Partial Isometries of a Sub-Riemannian Manifold

In this paper, we obtain the following generalisation of isometric $C^1$-immersion theorem of Nash and Kuiper. Let $M$ be a smooth manifold of dimension $m$ and $H$ a rank $k$ subbundle of the tangent bundle $TM$ with a Riemannian metric $g_H$. Then the pair $(H,g_H)$ defines a sub-Riemannian structure on $M$. We call a $C^1$-map $f:(M,H,g_H)\to (N,h)$ into a Riemannian manifold $(N,h)$ a {\em partial isometry} if the derivative map $df$ restricted to $H$ is isometric; in other words, $f^*h|_H=g_H$. The main result states that if $\dim N>k$ then a smooth $H$-immersion $f_0:M\to N$ satisfying $f^*h|_H<g_H$ can be homotoped to a partial isometry $f:(M,g_H)\to (N,h)$ which is $C^0$-close to $f_0$. In particular we prove that every sub-Riemannian manifold $(M,H,g_H)$ admits a partial isometry in $\R^n$ provided $n\geq m+k$.Comment: 13 pages. This is a revised version of an earlier submission (minor revision

Non-invasive imaging of subsurface paint layers with optical coherence tomography

Optical coherence tomography (OCT) systems are fast scanning infrared Michelson interferometers designed for the non-invasive examination of the interiors of the eye and subsurface structures of biological tissues. OCT has recently been applied to the non-invasive examinations of the stratigraphy of paintings and museum artefacts. So far this is the only technique capable of imaging non-invasively the subsurface structure of paintings and painted objects. Unlike the traditional method of paint cross-section examination where sampling is required, the non-invasive and non-contact nature of the technique enables the examination of the paint cross-section anywhere on a painting, as there is no longer an issue with conservation ethics regarding the taking of samples from historical artefacts. A range of applications of the technique including the imaging of stratigraphy of paintings and painted artefacts, the imaging of underdrawings to the analysis of the optical properties of paint and varnish layers is presented. Future projects on the application of OCT to art conservation are discussed

Practicing a Science of Security: A Philosophy of Science Perspective

Our goal is to refocus the question about cybersecurity research from 'is this process scientific' to 'why is this scientific process producing unsatisfactory results'. We focus on five common complaints that claim cybersecurity is not or cannot be scientific. Many of these complaints presume views associated with the philosophical school known as Logical Empiricism that more recent scholarship has largely modified or rejected. Modern philosophy of science, supported by mathematical modeling methods, provides constructive resources to mitigate all purported challenges to a science of security. Therefore, we argue the community currently practices a science of cybersecurity. A philosophy of science perspective suggests the following form of practice: structured observation to seek intelligible explanations of phenomena, evaluating explanations in many ways, with specialized fields (including engineering and forensics) constraining explanations within their own expertise, inter-translating where necessary. A natural question to pursue in future work is how collecting, evaluating, and analyzing evidence for such explanations is different in security than other sciences

Exome sequencing identifies nonsegregating nonsense ATM and PALB2 variants in familial pancreatic cancer.

We sequenced 11 germline exomes from five families with familial pancreatic cancer (FPC). One proband had a germline nonsense variant in ATM with somatic loss of the variant allele. Another proband had a nonsense variant in PALB2 with somatic loss of the variant allele. Both variants were absent in a relative with FPC. These findings question the causal mechanisms of ATM and PALB2 in these families and highlight challenges in identifying the causes of familial cancer syndromes using exome sequencing

Quantum protocols for anonymous voting and surveying

We describe quantum protocols for voting and surveying. A key feature of our schemes is the use of entangled states to ensure that the votes are anonymous and to allow the votes to be tallied. The entanglement is distributed over separated sites; the physical inaccessibility of any one site is sufficient to guarantee the anonymity of the votes. The security of these protocols with respect to various kinds of attack is discussed. We also discuss classical schemes and show that our quantum voting protocol represents a N-fold reduction in computational complexity, where N is the number of voters.Comment: 8 pages. V2 includes the modifications made for the published versio

Optical coherence tomography - a tool for high resolution non-invasive 3D-imaging of the subsurface structure of paintings

Optical Coherence Tomography (OCT) is an imaging technique originally developed for high-resolution 3D imaging of the human eye. In 2004, Targowski et al. and Liang et al. first reported its application to paintings, demonstrating that it was possible to produce cross-section images noninvasively with this technique. In 2005 Liang et al. explored further applications such as imaging of underdrawing at a resolution and contrast greater than that achievable with infrared reflectography Since then the authors have been conducting a project to investigate systematically the potential of O C T as a new tool in the non-invasive examination of paintings and to design an O C T optimised for use in museums. This paper discusses recent developments in this work and presents examples of the use of O CT on paintings undergoing conservation treatment in the National Gallery, London

Importance of relative humidity in the oxidative ageing of organic aerosols: case study of the ozonolysis of maleic acid aerosol

Many important atmospheric aerosol processes depend on the chemical composition of the aerosol, e.g. water uptake and particle cloud interactions. Atmospheric ageing processes, such as oxidation reactions, significantly and continuously change the chemical composition of aerosol particles throughout their lifetime. These ageing processes are often poorly understood. In this study we utilize an aerosol flow tube set up and an ultra-high resolution mass spectrometer to explore the effect of relative humidity (RH) in the range of &lt;5–90% on the ozonolysis of maleic acid aerosol which is employed as model organic aerosol system. Due to the slow reaction kinetics relatively high ozone concentrations of 160–200 ppm were used to achieve an appreciable degree of oxidation of maleic acid. The effect of oxidative ageing on the hygroscopicity of maleic acid particles is also investigated using an electrodynamic balance and thermodynamic modelling. RH has a profound effect on the oxidation of maleic acid particles. Very little oxidation is observed at RH &lt; 50% and the only observed reaction products are glyoxylic acid and formic acid. In comparison, when RH &gt; 50% there are about 15 oxidation products identified. This increased oxidation was observed even when the particles were exposed to high humidities long after a low RH ozonolysis reaction. This result might have negative implications for the use of water as an extraction solvent for the analysis of oxidized organic aerosols. These humidity-dependent differences in the composition of the ozonolyzed aerosol demonstrate that water is both a key reactant in the oxidation scheme and a determinant of particle phase and hence diffusivity. The measured chemical composition of the processed aerosol is used to model the hygroscopic growth, which compares favourably with water uptake results from the electrodynamic balance measurements. A reaction mechanism is presented which takes into account the RH dependent observations. This study emphasises the importance of studying the combined effects of several atmospheric parameters such as oxidants and RH to accurately describe the complex oxidation scheme of organic aerosols

The effect of cereal type and enzyme supplementation on carcass characteristics, volatile fatty acids and intestinal microflora and boar taint in entire male pigs

A 2 × 2 factorial experiment was conducted to investigate the effects of cereal type (barley v. oat) and exogenous enzyme supplementation (with or without) on intestinal fermentation, and on indole and skatole levels in the intestinal content and the adipose tissue in finisher boars. The experimental treatments were as follows: (i) barley-based diet, (ii) barley-based diet with enzyme supplement, (iii) oat-based diet and (iv) oat-based diet with enzyme supplement. The enzyme supplement contained endo-1,3(4)-β-glucanase (EC 3.2.1.6) and endo-1,4-β-xylanase (EC 3.2.1.8). The animals were fed ad libitum for 45 days from 76.0 to 113.6 kg live weight. Feeding barley-based diets led to higher (P 0.05) between the experimental treatments. Pigs offered the barley-based diets had lower (P < 0.001) indole concentrations in the adipose tissue compared with those fed the oat-based diet. In conclusion, barley-based diets were more efficient than oat-based diets in limiting concentrations of indole in the adipose tissu

Vanishing cycles and mutation

This is the writeup of a talk given at the European Congress of Mathematics, Barcelona. It considers Picard-Lefschetz theory from the Floer cohomology viewpoint.Comment: 20 pages, LaTeX2e. TeXnical problem should now be fixed, so that the images will appear even if you download the .ps fil

Skylab S-193 Radscat microwave measurements of sea surface winds

The S-193 Radscat made extensive measurements of many sea conditions. Measurements were taken in a tropical hurricane (Ava), a tropical storm (Christine), and in portions of extratropical cyclones. Approximately 200 scans of ocean data at 105 kilometer spacings were taken during the first two Skylab missions and another 200 during the final mission when the characteristics of the measurements changed due to damage of the antenna. Backscatter with four transmit/receive polarization combinations and emissions with horizontal and vertical receive polarizations were measured. Other surface parameters investigated for correlation with the measurements included sea temperature, air/sea temperature difference, and gravity-wave spectrum. Methods were developed to correct the microwave measurements for atmospheric effects. The radiometric data were corrected accurately for clear sky and light cloud conditions only. The radiometer measurements were used to recover the surface scattering characteristics for all atmospheric conditions excluding rain. The radiometer measurements also detected the presence of rain which signaled when the scattering measurement should not be used for surface wind estimation. Regression analysis was used to determine empirically the relation between surface parameters and the microwave measurements, after correction for atmospheric effects. Results indicate a relationship approaching square-law at 50 deg between differential scattering coefficient and wind speed with horizontally polarized scattering data showing slightly more sensitivity to wind speed than vertically polarized data