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The dynamical evolution of many economic, sociological, biological and physical systems tends to be dominated by a relatively small number of unexpected, large changes (`extreme events'). We study the large, internal changes produced in a…
Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…
Statistical science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators - even for purely descriptive goals. Statistical decision theory requires more…
This survey reviews recent developments in revealed preference theory. It discusses the testable implications of theories of choice that are germane to specific economic environments. The focus is on expected utility in risky environments;…
It is usually believed that Darwin's theory leads to a smooth gradual evolution, so that mass extinctions must be caused by external shocks. However, it has recently been argued that mass extinctions arise from the intrinsic dynamics of…
Most people agree that human activities are consistent with physical laws. One may naturally think that sensible economic theories can be derived from physical laws and evolutionary principles. This is indeed the case. In this paper, we…
Current concerns about reproducibility in many research communities can be traced back to a high value placed on empirical reproducibility of the physical details of scientific experiments and observations. For example, the detailed…
This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators…
Predicting competitive outcomes typically requires fitting dynamical models to data, from which interaction strengths and coexistence indicators such as invasion criteria can be produced. Methods that allow to propagate parameter…
We present a dynamical theory of statistical convergence in which the law of large numbers arises from outcome-outcome feedback rather than assumed independence. Defining the convergence field and its derivative, we show that empirical…
This book invites readers to see mathematics not just as formulas and rules, but as the deepest expression of human thought. It begins by exploring the timeless idea of mathematics as a universal language, contrasting its precision with the…
Ecology and evolution are inseparable. Motivated by some recent experiments, we have developed models of evolutionary ecology from the perspective of dynamic networks. In these models, in addition to the intra-node dynamics, which…
The risk-sensitive foraging theory formulated in terms of the (daily) energy budget rule has been influential in behavioural ecology as well as other disciplines. Predicting risk-aversion on positive budgets and risk-proneness on negative…
The interrelationship between energy and probability conservation is explored from the point of view of statistical physics and non-relativistic quantum mechanics. The simultaneous validity of the law of conservation of energy and the…
In 1972, Robert May triggered a worldwide research program studying ecological communities using random matrix theory. Yet, it remains unclear if and when we can treat real communities as random ecosystems. Here, we draw on recent progress…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
Recent theoretical progress in nonequilibrium thermodynamics, linking the physical principle of Maximum Entropy Production ("MEP") to the information-theoretical "MaxEnt" principle of scientific inference, together with conjectures from…
Recently, there has been a discussion on the origin of the quantum probability rules (Deutsch quant-ph/9906015, Polley quant-ph/9906124, Barnum et al. quant-ph/9907024, Finkelstein quant-ph/9907004). This contribution, which is a slightly…
The ecological principle of limiting similarity dictates that species similar in resource requirements will compete, with the superior eventually excluding the inferior competitor from the community. The observation that nonetheless…
Several simple growth and decay models use concepts and measures from fractal geometry. Kinetic models relevant to condensed matter observations arerecalled. They should be specifically adapted with appropriate degrees of freedom in order…