Symmetry, regression design, and sampling distributions

When values of regressors are symmetrically disposed, many M-estimators in a wide class of models have a reflection property, namely, that as the signs of the coefficients on regressors are reversed, their estimators' sampling distribution is reflected about the origin. When the coefficients are zero, sign reversal can have no effect. So in this case, the sampling distribution of regression coefficient estimators is symmetric about zero, the estimators are median unbiased and, when moments exist, the estimators are exactly uncorrelated with estimators of other parameters. The result is unusual in that it does not require response variates to have symmetric conditional distributions. It demonstrates the potential importance of covariate design in determining the distributions of estimators, and it is useful in designing and interpreting Monte Carlo experiments. The result is illustrated by a Monte Carlo experiment in which maximum likelihood and symmetrically censored least-squares estimators are calculated for small samples from a censored normal linear regression, Tobit, model. © 1994, Cambridge University Press. All rights reserved

Myocardial Architecture and Patient Variability in Clinical Patterns of Atrial Fibrillation

Atrial fibrillation (AF) increases the risk of stroke by a factor of four to five and is the most common abnormal heart rhythm. The progression of AF with age, from short self-terminating episodes to persistence, varies between individuals and is poorly understood. An inability to understand and predict variation in AF progression has resulted in less patient-specific therapy. Likewise, it has been a challenge to relate the microstructural features of heart muscle tissue (myocardial architecture) with the emergent temporal clinical patterns of AF. We use a simple model of activation wavefront propagation on an anisotropic structure, mimicking heart muscle tissue, to show how variation in AF behaviour arises naturally from microstructural differences between individuals. We show that the stochastic nature of progressive transversal uncoupling of muscle strands (e.g., due to fibrosis or gap junctional remodelling), as occurs with age, results in variability in AF episode onset time, frequency, duration, burden and progression between individuals. This is consistent with clinical observations. The uncoupling of muscle strands can cause critical architectural patterns in the myocardium. These critical patterns anchor micro-re-entrant wavefronts and thereby trigger AF. It is the number of local critical patterns of uncoupling as opposed to global uncoupling that determines AF progression. This insight may eventually lead to patient specific therapy when it becomes possible to observe the cellular structure of a patient's heart.Comment: 5 pages, 4 figures. For supplementary materials please contact Kishan A. Manani at [email protected]

Distorted charged dilaton black holes

We construct exact static, axisymmetric solutions of Einstein-Maxwell-dilaton gravity presenting distorted charged dilaton black holes. The thermodynamics of such distorted black holes is also discussed.Comment: 14 pages, latex; v2 typos corrected, references adde

Magnetic phases in the correlated Kondo-lattice model

We study magnetic ordering of an extended Kondo-lattice model including an additional on-site Coulomb interaction between the itinerant states. The model is solved in the dynamical mean-field theory using Wilson's numerical renormalization group approach as impurity solver. For a bipartite lattice we find at half filling the expected antiferromagnetic phase. Upon doping this phase is gradually suppressed and hints towards phase separation are observed. For large doping the model exhibits ferromagnetism, the appearance of which can at first sight be explained by Rudermann-Kittel-Kasuya-Yosida interaction. However, for large values of the Kondo coupling $J$ significant differences to a simple Rudermann-Kittel-Kasuya-Yosida picture can be found. We furthermore observe signs of quantum critical points for antiferromagnetic Kondo coupling between the local spins and band states