Uniform Random Sample and Symmetric Beta Distribution

N.L. Johnson and S. Kotz introduced in 1990 an interesting family of symmetric distributions which is based on randomly weighted average from uniform random samples. The only example that could be addressed to their work is the so-called "uniformly randomly modified tin" distribution from which two random samples have been computed. In this paper, we generalize a subfamily of their symmetric distributions and identify a concrete instance of this generalized subfamily. That instance turns out to belong to the family of Johnson and Kotz, which had not seemingly received proper attention in the literature

To Reduce Nothingness into a Reference by Falsity

Assuming the absolute nothingness as the most basic object of thought, I present a way to refer to this object, by reducing it onto a primitive object that supersedes and comes right after the absolute nothingness. The new primitive object that is constructed can be regarded as a formal system that can generate some infinite variety of symbols. [The PDF here is outdated, for a recent draft please contact me.

How Can Mathematical Objects Be Real but Mind-Dependent?

Taking mathematics as a language based on empirical experience, I argue for an account of mathematics in which its objects are abstracta that describe and communicate the structure of reality based on some of our ancestral interactions with their environment. I argue that mathematics as a language is mostly invented, and it is mind-dependent in a specific sense. However, the bases of mathematics will characterize it as a real, non-fictional science of structures

Connecting strategy and system dynamics: an example and lessons learned

This article is based on my talk at the 2015 International System Dynamics Conference upon receiving the Jay W. Forrester Award for the article “Impact of growth opportunities and competition on firm-level capability development tradeoffs” (Organization Science 2012; 23(1): 138–154). It summarizes how that research connects strategy concepts with system dynamics (SD) modeling to inform the pressures managers face to focus on the short term as a result of endogenous growth opportunities and competition. Drawing on this example I discuss some potentially useful research tools and assumptions. I close by sharing personal reflections on the process of writing for non-SD academics and why I think making those connections is worthwhile

Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models

When is it better to use agent based (AB) models, and when should differential equation (DE) models be used? Where DE models assume homogeneity and perfect mixing within compartments, AB models can capture heterogeneity in agent attributes and in the network of interactions among them. Using contagious disease as an example, we contrast the dynamics of AB models with those of the corresponding mean-field DE model, specifically, comparing the standard SEIR model-a nonlinear DE-to an explicit AB model of the same system. We examine both agent heterogeneity and the impact of different network structures, including fully connected, random, Watts-Strogatz small world, scale-free, and lattice networks. Surprisingly, in many conditions the AB and DE dynamics are quite similar. Differences between the DE and AB models are not statistically significant on key metrics relevant to public health, including diffusion speed, peak load on health services infrastructure and total disease burden. We explore the conditions under which the AB and DE dynamics differ, and consider implications for managing infectious disease. The results extend beyond epidemiology: from innovation adoption to the spread of rumor and riot to financial panics, many important social phenomena involve analogous processes of diffusion and social contagion

Human Growth and Body Weight Dynamics: An Integrative Systems Model

Quantifying human weight and height dynamics due to growth, aging, and energy balance can inform clinical practice and policy analysis. This paper presents the first mechanism-based model spanning full individual life and capturing changes in body weight, composition and height. Integrating previous empirical and modeling findings and validated against several additional empirical studies, the model replicates key trends in human growth including A) Changes in energy requirements from birth to old ages. B) Short and long-term dynamics of body weight and composition. C) Stunted growth with chronic malnutrition and potential for catch up growth. From obesity policy analysis to treating malnutrition and tracking growth trajectories, the model can address diverse policy questions. For example I find that even without further rise in obesity, the gap between healthy and actual Body Mass Indexes (BMIs) has embedded, for different population groups, a surplus of 14%–24% in energy intake which will be a source of significant inertia in obesity trends. In another analysis, energy deficit percentage needed to reduce BMI by one unit is found to be relatively constant across ages. Accompanying documented and freely available simulation model facilitates diverse applications customized to different sub-populations.National Institutes of Health (U.S.). Office of Behavioral and Social Sciences Research (Contract HHSN276201000004C)National Institutes of Health (U.S.). Office of Behavioral and Social Sciences Research (Contract 1R21HL113680-01)