Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.

Graph-based structural analysis of planar mechanisms.

Kinematic structure of planar mechanisms addresses the study of attributes determined exclusively by the joining pattern among the links forming a mechanism. The system group classification is central to the kinematic structure and consists of determining a sequence of kinematically and statically independent-simple chains which represent a modular basis for the kinematics and force analysis of the mechanism. This article presents a novel graph-based algorithm for structural analysis of planar mechanisms with closed-loop kinematic structure which determines a sequence of modules (Assur groups) representing the topology of the mechanism. The computational complexity analysis and proof of correctness of the implemented algorithm are provided. A case study is presented to illustrate the results of the devised method.

Network Construction and Graph Theoretical Analysis of Functional Language Networks in Pediatric Epilepsy

This dissertation introduces a new approach for assessing the effects of pediatric epilepsy on the language connectome. Two novel data-driven network construction approaches are presented. These methods rely on connecting different brain regions using either extent or intensity of language related activations as identified by independent component analysis of fMRI data. An auditory description decision task (ADDT) paradigm was used to activate the language network for 29 patients and 30 controls recruited from three major pediatric hospitals. Empirical evaluations illustrated that pediatric epilepsy can cause, or is associated with, a network efficiency reduction. Patients showed a propensity to inefficiently employ the whole brain network to perform the ADDT language task; on the contrary, controls seemed to efficiently use smaller segregated network components to achieve the same task. To explain the causes of the decreased efficiency, graph theoretical analysis was carried out. The analysis revealed no substantial global network feature differences between the patient and control groups. It also showed that for both subject groups the language network exhibited small-world characteristics; however, the patient’s extent of activation network showed a tendency towards more random networks. It was also shown that the intensity of activation network displayed ipsilateral hub reorganization on the local level. The left hemispheric hubs displayed greater centrality values for patients, whereas the right hemispheric hubs displayed greater centrality values for controls. This hub hemispheric disparity was not correlated with a right atypical language laterality found in six patients. Finally it was shown that a multi-level unsupervised clustering scheme based on self-organizing maps, a type of artificial neural network, and k-means was able to fairly and blindly separate the subjects into their respective patient or control groups. The clustering was initiated using the local nodal centrality measurements only. Compared to the extent of activation network, the intensity of activation network clustering demonstrated better precision. This outcome supports the assertion that the local centrality differences presented by the intensity of activation network can be associated with focal epilepsy.

Canonical discriminant analysis applied to broiler chicken performance

The mechanisms involved in the control of growth in chickens are too complex to be explained only under univariate analysis because all related traits are biologically correlated. Therefore, we evaluated broiler chicken performance under a multivariate approach, using the canonical discriminant analysis. A total of 1920 chicks from eight treatments, defined as the combination of four broiler chicken strains (Arbor Acres, AgRoss 308, Cobb 500 and RX) from both sexes, were housed in 48 pens. Average feed intake, average live weight, feed conversion and carcass, breast and leg weights were obtained for days 1 to 42. Canonical discriminant analysis was implemented by SAS((R)) CANDISC procedure and differences between treatments were obtained by the F-test (P < 0.05) over the squared Mahalanobis` distances. Multivariate performance from all treatments could be easily visualised because one graph was obtained from two first canonical variables, which explained 96.49% of total variation, using a SAS((R)) CONELIP macro. A clear distinction between sexes was found, where males were better than females. Also between strains, Arbor Acres, AgRoss 308 and Cobb 500 (commercial) were better than RX (experimental), Evaluation of broiler chicken performance was facilitated by the fact that the six original traits were reduced to only two canonical variables. Average live weight and carcass weight (first canonical variable) were the most important traits to discriminate treatments. The contrast between average feed intake and average live weight plus feed conversion (second canonical variable) were used to classify them. We suggest analysing performance data sets using canonical discriminant analysis.

XSophe-Sophe-XeprView (R). A computer simulation software suite (v. 1.1.3) for the analysis of continuous wave EPR spectra

The XSophe-Sophe-XeprView((R)) computer simulation software suite enables scientists to easily determine spin Hamiltonian parameters from isotropic, randomly oriented and single crystal continuous wave electron paramagnetic resonance (CW EPR) spectra from radicals and isolated paramagnetic metal ion centers or clusters found in metalloproteins, chemical systems and materials science. XSophe provides an X-windows graphical user interface to the Sophe programme and allows: creation of multiple input files, local and remote execution of Sophe, the display of sophelog (output from Sophe) and input parameters/files. Sophe is a sophisticated computer simulation software programme employing a number of innovative technologies including; the Sydney OPera HousE (SOPHE) partition and interpolation schemes, a field segmentation algorithm, the mosaic misorientation linewidth model, parallelization and spectral optimisation. In conjunction with the SOPHE partition scheme and the field segmentation algorithm, the SOPHE interpolation scheme and the mosaic misorientation linewidth model greatly increase the speed of simulations for most spin systems. Employing brute force matrix diagonalization in the simulation of an EPR spectrum from a high spin Cr(III) complex with the spin Hamiltonian parameters g(e) = 2.00, D = 0.10 cm(-1), E/D = 0.25, A(x) = 120.0, A(y) = 120.0, A(z) = 240.0 x 10(-4) cm(-1) requires a SOPHE grid size of N = 400 (to produce a good signal to noise ratio) and takes 229.47 s. In contrast the use of either the SOPHE interpolation scheme or the mosaic misorientation linewidth model requires a SOPHE grid size of only N = 18 and takes 44.08 and 0.79 s, respectively. Results from Sophe are transferred via the Common Object Request Broker Architecture (CORBA) to XSophe and subsequently to XeprView((R)) where the simulated CW EPR spectra (1D and 2D) can be compared to the experimental spectra. Energy level diagrams, transition roadmaps and transition surfaces aid the interpretation of complicated randomly oriented CW EPR spectra and can be viewed with a web browser and an OpenInventor scene graph viewer.

GUI Inspection from Source Code Analysis

Graphical user interfaces (GUIs) are critical components of todays software. Given their increased relevance, correctness and usability of GUIs are becoming essential. This paper describes the latest results in the development of our tool to reverse engineer the GUI layer of interactive computing systems. We use static analysis techniques to generate models of the user interface behaviour from source code. Models help in graphical user interface inspection by allowing designers to concentrate on its more important aspects. One particularly type of model that the tool is able to generate is state machines. The paper shows how graph theory can be useful when applied to these models. A number of metrics and algorithms are used in the analysis of aspects of the user interface's quality. The ultimate goal of the tool is to enable analysis of interactive system through GUIs source code inspection.

Slicing for architectural analysis

Current software development often relies on non-trivial coordination logic for combining autonomous services, eventually running on different platforms. As a rule, however, such a coordination layer is strongly woven within the application at source code level. Therefore, its precise identification becomes a major methodological (and technical) problem and a challenge to any program understanding or refactoring process. The approach introduced in this paper resorts to slicing techniques to extract coordination data from source code. Such data are captured in a specific dependency graph structure from which a coordination model can be recovered either in the form of an Orc specification or as a collection of code fragments corresponding to the identification of typical coordination patterns in the system. Tool support is also discussed

The role of coordination analysis in software integration projects

What sort of component coordination strategies emerge in a software integration process? How can such strategies be discovered and further analysed? How close are they to the coordination component of the envisaged architectural model which was supposed to guide the integration process? This paper introduces a framework in which such questions can be discussed and illustrates its use by describing part of a real case-study. The approach is based on a methodology which enables semi-automatic discovery of coordination patterns from source code, combining generalized slicing techniques and graph manipulation

Analysis of computing open source systems

Graphical user interfaces (GUIs) are critical components of today's open source software. Given their increased relevance, the correctness and usability of GUIs are becoming essential. This paper describes the latest results in the development of our tool to reverse engineer the GUI layer of interactive computing open source systems. We use static analysis techniques to generate models of the user interface behavior from source code. Models help in graphical user interface inspection by allowing designers to concentrate on its more important aspects. One particular type of model that the tool is able to generate is state machines. The paper shows how graph theory can be useful when applied to these models. A number of metrics and algorithms are used in the analysis of aspects of the user interface's quality. The ultimate goal of the tool is to enable analysis of interactive system through GUIs source code inspection.

Models and tools for value systems analysis in collaborative environments

Dissertation to obtain the degree of Doctor in Electrical and Computer Engineering, specialization of Collaborative Networks

Molecular analysis of the dengue virus type 1 and 2 in Brazil based on sequences of the genomic envelope-nonstructural protein 1 junction region

The genomic sequences of the Envelope-Non-Structural protein 1 junction region (E/NS1) of 84 DEN-1 and 22 DEN-2 isolates from Brazil were determined. Most of these strains were isolated in the period from 1995 to 2001 in endemic and regions of recent dengue transmission in São Paulo State. Sequence data for DEN-1 and DEN-2 utilized in phylogenetic and split decomposition analyses also include sequences deposited in GenBank from different regions of Brazil and of the world. Phylogenetic analyses were done using both maximum likelihood and Bayesian approaches. Results for both DEN-1 and DEN-2 data are ambiguous, and support for most tree bipartitions are generally poor, suggesting that E/NS1 region does not contain enough information for recovering phylogenetic relationships among DEN-1 and DEN-2 sequences used in this study. The network graph generated in the split decomposition analysis of DEN-1 does not show evidence of grouping sequences according to country, region and clades. While the network for DEN-2 also shows ambiguities among DEN-2 sequences, it suggests that Brazilian sequences may belong to distinct subtypes of genotype III.

Optimal scheduling with uncertainty in the numerical data on the basis of a stability analysis

Scheduling, job shop, uncertainty, mixed (disjunctive) graph, stability analysis

Attitudes toward corporate sustainability : a multi-item scale and a multi-country empirical analysis

Magdeburg, Univ., Fak. für Wirtschaftswiss., Diss., 2013

Incentive structures in economic experiments : a neuroeconomic analysis of decision making under risk

Magdeburg, Univ., Fak. für Wirtschaftswiss., Diss., 2013

Testing Cayley graph densities

We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: Given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m-generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2m. We test amenable and non-amenable groups, and also groups for which amenability is unknown. In the latter class we focus on Richard Thompson’s group F.