流形判别分析和支持向量机的恒星光谱数据自动分类方法

尽管经典的分类方法支持向量机SVM在天文学领域广泛应用,但其只考虑类间的绝对间隔而忽略类内的分布性状,因而分类性能有待于进一步提升。鉴于此,提出一种新颖的基于流形判别分析和支持向量机的恒星光谱数据自动分类方法。该方法引入流形判别分析的两个重要概念：基于流形的类内离散度M_W和基于流形的类间离散度M_B。所提方法找到的分类面同时保证M_W最小且M_B最大。可建立相应最优化问题,然后将原最优化问题转化为QP对偶形式求得支持向量和判别函数,最后利用判别函数判断测试样本的类属。该方法的最大优势在于进行分类决策时,不仅考虑样本的类间信息和分布特征,而且还保持了各类的局部流形结构。SDSS恒星光谱数据上的比较实验表明该方法的有效性。     

On practical aspects of Laser Guide Stars

The Gemini Observatory has developed an extensive Adaptive Optics (AO) program, including Classical AO, Laser Guide Star (LGS) AO, Multi-Conjugate AO (MCAO), extreme AO (eXAO) and Ground Layer AO (GLAO). Most of these instruments use one or several LGSs. A laser has been in operation at Gemini since May 2005. Most of the laser related systems (beam transport, launch, safety systems) have been developed in house. These are major components, requiring a development effort not to be underestimated. In this article, we propose to share the Gemini experience in terms of practical issues and calibration requirements associated with the use of lasers in AO. To cite this article: F. Rigaut, C. d'Orgeville, C. R. Physique 6 (2005).     

Multifunctional covalently stabilized vesicles acting simultaneously as the template of gold nanoparticle cluster and the nanocarrier of guest molecules

The terminal hydroxyl groups of amphiphilic multiarm star copolymers with a hydrophilic hyperbranched polyethylenimine (PEI) core and hydrophobic poly(ε-caprolactone) (PCL) arms were partially or completely transformed into the radical-crosslinkable methacrylate (MA) groups (PEI-b-PCL-MA). The resulting PEI-b-PCL-MA polymers with 100% MA substitution self-assembled in water into simple vesicles, whereas those with partial MA substitution aggregated into complex vesicles. These structures could be proved by transmission electron microscopy and dynamic light scattering only after crosslinking the intra-vesicular MA groups that generated the covalently stabilized vesicles (CSVs). The obtained CSVs could be used as host for the formation of gold nanoparticle (AuNP) cluster, and the AuNP clusters stabilized by the CSVs were stable under a wider range of CSV/AuNP feed ratio than those stabilized by the uncrosslinked precursors. The diameter of AuNPs in the clusters was in the range of 4-6 nm, and the distance of adjacent AuNPs could be modulated through altering the feed ratio of CSV/AuNP. The color of the solutions of AuNPs with CSV could be tuned from brown to red, purple, even blue. The composites of CSV and AuNPs could be further used as nanocarriers to accommodate hydrophobic guest of pyrene, and a higher amount of AuNPs in the nanocarriers led to a lower encapsulation capacity for pyrene guests.     

含C60的聚电解质自组装膜微摩擦性能的研究

通过自由基引发溶液聚合反应,合成星状C₆₀-苯乙烯-丙烯酸聚合物,其钠盐作为高聚物负离子,与高聚物正离子的重氮树脂在云母上自组装成膜,利用紫外光照射反应,使膜层间连接的离子键转化成共价键.用原子力显微镜(AFM)和摩擦力显微镜(FFM)研究了不同链长和不同层数自组装膜的表面形貌及微摩擦性能.     

对应模型中微连续类在两种拓扑下的应用

本文研究了微连续子类的性质 ,证明了 :S′( X,Y)在 *一致收敛拓扑下是 Ym X的闭集 ;若 X是 P空间 ,则 S( X,Y)在图拓扑下在 Ym X中是稠密的     

基于时域约束的卷帘曝光星敏感器星点校正方法

针对卷帘曝光模式星敏感器动态星点成像形状畸变和成像位置误差导致的导航星点定位精度降低、测姿误差增大的问题,提出了一种基于时域约束的导航星点校正方法.基于卷帘曝光的时间异步性特点,结合基于卡尔曼滤波的导航星点位置和帧间速度最优估计,将时域中不同时刻的导航星点校正到相同时刻,从而有效地解决星点畸变与位置偏移问题.展开了不同...     

A note on kernel methods for multiscale systems with critical transitions

We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast‐slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near fast subsystem bifurcation points can be computed to leading order. This leading order approximation shows that the MMD depends intricately on the fast‐slow systems parameters, which can influence the detection of potential early‐warning signs before critical transitions. However, the MMD turns out to be an excellent binary classifier to detect the change‐point location induced by the critical transition. We cross‐validate our results by numerical simulations for a van der Pol‐type model.     

On representations of star product algebras over cotangent spaces on Hermitian line bundles

For every formal power series B of closed two-forms on a manifold Q and every value of an ordering parameter κ∈[0,1] we construct a concrete star product ★_κ^B on the cotangent bundle T∗Q. The star product ★_κ^B is associated to the symplectic form on T∗Q given by the sum of the canonical symplectic form ω and the pull back of B to T∗Q. Deligne's characteristic class of ★_κ^B is calculated and shown to coincide with the formal de Rham cohomology class of π∗B divided by iλ. Therefore, every star product on T∗Q corresponding to the canonical Poisson bracket is equivalent to some ★_κ^B. It turns out that every ★_κ^B is strongly closed. In this paper, we also construct and classify explicitly formal representations of the deformed algebra as well as operator representations given by a certain global symbol calculus for pseudodifferential operators on Q. Moreover, we show that the latter operator representations induce the formal representations by a certain Taylor expansion. We thereby obtain a compact formula for the WKB expansion.     

Quasi-random 2- colorings of point sets

Given an arbitrary set of N points on the plane, one can two-color the points red and blue in such a way that the difference of the numbers of red and blue points in any half-plane has absolute value less than N^1/4(log N)⁴. This is essentially best possible.