Investigating the relationship between the diversity index and frequency of offending

Purpose Recent work has suggested that specialization is correlated with frequency of offending, but this observed relationship may actually depend on the measuring instrument used. The diversity index is a common method of measuring specialization in such studies, and this paper investigates whether this observed correlation is due in part to the mathematical form of the diversity index itself. The criminological question as to whether specialization increases or decreases with offense frequency cannot be answered until the behavior of the diversity index is better understood. We use simulations to investigate the behavior of the diversity index where the number of crimes is small (the small sample problem), simulating from known distributions of offending. Two of the distributions used in the simulation are defined to be unspecialized. The first uses an equiprobable distribution of offenses across offense categories. The second uses the distribution of offenses in the British population. The third distribution is from a specialist distribution, and assumes that different offenders have different probabilities of choosing particular offenses. We report these simulations for both three and ten crime categories. To set the simulated results in context, we use an extract from the UK Police National Computer to investigate the criminological question as to whether specialization increases with offense frequency. For all three simulation schemes, the diversity index $D$ increases steeply with the frequency of offending $N$ at low frequencies, with the increase slowing around $N=20$, and becoming flat when the number of offenses $N$ reaches 500. This relationship is observed for both three crime categories and ten crime categories. The observed relationship of D with N can be used to correct the diversity index to allow the true relationship of specialization with offense frequency to be investigated. We recommend that the diversity index be used with caution when there are small numbers of crimes over fixed time periods. Any increase or decrease of the diversity index over the criminal career life course may reflect the behavior of the measurement tool with the number of offenses, rather than any change in specialization itself. Applying one of the suggested suitable correction methods to $D$ will mitigate this problem

A survey on mentoring, first incumbency, and the role of retired clergy : listening to bishops

This study set out to explore current attitudes and practice of bishops and dioceses of the Church of England concerning the role of retired clergy, with special reference to the role of mentor to clergy serving in their first incumbency. Replies were received from 30 of the 43 diocesan bishops (or those responding on their behalf). The data demonstrated that of the 30 participating dioceses, 26 had experience of using retired clergy as mentors to clergy in their first incumbency, and 25 considered this to be a good idea in principle. The other most frequently named roles for retired clergy within these 30 dioceses were as mentors more generally, as interim ministers in vacant parishes, as rural deans, and as ministry or work consultants. Other roles identified were as reflective practitioner, as worship leader, and as an assistant archdeacon. These summary statistics are illuminated and enriched by qualitative data

Robust Maximum- Likelihood Position Estimation in Scintillation Cameras

The classical maximum-likelihood (ML) estimator for the position of a scintillation event in a gamma camera, as derived by Gray and Macovski in 1976, requires exact knowledge of the light-spread function (LSF) of each photomultiplier tube. In practice, one must determine each LSF from noisy measurements corrupted by Poisson noise, quantization error, and electronic noise and bias. Since the ML position estimator involves derivatives of each LSF, even small measurement errors can result in degraded estimator performance. In this paper we derive a robust ML position estimator that accounts for the statistical uncertainty in LSF measurements. The form of the robust estimator diminishes contributions from the tails of the LSF, where the relative measurement errors are the largest.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85879/1/Fessler117.pd

Regularized Emission Image Reconstruction Using Imperfect Side Information

A spatially variant penalized-likelihood method for tomographic image reconstruction based on a weighted Gibbs penalty was investigated. The penalty weights are determined from structural side information, such as the locations of anatomical boundaries in high-resolution magnetic resonance images. Such side information will be imperfect in practice, and a simple simulation demonstrated the importance of accounting for the errors in boundary locations. Methods are discussed for prescribing the penalty weights when the side information is noisy. Simulation results suggest that even imperfect side information is useful for guiding spatially variant regularization.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85869/1/Fessler110.pd

Design of a very high-resolution small animal PET scanner using a silicon scatter detector insert

A small animal positron emission tomography (PET) instrument using a high-resolution solid-state detector insert in a conventional PET system was investigated for its potential to achieve sub-millimeter spatial resolution for mouse imaging. Monte Carlo simulations were used to estimate the effect of detector configurations (thickness, length and radius) on sensitivity. From this initial study, a PET system having an inner cylindrical silicon detector (4 cm ID, 4 cm length and 1.6 cm thickness composed of 16 layers of 300 µm × 300 µm × 1 mm pads), for scattering, surrounded by an outer cylindrical BGO scintillation detector (17.6 cm ID, 16 cm length and 2 cm thickness segmented into 3 mm × 3 mm × 20 mm crystals), for capture was evaluated in detail. In order to evaluate spatial resolution, sensitivity and image quality of the PET system, 2D images of multiple point and cylinder sources were reconstructed with the simulation data including blurring from positron range and annihilation photon acollinearity using filtered backprojection (FBP). Simulation results for 18F demonstrate 340 µm FWHM at the center of the field of view with 1.0% sensitivity from the coincidence of single scattering events in both silicon detectors and 1.0 mm FWHM with 9.0% sensitivity from the coincidence of single scattering in the silicon and full energy absorption of the second photon in the BGO detector.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58095/2/pmb7_15_019.pd

Combinatorial recognition of a complex telomere repeat sequence by the Candida parapsilosis Cdc13AB heterodimer

The telomere repeat units of Candida species are substantially longer and more complex than those in other organisms, raising interesting questions concerning the recognition mechanisms of telomere-binding proteins. Herein we characterized the properties of Candida parapsilosis Cdc13A and Cdc13B, two paralogs that are responsible for binding and protecting the telomere G-strand tails. We found that Cdc13A and Cdc13B can each form complexes with itself and a heterodimeric complex with each other. However, only the heterodimer exhibits high-affinity and sequence-specific binding to the telomere G-tail. EMSA and crosslinking analysis revealed a combinatorial mechanism of DNA recognition, which entails the A and B subunit making contacts to the 3′ and 5′ region of the repeat unit. While both the DBD and OB4 domain of Cdc13A can bind to the equivalent domain in Cdc13B, only the OB4 complex behaves as a stable heterodimer. The unstable Cdc13ABDBD complex binds G-strand with greatly reduced affinity but the same sequence specificity. Thus the OB4 domains evidently contribute to binding by promoting dimerization of the DBDs. Our investigation reveals a rare example of combinatorial recognition of single-stranded DNA and offers insights into the co-evolution of telomere DNA and cognate binding proteins