Use Of Harmonic Functions Research Articles

Real-Time Path Planning Based on Harmonic Functions under a Proper Generalized Decomposition-Based Framework.

This paper presents a real-time global path planning method for mobile robots using harmonic functions, such as the Poisson equation, based on the Proper Generalized Decomposition (PGD) of these functions. The main property of the proposed technique is that the computational cost is negligible in real-time, even if the robot is disturbed or the goal is changed. The main idea of the method is the off-line generation, for a given environment, of the whole set of paths from any start and goal configurations of a mobile robot, namely the computational vademecum, derived from a harmonic potential field in order to use it on-line for decision-making purposes. Up until now, the resolution of the Laplace or Poisson equations has been based on traditional numerical techniques unfeasible for real-time calculation. This drawback has prevented the extensive use of harmonic functions in autonomous navigation, despite their powerful properties. The numerical technique that reverses this situation is the Proper Generalized Decomposition. To demonstrate and validate the properties of the PGD-vademecum in a potential-guided path planning framework, both real and simulated implementations have been developed. Simulated scenarios, such as an L-Shaped corridor and a benchmark bug trap, are used, and a real navigation of a LEGO®MINDSTORMS robot running in static environments with variable start and goal configurations is shown. This device has been selected due to its computational and memory-restricted capabilities, and it is a good example of how its properties could help the development of social robots.

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Abstract Isogeometric Analysis (IGA) involves unification of modelling and analysis by adopting the same basis functions (splines), for both. Hence, spline based parametric model is the starting step for IGA. Representing a complex domain, using parametric geometric model is a challenging task. Parameterization problem can be defined as, finding an optimal set of control points of a B-spline model for exact domain modelling. Also, the quality of parameterization, too has significant effect on IGA. Finding the B-spline control points for any given domain, which gives accurate results is still an open issue. In this paper, a new planar B-spline parameterization technique, based on domain mapping method is proposed. First step of the methodology is to map an input (non-convex) domain onto a unit circle (convex) with the use of harmonic functions. The unique properties of harmonic functions: global minima and mean value property, ensures the mapping is bi-jective and with no self-intersections. Next step is to map the unit circle to unit square to make it apt for B-spline modelling. Square domain is re-parameterized by using conventional centripetal method. Once the domain is properly parameterized, the required control points are computed by solving the B-spline tensor product equation. The proposed methodology is validated by applying the developed B-spline model for a static structural analysis of a plate, using isogeometric analysis. Different domains are modelled to show effectiveness of the given technique. It is observed that the proposed method is versatile and computationally efficient.

On the suitability of Elekta’s Agility 160 MLC for tracked radiation delivery: closed-loop machine performance

For motion adaptive radiotherapy, dynamic multileaf collimator tracking can be employed to reduce treatment margins by steering the beam according to the organ motion.The Elekta Agility 160 MLC has hitherto not been evaluated for its tracking suitability. Both dosimetric performance and latency are key figures and need to be assessed generically, independent of the used motion sensor.In this paper, we propose the use of harmonic functions directly fed to the MLC to determine its latency during continuous motion. Furthermore, a control variable is extracted from a camera system and fed to the MLC. Using this setup, film dosimetry and subsequent γ statistics are performed, evaluating the response when tracking (MRI)-based physiologic motion in a closed-loop.The delay attributed to the MLC itself was shown to be a minor contributor to the overall feedback chain as compared to the impact of imaging components such as MRI sequences. Delay showed a linear phase behaviour of the MLC employed in continuously dynamic applications, which enables a general MLC-characterization. Using the exemplary feedback chain, dosimetry showed a vast increase in pass rate employing γ statistics.In this early stage, the tracking performance of the Agility using the test bench yielded promising results, making the technique eligible for translation to tracking using clinical imaging modalities.

Eye-Opening Approach to Norovirus Surveillance

To the Editor: It is said that a picture is worth a thousand words. The Figure illustrates this axiom and provides several new insights into the spread of norovirus infections. These infections are assumed to greatly affect society, but little is known about the prevalence of the disease in the community. Samples sent to laboratories usually originate from hospitalized persons and thus give a good view of the situation in healthcare settings. We suspect, however, that these numbers do not depict the true prevalence of norovirus infections in society. We therefore present a new approach to estimate the number of cases and spread of norovirus infections in the community. We plotted the number of queries for *vomit* (asterisks denote any prefix or suffix) submitted to the search engine on a medical website in Sweden (www.vardguiden.se). This number was normalized to account for the increasing use of the website over time and aggregated by week, starting with week 40 in 2005. We also plotted the number of norovirus findings per week from 16 regional laboratories, as recorded by the Swedish Institute for Infectious Disease Control. For the time series on Web search queries and laboratory findings (Figure), we fitted harmonic functions on the half-year with no or little activity, defining baselines for each series (1,2). By performing this procedure, we can identify the onset of each activity that is assumed to occur when the level rises above the 99% prediction interval of the baseline. The week this increase occurs is shown in the Figure. The Figure also contains the number of media articles on winter vomiting disease provided by a search engine for news in Sweden (www.eniro.se/nyhetssok). By analyzing the figure and investigating the statistical outcomes, we glimpse the prevalence of norovirus infections in society, as estimated by the search pattern. Figure Number of queries for *vomit* submitted to a medical Web site (A), number of laboratory-verified norovirus samples (B), with baselines and 99% prediction intervals, and number of media articles about winter vomiting disease (C) in Sweden, 2005–2010. ... We found 3 striking insights. First, the onset of vomiting in the community precedes the onset of confirmed norovirus infections in healthcare settings. In 3 of the 4 full seasons investigated, this precedence was 1–4 weeks. Second, the curve for the Web queries shows much sharper increases and decreases than does the curve on the number of reported norovirus findings. Third, neither search behavior nor reporting of positive tests is driven by media for the winter vomiting disease (confirmed by a linear regression). In the 2005–06 season, the laboratory reporting raised above the defined prediction interval in week 13, much later than the Web queries. This season had no new variants of norovirus genotype GII.4. This season still showed community infections, even though few reports came from institutions. For the current season (2009–10), the interval between onset of Web queries and onset of norovirus infections in hospitals (week 46 and week 1, respectively) was 8 weeks. In comparison with previous seasons, this delay could mean a low total number of reported cases. However, in late December, a new variant of GII.4 affected healthcare settings in southern Sweden with increasing norovirus infections, while the rest of the country still showed relatively low virus activity. Other pathogens such as rotavirus, Salmonella spp., Staphylococcus aureus, and Bacillus cereus can cause vomiting. Usually in Sweden, rotavirus infections peak in late winter, and bacterial diseases have a minor incidence compared with norovirus. In our opinion, these other pathogens would not interfere with the interpretation of the results. In our routine surveillance of Web queries, we also include other query terms, such as diarrhea and stomach flu. However, searches for vomiting show the most distinct pattern, and vomiting is the most pronounced symptom of a norovirus infection. The use of harmonic functions for describing baseline Web searches and laboratory reporting is a simple model, especially because the parameters are estimated by using the half-year with the least activity. Nonetheless, it is a direct approach, and we believe that the method still captures the time of onsets well. Web queries indicate the presence of norovirus infections in communities. Predictions of the onset of the norovirus laboratory reporting should also be possible, but further studies are needed to confirm that theory. Web queries have previously been correlated with influenza (3–7) and have been explored retrospectively for listeriosis (8), Salmonella spp (9), West Nile virus, and respiratory syncytial virus (10). With the Web queries, we get an additional surveillance system for the time of the year when few norovirus tests are conducted. In addition, knowing more about the impact of norovirus in the community means that we could provide more adequate information and advocate wiser measures for prevention and control.

A HIGHER ORDER BOUNDARY INTEGRAL EQUATIONS FOR 3D STEADY STATE HEAT CONDUCTION

The manifest success of the Finite Element Method has led to progressively increased demands being made of it. In particular, there is increasing pressure to use sophisticated 3D models which result in large costly numerical systems. It has shown that the singular point of the fundamental solutions can validly be taken outside the domain of the problem thereby yielding regular boundary integral equations (1]. The location of the singular point outside the domain of the problem permits the use of harmonic functions with higher order singularities, as kernels in the boundary integral equations. This possibility is attractive because the higher order singularities decay rapidly away from the singular point thereby resulting in more diagonally dominant algebraic equations. In this paper, a set of higher order functions are used as kernel functions, which still satisfy the governing equation (Lapalce's equation) with discre-tization acheived as continuous, discontinuous and partially discontinuous elements.