A Periodic Analog of the Schwarzschild Solution

We construct a new exact solution of Einstein's equations in vacuo in terms of Weyl canonical coordinates. This solution may be interpreted as a black hole in a space-time which is periodic in one direction and which behaves asymptotically like the Kasner solution with Kasner index equal to $4M L^{-1}$, where $L$ is the period and $M$ is the mass of the black hole. Outside the horizon, the solution is free of singularities and approaches the Schwarzschild solution as $L \rightarrow \infty$.Comment: 6 pages, preprint DESY-TH 94-03

Integrable Classical and Quantum Gravity

In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom.Comment: 41 pages, 2 figures, Lectures given at NATO Advanced Study Institute on Quantum Fields and Quantum Space Time, Cargese, France, 22 July - 3 Augus

Monodromy Matrix in the PP-Wave Limit

We construct the monodromy matrix for a class of gauged WZWN models in the plane wave limit and discuss various properties of such systems.Comment: 16 page

Considering Systems of Power and Black and Latine Students’ Belonging in STEM

This dissertation focuses on (a) exploring the need for and strategies to facilitate the integration of Critical Race Theory (CRT) and educational psychology and (b) supporting Black and Latine students through examining the impact of systems of power via the integration of belonging and Critical Race Theory. This dissertation follows a three-paper format. In Paper 1, we recognize that psychology researchers can use CRT to explore race and racism. However, psychology scholars may confront growing pains when integrating CRT due to their respective inquiry worldviews–postpositivism and critical–which result in several tensions. These tensions may limit the uptake of CRT in psychology and cause people to not understand CRT. Therefore, we describe CRT and related frameworks, tensions when integrating CRT into psychology, and strategies to attenuate the tensions. In Paper 2, the case study drew from the belonging opportunities structures and CRT literatures to investigate Black and Latine STEM undergraduate students’ (N = 9) experiences of instructional belonging opportunity structures and which structures impacted their belonging to explore how instructors and administrators can support belonging. Based on interview and syllabus data, students had experiences related to all Belonging-Centered Instruction instructional opportunity subdimension. We discuss implications for practice, research, and policy. In Paper 3, undergraduate students, who were participants in the case study, and I provide recommendations on what instructors and administrators can do to support Black and Latine students’ belonging in STEM while drawing from CRT. Our recommendations include both instructor practices and practices administrators and universities can support

Offshoring in Europe—Evidence of a Two-Way Street from Denmark

Based on a large Danish survey of companies in tradable goods and services sectors, this working paper presents the results of offshoring and its impact on jobs, adding new perspectives to the globalization debate. Globalization entails a cross-border flow of jobs, but contrary to the mainstream media portrayal of globalization, it is not a one-way but a two-way street. In 2002–05 more jobs were created as a result of offshoring of activities into eastern Denmark from companies outside Denmark (i.e., inshored to Denmark) than were eliminated due to offshoring from companies in the Danish region. Overall, the employment effects of both offshoring and inshoring were found to be limited to less than 1 percent of all jobs either lost to offshoring or gained via inshoring. For Denmark, the worries in purely numerical terms regarding the employment effects of globalization seem overly alarmist. However, the trends revealed in the study do pose challenges for low-skilled workers—the group most negatively affected—and for highly skilled specialists, who face pressure to constantly upgrade their skills. Policy implications can be drawn in view of our results to ensure that labor markets are able to meet the demands of globalizing firms.Labor Market, Offshoring, Offshore Outsourcing, High- and Low-Skilled Workers, Skill Bias, Denmark, Flexicurity

On b-bit min-wise hashing for large-scale regression and classification with sparse data

Large-scale regression problems where both the number of variables, $p$, and the number of observations, $n$, may be large and in the order of millions or more, are becoming increasingly more common. Typically the data are sparse: only a fraction of a percent of the entries in the design matrix are non-zero. Nevertheless, often the only computationally feasible approach is to perform dimension reduction to obtain a new design matrix with far fewer columns and then work with this compressed data. $b$-bit min-wise hashing is a promising dimension reduction scheme for sparse matrices which produces a set of random features such that regression on the resulting design matrix approximates a kernel regression with the resemblance kernel. In this work, we derive bounds on the prediction error of such regressions. For both linear and logistic models, we show that the average prediction error vanishes asymptotically as long as $q \|\beta^*\|_2^2 /n \rightarrow 0$, where $q$ is the average number of non-zero entries in each row of the design matrix and $\beta^*$ is the coefficient of the linear predictor. We also show that ordinary least squares or ridge regression applied to the reduced data can in fact allow us fit more flexible models. We obtain non-asymptotic prediction error bounds for interaction models and for models where an unknown row normalisation must be applied in order for the signal to be linear in the predictors.The first author was supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1 and an EPSRC programme grant

Harmonic entanglement with second-order non-linearity

We investigate the second-order non-linear interaction as a means to generate entanglement between fields of differing wavelengths. And show that perfect entanglement can, in principle, be produced between the fundamental and second harmonic fields in these processes. Neither pure second harmonic generation, nor parametric oscillation optimally produce entanglement, such optimal entanglement is rather produced by an intermediate process. An experimental demonstration of these predictions should be imminently feasible.Comment: 4 pages, 4 figure

Integrable Classical and Quantum Gravity

In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom

The influence of bond-rigidity and cluster diffusion on the self-diffusion of hard spheres with square-well interaction

Hard spheres interacting through a square-well potential were simulated using two different methods: Brownian Cluster Dynamics (BCD) and Event Driven Brownian Dynamics (EDBD). The structure of the equilibrium states obtained by both methods were compared and found to be almost the identical. Self diffusion coefficients ($D$) were determined as a function of the interaction strength. The same values were found using BCD or EDBD. Contrary the EDBD, BCD allows one to study the effect of bond rigidity and hydrodynamic interaction within the clusters. When the bonds are flexible the effect of attraction on $D$ is relatively weak compared to systems with rigid bonds. $D$ increases first with increasing attraction strength, and then decreases for stronger interaction. Introducing intra-cluster hydrodynamic interaction weakly increases $D$ for a given interaction strength. Introducing bond rigidity causes a strong decrease of $D$ which no longer shows a maximum as function of the attraction strength