Reducing the Effects of Unequal Number of Games on Rankings

Ranking is an important mathematical process in a variety of contexts such as information retrieval, sports and business. Sports ranking methods can be applied both in and beyond the context of athletics. In both settings, once the concept of a game has been defined, teams (or individuals) accumulate wins, losses, and ties, which are then factored into the ranking computation. Many settings involve an unequal number of games between competitors. This paper demonstrates how to adapt two sports rankings methods, the Colley and Massey ranking methods, to settings where an unequal number of games are played between the teams. In such settings, the standard derivations of the methods can produce nonsensical rankings. This paper introduces the idea of including a super-user into the rankings and considers the effect of this fictitious player on the ratings. We apply such techniques to rank batters and pitchers in Major League baseball, professional tennis players, and participants in a free online social game. The ideas introduced in this paper can further the scope that such methods are applied and the depth of insight they offer

Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data

The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The results suggest that atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at http://neon.cchem.berkeley.edu/~dan

Phonon-Coupled Electron Tunneling in Two and Three-Dimensional Tunneling Configurations

We treat a tunneling electron coupled to acoustical phonons through a realistic electron phonon interaction: deformation potential and piezoelectric, in two or three-dimensional tunneling configurations. Making use of slowness of the phonon system compared to electron tunneling, and using a Green function method for imaginary time, we are able to calculate the change in the transition probability due to the coupling to phonons. It is shown using standard renormalization procedure that, contrary to the one-dimensional case, second order perturbation theory is sufficient in order to treat the deformation potential coupling, which leads to a small correction to the transmission coefficient prefactor. In the case of piezoelectric coupling, which is found to be closely related to the piezoelectric polaron problem, vertex corrections need to be considered. Summing leading logarithmic terms, we show that the piezoelectric coupling leads to a significant change of the transmission coefficient.Comment: 17 pages, 4 figure

Existence of radial stationary solutions for a system in combustion theory

In this paper, we construct radially symmetric solutions of a nonlinear noncooperative elliptic system derived from a model for flame balls with radiation losses. This model is based on a one step kinetic reaction and our system is obtained by approximating the standard Arrehnius law by an ignition nonlinearity, and by simplifying the term that models radiation. We prove the existence of 2 solutions using degree theory

Enteric Neural Cells From Hirschsprung Disease Patients Form Ganglia in Autologous Aneuronal Colon

Background & Aims: Hirschsprung disease (HSCR) is caused by failure of cells derived from the neural crest (NC) to colonize the distal bowel in early embryogenesis, resulting in absence of the enteric nervous system (ENS) and failure of intestinal transit postnatally. Treatment is by distal bowel resection, but neural cell replacement may be an alternative. We tested whether aneuronal (aganglionic) colon tissue from patients may be colonized by autologous ENS-derived cells. Methods: Cells were obtained and cryopreserved from 31 HSCR patients from the proximal resection margin of colon, and ENS cells were isolated using flow cytometry for the NC marker p75 (nine patients). Aneuronal colon tissue was obtained from the distal resection margin (23 patients). ENS cells were assessed for NC markers immunohistologically and by quantitative reverse-transcription polymerase chain reaction, and mitosis was detected by ethynyl-2\u27-deoxyuridine labeling. The ability of human HSCR postnatal ENS-derived cells to colonize the embryonic intestine was demonstrated by organ coculture with avian embryo gut, and the ability of human postnatal HSCR aneuronal colon muscle to support ENS formation was tested by organ coculture with embryonic mouse ENS cells. Finally, the ability of HSCR patient ENS cells to colonize autologous aneuronal colon muscle tissue was assessed. Results: ENS-derived p75-sorted cells from patients expressed multiple NC progenitor and differentiation markers and proliferated in culture under conditions simulating Wnt signaling. In organ culture, patient ENS cells migrated appropriately in aneural quail embryo gut, and mouse embryo ENS cells rapidly spread, differentiated, and extended axons in patient aneuronal colon muscle tissue. Postnatal ENS cells derived from HSCR patients colonized autologous aneuronal colon tissue in cocultures, proliferating and differentiating as neurons and glia. Conclusions: NC-lineage cells can be obtained from HSCR patient colon and can form ENS-like structures in aneuronal colonic muscle from the same patient

Improved Survival from Ovarian Cancer in Patients Treated in Phase III Trial Active Cancer Centres in the UK

Aims: Ovarian cancer is the principal cause of gynaecological cancer death in developed countries, yet overall survival in the UK has been reported as being inferior to that in some Western countries. As there is a range of survival across the UK we hypothesised that in major regional centres, outcomes are equivalent to the best internationally. Materials and methods: Data from patients treated in multicentre international and UK-based trials were obtained from three regional cancer centres in the UK; Manchester, University College London and Leeds (MUL). The median progression-free survival (PFS) and overall survival were calculated for each trial and compared with the published trial data. Normalised median survival values and the respective 95% confidence intervals (ratio of pooled MUL data to trial median survival) were calculated to allow inter-trial survival comparisons. This strategy then allowed a comparison of median survival across the UK, in three regional UK centres and in international centres. Results: The analysis showed that the trial-reported PFS was the same in the UK, in the MUL centres and in international centres for each of the trials included in the study. Overall survival was, however, 45% better in major regional centre-treated patients (95% confidence interval 9–73%) than the median overall survival reported in UK trials, whereas the median overall survival in MUL centres equated with that achieved in international centres. Conclusion: The data suggest that international survival statistics are achieved in UK regional cancer centres

Pasture, Hay and Silage Crops for East Texas.

28 p