On the Approximation Performance of Fictitious Play in Finite Games

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play fails to find a solution having an additive approximation guarantee significantly better than 1/2. Our construction shows that for n times n games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity 1/2 - O(1/n^(1-delta)) for arbitrarily small delta. We also show an essentially matching upper bound of 1/2 - O(1/n)

Monopole clusters in Abelian projected gauge theories

We show that the monopole currents which one obtains in the maximally Abelian gauge of SU(2) fall into two quite distinct classes (when the volume is large enough). In each field configuration there is precisely one cluster that permeates the whole lattice volume. It has a current density and a magnetic screening mass that scale and it produces the whole of the string tension. The remaining clusters have a number density that follows an approximate power law proportional to the inverse cube of l where l is the length of the monopole world line in lattice units. These clusters are localised in space-time with radii which vary as the square root of l. In terms of the radius r these `lumps' have a scale-invariant distribution proportional to (dr/r . 1/{r^4}). Moreover they appear not to contribute at all to the string tension. The fact that they are scale-invariant at small distances would seem to rule out an instanton origin.Comment: LaTeX, 31 pages, 11 PostScript figures. Typo in Table 2 correcte

Impact of a theoretically based sex education programme (SHARE) delivered by teachers on NHS registered conceptions and terminations: final results of cluster randomised trial

<b>Objective</b>: To assess the impact of a theoretically based sex education programme (SHARE) delivered by teachers compared with conventional education in terms of conceptions and terminations registered by the NHS. Design Follow-up of cluster randomised trial 4.5 years after intervention. <b>Setting</b>: NHS records of women who had attended 25 secondary schools in east Scotland. <b>Participants</b>: 4196 women (99.5% of those eligible). <b>Intervention</b>: SHARE programme (intervention group) v existing sex education (control group). <b>Main outcome measure</b>: NHS recorded conceptions and terminations for the achieved sample linked at age 20. <b>Results</b>: In an "intention to treat" analysis there were no significant differences between the groups in registered conceptions per 1000 pupils (300 SHARE v 274 control; difference 26, 95% confidence interval –33 to 86) and terminations per 1000 pupils (127 v 112; difference 15, –13 to 42) between ages 16 and 20. <b>Conclusions</b>: This specially designed sex education programme did not reduce conceptions or terminations by age 20 compared with conventional provision. The lack of effect was not due to quality of delivery. Enhancing teacher led school sex education beyond conventional provision in eastern Scotland is unlikely to reduce terminations in teenagers

The effect of attenuation on gross earth models

In most recent free oscillation studies of the earth's interior the effect of absorption upon the eigenperiods of the earth has been ignored. This is equivalent to assuming that the earth is close to perfectly elastic. Since the actual earth is significantly anelastic over seismic frequencies, a frequency-dependent correction of the order of 1% must be applied to the normal mode periods in order that models based on those modes may be compared with body wave results. The eigenperiods of an earth model based on uncorrected data, model C2 (Anderson and Hart, 1976a), are adjusted for attenuation and then inverted to determine the resulting overall perturbation in the earth model. The corrected normal mode data as well as the uncorrected data can be fitted by a spherically symmetric earth model. The effect of including the attenuation term is to generally increase seismic velocities, particularly shear velocities, throughout the model. An important consequence of this change is to reduce or eliminate base line discrepancies between body wave results and normal mode results

Psychopathy and the DSM-IV criteria for antisocial personality disorder.

The Axis II Work Group of the Task Force on Diagnostic and Statistical Manual of Mental Disorders (DSM-IV) has expressed concern that antisocial personality disorder (APD) criteria are too long and cumbersome and that they focus on antisocial behaviors rather than personality traits central to traditional conceptions of psychopathy and to international criteria. R. D. Hare et al describe an alternative to the approach taken in the DSM-III—Revised (DSM-III—R; American Psychiatric Association, 1987), namely, the revised Psychopathy Checklist. The authors also discuss the multisite APD field trials designed to evaluate and compare 4 criteria sets: the DSM-III—R criteria, a shortened list of these criteria, the criteria for dyssocial personality disorder from the 10th edition of the International Classification of Diseases (World Health Organization, 1990), and a 10-item criteria set for psychopathic personality disorder derived from the revised Psychopathy Checklist. (PsycINFO Database Record (c) 2015 APA, all rights reserved