A mathematical theory of microscale hydrodynamic cloaking and shielding by electro-osmosis

In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first establish the representation formula of the solution of the coupled system using the layer potential techniques. Based on Fourier series, the perfect hydrodynamic cloaking and shielding conditions are derived for the control region with the cross-sectional shape being annulus or confocal ellipses. Then we further propose an optimization scheme for the design of approximate cloaks and shields within general geometries. The well-posedness of the optimization problem is proved. In particular, the condition that can ensure the occurrence of approximate cloaks and shields for general geometries are also established. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking and shielding

Enhanced Microscale Hydrodynamic Near-cloaking using Electro-osmosis

In this paper, we develop a general mathematical framework for enhanced hydrodynamic near-cloaking of electro-osmotic flow for more complex shapes, which is obtained by simultaneously perturbing the inner and outer boundaries of the perfect cloaking structure. We first derive the asymptotic expansions of perturbed fields and obtain a first-order coupled system. We then establish the representation formula of the solution to the first-order coupled system using the layer potential techniques. Based on the asymptotic analysis, the enhanced hydrodynamic near-cloaking conditions are derived for the control region with general cross-sectional shape. The conditions reveal the inner relationship between the shapes of the object and the control region. Especially, for the shape of a deformed annulus or confocal ellipses cylinder, the cloaking conditions and relationship of shapes are quantified more accurately. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking

Strangeon matter and strangeon stars in a linked bag model

Inspired by various astrophysical phenomenons, it was suggested that pulsar-like compact stars may in fact be strangeon stars, comprised entirely of strangeons (quark-clusters with three-light-flavor symmetry) and a small amount of electrons. To examine such possibilities, in this work we propose a linked bag model, which can be adopted for strong condensed matter in both 2-flavoured (nucleons) and 3-flavoured (hyperons, strangeons, etc.) scenarios. The model parameters are calibrated to reproduce the saturation properties of nuclear matter, which are later applied to hyperonic matter and strangeon matter. The obtained energy per baryon of strangeon matter is reduced if we adopt larger quark numbers inside a strangeon, which stiffens the equation of state and consequently increases the maximum mass of strangeon stars. In a large parameter space, the maximum mass and tidal deformability of strangeon stars predicted in the linked bag model are consistent with the current astrophysical constraints. It is found that the maximum mass of strangeon stars can be as large as $\sim 2.5M_\odot$, while the tidal deformability of a $1.4M_\odot$ strangeon star lies in the range of $180\lesssim \Lambda_{1.4} \lesssim 340$. More refined theoretical efforts as well as observational tests to these results are necessary in the future

Training Classifiers under Covariate Shift by Constructing the Maximum Consistent Distribution Subset

The assumption that the training and testing samples are drawn from the same distribution is violated under covariate shift setting, and most algorithms for the covariate shift setting try to first estimate distributions and then reweight samples based on the distributions estimated. Due to the difficulty of estimating a correct distribution, previous methods can not get good classification performance. In this paper, we firstly present two types of covariate shift problems. Rather than estimating the distributions, we then desire an effective method to select a maximum subset following the target testing distribution based on feature space split from the auxiliary set or the target training set. Finally, we prove that our subset selection method can consistently deal with both scenarios of covariate shift. Experimental results demonstrate that training a classifier with the selected maximum subset exhibits good generalization ability and running efficiency over those of traditional methods under covariate shift setting

Clinicopathological characteristics and prognostic analysis of Lauren classification in gastric adenocarcinoma in China

BACKGROUND: According to the Lauren classification, gastric adenocarcinomas are divided into diffuse and intestinal types. The causative attribution explaining the dismal prognosis of diffuse-type remains unknown. METHODS: We examined the archive of 1000 patients with gastric adenocarcinomas who received radical gastrectomy in our center and assessed the effect of the Lauren classification on survival in a multivariate approach. Moreover we compared the variation of clinical features between the diffuse-type and intestinal-type and explored the contributing factors for the prognostic difference. RESULTS: There were 805 resectable patients for the final analysis. Diffuse-type comprised of 48.7% in the gastric carcinoma in our group and showed poorer prognosis than intestinal-type (P=0.013). Multivariate analysis revealed that independent prognostic factors for gastric carcinoma patients were T stage (P<0.001), N stage (P<0.001) tumor size (P<0.001) and Lauren classification (P=0.003). For the clinical features, diffuse-type was significantly associated with younger age (p<0.001), female preponderance (p <0.001), distal location (P<0.001), advanced pT (p < 0.001), advanced pN (p < 0.001) and advanced TNM stage (p = 0.027). CONCLUSIONS: Diffuse type adenocarcinoma carries a worse prognosis that may be partially explained by the tendency of this subtype to present at more advanced T and N stage. However, Lauren classification has prognostic significance that is independent of T and N stage as well as other prognostic variables based on the multivariate cox analysis

Prognostic effects of 25-hydroxyvitamin D levels in gastric cancer

<p>Abstract</p> <p>Background</p> <p>Results from large epidemiologic studies on the association between vitamin D and gastric cancer are controversial. Vitamin D significantly promotes apoptosis in the undifferentiated gastric cancer cell, but the prognostic effects of its levels are unknown.</p> <p>Methods</p> <p>197 gastric carcinoma patients who received treatment in the cancer centre of Sun Yat-sen University from January 2002 to January 2006 were involved in the study. The stored blood drawn before any treatment was assayed for 25-hydroxyvitamin D levels. The clinicopathologic data were collected to examine the prognostic effects of vitamin D.</p> <p>Results</p> <p>The mean vitamin D levels of the 197 gastric patients was 49.85 ± 23.68 nmol/L, among whom 114(57.9%) were deficient in Vitamin D(< 50 nmol/L), 67(34%) were insufficient (50-75 nmol/L) and 16(8.1%) were sufficient (> 75 nmol/L). Clinical stage (<it>P </it>= 0.004) and lymph node metastasis classification (<it>P </it>= 0.009) were inversely associated with vitamin D levels. The patients with high vitamin D levels group (≥ 50 nmol/L) had a higher overall survival compared with the low vitamin D levels group (< 50 nmol/L)(<it>P </it>= 0.018). Multivariate analysis indicated that vitamin D levels were an independent prognostic factor of gastric cancer (<it>P </it>= 0.019).</p> <p>Conclusions</p> <p>Vitamin D deficiency may be associated with poor prognosis in gastric cancer.</p