A Novel Multivariate Mapping Method for Analyzing High-Dimensional Numerical Datasets

Author(s):  
Edwin Aldana-Bobadilla ◽  
Alejandro Molina-Villegas
Author(s):  
Jing Wang ◽  
Jinglin Zhou ◽  
Xiaolu Chen

AbstractIndustrial data variables show obvious high dimension and strong nonlinear correlation. Traditional multivariate statistical monitoring methods, such as PCA, PLS, CCA, and FDA, are only suitable for solving the high-dimensional data processing with linear correlation. The kernel mapping method is the most common technique to deal with the nonlinearity, which projects the original data in the low-dimensional space to the high-dimensional space through appropriate kernel functions so as to achieve the goal of linear separability in the new space. However, the space projection from the low dimension to the high dimension is contradictory to the actual requirement of dimensionality reduction of the data. So kernel-based method inevitably increases the complexity of data processing.


Author(s):  
Xiang Yu ◽  
Shijian Zhu ◽  
Shuyong Liu

The abundant and complex dynamics of high-dimensional nonlinear systems have drawn increasing attentions in recent years, but further analyses have been confined because of the inefficiency of some analytic methods for high-dimensional systems. This paper focuses on the bifurcation and global analyses of a multi-degree-of-freedom nonlinear vibration isolation system using numerical methods. Firstly, the equations of motion of the multi-degree-of-freedom nonlinear vibration isolation system for onboard machine are formulated. Then, exhaustive bifurcation analyses are carried out and six branches are illustrated in the bifurcation diagrams revealing that several different types of stable motions may coexist in certain parameter regimes. A cell mapping method is modified to analyze the global characteristics including the locations and basins of the coexistent attractors of the multi-degree-of-freedom nonlinear vibration isolation system.


Author(s):  
Xiang Yu ◽  
Shi-Jian Zhu ◽  
Shu-Yong Liu

After analyzing the inefficiency of the conventional Cell Mapping Methods in global analysis for high-dimensional nonlinear systems, several principles should be followed for these methods’ implementations in high-dimensional systems are proposed in this paper. Those are: appropriate selection of investigating plane, reduction of data size, and projection of attractors to the investigating plane. According to these, the idea of dynamic array is introduced to the method of Point Mapping Under Cell Reference (PMUCR) to improve computing efficiency. The comparison of the CPU time between the applications of this modified method to a 2-dimensional system and to a 4-dimensional one is carried out, and the results confirm this modified method can be utilized to analyze high-dimensional systems effectively. Finally, as examples, the periodic and chaotic motions of a coupled Duffing system are investigated through this method and some diagrams of global characteristics are presented.


Author(s):  
Jose-Maria Carazo ◽  
I. Benavides ◽  
S. Marco ◽  
J.L. Carrascosa ◽  
E.L. Zapata

Obtaining the three-dimensional (3D) structure of negatively stained biological specimens at a resolution of, typically, 2 - 4 nm is becoming a relatively common practice in an increasing number of laboratories. A combination of new conceptual approaches, new software tools, and faster computers have made this situation possible. However, all these 3D reconstruction processes are quite computer intensive, and the middle term future is full of suggestions entailing an even greater need of computing power. Up to now all published 3D reconstructions in this field have been performed on conventional (sequential) computers, but it is a fact that new parallel computer architectures represent the potential of order-of-magnitude increases in computing power and should, therefore, be considered for their possible application in the most computing intensive tasks.We have studied both shared-memory-based computer architectures, like the BBN Butterfly, and local-memory-based architectures, mainly hypercubes implemented on transputers, where we have used the algorithmic mapping method proposed by Zapata el at. In this work we have developed the basic software tools needed to obtain a 3D reconstruction from non-crystalline specimens (“single particles”) using the so-called Random Conical Tilt Series Method. We start from a pair of images presenting the same field, first tilted (by ≃55°) and then untilted. It is then assumed that we can supply the system with the image of the particle we are looking for (ideally, a 2D average from a previous study) and with a matrix describing the geometrical relationships between the tilted and untilted fields (this step is now accomplished by interactively marking a few pairs of corresponding features in the two fields). From here on the 3D reconstruction process may be run automatically.


Author(s):  
Joanna BOEHNERT

This workshop will create a space for discussion on environmental politics and its impact on design for sustainable transitions. It will help participants identify different sustainability discourses; create a space for reflection on how these discourses influence design practice; and consider the environmental and social implications of different discourses. The workshop will do this work by encouraging knowledge sharing, reflection and interpretative mapping in a participatory space where individuals will create their own discourse maps. This work is informed by my research “Mapping Climate Communication” conducted at the Centre for Science and Technology Policy Research (CSTPR) in the Cooperative Institute for Environmental Sciences (CIRES), the University of Colorado, Boulder. With this research project I developed a discourse mapping method based on the discourse analysis method of political scientists and sustainability scholars. Using my own work as an example, I will facilitate a process that will enable participants to create new discourse maps reflecting their own ideas and agendas.


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