An investigation has been made into symmetry features of patterns as a means by which the patterns are described, or with which they are transformed prior to classification in order to assist a pattern recognition system. There are two main points of departure from existing symmetry use in the pattern recognition domain. The first is the adoption of the theory that patterns can be categorised solely using a map of the symmetry features that exist within the static pattern. The second is the application of symmetry transforms to aid non-trivial recognition in patterns which are not intended to be perfectly symmetrical. An experiment is conducted to classify the reflectional symmetry features of digits, using the Generalised Symmetry Transform to produce the features and Probabilistic Neural Networks to perform the classification. Symmetry feature information is also used to define parameters of affine transformations to achieve improved performance in tolerance to variances in position and orientation. The results lead to an investigation of the role of asymmetry. The Generalised Symmetry Transform is modified to produce two related transforms: the Generalised Asymmetry Transform and the Generalised Asymmetry and Symmetry Transform. Finally, a new symmetry transform is proposed which separates the factors affecting the degree of symmetry in an image into three non-linear functions of corresponding pairs of pixels. These factors are: the colour intensity values; the pixel orientations; and the respective distance between the point and potential reflection plane. The strictness of symmetry, or tolerance to non-symmetrical artifacts, is defined in variable parameters which are set to suit the desired application. This new transform is called the Reflectional Symmetry Transform. The structure of its input and output match those of the Generalised Symmetry Transform, which it is intended to replace.

M.Sc. (Mathematics) / Please refer to full text to view abstract

No description available.

This research investigates the characteristics of Parity Time symmetry breaking in two optically coupled, time delayed semiconductor lasers. A theoretical model is used to describe the controllable parameters in the experiment and intensity output of the coupled lasers. The PT parameters we control are the spatial separation between the two lasers, the frequency detuning, and the coupling strength. We find that the experimental data agrees with the predictions from the theoretical model confirming the intensity behaviors of the lasers, and the monotonic change in PT-threshold as a function of coupling scaled by the time delay. <br>

Thesis (Ph.D.)--Boston University / In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ~ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses and other properties of the new particles predicted by these theories. I find S > 0.1 in the specific theories I study. Although this result still disagrees with experiment, it is much closer to the experimental value than is the conventional wisdom S > 0.3. These results encourage further lattice studies to search for experimentally viable strongly-interacting theories of EWSB.

Objective: To perform kinematic and kinetic analyses on the static standing and ambulation in subjects after stroke with and without wearing a 5-degree lateral-wedged insole. Design: Ten hemiparetic individuals with unilateral stroke were recruited. Participants performed quiet stance and ambulation with no insole wedge, paretic side wedged, and nonparetic side wedged in a random order. The vertical ground reaction force and temporal-spatial parameters of gait were measured. Symmetry index was also calculated. Results: During quiet stance, the symmetry index of weight bearing improved significantly with nonparetic side-wedged (P < 0.017), but not with paretic side-wedged insoles. During ambulation, the symmetry indices of kinematic and kinetic measurements in the frontal plane were not significantly different among the three conditions. However, the contralateral knee abductor moment was significantly (P < 0.05) less than that of the nonparetic limb during nonparetic side-wedged ambulation. The ipsilateral hip and knee abductor moments were significantly (P < 0.05) less than the nonparetic limb during paretic side-wedged ambulation. Conclusions: Application of nonparetic side wedge insole can improve stance symmetry and tends to reduce the paretic knee abductor load during ambulation. The effects of paretic side-wedged insole are different. The present results provide guidelines for the placement of wedges in the shoes of individuals after stroke.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Physics. / M̲i̲c̲ṟo̲f̲i̲c̲ẖe̲ c̲o̲p̲y̲ a̲v̲a̲i̲ḻa̲ḇḻe̲ i̲ṉ A̲ṟc̲ẖi̲v̲e̲s̲ a̲ṉḏ S̲c̲i̲e̲ṉc̲e̲. / Vita. / Includes bibliographical references. / by Sylvester James Gates, Jr. / Ph.D.

In this dissertation, we utilize the discrete Fourier analysis on axially symmetric data generation and nonparametric estimation. We first represent the axially symmetric process as Fourier series on circles with the Fourier random coefficients expressed as circularlysymmetric complex random vectors. We develop an algorithm to generate the axially symmetric data that follow the given covariance function. Our simulation study demonstrates that our approach performs comparable with the classical approach using the given axially symmetric covariance function directly, while at the same time significantly reducing computational costs. For the second contribution of this dissertation, we apply the discrete Fourier transform to provide the nonparametric estimation on the covariance function of the above circularly-symmetric complex random vectors under gridded data structure. Our results show that these estimates has closely related to the simultaneous diagonalization of circulant matrices. The simulation study shows that our proposed estimates match well with their theoretical counterparts. Finally through the Fourier transform of the original gridded data, the covariance estimator of an axially symmetric process based on the method of moments can be represented as a quadratic form of transformed data that is associated with a rotation matrix.

No description available.

Landau-Ginzburg Mirror Symmetry provides for the construction of two algebraic objects, called the A- and B-models. Special cases of these models–constructed using invertible polynomials and abelian symmetry groups–are well understood. In this thesis, we consider generalizations of the B-model, and specifically address the associativity of the multiplication in these models. We also prove an explicit B-model isomorphism for a class of polynomials in three variables.