Singularity of Data Analytic Operations

Statistical data by their very nature are indeterminate in the sense that if one repeated the process of collecting the data the new data set would be somewhat different from the original. Therefore, a statistical method, a map $\Phi$ taking a data set $x$ to a point in some space F, should be stable at $x$: Small perturbations in $x$ should result in a small change in $\Phi(x)$. Otherwise, $\Phi$ is useless at $x$ or -- and this is important -- near $x$. So one doesn't want $\Phi$ to have "singularities," data sets $x$ s.t.\ the the limit of $\Phi(y)$ as $y$ approaches $x$ doesn't exist. (Yes, the same issue arises elsewhere in applied math.) However, broad classes of statistical methods have topological obstructions of continuity: They must have singularities. We show why and give lower bounds on the Hausdorff dimension, even Hausdorff measure, of the set of singularities of such data maps. There seem to be numerous examples. We apply mainly topological methods to study the (topological) singularities of functions defined (on dense subsets of) "data spaces" and taking values in spaces with nontrivial homology. At least in this book, data spaces are usually compact manifolds. The purpose is to gain insight into the numerical conditioning of statistical description, data summarization, and inference and learning methods. We prove general results that can often be used to bound below the dimension of the singular set. We apply our topological results to develop lower bounds on Hausdorff measure of the singular set. We apply these methods to the study of plane fitting and measuring location of data on spheres. \emph{This is not a "final" version, merely another attempt.}Comment: 325 pages, 8 figure

A Qualitative Study of Student-Centered Learning Practices in New England High Schools

In early 2015, the Nellie Mae Education Foundation (NMEF) contracted with the UMass Donahue Institute (UMDI) to conduct a qualitative study examining the implementation of student-centered learning (SCL) practices in select public high schools in New England. This study extends lines of inquiry explored through a prior (2014) project that UMDI conducted for NMEF. The 2014 study employed survey methodology to examine the prevalence of student-centered practices in public high schools across New England. The present study builds upon the investigation, using a variety of qualitative methods to further probe the richness and complexity of SCL approaches in use across the region. Specifically, this study was designed to address what student-centered practices "look like" in an array of contexts. The study also addresses the perceived impacts that SCL approaches have on students, staff, and schools. Additionally, it highlights the broad array of factors within and beyond school walls that reportedly foster and challenge the implementation of SCL practices. This study seeks to help NMEF understand the intricacies of SCL and provides strategic considerations for how Nellie Mae can promote the adoption and development of student-centered practices in the region.Nellie Mae organizes student-centered learning by four tenets: (1) learning is personalized; (2) learning is competency-based; (3) learning takes place anytime, anywhere; and (4) students take ownership.Specifically, the study addresses five research questions:What are the characteristics of student-centered practices in relation to the four SCL tenets? How are SCL approaches implemented?What are the salient contextual factors (e.g., systems, structures, policies, procedures) associated with the implementation of SCL practices? How do they support, impede, and otherwise shape the adoption, development, and implementation of SCL approaches?How are schools with moderate and high levels of SCL implementation organized to foster SCL practices? What mechanisms are in place to promote student-centered learning?What is the role of SCL approaches in schools and classrooms? In what ways, if at all, are they embedded in the goals and practices of schools and classrooms?What is the quality of SCL instructional practices in study schools? What relationships, if any, do administrators and educators perceive between these approaches and student learning

UK-wide evaluation of the Millennium Volunteers Programme

The Millennium Volunteers programme is a UK-wide government supported initiative designed to promote sustained volunteering among young people aged 16-24

An Algorithm for Unconstrained Quadratically Penalized Convex Optimization

A descent algorithm, "Quasi-Quadratic Minimization with Memory" (QQMM), is proposed for unconstrained minimization of the sum, $F$, of a non-negative convex function, $V$, and a quadratic form. Such problems come up in regularized estimation in machine learning and statistics. In addition to values of $F$, QQMM requires the (sub)gradient of $V$. Two features of QQMM help keep low the number of evaluations of the objective function it needs. First, QQMM provides good control over stopping the iterative search. This feature makes QQMM well adapted to statistical problems because in such problems the objective function is based on random data and therefore stopping early is sensible. Secondly, QQMM uses a complex method for determining trial minimizers of $F$. After a description of the problem and algorithm a simulation study comparing QQMM to the popular BFGS optimization algorithm is described. The simulation study and other experiments suggest that QQMM is generally substantially faster than BFGS in the problem domain for which it was designed. A QQMM-BFGS hybrid is also generally substantially faster than BFGS but does better than QQMM when QQMM is very slow.Comment: Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Gubernatorial Executive Orders Under the Michigan Constitution of 1963

Article published in the Michigan State University School of Law Student Scholarship Collection

In-Plane Shear Wall Performance as Affected by Compressed Earth Block Shape

This thesis investigates the in-plane shear performance of full-scale walls made from compressed earth blocks. Compressed earth blocks are a type of masonry where the blocks are composed of compressed soil and typically dry-stacked without mortar. Prior research has demonstrated that the in-plane shear strength of these blocks falls far short of capacities predicted by conventional masonry building codes, requiring new testing to develop effective and safe designs for seismic conditions. This thesis specifically studies the effects of block type and the use of grouted shear keys at the block head joints. Three full-scale walls were constructed and tested under in-plane, cyclic loading. To compare the effect of block type on shear strength, one wall was constructed from Rhino blocks as used by the Center for Vocational Building Technology, while another used V-Lock blocks designed by the Vermeer Corporation. Apart from differences in size and interlock mechanism, the standard Rhino blocks have shear keys at the head joints which are not present on the V-Lock blocks. To examine the effect of these shear keys, a third wall was built from Rhino blocks with the shear keys removed. The two standard block types displayed no major difference in strength that could not be attributed to grouted area or the presence/absence of the head joint shear keys. The Rhino block wall with shear keys reached a higher peak load relative to the grouted area but experienced a brittle drop in capacity after peaking, while the other two walls exhibited an extended loading plateau after the initial peak. All walls failed with cracking and block sliding along the main diagonals, a failure mode similar to conventional masonry. Proposals are made for modifying the equations for shear capacity from the Masonry Standards Joint Committee (MSJC) 2013 code for use in designing compressed earth block shear walls