Least Generalizations and Greatest Specializations of Sets of Clauses

The main operations in Inductive Logic Programming (ILP) are generalization and specialization, which only make sense in a generality order. In ILP, the three most important generality orders are subsumption, implication and implication relative to background knowledge. The two languages used most often are languages of clauses and languages of only Horn clauses. This gives a total of six different ordered languages. In this paper, we give a systematic treatment of the existence or non-existence of least generalizations and greatest specializations of finite sets of clauses in each of these six ordered sets. We survey results already obtained by others and also contribute some answers of our own. Our main new results are, firstly, the existence of a computable least generalization under implication of every finite set of clauses containing at least one non-tautologous function-free clause (among other, not necessarily function-free clauses). Secondly, we show that such a least generalization need not exist under relative implication, not even if both the set that is to be generalized and the background knowledge are function-free. Thirdly, we give a complete discussion of existence and non-existence of greatest specializations in each of the six ordered languages.Comment: See http://www.jair.org/ for any accompanying file

Haar expectations of ratios of random characteristic polynomials

We compute Haar ensemble averages of ratios of random characteristic polynomials for the classical Lie groups K = O(N), SO(N), and USp(N). To that end, we start from the Clifford-Weyl algebera in its canonical realization on the complex of holomorphic differential forms for a C-vector space V. From it we construct the Fock representation of an orthosymplectic Lie superalgebra osp associated to V. Particular attention is paid to defining Howe's oscillator semigroup and the representation that partially exponentiates the Lie algebra representation of sp in osp. In the process, by pushing the semigroup representation to its boundary and arguing by continuity, we provide a construction of the Shale-Weil-Segal representation of the metaplectic group. To deal with a product of n ratios of characteristic polynomials, we let V = C^n \otimes C^N where C^N is equipped with its standard K-representation, and focus on the subspace of K-equivariant forms. By Howe duality, this is a highest-weight irreducible representation of the centralizer g of Lie(K) in osp. We identify the K-Haar expectation of n ratios with the character of this g-representation, which we show to be uniquely determined by analyticity, Weyl group invariance, certain weight constraints and a system of differential equations coming from the Laplace-Casimir invariants of g. We find an explicit solution to the problem posed by all these conditions. In this way we prove that the said Haar expectations are expressed by a Weyl-type character formula for all integers N \ge 1. This completes earlier work by Conrey, Farmer, and Zirnbauer for the case of U(N).Comment: LaTeX, 70 pages, Complex Analysis and its Synergies (2016) 2:

Perfluoro (Imidoylamidine) diamidines

Perfluoroether triazine elastomers having improved properties are prepared from oligomeric imidoylamidines that were in turn, prepared by the process of: (1) reacting a perfluorodinitrile with liquid ammonia to yield a perfluorodiamidine, (2) isolating the perfluorodiamidine, (3) reacting the isolated diamidine with a perfluorodinitrile to yield a perfluoro(imidoylamidine) dinitrile, and then repeating the steps to sequentially grow an oligomer of desired molecular size. The isolated amidine and nitrile intermediates are also disclosed. The elastomers can be fashioned into seals, gaskets, and sealing components and the like

A design study for an optimal non-linear receiver/demodulator Final report

Design study for optimal nonlinear receiver demodulato

Process for preparing perfluorotriazine elastomers and precursors thereof

Perfluoroether triazine elastomers having improved properties and utility in seals, gaskets, sealing components and the like are prepared from oligomeric imidoylamidines that have, in turn, been prepared by the process of (1) reacting a perfluorodinitrile with liquid ammonia to yield a perfluorodiamidine, (2) isolating the perfluorodiamidine, (3) reacting the isolated diamidine with a perfluorodinitrile to yield a perfluoror(imidoylamidine) dinitrile, and then repeating step (1), (2), and (3) to sequentially grow an oligomer of desired molecular size. The isolated amidine and nitrile intermediates are also described

Field Scanner Design for MUSTANG of the Green Bank Telescope

MUSTANG is a bolometer camera for the Green Bank Telescope (GBT) working at a frequency of 90 GHz. The detector has a field of view of 40 arcseconds. To cancel out random emission change from atmosphere and other sources, requires a fast scanning reflecting system with a few arcminute ranges. In this paper, the aberrations of an off-axis system are reviewed. The condition for an optimized system is provided. In an optimized system, as additional image transfer mirrors are introduced, new aberrations of the off-axis system may be reintroduced, resulting in a limited field of view. In this paper, different scanning mirror arrangements for the GBT system are analyzed through the ray tracing analysis. These include using the subreflector as the scanning mirror, chopping a flat mirror and transferring image with an ellipse mirror, and chopping a flat mirror and transferring image with a pair of face-to-face paraboloid mirrors. The system analysis shows that chopping a flat mirror and using a well aligned pair of paraboloids can generate the required field of view for the MUSTUNG detector system, while other systems all suffer from larger off-axis aberrations added by the system modification. The spot diagrams of the well aligned pair of paraboloids produced is only about one Airy disk size within a scanning angle of about 3 arcmin.Comment: 7 pages, 9 figure

Soft computing for intelligent data analysis

Intelligent data analysis (IDA) is an interdisciplinary study concerned with the effective analysis of data. The paper briefly looks at some of the key issues in intelligent data analysis, discusses the opportunities for soft computing in this context, and presents several IDA case studies in which soft computing has played key roles. These studies are all concerned with complex real-world problem solving, including consistency checking between mass spectral data with proposed chemical structures, screening for glaucoma and other eye diseases, forecasting of visual field deterioration, and diagnosis in an oil refinery involving multivariate time series. Bayesian networks, evolutionary computation, neural networks, and machine learning in general are some of those soft computing techniques effectively used in these studies

Presymmetry beyond the Standard Model

We go beyond the Standard Model guided by presymmetry, the discrete electroweak quark-lepton symmetry hidden by topological effects which explain quark fractional charges as in condense matter physics. Partners of the particles of the Standard Model and the discrete symmetry associated with this partnership appear as manifestations of a residual presymmetry and its extension from matter to forces. This duplication of the spectrum of the Standard Model keeps spin and comes nondegenerated about the TeV scale.Comment: 6 pages, 11 figures. To be published in the proceedings of DPF-2009, Detroit, MI, July 2009, eConf C09072