959 research outputs found

### ITERA: IDL Tool for Emission-line Ratio Analysis

We present a new software tool to enable astronomers to easily compare
observations of emission line ratios with those determined by photoionization
and shock models, ITERA, the IDL Tool for Emission-line Ratio Analysis. This
tool can plot ratios of emission lines predicted by models and allows for
comparison of observed line ratios against grids of these models selected from
model libraries associated with the tool. We provide details of the libraries
of standard photoionization and shock models available with ITERA, and, in
addition, present three example emission line ratio diagrams covering a range
of wavelengths to demonstrate the capabilities of ITERA. ITERA, and associated
libraries, is available from \url{http://www.brentgroves.net/itera.html}Comment: Accepted for New Astronomy, 3 figures. ITERA tool available to
download from http://www.brentgroves.net/itera.htm

### Geometric Algebras and Extensors

This is the first paper in a series (of four) designed to show how to use
geometric algebras of multivectors and extensors to a novel presentation of
some topics of differential geometry which are important for a deeper
understanding of geometrical theories of the gravitational field. In this first
paper we introduce the key algebraic tools for the development of our program,
namely the euclidean geometrical algebra of multivectors Cl(V,G_{E}) and the
theory of its deformations leading to metric geometric algebras Cl(V,G) and
some special types of extensors. Those tools permit obtaining, the remarkable
golden formula relating calculations in Cl(V,G) with easier ones in Cl(V,G_{E})
(e.g., a noticeable relation between the Hodge star operators associated to G
and G_{E}). Several useful examples are worked in details fo the purpose of
transmitting the "tricks of the trade".Comment: This paper (to appear in Int. J. Geom. Meth. Mod. Phys. 4 (6) 2007)
is an improved version of material appearing in math.DG/0501556,
math.DG/0501557, math.DG/050155

### Trombe walls with nanoporous aerogel insulation applied to UK housing refurbishments

There is an opportunity to improve the efficiency of passive Trombe walls and active solar air collectors by replacing their conventional glass covers with lightweight polycarbonate panels filled with nanoporous aerogel insulation. This study investigates the thermal performance, energy savings, and financial payback period of passive Aerogel Trombe walls applied to the existing UK housing stock. Using parametric modeling, a series of design guidance tables have been generated, providing estimates of the energy savings and overheating risk associated with applying areas of Trombe wall to four different house types across the UK built to six notional construction standards. Calculated energy savings range from 183 kWh/m2/year for an 8 m2 system retrofitted to a solid walled detached house to 62 kWh/m2/year for a 32 m2 system retrofitted to a super insulated flat. Predicted energy savings from Trombe walls up to 24 m2 are found to exceed the energy savings from external insulation across all house types and constructions. Small areas of Trombe wall can provide a useful energy contribution without creating a significant overheating risk. If larger areas are to be installed, then detailed calculations would be recommended to assess and mitigate potential overheating issues.The EPSRC, Brunel University, and Buro Happold Lt

### Revisiting Clifford algebras and spinors III: conformal structures and twistors in the paravector model of spacetime

This paper is the third of a series of three, and it is the continuation of
math-ph/0412074 and math-ph/0412075. After reviewing the conformal spacetime
structure, conformal maps are described in Minkowski spacetime as the twisted
adjoint representation of the group Spin_+(2,4), acting on paravectors.
Twistors are then presented via the paravector model of Clifford algebras and
related to conformal maps in the Clifford algebra over the lorentzian R{4,1}$
spacetime. We construct twistors in Minkowski spacetime as algebraic spinors
associated with the Dirac-Clifford algebra Cl(1,3)(C) using one lower spacetime
dimension than standard Clifford algebra formulations, since for this purpose
the Clifford algebra over R{4,1} is also used to describe conformal maps,
instead of R{2,4}. Although some papers have already described twistors using
the algebra Cl(1,3)(C), isomorphic to Cl(4,1), the present formulation sheds
some new light on the use of the paravector model and generalizations.Comment: 17 page

### Hermitian versus holomorphic complex and quaternionic generalized supersymmetries of the M-theory. A classification

Relying upon the division-algebra classification of Clifford algebras and
spinors, a classification of generalized supersymmetries (or, with a slight
abuse of language,"generalized supertranslations") is provided. In each given
space-time the maximal, saturated, generalized supersymmetry, compatible with
the division-algebra constraint that can be consistently imposed on spinors and
on superalgebra generators, is furnished. Constraining the superalgebra
generators in both the complex and the quaternionic cases gives rise to the two
classes of constrained hermitian and holomorphic generalized supersymmetries.
In the complex case these two classes of generalized supersymmetries can be
regarded as complementary. The quaternionic holomorphic supersymmetry only
exists in certain space-time dimensions and can admit at most a single bosonic
scalar central charge.
The results here presented pave the way for a better understanding of the
various $M$ algebra-type of structures which can be introduced in different
space-time signatures and in association with different division algebras, as
well as their mutual relations. In a previous work, e.g., the introduction of a
complex holomorphic generalized supersymmetry was shown to be necessary in
order to perform the analytic continuation of the standard $M$-theory to the
11-dimensional Euclidean space. As an application of the present results, it is
shown that the above algebra also admits a 12-dimensional, Euclidean,
$F$-algebra presentation.Comment: 25 pages, LaTe

### Topological transversals to a family of convex sets

Let $\mathcal F$ be a family of compact convex sets in $\mathbb R^d$. We say
that $\mathcal F$ has a \emph{topological $\rho$-transversal of index $(m,k)$}
($\rho<m$, $0<k\leq d-m$) if there are, homologically, as many transversal
$m$-planes to $\mathcal F$ as $m$-planes containing a fixed $\rho$-plane in
$\mathbb R^{m+k}$.
Clearly, if $\mathcal F$ has a $\rho$-transversal plane, then $\mathcal F$
has a topological $\rho$-transversal of index $(m,k),$ for $\rho<m$ and $k\leq
d-m$. The converse is not true in general.
We prove that for a family $\mathcal F$ of $\rho+k+1$ compact convex sets in
$\mathbb R^d$ a topological $\rho$-transversal of index $(m,k)$ implies an
ordinary $\rho$-transversal. We use this result, together with the
multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann
category of the Grassmannian, and different versions of the colorful Helly
theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences

### Seismic sparse-spike deconvolution via Toeplitz-sparse matrix factorization

We have developed a new sparse-spike deconvolution (SSD) method based on Toeplitz-sparse matrix factorization (TSMF), a bilinear decomposition of a matrix into the product of a Toeplitz matrix and a sparse matrix, to address the problems of lateral continuity, effects of noise, and wavelet estimation error in SSD. Assuming the convolution model, a constant source wavelet, and the sparse reflectivity, a seismic profile can be considered as a matrix that is the product of a Toeplitz wavelet matrix and a sparse reflectivity matrix. Thus, we have developed an algorithm of TSMF to simultaneously deconvolve the seismic matrix into a wavelet matrix and a reflectivity matrix by alternatively solving two inversion subproblems related to the Toeplitz wavelet matrix and sparse reflectivity matrix, respectively. Because the seismic wavelet is usually compact and smooth, the fused Lasso was used to constrain the elements in the Toeplitz wavelet matrix. Moreover, due to the limitations of computer memory, large seismic data sets were divided into blocks, and the average of the source wavelets deconvolved from these blocks via TSMF-based SSD was used as the final estimation of the source wavelet for all blocks to deconvolve the reflectivity; thus, the lateral continuity of the seismic data can be maintained. The advantages of the proposed deconvolution method include using multiple traces to reduce the effect of random noise, tolerance to errors in the initial wavelet estimation, and the ability to preserve the complex structure of the seismic data without using any lateral constraints. Our tests on the synthetic seismic data from the Marmousi2 model and a section of field seismic data demonstrate that the proposed method can effectively derive the wavelet and reflectivity simultaneously from band-limited data with appropriate lateral coherence, even when the seismic data are contaminated by noise and the initial wavelet estimation is inaccurate

### Radial and angular derivatives of distributions

When expressing a distribution in Euclidean space in spherical coordinates, derivation with respect to the radial and angular co-ordinates is far from trivial. Exploring the possibilities of defining a radial derivative of the delta distribution 8{x) (the angular derivatives of S(x) being zero since the delta distribution is itself radial) led to the introduction of a new kind of distributions, the so-called signumdistributions, as continuous linear functionals on a space of test functions showing a singularity at the origin. In this paper we search for a definition of the radial and angular derivatives of a general standard distribution and again, as expected, we are inevitably led to consider signumdistributions. Although these signumdistributions provide an adequate framework for the actions on distributions aimed at, it turns out that the derivation with respect to the radial distance of a general (signum)distribution is still not yet unambiguous

### Large-Scale Distributed Bayesian Matrix Factorization using Stochastic Gradient MCMC

Despite having various attractive qualities such as high prediction accuracy
and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix
Factorization has not been widely adopted because of the prohibitive cost of
inference. In this paper, we propose a scalable distributed Bayesian matrix
factorization algorithm using stochastic gradient MCMC. Our algorithm, based on
Distributed Stochastic Gradient Langevin Dynamics, can not only match the
prediction accuracy of standard MCMC methods like Gibbs sampling, but at the
same time is as fast and simple as stochastic gradient descent. In our
experiments, we show that our algorithm can achieve the same level of
prediction accuracy as Gibbs sampling an order of magnitude faster. We also
show that our method reduces the prediction error as fast as distributed
stochastic gradient descent, achieving a 4.1% improvement in RMSE for the
Netflix dataset and an 1.8% for the Yahoo music dataset

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