Asymptotic properties of eigenmatrices of a large sample covariance matrix

Let $S_n=\frac{1}{n}X_nX_n^*$ where $X_n=\{X_{ij}\}$ is a $p\times n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)=\sqrt{p}({\mathbf {x}}_n(\mathbf {t}_1)^*(S_n+\sigma I)^{-1}{\mathbf {x}}_n(\mathbf {t}_2)-{\mathbf {x}}_n(\mathbf {t}_1)^*{\mathbf {x}}_n(\mathbf {t}_2)m_n(\sigma))$ in which $\sigma>0$ and $m_n(\sigma)=\int\frac{dF_{y_n}(x)}{x+\sigma}$ where $F_{y_n}(x)$ is the Mar\v{c}enko--Pastur law with parameter $y_n=p/n$; which converges to a positive constant as $n\to\infty$, and ${\mathbf {x}}_n(\mathbf {t}_1)$ and ${\mathbf {x}}_n(\mathbf {t}_2)$ are unit vectors in ${\Bbb{C}}^p$, having indices $\mathbf {t}_1$ and $\mathbf {t}_2$, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)$ converges weakly to a $(2m+1)$-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of $S_n$ is asymptotically close to that of a Haar-distributed unitary matrix.Comment: Published in at http://dx.doi.org/10.1214/10-AAP748 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Celecoxib inhibits tumor growth and angiogenesis in an orthotopic implantation tumor model of human colon cancer

Aim: To examine the effect of celecoxib on tumor growth and angiogenesis in an orthotopic implantation tumor model of colon cancer. Methods: Human colorectal adenocarcinoma HT-29 cells were implanted subcutaneously in nude mice. Four groups of animals received different doses of celecoxib after tumor implantation. After 42 days, all animals were evaluated for changes in body weight, the volume and weight of colorectal tumors, and tumor growth inhibition. The content of prostaglandin E2 (PGE2) in the tumor tissue homogenate was estimated by radioimmunoassay (RIA). Cyclooxygenase-2 (COX-2) and CD34 expression in tumor tissue was assessed by immunohistochemistry, and the microvessel density (MVD) of tumor tissue was determined. Apoptosis of the tumor cells was detected by the terminal deoxynucleotidyl transferase-mediated dUTP nick-end labeling (TUNEL). The expression of vascular endothelial growth factor (VEGF) mRNA and matrix metalloproteinase-2 (MMP-2) mRNA extracted from the tumor tissue was analyzed by reverse transcriptase polymerase chain reaction (RT-PCR). Results: There was no statistically significant change in the animals’ body weight between the treatment groups. However, with increasing doses of celecoxib, the volume and weight of the tumor decreased. The rates of tumor growth inhibition for the L (low), M (medium) and H (high) groups were 25.30%, 38.80%, and 76.92%, respectively, which were significant compared to the C (control) group. There were significant differences in COX-2 expression in the tumor tissue between all groups, except between the L and M groups. Celecoxib exposure also reduced PGE2 levels in the tumor tissue homogenates. The level of PGE2 correlated to the weight of tumor (r = 0.8814, P < 0.05) and to COX-2 expression (r = 0.8249, P < 0.05). Compared to the control group, the tumor cells from celecoxib-treated mice had a significantly higher apoptotic index. Celecoxib also decreased CD34+ expression in tumors from treated mice. There were significant differences in the MVD between all groups except between groups H and M. Celecoxib significantly reduced the expression of VEGF and MMP-2 mRNA in the group H but not in L and M groups. The MVD in tumor tissue was closely related to the PGE2 levels, as well as the expression of VEGF and MMP-2 mRNA (r = 0.9006, r = 0.8573 and r = 0.6427, respectively; P < 0.05). Conclusions: By inhibiting COX-2, PGE2 synthesis, and VEGF and MMP-2 mRNA expression in tumor tissue, celecoxib enhances tumor cell apoptosis, thereby inhibiting the growth and angiogenesis of orthotopically implanted tumors in a mouse model of human colorectal cancer.Цель: изучить влияние целекоксиба на рост опухоли и ангиогенез в модели ортопической имплантации опухоли толстой кишки человека. Методы: клетки колоректальной аденокарциномы человека НT-29 подкожно имплантировали бестимусным мышам. После имплантации опухоли четыре группы животных получали разные дозы целекоксиба. Через 42 дня изучали изменения веса животных, объем опухолей, эффект ингибирования роста опухоли. С помощью радиоиммунного анализа (RIA) в гомо- RIA) в гомо ) в гомогенате опухолей определяли содержание простогландина E2 (PGE2 ). В опухолевой ткани иммуногистохимическим методом выявляли экспрессию циклооксигеназы-2 (COX-2) и CD34 и оценивали плотность микрососудов (MVD). Апоптотические клетки выявляли методом TUNEL. Экспрессия мРНК фактора роста эндотелия сосудов (VEGF) и металлопротеиназы-2 (MMP-2) в опухолях проанализирована методом обратной транскриптазной реакции (RT-PCR). Результаты: статистически достоверных различий в весе животных между разными группами обнаружено не было. Вто же время, с увеличением дозы целекоксиба объем и вес опухоли уменьшался. По сравнению с контрольной группой (C), рост опухоли статистически достоверно ингибировался в L (низкая доза), M (средняя доза) и H (высокая доза) группах животных на 25,30%, 38,80% и 76,92% соответственно. Были обнаружены значительные отличия в экспрессии COX-2 в опухолевых тканях между всеми группами животных, кроме групп L и M. Было показано целекоксиб-зависимое уменьшение уровня PGE2 в гомогенатах опухолей. Уровень PGE2 коррелировал с весом опухоли (r = 0,8814, P < 0,05) и экспрессией COX-2 (r = 0,8249, P < 0,05). По сравнению с контрольной группой опухолевые клетки мышей, получавших целекоксиб, имели значительно более высокий апоптотический индекс. Целекоксиб также снижал экспрессию CD34+ на поверхности опухолевых клеток. Были обнаружены статистически достоверные различия в MVD между всеми исследованными группами, кроме H и M. Целекоксиб способствовал уменьшению экспрессии мРНК VEGF и MMP-2 в группе Н, но не в группах L и M. MVD в опухолевой ткани кореллировал с уровнем PGE2 , а также с экспрессией мРНК VEGF и MMP-2 (r = 0,9006, r = 0,8573 и r = 0,6427 соответственно; P < 0,05). Выводы: целекоксиб способствует апоптозу опухолевых клеток, ингибирует рост опухоли и ангиогенез при ортотопической имплантации мышам колоректальной аденокарциномы человека. Такой эффект целекоксиба связан с угнетением синтеза COX-2, PGE2 и экспрессии мРНК VEGF и MMP-2 в опухолевой ткани

Effect of nitrogen fertilization on net nitrogen mineralization in grassland soil of Northern China: implications for grassland management

Nitrogen (N) applications can have a significant effect on soil N availability. The effect of 3 years of N fertilization on soil net N mineralization during the growing season (May–September) was studied in 2005 and 2006 in grassland of northern China. The experimental design was a randomized complete block with four replications of five rates of N addition as urea (0, 2, 4, 8 and 16 g N m−2 year−1). Results indicated that net N mineralization rate varied seasonally and between years, ranging from −0.04 to 0.52 μg g−1 d−1 in 2005 and from −0.09 to 0.39 μg g−1 d−1 in 2006. Mean N mineralization and nitrification rates were highest in July, in 2005 and 2006, whereas highest ammonification rates occurred in September. Rainfall was significantly correlated with net nitrification. In comparison with the untreated control, N mineralization increased sharply when N fertilization increased from 2 to 8 g N m−2 year−1. Mobile soil NO3− accumulated late in the growing season for the 16 g N m−2 year−1 treatment, suggesting the potential for NO3 and associated cation leaching. These results suggest that N fertilization of 8 g N m−2 year−1 (80 kg N ha−1) is suitable for the management of grassland ecosystems of Inner Mongolia

A Population of Radio-loud Narrow Line Seyfert 1 Galaxies with Blazar-like Properties?

(abridged) We present a comprehensive study of a sample of 23 genuine radio-loud NLS1 galaxies which have the radio-loudness parameters greater than 100. The radio sources of the sample are ubiquitously compact. A significant fraction of these objects show interesting radio to X-ray properties that are unusual to most of the previously known radio-loud NLS1 AGN, but are reminiscent of blazars. These include flat radio spectra, large amplitude flux and spectral variability, compact VLBI cores, very high brightness temperatures derived from variability, enhanced optical emission in excess of the normal ionising continuum, flat X-ray spectra, and blazar-like SEDs. We interpret them as evidence for the postulated blazar nature of these very radio-loud NLS1 AGN, which might possess at least moderately relativistic jets. Intrinsically, some of the objects have relatively low radio power and would have been classified as radio-intermediate AGN. The black hole masses are estimated to be within 10^{6-8}Msun, and the inferred Eddington ratios are around unity. The results imply that radio-loud AGN may be powered by black holes with moderate masses (10^{6-7}Msun) accreting at high rates. We find that a significant fraction of the objects, despite having strong emission lines, resemble high-energy peaked BL Lacs (HBL) in their SED. Given the peculiarities of blazar-like NLS1 galaxies, questions arise as to whether they are plain downsizing extensions of normal radio-loud AGN, or whether they form a previously unrecognised population.Comment: Comments: 29 pages, 16 figures, 4 tables, accepted for publication in Ap

Hydrodynamic analysis of marine multibody systems by a nonlinear coupled model

This study investigates the hydrodynamic performance of two freely floating or interconnected barges. A nonlinear decomposition model in the framework of potential flow is employed to simulate the wave-body interactions in the time domain. This piece of work focuses on the accurate calculation of hydrodynamic forces and motions of a multibody floating system. The hydrodynamic forces are indirectly calculated through an auxiliary function approach, which is extended to application of two floating bodies in the present study. The resultant coupled motion equations for two bodies clearly demonstrate the influence of one body on the other. To incorporate an interconnection between two floating bodies, a constraint matrix method is developed where the connection constraints are mathematically represented by a constraint matrix. The constraint forces in the connection are solved in the modified motion equations. The newly formulated coupled auxiliary function and constraint matrix approaches for two bodies with and without interconnections are validated by comparisons of first-order response against linear frequency-domain models. Two types of interconnections, namely, the rigid connection and the middle-hinge connection, are examined in both beam sea and head sea to demonstrate the effectiveness of the proposed method. Coupling effects of different connection scenarios on body motions as well as the influence on constraint forces are discussed. Furthermore, simulations using relatively steeper waves are performed and compared with mild wave cases. The nonlinear effect is highlighted by decomposing the higher harmonic components of nonlinear responses

The Framework of Technical Evaluation Indicators for Constructing Low-Carbon Communities in China

In recent years, in order to promote the construction of low-carbon communities (LCCs) in China, many scholars have proposed an evaluation indicator system of LCC. The existing indicator systems are mostly established from the macro perspective of environmental impact and resource conservation, but few are from the micro technical perspective. Thus, the aim of this study is to construct a micro technical evaluation indicator system for LCCs. Firstly, the index system was divided into three categories: low-carbon building, low-carbon transportation, and low-carbon environment. Then, the technical indicators were selected through empirical analysis. The indicator weights were assigned by the improved analytic hierarchy process (AHP) and the multi-level fuzzy comprehensive evaluation method was used as the evaluation method of the indicators. Finally, in order to examine the practicality of the indicator system, two typical communities in Tianjin and Shanghai were selected as case studies. The results showed that the indicator system gave a reasonable low-carbon level for the two communities, which was in line with the actual low-carbon construction status of each community. In addition, the evaluation results pointed out that the low-carbon community (LCC) in Tianjin needs to further strengthen the construction of the low-carbon environment, including community compactness, rainwater collection and utilization, and waste recycling. For the LCC in Shanghai, it was pointed out that the construction of the low-carbon building and low-carbon transportation needs to be strengthened. The indicator system can be used as a tool for urban planning and construction personnel to evaluate the construction progress and low-carbon degree of LCC