An Agent-Based Model of Mortality Shocks, Intergenerational Effects, and Urban Crime

Rational criminals choose crime over lawfulness because it pays better; hence poverty correlates to criminal behavior. This correlation is an insufficient historical explanation. An agent-based model of urban crime, mortality, and exogenous population shocks supplements the standard economic story, closing the gap with an empirical reality that often breaks from trend. Agent decision making within the model is built around a career maximization function, with life expectancy as the key independent variable. Rational choice takes the form of a local information heuristic, resulting in subjectively rational suboptimal decision making. The effects of population shocks are explored using the Crime and Mortality Simulation (CAMSIM), with effects demonstrated to persist across generations. Past social trauma are found to lead to higher crime rates which subsequently decline as the effect degrades, though \'aftershocks\' are often experienced.Agent-Based Model, Crime, Bounded Rationality, Life Expectancy, Rational Choice

Religious Extremism, Clubs, and Civil Liberties: A Model of Religious Populations

This paper extends the club model of religion to better account for observed patterns of extremism. We adapt existing models to a multi-agent framework and analyze the distribution of agents and clubs. We find that extremism is more successful when religious groups are able to produce close substitutes for standard goods and that increased access to publicly provided goods can reduce the extremist population share. Quantile regression modeling of data from a multi-nation survey and institutional indices corresponds to the model’s key results. Our findings offer a mechanism supporting research linking terrorist origination to civil liberties.Extremism, Religion, Sacrifice and Stigma, Multi-Agent Model, Civil Liberties

Religion, Clubs, and Emergent Social Divides

Arguments for and against the existence of an American cultural divide are frequently placed in a religious context. This paper seeks to establish that, all politics aside, the American religious divide is real, that modern religious polarization is not a uniquely American phenomenon, and that religious divides can be understood as naturally emergent within the club theory of religion. Analysis of the 2005 Baylor Religion reveals a bimodal distribution of religious commitment in the US. International survey data reveals bimodal distributions in twenty-eight of thirty surveyed countries. The club theory of religion, when applied in a multi-agent model, generates bimodal distributions of religious commitment whose emergence correlates to substitutability of club goods for standard goods and the mean population wage rate. Ramifications of religious bimodality include potential instability of majority rule electoral outcomes. Median estimators, such as majority rule democracy, are non-robust with bimodal distributions. When religion is politically salient and polarized, small errors can disproportionately shift the election result from the preferences of the median voter.Culture Divide, Religious Divide, Club Theory, Multi-Agent Model, Sacrifice

On the exact learnability of graph parameters: The case of partition functions

We study the exact learnability of real valued graph parameters $f$ which are known to be representable as partition functions which count the number of weighted homomorphisms into a graph $H$ with vertex weights $\alpha$ and edge weights $\beta$. M. Freedman, L. Lov\'asz and A. Schrijver have given a characterization of these graph parameters in terms of the $k$-connection matrices $C(f,k)$ of $f$. Our model of learnability is based on D. Angluin's model of exact learning using membership and equivalence queries. Given such a graph parameter $f$, the learner can ask for the values of $f$ for graphs of their choice, and they can formulate hypotheses in terms of the connection matrices $C(f,k)$ of $f$. The teacher can accept the hypothesis as correct, or provide a counterexample consisting of a graph. Our main result shows that in this scenario, a very large class of partition functions, the rigid partition functions, can be learned in time polynomial in the size of $H$ and the size of the largest counterexample in the Blum-Shub-Smale model of computation over the reals with unit cost.Comment: 14 pages, full version of the MFCS 2016 conference pape

Weighted Automata and Monadic Second Order Logic

Let S be a commutative semiring. M. Droste and P. Gastin have introduced in 2005 weighted monadic second order logic WMSOL with weights in S. They use a syntactic fragment RMSOL of WMSOL to characterize word functions (power series) recognizable by weighted automata, where the semantics of quantifiers is used both as arithmetical operations and, in the boolean case, as quantification. Already in 2001, B. Courcelle, J.Makowsky and U. Rotics have introduced a formalism for graph parameters definable in Monadic Second order Logic, here called MSOLEVAL with values in a ring R. Their framework can be easily adapted to semirings S. This formalism clearly separates the logical part from the arithmetical part and also applies to word functions. In this paper we give two proofs that RMSOL and MSOLEVAL with values in S have the same expressive power over words. One proof shows directly that MSOLEVAL captures the functions recognizable by weighted automata. The other proof shows how to translate the formalisms from one into the other.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Finiteness conditions for graph algebras over tropical semirings

Connection matrices for graph parameters with values in a field have been introduced by M. Freedman, L. Lov{\'a}sz and A. Schrijver (2007). Graph parameters with connection matrices of finite rank can be computed in polynomial time on graph classes of bounded tree-width. We introduce join matrices, a generalization of connection matrices, and allow graph parameters to take values in the tropical rings (max-plus algebras) over the real numbers. We show that rank-finiteness of join matrices implies that these graph parameters can be computed in polynomial time on graph classes of bounded clique-width. In the case of graph parameters with values in arbitrary commutative semirings, this remains true for graph classes of bounded linear clique-width. B. Godlin, T. Kotek and J.A. Makowsky (2008) showed that definability of a graph parameter in Monadic Second Order Logic implies rank finiteness. We also show that there are uncountably many integer valued graph parameters with connection matrices or join matrices of fixed finite rank. This shows that rank finiteness is a much weaker assumption than any definability assumption.Comment: 12 pages, accepted for presentation at FPSAC 2014 (Chicago, June 29 -July 3, 2014), to appear in Discrete Mathematics and Theoretical Computer Scienc