Problems with Fitting to the Power-Law Distribution

This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents a new table for performing the Kolmogorov-Smirnof test for goodness-of-fit tailored to power-law distributions in which the power-law exponent is estimated using MLE. The techniques presented here will advance the application of complex network theory by allowing reliable estimation of power-law models from data and further allowing quantitative assessment of goodness-of-fit of proposed power-law models to empirical data.Comment: 4 pages, 1 figure, 2 table

A field expansions method for scattering by periodic multilayered media

The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein described is a boundary perturbation method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than finite difference and finite element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. The approach is a generalization to multiple layers of Bruno and Reitich’s “Method of Field Expansions” for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original field expansions method, this approach is extremely efficient and spectrally accurate

Reporting transparency: making the ethical mandate explicit.

Improving the transparency and quality of reporting in biomedical research is considered ethically important; yet, this is often based on practical reasons such as the facilitation of peer review. Surprisingly, there has been little explicit discussion regarding the ethical obligations that underpin reporting guidelines. In this commentary, we suggest a number of ethical drivers for the improved reporting of research. These ethical drivers relate to researcher integrity as well as to the benefits derived from improved reporting such as the fair use of resources, minimizing risk of harms, and maximizing benefits. Despite their undoubted benefit to reporting completeness, questions remain regarding the extent to which reporting guidelines can influence processes beyond publication, including researcher integrity or the uptake of scientific research findings into policy or practice. Thus, we consider investigation on the effects of reporting guidelines an important step in providing evidence of their benefits

The RECORD reporting guidelines: meeting the methodological and ethical demands of transparency in research using routinely-collected health data.

Routinely-collected health data (RCD) are now used for a wide range of studies, including observational studies, comparative effectiveness research, diagnostics, studies of adverse effects, and predictive analytics. At the same time, limitations inherent in using data collected without specific a priori research questions are increasingly recognized. There is also a growing awareness of the suboptimal quality of reports presenting research based on RCD. This has created a perfect storm of increased interest and use of RCD for research, together with inadequate reporting of the strengths and weaknesses of these data resources. The REporting of studies Conducted using Observational Routinely-collected Data (RECORD) statement was developed to address these limitations and to help researchers using RCD to meet their ethical obligations of complete and accurate reporting, as well as improve the utility of research conducted using RCD. The RECORD statement has been endorsed by more than 15 journals, including Clinical Epidemiology. This journal now recommends that authors submit the RECORD checklist together with any manuscript reporting on research using RCD

Detecting periodicity in experimental data using linear modeling techniques

Fourier spectral estimates and, to a lesser extent, the autocorrelation function are the primary tools to detect periodicities in experimental data in the physical and biological sciences. We propose a new method which is more reliable than traditional techniques, and is able to make clear identification of periodic behavior when traditional techniques do not. This technique is based on an information theoretic reduction of linear (autoregressive) models so that only the essential features of an autoregressive model are retained. These models we call reduced autoregressive models (RARM). The essential features of reduced autoregressive models include any periodicity present in the data. We provide theoretical and numerical evidence from both experimental and artificial data, to demonstrate that this technique will reliably detect periodicities if and only if they are present in the data. There are strong information theoretic arguments to support the statement that RARM detects periodicities if they are present. Surrogate data techniques are used to ensure the converse. Furthermore, our calculations demonstrate that RARM is more robust, more accurate, and more sensitive, than traditional spectral techniques.Comment: 10 pages (revtex) and 6 figures. To appear in Phys Rev E. Modified styl

A stochastic model for the evolution of the web allowing link deletion

Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. We present a generalisation of the basic model by allowing deletion of individual links and show that it also gives rise to a power-law distribution. We derive the mean-field equations for this stochastic model and show that by examining a snapshot of the distribution at the steady state of the model, we are able to tell whether any link deletion has taken place and estimate the link deletion probability. Our model enables us to gain some insight into the distribution of inlinks in the web graph, in particular it suggests a power-law exponent of approximately 2.15 rather than the widely published exponent of 2.1

The use of risk and need factors in forensic mental health decision-making and the role of gender and index offense severity

Canadian legislation makes Review Boards (RBs) responsible for rendering dispositions for individuals found Not Criminally Responsible on account of Mental Disorder (NCRMD) after considering public safety, the mental condition of the accused, and his/her potential for community reintegration. We reviewed 6,743 RB hearings for 1,794 individuals found NCRMD in the three largest Canadian provinces to investigate whether items from two empirically supported risk assessment measures, the Historical Clinical Risk Management‐20 and the Violence Risk Appraisal Guide, were considered. Less than half the items were included in expert reports or in RBs' reasons for dispositions, and consideration of these items differed according to gender and index offense severity of the accused. These items included evidence‐based risk factors and/or legally specified criteria: mental health, treatment, and criminal history. These results illustrate the gap between research on risk factors and the integration of this evidence into practice. In particular, we recommend the implementation of structured measures to reduce the potential for clinicians to be unduly influenced by gender and offense severity