Algebraic entropy and the space of initial values for discrete dynamical systems

A method to calculate the algebraic entropy of a mapping which can be lifted to an isomorphism of a suitable rational surfaces (the space of initial values) are presented. It is shown that the degree of the $n$th iterate of such a mapping is given by its action on the Picard group of the space of initial values. It is also shown that the degree of the $n$th iterate of every Painlev\'e equation in sakai's list is at most $O(n^2)$ and therefore its algebraic entropy is zero.Comment: 10 pages, pLatex fil

On the complexity of some birational transformations

Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions

A Force-Feedback Exoskeleton for Upper-Limb Rehabilitation in Virtual Reality

This paper presents the design and the clinical validation of an upper-limb force-feedback exoskeleton, the L-EXOS, for robotic-assisted rehabilitation in virtual reality (VR). The L-EXOS is a five degrees of freedom exoskeleton with a wearable structure and anthropomorphic workspace that can cover the full range of motion of human arm. A specific VR application focused on the reaching task was developed and evaluated on a group of eight post-stroke patients, to assess the efficacy of the system for the rehabilitation of upper limb. The evaluation showed a significant reduction of the performance error in the reaching task (paired t-test, p < 0.02

Substantiating a political public sphere in the Scottish press : a comparative analysis

This article uses content analysis to characterize the performance of the media in a national public sphere, by setting apart those qualities that typify internal press coverage of a political event. The article looks at the coverage of the 1999 devolved Scottish election from the day before the election until the day after. It uses a word count to measure the election material in Scottish newspapers the Herald, the Press and Journal and the Scotsman, and United Kingdom newspapers the Guardian, the Independent and The Times, and categorizes that material according to discourse type, day and page selection. The article finds a number of qualities that typify the Scottish sample in particular, and might be broadly indicative of a political public sphere in action. Firstly, and not unexpectedly, it finds that the Scottish newspapers carry significantly more election coverage. Just as tellingly, though, the article finds that the Scottish papers offer a greater proportion of advice and background information, in the form of opinion columns and feature articles. It also finds that the Scottish papers place a greater concentration of both informative and evaluative material in the period before the vote, consistent with their making a contribution to informed political action. Lastly, the article finds that the Scottish sample situates coverage nearer the front of the paper and places a greater proportion on recto pages. The article therefore argues that the Scottish papers display features that distinguish them from the UK papers, and are broadly consistent with their forming part of a deliberative public sphere, and suggests that these qualities might be explored as a means of judging future media performance

The solid-state photo-CIDNP effect

The solid-state photo-CIDNP effect is the occurrence of a non-Boltzmann nuclear spin polarization in rigid samples upon illumination. For solid-state NMR, which can detect this enhanced nuclear polarization as a strong modification of signal intensity, the effect allows for new classes of experiments. Currently, the photo- and spin-chemical machinery of various RCs is studied by photo-CIDNP MAS NMR in detail. Until now, the effect has only been observed at high magnetic fields with 13C and 15N MAS NMR and in natural photosynthetic RC preparations in which blocking of the acceptor leads to cyclic electron transfer. In terms of irreversible thermodynamics, the high-order spin structure of the initial radical pair can be considered as a transient order phenomenon emerging under non-equilibrium conditions and as a first manifestation of order in the photosynthetic process. The solid-state photo-CIDNP effect appears to be an intrinsic property of natural RCs. The conditions of its occurrence seem to be conserved in evolution. The effect may be based on the same fundamental principles as the highly optimized electron transfer. Hence, the effect may allow for guiding artificial photosynthesis

Complexity and integrability in 4D bi-rational maps with two invariants

In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief that maps with sufficiently many invariants can have at most quadratic growth. Cubic growth may reflect the existence of non-elliptic fibrations of invariants, whereas we conjecture that the exponentially growing cases lack the necessary conditions for the applicability of the discrete Liouville theorem.Comment: 16 pages, 2 figure

Functional Interpretations of Intuitionistic Linear Logic

We present three different functional interpretations of intuitionistic linear logic ILL and show how these correspond to well-known functional interpretations of intuitionistic logic IL via embeddings of IL into ILL. The main difference from previous work of the second author is that in intuitionistic linear logic (as opposed to classical linear logic) the interpretations of !A are simpler and simultaneous quantifiers are no longer needed for the characterisation of the interpretations. We then compare our approach in developing these three proof interpretations with the one of de Paiva around the Dialectica category model of linear logic