On meshfree numerical differentiation

2018 ◽  
Vol 16 (05) ◽  
pp. 717-739
Author(s):  
Leevan Ling ◽  
Qi Ye
Keyword(s):  
A Priori ◽  
Noisy Data ◽  
Numerical Differentiation ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Positive Definite Kernels ◽  
Approximation Quality ◽  
Symmetric Positive Definite ◽  
Optimal Kernel

We combine techniques in meshfree methods and Gaussian process regressions to construct kernel-based estimators for numerical derivatives from noisy data. Specially, we construct meshfree estimators from normal random variables, which are defined by kernel-based probability measures induced from symmetric positive definite kernels, to reconstruct the unknown partial derivatives from scattered noisy data. Our developed theories give rise to Tikhonov regularization methods with a priori parameter, but the shape parameters of the kernels remain tunable. For that, we propose an error measure that is computable without the exact values of the derivative. This allows users to obtain a quasi-optimal kernel-based estimator by comparing the approximation quality of kernel-based estimators. Numerical examples in two dimensions and three dimensions are included to demonstrate the convergence behavior and effectiveness of the proposed numerical differentiation scheme.

scholarly journals PARALLEL DELAUNAY REFINEMENT: ALGORITHMS AND ANALYSES

2007 ◽  
Vol 17 (01) ◽  
pp. 1-30 ◽  
Author(s):  
DANIEL A. SPIELMAN ◽  
SHANG-HUA TENG ◽  
ALPER ÜNGÖR
Keyword(s):  
Mesh Size ◽  
Constant Factor ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Delaunay Refinement ◽  
Steiner Points ◽  
Input Domain ◽  
Set Of Points ◽  
Refinement Algorithm

We present a parallel Delaunay refinement algorithm for generating well-shaped meshes in both two and three dimensions. Like its sequential counterparts, the parallel algorithm iteratively improves the quality of a mesh by inserting new points, the Steiner points, into the input domain while maintaining the Delaunay triangulation. The Steiner points are carefully chosen from a set of candidates that includes the circumcenters of poorly-shaped triangular elements. We introduce a notion of independence among possible Steiner points that can be inserted simultaneously during Delaunay refinements and show that such a set of independent points can be constructed efficiently and that the number of parallel iterations is O( log 2Δ), where Δ is the spread of the input — the ratio of the longest to the shortest pairwise distances among input features. In addition, we show that the parallel insertion of these set of points can be realized by sequential Delaunay refinement algorithms such as by Ruppert's algorithm in two dimensions and Shewchuk's algorithm in three dimensions. Therefore, our parallel Delaunay refinement algorithm provides the same shape quality and mesh-size guarantees as these sequential algorithms. For generating quasi-uniform meshes, such as those produced by Chew's algorithms, the number of parallel iterations is in fact O( log Δ). To the best of our knowledge, our algorithm is the first provably polylog(Δ) time parallel Delaunay-refinement algorithm that generates well-shaped meshes of size within a constant factor of the best possible.

LONG-TERM SEIZURES AND QUALITY OF LIFE AFTER EPILEPSY SURGERY COMPARED WITH MATCHED CONTROLS

Neurosurgery ◽  
2008 ◽  
Vol 62 (2) ◽  
pp. 326-335 ◽  
Author(s):  
Knut Stavem ◽  
Helge Bjørnæs ◽  
Iver A. Langmoen
Keyword(s):  
Quality Of Life ◽  
Epilepsy Surgery ◽  
Intractable Epilepsy ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Seizure Type ◽  
Seizure Outcome

Abstract OBJECTIVE We compared long-term seizure outcome and health-related quality of life (HRQoL) of patients who underwent epilepsy surgery and matched medically treated nonsurgical controls with intractable epilepsy. METHODS Medically treated controls were identified for patients operated on for epilepsy between January 1, 1949 and December 31, 1992. We used a matched cohort design, matching for age, sex, and seizure type. The analysis was based on 70 complete matching pairs. HRQoL was assessed with the Quality of Life in Epilepsy Inventory 89 questionnaire an average of 15 years after surgery. RESULTS Among surgery patients, 48% were seizure-free during the previous year compared with 19% of the controls (P = 0.0004). Fewer surgery patients used antiepileptic drugs (70%) than controls (93%). The odds of being seizure-free were higher for surgery patients in total and in subgroups divided according to length of follow-up. The mean HRQoL for surgery patients was higher in five of the 17 Quality of Life in Epilepsy Inventory 89 dimensions and worse in none. Among patients with more than 7 years of follow-up, HRQoL was better in three dimensions and worse in none. Among patients with 7 years of follow-up or less, HRQoL was better in two dimensions and worse in the language dimension of the Quality of Life in Epilepsy Inventory 89. CONCLUSION After an average of more than 15 years of follow-up, epilepsy surgery patients had fewer seizures, used less antiepileptic medication, and had better HRQoL in several dimensions of the Quality of Life in Epilepsy Inventory 89 instrument than matched medically treated controls with refractory epilepsy, although possibly at a slight disadvantage in the language dimension among those with 7 years of follow-up or less.

A Note on the Convergence Analysis of a Diffuse-domain Approach

2012 ◽  
Vol 12 (2) ◽  
pp. 153-167 ◽  
Author(s):  
Sebastian Franz ◽  
Hans-Görg Roos ◽  
Roland Gärtner ◽  
Axel Voigt
Keyword(s):  
Differential Equation ◽  
Convergence Analysis ◽  
Plane Problem ◽  
Half Plane ◽  
Numerical Experiments ◽  
Two Dimensions ◽  
Elliptic Differential Equation ◽  
One Dimension ◽  
Approximation Quality

Abstract We analyse the error behaviour of a diffuse-domain approximation of an elliptic differential equation. In one dimension and for a half-plane problem in two dimensions an approximation quality of order one in the interface parameter is shown. Some supporting numerical experiments are also presented.

Hilbert maps: Scalable continuous occupancy mapping with stochastic gradient descent

2016 ◽  
Vol 35 (14) ◽  
pp. 1717-1730 ◽  
Author(s):  
Fabio Ramos ◽  
Lionel Ott
Keyword(s):  
Probability Distributions ◽  
A Priori ◽  
Two Dimensions ◽  
Stochastic Gradient ◽  
Three Dimensions ◽  
Stochastic Gradient Descent ◽  
Adaptive Capabilities ◽  
Localization And Mapping ◽  
Before And After ◽  
Benchmark Datasets

The vast amount of data robots can capture today motivates the development of fast and scalable statistical tools to model the space the robot operates in. We devise a new technique for environment representation through continuous occupancy mapping that improves on the popular occupancy grip maps in two fundamental aspects: (1) it does not assume an a priori discrimination of the world into grid cells and therefore can provide maps at an arbitrary resolution; (2) it captures spatial relationships between measurements naturally, thus being more robust to outliers and possessing better generalization performance. The technique, named Hilbert maps, is based on the computation of fast kernel approximations that project the data in a Hilbert space where a logistic regression classifier is learnt. We show that this approach allows for efficient stochastic gradient optimization where each measurement is only processed once during learning in an online manner. We present results with three types of approximations: random Fourier; Nyström; and a novel sparse projection. We also extend the approach to accept probability distributions as inputs, for example, due to uncertainty over the position of laser scans due to sensor or localization errors. In this extended version, experiments were conducted in two dimensions and three dimensions, using popular benchmark datasets. Furthermore, an analysis of the adaptive capabilities of the technique to handle large changes in the data, such as trajectory update before and after loop closure during simultaneous localization and mapping, is also included.

scholarly journals hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes

2014 ◽  
Vol 24 (10) ◽  
pp. 2009-2041 ◽  
Author(s):  
Andrea Cangiani ◽  
Emmanuil H. Georgoulis ◽  
Paul Houston
Keyword(s):  
Discontinuous Galerkin ◽  
A Priori ◽  
Physical Space ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Interior Penalty ◽  
Polyhedral Meshes ◽  
Canonical Frame ◽  
Polygonal Elements ◽  
Polynomial Bases

An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical solution of second-order elliptic partial differential equations on general computational meshes consisting of polygonal/polyhedral elements is presented and analyzed. Utilizing a bounding box concept, the method employs elemental polynomial bases of total degree p (𝒫p-basis) defined on the physical space, without the need to map from a given reference or canonical frame. This, together with a new specific choice of the interior penalty parameter which allows for face-degeneration, ensures that optimal a priori bounds may be established, for general meshes including polygonal elements with degenerating edges in two dimensions and polyhedral elements with degenerating faces and/or edges in three dimensions. Numerical experiments highlighting the performance of the proposed method are presented. Moreover, the competitiveness of the p-version DGFEM employing a 𝒫p-basis in comparison to the conforming p-version finite element method on tensor-product elements is studied numerically for a simple test problem.

Enhancement of diffractions in prestack domain by means of a finite-offset double-square-root traveltime

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. V81-V96 ◽  
Author(s):  
Tiago A. Coimbra ◽  
Jorge H. Faccipieri ◽  
João H. Speglich ◽  
Leiv-J. Gelius ◽  
Martin Tygel
Keyword(s):  
Extraction Process ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Data Sets ◽  
Square Root ◽  
Data Set ◽  
Main Challenge ◽  
Two Parameters ◽  
General Source

Exploration of redundancy contained in the seismic data set assures enhancement of images that are based on stacking results. This enhancement is the goal of developing multiparametric traveltime equations that are able to approximate reflection and diffraction events in general source-receiver configurations. The main challenge of using these equations is to estimate a large number of parameters in a computationally feasible, reliable, and fast way. To obtain a better fit for diffraction traveltime events than the ones in the literature, we have derived a finite-offset (FO) double-square-root (DSR) diffraction traveltime equation (which depends on 10 parameters in three dimensions and four parameters in two dimensions). Moreover, to reduce the number of parameters, we have developed another version called simplified FO-DSR diffraction traveltime equation (which depends on five parameters in three dimensions and two parameters in two dimensions), which delivers a similar performance. We have developed operators that make use of the simplified FO-DSR traveltime equation to construct the so-called diffraction-only data set volumes (or, more simply, D-volumes) assuring enhancement in the diffraction extraction process. The D-volume construction has two steps: first, a stacking procedure to separate the diffraction events from the input data set and second, a spreading procedure to enhance the quality of these diffractions. As proof of concept, our approach has been tested on 2D/3D synthetic and 2D field data sets with successful results.

scholarly journals Forms of articulating epistemic Critique

2017 ◽  
pp. 40
Author(s):  
Oliver Dimbath ◽  
Stefan Böschen
Keyword(s):  
Two Dimensions ◽  
Three Dimensions ◽  
Policy Studies ◽  
Ongoing Debate ◽  
Political Landscape ◽  
Fundamental Understanding ◽  
Critical Policy

For many years now, there has been a vivid debate on contemporary forms of articulating epistemic critique, especially concerning the peer review mechanism but also dealing with fund mechanisms and, in some cases, focusing on book reviews. As reviews become more frequent and continue to exert considerable infl uence on the political landscape of academia, it is increasingly apparent that a fundamental understanding of the internal structure of articulating epistemic critique long overdue. Against this background, the aim of this article is to put forward two arguments. First, we argue these forms of articulating critique should be distinguished in regard to their distinctive characteristics and respective relations to academia as a whole. In doing so, we construct a research heuristic based on two dimensions, the opportunity to participate and the opportunity to react. Second, in response to an ongoing debate in Critical Policy Studies we conducted a small explorative empirical case study about on how scientific critique is articulated in book reviews. Besides providing a new overall perspective on how to categorize these forms of critique we found notable diff erences corresponding to the varied characteristics of the publication process in two disciplines (sociology/chemistry). We identified three dimensions as central for determining the quality of the expressed critique. As these differences might be related with underlying types of scientifi c communication, we fi nally argue that there is a necessity to take a closer look at how confi gurations of the diff erent forms of scientifi c critique should be analysed and to address these in their full scope as ‘cultures of critique’.

scholarly journals KEBERLANJUTAN PENGEMBANGAN LORONG GARDEN DALAM MEWUJUDKAN KAWASAN PERKOTAAN RAMAH LINGKUNGAN (ECO CITY) DI MAKASSAR

2021 ◽  
Vol 4 (2) ◽  
pp. 10-23
Author(s):  
Andi Wisneni ◽  
Abdullah Abdullah ◽  
Annas Boceng
Keyword(s):  
Two Dimensions ◽  
City Government ◽  
Three Dimensions ◽  
Residential Areas ◽  
Index Analysis ◽  
Interview Survey ◽  
The City ◽  
Ecological Dimension ◽  
Dimension Index

The Lorong Garden (aisle farming) program is one of the efforts of Makassar City Government to improve the area of narrow aisles or narrow streets in residential areas to make it more comfortable and healthier (ecological) and productive (economic). The program is expected to be able to improve the quality of the environment, community participation, and the economy of the community. The sustainability of its management is influenced by several integrated components. The study aims to analyze the sustainability of Lorong Garden development in Makassar City. Research in the form of a questionnaire interview survey of 126 respondents of the general public and 25 experts /stakeholders in the city of Makassar. Index analysis and sustainability status were using MDS methods Rap-Longgar-Potensial. The results showed that the multidimensional Lorong Garden Program is less sustainable (index 43.02%). Partially, there were two dimensions in the moderately sustainable category namely the ecological dimension (index 51.84%) and the technology dimension (index 65.09%) and three dimensions less sustainable, namely economy (index 46.15%), social (index 49.81) %) and institutional (index 39.20%). Of the total 37 attributes were analyzed, 17 sensitive attributes affected the sustainability of the Lorong Garden development in Makassar City.

scholarly journals Rancang Bangun Aplikasi Jam Tangan Pranata Laboratorium Pendidikan dengan Kemampuan Waterpas Tiga Dimensi untuk Mengatur Sambungan Modul Uji Pembebanan Motor

2020 ◽  
Vol 2 (2) ◽  
pp. 89-100
Author(s):  
Mochammad Darwis ◽  
Aris Eko Saputro
Keyword(s):  
Electric Motor ◽  
Two Dimensions ◽  
Electric Machine ◽  
Three Dimensions ◽  
Gyro Sensor ◽  
Electric Driving ◽  
Orientation Sensor ◽  
Rule Out ◽  
Angle Of Rotation

When testing the loading of an electric machine, we often experience problems in finding a tool to see the precision of the connection between the shaft of an electric machine. Shaft connections that are not straight and not right in the middle can damage the shaft of the rotating engine and the engine being rotated. This research is the development of previous research that uses Android phone as a tool. By reading the value of the orientation sensor on an android phone, we can measure the angle of rotation on the x, y and z axes. The Watpasdroid application will display the value on each axis. This application has also been used in the Electric Driving Laboratory at the Surabaya State Electronic Polytechnic (PENS), to check the connection (coupling) between an electric motor and a magnetic load (dynamo meter). The size of a cellphone that is still too large is sometimes become a problem  if the surface being measured is narrow. So we uses a wristband-shaped watch module that already has a gyro sensor and can be programmed according to our need. The size is almost 1/12 of ordinary cellphones. The M5Stick-C module is used to compare the gyro reading value displayed by the wristband. To test the quality of motor joint which  flatness checks have been assisted by using a wristband, a thermal observation camera is used. This application, does not rule out, can be used in other laboratories for the purpose of checking the plane levelness or equality in two dimensions or three dimensions.

scholarly journals Identifying the representational structure of affect using fMRI

2018 ◽  
Author(s):  
Alison Mattek ◽  
Daisy A. Burr ◽  
Jin Shin ◽  
Cady L. Whicker ◽  
M. Justin Kim
Keyword(s):  
A Priori ◽  
Two Dimensions ◽  
Linear Combinations ◽  
Four Dimensions ◽  
Affective Quality ◽  
Gradient Representation ◽  
Affective Psychology ◽  
Valence And Arousal ◽  
Affective Dimensions

The events we experience day to day can be described in terms of their affective quality: some are rewarding, others are upsetting, and still others are inconsequential. These natural distinctions reflect an underlying representational structure used to classify the affective quality of events. In affective psychology, many experiments model this representational structure with two dimensions, using either the dimensions of valence and arousal, or alternatively, the dimensions of positivity and negativity. Using an fMRI dataset, we show that these affective dimensions are not strictly linear combinations each other, and show that it is critical that all four dimensions be used to examined the data. Our findings include (1) a gradient representation of valence anatomically organized along the fusiform gyrus, and (2) distinct subregions within bilateral amygdala tracking arousal versus negativity. Importantly, these patterns would have remained concealed had either of the prevailing 2-dimensional approaches been adopted a priori.

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