On the rotational symmetry of 3-dimensional κ\kappa-solutions

In a recent paper, Brendle showed the uniqueness of the Bryant soliton among 3-dimensional $\kappa$-solutions. In this paper, we present an alternative proof for this fact and show that compact $\kappa$-solutions are rotational symmetric. Our proof arose from independent work relating to our Strong Stability Theorem for singular Ricci flows.Comment: 20 page

Ricci flow and diffeomorphism groups of 3-manifolds

We complete the proof of the Generalized Smale Conjecture, apart from the case of $RP^3$, and give a new proof of Gabai's theorem for hyperbolic 3-manifolds. We use an approach based on Ricci flow through singularities, which applies uniformly to spherical space forms other than $S^3$ and $RP^3$ and hyperbolic manifolds, to prove that the moduli space of metrics of constant sectional curvature is contractible. As a corollary, for such a 3-manifold $X$, the inclusion $\text{Isom} (X,g)\to \text{Diff}(X)$ is a homotopy equivalence for any Riemannian metric $g$ of constant sectional curvature.Comment: 29 pages, 1 figur

Using Digital Tools to Foster Critical Inquiry

How do adolescents use digital media as tools in ways that go beyond simply extracting information or playing games to engaging in the literacy practices involved in critical inquiry activities?published or submitted for publicationis peer reviewe

Uniqueness and stability of Ricci flow through singularities

We verify a conjecture of Perelman, which states that there exists a canonical Ricci flow through singularities starting from an arbitrary compact Riemannian 3-manifold. Our main result is a uniqueness theorem for such flows, which, together with an earlier existence theorem of Lott and the second named author, implies Perelman's conjecture. We also show that this flow through singularities depends continuously on its initial condition and that it may be obtained as a limit of Ricci flows with surgery. Our results have applications to the study of diffeomorphism groups of three manifolds --- in particular to the Generalized Smale Conjecture --- which will appear in a subsequent paper.Comment: 182 pages, 10 figures, minor correction

Adding Up the Spending: Fiscal Disparities and Philanthropy among New York City Charter Schools

This brief explores the financial resources of New York City charter schools. It also addresses differences in student population characteristics and student outcomes across New York City (NYC) charter schools, and evaluates how financial resources translate to other schooling inputs, such as more or less experienced teachers and smaller or larger class sizes.These schools are examined within the broader context of school funding equity and factors that other research has shown to have the potential to advance or disrupt educational equity. In American public education, funding equity involves multiple levels, linked to the multiple levels of our school systems. State systems govern local public school districts, with schools nested within districts. Public charter schools are either nested within districts or operate as independent entities.NYC charter schools are of particular interest to national audiences mainly because they have been used to argue that charter schools outperform public schools and that New York's experience with charter schools suggests a transferable, nationally scalable policy option. Three studies concerning NYC charter schools in particular are frequently cited: Dobbie & Fryer, 2009; Hoxby, Murarka and Kang, 2009; and CREDO, 2009.It is important to note, however, that the NYC context may be unique in terms of the role played by philanthropy and so-called venture philanthropy. Significant philanthropic attention has been focused on charter management organizations like the Knowledge is Power Program (KIPP) and Achievement First, which manage charter schools in NYC and elsewhere. NYC charter schools are both touted and blasted in the popular media as being the new favored charities of, for example, wealthy hedge fund managers. The extent that NYC charters have become philanthropic favorites means that NYC charter schools may be quite different from those in places like Missouri or Arizona, distant from the NYC philanthropic culture. In fact, even charter schools in Albany and Buffalo or across the river in New Jersey may be insulated from this unique financial setting. Therefore, additional philanthropic resources may explain a great deal of the claimed success of NYC charter schools. If this is the case, attempts to replicate or scale up these supposed successes would be more difficult and costly than assumed.This brief offers concrete information about NYC charters and their finances to help ground these important policy discussions.This brief is published by the National Education Policy Center (NEPC), and is one of a series of briefs made possible in part by funding from The Great Lakes Center for Education Research and Practice

Superconducting linear actuator

Special actuators are needed to control the orientation of large structures in space-based precision pointing systems. Electromagnetic actuators that presently exist are too large in size and their bandwidth is too low. Hydraulic fluid actuation also presents problems for many space-based applications. Hydraulic oil can escape in space and contaminate the environment around the spacecraft. A research study was performed that selected an electrically-powered linear actuator that can be used to control the orientation of a large pointed structure. This research surveyed available products, analyzed the capabilities of conventional linear actuators, and designed a first-cut candidate superconducting linear actuator. The study first examined theoretical capabilities of electrical actuators and determined their problems with respect to the application and then determined if any presently available actuators or any modifications to available actuator designs would meet the required performance. The best actuator was then selected based on available design, modified design, or new design for this application. The last task was to proceed with a conceptual design. No commercially-available linear actuator or modification capable of meeting the specifications was found. A conventional moving-coil dc linear actuator would meet the specification, but the back-iron for this actuator would weigh approximately 12,000 lbs. A superconducting field coil, however, eliminates the need for back iron, resulting in an actuator weight of approximately 1000 lbs

A Mean-field statistical theory for the nonlinear Schrodinger equation

A statistical model of self-organization in a generic class of one-dimensional nonlinear Schrodinger (NLS) equations on a bounded interval is developed. The main prediction of this model is that the statistically preferred state for such equations consists of a deterministic coherent structure coupled with fine-scale, random fluctuations, or radiation. The model is derived from equilibrium statistical mechanics by using a mean-field approximation of the conserved Hamiltonian and particle number for finite-dimensional spectral truncations of the NLS dynamics. The continuum limits of these approximated statistical equilibrium ensembles on finite-dimensional phase spaces are analyzed, holding the energy and particle number at fixed, finite values. The analysis shows that the coherent structure minimizes total energy for a given value of particle number and hence is a solution to the NLS ground state equation, and that the remaining energy resides in Gaussian fluctuations equipartitioned over wavenumbers. Some results of direct numerical integration of the NLS equation are included to validate empirically these properties of the most probable states for the statistical model. Moreover, a theoretical justification of the mean-field approximation is given, in which the approximate ensembles are shown to concentrate on the associated microcanonical ensemble in the continuum limit.Comment: 24 pages, 2 figure

EXODUS: Integrating intelligent systems for launch operations support

Kennedy Space Center (KSC) is developing knowledge-based systems to automate critical operations functions for the space shuttle fleet. Intelligent systems will monitor vehicle and ground support subsystems for anomalies, assist in isolating and managing faults, and plan and schedule shuttle operations activities. These applications are being developed independently of one another, using different representation schemes, reasoning and control models, and hardware platforms. KSC has recently initiated the EXODUS project to integrate these stand alone applications into a unified, coordinated intelligent operations support system. EXODUS will be constructed using SOCIAL, a tool for developing distributed intelligent systems. EXODUS, SOCIAL, and initial prototyping efforts using SOCIAL to integrate and coordinate selected EXODUS applications are described

A development framework for artificial intelligence based distributed operations support systems

Advanced automation is required to reduce costly human operations support requirements for complex space-based and ground control systems. Existing knowledge based technologies have been used successfully to automate individual operations tasks. Considerably less progress has been made in integrating and coordinating multiple operations applications for unified intelligent support systems. To fill this gap, SOCIAL, a tool set for developing Distributed Artificial Intelligence (DAI) systems is being constructed. SOCIAL consists of three primary language based components defining: models of interprocess communication across heterogeneous platforms; models for interprocess coordination, concurrency control, and fault management; and for accessing heterogeneous information resources. DAI applications subsystems, either new or existing, will access these distributed services non-intrusively, via high-level message-based protocols. SOCIAL will reduce the complexity of distributed communications, control, and integration, enabling developers to concentrate on the design and functionality of the target DAI system itself