The Cosmological Energy Density of Neutrinos from Oscillation Measurements

The emerging structure of the neutrino mass matrix, when combined with the primordial element abundances, places the most stringent constraint on the flavor asymmetries in the cosmological neutrino background and therefore its energy density. I review the mechanism of synchronized neutrino oscillations in the an early universe with degenerate (asymmetric) neutrino and antineutrino densities and the implications of refined measurements of neutrino parameters.Comment: 4 pages, Proceedings of NuFact 03, 5th International Workshop on Neutrino Factories & Superbeams, 5-11 June 2003, Columbia University, New Yor

Battered women presenting in general practice

The problems of battered women have recently been highlighted. They consult doctors, who can be an important source of help. We examined their initial presenting complaint to general practitioners. Questionnaires were sent to 27 London refuges for battered women and to 100 randomly selected general practitioners. Seventy-two women and 49 doctors replied. The results indicated that these women are more likely to present with psychological symptoms. Many cases are not detected because the battering is concealed. The attitude of doctors may prevent these patients discussing their real problems. Further studies are needed

Resonantly-Produced 7 keV Sterile Neutrino Dark Matter Models and the Properties of Milky Way Satellites

Sterile neutrinos produced through a resonant Shi-Fuller mechanism are arguably the simplest model for a dark matter interpretation origin of the recent unidentified X-ray line seen toward a number of objects harboring dark matter. Here, I calculate the exact parameters required in this mechanism to produce the signal. The suppression of small scale structure predicted by these models is consistent with Local Group and high-$z$ galaxy count constraints. Very significantly, the parameters necessary in these models to produce the full dark matter density fulfill previously determined requirements to successfully match the Milky Way Galaxy's total satellite abundance, the satellites' radial distribution and their mass density profile, or "too big to fail problem." I also discuss how further precision determinations of the detailed properties of the candidate sterile neutrino dark matter can probe the nature of the quark-hadron transition, which takes place during the dark matter production.Comment: 5 pages, 3 figures. v3: discussion added, matches version accepted to Phys. Rev. Let

Sterile neutrinos in cosmology

Sterile neutrinos are natural extensions to the standard model of particle physics in neutrino mass generation mechanisms. If they are relatively light, less than approximately 10 keV, they can alter cosmology significantly, from the early Universe to the matter and radiation energy density today. Here, we review the cosmological role such light sterile neutrinos can play from the early Universe, including production of keV-scale sterile neutrinos as dark matter candidates, and dynamics of light eV-scale sterile neutrinos during the weakly-coupled active neutrino era. We review proposed signatures of light sterile neutrinos in cosmic microwave background and large scale structure data. We also discuss keV-scale sterile neutrino dark matter decay signatures in X-ray observations, including recent candidate $\sim$3.5 keV X-ray line detections consistent with the decay of a $\sim$7 keV sterile neutrino dark matter particle.Comment: Accepted version of an invited review for Physics Reports. 33 pages, 7 figures, approximately 16,000 words; v3: expanded discussion of low reheating temperature universe models with a new figure, large scale structure effects, scalar decay model

Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand

This paper considers the classical Newsvendor model, also known as the Newsboy problem, with the demand to be fully observed and to follow in successive inventory cycles one of the Exponential, Rayleigh, and Log-Normal distributions. For each distribution, appropriate estimators for the optimal order quantity are considered, and their sampling distributions are derived. Then, through Monte-Carlo simulations, we evaluate the performance of corresponding exact and asymptotic confidence intervals for the true optimal order quantity. The case where normality for demand is erroneously assumed is also investigated. Asymptotic confidence intervals produce higher precision, but to attain equality between their actual and nominal confidence level, samples of at least a certain size should be available. This size depends upon the coefficients of variation, skewness and kurtosis. The paper concludes that having available data on the skewed demand for enough inventory cycles enables (i) to trace non-normality, and (ii) to use the right asymptotic confidence intervals in order the estimates for the optimal order quantity to be valid and precise.Inventory Control; Newsboy Problem; Skewed Demand; Exact and Asymptotic Confidence Intervals; Monte-Carlo Simulations

Estimating population means in covariance stationary process

In simple random sampling, the basic assumption at the stage of estimating the standard error of the sample mean and constructing the corresponding confidence interval for the population mean is that the observations in the sample must be independent. In a number of cases, however, the validity of this assumption is under question, and as examples we mention the cases of generating dependent quantities in Jackknife estimation, or the evolution through time of a social quantitative indicator in longitudinal studies. For the case of covariance stationary processes, in this paper we explore the consequences of estimating the standard error of the sample mean using however the classical way based on the independence assumption. As criteria we use the degree of bias in estimating the standard error, and the actual confidence level attained by the confidence interval, that is, the actual probability the interval to contain the true mean. These two criteria are computed analytically under different sample sizes in the stationary ARMA(1,1) process, which can generate different forms of autocorrelation structure between observations at different lags.Jackknife estimation; ARMA; Longitudinal data; Actual confidence level

Forecasting an ARIMA (0,2,1) using the random walk model with drift

In this paper we show that the random walk model with drift behaves like an ARIMA (0,2,1) when its parameter θ is greater but close to –1. Using the random walk for predicting future values of an ARIMA (0,2,1) process, we find out that when θ is not so close to –1, the performance of the prediction interval for the period forecast is not satisfactory. Particularly, for large, the achieved coverage, namely, the probability the prediction interval to include the future value is quite low. Even in the cases of large samples and small , although the random walk coverage approaches that of the ARIMA, the random walk produces wider prediction intervals. This picture changes when we forecast ARIMA (0,2,1) values for θ close to –1. The random walk should be preferred as it produces on average narrower confidence intervals, and its coverage is almost the same with the nominal coverage of the ARIMA (0,2,1).ARIMA; Random Walk; Monte Carlo Simulations

Confidence intervals in stationary autocorrelated time series

In this study we examine in covariance stationary time series the consequences of constructing confidence intervals for the population mean using the classical methodology based on the hypothesis of independence. As criteria we use the actual probability the confidence interval of the classical methodology to include the population mean (actual confidence level), and the ratio of the sampling error of the classical methodology over the corresponding actual one leading to equality between actual and nominal confidence levels. These criteria are computed analytically under different sample sizes, and for different autocorrelation structures. For the AR(1) case, we find significant differentiation in the values taken by the two criteria depending upon the structure and the degree of autocorrelation. In the case of MA(1), and especially for positive autocorrelation, we always find actual confidence levels lower than the corresponding nominal ones, while this differentiation between these two levels is much lower compared to the case of AR(1).Covariance stationary time series; Variance of the sample mean; Actual confidence level

Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand

In this paper we consider the classical newsvendor model with profit maximization. When demand is fully observed in each period and follows either the Rayleigh or the exponential distribution, appropriate estimators for the optimal order quantity and the maximum expected profit are established and their distributions are derived. Measuring validity and precision of the corresponding generated confidence intervals by respectively the actual confidence level and the expected half-length divided by the true quantity (optimal order quantity or maximum expected profit), we prove that the intervals are characterized by a very important and useful property. Either referring to confidence intervals for the optimal order quantity or the maximum expected profit, measurements for validity and precision take on exactly the same values. Furthermore, validity and precision do not depend upon the values assigned to the revenue and cost parameters of the model. To offer, therefore, a-priori knowledge for levels of precision and validity, values for the two statistical criteria, that is, the actual confidence level and the relative expected half-length are provided for different combinations of sample size and nominal confidence levels 90%, 95% and 99%. The values for the two criteria have been estimated by developing appropriate Monte-Carlo simulations. For the relative-expected half-length, values are computed also analytically.Inventory Control; Classical newsvendor model; Exponential and Rayleigh Distributions; Confidence Intervals; Monte-Carlo Simulations

Non-negative demand in newsvendor models:The case of singly truncated normal samples

This paper considers the classical newsvendor model when demand is normally distributed but with a large coefficient of variation. This leads to observe with a non-negligible probability negative values that do not make sense. To avoid the occurrence of such negative values, first, we derive generalized forms for the optimal order quantity and the maximum expected profit using properties of singly truncated normal distributions. Since truncating at zero produces non-symmetric distributions for the positive values, three alternative models are used to develop confidence intervals for the true optimal order quantity and the true maximum expected profit under truncation. The first model assumes traditional normality without truncation, while the other two models assume that demand follows (a) the log-normal distribution and (b) the exponential distribution. The validity of confidence intervals is tested through Monte-Carlo simulations, for low and high profit products under different sample sizes and alternative values for coefficient of variation. For each case, three statistical measures are computed: the coverage, namely the estimated actual confidence level, the relative average half length, and the relative standard deviation of half lengths. Only for very few cases the normal and the log-normal model produce confidence intervals with acceptable coverage but these intervals are characterized by low precision and stability.Inventory Management; Newsvendor model; Truncated normal; Demand estimation; Confidence intervals; Monte-Carlo simulations