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

Swimming Efficiency of Bacterium Escherichia Coli

We use in vivo measurements of swimming bacteria in an optical trap to determine fundamental properties of bacterial propulsion. In particular, we determine the propulsion matrix, which relates the angular velocity of the flagellum to the torques and forces propelling the bacterium. From the propulsion matrix dynamical properties such as forces, torques, swimming speed and power can be obtained from measurements of the angular velocity of the motor. We find significant heterogeneities among different individuals even though all bacteria started from a single colony. The propulsive efficiency, defined as the ratio of the propulsive power output to the rotary power input provided by the motors, is found to be 0.2%.Comment: 6 page

Optimal Location of Sources in Transportation Networks

We consider the problem of optimizing the locations of source nodes in transportation networks. A reduction of the fraction of surplus nodes induces a glassy transition. In contrast to most constraint satisfaction problems involving discrete variables, our problem involves continuous variables which lead to cavity fields in the form of functions. The one-step replica symmetry breaking (1RSB) solution involves solving a stable distribution of functionals, which is in general infeasible. In this paper, we obtain small closed sets of functional cavity fields and demonstrate how functional recursions are converted to simple recursions of probabilities, which make the 1RSB solution feasible. The physical results in the replica symmetric (RS) and the 1RSB frameworks are thus derived and the stability of the RS and 1RSB solutions are examined.Comment: 38 pages, 18 figure

Improved Lagrangian mixing models for passive scalars in isotropic turbulence

Lagrangian data for velocity, scalars, and energy and scalar dissipation from direct numerical simulations are used to validate Lagrangian mixing models for inert passive scalars in stationary isotropic turbulence. The scalar fluctuations are nearly Gaussian, and, as a result of production by uniform mean gradients, statistically stationary. Comparisons are made for Taylor-scale Reynolds numbers in the range 38 to about 240 and Schmidt numbers in the range 1/8 to 1. Model predictions for one-point, one-time Eulerian statistics ~Eulerian correspondence! and one-particle, two-time Lagrangian statistics ~Lagrangian correspondence! are examined. Two scalar mixing models, namely the Lagrangian Fokker–Planck model and the Lagrangian colored-noise ~LCN! model, are proposed and written in terms of stochastic differential equations ~SDE! with specified drift and diffusion terms. Both of these models rely on statistics of the scalar field conditioned upon the energy dissipation, as provided by the Lagrangian spectral relaxation ~LSR! model. With the exception of the scalar dissipation, the models are shown to capture the Reynolds and Schmidt-number dependence of the Lagrangian integral time scales. However, the LCN model provides a more realistic description of the Lagrangian scalar fluctuations as differentiable time series having the correct form of the scalar autocorrelation function. Further extensions of the new mixing models to non-Gaussian scalars are conceptually straightforward, but require a closure for the scalar-conditioned scalar dissipation rate matrix. Likewise, accurate prediction of joint statistics for differential diffusion between different scalars with unequal molecular diffusivities will require the formulation of a multiscale SDE similar to the LSR model

Measurement of Lagrangian velocity in fully developed turbulence

We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particule at a turbulent Reynolds number $R_{\lambda} = 740$. Its dynamics is analyzed with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentzian form $E^{L}(\omega) = u_{rms}^{2} T_{L} / (1 + (T_{L}\omega)^{2})$, in agreement with a Kolmogorov-like scaling in the inertial range. The probability density function (PDF) of the velocity time increments displays a change of shape from quasi-Gaussian a integral time scale to stretched exponential tails at the smallest time increments. This intermittency, when measured from relative scaling exponents of structure functions, is more pronounced than in the Eulerian framework.Comment: 4 pages, 5 figures. to appear in PR

Self-organization in social tagging systems

Individuals often imitate each other to fall into the typical group, leading to a self-organized state of typical behaviors in a community. In this paper, we model self-organization in social tagging systems and illustrate the underlying interaction and dynamics. Specifically, we introduce a model in which individuals adjust their own tagging tendency to imitate the average tagging tendency. We found that when users are of low confidence, they tend to imitate others and lead to a self-organized state with active tagging. On the other hand, when users are of high confidence and are stubborn to change, tagging becomes inactive. We observe a phase transition at a critical level of user confidence when the system changes from one regime to the other. The distributions of post length obtained from the model are compared to real data, which show good agreement

Evolution of speckle during spinodal decomposition

Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary systems which obey a local conservation law, the characteristic domain size is known to grow in time $\tau$ as $R = [B \tau]^n$ with n=1/3, where B is a constant. The intensities of individual speckles are found to be nonstationary, persistent time series. The two-time intensity covariance at wave vector ${\bf k}$ can be collapsed onto a scaling function $Cov(\delta t,\bar{t})$, where $\delta t = k^{1/n} B |\tau_2-\tau_1|$ and $\bar{t} = k^{1/n} B (\tau_1+\tau_2)/2$. Both analytically and numerically, the covariance is found to depend on $\delta t$ only through $\delta t/\bar{t}$ in the small-$\bar{t}$ limit and $\delta t/\bar{t} ^{1-n}$ in the large-$\bar{t}$ limit, consistent with a simple theory of moving interfaces that applies to any universality class described by a scalar order parameter. The speckle-intensity covariance is numerically demonstrated to be equal to the square of the two-time structure factor of the scattering material, for which an analytic scaling function is obtained for large $\bar{t}.$ In addition, the two-time, two-point order-parameter correlation function is found to scale as $C(r/(B^n\sqrt{\tau_1^{2n}+\tau_2^{2n}}),\tau_1/\tau_2)$, even for quite large distances $r$. The asymptotic power-law exponent for the autocorrelation function is found to be $\lambda \approx 4.47$, violating an upper bound conjectured by Fisher and Huse.Comment: RevTex: 11 pages + 12 figures, submitted to PR

Implementation of a national HIV pre-exposure prophylaxis service is associated with changes in characteristics of people with newly diagnosed HIV: a retrospective cohort study

OBJECTIVES: To review characteristics of individuals newly diagnosed with HIV following implementation of a national pre-exposure prophylaxis (PrEP) programme (comprehensive PrEP services, delivered in sexual health clinics) to inform future delivery and broader HIV prevention strategies. METHODS: We extracted data from national HIV databases (July 2015-June 2018). We compared sociodemographic characteristics of individuals diagnosed in the period before and after PrEP implementation, and determined the proportion of 'potentially preventable' infections with the sexual health clinic-based PrEP delivery model used. RESULTS: Those diagnosed with HIV before PrEP implementation were more likely to be male (342/418, 81.8% vs 142/197, 72.1%, p=0.005), be white indigenous (327/418, 78.2% vs 126/197, 64.0%, p<0.001), report transmission route as sex between men (219/418, 52.4% vs 81/197, 41.1%, p=0.014), and have acquired HIV in the country of the programme (302/418, 72.2% vs 114/197, 57.9% p<0.001) and less likely to report transmission through heterosexual sex (114/418, 27.3% vs 77/197, 39.1%, p=0.002) than after implementation.Pre-implementation, 8.6% (36/418) diagnoses were 'potentially preventable' with the PrEP model used. Post-implementation, this was 6.6% (13/197), but higher among those with recently acquired HIV (49/170, 28.8%). Overall, individuals with 'potentially preventable' infections were more likely to be male (49/49, 100% vs 435/566, 76.9%, p<0.001), aged <40 years (37/49, 75.5% vs 307/566, 54.2%, p=0.004), report transmission route as sex between men (49/49, 100% vs 251/566, 44.3%, p<0.001), have previously received post-exposure prophylaxis (12/49, 24.5% vs 7/566, 1.2%, p<0.001) and less likely to be black African (0/49, 0% vs 67/566, 11.8%, p=0.010) than those not meeting this definition. CONCLUSIONS: The sexual health clinic-based national PrEP delivery model appeared to best suit men who have sex with men and white indigenous individuals but had limited reach into other key vulnerable groups. Enhanced models of delivery and HIV combination prevention are required to widen access to individuals not benefiting from PrEP at present

Optimal Resource Allocation in Random Networks with Transportation Bandwidths

We apply statistical physics to study the task of resource allocation in random sparse networks with limited bandwidths for the transportation of resources along the links. Useful algorithms are obtained from recursive relations. Bottlenecks emerge when the bandwidths are small, causing an increase in the fraction of idle links. For a given total bandwidth per node, the efficiency of allocation increases with the network connectivity. In the high connectivity limit, we find a phase transition at a critical bandwidth, above which clusters of balanced nodes appear, characterised by a profile of homogenized resource allocation similar to the Maxwell's construction.Comment: 28 pages, 11 figure