Relativistic laser pulse compression in plasmas with a linear axial density gradient

The self-compression of a relativistic Gaussian laser pulse propagating in a non-uniform plasma is investigated. A linear density inhomogeneity (density ramp) is assumed in the axial direction. The nonlinear Schrodinger equation is first solved within a one-dimensional geometry by using the paraxial formalism to demonstrate the occurrence of longitudinal pulse compression and the associated increase in intensity. Both longitudinal and transverse self-compression in plasma is examined for a finite extent Gaussian laser pulse. A pair of appropriate trial functions, for the beam width parameter (in space) and the pulse width parameter (in time) are defined and the corresponding equations of space and time evolution are derived. A numerical investigation shows that inhomogeneity in the plasma can further boost the compression mechanism and localize the pulse intensity, in comparison with a homogeneous plasma. A 100 fs pulse is compressed in an inhomogeneous plasma medium by more than ten times. Our findings indicate the possibility for the generation of particularly intense and short pulses, with relevance to the future development of tabletop high-power ultrashort laser pulse based particle acceleration devices and associated high harmonic generation. An extension of the model is proposed to investigate relativistic laser pulse compression in magnetized plasmas.

Generalized social trust across 22 European countries: A multi-level analysis of four competing models

Concern with what can explain variation in generalized social trust has led to an abundance of theoretical models. Defining generalized social trust as a belief in human benevolence, we focus on the emancipation theory and social capital theory as well as the ethnic diversity and economic development models of trust. We then determine which dimensions of individuals’ behavior and attitudes as well as of their national context are the most important predictors. Using data from 20 countries that participated in round one of the European Social Survey, we test these models at their respective level of analysis, individual and/or national. Our analysis revealed that individuals’ own trust in the political system as a moral and competent institution was the most important predictor of generalized social trust at the individual level, while a country’s level of affluence was the most important contextual predictor, indicating that different dimensions are significant at the two levels of analysis. This analysis also raised further questions as to the meaning of social capital at the two levels of analysis and the conceptual equivalence of its civic engagement dimension across cultures.

CH abundance gradient in TMC-1

Aims. The aim of this study is to examine if the well-known chemical gradient in TMC-1 is reflected in the amount of rudimentary forms of carbon available in the gas-phase. As a tracer we use the CH radical which is supposed to be well correlated with carbon atoms and simple hydrocarbon ions. Methods. We observed the 9-cm ?-doubling lines of CH along the dense filament of TMC-1. The CH column densities were compared with the total H2 column densities derived using the 2MASS NIR data and previously published SCUBA maps and with OH column densities derived using previous observations with Effelsberg. We also modelled the chemical evolution of TMC-1 adopting physical conditions typical of dark clouds using the UMIST Database for Astrochemistry gas-phase reaction network to aid the interpretation of the observed OH/CH abundance ratios. Results. The CH column density has a clear peak in the vicinity of the cyanopolyyne maximum of TMC-1. The fractional CH abundance relative to H2 increases steadily from the northwestern end of the filament where it lies around 1.0 × 10-8 , to the southeast where it reaches a value of 2.0 × 10-8. The OH and CH column densities are well correlated, and we obtained OH/CH abundance ratios of ~16–20. These values are clearly larger than what has been measured recently in diffuse interstellar gas and is likely to be related to C to CO conversion at higher densities. The good correlation between CH and OH can be explained by similar production and destruction pathways. We suggest that the observed CH and OH abundance gradients are mainly due to enhanced abundances in a low-density envelope which becomes more prominent in the southeastern part and seems to continue beyond the dense filament. Conclusions. An extensive envelope probably signifies an early stage of dynamical evolution, and conforms with the detection of a large CH abundance in the southeastern part of the cloud. The implied presence of other simple forms of carbon in the gas phase provides a natural explanation for the observation of “early-type” molecules in this region.

Topological mappings between graphs, trees and generalized trees

We present novel topological mappings between graphs, trees and generalized trees that means between structured objects with different properties. The two major contributions of this paper are, first, to clarify the relation between graphs, trees and generalized trees, a graph class recently introduced. Second, these transformations provide a unique opportunity to transform structured objects into a representation that might be beneficial for a processing, e.g., by machine learning techniques for graph classification. (c) 2006 Elsevier Inc. All rights reserved.

Interhemispheric gradient of atmospheric radiocarbon reveals natural variability of Southern Ocean winds

Tree ring Delta C-14 data (Reimer et al., 2004; McCormac et al., 2004) indicate that atmospheric Delta C-14 varied on multi-decadal to centennial timescales, in both hemispheres, over the period between AD 950 and 1830. The Northern and Southern Hemispheric Delta C-14 records display similar variability, but from the data alone is it not clear whether these variations are driven by the production of C-14 in the stratosphere (Stuiver and Quay, 1980) or by perturbations to exchanges between carbon reservoirs (Siegenthaler et al., 1980). As the sea-air flux of (CO2)-C-14 has a clear maximum in the open ocean regions of the Southern Ocean, relatively modest perturbations to the winds over this region drive significant perturbations to the interhemispheric gradient. In this study, model simulations are used to show that Southern Ocean winds are likely a main driver of the observed variability in the interhemispheric gradient over AD 950-1830, and further, that this variability may be larger than the Southern Ocean wind trends that have been reported for recent decades (notably 1980-2004). This interpretation also implies that there may have been a significant weakening of the winds over the Southern Ocean within a few decades of AD 1375, associated with the transition between the Medieval Climate Anomaly and the Little Ice Age. The driving forces that could have produced such a shift in the winds at the Medieval Climate Anomaly to Little Ice Age transition remain unknown. Our process-focused suite of perturbation experiments with models raises the possibility that the current generation of coupled climate and earth system models may underestimate the natural background multi-decadal- to centennial-timescale variations in the winds over the Southern Ocean.

Improved conjugate gradient implementation for least squares support vector machines

As a promising method for pattern recognition and function estimation, least squares support vector machines (LS-SVM) express the training in terms of solving a linear system instead of a quadratic programming problem as for conventional support vector machines (SVM). In this paper, by using the information provided by the equality constraint, we transform the minimization problem with a single equality constraint in LS-SVM into an unconstrained minimization problem, then propose reduced formulations for LS-SVM. By introducing this transformation, the times of using conjugate gradient (CG) method, which is a greatly time-consuming step in obtaining the numerical solution, are reduced to one instead of two as proposed by Suykens et al. (1999). The comparison on computational speed of our method with the CG method proposed by Suykens et al. and the first order and second order SMO methods on several benchmark data sets shows a reduction of training time by up to 44%. (C) 2011 Elsevier B.V. All rights reserved.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.