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

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

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

Quantum process tomography of molecular dimers from two-dimensional electronic spectroscopy I: General theory and application to homodimers

Is it possible to infer the time evolving quantum state of a multichromophoric system from a sequence of two-dimensional electronic spectra (2D-ES) as a function of waiting time? Here we provide a positive answer for a tractable model system: a coupled dimer. After exhaustively enumerating the Liouville pathways associated to each peak in the 2D-ES, we argue that by judiciously combining the information from a series of experiments varying the polarization and frequency components of the pulses, detailed information at the amplitude level about the input and output quantum states at the waiting time can be obtained. This possibility yields a quantum process tomography (QPT) of the single-exciton manifold, which completely characterizes the open quantum system dynamics through the reconstruction of the process matrix. This is the first of a series of two articles. In this manuscript, we specialize our results to the case of a homodimer, where we prove that signals stemming from coherence to population transfer and viceversa vanish upon isotropic averaging, and therefore, only a partial QPT is possible in this case. However, this fact simplifies the spectra, and it follows that only two polarization controlled experiments (and no pulse-shaping requirements) suffice to yield the elements of the process matrix which survive under isotropic averaging. The angle between the two site transition dipole moments is self-consistently obtained from the 2D-ES. Model calculations are presented, as well as an error analysis in terms of the angle between the dipoles and peak overlap. In the second article accompanying this study, we numerically exemplify the theory for heterodimers and carry out a detailed error analysis for such case. This investigation provides an important benchmark for more complex proposals of quantum process tomography (QPT) via multidimensional spectroscopic experiments

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 1970

A Closer Look at Watering by Holman M. Griffin (page 3) Sulphur in Turfgrass Fertilization by J.D. Beaton (5) Those Extras on a Golf Course by Jack Fairhurst (9) Turf Bulletin\u27s Photo Quiz by Fred Cheney (9) Progress in Research on Live Oak Decline by E.P. Van Arsdel and Robert S. Halliwell (10) Editorial (15) The Perfermance Characteristics of Kentucky Bluegrass Mixtures by F.V. Juska and A.A. Hanson (16) Moss (23

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

Forward electromagnetic scattering models for sea ice

Journal ArticleRecent advances in forward modeling of the electromagnetic scattering properties of sea ice are presented. In particular, the principal results include the following: 1) approximate calculations of electromagnetic scattering from multilayer random media with rough interfaces, based on the distorted Born approximation and radiative transfer (RT) theory; 2) comprehensive theory of the effective complex permittivity of sea ice based on rigorous bounds in the quasi-static case and strong fluctuation theory in the weakly scattering regime; 3) rigorous analysis of the Helmholtz equation and its solutions for idealized sea ice models, which has led in the one dimensional (1-D) case to nonlinear generalizations of classical theorems in Fourier analysis

Orbital Symmetry of Ba(Fe1-xCox)2As2 Superconductors Probed with X-ray Absorption Spectroscopy

The orbital symmetries of electron doped iron-arsenide superconductors Ba(Fe1-xCox)2As2 have been measured with x-ray absorption spectroscopy. The data reveal signatures of Fe d electron itinerancy, weak electronic correlations, and a high degree of Fe-As hybridization related to the bonding topology of the Fe dxz+yz states, which are found to contribute substantially at the Fermi level. The energies and detailed orbital character of Fe and As derived unoccupied s and d states are found to be in remarkably good agreement with the predictions of standard density functional theory.Comment: Accepted for publication in Phys. Rev. B, 3 figures. Minor corrections adde