L\'evy-like behavior in deterministic models of intelligent agents exploring heterogeneous environments

Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually rely on mental maps to explore strongly heterogeneous environments. In this work we study a model of a deterministic walker, visiting sites randomly distributed on the plane and with varying weight or attractiveness. At each step, the walker minimizes a function that depends on the distance to the next unvisited target (cost) and on the weight of that target (gain). If the target weight distribution is a power-law, $p(k)\sim k^{-\beta}$, in some range of the exponent $\beta$, the foraging medium induces movements that are similar to L\'evy flights and are characterized by non-trivial exponents. We explore variations of the choice rule in order to test the robustness of the model and argue that the addition of noise has a limited impact on the dynamics in strongly disordered media.Comment: 15 pages, 7 figures. One section adde

Uncertainty in Economic Growth and Inequality

A step to consilience, starting with a deconstruction of the causality of uncertainty that is embedded in the fundamentals of growth and inequality, following a construction of aggregation laws that disclose the invariance principle across heterogeneous individuals, ending with a reconstruction of metric models that yields deeper structural connections via U.S. GDP and income data

Deterministic chaos theory and forecasting in Social Sciences. Contribution to the discussion

Forecasting social phenomena may be hampered in many ways. This is because in nature of these phenomena lies strong and multilateral connection with other social phenomena; but not only – also physical and biological (natural) ones. The content of this publication constitutes presentation of chosen problems of forecasting in social sciences. The attention in the article was focused among others on deterministic chaos theory, on the attempt of its implementation to phenomena from the scope (or from borderline) of social sciences: economy, logistics, science about safety etc. Moreover, one of the threads of ponderation was the attempt to consider whether it’s possible to create so-called final theory. The aim of the publication is to signalize possibilities of taking advantage of seemingly exotic for “political scientists” methodology of modeling and explaining phenomena, having its source in exact sciences (in chaos theory) to study social phenomena and processes

Deterministic Dynamics and Chaos: Epistemology and Interdisciplinary Methodology

We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary relation between mathematics and psychology, focused on the mathematical theory of deterministic dynamical systems, and in particular, on the theory of chaos. On one hand, there is the direct classic relation: the application of mathematics to psychology. On the other hand, we propose the converse relation which consists in the formulation of new abstract mathematical problems appearing from processes and structures under research of psychology. The bidirectional multidisciplinary relation from-to pure mathematics, largely holds with the "hard" sciences, typically physics and astronomy. But it is rather new, from the social and human sciences, towards pure mathematics

Non-L\'evy mobility patterns of Mexican Me'Phaa peasants searching for fuelwood

We measured mobility patterns that describe walking trajectories of individual Me'Phaa peasants searching and collecting fuelwood in the forests of "La Monta\~na de Guerrero" in Mexico. These one-day excursions typically follow a mixed pattern of nearly-constant steps when individuals displace from their homes towards potential collecting sites and a mixed pattern of steps of different lengths when actually searching for fallen wood in the forest. Displacements in the searching phase seem not to be compatible with L\'evy flights described by power-laws with optimal scaling exponents. These findings however can be interpreted in the light of deterministic searching on heavily degraded landscapes where the interaction of the individuals with their scarce environment produces alternative searching strategies than the expected L\'evy flights. These results have important implications for future management and restoration of degraded forests and the improvement of the ecological services they may provide to their inhabitants.Comment: 15 pages, 4 figures. First version submitted to Human Ecology. The final publication will be available at http://www.springerlink.co

A Formal Sociologic Study of Free Will

We make a formal sociologic study of the concept of free will. By using the language of mathematics and logic, we define what we call everlasting societies. Everlasting societies never age: persons never age, and the goods of the society are indestructible. The infinite history of an everlasting society unfolds by following deterministic and probabilistic laws that do their best to satisfy the free will of all the persons of the society. We define three possible kinds of histories for everlasting societies: primitive histories, good histories, and golden histories. In primitive histories, persons are inherently selfish, and they use their free will to obtain the personal ownerships of all the goods of the society. In good histories, persons are inherently good, and they use their free will to distribute the goods of the society. In good histories, a person is not only able to desire the personal ownership of goods, but is also able to desire that a good be owned by another person. In golden histories, free will is bound by the ethic of reciprocity, which states that "you should wish upon others as you would like others to wish upon yourself". In golden societies, the ethic of reciprocity becomes a law that partially binds free will, and that must be abided at all times. In other words, the verb "should" becomes the verb "must"

Scale-free law: network science and copyright

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