The present thesis reports psychophysical and modeling studies on the spatial properties of visual mechanisms mediating the perception of mirror symmetry in human vision. In a first set of experiments, patterns were filtered for power spectra that decayed with spatial frequency according to variable slopes. Results revealed that symmetry detection is optimal if contrast energy is roughly equated across log-frequency bands (i.e. 1/f2) and that, under such conditions, spatial scales contribute equally and independently to symmetry perception. In a second study, random-noise patterns were filtered for various orientation bands. Results showed that symmetry perception is possible at all orientations, is mediated by oriented mechanisms, and is computed independently in different orientation channels. Data also revealed that the dimensions of the spatial integration region (IR) for symmetry vary with orientation in a way that approximately matches the spatial distribution of information in the stimulus. Finally, symmetry detection was measured for bandpass textures of variable spatial density and variable contrast polarity. For such patterns, it was found that symmetry is computed at a spatial scale proportional to stimulus density and that mechanisms insensitive to contrast polarity (i.e. second-order) are involved in the scale-selection process. / Overall, results from empirical and modeling work revealed an intimate link between symmetry perception and the properties of spatial filters. In particular, I argue that the size of the IR tends to vary such that a fixed amount of information is integrated irrespective of the spatial properties of the stimulus. Implications for the functional architecture of symmetry perception are discussed, and a paradigm for future research in symmetry perception is proposed in which spatial filtering is extended to higher orders of spatial complexity.

Thesis (M.Sc.)--University of Western Australia, 2008.

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.

It is conjectured that the SYZ map equals to the inverse mirror map. In dimension two this conjecture is proved, and in dimension three supporting evidences of the equality are studied in various examples. Since the SYZ map is expressed in terms of open Gromov-Witten invariants, this conjectural equality established an enumerative meaning of the inverse mirror map. / Moreover a computational method of open Gromov-Witten invariants for toric Calabi-Yau manifolds is invented. As an application, the Landau-Ginzburg mirrors of compact semi-Fano toric surfaces are computed explicitly. / This thesis gives a procedure to carry out SYZ construction of mirrors with quantum corrections by Fourier transform of open Gromov-Witten invariants. Applying to toric Calabi-Yau manifolds, one obtains the Hori-Iqbel-Vafa mirror together with a map from the Kahler moduli to the complex moduli of the mirror, called the SYZ map. / Lau, Siu Cheong. / Adviser: N.C. Leung. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 143-148). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

This work describes detailed convergent beam electron diffraction (CBED) studies of GdAlO3 and LaAlO3 perovskites. CBED patterns tilted away from major zone axes have been found to have high sensitivity to the presence of mirror or glide mirror symmetry. Such patterns confirm to high accuracy that the space group of GdAlO3 is orthorhombic, Pnma. Tilted patterns from this well characterised structure also serve as benchmarks against which similar patterns may be compared. In the case of LaAlO3, tilted patterns enable the space group to be confirmed as rhombohedral R3c, previously claimed to be cubic (Fm3c) by CBED. Furthermore, no evidence for the low symmetry (I2/a or F1) phases proposed for LaAlO3 has been observed. The LaAlO3 study also gives a careful assessment of the influence of tilted specimen surfaces on the CBED data. Within the qualitative scope of these experiments, no symmetry degrading effects could be observed. Some preliminary Quantitative CBED (QCBED) data from LaAlO3 is also presented. This shows it will be possible to make a detailed study of the bonding charge density (Δρ) in this material when combined with X-ray diffraction data. Also included is a brief CBED study of LaFeO3, a material that is isostructural with GdAlO3. Although this is restricted to exact zone axis patterns, it is noted that tilted patterns have significant potential to improve the quality of the symmetry determination.

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 113-117). Available also in a digital version from Dissertation Abstracts.

Mirror symmetry has been a significant area of research for geometry and physics for over two decades. Berglund and Hubsch proposed that for a certain family of singularities W, the so called "transposed" singularity WT should be the mirror partner of W. cite{BH} The techniques for constructing the orbifold LG models to test this conjecture were developed by FJR in cite{FJR} with a cohomological field theory generalized from the study of r-spin curves. The duality of LG A- and B-models became more elaborate when Krawitz cite{Krawitz} generalized the Intriligator-Vafa orbifold B-model to include contributions from more than one sector.This thesis presents a program written in Maple for explicitly computing bases for both LG A- and B-model rings, as well as the correlators for A-models to the extent of current knowledge. Included is a list of observations and conjectures drawn from computations done in the program.

We consider Landau-Ginzburg models stemming from non-abelian groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group G*, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors in general.

This thesis is devoted to a discussion of two-dimensional theories with (0,2) supersymmetry. Examples of two-dimensional (0,2) gauged linear sigma models (GLSMs) are constructed for various spaces including Grassmannians, complete intersections in Grassmannians, and non-complete intersections such as Pfaffians. Generalizations of (2,2) Toda dual theories to (0,2) Toda-like theories are also discussed and some examples are given, including products of projective spaces and del Pezzo surfaces. Correlation functions are computed to show the examples are the correct mirror models. / Ph. D. / This thesis is devoted to a discussion in a specific branch of string theory in particle physics. String theory is a model of elementary particles, which are currently described by a theory called the Standard Model. String theory is a more fundamental theory than the Standard Model in two ways: it incorporates general relativity, <i>i.e.</i>, the theory of gravity; and it is a ultraviolet theory of the Standard Model, or equivalently, the Standard model is seen as a low energy approximation of string theory. This thesis is concerned with the quantum mechanics of string theory, described by quantum field theory along a two-dimensional worldsheet swept out by a one-dimensional string as it propagates in time. Specifically, this thesis explores examples of two-dimensional worldsheet theories with a technical property known as (0,2) supersymmetry.

The Landau-Ginzburg (LG) B-Model is a significant feature of singularity theory and mirror symmetry. Krawitz in 2010, guided by work of Kaufmann, provided an explicit construction for the LG B-model when using diagonal symmetries of a quasihomogeneous, nondegenerate polynomial. In this thesis we discuss aspects of how to generalize the LG B-model construction to allow for nondiagonal symmetries of a polynomial, and hence nonabelian symmetry groups. The construction is generalized to the level of graded vector space and the multiplication developed up to an unknown factor. We present complete examples of nonabelian LG B-models for the polynomials x^2y + y^3, x^3y + y^4, and x^3 + y^3 + z^3 + w^2.