Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

The classification and application of toxic Chinese Materia Medica

Many important drugs in the Chinese materia medica (CMM) are known to be toxic, and it has long been recognized in classical Chinese medical theory that toxicity can arise directly from the components of a single CMM or may be induced by an interaction between combined CMM. Traditional Chinese Medicine presents a unique set of pharmaceutical theories that include particular methods for processing, combining and decocting, and these techniques contribute to reducing toxicity as well as enhancing efficacy. The current classification of toxic CMM drugs, traditional methods for processing toxic CMM and the prohibited use of certain combinations, is based on traditional experience and ancient texts and monographs, but accumulating evidence increasingly supports their use to eliminate or reduce toxicity. Modern methods are now being used to evaluate the safety of CMM; however, a new system for describing the toxicity of Chinese herbal medicines may need to be established to take into account those herbs whose toxicity is delayed or otherwise hidden, and which have not been incorporated into the traditional classification. This review explains the existing classification and justifies it where appropriate, using experimental results often originally published in Chinese and previously not available outside China.

Economic forecasting in a changing world

This article explains the basis for a theory of economic forecasting developed over the past decade by the authors. The research has resulted in numerous articles in academic journals, two monographs, Forecasting Economic Time Series, 1998, Cambridge University Press, and Forecasting Nonstationary Economic Time Series, 1999, MIT Press, and three edited volumes, Understanding Economic Forecasts, 2001, MIT Press, A Companion to Economic Forecasting, 2002, Blackwells, and the Oxford Bulletin of Economics and Statistics, 2005. The aim here is to provide an accessible, non-technical, account of the main ideas. The interested reader is referred to the monographs for derivations, simulation evidence, and further empirical illustrations, which in turn reference the original articles and related material, and provide bibliographic perspective.

The catastrophic flash-flood event of 8–9 September 2002 in the Gard region, France: a first case study for the Cévennes–Vivarais Mediterranean Hydrometeorological Observatory

The Cévennes–Vivarais Mediterranean Hydrometeorological Observatory (OHM-CV) is a research initiative aimed at improving the understanding and modeling of the Mediterranean intense rain events that frequently result in devastating flash floods in southern France. A primary objective is to bring together the skills of meteorologists and hydrologists, modelers and instrumentalists, researchers and practitioners, to cope with these rather unpredictable events. In line with previously published flash-flood monographs, the present paper aims at documenting the 8–9 September 2002 catastrophic event, which resulted in 24 casualties and an economic damage evaluated at 1.2 billion euros (i.e., about 1 billion U.S. dollars) in the Gard region, France. A description of the synoptic meteorological situation is first given and shows that no particular precursor indicated the imminence of such an extreme event. Then, radar and rain gauge analyses are used to assess the magnitude of the rain event, which was particularly remarkable for its spatial extent with rain amounts greater than 200 mm in 24 h over 5500 km2. The maximum values of 600–700 mm observed locally are among the highest daily records in the region. The preliminary results of the postevent hydrological investigation show that the hydrologic response of the upstream watersheds of the Gard and Vidourle Rivers is consistent with the marked space–time structure of the rain event. It is noteworthy that peak specific discharges were very high over most of the affected areas (5–10 m3 s−1 km−2) and reached locally extraordinary values of more than 20 m3 s−1 km−2. A preliminary analysis indicates contrasting hydrological behaviors that seem to be related to geomorphological factors, notably the influence of karst in part of the region. An overview of the ongoing meteorological and hydrological research projects devoted to this case study within the OHM-CV is finally presented.

The representation of bodily pain in late nineteenth-century English culture

This book deals with bodily pain in the late Victorian period, considering the ways in which its understanding is shaped by medicine and theology.

Anticipatory engineering: anticipation in sensory-motor systems of human

In visual tracking experiments, distributions of the relative phase be-tween target and tracer showed positive relative phase indicating that the tracer precedes the target position. We found a mode transition from the reactive to anticipatory mode. The proposed integrated model provides a framework to understand the antici-patory behaviour of human, focusing on the integration of visual and soma-tosensory information. The time delays in visual processing and somatosensory feedback are explicitly treated in the simultaneous differential equations. The anticipatory behaviour observed in the visual tracking experiments can be ex-plained by the feedforward term of target velocity, internal dynamics, and time delay in somatosensory feedback.

Synapses in digital medium: computational investigations of neural basis of anticipation

Anticipation is an emerging concept that can provide a bridge between the deepest philosophical theories about the nature of life and cognition on one hand and the empirical biological sciences steeped in reductionist and Newtonian conception of causality. Three conceptions of anticipation have been emerging from the literature that may be operationalised in a way leading to a viable empirical programme. The discussion of the research into a novel dynamical concept of anticipating synchronisation lends credence to such a possibility and suggests further links between the three anticipation paradigms. A careful progress mindful to the deep philosophical concerns but also respecting empirical evidence will ultimately lead towards unifying theoretical and empirical biological sciences and may offer progress where reductionist science have been so far faltering.