Identifying adequate models in physico-mathematics: Descartes' analysis of the rainbow

The physico-mathematics that emerged at the beginning of the seventeenth century entailed the quantitative analysis of the physical nature with optics, meteorology and hydrostatics as its main subjects. Rather than considering physico-mathematics as the mathematization of natural philosophy, it can be characterized it as the physicalization of mathematics, in particular the subordinate mixed mathematics. Such transformation of mixed mathematics was a process in which physico-mathematics became liberated from Aristotelian constraints. This new approach to natural philosophy was strongly influenced by Jesuit writings and experimental practices. In this paper we will look at the strategies in which models were selected from the mixed sciences, engineering and technology adequate for an analysis of the specific phenomena under investigation. We will discuss Descartes’ analysis of the rainbow in the eight discourse of his Meteorology as an example of carefully selected models for physico-mathematical reasoning. We will further demonstrate that these models were readily available from Jesuit education and literature

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Insights into the regulation of DMSP synthesis in the diatom Thalassiosira pseudonana through APR activity, proteomics and gene expression analyses on cells acclimating to changes in salinity, light and nitrogen

Despite the importance of dimethylsulphoniopropionate (DMSP) in the global sulphur cycle and climate regulation, the biological pathways underpinning its synthesis in marine phytoplankton remain poorly understood. The intracellular concentration of DMSP increases with increased salinity, increased light intensity and nitrogen starvation in the diatom Thalassiosira pseudonana. We used these conditions to investigate DMSP synthesis at the cellular level via analysis of enzyme activity, gene expression and proteome comparison. The activity of the key sulphur assimilatory enzyme, adenosine 5′- phosphosulphate reductase was not coordinated with increasing intracellular DMSP concentration. Under all three treatments coordination in the expression of sulphur assimilation genes was limited to increases in sulphite reductase transcripts. Similarly, proteomic 2D gel analysis only revealed an increase in phosphoenolpyruvate carboxylase following increases in DMSP concentration. Our findings suggest that increased sulphur assimilation might not be required for increased DMSP synthesis, instead the availability of carbon and nitrogen substrates may be important in the regulation of this pathway. This contrasts with the regulation of sulphur metabolism in higher plants, which generally involves upregulation of several sulphur assimilatory enzymes. In T. pseudonana changes relating to sulphur metabolism were specific to the individual treatments and, given that little coordination was seen in transcript and protein responses across the three growth conditions, different patterns of regulation might be responsible for the increase in DMSP concentration seen under each treatment

Effect of maternal Schistosoma mansoni infection and praziquantel treatment during pregnancy on Schistosoma mansoni infection and immune responsiveness among offspring at age five years.

INTRODUCTION: Offspring of Schistosoma mansoni-infected women in schistosomiasis-endemic areas may be sensitised in-utero. This may influence their immune responsiveness to schistosome infection and schistosomiasis-associated morbidity. Effects of praziquantel treatment of S. mansoni during pregnancy on risk of S. mansoni infection among offspring, and on their immune responsiveness when they become exposed to S. mansoni, are unknown. Here we examined effects of praziquantel treatment of S. mansoni during pregnancy on prevalence of S. mansoni and immune responsiveness among offspring at age five years. METHODS: In a trial in Uganda (ISRCTN32849447, http://www.controlled-trials.com/ISRCTN32849447/elliott), offspring of women treated with praziquantel or placebo during pregnancy were examined for S. mansoni infection and for cytokine and antibody responses to SWA and SEA, as well as for T cell expression of FoxP3, at age five years. RESULTS: Of the 1343 children examined, 32 (2.4%) had S. mansoni infection at age five years based on a single stool sample. Infection prevalence did not differ between children of treated or untreated mothers. Cytokine (IFNγ, IL-5, IL-10 and IL-13) and antibody (IgG1, Ig4 and IgE) responses to SWA and SEA, and FoxP3 expression, were higher among infected than uninfected children. Praziquantel treatment of S. mansoni during pregnancy had no effect on immune responses, with the exception of IL-10 responses to SWA, which was higher in offspring of women that received praziquantel during pregnancy than those who did not. CONCLUSION: We found no evidence that maternal S. mansoni infection and its treatment during pregnancy influence prevalence and intensity of S. mansoni infection or effector immune response to S. mansoni infection among offspring at age five years, but the observed effects on IL-10 responses to SWA suggest that maternal S. mansoni and its treatment during pregnancy may affect immunoregulatory responsiveness in childhood schistosomiasis. This might have implications for pathogenesis of the disease

Moving out of the shadows: accomplishing bisexual motherhood

Our qualitative study explored the ways in which bisexual mothers came to identify as such and how they structured their relationships and parenting within hetero-patriarchal society. The experiences of seven self-identified White bisexual women (aged from 28 to 56-years-old) from across England and the Republic of Ireland were investigated through semi-structured interviews. Participants’ children were aged 8 months to 28 years old at the time of their interviews. A thematic narrative analysis highlighted the following issues that participants had encountered in constructing their self-identity: prioritizing children; connecting and disconnecting with others and finessing self-definition; questioning societal relationship expectations. Nevertheless, participants varied considerably in how each of the themes identified were reflected in their lives, in particular depending upon each participant’s interpretation of her local social context. Both motherhood and self-identifying as bisexual gave a sense of meaning and purpose to participants’ life stories, although participants sometimes foregrounded their commitment to their children even at a personal cost to their bisexual identity. Using three different theoretical perspectives from feminist theory, queer theory and life course theory, the narratives analysed revealed ways in which bisexual motherhood not only had been influenced both intentionally and unintentionally by heteronormative expectations but also had directly and indirectly challenged these expectations

Image-based Search and Retrieval for Biface Artefacts using Features Capturing Archaeologically Significant Characteristics

Archaeologists are currently producing huge numbers of digitized photographs to record and preserve artefact finds. These images are used to identify and categorize artefacts and reason about connections between artefacts and perform outreach to the public. However, finding specific types of images within collections remains a major challenge. Often, the metadata associated with images is sparse or is inconsistent. This makes keyword-based exploratory search difficult, leaving researchers to rely on serendipity and slowing down the research process. We present an image-based retrieval system that addresses this problem for biface artefacts. In order to identify artefact characteristics that need to be captured by image features, we conducted a contextual inquiry study with experts in bifaces. We then devised several descriptors for matching images of bifaces with similar artefacts. We evaluated the performance of these descriptors using measures that specifically look at the differences between the sets of images returned by the search system using different descriptors. Through this nuanced approach, we have provided a comprehensive analysis of the strengths and weaknesses of the different descriptors and identified implications for design in the search systems for archaeology

Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Differential game theory for versatile physical human-robot interaction

The last decades have seen a surge of robots working in contact with humans. However, until now these contact robots have made little use of the opportunities offered by physical interaction and lack a systematic methodology to produce versatile behaviours. Here, we develop an interactive robot controller able to understand the control strategy of the human user and react optimally to their movements. We demonstrate that combining an observer with a differential game theory controller can induce a stable interaction between the two partners, precisely identify each other’s control law, and allow them to successfully perform the task with minimum effort. Simulations and experiments with human subjects demonstrate these properties and illustrate how this controller can induce different representative interaction strategies