Warfare is commonly viewed as a driving force of the process of aggregation of initially independent villages into larger and more complex political units that started several thousand years ago and quickly lead to the appearance of chiefdoms, states, and empires. Here we build on extensions and generalizations of Carneiro’s (1970) argument to develop a spatially explicit agent-based model of the emergence of early complex societies via warfare. In our model polities are represented as hierarchically structured networks of villages whose size, power, and complexity change as a result of conquest, secession, internal reorganization (via promotion and linearization), and resource dynamics. A general prediction of our model is continuous stochastic cycling in which the growth of individual polities in size, wealth/power, and complexity is interrupted by their quick collapse. The model dynamics are mostly controlled by two parameters, one of which scales the relative advantage of wealthier polities in between and within-polity conflicts, and the other is the chief’s expected time in power. Our results demonstrate that the stability of large and complex polities is strongly promoted if the outcomes of the conflicts are mostly determined by the polities’ wealth/power, if there exist well-defined and accepted means of succession, and if control mechanisms are internally specialized.
Pre-2018 CSE ID: CS2007-0887
As the amount of data collected in our world increases, reliable compression algorithms are needed when datasets become too large for practical analysis, when significant noise is present in the data, or when the strongest signals in the data are needed. In this work, two data compression algorithms are presented. The main result is a low-rank approximation algorithm (a type of compression algorithm) that uses modern techniques in randomization to repurpose a classic algorithm in the field of linear algebra called the LU decomposition to perform data compression. The resulting algorithm is called Spectrum-Revealing LU (SRLU).
Both rigorous theory and numeric experiments demonstrate the effectiveness of SRLU. The theoretical work presented also develops a framework with which other low-rank approximation algorithms can be analyzed. As the name implies, Spectrum-Revealing LU seeks to capture the entire spectrum of the data (i.e. to capture all signals present in the data).
A second compression algorithm is also introduced, which seeks to compression graphs. Called a sparsification algorithm, this algorithm can accept a weighted or unweighted graph and produce an approximation without changing the weights (or introducing weights in the case of an unweighted graph). Theoretical results provide a bound on the quality of the results, and a numeric example is also explored.
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