Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet

The wide range of industrial applications of flow across moving or static solid surfaces has aroused the curiosity of researchers. In order to generate a more exact estimate of flow and heat transfer properties, three-dimensional modelling must be addressed. This plays a vital role in metalworking operations, producing plastic and rubber films, and the continuous cooling of fibre. In view of the above scope, an incompressible, laminar three-dimensional flow of a Casson nanoliquid in the occurrence of thermophoretic particle deposition over a non-linearly extending sheet is examined. To convert the collection of partial differential equations into ordinary differential equations, the governing equations are framed with sufficient assumptions, and appropriate similarity transformations are employed. The reduced equations are solved by implementing Runge Kutta Fehlberg 4th 5th order technique with the aid of a shooting scheme. The numerical results are obtained for linear and non-linear cases, and graphs are drawn for various dimensionless constraints. The present study shows that improvement in the Casson parameter values will diminish the axial velocities, but improvement is seen in thermal distribution. The escalation in the thermophoretic parameter will decline the concentration profiles. The rate of mass transfer, surface drag force will reduce with the improved values of the power law index. The non-linear stretching case shows greater impact in all of the profiles compared to the linear stretching case.

The Impact of Variant Allele Frequency in EGFR Mutated NSCLC Patients on Targeted Therapy

EGFR mutations represent the most common currently targetable oncogenic driver in non-small cell lung cancer. There has been tremendous progress in targeting this alteration over the course of the last decade, and third generation tyrosine kinase inhibitors offer previously unseen survival rates among these patients. Nonetheless, a better understanding is still needed, as roughly a third of patients do not respond to targeted therapy and there is an important heterogeneity among responders. Allelic frequency, or the variant EGFR allele frequency, corresponds to the fraction of sequencing reads harboring the mutation. The allelic fraction is influenced by the proportion of tumor cells in the sample, the presence of copy number alterations but also, most importantly, by the proportion of cells within the tumor that carry the mutation. Mutations that occur early in tumor evolution, often called clonal or truncal, have a higher allelic frequency than late, subclonal mutations, and are more often drivers of cancer evolution and attractive therapeutic targets. Most, but not all, EGFR mutations are clonal. Although an exact estimate of clonal proportion is hard to derive computationally, the allelic frequency is readily available to clinicians and could be a useful surrogate. We hypothesized that tumors with low allelic frequency of the EGFR mutation will respond less favorably to targeted treatment.

Integral operators, bispectrality and growth of Fourier algebras

In the mid 1980s it was conjectured that every bispectral meromorphic function {\psi(x,y)} gives rise to an integral operator {K_{\psi}(x,y)} which possesses a commuting differential operator. This has been verified by a direct computation for several families of functions {\psi(x,y)} where the commuting differential operator is of order {\leq 6}. We prove a general version of this conjecture for all self-adjoint bispectral functions of rank 1 and all self-adjoint bispectral Darboux transformations of the rank 2 Bessel and Airy functions. The method is based on a theorem giving an exact estimate of the second- and first-order terms of the growth of the Fourier algebra of each such bispectral function. From it we obtain a sharp upper bound on the order of the commuting differential operator for the integral kernel {K_{\psi}(x,y)} leading to a fast algorithmic procedure for constructing the differential operator; unlike the previous examples its order is arbitrarily high. We prove that the above classes of bispectral functions are parametrized by infinite-dimensional Grassmannians which are the Lagrangian loci of the Wilson adelic Grassmannian and its analogs in rank 2.

Validation of the 3-variable prognostic score (3-PS) in mCRPC patients treated with 223Radium-dichloride: a national multicenter study

Objective Radium-223 (223Ra) has been approved for treatment in patients with metastatic castration-resistant prostatic cancer (mCRPC) and bone metastasis. This α-emitting radionuclide has a beneficial effect on pain and is also capable to increase overall survival (OS). Several studies evaluated the prognostic value of different biomarkers at baseline, such as serum values, imaging parameters or pain. To date, however, clinicians lack a validated and simple system to assess which patients will most likely benefit from 223Ra treatment. The 3-variable prognostic score (3-PS), proposed in a single-center study in 2017 classifies patients in five prognostic groups with a specific OS. This study aims to validate the 3-PS in a larger multicenter population. Methods Four hundred and thirty mCRPC patients treated with 223Ra from six different centers were analyzed. The 3-PS score consists of the collection of baseline hemoglobin, prostatic specific antigen and Eastern cooperative oncology group performance status and was initially applied to the whole population (total group). The score was then validated on the 338 patient’s subgroup (clean group) obtained by subtracting the 92 patients enrolled for the original study of the 3-PS score. This purified group served as further validation evidence. Results Statistical analysis showed that the 3-PS score was valid on the total group as well as in the clean group as the AUC estimated (0.74) falls within the CI of the AUC calculated on the validation sample (95% CI 0.66–0.82). Conclusion This study confirms the validity of the 3-PS score for mCRPC patients. This score is simple, noninvasive and affordable and can be easily used to select patients that will most probably complete 223Ra treatment. In addition, this tool provides an exact estimate of life expectancy in terms of OS.

Use of a Single Ventilator to Support Multiple Patients: Modeling Tidal Volume Response to Heterogeneous Lung Mechanics

The COVID-19 pandemic is creating ventilator shortages in many countries that is sparking a conversation about placing multiple people on a single ventilator. However, on March 26th the American College of Chest Physicians (CHEST), along with other leading medical organizations, released a joint statement warning clinicians that attempting this technique could lead to poor outcomes and high mortality. Nevertheless, several hospitals around the United States and abroad are turning to this technique out of desperation (e.g. New York), but little data exists to guide their approach. The overall objective of this study is to utilize a computational model of mechanically ventilated lungs to assess how patient-specific lung mechanics and ventilator settings impact lung tidal volume (Vt).MethodsWe developed a single compartment computational model of four patients connected to a shared ventilator and validated it against a similar experimental study. We used this model to evaluate how patient-specific lung compliance (C) and resistance (R) would impact Vt under 5 ventilator settings of pre-set PIP, PEEP, and I:E ratio (suggested by Farkas, J.D. MD as an approach by hospitals to manage multiple patients on a single ventilator).ResultsOur computational model predicts Vt within 10% of experimental measurements. Using this model to perform a parametric study, we provide proof-of-concept for an algorithm to better match patients in different hypothetical scenarios of a single ventilator shared by more than one patient.ConclusionsAssigning patients to pre-set ventilators based on their lung mechanics could be used to overcome some of the legitimate concerns of placing multiple patients on a single ventilator. We emphasize that our results are currently based on a computational model that has not been validated against any pre-clinical/clinical data. Therefore, clinicians considering this approach should not look to our study as an exact estimate of predicted patient tidal volumes.

Does Union Membership Pay Off? Evidence from Vietnamese SMEs

In the absence of adequate institutional mechanisms, trade unions can potentially promote some measure of equity and social justice for workers including for instance higher wages and other worker benefits. Yet limited data availability means little is known about the effect local firm-based trade unions may have on individual earnings in developing and transition economies. Using matched employer–employee data from the 2013 and 2015 SME surveys, this chapter examines the union wage premium among workers in Vietnamese small and medium-sized enterprises. Controlling for both firm and worker characteristics, including time-varying unobserved heterogeneity, the results show that unionized workers’ wages are 9–22 per cent higher than those of non-union workers, with the exact estimate depending on the econometric approach chosen.

On the nonsymmetric approximation of continuous functions in the integral metric

In the paper, an exact estimate of the best nonsymmetric approximation in the integral metric by the constants of continuous functions that belong to the classes $H^\omega[a,b]$ is proved. Taking into account Babenko's theorem on the connection of nonsymmetric approximation with the usual best approximation in the integral metric and the best one-sided approximations, from the proved result we obtain the exact estimate for the usual best approximation obtained by N.P. Korneichuk, and the exact estimate for the best one-sided approximation obtained by V.G. Doronin and A.A. Ligun.

A comparison of error estimates at a point and on a set when solving ill-posed problems

The problem of correlating the error estimates at a point and on a correctness class is of interest to many mathematicians. Since the desired solution to a real ill-posed problem is unique, the error estimate obtained on the class becomes crude. In this paper, by assuming that an exact solution is a piecewise smooth function, we prove, for a special class of incorrect problems, that an error estimate at a point is an infinitely small quantity compared with an exact estimate on a correctness set.