Local spin polarization in underdoped cuprates with impurities

We present a theory of magnetic (Ni) and nonmagnetic (Zn) impurities substituted into planar Cu sites in the normal state of underdoped cuprates exhibiting a spin gap. Both types of impurities induce magnetic moments on neighboring Cu sites. In the case of Ni these moments partially screen the inherent impurity spin, resulting in an effective S=1/2 moment. The characteristic Kondo scale is found to have a power-law dependence on the coupling constant. We investigate the spatial shape of the impurity-induced spin density, taking into account the presence of short-ranged AF correlations, and calculate the ^{17}O NMR line broadening induced by impurity doping.Comment: To appear in: Physica C, Proceedings of ACS '9

Catastrophic forgetting: still a problem for DNNs

We investigate the performance of DNNs when trained on class-incremental visual problems consisting of initial training, followed by retraining with added visual classes. Catastrophic forgetting (CF) behavior is measured using a new evaluation procedure that aims at an application-oriented view of incremental learning. In particular, it imposes that model selection must be performed on the initial dataset alone, as well as demanding that retraining control be performed only using the retraining dataset, as initial dataset is usually too large to be kept. Experiments are conducted on class-incremental problems derived from MNIST, using a variety of different DNN models, some of them recently proposed to avoid catastrophic forgetting. When comparing our new evaluation procedure to previous approaches for assessing CF, we find their findings are completely negated, and that none of the tested methods can avoid CF in all experiments. This stresses the importance of a realistic empirical measurement procedure for catastrophic forgetting, and the need for further research in incremental learning for DNNs.Comment: 10 pages, 11 figures, Artificial Neural Networks and Machine Learning - ICANN 201

Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms $\R^3$, \bbS^3 and \bbH^3. Additionally, we compute the extended frame for any associated family of Delaunay surfaces.Comment: 18 pages, revised versio

Constant mean curvature surfaces of any positive genus

We show the existence of several new families of non-compact constant mean curvature surfaces: (i) singly-punctured surfaces of arbitrary genus $g \geq 1$, (ii) doubly-punctured tori, and (iii) doubly periodic surfaces with Delaunay ends.Comment: 14 pages, 10 figure

Random walks reaching against all odds the other side of the quarter plane

For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state $(i_0,j_0)$, we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive an exact expression for the probability of this event, and derive an asymptotic expression for the case when $i_0$ becomes large, a situation in which the event becomes highly unlikely. The exact expression follows from the solution of a boundary value problem and is in terms of an integral that involves a conformal gluing function. The asymptotic expression follows from the asymptotic evaluation of this integral. Our results find applications in a model for nucleosome shifting, the voter model and the asymmetric exclusion process.Comment: 18 pages, 2 figures, to appear in Journal of Applied Probabilit

A new generalized domain decomposition strategy for the efficient parallel solution of the FDS-pressure equation. Part I: Theory, Concept and Implementation

Due to steadily increasing problem sizes and accuracy requirements as well as storage restrictions on single-processor systems, the efficient numerical simulation of realistic fire scenarios can only be obtained on modern high-performance computers based on multi-processor architectures. The transition to those systems requires the elaborate parallelization of the underlying numerical concepts which must guarantee the same result as a potentially corresponding serial execution and preserve the convergence order of the original serial method. Because of its low degree of inherent parallelizm, especially the efficient parallelization of the elliptic pressure equation is still a big challenge in many simulation programs for fire-induced flows such as the Fire Dynamics Simulator (FDS). In order to avoid losses of accuracy or numerical instabilities, the parallelization process must definitely take into account the strong global character of the physical pressure. The current parallel FDS solver is based on a relatively coarse-grained parallellization concept which can’t guarantee these requirements in all cases. Therefore, an alternative parallel pressure solver, ScaRC, is proposed which ensures a high degree of global coupling and a good computational performance at the same time. Part I explains the theory, concept and implementation of this new strategy, whereas Part II describes a series of validation and verification tests to proof its correctness