The last 15 years have seen a significant progress in the development of general purpose algorithms and software for polyhedral computation. Many polytopes of practical interest have enormous output complexity and are often highly degenerate, posing severe difficulties for known general purpose algorithms. They are, however, highly structured and attention has turned to exploiting this structure, particularly symmetry. We focus on polytopes arising from combinatorial optimization problems. In particular, we study the face lattice of the metric polytope associated with the well-known maxcut and multicommodity flow problems, as well as with finite metric spaces. Exploiting the high degree of symmetry, we provide the first complete orbitwise description of the higher layers of the face lattice of the metric polytope for any dimension. Further computational and combinatorial issues are presented. / Thesis / Master of Applied Science (MASc)

The research presented in this thesis addresses the problem of updating an analytical model using a parametric Reference Basis approach. In this method, some parameters are assumed to be accurate (e.g. natural frequencies, mode shapes and mass matrix), while others are adjusted so that the eigenvalue equation is satisfied. Updating is done with the use of principal submatrices, and the method seeks the best parameters multiplying these matrices. This is a departure from classical model reference, and is closer to the formulation of sensitivity methods. The submatrices allow updating of the stiffness matrix with certain freedom while preserving connectivity. Closed form solution can be achieved through multiple ways; two different approaches, denoted as the Quadratic Compression Method (QCM) and the Full Vector Method (FVM), are described in this paper. It is shown that the QCM possesses superior robustness properties with respect to noise in the data. This fact, as well as the simplicity offered by QCM, is demonstrated theoretically and experimentally. The experiments are presented to show the advantage of the QCM in the updating process. / Master of Science

This dissertation examines some of the more subjective aspects of individuals' experiences of isolation within the context of racialized and gendered work organizations. This research develops two constructs--institutional and social isolation--and attempts to ascertain the extent to which racial and gender groups experience isolation similarly. Other attitudes, such as intent to turnover, affective commitment, and alienation, are analyzed with respect to feelings of isolation for these groups. Finally, because current thinking has advocated the use of organizational interventions, such as mentoring programs, to ameliorate individuals' feelings of separateness within the organization, the relationship of mentoring to the aforementioned constructs was examined for its usefulness in understanding similarities and differences between these groups. This research extends previous work by providing support for new conceptualizations of social isolation and isolation. It extends work done by Nkomio and Cox (1990) and others who found that individuals who had achieved some objective measures of success in organizations, still did not feel, subjectively, as if they were a part of the organization. Thus, the use of these isolation constructs will expand our knowledge of organizational processes in examining groups based on gender and race/ethnicity. The results indicate that isolation docs exist on two dimensions: institutional isolation and social isolation. Asian-Americans have higher levels of institutional isolation, and African-Americans have higher levels of social isolation than any other group. Females experience higher levels of social isolation--but not institutional isolation--than males. There are some differences when race and gender are examined simultaneously in levels of experienced institutional and social isolation. Younger faculty feel more institutionally and socially isolated than older faculty. There is no significant effect of the presence of mentoring on institutional or social isolation; nor is there differential access to mentoring relationships by race. However, females enter mentoring relationships in greater proportions than males. There are also effects from cross-racial mentoring relationships. Finally, there are no significant differences, by race or gender, in the levels of affective organizational commitment or intent to turnover. / Ph. D.

An n-Venn diagram is defined as a collection of n finitely intersecting closed curves dividing the plane into 2^n distinct regions, where each region is in the interior of a unique subset of the curves. A Venn diagram is simple if at most two curves intersect at any point, and it is monotone if it has some embedding on the plane in which all curves are convex. An n-Venn diagram has n-fold rotational symmetry if a rotation of 180 degrees about a centre point in the plane leaves the diagram unchanged, up to a relabeling of the curves. It has been known that rotationally symmetric Venn diagrams could exist only if the number of curves is prime. Moreover, non-simple Venn diagrams with rotational symmetry have been proven to exist for any prime number of curves. However, the largest prime for which a simple rotationally symmetric Venn diagram was known prior to this, was 7. In this thesis, we are concerned with generating simple monotone Venn diagrams, especially those that have some type(s) of symmetry. Several representations of these diagrams are introduced and different backtracking search algorithms are provided based on these representations. Using these algorithms we show that there are 39,020 non-isomorphic simple monotone 6-Venn diagrams in total. In the case of drawing Venn diagrams on a sphere, we prove that there exists a simple symmetric n-Venn diagram, for any n >= 6, with the following set(s) of isometries : (a) a 4-fold rotational symmetry about the polar axis, together with an additional involutional symmetry about an axis through the equator, or (b) an involutional symmetry about the polar axis together with two reflectional symmetries about orthogonal planes that intersect at the polar axis. Finally, we introduce a new type of symmetry of Venn diagrams which leads us to the discovery of the first simple rotationally symmetric Venn diagrams of 11 and 13 curves. / Graduate / 0984 / Khalegh@GMail.com

Indiana University-Purdue University Indianapolis (IUPUI) / Symmetry plays a significant role in protein structural assembly and function. This is especially true for large homo-oligomeric protein complexes due to stability and finite control of function. But, symmetry in proteins are not perfect due to unknown reasons and leads to pseudosymmetry. This study focuses on symmetry analysis of homo-oligomers, specifically homo-dimers, homo-trimers and homo-tetramers. We defined Off Symmetry (OS) to measure the overall symmetry of the protein and Structural Index (SI) to quantify the structural difference and Assembly Index (AI) to quantify the assembly difference between the subunits. In most of the symmetrical homo-trimer and homo-tetramer proteins, Assembly Index contributes more to Off Symmetry and in the case of homo-dimer, Structural index contributes more than the Assembly Index. The main chain atom Carbon-Alpha (CA) is more symmetrical than the first side chain atom Carbon-Beta (CB), suggesting protein mobility may contribute to the pseudosymmetry. In addition, Pearson coefficient correlation between their Off-Symmetry and their respective atoms B-Factor (temperature factor) are calculated. We found that the individual residues of a protein in all the subunits are correlated to their average B-Factor of these residues. The correlation with BFactor is stronger in Structure Index than Assembly Index. All these results suggest that protein dynamics play an important role and therefore a larger off-symmetry may indicate a more mobile and flexible protein complex.

The present work generalizes the necessary condition of univariate symmetry of Patil et al. (2012) to the bivariate setting, develops a test of bivariate symmetry based on it, and generalizes the measure of asymmetry in Patil et al. (2014) to the bivariate setting. In doing so, as a byproduct, it pays attention to the interrelation between central symmetry and symmetry about an axis of a continuous bivariate density function.

In this paper, two equations from plasma physics are analyzed using two different mathematical procedures to yield information of interest for fusion energy. In the first case, Lie’s technique of computing symmetries of differential equations is applied to a specific case of the Grad-Shafranov equation. The case considered contains the majority of exact solutions from the literature. The full symmetry group is computed and new group-invariant solutions are obtained from these symmetries. The basic results and methods behind this technique are given along with several plots of the level sets or flux surfaces of the new solutions. In addition, a mathematical technique which was first used to prove the non-existence of solitons in quantum field theory is employed to derive an integral relation for any solution of the Sinh-Poisson equation. The original technique is modified to allow for a finite boundary and results are computed for two different boundary geometries. / text

No description available.

No description available.

No description available.