From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491

A mother-child intervention program in adolescent mothers and their children to improve maternal sensitivity, child responsiveness and child development (the TeeMo study): study protocol for a randomized controlled trial

Background: Children of adolescent mothers present a high-risk group for child neglect and maltreatment. Previous findings suggest that early interventions can reduce maltreatment by improving the quality of mother-child interaction, particularly maternal sensitivity. The aim of the current study is to evaluate the effects of a mother-child intervention program using home visits and video-feedback regarding mother-child interaction (STEEP-b) plus psychiatric treatment of the mother in cases where mental illness is present compared with TAU (treatment as usual, that is, standardized support by the child welfare system) on enhancing maternal sensitivity and child responsiveness in adolescent, high-risk mothers. The second aim of the current project is to investigate behavioral and neural differences between adolescent and adult mothers at baseline and postintervention. Methods/Design: This is a randomized controlled trial (RCT) with 120 high-risk adolescent mothers (25 years) will additionally be recruited to investigate behavioral and neural differences between the adolescent and adult group. Blind assessments will take place at T1 (pre-intervention), at the end of the 9-month intervention (T2, postintervention) and 6 months postintervention (T3, follow-up). Moderators of treatment outcomes and sociodemographic data will be assessed at T1. The primary outcome hypothesis is that STEEP-b added to treatment as usual will improve maternal sensitivity and child responsiveness compared with treatment as usual alone in high-risk adolescent mothers. The primary hypothesis will be evaluated at the end of the 9-month follow-up assessment based on the intention-to-treat principle. The trial is funded by the German Ministry for Research and Education (BMBF). Data collection started in October 2012. Discussion: This is a randomized controlled trial that evaluates the effects of an early intervention program (STEEP-b) on the quality of mother-child interaction and child development in adolescent, high-risk mothers. Trial registration DRKS00004409 (27 September 2012

Machine-learning-based calving prediction from activity, lying, and ruminating behaviors in dairy cattle

The objective of this study was to use automated activity, lying, and rumination monitors to characterize prepartum behavior and predict calving in dairy cattle. Data were collected from 20 primiparous and 33 multiparous Holstein dairy cattle from September 2011 to May 2013 at the University of Kentucky Coldstream Dairy. The HR Tag (SCR Engineers Ltd., Netanya, Israel) automatically collected neck activity and rumination data in 2-h increments. The IceQube (IceRobotics Ltd., South Queensferry, United Kingdom) automatically collected number of steps, lying time, standing time, number of transitions from standing to lying (ly-. ing bouts), and total motion, summed in 15-min increments. IceQube data were summed in 2-h increments to match HR Tag data. All behavioral data were collected for 14 d before the predicted calving date. Retrospective data analysis was performed using mixed linear models to examine behavioral changes by day in the 14 d before calving. Bihourly behavioral differences from baseline values over the 14 d before calving were also evaluated using mixed linear models. Changes in daily rumination time, total motion, lying time, and lying bouts occurred in the 14 d before calving. In the bihourly analysis, extreme values for all behaviors occurred in the final 24 h, indicating that the monitored behaviors may be useful in calving prediction. To determine whether technologies were useful at predicting calving, random forest, linear discriminant analysis, and neural network machine -learning techniques were constructed and implemented using R version 3.1.0 (R Foundation for Statistical Computing, Vienna, Austria). These methods were used on variables from each technology and all combined variables from both technologies. A neural network analysis that combined variables from both technologies at the daily level yielded 100.0% sen-sitivity and 86.8% specificity. A neural network analysis that combined variables from both technologies in bihourly increments was used to identify 2-h periods in the 8 h before calving with 82.8% sensitivity and 80.4% specificity. Changes in behavior and machine-learning alerts indicate that commercially marketed behavioral monitors may have calving prediction potential

Sharing Yet Caring - Mitigating Moral Hazard in Access-Based Consumption through IS-Enabled Value Co-Capturing with Consumers

The quest for creating smart and sustainable cities entails various substantial challenges, such as environmental degradation and a shortage of space. To negotiate these hurdles, innovative approaches must be implemented. A key aspect in this regard is the shared use of resources via forms of access-based consumption. Owing to advances in the digitalization of contemporary societies, these concepts have recently attracted both consumer and scholarly interest. However, the digitally enabled separation of ownership and use brings along the risk of moral hazard by consumers using resources in careless or wasteful ways, which is detrimental to the sustainability of the overall system. In this study, the authors conceptualize and empirically investigate how these adverse effects can be mitigated by applying the potentials of connectivity and digital data to enable users to participate economically while acting favorably from a collective perspective. The results of the quasi-experimental research design, situated in a carsharing context and comprising data records of 2,983 bookings, indicate that this form of value co-capturing with consumers can significantly motivate users to alter their behavior. From these findings, the authors derive important implications for research on the sustainability of digital business eco-systems in the specific context of smart cities