On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.

Species divergence and trait convergence in experimental plant community assembly

Despite decades of research, it remains controversial whether ecological communities converge towards a common structure determined by environmental conditions irrespective of assembly history. Here, we show experimentally that the answer depends on the level of community organization considered. In a 9-year grassland experiment, we manipulated initial plant composition on abandoned arable land and subsequently allowed natural colonization. Initial compositional variation caused plant communities to remain divergent in species identities, even though these same communities converged strongly in species traits. This contrast between species divergence and trait convergence could not be explained by dispersal limitation or community neutrality alone. Our results show that the simultaneous operation of trait-based assembly rules and species-level priority effects drives community assembly, making it both deterministic and historically contingent, but at different levels of community organization.

Endocrine disrupters and human health: Could oestrogenic chemicals in body care cosmetics adversely affect breast cancer incidence in women? A review of evidence and call for further research

In the decade that has elapsed since the suggestion that exposure of the foetal/developing male to environmental oestrogens could be the cause of subsequent reproductive and developmental effects in men, there has been little definitive research to provide conclusions to the hypothesis. Issues of exposure and low potency of environmental oestrogens may have reduced concerns. However, the hypothesis that chemicals applied in body care cosmetics (including moisturizers, creams, sprays or lotions applied to axilla or chest or breast areas) may be affecting breast cancer incidence in women presents a different case scenario, not least in the consideration of the exposure issues. The specific cosmetic type is not relevant but the chemical ingredients in the formulations and the application to the skin is important. The most common group of body care cosmetic formulation excipients, namely p-hydroxybenzoic acid esters or parabens, have been shown recently to be oestrogenic in vitro and in vivo and now have been detected in human breast tumour tissue, indicating absorption (route and causal associations have yet to be confirmed). The hypothesis for a link between oestrogenic ingredients in underarm and body care cosmetics and breast cancer is forwarded and reviewed here in terms of. data on exposure to body care cosmetics and parabens, including dermal absorption; paraben oestrogenicity; the role of oestrogen in breast cancer; detection of parabens in breast tumours; recent epidemiology studies of underarm cosmetics use and breast cancer; the toxicology database; the current regulatory status of parabens and regulatory toxicology data uncertainties. Notwithstanding the major public health issue of the causes of the rising incidence of breast cancer in women, this call for further research may provide the first evidence that environmental factors may be adversely affecting human health by endocrine disruption, because exposure to oestrogenic chemicals through application of body care products (unlike diffuse environmental chemical exposures) should be amenable to evaluation, quantification and control. The exposure issues are clear and the exposed population is large, and these factors should provide the necessary impetus to investigate this potential issue of public health. Copyright (C) 2004 John Wiley Sons, Ltd.

The symbiotic roles of empirical experimentation and thought experimentation in the learning of physics

This study was an attempt to identify the epistemological roots of knowledge when students carry out hands-on experiments in physics. We found that, within the context of designing a solution to a stated problem, subjects constructed and ran thought experiments intertwined within the processes of conducting physical experiments. We show that the process of alternating between these two modes- empirically experimenting and experimenting in thought- leads towards a convergence on scientifically acceptable concepts. We call this process mutual projection. In the process of mutual projection, external representations were generated. Objects in the physical environment were represented in an imaginary world and these representations were associated with processes in the physical world. It is through this coupling that constituents of both the imaginary world and the physical world gain meaning. We further show that the external representations are rooted in sensory interaction and constitute a semi-symbolic pictorial communication system, a sort of primitive 'language', which is developed as the practical work continues. The constituents of this pictorial communication system are used in the thought experiments taking place in association with the empirical experimentation. The results of this study provide a model of physics learning during hands-on experimentation.

The development of convergence and accommodation

Aim: To review current literature on the development of convergence and accommodation. The accommodation and vergence systems provide the foundation upon which bifoveal binocular single vision develops. Deviations from their normal development not only are implicated in the aetiology of convergence anomalies, accommodative anomalies and strabismus, but may also be implicated in failure of the emmetropisation process. Method: This review considers the problems of researching the development of accommodation and vergence in infants and how infant research has had to differ from adult methods. It then reviews and discusses the implications of current research into the development of both systems and their linkages. Results: Vergence and accommodation develop rapidly in the first months of life, with accommodation changing from relatively fixed myopic focus in the neonatal period to adult-like responses by 4 months of age. Vergence develops gradually and becomes more accurate after 4 months of age, but has been demonstrated in infants well before the age that binocular disparity detection mechanisms are thought to develop. Hypotheses for this early vergence mechanism are discussed. The relationship between accommodation and vergence shows much more variability in infants than adult literature has found, but this apparent adult/infant difference may be partly attributed to methodological differences rather than maturational change alone. Conclusions: Variability and flexibility characterise infant responses. This variability may enable infants to develop a flexible and robust binocular system for later life. Studies of infant visual cue use may give clues to the aetiology of strabismus and refractive error.