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Register a new userToward a General Theory of Societal Collapse. A Biophysical Examination of Tainter s Model of the Diminishing Returns of Complexity
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The collapse of large social systems, often referred to as civilizations or empires, is a well known historical phenomenon, but its origins are the object of an unresolved debate. In this paper, we present a simple biophysical model which we link to the concept that societies collapse because of the diminishing returns of complexity proposed by Joseph Tainter. Our model is based on the description of a socioeconomic system as a trophic chain of energy stocks which dissipate the energy potential of the available resources. The model produces various trajectories of decline, in some cases rapid enough that they can be defined as collapses. At the same time, we observe that the exploitation of the resource stock (production) has a strongly nonlinear relationship with the complexity of the system, assumed to be proportional to the size of the stock termed bureaucracy. These results provide support for Tainter s hypothesis.
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We study properties of quantum strategies, which are complete specifications of a given partys actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus on a representation of quantum strategies that generalizes the Choi-Jamio{l}kowski representation of quantum operations. This new representation associates with each strategy a positive semidefinite operator acting only on the tensor product of its input and output spaces. Various facts about such representations are established, and two applications are discussed: the first is a new and conceptually simple proof of Kitaevs lower bound for strong coin-flipping, and the second is a proof of the exact characterization QRG = EXP of the class of problems having quantum refereed games.
A general construction of transmutation operators is developed for selfadjoint operators in Gelfand triples. Theorems regarding analyticity of generalized eigenfunctions and Paley-Wiener properties are proved.
In this paper, we discuss the current status of core collapse supernova models and the future developments needed to achieve significant advances in understanding the supernova mechanism and supernova phenomenology, i.e., in developing a supernova standard model.
In this paper we address the question of the size distribution of firms. To this aim, we use the Bloomberg database comprising multinational firms within the years 1995-2003, and analyze the data of the sales and the total assets of the separate financial statement of the Japanese and the US companies, and make a comparison of the size distributions between the Japanese companies and the US companies. We find that (i) the size distribution of the US firms is approximately log-normal, in agreement with Gibrats observation (Gibrat 1931), and in contrast (ii) the size distribution of the Japanese firms is clearly not log-normal, and the upper tail of the size distribution follows the Pareto law. It agree with the predictions of the Simon model (Simon 1955). Key words: the size distribution of firms, the Gibrats law, and the Pareto law
Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that the damage in the network due to a failure is a continuous function of the fraction of failed nodes. In sharp contrast, in NetONet, due to the cascading failures, the percolation transition may be discontinuous and even a single node failure may lead to abrupt collapse of the system. We demonstrate our general framework for a NetONet composed of $n$ classic ErdH{o}s-R{e}nyi (ER) networks, where each network depends on the same number $m$ of other networks, i.e., a random regular network of interdependent ER networks. In contrast to a emph{treelike} NetONet in which the size of the largest connected cluster (mutual component) depends on $n$, the loops in the RR NetONet cause the largest connected cluster to depend only on $m$. We also analyzed the extremely vulnerable feedback condition of coupling. In the case of ER networks, the NetONet only exhibits two phases, a second order phase transition and collapse, and there is no first phase transition regime unlike the no feedback condition. In the case of NetONet composed of RR networks, there exists a first order phase transition when $q$ is large and second order phase transition when $q$ is small. Our results can help in designing robust interdependent systems.
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