Adaptive Probability Theory: Human Biases as an Adaptation

Humans make mistakes in our decision-making and probability judgments. While the heuristics used for decision-making have been explained as adaptations that are both efficient and fast, the reasons why people deal with probabilities using the reported biases have not been clear. We will see that some of these biases can be understood as heuristics developed to explain a complex world when little information is available. That is, they approximate Bayesian inferences for situations more complex than the ones in laboratory experiments and in this sense might have appeared as an adaptation to those situations. When ideas as uncertainty and limited sample sizes are included in the problem, the correct probabilities are changed to values close to the observed behavior. These ideas will be used to explain the observed weight functions, the violations of coalescing and stochastic dominance reported in the literature

Synchronisation Induced by Repulsive Interactions in a System of van der Pol Oscillators

We consider a system of identical van der Pol oscillators, globally coupled through their velocities, and study how the presence of competitive interactions affects its synchronisation properties. We will address the question from two points of view. Firstly, we will investigate the role of competitive interactions on the synchronisation among identical oscillators. Then, we will show that the presence of an intermediate fraction of repulsive links results in the appearance of macroscopic oscillations at that signal's rhythm, in regions where the individual oscillator is unable to synchronise with a weak external signal

Cosmic Strings in an Open Universe: Quantitative Evolution and Observational Consequences

The cosmic string scenario in an open universe is developed -- including the equations of motion, a model of network evolution, the large angular scale CMB temperature anisotropy, and the power spectrum of density fluctuations produced by cosmic strings with dark matter. First we derive the equations of motion for cosmic string in an open FRW space-time and construct a quantitative model of the evolution of the gross features of a cosmic string network. Second, we apply this model of network evolution to estimate the rms CMB temperature anisotropy induced by cosmic strings, obtaining the normalization for the mass per unit length $\mu$ as a function of $\Omega$. Third, we consider the effects of the network evolution and normalization in an open universe on the large scale structure formation scenarios with either cold or hot dark matter.Comment: 15 pages, Latex, 3 postscript figures, accepted for publication in Phys. Rev.