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.

Carry-over of force production symmetry in athletes of differing strength levels. J Strength Cond Res 29(11): 3188–3196, 2015—This study sought to determine the level of association between bilateral force production symmetry assessment methods (standing weight distribution [WtD], unloaded and lightly loaded jumps, and isometric strength) and to determine whether the amount of symmetry carry-over between these tasks differs for strong and weak athletes. Subjects for this study included male (n = 31) and female (n = 32) athletes from National Collegiate Athletic Association Division I sports. Athletes performed WtD, unloaded and lightly loaded (20 kg) static and countermovement jumps, and isometric midthigh pull (IMTP) assessments on 2 adjacent force plates. Ground reaction force data were used to calculate symmetry variables and performance-related variables. Using Pearson zero order correlations, evaluations of the amount of symmetry carry-over were made. Weight distribution correlated strongly with jump peak force (PF) (r = 0.628–0.664). Strong relationships were also observed between loading conditions for jump variables (r = 0.568–0.957) as were the relationships between jump types for PF, peak power, and net impulse (r = 0.506–0.834). Based on the pooled sample, there was a lack of association between IMTP and WtD for jump symmetry variables. However, when examining strong and weak groups, rate of force development showed moderate to strong symmetry carry-over in the strongest athletes (r = 0.416–0.589). Stronger athletes appear to display similar explosive strength symmetry characteristics in dynamic and isometric assessments, unlike weaker athletes. Strength seems to influence the amount of force production symmetry carry-over between bilateral assessments. There may be optimal loads and variables for symmetry assessment, but these may differ based on population characteristics.

Coupled nonlinear Schrodinger equations (CNLS) govern many physical phenomena, such as nonlinear optics and Bose-Einstein condensates. For their wide applications, many studies have been carried out by physicists, mathematicians and engineers from different respects. In this dissertation, we focused on standing wave solutions, which are of particular interests for their relatively simple form and the important roles they play in studying other wave solutions. We studied the multiplicity of this type of solutions of CNLS via variational methods and bifurcation methods. Variational methods are useful tools for studying differential equations and systems of differential equations that possess the so-called variational structure. For such an equation or system, a weak solution can be found through finding the critical point of a corresponding energy functional. If this equation or system is also invariant under a certain symmetric group, multiple solutions are often expected. In this work, an integer-valued function that measures symmetries of CNLS was used to determine critical values. Besides variational methods, bifurcation methods may also be used to find solutions of a differential equation or system, if some trivial solution branch exists and the system is degenerate somewhere on this branch. If local bifurcations exist, then new solutions can be found in a neighborhood of each bifurcation point. If global bifurcation branches exist, then there is a continuous solution branch emanating from each bifurcation point. We consider two types of CNLS. First, for a fully symmetric system, we introduce a new index and use it to construct a sequence of critical energy levels. Using variational methods and the symmetric structure, we prove that there is at least one solution on each one of these critical energy levels. Second, we study the bifurcation phenomena of a two-equation asymmetric system. All these bifurcations take place with respect to a positive solution branch that is already known. The locations of the bifurcation points are determined through an equation of a coupling parameter. A few nonexistence results of positive solutions are also given

This study sought to further build on previous empirical findings regarding Johnsons theory that the gender symmetry debate can at least be partially resolved by acknowledging that two distinct subgroups of physical violence exist within intimate partner violence: Intimate Terrorism (IT) and Situational Couple Violence (SCV). According to Johnsons predictions these separate groups can be distinguished by the use of non-violent control tactics. This study focused on testing the ability of non-violent control tactics to predict the frequency and severity of violence within the sub-group intimate terrorism. It further explored Johnsons assertion that intimate terrorism is gender asymmetric with females experiencing a greater amount of victimization. Previous studies demonstrated moderate support that two subgroups do exist within intimate partner violence and that intimate terrorism may be asymmetrical. However, only one of the previous studies included a male sample that was not reflective of the general population. This study will test the gender asymmetry of intimate terrorism by using both a male and female sub-sample form the National Violence Against Women Survey. This studies sample consisted of males and females reporting at least on incident of physical violence by either their current spouse or cohabitating heterosexual partner. The statistical analysis showed moderate support that there are two subgroups within intimate partner violence that can be distinguished by the use of non-violent control tactics. It also demonstrated that for the subgroup intimate terrorism there are some differences across gender when examining severity and frequency of violence. However, only a small amount of the variance in intimate terrorism can be explained by non-violent control tactics.

Abstract not available

<p>Våld i nära relationer existerar i de flesta samhällen och förekommer bland såväl heterosexuella som samkönade par. Mycket forskning har främst ägnats åt mäns våld mot kvinnor där offret ofta orsakas stort lidande. Men våld som konfliktlösningsmetod är inte förbehållet män utan används även av kvinnor. En kartläggning av mäns och kvinnors våld i nära relationer i en svensk allmänpopulation planeras och ett frågeformulär har sammansatts och översatts från engelska. Denna uppsats ingår i valideringsstudien av formuläret. Syftet har varit att undersöka frågeformulärets giltighet i en svensk allmänpopulation. Valideringen har skett genom fyra fokusgruppsdiskussioner med experter. Resultatet visar att formuläret ger en giltig bild av mäns våld mot kvinnor. Fokusgrupperna har i lägre grad kunnat validera formulärets giltighet för kvinnors våld mot män i heterosexuella relationer. Våld i samkönade relationer berördes i princip inte alls under diskussionerna. Fokusgruppernas sammansättning antas i hög grad ha påverkat resultatet.</p>

<p>Many problems in business, industry, and academia can be modelled as constraint programs consisting of matrices of decision variables. Such “matrix models” often have symmetry. In particular, they often have row and column symmetry as the rows and columns can freely be permuted without affecting the satisfiability of assignments. Existing methods have difficulty in dealing with the super-exponential number of symmetries in a problem with row and column symmetry. We therefore propose some ordering constraints which can effectively break such symmetries. To use these constraints in practice, we develop some efficient linear time propagators. We demonstrate the effectiveness of these symmetry breaking ordering constraints on a wide range of problems. We also show how such ordering constraints can be used to deal with partial symmetries, as well as value symmetries.</p>

A time-reversible Maxwell's demon is demonstrated which creates a density difference between two chambers initialized to have equal density. The density difference is estimated theoretically and confirmed by computer simulations. It is found that the reversible Maxwell's demon compresses phase space volume even though its dynamics are time reversible. The significance of phase space volume compression in operating a microscopic heat engine is also discussed.

Human activity analysis has attracted great interest from computer vision researchers due to its promising applications in many areas such as automated visual surveillance, computer-human interactions, and motion-based identification and diagnosis. This dissertation presents work in two areas: general human activity recognition from video, and human activity analysis for the purpose of identifying pathological gait from both 3D captured data and from video. Even though the research in human activity recognition has been going on for many years, still there are many issues that need more research. This includes the effective representation and modeling of human activities and the segmentation of sequences of continuous activities. In this thesis we present an algorithm that combines shape and motion features to represent human activities. In order to handle the activity recognition from any viewing angle we quantize the viewing direction and build a set of Hidden Markov Models (HMMs), where each model represents the activity from a given view. Finally, a voting based algorithm is used to segment and recognize a sequence of human activities from video. Our method of representing activities has good attributes and is suitable for both low resolution and high resolution video. The voting based algorithm performs the segmentation and recognition simultaneously. Experiments on two sets of video clips of different activities show that our method is effective. Our work on identifying pathological gait is based on the assumption of gait symmetry. Previous work on gait analysis measures the symmetry of gait based on Ground Reaction Force data, stance time, swing time or step length. Since the trajectories of the body parts contain information about the whole body movement, we measure the symmetry of the gait based on the trajectories of the body parts. Two algorithms, which can work with different data sources, are presented. The first algorithm works on 3D motion-captured data and the second works on video data. Both algorithms use support vector machine (SVM) for classification. Each of the two methods has three steps: the first step is data preparation, i.e., obtaining the trajectories of the body parts; the second step is gait representation based on a measure of gait symmetry; and the last step is SVM based classification. For 3D motion-captured data, a set of features based on Discrete Fourier Transform (DFT) is used to represent the gait. We demonstrate the accuracy of the classification by a set of experiments that shows that the method for 3D motion-captured data is highly effective. For video data, a model based tracking algorithm for human body parts is developed for preparing the data. Then, a symmetry measure that works on the sequence of 2D data, i.e. sequence of video frames, is derived to represent the gait. We performed experiments on both 2D projected data and real video data to examine this algorithm. The experimental results on 2D projected data showed that the presented algorithm is promising for identifying pathological gait from video. The experimental results on the real video data are not good as the results on 2D projected data. We believe that better results could be obtained if the accuracy of the tracking algorithm is improved.

Thesis (Ph. D.)--University of Chicago, Department of Physics, December 2001. / Includes bibliographical references. Also available on the Internet.