Determination of one‐dimensional spherically aberrated point spread function in depth profiling by confocal Raman microscopy

We present a simple experiment that allows the complete and direct characterization of the point spread function (PSF) in refraction‐aberrated depth profiling experiments with confocal Raman microscopy. We used a wedge‐shaped solid polymer film to induce refraction aberrations on the response of an infinitesimally thin Raman scatterer, represented by a polished silicon wafer. The system, with the film pasted on top of the Si wafer, was probed by a depth slicing technique under a dry‐optics configuration. Post‐acquisition processing of the Si and polymer intensity maps allowed the reconstruction of the axial PSF spatially resolved each 1 µm or less in the z‐axis and for virtually continuous values of focusing depth. In agreement with theory, we found that PSF broadens asymmetrically with focusing depth, with a marked shift in the focus point. From the shape of PSF, we obtained values of depth resolution within the film that confirm that axial discrimination is not drastically deteriorated, as suggested by previous works, and that confocal aperture effectively reduces the collection volume even under severe refraction interference. Copyright © 2013 John Wiley & Sons, Ltd.     

Cohesive zone model for high-cycle fatigue of adhesively bonded joints under mode I loading

A cohesive zone model adequate for simulating the behaviour of adhesively bonded joints subjected to high-cycle fatigue and pure mode I loading is presented. The bilinear cohesive zone law with linear softening relationship was considered. The main advantage of the proposed formulation is the use of a unique damage parameter accounting for cumulative damage resulting from static and fatigue loading. The method was implemented in a user subroutine of the commercial finite element software Abaqus®. Two-dimensional numerical simulations of the double cantilever beam test using different representative combinations of the modified Paris law coefficients were performed. It was verified that the results of the model simulate with excellent agreement the several Paris laws used as input, thus demonstrating the good performance of the method as a predictive tool.     

Direct Evaluation of Cohesive Law in Mode I of Pinus pinaster by Digital Image Correlation

The direct identification of the cohesive law in pure mode I of Pinus pinaster is addressed in this work. The approach couples the double cantilever beam (DCB) test with digital image correlation (DIC). Wooden beam specimens loaded in the radial-longitudinal (RL) fracture propagation system are used. The strain energy release rate in mode I (G _I) is uniquely determined from the load–displacement curve by means of the compliance-based beam method (CBBM). This method relies on the concept of equivalent elastic crack length (a _eq) and therefore does not require the monitoring of crack propagation during test. DIC measurements are processed with two different purposes. Firstly, the physical evidence of a _eq is discussed with regard to actual estimation of the crack length based on post-processing full-field displacement measurements. Secondly, the crack tip opening displacement in mode I (w _I) is determined from the displacements near the initial crack tip. The cohesive law in mode I (σ _I???w _I) is then identified by numerical differentiation of the G _I???w _I relationship. The methodology and accuracy on this reconstruction are addressed. Moreover, the proposed procedure is validated by finite element analyses including cohesive zone modelling. It is concluded that the proposed data reduction scheme is adequate for assessing the cohesive law in pure mode I of P. pinaster.     

Learning temporal nodes Bayesian networks

Temporal Nodes Bayesian Networks (TNBNs) are an alternative to Dynamic Bayesian Networks for temporal reasoning with much simpler and efficient models in some domains. TNBNs are composed of temporal nodes, temporal intervals, and probabilistic dependencies. However, methods for learning this type of models from data have not yet been developed. In this paper, we propose a learning algorithm to obtain the structure and temporal intervals for TNBNs from data. The method consists of three phases: (i) obtain an initial approximation of the intervals, (ii) obtain a structure using a standard algorithm and (iii) refine the intervals for each temporal node based on a clustering algorithm. We evaluated the method with synthetic data from three different TNBNs of different sizes. Our method obtains the best score using a combined measure of interval quality and prediction accuracy, and a competitive structural quality with lower running times, compared to other related algorithms. We also present a real world application of the algorithm with data obtained from a combined cycle power plant in order to diagnose temporal faults.     

Studying the bandwidth in k-sample smooth tests

In this paper, the problem of bandwidth choice in smooth k-sample tests is considered. Three different bootstrap methods are discussed and implemented. All the methods persecute the bandwidth leading to the maximum power, while preserving the level of the test. The relative performance of the methods is investigated in a simulation study. Illustration through real medical data is provided. The main conclusion is that the bootstrap minimum method provides a good compromise between statistical power and conservativeness. Robustness of the methods with respect to the number of bootstrap resamples and practical limitations are discussed.     

The Cauchy Problem for a Tenth-Order Thin Film Equation I. Bifurcation of Oscillatory Fundamental Solutions

Fundamental global similarity solutions of the tenth-order thin film equation $$u_{t} = \nabla . (|u|^{n} \nabla \Delta^{4}u) \,\,\,\, {\rm in} \,\,\,\, \mathbb{R}^{N} \times \mathbb{R}_{+}$$ , where n >  0 are studied. The main approach consists in passing to the limit ${n \rightarrow 0^{+}}$ by using Hermitian non-self-adjoint spectral theory corresponding to the rescaled linear poly-harmonic equation $$u_{t} = \Delta^{5}u \,\,\,\, {\rm in} \,\,\,\, \mathbb{R}^{N} \times \mathbb{R}_{+}$$ .     

Biholomorphic Functions in Dual Banach Spaces

We present an infinite-dimensional version of Cartan-Carathéodory-Kaup-Wu theorem about the analyticity of the inverse of a given analytic mapping. It is valid for a class of domains in separable Banach dual spaces that includes all bounded convex domains.     

NP-hardness of deciding convexity of quartic polynomials and related problems

We show that unless P = NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a problem that has been open since 1992 when N. Z. Shor asked for the complexity of deciding convexity for quartic polynomials. We also prove that deciding strict convexity, strong convexity, quasiconvexity, and pseudoconvexity of polynomials of even degree four or higher is strongly NP-hard. By contrast, we show that quasiconvexity and pseudoconvexity of odd degree polynomials can be decided in polynomial time.