Intrinsic Fluorescence of Protoporphyrin IX from Blood Samples Can Yield Information on the Growth of Prostate Tumours

Prostate cancer is one of the most common types of cancer in men, and unfortunately many prostate tumours remain asymptomatic until they reach advanced stages. Diagnosis is typically performed through Prostate-Specific Antigen (PSA) quantification, Digital Rectal Examination (DRE) and Transrectal Ultrasonography (TU). The antigen (PSA) is secreted by all prostatic epithelial cells and not exclusively by cancerous ones, so its concentration also increases in the presence of other prostatic diseases. DRE and TU are not reliable for early detection, when histological analysis of prostate tissue obtained from a biopsy is necessary. In this context, fluorescence techniques are very important for the diagnosis of cancer. In this paper we explore the potential of using endogenous phorphyrin blood fluorescence as tumour marker for prostate cancer. Substances such as porphyrin derivatives accumulate substantially more in tumours than in normal tissues; thus, measuring blood porphyrin concentration by autofluorescence intensity may provide a good parameter for determining tumour stage. In this study, the autofluorescence of blood porphyrin was analyzed using fluorescence and excitation spectroscopy on healthy male NUDE mice and in those with prostate cancer induced by inoculation of DU145 cells. A significant contrast between the blood of normal and cancer subjects could be established. Blood porphyrin fluorophore showed an enhancement on the fluorescence band around 632 nm following tumour growth. Fluorescence detection has advantages over other light-based investigation methods: high sensitivity, high speed and safety. However it does carry the drawback of low specificity of detection. The extraction of blood porphyrin using acetone can solve this problem, since optical excitation of further molecular species can be excluded, and light scattering from blood samples is negligible.     

Analysis of reflection speckle holograms in a BSO crystal

A theoretical and experimental study of speckle registering in photorefractive BSO crystals through reflection hologram geometry is implemented. The three-dimensional speckle nature is considered in the diffraction efficiency calculations. The interference process produces index-of-refraction gratings in the speckle volume via the photorefractive effect. It is demonstrated that the coupled-wave theory for reflection geometry allows explaining the diffraction efficiency behavior when the interaction length is properly taken into account. It means that the speckle depth is related with the interaction length. The speckle depth can be controlled by the imaging system pupil aperture diameter. Under this condition, the influence of the speckle depth on the diffraction efficiency is analyzed. An agreement between the numerical model based on the coupled-wave theory and the experimental results is obtained.     

The structure and ordering of zirconium and hafnium containing garnets studied by electron channelling, neutron diffraction and Mössbauer spectroscopy

Garnets, A₃B₂C₃O₁₂, are an important group of minerals and have potential uses in the safe immobilisation of high-level nuclear waste. They have been found naturally to incorporate Zr, Ti and Fe, three elements of interest in the safe storage of nuclear waste. Kimzeyite, Ca₃(Zr,Ti)₂(Si,Al,Fe)₃O₁₂, is a naturally occurring garnet that contains Zr in a high percentage∼30 wt%. For such a material to be of potential immobilisation for nuclear waste the structure needs to be completely understood. Electron channelling studies have shown that the Zr/Ti cations are located on the Y-site, with the Al/Fe cations located on the Z-site. This work has investigated synthetic analogues of kimzeyite, Ca₃(Zr,Hf)₂(Al,Fe,Si)₃O₁₂, by neutron powder diffraction, using the C2 spectrometer at the Chalk River nuclear facility, coupled with ⁵⁷Fe Mössbauer spectroscopy. Such work has allowed the structure of the synthetic material to be determined along with the distribution of cations across the X (CN=8), Y (CN=6), and Z (CN=4) sites. Results have shown that it is possible to synthesise Ca₃(Zr,Hf)₂(Al,Fe,Si)₃O₁₂ with a range of Al/Fe ratios containing Zr and Hf. The Mössbauer data has indicated the Fe is located on the Z site. The structural analyses show that the unit cell changes linearly as a function of composition, and analysis of the disorder indicates that the Zr, Hf reside on the Y site and the Al, Fe, and Si reside on the Z site.     

On Priestley Spaces of Lattice-Ordered Algebraic Structures

The laws defining many important varieties of lattice-ordered algebras, such as linear Heyting algebras, MV-algebras and l-groups, can be cast in a form which allows dual representations to be derived in a very direct, and semi-automatic, way. This is achieved by developing a new duality theory for implicative lattices, which encompass all the varieries above. The approach focuses on distinguished subsets of the prime lattice filters of an implicative lattice, ordered as usual by inclusion. A decomposition theorem is proved, and the extent to which the order on the prime lattice filters determines the implicative structure is thereby revealed.     

Strategies for detecting fraudulent claims in the automobile insurance industry

Some property and casualty insurers use automated detection systems to help to decide whether or not to investigate claims suspected of fraud. Claim screening systems benefit from the coded experience of previously investigated claims. The embedded detection models typically consist of scoring devices relating fraud indicators to some measure of suspicion of fraud. In practice these scoring models often focus on minimizing the error rate rather than on the cost of (mis)classification. We show that focusing on cost is a profitable approach. We analyse the effects of taking into account information on damages and audit costs early on in the screening process. We discuss several scenarios using real-life data. The findings suggest that with claim amount information available at screening time detection rules can be accommodated to increase expected profits. Our results show the value of cost-sensitive claim fraud screening and provide guidance on how to render this strategy operational.     

Evidence of the harmonic Faraday instability in ultrasonic atomization experiments with a deep, inviscid fluid

A popular method for generating micron-sized aerosols is to submerge ultrasonic (ω~MHz) piezoelectric oscillators in a water bath. The submerged oscillator atomizes the fluid, creating droplets with radii proportional to the wavelength of the standing wave at the fluid surface. Classical theory for the Faraday instability predicts a parametric instability driving a capillary wave at the subharmonic (ω/2) frequency. For many applications it is desirable to reduce the size of the droplets; however, using higher frequency oscillators becomes impractical beyond a few MHz. Observations are presented that demonstrate that smaller droplets may also be created by increasing the driving amplitude of the oscillator, and that this effect becomes more pronounced for large driving frequencies. It is shown that these observations are consistent with a transition from droplets associated with subharmonic (ω/2) capillary waves to harmonic (ω) capillary waves induced by larger driving frequencies and amplitudes, as predicted by a stability analysis of the capillary waves.     

Mean Curvature,Threshold Dynamics,and Phase Field Theory on Finite Graphs

In the continuum, close connections exist between mean curvature flow, the Allen-Cahn (AC) partial differential equation, and the Merriman-Bence-Osher (MBO) threshold dynamics scheme. Graph analogues of these processes have recently seen a rise in popularity as relaxations of NP-complete combinatorial problems, which demands deeper theoretical underpinnings of the graph processes. The aim of this paper is to introduce these graph processes in the light of their continuum counterparts, provide some background, prove the first results connecting them, illustrate these processes with examples and identify open questions for future study. We derive a graph curvature from the graph cut function, the natural graph counterpart of total variation (perimeter). This derivation and the resulting curvature definition differ from those in earlier literature, where the continuum mean curvature is simply discretized, and bears many similarities to the continuum nonlocal curvature or nonlocal means formulation. This new graph curvature is not only relevant for graph MBO dynamics, but also appears in the variational formulation of a discrete time graph mean curvature flow. We prove estimates showing that the dynamics are trivial for both MBO and AC evolutions if the parameters (the time-step and diffuse interface scale, respectively) are sufficiently small (a phenomenon known as “freezing” or “pinning”) and also that the dynamics for MBO are nontrivial if the time step is large enough. These bounds are in terms of graph quantities such as the spectrum of the graph Laplacian and the graph curvature. Adapting a Lyapunov functional for the continuum MBO scheme to graphs, we prove that the graph MBO scheme converges to a stationary state in a finite number of iterations. Variations on this scheme have recently become popular in the literature as ways to minimize (continuum) nonlocal total variation.     

Relative response of TL and component-resolved OSL to alpha and beta radiations in annealed sedimentary quartz

Knowledge of the relative luminescence response to alpha and beta radiation is very important in TL and OSL dating. In the present study the relative alpha to beta response is studied in a sedimentary quartz sample, previously fired at 900 °C for 1 h, in the dose region between 1 and 128 Gy, for both thermoluminescence (TL) and linearly modulated optically stimulated luminescence (LM – OSL). The LM – OSL measurements were performed at room temperature and at 125 °C. All OSL signals were deconvolved into their individual components. Comparison of OSL curves after alpha and beta irradiation strongly supports that quartz OSL components follow first order kinetics in both cases. In the case of TL, the relative alpha to beta response is found to be very different for each TL glow-peak, but it does not depend strongly on irradiation dose. In the case of LM – OSL measurements, it is found that the relative behaviour of the alpha to beta response is different for three distinct regions, namely the fast OSL component, the region of medium OSL component originating from the TL glow-peak at 110 °C when stimulation takes place at room temperature and finally the region of slow OSL component. Following stimulation at ambient temperature, the relative alpha to beta response of all components was not observed to depend significantly on dose, with the value of ratio being 0.03 and a tendency to decrease with increasing dose. However, in the case of measurements performed at 125 °C, the relative response of the fast components is much enhanced, and for the remaining components it increases with increasing dose. Special care must be taken to examine the relative alpha to beta response of the fast component at 125 °C which contrasts the relative response of the TL peak at ca. 325 °C. The implications for the dating of annealed quartz are also briefly discussed.     

Aleksandrov–Bakelman–Pucci Type Estimates for Integro-Differential Equations

In this work we provide an Aleksandrov–Bakelman–Pucci type estimate for a certain class of fully nonlinear elliptic integro-differential equations, the proof of which relies on an appropriate generalization of the convex envelope to a nonlocal, fractional-order setting and on the use of Riesz potentials to interpret second derivatives as fractional order operators. This result applies to a family of equations involving some nondegenerate kernels and, as a consequence, provides some new regularity results for previously untreated equations. Furthermore, this result also gives a new comparison theorem for viscosity solutions of such equations which depends only on the L ^∞ and L ⁿ norms of the right-hand side, in contrast to previous comparison results which utilize the continuity of the right-hand side for their conclusions. These results appear to be new, even for the linear case of the relevant equations.