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Inverse problems involving systems of partial differential equations (PDEs) with many measurements or experiments can be very expensive to solve numerically. In a recent paper we examined dimensionality reduction methods, both stochastic and deterministic, to reduce this computational burden, assuming that all experiments share the same set of receivers. In the present article we consider the more general and practically important case where receivers are not shared across experiments. We propose a data completion approach to alleviate this problem. This is done by means of an approximation using an appropriately restricted gradient or Laplacian regularization, extending existing data for each experiment to the union of all receiver locations. Results using the method of simultaneous sources (SS) with the completed data are then compared to those obtained by a more general but slower random subset (RS) method which requires no modifications.

Much recent attention has been devoted to gradient descent algorithms where the steepest descent step size is replaced by a similar one from a previous iteration or gets updated only once every second step, thus forming a {\em faster gradient descent method}. For unconstrained convex quadratic optimization these methods can converge much faster than steepest descent. But the context of interest here is application to certain ill-posed inverse problems, where the steepest descent method is known to have a smoothing, regularizing effect, and where a strict optimization solution is not necessary. Specifically, in this paper we examine the effect of replacing steepest descent by a faster gradient descent algorithm in the practical context of image deblurring and denoising tasks. We also propose several highly efficient schemes for carrying out these tasks independently of the step size selection, as well as a scheme for the case where both blur and significant noise are present. In the above context there are situations where many steepest descent steps are required, thus building slowness into the solution procedure. Our general conclusion regarding gradient descent methods is that in such cases the faster gradient descent methods offer substantial advantages. In other situations where no such slowness buildup arises the steepest descent method can still be very effective.

This article is concerned with Monte-Carlo methods for the estimation of the trace of an implicitly given matrix $A$ whose information is only available through matrix-vector products. Such a method approximates the trace by an average of $N$ expressions of the form $\ww^t (A\ww)$, with random vectors $\ww$ drawn from an appropriate distribution. We prove, discuss and experiment with bounds on the number of realizations $N$ required in order to guarantee a probabilistic bound on the relative error of the trace estimation upon employing Rademacher (Hutchinson), Gaussian and uniform unit vector (with and without replacement) probability distributions. In total, one necessary bound and six sufficient bounds are proved, improving upon and extending similar estimates obtained in the seminal work of Avron and Toledo (2011) in several dimensions. We first improve their bound on $N$ for the Hutchinson method, dropping a term that relates to $rank(A)$ and making the bound comparable with that for the Gaussian estimator. We further prove new sufficient bounds for the Hutchinson, Gaussian and the unit vector estimators, as well as a necessary bound for the Gaussian estimator, which depend more specifically on properties of the matrix $A$. As such they may suggest for what type of matrices one distribution or another provides a particularly effective or relatively ineffective stochastic estimation method.

The half-lives of the Tz = -2, 56Zn and Tz = -1, 58Zn isotopes and other nuclei were measured in a {\beta}-decay experiment at GANIL. The energy levels populated by the 56Zn {\beta} decay were determined. The 56Zn results are compared with the results of the mirror process, the charge exchange reaction 56Fe(3He,t)56Co., Comment: Conference: C12-07-09.4 Proceedings

Across the nation, urban school districts struggle to raise often abysmally low high school graduation rates. New York City, with a four-year graduation rate of 57 percent, is no exception. Yet, some high schools in New York, as elsewhere, succeed beyond expectations in bringing students with low academic skills and high needs to graduation in four years, followed by enrollment in college. This report describes a follow-up qualitative study, conducted in 2006 by the Annenberg Institute for School Reform, of a small group of New York City high schools that, according to 2001 data, were "beating the odds" in preparing low-performing ninth-grade students for timely high school graduation and college going. The thirteen schools included two long-established technical-vocational schools, nine small high schools created between 1993 and 1998, and two high schools created in the reconstitution of large, failing high schools. The study was inspired by students in the Urban Youth Collaborative, a citywide high school organizing group that works to improve college-going rates in their schools and communities. Institute staff designed interviews with administrators, counselors, and other relevant staff to understand how the thirteen high schools identified in the earlier study were able to beat the odds, and to suggest ways that the success of these schools could be maintained and scaled up. Appended are: (1) BTO School Data; and (2) Rubric: Achieving College-Preparation Success for Low-Performing Students. (Contains 4 figures and 5 footnotes.) [For related reports, see "Beating the Odds: How Thirteen NYC Schools Bring Low-Performing Ninth-Graders to Timely Graduation and College Enrollment. Executive Summary" (ED522198) and "Putting Kids on the Pathway to College: How Is Your School Doing? The College Pathways Tools" (ED522170).]

This report is the result of a nine-month, national study of nontraditional funding and financing of facilities for charter and other public schools. The qualitative research in this report, based on fourteen study states and the District of Columbia, describes the growing range of private involvement in the acquisition, construction, and renovation of public school facilities and identifies new mechanisms through which both the public and private sectors are becoming involved in facilities financing. This report focuses largely on charter schools, which generally do not have access to the public capital funding streams available to traditional public schools. As a result, they rely heavily on nonprofit and for-profit institutions to obtain facilities funding and financing. In an era of limited public funds for facilities and increased pressure on public schools to produce high achievement, the lessons learned through the charter school experience with nontraditional financing may provide solutions and warnings for all public schools. Appended are: (1) School Facilities Funding--An Annotated Bibliography; (2) State Pressure Filter; (3) Funding and Financing Mechanism Typology; and (4) List of Interviewees. [Report published by the Educational Facilities Financing Center of the Local Initiatives Support Corporation.]

In this final report of a 3-year evaluation, researchers explored the developing infrastructure in New York City charter schools and identified areas in which school stakeholders--private partners, boards of trustees, school leaders, parents, and teachers--needed support to help charter schools succeed. The study was based on monthly visits to eight charter schools in metropolitan New York City. Of the eight schools, two have for-profit institutional partners and four have nonprofit institutional partners; two are not partnered. Six were start-up charter schools and two were traditional schools that converted to charter status. In the schools that had partners, these partners provided many of the supports offered by school districts to traditional public schools. The schools with nonprofit partners did not have formal agreements in the first year, but in the second year, two partners began to itemize services they provided within the school budget. The charter schools that were startup schools were entitled to waive collective bargaining agreements, but the charter schools had to create their own policies to clarify and normalize teachers working conditions. Operators of charter schools also had to make important financing and management decisions within the pressures of a 5-year performance-based charter. It was essential that school stakeholders have the knowledge and supports to make informed decisions on behalf of their schools. The range of capacity in these sample charter schools suggests that institutional partners, boards of trustees, and charter school leaders need technical assistance in developing the governance and administrative infrastructure associated with new school development and organizational change. (Contains 15 references.) (SLD)

New York State currently has three charter school authorizing agencies. Until now, their oversight has focused on performance based, contractual, and regulatory accountability. An emerging literature suggests that authorizers are reluctant to actualize the accountability/autonomy exchange by closing schools for failure to meet performance targets. This qualitative study, however, suggests that the promise of performance based accountability is primed to be actualized in New York. Since the oldest charter schools in New York are 3 years old, 2 years remain before performance based accountability faces the 5-year renewal test. All three authorizers insist that schools' performance goals are defined and measurable. Several New York charter schools have already been closed for performance and fiscal reasons. The fact that New York has a highly developed performance based accountability system suggests that authorizers will take performance based accountability seriously. New York's charter schools are subject to contractual accountability. While charters serve an important planning function for prospective school founders, helping authorizers to identify both strengths and weaknesses in developing schools, contractual accountability, if inflexibly interpreted by authorizers, may lead to fear of making needed school changes and a "compliance mentality" by charter school practitioners. The study asserts that authorizers should use periodic site visits and detailed review of required records to ensure regulatory accountability. (Contains 31 references.) (SM)

This report synthesizes the year 2 findings of a 3-year qualitative study of autonomy, accountability, finance, and supports in New York City charter schools. In 2000-2001, the study sample included 10 schools (8 charter and 2 alternative schools considering charter status). Section 1 reviews the literature on supports provided to traditional public schools, analyzes the school district's role, reviews the literature on intermediary organizations, and examines studies on the relationship between charter schools and the private nonprofit and for-profit organizations partnering with them. Section 2 describes the research methodology. Section 3 maps the sources of support being built and used by charter schools in New York City and notes implications of these new support arrangements. Overall, the 10 study schools used a range of voluntary overlapping supports that added to the material and human resources available from their public funding. Policy recommendations include increasing funding for charter schools to the level received by other public schools, encouraging charter schools to draw on traditional public schools' and districts' services and expertise, and helping charter school educators and representatives from the private sector to work out issues of governance and authority. (Contains 16 references.) (SM)

Issues related to educational equity and charter schools are discussed, and evidence is presented from a national study of equity in charter schools. Three standards of equity are discussed, and the equity provisions of state charter legislation are reviewed. To supplement existing studies of charter school demography, researchers at New York University's Institute for Education and Social Policy began to collect demographic data on charter schools. The database for this study included 801 charter schools. Data from these schools indicate that 70% of all charter schools are not distinct from their surrounding districts in the percentage of white students. In 31% of all charter schools, more than two-thirds of students are students of color, and only 47% of these schools are indistinct from their district averages. Overall, data suggest that charter schools may be proliferating at both the low and high ends of the race/ethnicity and affluence/poverty continuums. Data from this study cannot show that charter schools are exacerbating racial isolation or creating more isolation by social class, but some state-level case studies suggest that this is the case. Fieldwork suggests that some charter schools may well have developed educational programs that draw a range of students, and some may be providing high quality educational opportunities to low income students of color. However, state studies suggest that charter schools serving low-income children of color are less likely to provide an academic curriculum and are generally not as rich in resources as charter schools serving white, middle-class students. Some equity issues, particularly those associated with outcomes of education, remain unresolved for charter schools. (Contains 4 figures, 1 table, and 52 references.) (SLD)

The Institute for Education and Social Policy assessed the relationship between standards-based reform and the charter school movement in four states: Texas, Massachusetts, California, and Louisiana. These states were selected because they are the focus of other projects sponsored by the Edna McConnell Clark Foundation and because, as a group, they offer interesting variations in the status of standards-based reform. Site visits were made to nine schools, two in three states, and three in California. Researchers held interviews with 13 administrators, 24 teachers, and many students, and conducted 14 teacher and parent focus groups. Sites visits were supplemented by document collection and telephone interviews with state education officials and interviews with state charter resource staff. The charters of schools in this sample were at times superseded by state or district decisions that reshaped aspects of the charter school, eroding its accountability. Five of the nine schools served local students as well as choice students. Charter schools also experienced state and district standards through the interaction of specific teachers, specific students, and curriculum over the school year. Charter schools in this sample appeared to receive relatively little professional development for standards-based reform, but they generally were not out of the loop when it came to receiving state and district mandates. Experience with these schools suggests that charter school funding may be reproducing the resource disparities that exist in traditional public schools. (Contains 17 references.) (SLD)

This descriptive study examines the operation of youth mentoring programs in New York City. In particular, the study maps the experiences of developing and operating youth mentoring programs as articulated by the organizers or directors of 21 such programs; reviews and analyzes the research and descriptions of mentoring programs nationally to provide a framework for understanding the goals and operating conditions of the programs; and develops an inventory of the concerns of the program developers and directors, drawing implications from program practice, public policy, and research. The bulk of the study is based on extended, open-ended interviews with program directors and others in supervisory or managerial roles. The research shows that: (1) mentoring is usually regarded as a one-to-one relationship between an adult and a youth that continues over time; (2) a wide range of perceptions of the goals of the mentoring relationship exists; and (3) good mentors have motivation, personal commitment, realistic or high expectations, flexibility, respect for the individual's right to make choices, firmness, supportive tendencies, and good listening skills. Specific recommendations are provided for supporting and improving mentoring programs. The 21 programs in the study and 14 references are listed. (JB)