Statistical Models with Uncertain Error Parameters

In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable with a given standard deviation (the corresponding "systematic error"). Although the assigned systematic errors are usually treated as constants, in general they are themselves uncertain. A type of model is presented where the uncertainty in the assigned systematic errors is taken into account. Estimates of the systematic variances are modeled as gamma distributed random variables. The resulting confidence intervals show interesting and useful properties. For example, when averaging measurements to estimate their mean, the size of the confidence interval increases for decreasing goodness-of-fit, and averages have reduced sensitivity to outliers. The basic properties of the model are presented and several examples relevant for Particle Physics are explored.Comment: 26 pages, 27 figure

Book Review: The Shaping of an Effective Leader

The Shaping of an Effective Leader has been fundamentally encouraging to me in the area of leadership because I have been fortunate enough to be a recipient of the leadership of the author. Serving on my dissertation committee, Gayle Beebe encouraged me to development a Christian theology of suffering. He recommended reading the works of Diogenes Allen, Lawrence Bowker, Herbert Lockyear, Henri Nouwen, as well as others. In our meetings to discuss these works, it did not take long for me to discover that I was in the presence of one of the most Christlike individuals I had ever encountered. The knowledge, skills, and dispositions of leadership modeled to me by the author are reflected in the principles of this work

Chen's conjecture and epsilon-superbiharmonic submanifolds of Riemannian manifolds

B.-Y. Chen famously conjectured that every submanifold of Euclidean space with harmonic mean curvature vector is minimal. In this note we establish a much more general statement for a large class of submanifolds satisfying a growth condition at infinity. We discuss in particular two popular competing natural interpretations of the conjecture when the Euclidean background space is replaced by an arbitrary Riemannian manifold. Introducing the notion of epsilon-superbiharmonic submanifolds, which contains each of the previous notions as special cases, we prove that epsilon-superbiharmonic submanifolds of a complete Riemannian manifold which satisfy a growth condition at infinity are minimal.Comment: 5 page

Bovine colostrum and immune function after exercise

Strenuous and/or prolonged exercise causes transient perturbations in immune function. It is well accepted that this is one mechanism contributing to the higher occurrence of infection (e.g. upper respiratory tract infection (URTI)) in athletes, especially endurance athletes. URTI or upper respiratory tract (URT) symptoms can negatively affect training and competition performance but athletes must train intensively to be successful. Therefore, interventions that can legitimately enhance immune function and reduce URTI risk can be of benefit to athletes. Bovine colostrum supplementation has been investigated as a possible nutritional countermeasure to enhance (or maintain) immune function, and reduce URTI risk, following strenuous or prolonged exercise and during intensive training periods. There is convincing evidence that daily supplementation with bovine colostrum, for a number of weeks (and preliminary evidence for acute effects after a single dose), can maintain intestinal barrier integrity, immune function and reduce the chances of suffering URTI or URT symptoms in athletes or those undertaking heavy training. The mechanisms are not fully understood at present but there is preliminary evidence suggesting that the effects on immune function are attributable, at least in part, to small bioactive components that survive digestion and are biologically available after consumption, but further work is required. In summary, the balance of existing evidence does support the notion that bovine colostrum is beneficial for certain groups of athletes, such as those involved in strenuous training (e.g. endurance athletes), in terms of immunity and resistance to infection