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Register a new userA Tale of Two (and More) Altruists
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We introduce a minimalist dynamical model of wealth evolution and wealth sharing among $N$ agents as a platform to compare the relative merits of altruism and individualism. In our model, the wealth of each agent independently evolves by diffusion. For a population of altruists, whenever any agent reaches zero wealth (that is, the agent goes bankrupt), the remaining wealth of the other $N-1$ agents is equally shared among all. The population is collectively defined to be bankrupt when its total wealth falls below a specified small threshold value. For individualists, each time an agent goes bankrupt (s)he is considered to be dead and no wealth redistribution occurs. We determine the evolution of wealth in these two societies. Altruism leads to more global median wealth at early times; eventually, however, the longest-lived individualists accumulate most of the wealth and are richer and more long lived than the altruists.
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Continuum models of epidemics do not take into account the underlying microscopic network structure of social connections. This drawback becomes extreme during quarantine when most people dramatically decrease their number of social interactions, while others (like cashiers in grocery stores) continue maintaining hundreds of contacts per day. We formulate a two-level model of quarantine. On a microscopic level, we model a single neighborhood assuming a star-network structure. On a mesoscopic level, the neighborhoods are placed on a two-dimensional lattice with nearest neighbors interactions. The modeling results are compared with the COVID-19 data for several counties in Michigan (USA) and the phase diagram of parameters is identified.
The importance of a strict quarantine has been widely debated during the COVID-19 epidemic even from the purely epidemiological point of view. One argument against strict lockdown measures is that once the strict quarantine is lifted, the epidemic comes back, and so the cumulative number of infected individuals during the entire epidemic will stay the same. We consider an SIR model on a network and follow the disease dynamics, modeling the phases of quarantine by changing the node degree distribution. We show that the system reaches different steady states based on the history: the outcome of the epidemic is path-dependent despite the same final node degree distribution. The results indicate that two-phase route to the final node degree distribution (a strict phase followed by a soft phase) are always better than one phase (the same soft one) unless all the individuals have the same number of connections at the end (the same degree); in the latter case, the overall number of infected is indeed history-independent. The modeling also suggests that the optimal procedure of lifting the quarantine consists of releasing nodes in the order of their degree - highest first.
This paper analyses the impact of random failure or attack on the public transit networks of London and Paris in a comparative study. In particular we analyze how the dysfunction or removal of sets of stations or links (rails, roads, etc.) affects the connectivity properties within these networks. We show how accumulating dysfunction leads to emergent phenomena that cause the transportation system to break down as a whole. Simulating different directed attack strategies, we find minimal strategies with high impact and identify a-priory criteria that correlate with the resilience of these networks. To demonstrate our approach, we choose the London and Paris public transit networks. Our quantitative analysis is performed in the frames of the complex network theory - a methodological tool that has emerged recently as an interdisciplinary approach joining methods and concepts of the theory of random graphs, percolation, and statistical physics. In conclusion we demonstrate that taking into account cascading effects the network integrity is controlled for both networks by less than 0.5 % of the stations i.e. 19 for Paris and 34 for London.
Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barabasi-Albert model when applied to protein-protein interaction networks. In this work we derive a master equation for the node degree distribution of networks growing via Duplication and Divergence and we obtain an expression for the total number of links and for the degree distribution as a function of the number of nodes. Using algebra tools we investigate the degree distribution asymptotic behavior. Analytic results show that the network nodes average degree converges if the total mutation rate is greater than 0.5 and diverges otherwise. Treating original and duplicated node mutation rates as independent parameters has no effect on this result. However, difference in these parameters results in a slower rate of convergence and in different degree distributions. The more different these parameters are, the denser the tail of the distribution. We compare the solutions obtained with simulated networks. These results are in good agreement with the expected values from the derived expressions. The method developed is a robust tool to investigate other models for network growing dynamics.
We present a detailed analysis of the self-organization phenomenon in which the stylized facts originate from finite size effects with respect to the number of agents considered and disappear in the limit of an infinite population. By introducing the possibility that agents can enter or leave the market depending on the behavior of the price, it is possible to show that the system self-organizes in a regime with a finite number of agents which corresponds to the stylized facts. The mechanism to enter or leave the market is based on the idea that a too stable market is unappealing for traders while the presence of price movements attracts agents to enter and speculate on the market. We show that this mechanism is also compatible with the idea that agents are scared by a noisy and risky market at shorter time scales. We also show that the mechanism for self-organization is robust with respect to variations of the exit/entry rules and that the attempt to trigger the system to self-organize in a region without stylized facts leads to an unrealistic dynamics. We study the self-organization in a specific agent based model but we believe that the basic ideas should be of general validity.
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