test features compared with respondents in the United Kingdom. CONCLUSIONS: Respondents preferred less invasive diagnostic procedures and tests with higher accuracy and expressed a willingness to pay up to €700 to receive a less invasive test with the highest accuracy.

Diagnosis of tuberculosis: update of interferon gamma release tests in clinical practice

info:eu-repo/semantics/nonPublished

Basophil activation tests for the diagnosis of food allergy in children.

BACKGROUND: Positive skin prick tests (SPT) for food allergens and specific IgE (sIgE) in serum indicate sensitization but do not enable distinction between sensitized but tolerant and clinically allergic patients. OBJECTIVE: Herein, we evaluate the clinical relevance of basophil activation tests (BATs) for peanut or egg allergy diagnosis. METHODS: Thirty-two peanut-allergic, 14 peanut-sensitized (sIgE(+) and/or SPT(+) to peanuts) but tolerant children and 29 controls with no history of an adverse reaction to peanuts were included. Similarly, 31 egg-allergic, 14 egg-sensitized children (sIgE(+) and/or SPT(+) to egg white) and 22 controls were studied. Flow cytometric analysis of CD63 expression or CD203c upregulation on basophils and the production of leukotrienes (LT) were performed in response to an in vitro crude peanut extract or ovalbumin (OVA) challenge. RESULTS: After in vitro peanut challenge, the basophils from peanut-allergic children showed significantly higher levels of activation than those from controls (P<0.001). After OVA challenge, a similar distinction (P<0.001) was observed between egg-allergics and controls. Interestingly, the majority of egg- or peanut-sensitized children failed to activate basophils, respectively, in response to OVA and peanut challenge. The sensitivity of the CD63, CD203c and LT assay was 86.7%, 89.5% and 76.0% with a specificity of 94.1%, 97.1% and 94.6% for peanut allergy diagnosis. The corresponding performances of BATs applied to egg allergy diagnosis were 88.9%, 62.5% and 77.8% for the sensitivity and 100%, 96.4% and 96.4% for the specificity. CONCLUSION: Neither conventional tests nor BATs are sensitive and specific enough to predict food allergy accurately. However, BATs may helpfully complete conventional tests, especially SPT, allowing improved discrimination between allergic and non-allergic individuals.

An integrated approach to flow, thermal and mechanical modeling of electronics devices

The future success of many electronics companies will depend to a large extent on their ability to initiate techniques that bring schedules, performance, tests, support, production, life-cycle-costs, reliability prediction and quality control into the earliest stages of the product creation process. Earlier papers have discussed the benefits of an integrated analysis environment for system-level thermal, stress and EMC prediction. This paper focuses on developments made to the stress analysis module and presents results obtained for an SMT resistor. Lifetime predictions are made using the Coffin-Manson equation. Comparison with the creep strain energy based models of Darveaux (1997) shows the shear strain based method to underestimate the solder joint life. Conclusions are also made about the capabilities of both approaches to predict the qualitative and quantitative impact of design changes.

Finite element modelling of crack detection tests

Four non-destructive tests for determining the length of fatigue cracks within the solder joints of a 2512 surface mount resistor are investigated. The sensitivity of the tests is obtained using finite element analysis with some experimental validation. Three of the tests are mechanically based and one is thermally based. The mechanical tests all operate by applying different loads to the PCB and monitoring the strain response at the top of the resistor. The thermal test operates by applying a heat source underneath the PCB, and monitoring the temperature response at the top of the resistor. From the modelling work done, two of these tests have shown to be sensitive to cracks. Some experimental results are presented but further work is required to fully validate the simulation results.

Assessing the performance of crack detection tests for solder joints

This paper presents both modelling and experimental test data to characterise the performance of four non-destructive tests. The focus is on determining the presence and rough magnitude of thermal fatigue cracks within the solder joints for a surface mount resistor on a strip of FR4 PCB. The tests all operate by applying mechanical loads to the PCB and monitoring the strain response at the top of the resistor. The modelling results show that of the four tests investigated, three are sensitive to the presence of a crack in the joint and its magnitude. Hence these tests show promise in being able to detect cracking caused by accelerated testing. The experimental data supports these results although more validation is required.

Study of the rheological behaviour of Sn-Ag-Cu solder pastes and their correlation with printing performance

Solder paste plays an important role in the electronic assembly process by providing electrical, mechanical and thermal bonding between the components and the substrate. The rheological characterisation of pastes is an important step in the design and development of new paste formulations. With the ever increasing trend of miniaturisation of electronic products, the study of the rheological properties of solder pastes is becoming an integral part in the R&D of new paste formulations and in the quality monitoring and control during paste manufacture and electronic assembly process. This research work outlines some of the novel techniques which can be successfully used to investigate the rheology of leadfree solder pastes. The report also presents the results of the correlation of rheological properties with solder paste printing performance. Four different solder paste samples (namely paste P1, P2, P3 and P4) with different flux vehicle systems and particle size distributions were investigated in the study. As expected, all the paste samples showed shear thinning behaviour. Although the samples displayed similar flow behaviour at high shear rates, differences were observed at low shear rates. In the stencil printing trials, round deposits showed better results than rectangular deposits in terms of paste heights and aperture filling. Our results demonstrate a good correlation between higher paste viscosity and good printing performance. The results of the oscillatory and thixotropy tests were also successfully correlated to the printing behaviour of solder paste.