Non-contact thickness measurement using UTG

A measurement structure for determining the thickness of a specimen without mechanical contact but instead employing ultrasonic waves including an ultrasonic transducer and an ultrasonic delay line connected to the transducer by a retainer or collar. The specimen, whose thickness is to be measured, is positioned below the delay line. On the upper surface of the specimen a medium such as a drop of water is disposed which functions to couple the ultrasonic waves from the delay line to the specimen. A receiver device, which may be an ultrasonic thickness gauge, receives reflected ultrasonic waves reflected from the upper and lower surface of the specimen and determines the thickness of the specimen based on the time spacing of the reflected waves

Necessary Conditions for Non-Intersection of Collections of Sets

This paper continues studies of non-intersection properties of finite collections of sets initiated 40 years ago by the extremal principle. We study elementary non-intersection properties of collections of sets, making the core of the conventional definitions of extremality and stationarity. In the setting of general Banach/Asplund spaces, we establish new primal (slope) and dual (generalized separation) necessary conditions for these non-intersection properties. The results are applied to convergence analysis of alternating projections.Comment: 26 page

Cutting Plane Algorithms are Exact for Euclidean Max-Sum Problems

This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated, generalised and bi-level diversity problems as special cases. We introduce two exact cutting plane algorithms to solve this class of optimisation problems. The new algorithms remove the need for a concave reformulation, which is known to significantly slow down convergence. We establish exactness of the new algorithms by examining the concavity of the quadratic objective in a given direction, a concept we refer to as directional concavity. Numerical results show that the algorithms outperform other exact methods for benchmark diversity problems (capacitated, generalised and bi-level), and can easily solve problems of up to three thousand variables

An exact cutting plane method for solving p-dispersion-sum problems

This paper aims to answer an open question recently posed in the literature, that is to find a fast exact method for solving the p-dispersion-sum problem (PDSP), a nonconcave quadratic binary maximization problem. We show that, since the Euclidean distance matrix defining the quadratic term in (PDSP) is always conditionally negative definite, the cutting plane method is exact for (PDSP) even in the absence of concavity. As such, the cutting plane method, which is primarily designed for concave maximisation problems, converges to the optimal solution of the (PDSP). The numerical results show that the method outperforms other exact methods for solving (PDSP), and can solve to optimality large instances of up to two thousand variables

A Note on the Finite Convergence of Alternating Projections

We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality, which until now has been restricted to sets with nonempty intersection. In the special case of a polyhedron and closed half space, our sufficient conditions define the minimum distance between the two sets that is required for alternating projections to converge in a single iteration.Comment: 9 pages, 7 figure

Magneto-transport properties of monolayer borophene in perpendicular magnetic field: influence of electron-phonon interaction

The magneto-transport properties of a borophene monolayer in a perpendicular magnetic field B are studied via calculating the conductivity tensor and resistance under electron-optical phonon interaction by using the linear response theory. Numerical results are obtained and discussed for some specific parameters. The magnetic field-dependent longitudinal conductivity shows the magneto-phonon resonance effect that describes the transition of electrons between Landau levels by absorbing/emitting an optical phonon. The Hall conductivity increases first and then decreases with the magnetic field strength. Also, the longitudinal resistance increases significantly with increasing temperature, which shows the metal behaviour of the material. Practically, the observed magneto-phonon resonance can be applied to experimentally determine some material parameters, such as the distance between Landau levels and the optical phonon energy

Variational Analysis Down Under Open Problem Session

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We state the problems discussed in the open problem session at Variational Analysis Down Under conference held in honour of Prof. Asen Dontchev on 19–21 February 2018 at Federation University Australia

ElliPro: a new structure-based tool for the prediction of antibody epitopes

<p>Abstract</p> <p>Background</p> <p>Reliable prediction of antibody, or B-cell, epitopes remains challenging yet highly desirable for the design of vaccines and immunodiagnostics. A correlation between antigenicity, solvent accessibility, and flexibility in proteins was demonstrated. Subsequently, Thornton and colleagues proposed a method for identifying continuous epitopes in the protein regions protruding from the protein's globular surface. The aim of this work was to implement that method as a web-tool and evaluate its performance on discontinuous epitopes known from the structures of antibody-protein complexes.</p> <p>Results</p> <p>Here we present ElliPro, a web-tool that implements Thornton's method and, together with a residue clustering algorithm, the MODELLER program and the Jmol viewer, allows the prediction and visualization of antibody epitopes in a given protein sequence or structure. ElliPro has been tested on a benchmark dataset of discontinuous epitopes inferred from 3D structures of antibody-protein complexes. In comparison with six other structure-based methods that can be used for epitope prediction, ElliPro performed the best and gave an AUC value of 0.732, when the most significant prediction was considered for each protein. Since the rank of the best prediction was at most in the top three for more than 70% of proteins and never exceeded five, ElliPro is considered a useful research tool for identifying antibody epitopes in protein antigens. ElliPro is available at <url>http://tools.immuneepitope.org/tools/ElliPro</url>.</p> <p>Conclusion</p> <p>The results from ElliPro suggest that further research on antibody epitopes considering more features that discriminate epitopes from non-epitopes may further improve predictions. As ElliPro is based on the geometrical properties of protein structure and does not require training, it might be more generally applied for predicting different types of protein-protein interactions.</p