A theory of slow feature analysis for transformation-based input signals with an application to complex cells

We develop a group-theoretical analysis of slow feature analysis for the case where the input data are generated by applying a set of continuous transformations to static templates. As an application of the theory, we analytically derive nonlinear visual receptive fields and show that their optimal stimuli, as well as the orientation and frequency tuning, are in good agreement with previous simulations of complex cells in primary visual cortex (Berkes and Wiskott, 2005). The theory suggests that side and end stopping can be interpreted as a weak breaking of translation invariance. Direction selectivity is also discussed. © 2011 Massachusetts Institute of Technology.

Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.

A duality principle for homogeneous vectorfields with applications

A duality transformation principle was proposed for converting a positive order homogeneous vectorfield into a negative order homogeneous vectorfield. The principle also converted a uniformly locally asymptotically stable differential equation into a uniformly bounded differential equation. The duality transformations included the geometric framework for homogeneity and the removal of origin from the state space.

Local equilibrium of the Gibbs interface in two-phase systems

We analyze the local equilibrium assumption for interfaces from the perspective of gauge transformations, which are the small displacements of Gibbs' dividing surface. The gauge invariance of thermodynamic properties turns out to be equivalent to conditions for jumps of bulk densities across the interface. This insight strengthens the foundations of the local equilibrium assumption for interfaces and can be used to characterize nonequilibrium interfaces in a compact and consistent way, with a clear focus on gauge-invariant properties. Using the principle of gauge invariance, we show that the validity of Clapeyron equations can be extended to nonequilibrium interfaces, and an additional jump condition for the momentum density is recognized to be of the Clapeyron type. © 2012 Europhysics Letters Association.

VERTICAL DISTRIBUTIONS OF SIZE-FRACTIONATED IRON IN THREE TYPICAL BAYS OF LAKE DIANCHI (CHINA)

In order to elucidate the vertical distributions of iron in three typical bays (Haigeng bay, Macun bay and Haidong bay) of Lake Dianchi (China), the investigation was conducted on March, 2003. Results showed that the vertical distributions were influenced by monsoon, cyanobacterial bloom and water depth as well as sediment resuspension, which indicated that their translocations and transformations were decided by geographical and physical as well as chemical and biological characteristics.

Structural evolution of mechanically alloyed nanocrystalline FeAl intermetallics

Nanostructured FeAl intermetallics were prepared directly by mechanical alloying (MA) in a high-energy planetary ball-mill. The phase transformations and structural changes occurring in the studied material during mechanical alloying were investigated by X-ray diffraction (XRD). Transmission electron microscopy (TEM) was employed to examine the morphology of the powders. Thermal behavior of the milled powders was examined by differential scanning calorimetry (DSC). Disordered Fe(Al) solid solution was formed at the early stage. After 30 h of milling, Fe(Al) solid solution transformed into an ordered FeAl phase. The average crystallite size reduction down to about 12 nm was accompanied by the introduction of the average lattice strain up to 1.7%. The TEM picture showed that the size of milled powders was less than 30 nm. (c) 2007 Elsevier B.V. All rights reserved.

The quantum tunnelling between two-component Bose-Einstein condensates in a double-well configuration

We examine in terms of exact solutions of the time-dependent Schrodinger equation, the quantum tunnelling process in Bose-Einstein condensates of two interacting species trapped in a double well configuration. Based on the two series of time-dependent SU(2) gauge transformations, we diagonalize the Hamilton operator and obtain analytic time-evolution formulas of the population imbalance and the berry phase. the particle population imbalance (a(L)(+)aL - a(R)(+)a(R)) of species A between the two wells is studied analytically.

An investigation on the pressure-induced phase transition of nanocrystalline ZnS

An in situ energy dispersive x-ray diffraction study on nanocrystalline ZnS was carried out under high pressure up to 30.8 GPa by using a diamond anvil cell. The phase transition from the wurtzite to the zinc-blende structure occurred at 11.5 GPa, and another obvious transition to a new phase with rock-salt structure also appeared at 16.0 GPa-which was higher than the value for the bulk material. The bulk modulus and the pressure derivative of nanocrystalline ZnS were derived by fitting the Birch-Murnaghan equation. The resulting modulus was higher than that of the corresponding bulk material, indicating that the nanomaterial has higher hardness than the bulk material.

Quantum fluctuation of dissipative mesoscopic capacitance coupling circuit

The quantum wave function and the corresponding energy levels of the dissipative mesoscopic capacitance coupling circuits are obtained by using unitary and linear transformations. The quantum fluctuation of charge and current in an arbitrary eigenstate of the system have been also given. The results show that the fluctuation of charge and current depends on not only the eigenstate but also the electronic device parameters.

Formal specification and refinement of a safe train control function

Motivated by the design and development challenges of the BART case study, an approach for developing and analyzing a formal model for reactive systems is presented. The approach makes use of a domain specific language for specifying control algorithms able to satisfy competing properties such as safety and optimality. The domain language, called SPC, offers several key abstractions such as the state, the profile, and the constraint to facilitate problem specification. Using a high-level program transformation system such as HATS being developed at the University of Nebraska at Omaha, specifications in this modelling language can be transformed to ML code. The resulting executable specification can be further refined by applying generic transformations to the abstractions provided by the domain language. Problem dependent transformations utilizing the domain specific knowledge and properties may also be applied. The result is a significantly more efficient implementation which can be used for simulation and gaining deeper insight into design decisions and various control policies. The correctness of transformations can be established using a rewrite-rule based induction theorem prover Rewrite Rule Laboratory developed at the University of New Mexico.

基于时序逻辑证明编译优化程序变换的保义性

基于时序逻辑CTL(computation tree logic)的一种扩展CTL-FV对优化编译中的语句交换和变量替换这两种常见变换的保义性条件给出了形式刻画,采用含条件重写规则定义了保义语句交换Texch和保义变量替换Tsub,并基于一种归纳证明框架对它们的保义性进行了证明.此外,基于变换Texch对程序基本块内保依赖语句重排的保义性也给出了一种构造性的证明.

氮沉降对长白山森林表层土壤碳氮周转过程的影响

在大气CO2升高和氮(N)沉降增加等全球变化背景下，N元素对生态系统碳(C)、N元素周转过程的影响开始引起越来越多的关注。作为陆地生态系统C库重要组成部分的森林土壤，也逐渐成为研究的重点之一。 本文选择长白山地区典型森林生态系统表层土壤和凋落物，利用人工施N，在实验室控制条件下，模拟N沉降对森林土壤表层C、N元素周转过程影响。旨在从微观上揭示N沉降对凋落物和土壤表层腐殖质分解过程中C、N元素周转过程和土壤C库的影响，主要结论如下: (1) 外源N输入加快了凋落物早期的分解。阔叶树种（岳桦 Betula ermanii、蒙古栎 Quercus mongolica、椴树 Tilia amurensis）的凋落物的分解速度明显快于针叶树种（红松 Pinus koraiensis、鱼鳞云杉 Picea jezoensis）。凋落物的木质素含量是控制其分解速度的主导因子。 (2) N添加对凋落物可溶性有机C（DOC）淋失没有显著影响。DOC淋失主要受凋落物基本性质的控制。阔叶树种的凋落物DOC淋失量明显高于针叶树种。 (3) 不同植被下的土壤性质和C、N周转过程有较大的差异，岳桦林下土壤的微生物生物量和N矿化速率都显著高于暗针叶林，而土壤的C矿化量却低于暗针叶林。岳桦林土壤的DOC和DON淋失量也高于暗针叶林。 (4) N添加显著降低了森林表层土壤的呼吸速率。外加氮对土壤DOC淋失的影响存在一个平衡点，过高的N输入可能加快土壤中DOC的分解速度，降低DOC的淋失量。 研究结果表明，尽管长白山森林生态系统还没有达到“N饱和”，但不断升高的N沉降水平将对长白山典型森林生态系统土壤的C、N元素的周转过程产生较大的影响。但要全面评估N沉降对长白山地区森林土壤C库的影响，还需在野外进行长期定位研究。

半干旱地区固沙林土壤氮素转化及其有效性研究

土壤氮素（N）转化是生态系统关键的生态学过程之一；而土壤N有效性是沙地生态系统生产力和稳定性的关键限制性因子。以科尔沁沙地东南缘樟子松（pinus sylvestris var．mongolica）、赤松（P.densiflora）和小叶杨（populus simonii）固沙林以及草地为研究对象，采用野外试验和室内实验相结合的方法，全面系统地开展了凋落物分解、土壤N矿化、淋溶等过程及土壤N有效性的研究，旨在揭示半干旱区固沙林土壤N转化及其有效性的特征和机制，为沙地植被恢复、重建、管理和评价提供科学依据。主要结论如下：（1）采用网袋法进行凋落物的分解试验，结果表明不同类型凋落物乘量衰减、元索释放、质员变化均存在明显差异，分解第1年供N能力表现为小叶杨＞草＞樟子松＞赤松；（2）采用PVC顶盖理管法和离子交换树脂袋法分别研究了林地和草地土壤N矿化过程，结果表明土壤N矿化速率表现为小叶杨川章子松七赤松＞草地，N相对有效性表现为赤松＞樟子松＞草地全小叶杨；（3）草地和小叶杨林地土壤N潜在性淋济较高，而樟子松林地较轻；（4）土壤容重、pH值、养分、温度、水分、土壤微生物、土壤动物、林下植被等环境和生物因子反映区域土壤N转化及共有效性的一般特征，而强烈的人类干扰是引起生态系统问差异的关键因索：造林有利于提高沙地土壤N积累和有效性，但樟子松造林30年后才有明显效果：放牧地土壤N硝化速率及其有效性明显高于禁牧地，但质量下降，即NH4+-N/NO3--N失衡，不利于植物吸收、微生物调控和环境保护；（5）赤松、樟子松和小叶杨均为研究区固沙造林的可选树种，合理和科学管理有利于维护生态系统N平衡，实现．可持续经营。

2-C-支链-1,6-脱水吡喃葡萄糖的开环反应及吡喃烯糖的合成研究

在糖化学合成中，1,6-脱水吡喃糖不仅是合成具有生物活性低聚糖、糖共体、抗原、抗体以及天然产物等化合物重要原料，而且还是许多具有生物活性的天然产物的结构单元。同时，它还具有[3,2,1]的双环缩醛结构，使其在糖化学合成中具有高的立体选择性和区域选择性，同时减少了C-1 和C-6 位的保护和去保护的优点。此外，环内的缩醛开环后，又可以相应地在C-1 和C-6 位进行官能团转化以及糖苷化反应。 本文报道了一种新的1,6-脱水吡喃糖的合成方法，并设计合成了2-C-支链-1,6-脱水吡喃葡萄糖1-195、1-197、1-198 以及2-C-支链-6-硫代1,6-脱水吡喃葡萄糖1-225。到目前为止，1,6-脱水糖开环并进行糖苷化反应，存在选择性较差、产率低的缺点。我们发现，在乙腈做溶剂的条件下，NiCl5 能高立体选择性高产率地催化化合物1-195、1-197、1-198 开环并与ROH、RSH 发生糖苷化反应。在NiCl5-乙腈条件下，合成了一系列2-C-支链-α-糖苷和2-C-支链-β-硫代糖苷，并对2-C-支链1,6-脱水吡喃葡萄糖的生成机理以及开环机理进行了探讨。 烯糖在糖化学合成中是重要的起始原料，从Fischer 首次合成烯糖至今，一直不断地有新的合成方法出现。但目前文献报道的方法存在所用试剂有毒、价格贵和操作繁琐等缺点。我们对Fischer-Zach 方法进行了改进， 发现Zn-NaH2PO4-H2O 和Zn-PEG600-H2O 体系都能很好地合成烯糖。该方法具有条件温和、绿色环保、操作简单的优点。在Zn-NaH2PO4 溶液或Zn-PEG600 条件下，以溴代糖为原料，高产率地合成一系列的烯糖。 The 1,6-anhydrohexopyranoses are crucial subunits of myriad bioactive nature products, as well as important syntons of carbohydrate chemistry which have been extensively used to prepare the biologically potential oligosaccharides, glycoconjugates, antibiotics, and structurally varied nature products. Their particular [3.2.1] bicyclic skeleton makes them have high regio- and stereo-control in a variety of reactions, and such structure avoids protecting hydroxyl groups at C1 and C6.Additionally, the cleavage of the internal acetal under acidic conditions could be beneficial for further transformations of functional group and glycosylation of the corresponding pyranosyl sugar at the C6 or C1 site. Herein we developed a novel approach to prepare the 1,6-anhydrohexopyranose, and synthesized the 2-C-branched-1,6-anhydrohexopyranose 1-195, 1-197, 1-198 and 2-C-branched-6-thio-1,6-anhydrohexopyranose 1-225. Until now, glycosylation of 1,6-anhydrohexopyranoses has been limited because of the low yields and low stereoselectivity. In this paper, we found that NiCl5-MeCN system could selectively cleave the ring of 1,6-anhydrohexopyranoses with alcohols and thiols at room temperature in high yields. A series of 2-C-branched-α-glycosides and 2-C-branched-β-thioglycosides have been synthesized via NiCl5-catalyzed. Furthermore, we investigated the formation and ring-opening mechanism of 2-C-acetylmethyl-1,6-anhydrohexopyranose. Glycals are significant starting material in carbohydrate chemistry. After the Fischer-Zach method for forming glucal was reported for the first time, the numerous synthetic methods for glycals have been explored. However, there are several drawbacks in the existing methods, such as the usage of very expensive and toxic reagents, intricate operation, and the influence of acid-sensitive and base-sensitive functional group. We improved the Fischer-Zach method and developed a facile, mild and environmentally benign methodology towards the synthesis of the glycals in Zn-NaH2PO4-H2O or Zn-PEG600-H2O system. Our method involves the treatment of glycosyl bromides with Zn in NaH2PO4 aqueous solution or PEG600-H2O at room temperature, affording various glycals in excellent yields.

Decomposition of Noncommutative U(1) Gauge Potential

We investigate the decomposition of noncommutative gauge potential (A) over cap (i), and find that it has inner structure, namely, (A) over cap (i) can he decomposed in two parts, (b) over cap (i) and (a) over cap (i), where (b) over cap (i) satisfies gauge transformations while (a) over cap (i) satisfies adjoint transformations, so close the Seiberg-Witten mapping of noncommutative, U(1) gauge potential. By, means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor