Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

A survey of kernel and spectral methods for clustering

Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved

Batch kernel SOM and related Laplacian methods for social network analysis

Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic tools are required to get a synthetic view of the graph and to reach a good understanding of the underlying problem. In particular, discovering groups of tightly connected vertices and understanding the relations between those groups is very important in practice. This paper shows how a kernel version of the batch Self Organizing Map can be used to achieve these goals via kernels derived from the Laplacian matrix of the graph, especially when it is used in conjunction with more classical methods based on the spectral analysis of the graph. The proposed method is used to explore the structure of a medieval social network modeled through a weighted graph that has been directly built from a large corpus of agrarian contracts

A novel method of combining blood oxygenation and blood flow sensitive magnetic resonance imaging techniques to measure the cerebral blood flow and oxygen metabolism responses to an unknown neural stimulus.

Simultaneous implementation of magnetic resonance imaging methods for Arterial Spin Labeling (ASL) and Blood Oxygenation Level Dependent (BOLD) imaging makes it possible to quantitatively measure the changes in cerebral blood flow (CBF) and cerebral oxygen metabolism (CMRO(2)) that occur in response to neural stimuli. To date, however, the range of neural stimuli amenable to quantitative analysis is limited to those that may be presented in a simple block or event related design such that measurements may be repeated and averaged to improve precision. Here we examined the feasibility of using the relationship between cerebral blood flow and the BOLD signal to improve dynamic estimates of blood flow fluctuations as well as to estimate metabolic-hemodynamic coupling under conditions where a stimulus pattern is unknown. We found that by combining the information contained in simultaneously acquired BOLD and ASL signals through a method we term BOLD Constrained Perfusion (BCP) estimation, we could significantly improve the precision of our estimates of the hemodynamic response to a visual stimulus and, under the conditions of a calibrated BOLD experiment, accurately determine the ratio of the oxygen metabolic response to the hemodynamic response. Importantly we were able to accomplish this without utilizing a priori knowledge of the temporal nature of the neural stimulus, suggesting that BOLD Constrained Perfusion estimation may make it feasible to quantitatively study the cerebral metabolic and hemodynamic responses to more natural stimuli that cannot be easily repeated or averaged