A note on the Kutta condition in Glauert's solution of the thin aerofoil problem

Glauert's classical solution of the thin aerofoil problem (a coordinate transformation, and splitting the solution into a sum of a singular part and an assumed regular part written as a Fourier sine series) is usually presented in textbooks on aerodynamics without a great deal of attention being paid to the rôle of the Kutta condition. Sometimes the solution is merely stated, apparently satisfying the Kutta condition automatically. Quite often, however, it is misleadingly suggested that it is by the choice of a sine series that the Kutta condition is satisfied. It is shown here that if Glauert's approach is interpreted in the context of generalised functions, (1) the whole solution, i.e. both the singular part and any non-Kutta condition solution, can be written as a sine-series, and (2) it is really the coordinate transformation which compels the Kutta condition to be satisfied, as it enhances the edge singularities from integrable to non-integrable, and so sifts out solutions not normally representable by a Fourier series. Furthermore, the present method provides a very direct way to construct other, more singular solutions. A practical consequence is that (at least, in principle) in numerical solutions based on Glauert's method, more is needed for the Kutta condition than a sine series expansion

Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm

Over the past five decades, k-means has become the clustering algorithm of choice in many application domains primarily due to its simplicity, time/space efficiency, and invariance to the ordering of the data points. Unfortunately, the algorithm's sensitivity to the initial selection of the cluster centers remains to be its most serious drawback. Numerous initialization methods have been proposed to address this drawback. Many of these methods, however, have time complexity superlinear in the number of data points, which makes them impractical for large data sets. On the other hand, linear methods are often random and/or sensitive to the ordering of the data points. These methods are generally unreliable in that the quality of their results is unpredictable. Therefore, it is common practice to perform multiple runs of such methods and take the output of the run that produces the best results. Such a practice, however, greatly increases the computational requirements of the otherwise highly efficient k-means algorithm. In this chapter, we investigate the empirical performance of six linear, deterministic (non-random), and order-invariant k-means initialization methods on a large and diverse collection of data sets from the UCI Machine Learning Repository. The results demonstrate that two relatively unknown hierarchical initialization methods due to Su and Dy outperform the remaining four methods with respect to two objective effectiveness criteria. In addition, a recent method due to Erisoglu et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms (Springer, 2014). arXiv admin note: substantial text overlap with arXiv:1304.7465, arXiv:1209.196

Heritable patterns of tooth decay in the permanent dentition: principal components and factor analyses

<p>Abstract</p> <p>Background</p> <p>Dental caries is the result of a complex interplay among environmental, behavioral, and genetic factors, with distinct patterns of decay likely due to specific etiologies. Therefore, global measures of decay, such as the DMFS index, may not be optimal for identifying risk factors that manifest as specific decay patterns, especially if the risk factors such as genetic susceptibility loci have small individual effects. We used two methods to extract patterns of decay from surface-level caries data in order to generate novel phenotypes with which to explore the genetic regulation of caries.</p> <p>Methods</p> <p>The 128 tooth surfaces of the permanent dentition were scored as carious or not by intra-oral examination for 1,068 participants aged 18 to 75 years from 664 biological families. Principal components analysis (PCA) and factor analysis (FA), two methods of identifying underlying patterns without <it>a priori </it>surface classifications, were applied to our data.</p> <p>Results</p> <p>The three strongest caries patterns identified by PCA recaptured variation represented by DMFS index (correlation, r = 0.97), pit and fissure surface caries (r = 0.95), and smooth surface caries (r = 0.89). However, together, these three patterns explained only 37% of the variability in the data, indicating that <it>a priori </it>caries measures are insufficient for fully quantifying caries variation. In comparison, the first pattern identified by FA was strongly correlated with pit and fissure surface caries (r = 0.81), but other identified patterns, including a second pattern representing caries of the maxillary incisors, were not representative of any previously defined caries indices. Some patterns identified by PCA and FA were heritable (h²= 30-65%, p = 0.043-0.006), whereas other patterns were not, indicating both genetic and non-genetic etiologies of individual decay patterns.</p> <p>Conclusions</p> <p>This study demonstrates the use of decay patterns as novel phenotypes to assist in understanding the multifactorial nature of dental caries.</p

The quest for the solar g modes

Solar gravity modes (or g modes) -- oscillations of the solar interior for which buoyancy acts as the restoring force -- have the potential to provide unprecedented inference on the structure and dynamics of the solar core, inference that is not possible with the well observed acoustic modes (or p modes). The high amplitude of the g-mode eigenfunctions in the core and the evanesence of the modes in the convection zone make the modes particularly sensitive to the physical and dynamical conditions in the core. Owing to the existence of the convection zone, the g modes have very low amplitudes at photospheric levels, which makes the modes extremely hard to detect. In this paper, we review the current state of play regarding attempts to detect g modes. We review the theory of g modes, including theoretical estimation of the g-mode frequencies, amplitudes and damping rates. Then we go on to discuss the techniques that have been used to try to detect g modes. We review results in the literature, and finish by looking to the future, and the potential advances that can be made -- from both data and data-analysis perspectives -- to give unambiguous detections of individual g modes. The review ends by concluding that, at the time of writing, there is indeed a consensus amongst the authors that there is currently no undisputed detection of solar g modes.Comment: 71 pages, 18 figures, accepted by Astronomy and Astrophysics Revie

Asteroseismology and Interferometry

Asteroseismology provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Recent developments, including the first systematic studies of solar-like pulsators, have boosted the impact of this field of research within Astrophysics and have led to a significant increase in the size of the research community. In the present paper we start by reviewing the basic observational and theoretical properties of classical and solar-like pulsators and present results from some of the most recent and outstanding studies of these stars. We centre our review on those classes of pulsators for which interferometric studies are expected to provide a significant input. We discuss current limitations to asteroseismic studies, including difficulties in mode identification and in the accurate determination of global parameters of pulsating stars, and, after a brief review of those aspects of interferometry that are most relevant in this context, anticipate how interferometric observations may contribute to overcome these limitations. Moreover, we present results of recent pilot studies of pulsating stars involving both asteroseismic and interferometric constraints and look into the future, summarizing ongoing efforts concerning the development of future instruments and satellite missions which are expected to have an impact in this field of research.Comment: Version as published in The Astronomy and Astrophysics Review, Volume 14, Issue 3-4, pp. 217-36

Interaction Between Convection and Pulsation

This article reviews our current understanding of modelling convection dynamics in stars. Several semi-analytical time-dependent convection models have been proposed for pulsating one-dimensional stellar structures with different formulations for how the convective turbulent velocity field couples with the global stellar oscillations. In this review we put emphasis on two, widely used, time-dependent convection formulations for estimating pulsation properties in one-dimensional stellar models. Applications to pulsating stars are presented with results for oscillation properties, such as the effects of convection dynamics on the oscillation frequencies, or the stability of pulsation modes, in classical pulsators and in stars supporting solar-type oscillations.Comment: Invited review article for Living Reviews in Solar Physics. 88 pages, 14 figure

Corticosteroid effects on ventilator-induced diaphragm dysfunction in anesthetized rats depend on the dose administered

<p>Abstract</p> <p>Background</p> <p>High dose of corticosteroids has been previously shown to protect against controlled mechanical ventilation (CMV)-induced diaphragmatic dysfunction while inhibiting calpain activation. Because literature suggests that the calpain inhibiting effect of corticosteroid depends on the dose administered, we determined whether lower doses of corticosteroids would also provide protection of the diaphragm during CMV. This may be important for patients undergoing mechanical ventilation and receiving corticosteroids.</p> <p>Methods</p> <p>Rats were assigned to controls or to 24 hours of CMV while being treated at the start of mechanical ventilation with a single intramuscular administration of either saline, or 5 mg/kg (low MP) or 30 mg/kg (high MP) of methylprednisolone.</p> <p>Results</p> <p>Diaphragmatic force was decreased after CMV and this was exacerbated in the low MP group while high MP rescued this diaphragmatic dysfunction. Atrophy was more severe in the low MP group than after CMV while no atrophy was observed in the high MP group. A significant and similar increase in calpain activity was observed in both the low MP and CMV groups whereas the high dose prevented calpain activation. Expression of calpastatin, the endogenous inhibitor of calpain, was decreased in the CMV and low MP groups but its level was preserved to controls in the high MP group. Caspase-3 activity increased in all CMV groups but to a lesser extent in the low and high MP groups. The 20S proteasome activity was increased in CMV only.</p> <p>Conclusions</p> <p>Administration of 30 mg/kg methylprednisolone during CMV protected against CMV-induced diaphragm dysfunction while 5 mg/kg was more deleterious. The protective effect is due mainly to an inhibition of the calpain system through preservation of calpastatin levels and to a lesser extent to a caspase-3 inhibition.</p

Identification of novel targets for breast cancer by exploring gene switches on a genome scale

<p>Abstract</p> <p>Background</p> <p>An important feature that emerges from analyzing gene regulatory networks is the "switch-like behavior" or "bistability", a dynamic feature of a particular gene to preferentially toggle between two steady-states. The state of gene switches plays pivotal roles in cell fate decision, but identifying switches has been difficult. Therefore a challenge confronting the field is to be able to systematically identify gene switches.</p> <p>Results</p> <p>We propose a top-down mining approach to exploring gene switches on a genome-scale level. Theoretical analysis, proof-of-concept examples, and experimental studies demonstrate the ability of our mining approach to identify bistable genes by sampling across a variety of different conditions. Applying the approach to human breast cancer data identified genes that show bimodality within the cancer samples, such as estrogen receptor (ER) and ERBB2, as well as genes that show bimodality between cancer and non-cancer samples, where tumor-associated calcium signal transducer 2 (TACSTD2) is uncovered. We further suggest a likely transcription factor that regulates TACSTD2.</p> <p>Conclusions</p> <p>Our mining approach demonstrates that one can capitalize on genome-wide expression profiling to capture dynamic properties of a complex network. To the best of our knowledge, this is the first attempt in applying mining approaches to explore gene switches on a genome-scale, and the identification of TACSTD2 demonstrates that single cell-level bistability can be predicted from microarray data. Experimental confirmation of the computational results suggest TACSTD2 could be a potential biomarker and attractive candidate for drug therapy against both ER+ and ER- subtypes of breast cancer, including the triple negative subtype.</p

Two Component Systems: Physiological Effect of a Third Component

Signal transduction systems mediate the response and adaptation of organisms to environmental changes. In prokaryotes, this signal transduction is often done through Two Component Systems (TCS). These TCS are phosphotransfer protein cascades, and in their prototypical form they are composed by a kinase that senses the environmental signals (SK) and by a response regulator (RR) that regulates the cellular response. This basic motif can be modified by the addition of a third protein that interacts either with the SK or the RR in a way that could change the dynamic response of the TCS module. In this work we aim at understanding the effect of such an additional protein (which we call “third component”) on the functional properties of a prototypical TCS. To do so we build mathematical models of TCS with alternative designs for their interaction with that third component. These mathematical models are analyzed in order to identify the differences in dynamic behavior inherent to each design, with respect to functionally relevant properties such as sensitivity to changes in either the parameter values or the molecular concentrations, temporal responsiveness, possibility of multiple steady states, or stochastic fluctuations in the system. The differences are then correlated to the physiological requirements that impinge on the functioning of the TCS. This analysis sheds light on both, the dynamic behavior of synthetically designed TCS, and the conditions under which natural selection might favor each of the designs. We find that a third component that modulates SK activity increases the parameter space where a bistable response of the TCS module to signals is possible, if SK is monofunctional, but decreases it when the SK is bifunctional. The presence of a third component that modulates RR activity decreases the parameter space where a bistable response of the TCS module to signals is possible