Heterogeneity, convergence, and autocorrelations

This paper is a contribution to the literature on the explanatory power and calibration of heterogeneous asset pricing models. We set out a new stochastic market-fraction asset pricing model of fundamentalists and trend followers under a market maker. Our model explains key features of financial market behaviour such as market dominance, convergence to the fundamental price and under- and over-reaction. We use the dynamics of the underlying deterministic system to characterize these features and statistical properties, including convergence of the limiting distribution and autocorrelation structure. We confirm these properties using Monte Carlo simulations.

Compositional Divergence and Convergence in Local Communities and Spatially Structured Landscapes

Community structure depends on both deterministic and stochastic processes. However, patterns of community dissimilarity (e.g. difference in species composition) are difficult to interpret in terms of the relative roles of these processes. Local communities can be more dissimilar (divergence) than, less dissimilar (convergence) than, or as dissimilar as a hypothetical control based on either null or neutral models. However, several mechanisms may result in the same pattern, or act concurrently to generate a pattern, and much research has recently been focusing on unravelling these mechanisms and their relative contributions. Using a simulation approach, we addressed the effect of a complex but realistic spatial structure in the distribution of the niche axis and we analysed patterns of species co-occurrence and beta diversity as measured by dissimilarity indices (e.g. Jaccard index) using either expectations under a null model or neutral dynamics (i.e., based on switching off the niche effect). The strength of niche processes, dispersal, and environmental noise strongly interacted so that niche-driven dynamics may result in local communities that either diverge or converge depending on the combination of these factors. Thus, a fundamental result is that, in real systems, interacting processes of community assembly can be disentangled only by measuring traits such as niche breadth and dispersal. The ability to detect the signal of the niche was also dependent on the spatial resolution of the sampling strategy, which must account for the multiple scale spatial patterns in the niche axis. Notably, some of the patterns we observed correspond to patterns of community dissimilarities previously observed in the field and suggest mechanistic explanations for them or the data required to solve them. Our framework offers a synthesis of the patterns of community dissimilarity produced by the interaction of deterministic and stochastic determinants of community assembly in a spatially explicit and complex context.

The Effect of Human RIghts on Criminal Evidentiary Processes: Convergence, Divergence or Realignment?

This article examines the contribution which the European Court of Human Rights has made to the development of common evidentiary processes across the common law and civil law systems of criminal procedure in Europe. It is argued that the continuing use of terms such as 'adversarial' and 'inquisitorial' to describe models of criminal proof and procedure has obscured the genuinely transformative nature of the Court's jurisprudence. It is shown that over a number of years the Court has been steadily developing a new model of proof that is better characterised as 'participatory' than as 'adversarial' or 'inquisitorial'. Instead of leading towards a convergence of existing 'adversarial' and 'inquisitorial' models of proof, this is more likely to lead towards a realignment of existing processes of proof which nonetheless allows plenty of scope for diverse application in different institutional and cultural settings.

Second-Order Training of Adaptive Critics for Online Process Control

A new algorithm for training of nonlinear optimal neuro-controllers (in the form of the model-free, action-dependent, adaptive critic paradigm). Overcomes problems with existing stochastic backpropagation training: need for data storage, parameter shadowing and poor convergence, offering significant benefits for online applications.

Analytical description of stochastic field-Line wandering in magnetic turbulence

A nonperturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line wandering (random walk) is derived. By considering the solution of this equation for different limits several new results are obtained. As an example, it is demonstrated that the stochastic wandering of magnetic field-lines in a two-component turbulence model leads to superdiffusive transport, contrary to an existing diffusive picture. The validity of quasilinear theory for field-line wandering is discussed, with respect to different turbulence geometry models, and previous diffusive results are shown to be deduced in appropriate limits.