Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations

We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method denoted as Classic II given in [J. Helsing, Faster convergence and higher accuracy for the Dirichlet–Neumann map, J. Comput. Phys. 228 (2009), pp. 2578–2576, Section 3], which is based on Fredholm integral equations and Nyström discretization schemes. Then, for stability reasons, to solve the discretized integral equation we use the method of smoothing projection introduced in [J. Helsing and B.T. Johansson, Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques, Inverse Probl. Sci. Eng. 18 (2010), pp. 381–399, Section 7], which makes it possible to solve the discretized operator equation in a stable way with minor computational cost and high accuracy. With this approach, for sufficiently smooth Cauchy data, the normal derivative can also be accurately computed on the part of the boundary where no data is initially given.

Measurement of intervertebral cervical motion by means of dynamic X-ray image processing and data interpolation

Accurate measurement of intervertebral kinematics of the cervical spine can support the diagnosis of widespread diseases related to neck pain, such as chronic whiplash dysfunction, arthritis, and segmental degeneration. The natural inaccessibility of the spine, its complex anatomy, and the small range of motion only permit concise measurement in vivo. Low dose X-ray fluoroscopy allows time-continuous screening of cervical spine during patient's spontaneous motion. To obtain accurate motion measurements, each vertebra was tracked by means of image processing along a sequence of radiographic images. To obtain a time-continuous representation of motion and to reduce noise in the experimental data, smoothing spline interpolation was used. Estimation of intervertebral motion for cervical segments was obtained by processing patient's fluoroscopic sequence; intervertebral angle and displacement and the instantaneous centre of rotation were computed. The RMS value of fitting errors resulted in about 0.2 degree for rotation and 0.2 mm for displacements. © 2013 Paolo Bifulco et al.

Estimation of computer waste quantities using forecasting techniques

Technology changes rapidly over years providing continuously more options for computer alternatives and making life easier for economic, intra-relation or any other transactions. However, the introduction of new technology “pushes” old Information and Communication Technology (ICT) products to non-use. E-waste is defined as the quantities of ICT products which are not in use and is bivariate function of the sold quantities, and the probability that specific computers quantity will be regarded as obsolete. In this paper, an e-waste generation model is presented, which is applied to the following regions: Western and Eastern Europe, Asia/Pacific, Japan/Australia/New Zealand, North and South America. Furthermore, cumulative computer sales were retrieved for selected countries of the regions so as to compute obsolete computer quantities. In order to provide robust results for the forecasted quantities, a selection of forecasting models, namely (i) Bass, (ii) Gompertz, (iii) Logistic, (iv) Trend model, (v) Level model, (vi) AutoRegressive Moving Average (ARMA), and (vii) Exponential Smoothing were applied, depicting for each country that model which would provide better results in terms of minimum error indices (Mean Absolute Error and Mean Square Error) for the in-sample estimation. As new technology does not diffuse in all the regions of the world with the same speed due to different socio-economic factors, the lifespan distribution, which provides the probability of a certain quantity of computers to be considered as obsolete, is not adequately modeled in the literature. The time horizon for the forecasted quantities is 2014-2030, while the results show a very sharp increase in the USA and United Kingdom, due to the fact of decreasing computer lifespan and increasing sales.

Dynamic Bayesian network for semantic place classification in mobile robotics

In this paper, the problem of semantic place categorization in mobile robotics is addressed by considering a time-based probabilistic approach called dynamic Bayesian mixture model (DBMM), which is an improved variation of the dynamic Bayesian network. More specifically, multi-class semantic classification is performed by a DBMM composed of a mixture of heterogeneous base classifiers, using geometrical features computed from 2D laserscanner data, where the sensor is mounted on-board a moving robot operating indoors. Besides its capability to combine different probabilistic classifiers, the DBMM approach also incorporates time-based (dynamic) inferences in the form of previous class-conditional probabilities and priors. Extensive experiments were carried out on publicly available benchmark datasets, highlighting the influence of the number of time-slices and the effect of additive smoothing on the classification performance of the proposed approach. Reported results, under different scenarios and conditions, show the effectiveness and competitive performance of the DBMM.