Wavelet-Based Estimation for Univariate Stable Laws

Stable distributions are characterized by four parameters which can be estimated via a number of methods, and although approximate maximum likelihood estimation techniques have been proposed, they are computationally intensive and difficult to implement. This article describes a fast, wavelet-based, regression-type method for estimating the parameters of a stable distribution. Fourier domain representations, combined with a wavelet multiresolution approach, are shown to be effective and highly efficient tools for inference in stable law families. Our procedures are illustrated and compared with other estimation methods using simulated data, and an application to a real data example is explored. One novel aspect of this work is that here wavelets are being used to solve a parametric problem, rather than a nonparametric one, which is the more typical context in wavelet applications.     

Correlating natural ageing and Xenon irradiation of Paraloid B72 applied on stone

The ageing of Paraloid^® B72, an acrylic copolymer extensively used in conservation of works of art, has been investigated either under artificial irradiation (Xenon lamp) or in natural environment (external exposure) with the aim to correlate the results of the accelerate test with the real situation. For a better understanding of the involved mechanisms some acrylic homo-polymers were also subjected to the artificial ageing test. Molecular changes induced by ageing were followed by infrared spectroscopy (FT-IR) and size exclusion chromatography (SEC), while the efficiency of the treatment was checked by water capillary absorption test and colour determinations. The results obtained indicate that it is possible to discriminate, easily and within reasonable laboratory time experiment, between polymers that can be used in Conservation, and the macromolecules that should not be employed due to short efficacy life-times.     

The Forbes 400, the Pareto power-law and efficient markets

Statistical regularities at the top end of the wealth distribution in the United States are examined using the Forbes 400 lists of richest Americans, published between 1988 and 2003. It is found that the wealths are distributed according to a power-law (Pareto) distribution. This result is explained using a simple stochastic model of multiple investors that incorporates the efficient market hypothesis as well as the multiplicative nature of financial market fluctuations.     

Geometry of quasilinear hyperbolic systems with characteristic fields of constant multiplicity

In this paper, we study the regularity of the eigenvalues and eigenvectors and the existence of normalized coordinates for quasilinear hyperbolic systems with characteristic fields of constant multiplicity. We prove that the eigenvalues and eigenvectors of the system have the same regularity as the coefficients of the system. On the other hand, we show that, for the quasilinear hyperbolic system of conservation laws with characteristic fields of constant multiplicity, the normalized coordinates exist on the domain under consideration.     

Space-Time Point-Process Models for Earthquake Occurrences

Several space-time statistical models are constructed based on both classical empirical studies of clustering and some more speculative hypotheses. Then we discuss the discrimination between models incorporating contrasting assumptions concerning the form of the space-time clusters. We also examine further practical extensions of the model to situations where the background seismicity is spatially non-homogeneous, and the clusters are non-isotropic. The goodness-of-fit of the models, as measured by AIC values, is discussed for two high quality data sets, in different tectonic regions. AIC also allows the details of the clustering structure in space to be clarified. A simulation algorithm for the models is provided, and used to confirm the numerical accuracy of the likelihood calculations. The simulated data sets show the similar spatial distributions to the real ones, but differ from them in some features of space-time clustering. These differences may provide useful indicators of directions for further study.     

Solution of convex conservation laws in a strip

In this paper we consider scalar convex conservation laws in one space variable in a stripD =(x, t): 0 ≤x ≤1,t > 0 and obtain an explicit formula for the solution of the mixed initial boundary value problem, the boundary data being prescribed in the sense of Bardos-Leroux and Nedelec. We also get an explicit formula for the solution of weighted Burgers equation in a strip.     

Deposition and evaporation ofk-mers: Dynamics of a many-state system

When the dynamics of a system partitions the phase space of configurations into very many disjoint sectors, we are faced with an assignment problem: Given a configuration, how can we tell which sector it belongs to? We study this problem in connection with the dynamics of deposition and evaporation ofk particles at a time, from a lattice substrate. Fork ≥ 3, the system shows complex behaviour: (a) The number of disjoint sectors in phase space grows exponentially with the size. (b) The asymptotic time dependence of the autocorrelation function shows slow decays, with power laws which depend on the sector. Both (a) and (b) are explained in terms of a nonlocal construct known as the irreducible string (IS), formed from a particle configuration by applying a deletion algorithm. The IS provides a label for sectors; the multiplicity of possible IS’s accounts for (a), and let us determine sector numbers and sizes. The elements of the IS are conserved; thus their motion is responsible for the slow modes of the system, and accounts for (b) as well.     

非完整非保守系统的积分因子和守恒律

通过寻找积分因子来建立非完整非保守系统的守恒律，讨论了存在守恒定律的必要条件，并举例说明其应用。     

Dynamics of Triangulations

We study a few problems related to Markov processes of flipping triangulations of the sphere. We show that these processes are ergodic and mixing, but find a natural example which does not satisfy detailed balance. In this example, the expected distribution of the degrees of the nodes seems to follow the power law d ⁻⁴.