Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the investigated variables. A non-equilibrium difference of money temperatures between different systems generates net fluxes of money and population. To describe income distribution, a stochastic process with additive and multiplicative components is introduced. The resultant distribution interpolates between exponential at the low end and power law at the high end, in agreement with the empirical data for USA. We show that the increase of income inequality in USA originates primarily from the increase of the income fraction going to the upper tail, which now exceeds 20% of the total income. Analyzing the data from the World Resources Institute, we find that the distribution of energy consumption per capita around the world can be approximately described by the exponential function. Comparing the data for 1990, 2000, and 2005, we discuss the effect of globalization on the inequality of energy consumption. Physics ‡ Throughout the paper, we use the indices k and n to label the money bins m k and the indices i and j to label the individual money balances m i of the agents.

Summary Switch-like activation of the Spindle Assembly Checkpoint (SAC) is critical for accurate chromosomes segregation and for cell division in a timely manner. To determine the mechanisms that achieve this, we engineered an ectopic, kinetochore-independent SAC activator: the “eSAC”. The eSAC stimulates SAC signaling by artificially dimerizing Mps1 kinase domain and a cytosolic KNL1 phosphodomain, the kinetochore signaling scaffold. By exploiting variable eSAC expression in a cell population, we defined the dependence of the eSAC-induced mitotic delay on eSAC concentration in a cell to reveal the dose-response behavior of the core signaling cascade of the SAC. These quantitative analyses and subsequent mathematical modeling of the dose-response data uncover two crucial properties of the core SAC signaling cascade: (1) a cellular limit on the maximum anaphase-inhibitory signal that the cascade can generate due to the limited supply of SAC proteins, and (2) the ability of the KNL1 phosphodomain to produce the anaphase-inhibitory signal synergistically, when it recruits multiple SAC proteins simultaneously. We propose that these properties together achieve inverse, non-linear scaling between the signal output per kinetochore and the number of signaling kinetochores. When the number of kinetochores is low, synergistic signaling by KNL1 enables each kinetochore to produce a disproportionately strong signal output. However, when many kinetochores signal concurrently, they compete for a limited supply of SAC proteins. This frustrates synergistic signaling and lowers their signal output. Thus, the signaling activity of unattached kinetochores will adapt to the changing number of signaling kinetochores to enable the SAC to approximate switch-like behavior.

We analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The log-normal and gamma functions do not improve the fit significantly, despite having more parameters, and mimic the exponential function. We find that the probability density at zero income is not zero, which contradicts the log-normal and gamma distributions, but is consistent with the exponential one. The high-resolution histogram of the probability density shows a very sharp and narrow peak at low incomes, which we interpret as the result of a government policy on income redistribution.Comment: 7 pages, 4 figures, Proceedings of the Econophysics Colloquium, Canberra, 14-18 November 200

In recent years, fluorescence microscopy has enabled researchers to observe the dynamics of clathrin-coated pit (CCP) assembly in real time. The assembly dynamics of CCPs shows striking heterogeneity. Some CCPs are long-lived (productive CCPs); they bind cargo and grow in size to form clathrin-coated vesicles. In contrast, other CCPs (abortive CCPs) are relatively short-lived and disassemble well before reaching vesicle size. Within both populations there is significant variance in CCP lifetime. We propose a stochastic biophysical model that links these observations with the energetics of CCPs and kinetics of their assembly. We show that without cargo, CCP assembly faces a high energy barrier that is difficult to overcome. As a consequence, CCPs without cargo are almost always abortive. We suggest a mechanism by which cargo binding stabilizes CCPs and facilitates their growth. The lifetime distribution of abortive pits calculated from our model agrees well with published experimental data. We also estimate the lifetimes of productive CCPs and show that the stochastic nature of CCP assembly plays a crucial role in causing their observed wide distribution.