Earthquake source parameters of the 2009 Mw 7.8 Fiordland (New Zealand) earthquake from L-band InSAR observations

The 2009 MW7.8 Fiordland (New Zealand) earthquake is the largest to have occurred in New Zealand since the 1931 Mw 7.8 Hawke’s Bay earthquake, 1 000 km to the northwest. In this paper two tracks of ALOS PALSAR interferograms (one ascending and one descending) are used to determine fault geometry and slip distribution of this large earthquake. Modeling the event as dislocation in an elastic half-space suggests that the earthquake resulted from slip on a SSW-NNE orientated thrust fault that is associated with the subduction between the Pacific and Australian Plates, with oblique displacement of up to 6.3 m. This finding is consistent with the preliminary studies undertaken by the USGS using seismic data

Properties of estimators of parameters in logistic regression models

Properties of various types of estimators of the regression coefficients in linear logistic regression models are considered. The estimators include those based on maximum likelihood, minimum chi-square and weighted least squares. Theoretical approximations to the biases of the estimators are developed. The results of a large scale simulation investigation evaluating the moment properties of the estimators are presented for the case of a logistic model with a single explanatory variable

The extreme residuals in logistic regression models

Goodness of fit tests for logistic regression models using extreme residuals are considered. Moment properties of the Pearson residuals are developed and used to define modified residuals, for the cases when the model fit is made by maximum likelihood, minimum chi-square and weighted least squares. Approximations to the critical values of the extreme statistics based on the ordinary and modified Pearson residuals are developed and assessed for the case when the logistic regression model has a single explanatory variable

Null distribution of some goodness of fit statistics for logistic regression

The null distribution moment and percentile properties of several goodness of fit statistics for logistic regression models are considered. Small sample approximations to the critical values of the statistics are evaluated for the case of a single explanatory variable with equally spaced values

The complex geomety of a domain related to μ\mu-synthesis

We describe the basic complex geometry and function theory of the {\em pentablock} $\mathcal{P}$, which is the bounded domain in $\mathbb{C}^3$ given by $$\mathcal{P}= \{(a_{21}, \mathrm{tr} A, \det A): A= \begin{bmatrix} a_{ij}\end{bmatrix}_{i,j=1}^2 \in \mathbb{B}\}$$ where $\mathbb{B}$ denotes the open unit ball in the space of $2\times 2$ complex matrices. We prove several characterizations of the domain. We describe its distinguished boundary and exhibit a $4$-parameter group of automorphisms of $\mathcal{P}$. We show that $\mathcal{P}$ is intimately connected with the problem of $\mu$-synthesis for a certain cost function $\mu$ on the space of $2\times 2$ matrices defined in connection with robust stabilization by control engineers. We demonstrate connections between the function theories of $\mathcal{P}$ and $\mathbb{B}$. We show that $\mathcal{P}$ is polynomially convex and starlike.Comment: 36 pages, 2 figures. This version contains corrections of some inaccuracies and an expanded argument for Proposition 12.

Universality of Ionic Criticality: Size- and Charge-Asymmetric Electrolytes

Grand canonical simulations designed to resolve critical universality classes are reported for $z$:1 hard-core electrolyte models with diameter ratios $\lambda {=} a_+/a_- {\lesssim} 6$. For $z {=} 1$ Ising-type behavior prevails. Unbiased estimates of $T_c(\lambda)$ are within 1% of previous (biased) estimates but the critical densities are $\sim$5 % lower. Ising character is also established for the 2:1 and 3:1 equisized models, along with critical amplitudes and improved $T_c$ estimates. For $z {=} 3$, however, strong finite-size effects reduce the confidence level although classical and O$(n {\geq} 3)$ criticality are excluded.Comment: 4 pages, 3 figure