Nominal Logic Programming

Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates logic programming based on nominal logic. We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as of July 23, 200

Local perspectives on weirs in the Upper Nepean

The Independent Expert Panel of the HawkesburyâNepean River Management Forum commissioned the Institute for Sustainable Futures to conduct research into the values held by river users and community members in relation to the weirs on the Upper Nepean River and concerns they would have with any change to the current situation. The weirs at the centre of this research are Bergins, Thurns, Sharpes and Brownlow Hill. The research questions guiding the project are: What is the nature of the social and economic relationship between people and weirs at a local level In what ways would people want to participate in decisions about the weirs and river management Local people were asked about how they use the weirs, what value they see the weirs having for their community, culture and industry and what concerns there may be about potential changes. The research aims to help the Expert Panel and the Forum make appropriate decisions about potential retention, modification or removal of the weirs and the fishways associated with them. A further aim is to facilitate public participation in the decision-making process. Within any community, there are different individuals and groups with diverse interests and experiences. These differences might result in multiple perspectives between and within groups. To differentiate some of these perspectives, the broader community was divided into four sectors: general public, community groups, identifiable water users such as irrigators and recreational users and Indigenous groups. The general public participants emphasised the aesthetic and leisure value of the river. They appear to identify very strongly with the river, with participants interpreting the existence of the weirs as integral to both the riverâs survival and the ongoing economic survival of the region. The findings indicate that this group view the weirs as an integral part of the river and the river as an integral part of the Camden community

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

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

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

Signatures of Intergalactic Dust From the First Supernovae

We quantify the consequences of intergalactic dust produced by the first Type II supernovae in the universe. The fraction of gas converted into stars is calibrated based on the observed C/H ratio in the intergalactic medium at z=3, assuming a Scalo mass function for the stars. The associated dust absorbs starlight energy and emits it at longer wavelengths. For a uniform mix of metals and dust with the intergalactic gas, we find that the dust distorts the microwave background spectrum by a y-parameter in the range (0.02-2)x10^{-5}(M_d/0.3M_sun), where M_d is the average mass of dust produced per supernova. The opacity of intergalactic dust to infrared sources at redshifts z>10 is significant, tau=(0.1-1)x(M_d/0.3M_sun), and could be detected with the Next Generation Space Telescope. Although dust suppresses the Ly-alpha emission from early sources, the redshifts of star clusters at z=10-35 can be easily inferred from the Lyman-limit break in their infrared spectrum between 1-3.5 micron.Comment: 12 pages, latex, 2 figures, submitted to ApJ

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

Exosome-mediated shuttling of microRNA-29 regulates HIV Tat and morphine-mediated neuronal dysfunction.

Neuronal damage is a hallmark feature of HIV-associated neurological disorders (HANDs). Opiate drug abuse accelerates the incidence and progression of HAND; however, the mechanisms underlying the potentiation of neuropathogenesis by these drugs remain elusive. Opiates such as morphine have been shown to enhance HIV transactivation protein Tat-mediated toxicity in both human neurons and neuroblastoma cells. In the present study, we demonstrate reduced expression of the tropic factor platelet-derived growth factor (PDGF)-B with a concomitant increase in miR-29b in the basal ganglia region of the brains of morphine-dependent simian immunodeficiency virus (SIV)-infected macaques compared with the SIV-infected controls. In vitro relevance of these findings was corroborated in cultures of astrocytes exposed to morphine and HIV Tat that led to increased release of miR-29b in exosomes. Subsequent treatment of neuronal SH-SY5Y cell line with exosomes from treated astrocytes resulted in decreased expression of PDGF-B, with a concomitant decrease in viability of neurons. Furthermore, it was shown that PDGF-B was a target for miR-29b as evidenced by the fact that binding of miR-29 to the 3\u27-untranslated region of PDGF-B mRNA resulted in its translational repression in SH-SY5Y cells. Understanding the regulation of PDGF-B expression may provide insights into the development of potential therapeutic targets for neuronal loss in HIV-1-infected opiate abusers

Winter 1972

The Mode of Action of Arsenicals in the Soil by Cecil F. Kerr (page 3) The Golf Course Superintendent: A Job Description (5) Factors Affecting Carbohydrate Reserves of Cool Season Turfgrasses by L.J. Zanoni, L. F. Michelson, W.G. COlby, and M. Drake (6) Turf Bulletin\u27s Photo Quiz by Frederick G. Cheney (9) A Close Look at TCDD (10) Environmental News--Environmental Protection Agency Cancels Registration of Herbicide Amitrole (11) Homeowner\u27s Section--Crabgrass in Perspective by R.A. Peters (12) Merion Tees--Maintenance Suggestions (14) Use of Ammonium Sulfate in Fluid Fertilizers by Frank P. Achorn and W.C. Scott, Jr. (15) River Ecology and the Impact on Man (17) To Roll or Not to Roll (18) Editorial--Talkin\u27 Turfie (24

Mathematical practice, crowdsourcing, and social machines

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. Mathematical practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system {\it mathoverflow} contains around 40,000 mathematical conversations, and {\it polymath} collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent Computer Mathematics, CICM 2013, July 2013 Bath, U