High-throughput methods systematically measure the internal state of the entire cell, but powerful computational tools are needed to infer dynamics from their raw data. Therefore, we have developed a new computational method, Eigen-genomic System Dynamic-pattern Analysis (ESDA), which uses systems theory to infer dynamic parameters from a time series of gene expression measurements. As many genes are measured at a modest number of time points, estimation of the system matrix is underdetermined and traditional approaches for estimating dynamic parameters are ineffective; thus, ESDA uses the principle of dimensionality reduction to overcome the data imbalance. We identify degradation dynamic patterns of a genomic system using ESDA. We also combine ESDA and Principal-oscillation-pattern (POP) analysis, which has been widely used in geosciences, to identify oscillation patterns. We demonstrate the first application of POP analysis to genome-wide time-series gene-expression data. Both simulation data and real-world data are used in this study to demonstrate the applicability of ESDA to genomic data. The biological interpretations of dynamic patterns are provided. We also show that ESDA not only compares favorably with previous experimental methods and existing computational methods, but that it also provides complementary information relative to other approaches. / text

The number of high-dimensional datasets recording multiple aspects of a single phenomenon is ever increasing in many areas of science. This is accompanied by a fundamental need for mathematical frameworks that can compare data tabulated as multiple large-scale matrices of di erent numbers of rows. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. This thesis addresses this limitation and de fines a higher-order GSVD (HO GSVD) of N > 2 datasets, that provides a mathematical framework that can compare multiple high-dimensional datasets tabulated as large-scale matrices of different numbers of rows. / text

Since their discovery, organic electronic materials have been of great interest as an alternative active layer material for active area materials in electronic applications. Initially studied as probes or lasing material the field has progressed to the point where both conjugated polymers and small organics have become fashionable objects of current device oriented solid state research. Organic electronic materials are liquid crystalline materials, packing into well-ordered domains when annealed thermally or via solvent annealing. The macromolecular orientation of the molecules in the solid state causes a shift in the electronic properties due to coupling of the dipoles. The amount of interaction between molecules can be correlated to different nanoscale morphologies. Such morphologies can be measured using microscopy techniques and compared to the spectroscopic results. This can then be extrapolated out to infer how the charges move within a film. Cyanine dyes represent an interesting form class of dyes as the molecular packing is strongly affected by hydrophilic and hydrophobic pendent groups, which cause the dye to arrange into a tubular bilayer. Spectroelectrochemistry is used to monitor and controllably oxidize the samples. Using singular value decomposition (SVD) it is possible to extract each electronic species formed during electrochemical oxidation and model the proposed species using semi empirical quantum mechanical calculations. Polyfluorene is a blue luminescent polymer of interest for its high quantum yield. The solution and solid-state conformation has shown two distinct phases. The formation of the secondary phase shows a dependence on the molecular weight. In a poor solvent, as the molecular weight increases, the secondary phase forms easier. In the solid state, the highly efficient blue emission from polyfluorene is degraded by ketone defects. The energy transfer to preexisting ketone defects is increased as the filmed is thermally ordered. Glass transitions of block copolymers are studied using synthetically novel polymers where an environmentally sensitive fluorescent reporter is placed within various regions of a self-assembled film. Different dynamics are observed within the block of the film then specifically at the interface of two blocks. / text

A systematic procedure is followed to develop singularity-reduced integral equations for modeling cracks in two-dimensional, linear multi-field media. The class of media treated is quite general and includes, as special cases, anisotropic elasticity, piezoelectricity and magnetoelectroelasticity. Of particular interest is the development of a pair of weakly-singular, weak-form integral equations (IEs) for "generalized displacement" and "generalized stress"; these serve as the basis for the development of a Symmetric Galerkin Boundary Element Method (SGBEM). The implementation is carried out to allow treatment of general mixed boundary conditions, an arbitrary number of cracks, and multi-region domains (in which regions having different material properties are bonded together). Finally, a procedure for calculation of T-stress, the constant term in the asymptotic series expansion of crack-tip stress field, is developed for anisotropic elastic media. The pair of weak-form boundary IEs that is derived (one for generalized displacement and the other one for generalized stress) are completely regularized in the sense that all kernels that appear are (at most) weakly-singular. This feature allows standard Co elements to be utilized in the SGBEM, and such elements are employed everywhere except at the crack tip. A special crack-tip element is developed to properly model the asymptotic behavior of the relative crack-face displacements. This special element contains "extra" degrees of freedom that allow the generalized stress intensity factors to be directly obtained from the solution of the governing system of discretized equations. It should be noted that while the integral equations contain only weakly-singular kernels (and so are integrable in the usual sense) there remains a need to devise special integration techniques to accurately evaluate these integrals as part of the numerical implementation. Various examples for crack problems are treated to illustrate the accuracy and versatility of the proposed procedure for both unbounded and finite domains and for both single-region and multi-region problems. It is found that highly accurate fracture data can be obtained using relatively course meshes. Finally, this dissertation addresses the development of a numerical procedure to calculate T-stress for crack problems in general anisotropic elastic media. T-stress is obtained from the sum of crack-face displacements which are computed via a (regularized) integral equation of the boundary data. Two approaches for computing the derivative of the sum of crack-face displacements are proposed: one uses numerical differentiation, and the other one uses a weak-form integral equation. Various examples are examined to demonstrate that highly accurate results are obtained by means of both approaches. / text

Στόχος της εργασίας είναι η μελέτη πιθανοτικών αλγορίθμων για προσεγγιστική επίλυση προβλημάτων του επιστημονικού υπολογισμού. Τα προβλήματα τα οποία θα μας απασχολήσουν είναι ο πολλαπλασιασμός μητρών, ο υπολογισμός της διάσπασης ιδιαζουσών τιμών (SVD) ενός μητρώου και ο υπολογισμός μιας "συμπιεσμένης" διάσπασης ενός μητρώου. / -

Computational efficiency of solving the dynamics of highly oscillatory systems is an important issue due to the requirement of small step size of explicit numerical integration algorithms. A system is considered to be highly oscillatory if it contains a fast solution that varies regularly about a slow solution. As for multibody systems, stiff force elements and contacts between bodies can make a system highly oscillatory. Standard explicit numerical integration methods should take a very small step size to satisfy the absolute stability condition for all eigenvalues of the system and the computational cost is dictated by the fast solution. In this research, a new hybrid integration scheme is proposed, in which the local linearization method is combined with a conventional integration method such as the fourth-order Runge-Kutta. In this approach, the system is partitioned into fast and slow subsystems. Then, the two subsystems are transformed into a reduced and a boundary-layer system using the singular perturbation theory. The reduced system is solved by the fourth-order Runge-Kutta method while the boundary-layer system is solved by the local linearization method. This new hybrid scheme can handle the coupling between the fast and the slow subsystems efficiently. Unlike other multi-rate or multi-method schemes, extrapolation or interpolation process is not required to deal with the coupling between subsystems. Most of the coupling effect can be accounted for by the reduced (or quasi-steady-state) system while the minor transient effect is taken into consideration by averaging. In this research, the absolute stability region for this hybrid scheme is derived and it is shown that the absolute stability region is almost independent of the fast variables. Thus, the selection of the step size is not dictated by the fast solution when a highly oscillatory system is solved, in turn, the computational efficiency can be improved. The advantage of the proposed hybrid scheme is validated through several dynamic simulations of a vehicle system including a flexible tire model. The results reveal that the hybrid scheme can reduce the computation time of the vehicle dynamic simulation significantly while attaining comparable accuracy.

The idea of effective field theory (EFT) was developed decades ago in low-energy strong-interaction - hadronic and nuclear - physics. After introducing chiral perturbation theory (ChPT), we focus in this dissertation on three non-perturbative cases that standard ChPT cannot deal with by itself. First, we investigate pion-nucleon (πN) scattering around the delta resonance, which is an important non-perturbative feature of low-energy nuclear physics. We show that in order to describe πN scattering around the delta peak, a power counting is necessary that goes beyond the power counting of ChPT. Using this new power counting, we calculate the phase shifts in the spin-3/2 P-wave channel up to next-to-next-to-leading order (NNLO). Second, in order to clarify the issue of renormalization and power counting of nucleon-nucleon potentials, we use a toy model to illustrate how to build effective theories for singular potentials, which some nuclear potentials belong to. We consider a central attractive 1/r² potential perturbed by a 1/r⁴ correction. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis. Finally, we illustrate how non-perturbative EFT can be used to study neutron-antineutron oscillation inside the deuteron. We build an EFT for a model-independent, systematic study of two-unit baryon-number (|ΔB| = 2) violation in the context of nuclear physics. To cope with the non-perturbative deuteron structure, we apply the pionless version of this EFT to calculate deuteron decay. The decay width is obtained up to next-to-leading order. We show that the contribution of direct two-nucleon annihilation to the deuteron decay appears only at NNLO.

Electromyogram (EMG) is an established tool to study operation of neuromuscular systems. In analysing EMG signals, accurate detection of the movement-related events in the signal is frequently necessary. I explored the application of change-point detection algorithm proposed by Moskvina et. al., 2003 to EMG event detection, and evaluated the technique’s performance comparing it to two common threshold-based event detection methods and to the visual estimates of the EMG events performed by trained practitioners in the field. The algorithm was implemented in MATLAB and applied to EMG segments recorded from wrist and trunk muscles. The quality and frequency of successful detection were assessed for all methods, using the average visual estimate as the baseline, against which techniques were evaluated. The application showed that the change-point detection can successfully locate multiple changes in the EMG signal, but the maximum value of the detection statistic did not always identify the muscle activation onset.

We consider two transceivers equipped with multiple antennas that intend to communicate i.e. both of which transmit and receive data in a TDD fashion. Assuming that the responses of the physical communication channels between these two nodes are linear and reciprocal (time invariant or with very slow time variations), and by exploiting the closed loop conversation between these nodes, we have proposed efficient algorithms allowing to adaptively identify the Best Singular Mode (BSM) of the channel (those algorithms are for training, blind, and semi-blind channel identification). Unlike other proposed algorithms, our proposed adaptive algorithms are robust to noise as the involved step-size allows a trade-off to reduce the impact of the additive noise at the expense of some estimation delay. In practice, however, the reciprocity of the equivalent channels is lost because of the mismatch between the transmit and the receive filters of the communicating nodes. This mismatch causes significant degradation in the performance of the BSM estimation. Therefore, we have also proposed adaptive self-calibrating algorithms (which do not require any additional RF circuitry) that account for such a mismatch. In addition, we have conducted a convergence analysis of the BSM algorithm and extended it to estimate multiple modes simultaneously. Finally, we have also proposed an adaptive, iterative algorithm that is capable of allocating power in such a way that maximizes the capacity of a SISO OFDM communication system. / Thesis (Ph.D, Electrical & Computer Engineering) -- Queen's University, 2010-07-21 16:53:33.077

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