Reading “Women Don’t Riot” After the Riot: Creating a University-Prison Collaboration

We examine a case study of a collaboration between a University and a Women’s Correctional Institution: an Inside Out college course that brings together incarcerated and traditional students. We analyze the creation of a class in the aftermath of a riot in the region and in the ongoing context of internal and external reforms. We provide specific examples of mistakes, lessons learned, and the impact of our pedagogical values and techniques, and provide links to our class materials. We emphasize communication between the institutions, from the students to instructors, among the instructors, and from instructors to students. In the classroom, we exploit our expertise and our non-expertise as learners together to break down perceived barriers. We also emphasize the value of self-care and recognition of all students as agentic. We conclude with a call for future research that attends to student agency and that examines who benefits from prison-university partnerships

Exterior spacetime for stellar models in 5-dimensional Kaluza-Klein gravity

It is well-known that Birkhoff's theorem is no longer valid in theories with more than four dimensions. Thus, in these theories the effective 4-dimensional picture allows the existence of different possible, non-Schwarzschild, scenarios for the description of the spacetime outside of a spherical star, contrary to general relativity in 4D. We investigate the exterior spacetime of a spherically symmetric star in the context of Kaluza-Klein gravity. We take a well-known family of static spherically symmetric solutions of the Einstein equations in an empty five-dimensional universe, and analyze possible stellar exteriors that are conformal to the metric induced on four-dimensional hypersurfaces orthogonal to the extra dimension. All these exteriors are continuously matched with the interior of the star. Then, without making any assumptions about the interior solution, we prove the following statement: the condition that in the weak-field limit we recover the usual Newtonian physics singles out an unique exterior. This exterior is "similar" to Scharzschild vacuum in the sense that it has no effect on gravitational interactions. However, it is more realistic because instead of being absolutely empty, it is consistent with the existence of quantum zero-point fields. We also examine the question of how would the deviation from the Schwarzschild vacuum exterior affect the parameters of a neutron star. In the context of a model star of uniform density, we show that the general relativity upper limit M/R < 4/9 is significantly increased as we go away from the Schwarzschild vacuum exterior. We find that, in principle, the compactness limit of a star can be larger than 1/2, without being a black hole. The generality of our approach is also discussed.Comment: Typos corrected. Accepted for publication in Classical and Quantum Gravit

Scaling Sparse Matrices for Optimization Algorithms

To iteratively solve large scale optimization problems in various contexts like planning, operations, design etc., we need to generate descent directions that are based on linear system solutions. Irrespective of the optimization algorithm or the solution method employed for the linear systems, ill conditioning introduced by problem characteristics or the algorithm or both need to be addressed. In [GL01] we used an intuitive heuristic approach in scaling linear systems that improved performance of a large scale interior point algorithm significantly. We saw a factor of 10*3* improvements in condition number estimates. In this paper, given our experience with optimization problems from a variety of application backgrounds like economics, finance, engineering, planning etc., we examine the theoretical basis for scaling while solving the linear systems. Our goal is to develop reasonably "good" scaling schemes with sound theoretical basis. We introduce concepts and define "good" scaling schemes in section (1), as well as explain related work in this area. Scaling has been studied extensively and though there is a broad agreement on its importance, the same cannot be said about what constitutes good scaling. A theoretical framework to scale an m x n real matrix is established in section (2). We use the first order conditions associated with the Euclidean metric to develop iterative schemes in section (2.3) that approximate solution in O(mn) time for real matrice. We discuss symmetry preserving scale factors for an n x n symmetric matrix in (3). The importance of symmetry preservation is discussed in section (3.1). An algorithm to directly compute symmetry preserving scale factors in O(n2) time based on Euclidean metric is presented in section (3.4) We also suggest scaling schemes based on rectilinear norm in section (2.4). Though all p-norms are theoretically equivalent, the importance of outliers increases as p increases. For barrier methods, due to large diagnal corrections, we believe that the taxicab metric (p = 1) may be more appropriate. We develop a linear programming model for it and look at a "reduced" dual that can be formulated as a minimum cost flow problem on networks. We are investigating algorithms to solve it in O(mn) time that we require for an efficient scaling procedure. We hope that in future special structure of the "reduced" dual could be exploited to solve it quickly. The dual information can then be used to compute the required scale factors. We discuss Manhattan metric for symmetric matrices in section (3.5) and as in the case of real matrices, we are unable to propose an efficient computational scheme for this metric. We look at a linearized ideal penalty function that only uses deviations out of the desired range in section (2.5). If we could use such a metric to generate an efficient solution, then we would like to see impact of changing the range on the numerical behavior.

Scaling Sparse Constrained Nonlinear Problems for Iterative Solvers

We look at scaling a nonlinear optimization problem for iterative solvers that use at least first derivatives. These derivatives are either computed analytically or by differncing. We ignore iterative methods that are based on function evaluations only and that do not use any derivative information. We also exclude methods where the full problem structure is unknown like variants of delayed column generation. We look at related work in section (1). Despite its importance as evidenced in widely used implementations of nonlinear programming algorithms, scaling has not received enough attention from a theoretical point of view. What do we mean by scaling a nonlinear problem itself is not very clear. In this paper we attempt a scaling framework definition. We start with a description of a nonlinear problem in section (2). Various authors prefer different forms, but all forms can be converted to the form we show. We then describe our scaling framework in section (3). We show the equivalence between the original problem and the scaled problem. The correctness results of section (3.3) play an important role in the dynamic scaling scheme suggested. In section (4), we develop a prototypical algorithm that can be used to represent a variety of iterative solution methods. Using this we examine the impact of scaling in section (5). In the last section (6), we look at what the goal should be for an ideal scaling scheme and make some implementation suggestions for nonlinear solvers.

Wave-like Solutions for Bianchi type-I cosmologies in 5D

We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and "wave-like". In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a large number of anisotropic cosmological models of Bianchi type-I, which can be applied to our universe after the big-bang, when anisotropies could have played an important role. We present a complete review of all possible cases of self-similar anisotropic cosmologies in 5D. Our analysis extends a number of previous studies on wave-like solutions in 5D with spatial spherical symmetry