Coarsening Dynamics of a One-Dimensional Driven Cahn-Hilliard System

We study the one-dimensional Cahn-Hilliard equation with an additional driving term representing, say, the effect of gravity. We find that the driving field $E$ has an asymmetric effect on the solution for a single stationary domain wall (or `kink'), the direction of the field determining whether the analytic solutions found by Leung [J.Stat.Phys.{\bf 61}, 345 (1990)] are unique. The dynamics of a kink-antikink pair (`bubble') is then studied. The behaviour of a bubble is dependent on the relative sizes of a characteristic length scale $E^{-1}$, where $E$ is the driving field, and the separation, $L$, of the interfaces. For $EL \gg 1$ the velocities of the interfaces are negligible, while in the opposite limit a travelling-wave solution is found with a velocity $v \propto E/L$. For this latter case ($EL \ll 1$) a set of reduced equations, describing the evolution of the domain lengths, is obtained for a system with a large number of interfaces, and implies a characteristic length scale growing as $(Et)^{1/2}$. Numerical results for the domain-size distribution and structure factor confirm this behavior, and show that the system exhibits dynamical scaling from very early times.Comment: 20 pages, revtex, 10 figures, submitted to Phys. Rev.

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

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

The reinforcing influence of recommendations on global diversification

Recommender systems are promising ways to filter the overabundant information in modern society. Their algorithms help individuals to explore decent items, but it is unclear how they allocate popularity among items. In this paper, we simulate successive recommendations and measure their influence on the dispersion of item popularity by Gini coefficient. Our result indicates that local diffusion and collaborative filtering reinforce the popularity of hot items, widening the popularity dispersion. On the other hand, the heat conduction algorithm increases the popularity of the niche items and generates smaller dispersion of item popularity. Simulations are compared to mean-field predictions. Our results suggest that recommender systems have reinforcing influence on global diversification.Comment: 6 pages, 6 figure

O(^3P) +CO_2 Collisions at Hyperthermal Energies: Dynamics of Nonreactive Scattering, Oxygen Isotope Exchange, and Oxygen-Atom Abstraction

The dynamics of O(^3P) + CO_2 collisions at hyperthermal energies were investigated experimentally and theoretically. Crossed-molecular-beams experiments at Ecoll = 98.8 kcal mol^(–1) were performed with isotopically labeled ^(12)C^(18)O_2 to distinguish products of nonreactive scattering from those of reactive scattering. The following product channels were observed: elastic and inelastic scattering (^(16)O(^3P) + ^(12)C^(18)O^2), isotope exchange (^(18)O + ^(16)O^(12)C^(18)O), and oxygen-atom abstraction (^(18)O^(16)O + ^(12)C^(18)O). Stationary points on the two lowest triplet potential energy surfaces of the O(^3P) + CO_2 system were characterized at the CCSD(T)/aug-cc-pVTZ level of theory and by means of W4 theory, which represents an approximation to the relativistic basis set limit, full-configuration-interaction (FCI) energy. The calculations predict a planar CO_3(C_(2v),^3A″) intermediate that lies 16.3 kcal mol^(–1) (W4 FCI excluding zero point energy) above reactants and is approached by a C_(2v) transition state with energy 24.08 kcal mol^(–1). Quasi-classical trajectory (QCT) calculations with collision energies in the range 23–150 kcal mol^(–1) were performed at the B3LYP/6-311G(d) and BMK/6-311G(d) levels. Both reactive channels observed in the experiment were predicted by these calculations. In the isotope exchange reaction, the experimental center-of-mass (c.m.) angular distribution, T(θ_(c.m.)), of the ^(16)O^(12)C^(18)O products peaked along the initial CO_2 direction (backward relative to the direction of the reagent O atoms), with a smaller isotropic component. The product translational energy distribution, P(E_T), had a relatively low average of E_T = 35 kcal mol^(–1), indicating that the ^(16)O^(12)C^(18)O products were formed with substantial internal energy. The QCT calculations give c.m. P(E_T) and T(θ_(c.m.)) distributions and a relative product yield that agree qualitatively with the experimental results, and the trajectories indicate that exchange occurs through a short-lived CO_3^* intermediate. A low yield for the abstraction reaction was seen in both the experiment and the theory. Experimentally, a fast and weak ^(16)O^(18)O product signal from an abstraction reaction was observed, which could only be detected in the forward direction. A small number of QCT trajectories leading to abstraction were observed to occur primarily via a transient CO_3 intermediate, albeit only at high collision energies (149 kcal mol^(–1)). The oxygen isotope exchange mechanism for CO_2 in collisions with ground state O atoms is a newly discovered pathway through which oxygen isotopes may be cycled in the upper atmosphere, where O(^3P) atoms with hyperthermal translational energies can be generated by photodissociation of O_3 and O_2

Calibrating the dice loss to handle neural network overconfidence for biomedical image segmentation

The Dice similarity coefficient (DSC) is both a widely used metric and loss function for biomedical image segmentation due to its robustness to class imbalance. However, it is well known that the DSC loss is poorly calibrated, resulting in overconfident predictions that cannot be usefully interpreted in biomedical and clinical practice. Performance is often the only metric used to evaluate segmentations produced by deep neural networks, and calibration is often neglected. However, calibration is important for translation into biomedical and clinical practice, providing crucial contextual information to model predictions for interpretation by scientists and clinicians. In this study, we provide a simple yet effective extension of the DSC loss, named the DSC++ loss, that selectively modulates the penalty associated with overconfident, incorrect predictions. As a standalone loss function, the DSC++ loss achieves significantly improved calibration over the conventional DSC loss across six well-validated open-source biomedical imaging datasets, including both 2D binary and 3D multi-class segmentation tasks. Similarly, we observe significantly improved calibration when integrating the DSC++ loss into four DSC-based loss functions. Finally, we use softmax thresholding to illustrate that well calibrated outputs enable tailoring of recall-precision bias, which is an important post-processing technique to adapt the model predictions to suit the biomedical or clinical task. The DSC++ loss overcomes the major limitation of the DSC loss, providing a suitable loss function for training deep learning segmentation models for use in biomedical and clinical practice. Source code is available at https://github.com/mlyg/DicePlusPlus

Enhancing the Financial Returns of R&D Investments through Operations Management

Although much research has been carried out to examine various contextual issues and moderating factors for successful R&D investments, very little research has been conducted to explore the role of a firm’s operational and process characteristics. In this study, we explore how firms could possibly enhance the financial returns of R&D investments through quality management, using Six Sigma implementation as an example, and efficiency improvement, using the stochastic frontier estimation of relative efficiency as a proxy. Based on data from 468 manufacturing firms in the U.S. over the period 2007-2014, we construct a dynamic panel data model to capture the effects of R&D investments on firms’ financial returns in terms of Tobin’s q. Using the system generalized method of moments estimator, our results indicate that the financial returns of R&D investments are significantly enhanced when firms adopt Six Sigma and improve efficiency in operations. Our additional analyses further suggest that such an enhancement effect through quality and efficiency improvements is more pronounced under high operational complexity as approximated by labor intensity and geographical diversity. Instead of considering innovation activities and process management as contradictory functions, we show that quality and efficiency improvements indeed support firms’ R&D investments, leading to higher financial returns