New dimension spectra: Finer information on scaling and homogeneity

We introduce a new dimension spectrum motivated by the Assouad dimension; a familiar notion of dimension which, for a given metric space, returns the minimal exponent $\alpha\geq 0$ such that for any pair of scales $0<r<R$, any ball of radius $R$ may be covered by a constant times $(R/r)^\alpha$ balls of radius $r$. To each $\theta \in (0,1)$, we associate the appropriate analogue of the Assouad dimension with the restriction that the two scales $r$ and $R$ used in the definition satisfy $\log R/\log r = \theta$. The resulting `dimension spectrum' (as a function of $\theta$) thus gives finer geometric information regarding the scaling structure of the space and, in some precise sense, interpolates between the upper box dimension and the Assouad dimension. This latter point is particularly useful because the spectrum is generally better behaved than the Assouad dimension. We also consider the corresponding `lower spectrum', motivated by the lower dimension, which acts as a dual to the Assouad spectrum. We conduct a detailed study of these dimension spectra; including analytic, geometric, and measureability properties. We also compute the spectra explicitly for some common examples of fractals including decreasing sequences with decreasing gaps and spirals with sub-exponential and monotonic winding. We also give several applications of our results, including: dimension distortion estimates under bi-H\"older maps for Assouad dimension and the provision of new bi-Lipschitz invariants.Comment: 38 pages, 4 figures. The original version of this paper has been split into two parts. This is now the first part and the second part is arXiv:1611.0885

Highly efficient spatially offset Raman spectroscopy to profile molecular composition in bone

Spatially offset Raman spectroscopy (SORS) offers the prospect of collecting spectral information detailing the molecular composition of biomaterials at greater depths below the surface layers than are normally probed by conventional Raman spectroscopy. By collecting off-axial scattered light, the technique overcomes the large background from in-line light within scattering media. In this paper we present a configuration which enables the highly efficient collection of spectral markers, indicative of bone health, including Raman signatures to assess phosphate, collagen and carbonate content, at millimeter depths. We demonstrate the effectiveness of the technique by performing spectral decompositions to analyze the molecular distribution of these markers non-invasively, using in vitro model systems, comprising bone and tissue, in situ

Toward the stereochemical assignment and synthesis of hemicalide: DP4f GIAO-NMR analysis and synthesis of a reassigned C16-C28 subunit.

Using the DP4f GIAO-NMR method, the stereochemistry of hemicalide was computationally analysed, resulting in a reassignment at C18 as supported by improved NMR shift correlations with a model C13-C25 fragment 23. An advanced C16-C28 subunit 6 of this potent anticancer agent was then synthesised with the revised 18,19-syn relationship.We thank the EPSRC for financial support (studentship to CIM) and the National Mass Spectrometry Centre (Swansea) for mass spectra.This is the final version of the article. It first appeared from the Royal Society of Chemistry via https://doi.org//10.1039/c6cc01074

A flexible organic reflectance oximeter array.

Transmission-mode pulse oximetry, the optical method for determining oxygen saturation in blood, is limited to only tissues that can be transilluminated, such as the earlobes and the fingers. The existing sensor configuration provides only single-point measurements, lacking 2D oxygenation mapping capability. Here, we demonstrate a flexible and printed sensor array composed of organic light-emitting diodes and organic photodiodes, which senses reflected light from tissue to determine the oxygen saturation. We use the reflectance oximeter array beyond the conventional sensing locations. The sensor is implemented to measure oxygen saturation on the forehead with 1.1% mean error and to create 2D oxygenation maps of adult forearms under pressure-cuff-induced ischemia. In addition, we present mathematical models to determine oxygenation in the presence and absence of a pulsatile arterial blood signal. The mechanical flexibility, 2D oxygenation mapping capability, and the ability to place the sensor in various locations make the reflectance oximeter array promising for medical sensing applications such as monitoring of real-time chronic medical conditions as well as postsurgery recovery management of tissues, organs, and wounds

A newly identified population of Gambusia affinis (Baird and Girard, 1853), a non-native invasive species, in Lake Kenyir, Malaysia: Implications for management

Gambusia affinis (Baird and Girard, 1853), a notorious non-native invasive fish species, has negatively impacted aquatic ecosystems around the world. This species was recently identified in Lake Kenyir, one of the largest impoundments in SouTheast Asia, using DNA barcoding. The coxI sequence of Gambusia caught in Lake Kenyir was compared with the sequences of topotypic voucher specimens of G. affinis and two other candidate Poeciliidae. The species was found to cluster with G. affinis but not with monophyletic clades of either G. holbrooki or P. reticulata thus confirming species identity. The fish is yet to be widely established in the lake with the current distribution limited to areas of anthropogenic disturbance

Synchronous nanoscale topographic and chemical mapping by differential-confocal controlled Raman microscopy

Confocal Raman microscopy is currently used for label-free optical sensing and imaging within the biological, engineering, and physical sciences as well as in industry. However, currently these methods have limitations, including their low spatial resolution and poor focus stability, that restrict the breadth of new applications. This paper now introduces differential-confocal controlled Raman microscopy as a technique that fuses differential confocal microscopy and Raman spectroscopy, enabling the point-to-point collection of three-dimensional nanoscale topographic information with the simultaneous reconstruction of corresponding chemical information. The microscope collects the scattered Raman light together with the Rayleigh light, both as Rayleigh scattered and reflected light (these are normally filtered out in conventional confocal Raman systems). Inherent in the design of the instrument is a significant improvement in the axial focusing resolution of topographical features in the image (to ∼1 nm ), which, when coupled with super-resolution image restoration, gives a lateral resolution of 220 nm. By using differential confocal imaging for controlling the Raman imaging, the system presents a significant enhancement of the focusing and measurement accuracy, precision, and stability (with an antidrift capability), mitigating against both thermal and vibrational artefacts. We also demonstrate an improved scan speed, arising as a consequence of the nonaxial scanning mode

A synthesis-enabled relative stereochemical assignment of the C1-C28 region of hemicalide.

Through synthesising both candidate diastereomers of a model C1-C28 fragment of the potent cytotoxic marine polyketide hemicalide, an assignment of the relative configuration between the C1-C15 and C16-C26 regions has been achieved. By detailed NMR comparisons with the natural product, the relative stereochemistry between these two 1,6-related stereoclusters is elucidated as 13,18-syn rather than the previously proposed 13,18-anti relationship. A flexible and modular strategy using an advanced C1-C28 ketone fragment 22 is outlined to elucidate the remaining stereochemical features and achieve a total synthesis