Dynamics underlying Box-office: Movie Competition on Recommender Systems

We introduce a simple model to study movie competition in the recommender systems. Movies of heterogeneous quality compete against each other through viewers' reviews and generate interesting dynamics of box-office. By assuming mean-field interactions between the competing movies, we show that run-away effect of popularity spreading is triggered by defeating the average review score, leading to hits in box-office. The average review score thus characterizes the critical movie quality necessary for transition from box-office bombs to blockbusters. The major factors affecting the critical review score are examined. By iterating the mean-field dynamical equations, we obtain qualitative agreements with simulations and real systems in the dynamical forms of box-office, revealing the significant role of competition in understanding box-office dynamics.Comment: 8 pages, 6 figure

How the presentation of patient information and decision-support advisories influences opioid prescribing behavior: A simulation study

ObjectiveThe United States faces an opioid crisis. Integrating prescription drug monitoring programs into electronic health records offers promise to improve opioid prescribing practices. This study aimed to evaluate 2 different user interface designs for prescription drug monitoring program and electronic health record integration.Materials and MethodsTwenty-four resident physicians participated in a randomized controlled experiment using 4 simulated patient cases. In the conventional condition, prescription opioid histories were presented in tabular format, and computerized clinical decision support (CDS) was provided via interruptive modal dialogs (ie, pop-ups). The alternative condition featured a graphical opioid history, a cue to visit that history, and noninterruptive CDS. Two attending pain specialists judged prescription appropriateness.ResultsParticipants in the alternative condition wrote more appropriate prescriptions. When asked after the experiment, most participants stated that they preferred the alternative design to the conventional design.ConclusionsHow patient information and CDS are presented appears to have a significant influence on opioid prescribing behavior

Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio

Effect of a magnetic flux on the critical behavior of a system with long range hopping

We study the effect of a magnetic flux in a 1D disordered wire with long range hopping. It is shown that this model is at the metal-insulator transition (MIT) for all disorder values and the spectral correlations are given by critical statistics. In the weak disorder regime a smooth transition between orthogonal and unitary symmetry is observed as the flux strength increases. By contrast, in the strong disorder regime the spectral correlations are almost flux independent. It is also conjectured that the two level correlation function for arbitrary flux is given by the dynamical density-density correlations of the Calogero-Sutherland (CS) model at finite temperature. Finally we describe the classical dynamics of the model and its relevance to quantum chaos.Comment: 5 pages, 4 figure

Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I

We study the dynamics of ordering of a nonconserved Heisenberg magnet. The dynamics consists of two parts --- an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches to zero temperature, we provide convincing arguments, both numerically (Langevin simulation) and analytically (approximate closure scheme due to Mazenko), that the torque is irrelevant at late times. We subject the Mazenko closure scheme to systematic numerical tests. Such an analysis, carried out for the first time on a vector order parameter, shows that the closure scheme performs respectably well. For quenches to $T_c$, we show, to ${\cal O}(\epsilon^2)$, that the torque is irrelevant at the Wilson-Fisher fixed point.Comment: 13 pages, REVTEX, and 19 .eps figures, compressed, Submitted to Phys. Rev.