Causal graph dynamics

We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that information can only ever be transmitted at a bounded speed, with respect to the distance given by the graph. The notion of translation-invariance is also generalized. The definition we provide for these "causal graph dynamics" is simple and axiomatic. The theorems we provide also show that it is robust. For instance, causal graph dynamics are stable under composition and under restriction to radius one. In the finite case some fundamental facts of Cellular Automata theory carry through: causal graph dynamics admit a characterization as continuous functions, and they are stable under inversion. The provided examples suggest a wide range of applications of this mathematical object, from complex systems science to theoretical physics. KEYWORDS: Dynamical networks, Boolean networks, Generative networks automata, Cayley cellular automata, Graph Automata, Graph rewriting automata, Parallel graph transformations, Amalgamated graph transformations, Time-varying graphs, Regge calculus, Local, No-signalling.Comment: 25 pages, 9 figures, LaTeX, v2: Minor presentation improvements, v3: Typos corrected, figure adde

Peacemaking among inconsistent rationalities?

Kacelnik, Schuck-Paim and Pompilio (this volume, p. 377) show that rationality axioms from economics are neither necessary nor sufficient to guarantee that animal behavior is biologically adaptive. To illustrate that biological adaptiveness does not imply conformity with the consistency axioms of economics, Kacelnik et al describe animals that sensibly experiment with actions yielding sub-maximum levels of short-term energy intake to monitor their environments for change, leading to apparently intransitive patterns of choice that are nevertheless biologically adaptive. Invalidating the converse claim that economic rationality implies biological adaptiveness is Kacelnik et al’s example of female ruffs that are worse off when they conform to the constant-ratio rule, frequently interpreted as a normative consistency requirement of economic rationality. Together, the two examples demonstrate that axiomatic norms are both unnecessary and insufficient for determining whether a particular behavior is biologically adaptive. Additionally, Kacelnik et al call into question what has been reported in the animal behavior literature as preference reversals, such as risk attitudes among wild rufous hummingbirds or the food-hoarding propensities of grey jays. Kacelnik et al attribute apparent reversals to state-dependent fitness functions modulated by subtle differences in the training phase of animal experiments. For example, animals trained on menus that include a strictly dominated option will tend to have lower accumulated energy reserves and therefore exhibit systematically different patterns of choice––not because they fail to maximize, but because their training has induced systematically different nutritional states. Another possible explanation for preference reversals in animal studies with strictly dominated, or “decoy” options is that menus containing dominated items may convey valid information about future opportunities (Houston and McNamara, 1999). If menus are correlated through time, then menus with inferior options today predict scarcity in the future and imply a distinct optimal course of action, in violation of regularity assumptions that posit invariance with respect to the inclusion of strictly dominated alternatives. In environments with payoff structures that can be modeled as cooperative games, a family’s best response sometimes requires individual family members to behave suboptimally as part of a diversification strategy that reduces the risk of reproductive failure (Hutchinson, 1996). Futhermore, theoretical biologists have documented the fragility of expected fitness maximizing behaviour with respect to the assumption of stable environments. Once the model allows for shocks to the environment’s stochastic structure, simple behavior rules that are suboptimal (in terms of expected fitness) when viewed narrowly from the perspective of unchanging payoffs in a fixed environment may outperform rules based on maximazation within a static small world (Bookstaber and Langsam, 1985).Rationality, rationalities, irrationality, bounded rationality, biology, biological rationality

Managing Cultural Diversity in the Multinational Corporate Workplace: Solution or Symptom?

The aim of this paper is to show the critical relevance of post-structuralist political theory to cross-cultural management studies. By emphasizing the key role that questions of identity, difference, and struggle play in the multinational corporate context, we argue for a shift in our understandings away from essentialist conceptions of culture to an explicitly critical and political understanding of the way culture and cultural difference is invoked. Of crucial importance in understanding the nature of the shift of perspective we advocate is the affirmation of a negative ontology for which the radical contingency of social relations is axiomatic

Toward an Organizational Theory of Membership Structural Design

Various events have led to the development of highly complex cooperative operations and to concepts for understanding operations. However. development of membership structures and concepts for understanding these structures has lagged. This paper imports organizational design and contingency theory into the member control literature. Membership structure is understood as organization-like, producing a service (Le., member control). Member control structure is understood as having three aspects (representation, policy making, and oversight) and two environments (the members themselves, and management and operations). Building from cooperative principles and following the development of cooperatives from simple to complex organizations, this paper develops a series of axiomatic propositions for understanding and designing membership structure. Only some of the propositions are testable, and still others are meant only to give continuity and relevance to the propositions as a group (as a theory). Such work should help develop a language for understanding and furthering discussion and research of membership structure and member control in agricultural cooperatives.Agribusiness,

Comparing Multidimensional Indices of Inequality: methods and application

The paper provides an examination into the measures of multidimensional inequality proposed in the past few years, their properties and majorization criteria. It offers a generalisation of Bourguignon index proposed so that it includes Tsui measures (1999) while preserving the virtues of Maasoumi’s method (1986) of explicitly acknowledging the role of parameters relevant of multivariate settings. An application to the Argentine data is provided to illustrate the decisions involved in the process of applying these measures and the usefulness of having appropriate criteria for the choice.Inequalities, Multidimensional Distributions, Well-being, Multivariate indices.

Knowledge Agents Represented by Knowledge Functions

Knowledge as the basis of science has up to now only verbally defined features which are not accepted between all sciences. On the other hand knowledge must have some interoperable, physical related features since otherwise we wouldn’t be able to exchange knowledge between humans. With the discovery of operable features knowledge becomes, like information, a tool for interdisciplinary use. It is analysed how this discovery can also contribute to the concept of economic agents. The fundamental frame for agent concepts is set by physical condi-tions, which are explained. It is shown how within this frame operable knowledge can act in a way that new economic features appear. Operable knowledge features present a structure of knowledge which is independent of the specific meaning or use of knowledge. This discovery presents a completely new mathematically based concept of knowledge for different disciplines like economy, sociology, communication science, physics or biology. It is explained how this arises by extending the well known Shannon concept of information. It is shown how competence and innovation appear as specific features of knowledge. Also it is explained how knowledge adds value to money. Some initial practical results of a pilot project in a company are discussed. Hints for application in different disciplines are given.bit of knowledge, measure of knowledge, knowledge functions of agents, quantization of knowledge