Regularization of the semilinear sideways heat equation

A classical physical example of the sideways heat equation is represented by re-entry vehicles in the atmosphere where the temperature at the nozzle of a rocket is so high that any thermocouple attached to it would be destroyed. Instead one could measure both the temperature and heat flux, i.e. Cauchy data, at an interior boundary inward the capsule. In addition, we assume that there exists a heat source which is significantly dependent on space, time and temperature, and hence it cannot be neglected. This gives rise to a non-characteristic Cauchy inverse boundary value problem in the sense that the interior accessible boundary is overspecified, while the exterior hostile boundary is underspecified as nothing is prescribed on it. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the Cauchy data. In order to obtain a stable numerical solution, we propose two regularization methods to solve the semilinear problem in which the heat source is a Lipschitz function of temperature. We show rigourously, with error estimates provided, that the corresponding regularized solutions converge to the true solution strongly in L² uniformly with respect to the space coordinate under some a priori assumptions on the solution. These assumptions place no serious restrictions on the applicability of the results since in practice we always have some control and knowledge about how large the absolute temperature and heat flux are likely to be. Finally, in order to increase the significance of the study, numerical results are presented and discussed illustrating the theoretical findings in terms of accuracy and stability

Recovering the initial distribution for strongly damped wave equation

We study for the first time the inverse backward problem for the strongly damped wave equation. First, we show that the problem is severely ill-posed in the sense of Hadamard. Then, under the a priori assumption on the exact solution belonging to a Gevrey space, we propose the Fourier truncation method for stabilizing the ill-posed problem. A stability estimate of logarithmic type is established

So Small, So Loud: Extremely High Sound Pressure Level from a Pygmy Aquatic Insect (Corixidae, Micronectinae)

To communicate at long range, animals have to produce intense but intelligible signals. This task might be difficult to achieve due to mechanical constraints, in particular relating to body size. Whilst the acoustic behaviour of large marine and terrestrial animals has been thoroughly studied, very little is known about the sound produced by small arthropods living in freshwater habitats. Here we analyse for the first time the calling song produced by the male of a small insect, the water boatman Micronecta scholtzi. The song is made of three distinct parts differing in their temporal and amplitude parameters, but not in their frequency content. Sound is produced at 78.9 (63.6–82.2) SPL rms re 2.10−5 Pa with a peak at 99.2 (85.7–104.6) SPL re 2.10−5 Pa estimated at a distance of one metre. This energy output is significant considering the small size of the insect. When scaled to body length and compared to 227 other acoustic species, the acoustic energy produced by M. scholtzi appears as an extreme value, outperforming marine and terrestrial mammal vocalisations. Such an extreme display may be interpreted as an exaggerated secondary sexual trait resulting from a runaway sexual selection without predation pressure

Mechanism of endothelial progenitor cell recruitment into neo-vessels in adjacent non-tumor tissues in hepatocellular carcinoma

Abstract Background We investigated the distribution and clinical significance of mobilized endothelial progenitor cells (EPCs) in hepatocellular carcinoma (HCC). We found that many more EPCs were recruited to nonmalignant liver tissue (especially into adjacent non-tumor tissues (AT)) than to tumor vessels. These results suggest that the mechanism underlying the recruitment of EPCs into microvessels in AT merits further investigation Methods Angiogenic factors were detected in three tissue microarrays comprising normal liver, paired tumor tissue (TT) and AT from 105 patients (who had undergone hepatectomy for HCC) using immunohistochemistry. Also, the number of EPCs (positive for Sca-1, Flk-1 and c-Kit) in the blood and liver of cirrhotic mice were determined by flow cytometry and immunohistochemistry. The distribution of these labeled EPCs in tumor and non-tumor tissues was then studied. Results The results from the tissue microarrays showed that the expression levels of VEGF-A, bFGF, TGF-β, MCP-1, TSP-1, MMP-9, TIMP-2, and endostatin were significantly higher in AT than in either normal liver or TT (p Conclusions Both liver cirrhosis and HCC led to increased expression of pro-angiogenic factors, which resulted in the recruitment of EPCs into AT. Also, EPCs were mobilized, recruited and homed to cirrhotic liver. The unique pathology of HCC coupled with liver cirrhosis may, therefore, be associated with the distribution and function of EPCs.</p

Prognostic and predictive value of TOPK stratified by KRAS and BRAF gene alterations in sporadic, hereditary and metastatic colorectal cancer patients

BACKGROUND: Our aim was to investigate the prognostic and predictive value of the oncogenic MAPKK-like protein T-cell-originated protein kinase (TOPK) stratified by KRAS and BRAF mutations in patients with sporadic, hereditary and metastatic colorectal cancer (CRC) treated with anti-EGFR therapy. METHODS: Immunohistochemistry (IHC) for TOPK was performed on four study groups. Group 1 included two subgroups of 543 and 501 sporadic CRC patients used to test the reliability of TOPK expression by IHC. In Group 2, representing an additional 222 sporadic CRCs, the prognostic effect of TOPK stratified by KRAS and BRAF was assessed. The prognostic effect of TOPK was further analysed in Group 3, representing 71 hereditary Lynch syndrome-associated CRC patients. In Group 4, the predictive and prognostic value of TOPK was analysed on 45 metastatic patients treated with cetuximab or panitumumab stratified by KRAS and BRAF gene status. RESULTS: In both sporadic CRC subgroups (Group 1), associations of diffuse TOPK expression with clinicopathological features were reproducible. Molecular analysis of sporadic CRCs in Group 2 showed that diffuse TOPK expression was associated with KRAS and BRAF mutations (p<0.001) and with poor outcome in patients with either mutation in univariate and multivariate analysis (P=0.017). In hereditary patients (Group 3), diffuse TOPK was linked to advanced pT stage. In metastatic patients treated with anti-EGFR therapy (Group 4), diffuse TOPK expression was linked to dismal outcome despite objective response to treatment (P=0.01). CONCLUSIONS: TOPK expression is an unfavourable prognostic indicator in sporadic patients with KRAS or BRAF mutations and also in patients with metastatic disease experiencing a response to anti-EGFR therapies. The inhibition of TOPK, which could benefit 30-40% of CRC patients, may represent a new avenue of investigation for targeted therapy

High source levels and small active space of high-pitched song in bowhead whales (Balaena mysticetus)

© The Author(s), 2012. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Public Library of Science, doi:10.1371/journal.pone.0052072.The low-frequency, powerful vocalizations of blue and fin whales may potentially be detected by conspecifics across entire ocean basins. In contrast, humpback and bowhead whales produce equally powerful, but more complex broadband vocalizations composed of higher frequencies that suffer from higher attenuation. Here we evaluate the active space of high frequency song notes of bowhead whales (Balaena mysticetus) in Western Greenland using measurements of song source levels and ambient noise. Four independent, GPS-synchronized hydrophones were deployed through holes in the ice to localize vocalizing bowhead whales, estimate source levels and measure ambient noise. The song had a mean apparent source level of 185±2 dB rms re 1 µPa @ 1 m and a high mean centroid frequency of 444±48 Hz. Using measured ambient noise levels in the area and Arctic sound spreading models, the estimated active space of these song notes is between 40 and 130 km, an order of magnitude smaller than the estimated active space of low frequency blue and fin whale songs produced at similar source levels and for similar noise conditions. We propose that bowhead whales spatially compensate for their smaller communication range through mating aggregations that co-evolved with broadband song to form a complex and dynamic acoustically mediated sexual display.This work was funded by the Oticon Foundation (grant # 08-3469 to Arctic Station, OT). OT and MC were additionally funded by AP Møller og Hustru Chastine Mc-Kinney Møllers Fond til almene Formaal, MS by a PhD scholarship from the Oticon Foundation, FHJ by a Danish Council for Independent Research, Natural Sciences post-doctoral grant, SEP by a grant from the U.S. Office of Naval Research, and PTM by frame grants from the Danish Natural Science Research Council

Persistence of viral reservoirs in multiple tissues after antiretroviral therapy suppression in a macaque RT-SHIV model

Although antiretroviral therapy (ART) can suppress HIV-1 replication sufficiently to eliminate measurable plasma viremia, infected cells remain and ensure viral recrudescence after discontinuation of ART. We used a macaque model of HIV-1/AIDS to evaluate the location of infected cells during ART. Twelve macaques were infected with RT-SHIVmne, a SIV containing HIV-1 reverse transcriptase, conferring sensitivity to non-nucleoside reverse transcriptase inhibitors (NNRTIs). Ten to fourteen weeks post-infection, 6 animals were treated with 3 or 4 antiretroviral drugs for 17-20 weeks; 6 control animals remained untreated. Viral DNA (vDNA) and RNA (vRNA) were measured in peripheral blood mononuclear cells (PBMC) and at necropsy in multiple tissues by quantitative PCR and RT-PCR. The majority of virally infected cells were located in lymphoid tissues with variable levels in the gastrointestinal tract of both treated and untreated animals. Tissue viral DNA levels correlated with week 1 plasma viremia, suggesting that tissues that harbor proviral DNA are established within the first week of infection. PBMC vDNA levels did not correlate with plasma viremia or tissue levels of vDNA. vRNA levels were high in lymphoid and gastrointestinal tissues of the untreated animals; animals on ART had little vRNA expressed in tissues and virus could not be cultured from lymph node resting CD4+ cells after 17-20 weeks on ART, indicating little or no ongoing viral replication. Strategies for eradication of HIV-1 will need to target residual virus in ART suppressed individuals, which may not be accurately reflected by frequencies of infected cells in blood. © 2013 Kline et al

Ribavirin-Induced Anemia in Hepatitis C Virus Patients Undergoing Combination Therapy

The current standard of care for hepatitis C virus (HCV) infection – combination therapy with pegylated interferon and ribavirin – elicits sustained responses in only ∼50% of the patients treated. No alternatives exist for patients who do not respond to combination therapy. Addition of ribavirin substantially improves response rates to interferon and lowers relapse rates following the cessation of therapy, suggesting that increasing ribavirin exposure may further improve treatment response. A key limitation, however, is the toxic side-effect of ribavirin, hemolytic anemia, which often necessitates a reduction of ribavirin dosage and compromises treatment response. Maximizing treatment response thus requires striking a balance between the antiviral and hemolytic activities of ribavirin. Current models of viral kinetics describe the enhancement of treatment response due to ribavirin. Ribavirin-induced anemia, however, remains poorly understood and precludes rational optimization of combination therapy. Here, we develop a new mathematical model of the population dynamics of erythrocytes that quantitatively describes ribavirin-induced anemia in HCV patients. Based on the assumption that ribavirin accumulation decreases erythrocyte lifespan in a dose-dependent manner, model predictions capture several independent experimental observations of the accumulation of ribavirin in erythrocytes and the resulting decline of hemoglobin in HCV patients undergoing combination therapy, estimate the reduced erythrocyte lifespan during therapy, and describe inter-patient variations in the severity of ribavirin-induced anemia. Further, model predictions estimate the threshold ribavirin exposure beyond which anemia becomes intolerable and suggest guidelines for the usage of growth hormones, such as erythropoietin, that stimulate erythrocyte production and avert the reduction of ribavirin dosage, thereby improving treatment response. Our model thus facilitates, in conjunction with models of viral kinetics, the rational identification of treatment protocols that maximize treatment response while curtailing side effects

Mortality Risk of Hypnotics: Strengths and Limits of Evidence

Sleeping pills, more formally defined as hypnotics, are sedatives used to induce and maintain sleep. In a review of publications for the past 30 years, descriptive epidemiologic studies were identified that examined the mortality risk of hypnotics and related sedative-anxiolytics. Of the 34 studies estimating risk ratios, odds ratios, or hazard ratios, excess mortality associated with hypnotics was significant (p &lt; 0.05) in 24 studies including all 14 of the largest, contrasted with no studies at all suggesting that hypnotics ever prolong life. The studies had many limitations: possibly tending to overestimate risk, such as possible confounding by indication with other risk factors; confusing hypnotics with drugs having other indications; possible genetic confounders; and too much heterogeneity of studies for meta-analyses. There were balancing limitations possibly tending towards underestimates of risk such as limited power, excessive follow-up intervals with possible follow-up mixing of participants taking hypnotics with controls, missing dosage data for most studies, and over-adjustment of confounders. Epidemiologic association in itself is not adequate proof of causality, but there is proof that hypnotics cause death in overdoses; there is thorough understanding of how hypnotics euthanize animals and execute humans; and there is proof that hypnotics cause potentially lethal morbidities such as depression, infection, poor driving, suppressed respiration, and possibly cancer. Combining these proofs with consistent evidence of association, the great weight of evidence is that hypnotics cause huge risks of decreasing a patient's duration of survival