Non-equispaced B-spline wavelets

This paper has three main contributions. The first is the construction of wavelet transforms from B-spline scaling functions defined on a grid of non-equispaced knots. The new construction extends the equispaced, biorthogonal, compactly supported Cohen-Daubechies-Feauveau wavelets. The new construction is based on the factorisation of wavelet transforms into lifting steps. The second and third contributions are new insights on how to use these and other wavelets in statistical applications. The second contribution is related to the bias of a wavelet representation. It is investigated how the fine scaling coefficients should be derived from the observations. In the context of equispaced data, it is common practice to simply take the observations as fine scale coefficients. It is argued in this paper that this is not acceptable for non-interpolating wavelets on non-equidistant data. Finally, the third contribution is the study of the variance in a non-orthogonal wavelet transform in a new framework, replacing the numerical condition as a measure for non-orthogonality. By controlling the variances of the reconstruction from the wavelet coefficients, the new framework allows us to design wavelet transforms on irregular point sets with a focus on their use for smoothing or other applications in statistics.Comment: 42 pages, 2 figure

Los señoríos de Ñuu Dzaui y la expansión tolteca

Los códices pictográficos de la región mixteca (Estado de Oaxaca, México) son ejemplos fascinantes de la historiografía mesoamericana precolonial. El protagonista más importante de estos manuscritos es el Señor 8 Venado 'Garra de Jaguar' (1063 1115 d.C.). Un elemento clave de su biografía dramatizada es su interacción con un rey de los toltecas, llamado Señor 4 Jaguar. Este artículo compara las escenas en que figuran estos personajes con la información que dan las crónicas nahuas y mayas sobre la historia tolteca. La capital tolteca mencionada por los códices mixtecos se identifica como Cholula. La descripción mixteca del Señor 4 Jaguar coincide completamente con lo que las otras fuentes relatan sobre el gobernante de Cholula, llamado Nacxitl Topiltzin Quetzalcoatl o Kukulcan, quien estableció contactos entre el reino tolteca y el mundo maya en la época postclásica temprana.The pictographic codices from the Mixtec region (State of Oaxaca, Mexico) are fascinating examples of precolonial Mesoamerican historiography. The most important protagonist of these manuscripts is Lord 8 Deer 'Jaguar Claw' (A.D. 1063 1115). A crucial element in his dramatized biography is his interaction with a king of the Toltecs, called Lord 4 Jaguar. This article compares the codex scenes in which these personages are present with the information given by Central-Mexican and Maya chronicles on Toltec history. The Toltec capital mentioned by the Mixtec codices is identified as Cholula. The Mixtec description of Lord 4 Jaguar coincides completely with what other sources tell about the ruler of Cholula, known as Nacxitl Topiltzin Quetzalcoatl or Kukulcan, who connected the Toltec realm with the Maya world in the Early Postclassic period

Lack-of-fit tests in semiparametric mixed models.

In this paper we obtain the asymptotic distribution of restricted likelihood ratio tests in mixed linear models with a fixed and finite number of random effects. We explain why for such models the often quoted 50:50 mixture of a chi-s quared random variable with one degree of freedom and a point mass at zero does not hold. Our motivation is a study of the use of wavelets for lack-of-fit testing within a mixed model framework. Even though wavelet shave received a lot of attention in the last say 15 years for the estimation of piecewise smooth functions, much less is known about their ability to check the adequacy of a parametric model when fitting the observed data. In particular we study the testing power of wavelets for testing a hypothesized parametric model within a mixed model framework. Experimental results show that in several situations the wavelet-based test significantly outperforms the com-petitor based on penalized regression splines. The obtained results are also applicable for testing in mixed models in general, and shed some new insight into previous results.Lack-off-fittest; Likelihood ratio test; Mixed models; One-sided test; Penalization; Restricted maximum likelihood; Variance components; Wavel; Asymptotic distribution; Distribution; Likelihood; Tests; Models; Model; Random effects; Effects; Studies; Lack-of-fit; Mixed model; Framework; Functions; Data; Power; Regression;

Chiral gauge theories with domain wall fermions

We have investigated a proposal to construct chiral gauge theories on the lattice using domain wall fermions. The model contains two opposite chirality zeromodes, which live on two domain walls. We couple only one of them to a gauge field, but find that mirror fermions which also couple to the gauge field always seem to exist.Comment: 3 pages. ref. added, some rewording at the end. contribution to Lattice'93. latex file, style file espcrc2.sty needed (appended), compressed tar file with two figures appended at the end (look for FIGURES

A Gauge-Fixing Action for Lattice Gauge Theories

We present a lattice gauge-fixing action $S_{gf}$ with the following properties: (a) $S_{gf}$ is proportional to the trace of $(\sum_\mu \partial_\mu A_\mu)^2$, plus irrelevant terms of dimension six and higher; (b) $S_{gf}$ has a unique absolute minimum at $U_{x,\mu}=I$. Noting that the gauge-fixed action is not BRST invariant on the lattice, we discuss some important aspects of the phase diagram.Comment: 13 pages, Latex, improved presentation, no change in result

Architecture Design Space Exploration for Streaming Applications Through Timing Analysis

In this paper we compare the maximum achievable throughput of different memory organisations of the processing elements that constitute a multiprocessor system on chip. This is done by modelling the mapping of a task with input and output channels on a processing element as a homogeneous synchronous dataflow graph, and use maximum cycle mean analysis to derive the throughput. In a HiperLAN2 case study we show how these techniques can be used to derive the required clock frequency and communication latencies in order to meet the application's throughput requirement on a multiprocessor system on chip that has one of the investigated memory organisations