An objective classification of climatic regions in the Pacific and Indian oceans

We have applied a number of objective statistical techniques to define homogeneous climatic regions for the Pacific Ocean, using COADS (Woodruff et al 1987) monthly sea surface temperature (SST) for 1950-1989 as the key variable. The basic data comprised all global 4°x4° latitude/longitude boxes with enough data available to yield reliable long-term means of monthly mean SST. An R-mode principal components analysis of these data, following a technique first used by Stidd (1967), yields information about harmonics of the annual cycles of SST. We used the spatial coefficients (one for each 4-degree box and eigenvector) as input to a K-means cluster analysis to classify the gridbox SST data into 34 global regions, in which 20 comprise the Pacific and Indian oceans. Seasonal time series were then produced for each of these regions. For comparison purposes, the variance spectrum of each regional anomaly time series was calculated. Most of the significant spectral peaks occur near the biennial (2.1-2.2 years) and ENSO (~3-6 years) time scales in the tropical regions. Decadal scale fluctuations are important in the mid-latitude ocean regions.

TWO TUTORIAL EXAMPLES OF MULTIVARIABLE CONTROL SYSTEM DESIGN.

Two tutorial examples are presented which illustrate different methods of designing practical multivariable control systems using frequency-domain techniques. In the first case eigenvector alignment techniques are used to manipulate and shape the generalized Nyquist diagrams, while in the second case LQG theory in conjunction with singular value plots is employed. In both cases the designs are carried out on a modern computer-aided control-system design package.

Applications of the dynamic mode decomposition

The decomposition of experimental data into dynamic modes using a data-based algorithm is applied to Schlieren snapshots of a helium jet and to time-resolved PIV-measurements of an unforced and harmonically forced jet. The algorithm relies on the reconstruction of a low-dimensional inter-snapshot map from the available flow field data. The spectral decomposition of this map results in an eigenvalue and eigenvector representation (referred to as dynamic modes) of the underlying fluid behavior contained in the processed flow fields. This dynamic mode decomposition allows the breakdown of a fluid process into dynamically revelant and coherent structures and thus aids in the characterization and quantification of physical mechanisms in fluid flow. © 2010 Springer-Verlag.

Impact of mode localization on the motional resistance of coupled MEMS resonators

This paper investigates the effect of mode-localization that arises from structural asymmetry induced by manufacturing tolerances in mechanically coupled, electrically transduced Si MEMS resonators. We demonstrate that in the case of such mechanically coupled resonators, the achievable series motional resistance (R x) is dependent not only on the quality factor (Q) but also on the variations in the eigenvector of the chosen mode of vibration induced by mode localization due to manufacturing tolerances during the fabrication process. We study this effect of mode-localization both theoretically and experimentally in two pairs of coupled double-ended tuning fork resonators with different levels of initial structural asymmetry. The measured series R x is minimal when the system is close to perfect symmetry and any deviation from structural symmetry induced by fabrication tolerances leads to a degradation in the effective R x. Mechanical tuning experiments of the stiffness of one of the coupled resonators was also conducted to study variations in R x as a function of structural asymmetry within the system, the results of which demonstrated consistent variations in motional resistance with predictions. © 2012 IEEE.

Linear dimensionality reduction: Survey, insights, and generalizations

© 2015 John P. Cunningham and Zoubin Ghahramani. Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, input-output relationships, and margin between data classes. Methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the connections between all these methods have not been highlighted. Here we survey methods from this disparate literature as optimization programs over matrix manifolds. We discuss principal component analysis, factor analysis, linear multidimensional scaling, Fisher's linear discriminant analysis, canonical correlations analysis, maximum autocorrelation factors, slow feature analysis, sufficient dimensionality reduction, undercomplete independent component analysis, linear regression, distance metric learning, and more. This optimization framework gives insight to some rarely discussed shortcomings of well-known methods, such as the suboptimality of certain eigenvector solutions. Modern techniques for optimization over matrix manifolds enable a generic linear dimensionality reduction solver, which accepts as input data and an objective to be optimized, and returns, as output, an optimal low-dimensional projection of the data. This simple optimization framework further allows straightforward generalizations and novel variants of classical methods, which we demonstrate here by creating an orthogonal-projection canonical correlations analysis. More broadly, this survey and generic solver suggest that linear dimensionality reduction can move toward becoming a blackbox, objective-agnostic numerical technology.

Ground-state properties of an artificial molecule: a simple model calculation for the double quantum dot

The ground state of a double quantum-dot structure is studied by a simplified Anderson-type model. Numerical calculations reveal that the ground-state level of this artificial molecule increases with the increasing single particle level of the dot, and also increases with the decreasing transfer integrals. We show the staircase feature of the electron occupation and the properties of the ground-state eigenvector by varying the;single particle level of the dot.

Reconstruction of vertical thermal structure from several subsurface temperatures in the China Seas and adjacent waters

Empirical Orthogonal Function (EOF) analysis is used in this study to generate main eigenvector fields of historical temperature for the China Seas (here referring to Chinese marine territories) and adjacent waters from 1930 to 2002 (510 143 profiles). A good temperature profile is reconstructed based on several subsurface in situ temperature observations and the thermocline was estimated using the model. The results show that: 1) For the study area, the former four principal components can explain 95% of the overall variance, and the vertical distribution of temperature is most stable using the in situ temperature observations near the surface. 2) The model verifications based on the observed CTD data from the East China Sea (ECS), South China Sea (SCS) and the areas around Taiwan Island show that the reconstructed profiles have high correlation with the observed ones with the confidence level > 95%, especially to describe the characteristics of the thermocline well. The average errors between the reconstructed and observed profiles in these three areas are 0.69A degrees C, 0.52A degrees C and 1.18A degrees C respectively. It also shows the model RMS error is less than or close to the climatological error. The statistical model can be used to well estimate the temperature profile vertical structure. 3) Comparing the thermocline characteristics between the reconstructed and observed profiles, the results in the ECS show that the average absolute errors are 1.5m, 1.4 m and 0.17A degrees C/m, and the average relative errors are 24.7%, 8.9% and 22.6% for the upper, lower thermocline boundaries and the gradient, respectively. Although the relative errors are obvious, the absolute error is small. In the SCS, the average absolute errors are 4.1 m, 27.7 m and 0.007A degrees C/m, and the average relative errors are 16.1%, 16.8% and 9.5% for the upper, lower thermocline boundaries and the gradient, respectively. The average relative errors are all < 20%. Although the average absolute error of the lower thermocline boundary is considerable, but contrast to the spatial scale of average depth of the lower thermocline boundary (165 m), the average relative error is small (16.8%). Therefore the model can be used to well estimate the thermocline.

中国近海和西北太平洋温跃层时空变化分析、模拟及预报

温度跃层是反映海洋温度场的重要物理特性指标，对水下通讯、潜艇活动及渔业养殖、捕捞等有重要影响。本文利用中国科学院海洋研究所“中国海洋科学数据库”在中国近海及西北太平洋（110ºE-140ºE,10ºN-40ºN）的多年历史资料（1930-2002年，510143站次），基于一种改进的温跃层判定方法，分析了该海域温跃层特征量的时空分布状况。同时利用Princeton Ocean Model(POM)，对中国近海，特别是东南沿海的水文结构进行了模拟，研究了海洋水文环境对逆温跃层的影响。最后根据历史海温观测资料，利用EOF分解统计技术，提出了一种适于我国近海及毗邻海域，基于现场有限层实测海温数据，快速重构海洋水温垂直结构的统计预报方法，以达到对现场温跃层的快速估计。 历史资料分析结果表明，受太阳辐射和风应力的影响，20°N以北研究海域，温跃层季节变化明显，夏季温跃层最浅、最强，冬季相反，温跃层厚度的相位明显滞后于其他变量，其在春季最薄、秋季最厚。12月份到翌年3月份，渤、黄及东海西岸，呈无跃层结构，西北太平洋部分海域从1月到3月份，也基本无跃层结构。在黄海西和东岸以及台湾海峡附近的浅滩海域，由于风力搅拌和潮混合作用，温跃层出现概率常年较低。夏季，海水层化现象在近海陆架海域得到了加强，陆架海域温跃层强度季节性变化幅度(0.31°C/m)明显大于深水区(约0.05°C/m)，而前者温跃层深度和厚度的季节性变化幅度小于后者。20°N以南研究海域，温跃层季节变化不明显。逆温跃层主要出现在冬、春季节（10月-翌年5月）。受长江冲淡水和台湾暖流的影响，东南沿海区域逆温跃层持续时间最长，出现概率最大，而在山东半岛北及东沿岸、朝鲜半岛西及北岸，逆温跃层消长过程似乎和黄海暖流有关。多温跃层结构常年出现于北赤道流及对马暖流区。在黑潮入侵黄、东、南海的区域，多温跃层呈现明显不同的季节变化。在黄海中部，春季多温跃层发生概率高于夏季和秋季，在东海西部，多跃层主要出现在夏季，在南海北部，冬季和春季多温跃层发生概率大于夏季和秋季。这些变化可能主要受海表面温度变化和风力驱动的表层流的影响。 利用Princeton Ocean Model(POM)，对中国东南沿海逆温跃层结构进行了模拟，模拟结果显示，长江冲淡水的季节性变化以及夏季转向与实际结果符合较好，基本再现了渤、黄、东海海域主要的环流、温盐场以及逆温跃层的分布特征和季节变化。通过数值实验发现，若无长江、黄河淡水输入，则在整个研究海域基本无逆温跃层出现，因此陆源淡水可能是河口附近逆温跃层出现的基本因素之一。长江以及暖流（黑潮和台湾暖流）流量的增加，均可在不同程度上使逆温跃层出现概率及强度、深度和厚度增加，且暖流的影响更加明显。长江对东南沿海逆温跃层的出现，特别是秋季到冬季初期，有明显的影响，使长江口海域逆温跃层位置偏向东南。暖流对于中国东南沿海的逆温跃层结构，特别是初春时期，有较大影响，使长江口海域的逆温跃层位置向东北偏移。 通过对温跃层长期变化分析得出，黄海冷水团区域，夏季温跃层强度存在3.8年左右的年际变化及18.9年左右的年代际变化，此变化可能主要表现为对当年夏季和前冬东亚地区大气气温的热力响应。东海冷涡区域，夏季温跃层强度存在3.7年的年际变化，在El Nino年为正的强度异常，其可能主要受局地气旋式大气环流变异所影响。谱分析同时表明，该海域夏季温跃层强度还存在33.2年的年代际变化，上世纪70年代中期，温跃层强度由弱转强，而此变化可能与黑潮流量的年代际变化有关。 海洋水温垂直结构的统计预报结果显示，EOF分解的前四个主分量即能够解释原空间点温度距平总方差的95%以上，以海洋表层附近观测资料求解的特征系数推断温度垂直结构分布的结果最稳定。利用东海陆架区、南海深水区和台湾周边海域三个不同区域的实测CTD样本廓线资料，对重构模型的检验结果表明，重构与实测廓线的相关程度超过95%的置信水平。三个区重构与实测温度廓线值的平均误差分别为0.69℃，0.52℃，1.18℃，平均重构廓线误差小于平均气候偏差，统计模式可以很好的估算温度廓线垂直结构。东海陆架海区温度垂直重构廓线与CTD观测廓线获得的温跃层结果对比表明，重构温跃层上界、下界深度和强度的平均绝对误差分别为1.51m、1.36m和0.17℃/m，它们的平均相对误差分别为24.7%、8.9%和22.6%，虽然温跃层深度和强度的平均相对误差较大，但其绝对误差量值较小。而在南海海区，模型重构温跃层上界、下界和强度的平均绝对预报误差分别为4.1m、27.7m和0.007℃/m，它们的平均相对误差分别为16.1%、16.8%和9.5%，重构温跃层各特征值的平均相对误差都在20%以内。虽然南海区温跃层下界深度平均绝对预报误差较大，但相对于温跃层下界深度的空间尺度变化而言（平均温跃层下界深度为168m），平均相对误差仅为16.8%。因此说模型重构的温度廓线可以达到对我国陆架海域、深水区温跃层的较好估算。 基于对历史水文温度廓线观测资料的分析及自主温跃层统计预报模型，研制了实时可利用微机简单、快捷地进行温跃层估算及查询的可视化系统，这是迄今进行大范围海域温跃层统计与实时预报研究的较系统成果。

Colour Doppler ultrasound of the ocular circulation in patients with systemic lupus erythematosus identifies altered microcirculatory haemodynamics

We assessed whether quantitative analysis of Doppler flow velocity waveforms is able to identify subclinical microvascular abnormalities in SLE and whether eigenvector analysis can detect changes not detectable using the resistive index (RI). Fifty-four SLE patients with no conventional cardiovascular risk factors, major organ involvement or retinopathy were compared to 32 controls. Flow velocity waveforms were obtained from the ophthalmic artery (OA), central retinal artery (CRA) and common carotid artery (CA). The waveforms were analysed using eigenvector decomposition and compared between groups at each arterial site. The RI was also determined. The RI was comparable between groups. In the OA and CRA, there were significant differences in the lower frequency sinusoidal components (P <0.05 for each component). No differences were apparent in the CA between groups. Eigenvector analysis of Doppler flow waveforms, recorded in proximity of the terminal vascular bed, identified altered ocular microvascular haemodynamics in SLE. Altered waveform structure could not be identified by changes in RI, the traditional measure of downstream vascular resistance. This analytical approach to waveform analysis is more sensitive in detecting preclinical microvascular abnormalities in SLE. It may hold potential as a useful tool for assessing disease activity, response to treatment, and predicting future vascular complications.