Evaluating foam heterogeneity

New analytical tool is available to calculate the degree of foam heterogeneity based on the measurement of gas diffusivity values. Diffusion characteristics of plastic foam are described by a system of differential equations based on conventional diffusion theory. This approach saves research and computation time in studying mass or heat diffusion problems

Symmetry based Structure Entropy of Complex Networks

Precisely quantifying the heterogeneity or disorder of a network system is very important and desired in studies of behavior and function of the network system. Although many degree-based entropies have been proposed to measure the heterogeneity of real networks, heterogeneity implicated in the structure of networks can not be precisely quantified yet. Hence, we propose a new structure entropy based on automorphism partition to precisely quantify the structural heterogeneity of networks. Analysis of extreme cases shows that entropy based on automorphism partition can quantify the structural heterogeneity of networks more precisely than degree-based entropy. We also summarized symmetry and heterogeneity statistics of many real networks, finding that real networks are indeed more heterogenous in the view of automorphism partition than what have been depicted under the measurement of degree based entropies; and that structural heterogeneity is strongly negatively correlated to symmetry of real networks.Comment: 7 pages, 6 figure

Heterogeneity induces spatiotemporal oscillations in reaction-diffusions systems

We report on a novel instability arising in activator-inhibitor reaction-diffusion (RD) systems with a simple spatial heterogeneity. This instability gives rise to periodic creation, translation, and destruction of spike solutions that are commonly formed due to Turing instabilities. While this behavior is oscillatory in nature, it occurs purely within the Turing space such that no region of the domain would give rise to a Hopf bifurcation for the homogeneous equilibrium. We use the shadow limit of the Gierer-Meinhardt system to show that the speed of spike movement can be predicted from well-known asymptotic theory, but that this theory is unable to explain the emergence of these spatiotemporal oscillations. Instead, we numerically explore this system and show that the oscillatory behavior is caused by the destabilization of a steady spike pattern due to the creation of a new spike arising from endogeneous activator production. We demonstrate that on the edge of this instability, the period of the oscillations goes to infinity, although it does not fit the profile of any well known bifurcation of a limit cycle. We show that nearby stationary states are either Turing unstable, or undergo saddle-node bifurcations near the onset of the oscillatory instability, suggesting that the periodic motion does not emerge from a local equilibrium. We demonstrate the robustness of this spatiotemporal oscillation by exploring small localized heterogeneity, and showing that this behavior also occurs in the Schnakenberg RD model. Our results suggest that this phenomenon is ubiquitous in spatially heterogeneous RD systems, but that current tools, such as stability of spike solutions and shadow-limit asymptotics, do not elucidate understanding. This opens several avenues for further mathematical analysis and highlights difficulties in explaining how robust patterning emerges from Turing's mechanism in the presence of even small spatial heterogeneity

Heterogeneity of Research Results: A New Perspective From Which to Assess and Promote Progress in Psychological Science

Heterogeneity emerges when multiple close or conceptual replications on the same subject produce results that vary more than expected from the sampling error. Here we argue that unexplained heterogeneity reflects a lack of coherence between the concepts applied and data observed and therefore a lack of understanding of the subject matter. Typical levels of heterogeneity thus offer a useful but neglected perspective on the levels of understanding achieved in psychological science. Focusing on continuous outcome variables, we surveyed heterogeneity in 150 meta-analyses from cognitive, organizational, and social psychology and 57 multiple close replications. Heterogeneity proved to be very high in meta-analyses, with powerful moderators being conspicuously absent. Population effects in the average meta-analysis vary from small to very large for reasons that are typically not understood. In contrast, heterogeneity was moderate in close replications. A newly identified relationship between heterogeneity and effect size allowed us to make predictions about expected heterogeneity levels. We discuss important implications for the formulation and evaluation of theories in psychology. On the basis of insights from the history and philosophy of science, we argue that the reduction of heterogeneity is important for progress in psychology and its practical applications, and we suggest changes to our collective research practice toward this end

Learning about heterogeneity in returns to schooling

Using data from the National Longitudinal Survey of Youth (NLSY) we introduce and estimate various Bayesian hierarchical models that investigate the nature of unobserved heterogeneity in returns to schooling. We consider a variety of possible forms for the heterogeneity, some motivated by previous theoretical and empirical work and some new ones, and let the data decide among the competing specifications. Empirical results indicate that heterogeneity is present in returns to education. Furthermore, we find strong evidence that the heterogeneity follows a continuous rather than a discrete distribution, and that bivariate normality provides a very reasonable description of individual-level heterogeneity in intercepts and returns to schooling