On the Green and Wald formalism

Backreaction in the cosmological context is a longstanding problem that is especially important in the present era of precise cosmology. The standard model of a homogeneous background plus density perturbations is most probably oversimplified and is expected to fail to fully account for the near-future observations of sub-percent precision. From a theoretical point of view, the problem of backreaction is very complicated and deserves careful examination. Recently, Green and Wald claimed in a series of papers to have developed a formalism to properly describe the influence of density inhomogeneities on average properties of the Universe, i.e., the backreaction effect. A brief discussion of this framework is presented, focussing on its drawbacks and on misconceptions that have arisen during the "backreaction debate".Comment: Contribution to the proceedings of MG1

On the relativistic mass function and averaging in cosmology

The general relativistic description of cosmological structure formation is an important challenge from both the theoretical and the numerical point of views. In this paper we present a brief prescription for a general relativistic treatment of structure formation and a resulting mass function on galaxy cluster scales in a highly generic scenario. To obtain this we use an exact scalar averaging scheme together with the relativistic generalization of Zel'dovich's approximation (RZA) that serves as a closure condition for the averaged equations.Comment: Contribution to the proceedings of MG1

Universality of citation distributions revisited

Radicchi, Fortunato, and Castellano [arXiv:0806.0974, PNAS 105(45), 17268] claim that, apart from a scaling factor, all fields of science are characterized by the same citation distribution. We present a large-scale validation study of this universality-of-citation-distributions claim. Our analysis shows that claiming citation distributions to be universal for all fields of science is not warranted. Although many fields indeed seem to have fairly similar citation distributions, there are quite some exceptions as well. We also briefly discuss the consequences of our findings for the measurement of scientific impact using citation-based bibliometric indicators

The quantum double well anharmonic oscillator in an external field

The aim of this paper is twofold. First of all, we study the behaviour of the lowest eigenvalues of the quantum anharmonic oscillator under influence of an external field. We try to understand this behaviour using perturbation theory and compare the results with numerical calculations. This brings us to the second aim of selecting the best method to carry out the numerical calculations accurately.Comment: 9 pages, 6 figure

A triclinic polymorph of benzanilide : disordered molecules form hydrogen-bonded chains

Peer reviewedPublisher PD

Statistical Software for State Space Methods

In this paper we review the state space approach to time series analysis and establish the notation that is adopted in this special volume of the Journal of Statistical Software. We first provide some background on the history of state space methods for the analysis of time series. This is followed by a concise overview of linear Gaussian state space analysis including the modelling framework and appropriate estimation methods. We discuss the important class of unobserved component models which incorporate a trend, a seasonal, a cycle, and fixed explanatory and intervention variables for the univariate and multivariate analysis of time series. We continue the discussion by presenting methods for the computation of different estimates for the unobserved state vector: filtering, prediction, and smoothing. Estimation approaches for the other parameters in the model are also considered. Next, we discuss how the estimation procedures can be used for constructing confidence intervals, detecting outlier observations and structural breaks, and testing model assumptions of residual independence, homoscedasticity, and normality. We then show how ARIMA and ARIMA components models fit in the state space framework to time series analysis. We also provide a basic introduction for non-Gaussian state space models. Finally, we present an overview of the software tools currently available for the analysis of time series with state space methods as they are discussed in the other contributions to this special volume.

Hierarchical Subquery Evaluation for Active Learning on a Graph

To train good supervised and semi-supervised object classifiers, it is critical that we not waste the time of the human experts who are providing the training labels. Existing active learning strategies can have uneven performance, being efficient on some datasets but wasteful on others, or inconsistent just between runs on the same dataset. We propose perplexity based graph construction and a new hierarchical subquery evaluation algorithm to combat this variability, and to release the potential of Expected Error Reduction. Under some specific circumstances, Expected Error Reduction has been one of the strongest-performing informativeness criteria for active learning. Until now, it has also been prohibitively costly to compute for sizeable datasets. We demonstrate our highly practical algorithm, comparing it to other active learning measures on classification datasets that vary in sparsity, dimensionality, and size. Our algorithm is consistent over multiple runs and achieves high accuracy, while querying the human expert for labels at a frequency that matches their desired time budget.Comment: CVPR 201

Variational matrix product state approach to quantum impurity models

We present a unified framework for renormalization group methods, including Wilson's numerical renormalization group (NRG) and White's density-matrix renormalization group (DMRG), within the language of matrix product states. This allows improvements over Wilson's NRG for quantum impurity models, as we illustrate for the one-channel Kondo model. Moreover, we use a variational method for evaluating Green's functions. The proposed method is more flexible in its description of spectral properties at finite frequencies, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting potentially \emph{linear} scaling of complexity for $n$-channel problems.Comment: revised version with application to Kondo model at large magnetic field (5 pages, 2 figures