Institut für Informatik und Computational Science
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Institute
(Near-)inverses of sequences
(2006)
We introduce the notion of a near-inverse of a non-decreasing sequence of positive integers; near-inverses are intended to assume the role of inverses in cases when the latter cannot exist. We prove that the near-inverse of such a sequence is unique; moreover, the relation of being near-inverses of each other is symmetric, i.e. if sequence g is the near-inverse of sequence f, then f is the near-inverse of g. There is a connection, by approximations, between near- inverses of sequences and inverses of continuous strictly increasing real-valued functions which can be exploited to derive simple expressions for near-inverses
In this article, we consider high-dimensional data which contains a low-dimensional non-Gaussian structure contaminated with Gaussian noise and propose a new linear method to identify the non-Gaussian subspace. Our method NGCA (Non-Gaussian Component Analysis) is based on a very general semi-parametric framework and has a theoretical guarantee that the estimation error of finding the non-Gaussian components tends to zero at a parametric rate. NGCA can be used not only as preprocessing for ICA, but also for extracting and visualizing more general structures like clusters. A numerical study demonstrates the usefulness of our method
This thesis discusses challenges in IT security education, points out a gap between e-learning and practical education, and presents a work to fill the gap. E-learning is a flexible and personalized alternative to traditional education. Nonetheless, existing e-learning systems for IT security education have difficulties in delivering hands-on experience because of the lack of proximity. Laboratory environments and practical exercises are indispensable instruction tools to IT security education, but security education in conventional computer laboratories poses particular problems such as immobility as well as high creation and maintenance costs. Hence, there is a need to effectively transform security laboratories and practical exercises into e-learning forms. In this thesis, we introduce the Tele-Lab IT-Security architecture that allows students not only to learn IT security principles, but also to gain hands-on security experience by exercises in an online laboratory environment. In this architecture, virtual machines are used to provide safe user work environments instead of real computers. Thus, traditional laboratory environments can be cloned onto the Internet by software, which increases accessibility to laboratory resources and greatly reduces investment and maintenance costs. Under the Tele-Lab IT-Security framework, a set of technical solutions is also proposed to provide effective functionalities, reliability, security, and performance. The virtual machines with appropriate resource allocation, software installation, and system configurations are used to build lightweight security laboratories on a hosting computer. Reliability and availability of laboratory platforms are covered by a virtual machine management framework. This management framework provides necessary monitoring and administration services to detect and recover critical failures of virtual machines at run time. Considering the risk that virtual machines can be misused for compromising production networks, we present a security management solution to prevent the misuse of laboratory resources by security isolation at the system and network levels. This work is an attempt to bridge the gap between e-learning/tele-teaching and practical IT security education. It is not to substitute conventional teaching in laboratories but to add practical features to e-learning. This thesis demonstrates the possibility to implement hands-on security laboratories on the Internet reliably, securely, and economically.
An Extended Query language for action languages (and its application to aggregates and preferences)
(2006)
Advances in biotechnologies rapidly increase the number of molecules of a cell which can be observed simultaneously. This includes expression levels of thousands or ten-thousands of genes as well as concentration levels of metabolites or proteins. Such Profile data, observed at different times or at different experimental conditions (e.g., heat or dry stress), show how the biological experiment is reflected on the molecular level. This information is helpful to understand the molecular behaviour and to identify molecules or combination of molecules that characterise specific biological condition (e.g., disease). This work shows the potentials of component extraction algorithms to identify the major factors which influenced the observed data. This can be the expected experimental factors such as the time or temperature as well as unexpected factors such as technical artefacts or even unknown biological behaviour. Extracting components means to reduce the very high-dimensional data to a small set of new variables termed components. Each component is a combination of all original variables. The classical approach for that purpose is the principal component analysis (PCA). It is shown that, in contrast to PCA which maximises the variance only, modern approaches such as independent component analysis (ICA) are more suitable for analysing molecular data. The condition of independence between components of ICA fits more naturally our assumption of individual (independent) factors which influence the data. This higher potential of ICA is demonstrated by a crossing experiment of the model plant Arabidopsis thaliana (Thale Cress). The experimental factors could be well identified and, in addition, ICA could even detect a technical artefact. However, in continuously observations such as in time experiments, the data show, in general, a nonlinear distribution. To analyse such nonlinear data, a nonlinear extension of PCA is used. This nonlinear PCA (NLPCA) is based on a neural network algorithm. The algorithm is adapted to be applicable to incomplete molecular data sets. Thus, it provides also the ability to estimate the missing data. The potential of nonlinear PCA to identify nonlinear factors is demonstrated by a cold stress experiment of Arabidopsis thaliana. The results of component analysis can be used to build a molecular network model. Since it includes functional dependencies it is termed functional network. Applied to the cold stress data, it is shown that functional networks are appropriate to visualise biological processes and thereby reveals molecular dynamics.