The Geometry of Gauged Linear Sigma Model Correlation Functions

Applying advances in exact computations of supersymmetric gauge theories, we study the structure of correlation functions in two-dimensional N=(2,2) Abelian and non-Abelian gauge theories. We determine universal relations among correlation functions, which yield differential equations governing the dependence of the gauge theory ground state on the Fayet-Iliopoulos parameters of the gauge theory. For gauge theories with a non-trivial infrared N=(2,2) superconformal fixed point, these differential equations become the Picard-Fuchs operators governing the moduli-dependent vacuum ground state in a Hilbert space interpretation. For gauge theories with geometric target spaces, a quadratic expression in the Givental I-function generates the analyzed correlators. This gives a geometric interpretation for the correlators, their relations, and the differential equations. For classes of Calabi-Yau target spaces, such as threefolds with up to two Kahler moduli and fourfolds with a single Kahler modulus, we give general and universally applicable expressions for Picard-Fuchs operators in terms of correlators. We illustrate our results with representative examples of two-dimensional N=(2,2) gauge theories.Comment: 76 pages, v2: references added and minor improvement

String Compactifications from the Worldsheet and Target Space Point of View

This thesis presents research on compactifications of type II superstring theories, combining worldsheet and target space approaches. This is achieved by using supersymmetric gauge theory techniques together with geometrical methods. After reviewing relevant physical and mathematical concepts we turn to a study of correlation functions in two-dimensional gauged linear sigma models and demonstrate how these encode the target space geometry to a large extent. We present an elementary algorithm to determine the Picard--Fuchs differential operators, governing the moduli space geometries, from the defining gauge theory spectrum directly. Next, we employ the Givental I-function to propose explicit formulas for the holomorphic solutions annihilated by these differential operators for models with general non-Abelian gauge groups and a large class of matter spectra. These formulas provide an alternative, efficient way of deriving the Picard--Fuchs operators for non-Abelian gauge theories, where other approaches quickly become computationally unfeasible. Lastly, we consider Calabi--Yau fourfolds that arise as target spaces of non-Abelian gauged linear sigma models. We demonstrate that their quantum cohomology ring is not necessarily generated by products of marginal deformations alone and discuss implications of this property

A study of the emotional intelligence levels of first year student teachers at the Central University of Technology, Free State

Thesis (M. Ed. (Education)) - Central University of Technology, Free State, 2014The goal of the education system is to increase cognitive capacity, competencies and skills such as acquiring new knowledge, recalling facts and figures and applying this information to reasoning, understanding and solving problems. To achieve all these competencies teachers and lecturers traditionally use Bloom’s Taxonomy of Learning Domains. The competencies and skills as described by Bloom are measured by standardised intelligence tests. Society takes it for granted that the higher a person’s IQ (Intelligence quotient), the better he/she will perform at school level. But what happens after school? While cognitive intelligence may be able to predict quite accurately how one will perform at school, it predicts very little else in the way of social performance and interaction after school. As such, IQ is a rather weak predictor of performance in interpersonal relations, at work and in coping with a wide variety of challenges that surface in the course of one's life on a daily basis (Wagner, 1997). Some writers makes a strong case that people owe their success in their professional careers to much more than mere IQ. Wagner reviews data and offers convincing cases to show that an IQ above 110, fails as an accurate predictor of success in a career. In other words, you need to be smart enough to handle the cognitive complexity of the information you need for a given role or job, be it engineering, law, medicine, or business. But after reaching this threshold of “smart enough,” your intellect makes little difference. Wagner concludes that IQ alone predicts just 6 to 10 percent of career success. It has been argued for over a century, as early as Charles Darwin that something is missing from the human performance formula that is needed to explain why some people do very well in life while others do not, irrespective of how cognitively intelligent they may be. One of the first attempts by psychologists to identify additional predictors of performance in other aspects of life was made by Edward Thorndike (1920) when he described "social intelligence" as the ability to perceive one's own and others' internal states, motives and behaviours, and to act towards them appropriately on the basis of that information. Mayer, Salovey and Caruso (2000:273) state that emotional intelligence includes “the ability to perceive, appraise and express emotion accurately and adaptively; the ability to understand emotion and emotional knowledge; the ability to access and generate feelings where they facilitate cognitive activities and adaptive action; and the ability to regulate emotions in oneself and others”. All of these skills are necessary for the teacher to function successfully in the classroom. The question is: does the modern teacher have the necessary EI skills? This dissertation explores and describes the level of Emotional Intelligence of the first year student teachers at the Central University of Technology, Free State. Seventy-nine (79) students were tested during 2012 and 2013 to establish whether they have the necessary levels of Emotional Intelligence to ensure that they will be able to become good classroom leaders upon entering the teacher’s profession. Traits of Emotional Intelligence were assessed by means of the Trait Emotional Intelligence Questionnaire (TEIQue). The study investigates the Emotional Intelligence attributes and skills that a teacher will need to become a good classroom leader. The study examines the four main areas tested in the TEIQue, namely the well-being, the emotionality, the sociability and the self-control of the student teacher. Findings suggest that the student teachers still need to develop their emotional intelligence as their results fall in the lower level of the acceptable range

High-recall causal discovery for autocorrelated time series with latent confounders

We present a new method for linear and nonlinear, lagged and contemporaneous constraint-based causal discovery from observational time series in the presence of latent confounders. We show that existing causal discovery methods such as FCI and variants suffer from low recall in the autocorrelated time series case and identify low effect size of conditional independence tests as the main reason. Information-theoretical arguments show that effect size can often be increased if causal parents are included in the conditioning sets. To identify parents early on, we suggest an iterative procedure that utilizes novel orientation rules to determine ancestral relationships already during the edge removal phase. We prove that the method is order-independent, and sound and complete in the oracle case. Extensive simulation studies for different numbers of variables, time lags, sample sizes, and further cases demonstrate that our method indeed achieves much higher recall than existing methods for the case of autocorrelated continuous variables while keeping false positives at the desired level. This performance gain grows with stronger autocorrelation. At https://github.com/jakobrunge/tigramite we provide Python code for all methods involved in the simulation studies.Comment: 55 pages, 26 figures; added reference to related work plus accompanying dicussion in section 3.

Causal discovery in time series with unobserved confounders

Understanding cause and effect relationships is an essential part of the scientific inquiry. There are, however, many circumstances in which the classical approach of controlled experimentation is not feasible. This is the case, for example, for most aspects of Earth's complex climate system. In the first part of the talk we will give a brief introduction into the modern framework of causal inference and causal discovery, which provides alternative methods for learning and reasoning about cause and effect from observational, i.e., non-experimental data. These methods have in recent years been gaining increasing attention from various research fields, for example from the climate and Earth system sciences as well as from the machine learning and artificial intelligence community. We will then present the novel LPCMCI causal discovery algorithm for learning the cause and effect relationships in multivariate time series. This algorithm is specifically adapted to several challenges that are prevalent in time series considered in the climate and Earth system sciences, for example strong autocorrelations, combinations of time lagged and contemporaneous causal relationships, as well as nonlinearities. It moreover allows for the existence of latent confounders, i.e., unobserved common causes, a complication that is faced in most realistic scenarios

Reliable causal discovery in time series

In this talk I will, first, introduce the so-called causal discovery task, that is, the task of learning cause-and-effect relationships from observational data. I will then present three algorithms for causal discovery that have been (co-)developed by the Causal Inference research group at the DLR-Institute of Data Science in Jena. These algorithms are specifically designed to deal with the specifics of time series data and are available as part of the Python package tigramite