A model of adaptive decision making from representation of information environment by quantum fields

We present the mathematical model of decision making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioral, and geo-political factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are of the purely informational nature. The QFT-model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism (QBism). We demonstrate the quantum-like interference effect in DM which is exhibited as a violation of the formula of total probability and hence the classical Bayesian inference scheme.Comment: in press in Philosophical Transactions

Overview on agent-based social modelling and the use of formal languages

Transdisciplinary Models and Applications investigates a variety of programming languages used in validating and verifying models in order to assist in their eventual implementation. This book will explore different methods of evaluating and formalizing simulation models, enabling computer and industrial engineers, mathematicians, and students working with computer simulations to thoroughly understand the progression from simulation to product, improving the overall effectiveness of modeling systems.Postprint (author's final draft

Model Creation and Equivalence Proofs of Cellular Automata and Artificial Neural Networks

Computational methods and mathematical models have invaded arguably every scientific discipline forming its own field of research called computational science. Mathematical models are the theoretical foundation of computational science. Since Newton's time, differential equations in mathematical models have been widely and successfully used to describe the macroscopic or global behaviour of systems. With spatially inhomogeneous, time-varying, local element-specific, and often non-linear interactions, the dynamics of complex systems is in contrast more efficiently described by local rules and thus in an algorithmic and local or microscopic manner. The theory of mathematical modelling taking into account these characteristics of complex systems has to be established still. We recently presented a so-called allagmatic method including a system metamodel to provide a framework for describing, modelling, simulating, and interpreting complex systems. Implementations of cellular automata and artificial neural networks were described and created with that method. Guidance from philosophy were helpful in these first studies focusing on programming and feasibility. A rigorous mathematical formalism, however, is still missing. This would not only more precisely describe and define the system metamodel, it would also further generalise it and with that extend its reach to formal treatment in applied mathematics and theoretical aspects of computational science as well as extend its applicability to other mathematical and computational models such as agent-based models. Here, a mathematical definition of the system metamodel is provided. Based on the presented formalism, model creation and equivalence of cellular automata and artificial neural networks are proved. It thus provides a formal approach for studying the creation of mathematical models as well as their structural and operational comparison.Comment: 13 pages, 1 tabl

A framework for epidemic spreading in multiplex networks of metapopulations

We propose a theoretical framework for the study of epidemics in structured metapopulations, with heterogeneous agents, subjected to recurrent mobility patterns. We propose to represent the heterogeneity in the composition of the metapopulations as layers in a multiplex network, where nodes would correspond to geographical areas and layers account for the mobility patterns of agents of the same class. We analyze both the classical Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models within this framework, and compare macroscopic and microscopic indicators of the spreading process with extensive Monte Carlo simulations. Our results are in excellent agreement with the simulations. We also derive an exact expression of the epidemic threshold on this general framework revealing a non-trivial dependence on the mobility parameter. Finally, we use this new formalism to address the spread of diseases in real cities, specifically in the city of Medellin, Colombia, whose population is divided into six socio-economic classes, each one identified with a layer in this multiplex formalism.Comment: 13 pages, 11 figure