Let K be an algebraic number field, OK the ring of integers of K, and f : X → Spec(OK) an arithmetic surface. Let (E, h) be a rank r Hermitian vector bundle on X such that E Q is semistable on the geometric generic fiber X Q of f . In this paper, we will prove an arithmetic analogy of Bogomolov-Gieseker’s inequality: ĉ2(E, h)− r − 1 2r ĉ1(E, h) 2 ≥ 0. Table of

We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a weaker condition than most other properties considered so far in the literature, and yet enables robust estimation in a broader variety of settings, including t...

We define the determinantal divisor rank of an integral matrix to be the number of invariant factors which equal 1. Some properties of the determinantal divisor rank are proved, which are analogous to known properties of the usual rank. These include the Frobenious inequality for the rank of a product and a relation between the rank of a submatrix of a matrix and that of its complementary subma...

BACKGROUND Following previous cross-sectional research adopting an evolutionary approach to social rank and eating disorders, the present study explored the predictive value of social rank for changes in eating disorder symptoms in a 6-month longitudinal study. METHODS Seventy-three women and men with a history of eating disorders were followed up over 6 months. A broad range of measures of s...

Recent advances in imaging have enabled the study of social rank, which refers generally to an individual’s social standing as either dominant or subordinate in a group, in relation to brain structure and function. From an evolutionary perspective, the mind is a modular structure from which various psychological traits and processes evolved in order to promote the success of the individual and ...

High social rank is expected to incur fitness costs under unstable social conditions. A disruption of the oxidative balance may underlie such effects, but how markers of oxidative stress vary in relation to social rank and stability is unknown. We examined in mandrills whether the mating season characterized by social instability between males (but not between females) affected their oxidative ...

BACKGROUND This study explored the role of meaning in the link between stress and disordered eating, in particular focusing on social rank. METHOD Two hundred and eleven women completed measures of eating pathology, depression, social comparison and life events where life events were assessed in terms of general loss, threat, shame and loss of social status. RESULTS Events involving loss of...