Nonprofit Capacity Assessment: Indiana Charities, 2007

Presents findings from a survey of Indiana nonprofit organizations about their needs for technical assistance and capacity building. Aims to provide grantmakers with reliable data to inform charitable efforts and strategies in these areas

Database Queries that Explain their Work

Provenance for database queries or scientific workflows is often motivated as providing explanation, increasing understanding of the underlying data sources and processes used to compute the query, and reproducibility, the capability to recompute the results on different inputs, possibly specialized to a part of the output. Many provenance systems claim to provide such capabilities; however, most lack formal definitions or guarantees of these properties, while others provide formal guarantees only for relatively limited classes of changes. Building on recent work on provenance traces and slicing for functional programming languages, we introduce a detailed tracing model of provenance for multiset-valued Nested Relational Calculus, define trace slicing algorithms that extract subtraces needed to explain or recompute specific parts of the output, and define query slicing and differencing techniques that support explanation. We state and prove correctness properties for these techniques and present a proof-of-concept implementation in Haskell.Comment: PPDP 201

A dependent nominal type theory

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple, dependent and ML-like polymorphic languages have been studied, but decidability and normalization results have only been established for simple nominal type theories. We present a LF-style dependent type theory extended with name-abstraction types, prove soundness and decidability of beta-eta-equivalence checking, discuss adequacy and canonical forms via an example, and discuss extensions such as dependently-typed recursion and induction principles

First-Order Provenance Games

We propose a new model of provenance, based on a game-theoretic approach to query evaluation. First, we study games G in their own right, and ask how to explain that a position x in G is won, lost, or drawn. The resulting notion of game provenance is closely related to winning strategies, and excludes from provenance all "bad moves", i.e., those which unnecessarily allow the opponent to improve the outcome of a play. In this way, the value of a position is determined by its game provenance. We then define provenance games by viewing the evaluation of a first-order query as a game between two players who argue whether a tuple is in the query answer. For RA+ queries, we show that game provenance is equivalent to the most general semiring of provenance polynomials N[X]. Variants of our game yield other known semirings. However, unlike semiring provenance, game provenance also provides a "built-in" way to handle negation and thus to answer why-not questions: In (provenance) games, the reason why x is not won, is the same as why x is lost or drawn (the latter is possible for games with draws). Since first-order provenance games are draw-free, they yield a new provenance model that combines how- and why-not provenance

Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices

Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely studied in the statistics, signal processing and machine learning communities. We exactly resolve the threshold at which noisy super-resolution is possible. In particular, we establish a sharp phase transition for the relationship between the cutoff frequency ($m$) and the separation ($\Delta$). If $m > 1/\Delta + 1$, our estimator converges to the true values at an inverse polynomial rate in terms of the magnitude of the noise. And when $m < (1-\epsilon) /\Delta$ no estimator can distinguish between a particular pair of $\Delta$-separated signals even if the magnitude of the noise is exponentially small. Our results involve making novel connections between {\em extremal functions} and the spectral properties of Vandermonde matrices. We establish a sharp phase transition for their condition number which in turn allows us to give the first noise tolerance bounds for the matrix pencil method. Moreover we show that our methods can be interpreted as giving preconditioners for Vandermonde matrices, and we use this observation to design faster algorithms for super-resolution. We believe that these ideas may have other applications in designing faster algorithms for other basic tasks in signal processing.Comment: 19 page

A New Method of Synthesizing Black Birnessite Nanoparticles: From Brown to Black Birnessite with Nanostructures

A new method for preparing black birnessite nanoparticles is introduced. The initial synthesis process resembles the classical McKenzie method of preparing brown birnessite except for slower cooling and closing the system from the ambient air. Subsequent process, including wet-aging at 7◦C for 48 hours, overnight freezing, and lyophilization, is shown to convert the brown birnessite into black birnessite with complex nanomorphology with folded sheets and spirals. Characterization of the product is performed by X-ray diffraction (XRD), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), thermogravimetric analysis (TGA), and N2 adsorption (BET) techniques. Wet-aging and lyophilization times are shown to affect the architecture of the product. XRD patterns show a single phase corresponding to a semicrystalline birnessite-based manganese oxide. TEM studies suggest its fibrous and petal-like structures. The HRTEM images at 5 and 10 nm length scales reveal the fibrils in folding sheets and also show filamentary breaks. The BET surface area of this nanomaterial was found to be 10.6m2/g. The TGA measurement demonstrated that it possessed an excellent thermal stability up to 400◦C. Layerstructured black birnessite nanomaterial containing sheets, spirals, and filamentary breaks can be produced at low temperature (−49◦C) from brown birnessite without the use of cross-linking reagents

Spectral structure and decompositions of optical states, and their applications

We discuss the spectral structure and decomposition of multi-photon states. Ordinarily `multi-photon states' and `Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of `multi-photon' states is much broader than the class of `Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states that in many situations simplifies calculations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong-Ou-Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schr\"odinger Kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples.Comment: 12 page

Improving the condition number of estimated covariance matrices

High dimensional error covariance matrices and their inverses are used to weight the contribution of observation and background information in data assimilation procedures. As observation error covariance matrices are often obtained by sampling methods, estimates are often degenerate or ill-conditioned, making it impossible to invert an observation error covariance matrix without the use of techniques to reduce its condition number. In this paper we present new theory for two existing methods that can be used to ‘recondition’ any covariance matrix: ridge regression, and the minimum eigenvalue method. We compare these methods with multiplicative variance inflation, which cannot alter the condition number of a matrix, but is often used to account for neglected correlation information. We investigate the impact of reconditioning on variances and correlations of a general covariance matrix in both a theoretical and practical setting. Improved theoretical understanding provides guidance to users regarding method selection, and choice of target condition number. The new theory shows that, for the same target condition number, both methods increase variances compared to the original matrix, with larger increases for ridge regression than the minimum eigenvalue method. We prove that the ridge regression method strictly decreases the absolute value of off-diagonal correlations. Theoretical comparison of the impact of reconditioning and multiplicative variance inflation on the data assimilation objective function shows that variance inflation alters information across all scales uniformly, whereas reconditioning has a larger effect on scales corresponding to smaller eigenvalues. We then consider two examples: a general correlation function, and an observation error covariance matrix arising from interchannel correlations. The minimum eigenvalue method results in smaller overall changes to the correlation matrix than ridge regression, but can increase off-diagonal correlations. Data assimilation experiments reveal that reconditioning corrects spurious noise in the analysis but underestimates the true signal compared to multiplicative variance inflation

Negative thermal expansion of MgB2_{2} in the superconducting state and anomalous behavior of the bulk Gr\"uneisen function

The thermal expansion coefficient $\alpha$ of MgB$_2$ is revealed to change from positive to negative on cooling through the superconducting transition temperature $T_c$. The Gr\"uneisen function also becomes negative at $T_c$ followed by a dramatic increase to large positive values at low temperature. The results suggest anomalous coupling between superconducting electrons and low-energy phonons.Comment: 5 figures. submitted to Phys. Rev. Let