198,582 research outputs found
Universal attraction force-inspired freeform surface modeling for 3D sketching
This paper presents a novel freeform surface modeling method to construct a freeform surface from 3D sketch. The approach is inspired by Newton’s universal attraction force law to construct a surface model from rough boundary curves and unorganized interior characteristic curves which may cross the boundary curves or not.
Based on these unorganized curves, an initial surface can be obtained for conceptual design and it can be improved later in a commercial package. The approach has been tested with examples and it is capable of dealing with unorganized design curves for surface modeling
Scalable approximate FRNN-OWA classification
Fuzzy Rough Nearest Neighbour classification with Ordered Weighted Averaging operators (FRNN-OWA) is an algorithm that classifies unseen instances according to their membership in the fuzzy upper and lower approximations of the decision classes. Previous research has shown that the use of OWA operators increases the robustness of this model. However, calculating membership in an approximation requires a nearest neighbour search. In practice, the query time complexity of exact nearest neighbour search algorithms in more than a handful of dimensions is near-linear, which limits the scalability of FRNN-OWA. Therefore, we propose approximate FRNN-OWA, a modified model that calculates upper and lower approximations of decision classes using the approximate nearest neighbours returned by Hierarchical Navigable Small Worlds (HNSW), a recent approximative nearest neighbour search algorithm with logarithmic query time complexity at constant near-100% accuracy. We demonstrate that approximate FRNN-OWA is sufficiently robust to match the classification accuracy of exact FRNN-OWA while scaling much more efficiently. We test four parameter configurations of HNSW, and evaluate their performance by measuring classification accuracy and construction and query times for samples of various sizes from three large datasets. We find that with two of the parameter configurations, approximate FRNN-OWA achieves near-identical accuracy to exact FRNN-OWA for most sample sizes within query times that are up to several orders of magnitude faster
Training a personal alert system for research information recommendation
Information Systems, and in particular Current Research Information Systems (CRISs), are usually quite difficult to query when looking for specific information, due to the huge amounts of data they contain. To solve this problem, we propose to use a personal search agent that uses fuzzy and rough sets to inform the user about newly available information. Additionally, in order to automate the operation of our solution and to provide it with sufficient information, a document classification module is developed and tested. This module also generates fuzzy relations between research domains that are used by the agent during the mapping process
Rough solutions of the Einstein Constraint Equations on Asymptotically Flat Manifolds without Near-CMC Conditions
In this article we consider the conformal decomposition of the Einstein
constraint equations introduced by Lichnerowicz, Choquet-Bruhat, and York, on
asymptotically flat (AF) manifolds. Using the non-CMC fixed-point framework
developed in 2009 by Holst, Nagy, and Tsogtgerel and by Maxwell, we establish
existence of coupled non-CMC weak solutions for AF manifolds. As is the case
for the analogous existence results for non-CMC solutions on closed manifolds
and compact manifolds with boundary, our results here avoid the near-CMC
assumption by assuming that the freely specifiable part of the data given by
the traceless-transverse part of the rescaled extrinsic curvature and the
matter fields are sufficiently small. The non-CMC rough solutions results here
for AF manifolds may be viewed as extending to AF manifolds the 2009 and 2014
results on rough far-from-CMC positive Yamabe solutions for closed and compact
manifolds with boundary. Similarly, our results may be viewed as extending the
recent 2014 results for AF manifolds of Dilts, Isenberg, Mazzeo and Meier, and
of Holst and Meier; while their results are restricted to smoother background
metrics and data, the results here allow the regularity to be extended down to
the minimum regularity allowed by the background metric and the matter, further
completing the rough solution program initiated by Maxwell and Choquet-Bruhat
in 2004.Comment: 82 pages. Version 2 has minor changes reflecting comments and minor
typos fixed. Version 3 updates a bibliography entr
Analysing imperfect temporal information in GIS using the Triangular Model
Rough set and fuzzy set are two frequently used approaches for modelling and reasoning about imperfect time intervals. In this paper, we focus on imperfect time intervals that can be modelled by rough sets and use an innovative graphic model [i.e. the triangular model (TM)] to represent this kind of imperfect time intervals. This work shows that TM is potentially advantageous in visualizing and querying imperfect time intervals, and its analytical power can be better exploited when it is implemented in a computer application with graphical user interfaces and interactive functions. Moreover, a probabilistic framework is proposed to handle the uncertainty issues in temporal queries. We use a case study to illustrate how the unique insights gained by TM can assist a geographical information system for exploratory spatio-temporal analysis
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