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| 2. |
- Engström, Christopher, et al.
(författare)
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An evaluation of centrality measures used in cluster analysis
- 2014
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Ingår i: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014. - : American Institute of Physics (AIP). - 9780735412767 ; , s. 313-320
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Konferensbidrag (refereegranskat)abstract
- Clustering of data into groups of similar objects plays an important part when analysing many types of data especially when the datasets are large as they often are in for example bioinformatics social networks and computational linguistics. Many clustering algorithms such as K-means and some types of hierarchical clustering need a number of centroids representing the 'center' of the clusters. The choice of centroids for the initial clusters often plays an important role in the quality of the clusters. Since a data point with a high centrality supposedly lies close to the 'center' of some cluster this can be used to assign centroids rather than through some other method such as picking them at random. Some work have been done to evaluate the use of centrality measures such as degree betweenness and eigenvector centrality in clustering algorithms. The aim of this article is to compare and evaluate the usefulness of a number of common centrality measures such as the above mentioned and others such as PageRank and related measures.
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| 3. |
- Lukkassen, Dag, et al.
(författare)
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On the role of homogenization in lubrication theory
- 2014
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Ingår i: 10th International conference on mathematical problems in engineering, aerosace and sciences. - Melville, NY : American Institute of Physics (AIP). - 9780735412767 ; , s. 1170-1176
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Konferensbidrag (refereegranskat)abstract
- Tribology is an interdisciplinary subject dealing with science and technology of interacting surfaces in relative motion. We discuss some new mathematical tools which may be useful in the further development of this field.
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| 4. |
- Lundberg, Staffan
(författare)
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On precise differentiation formula for weighted singular integrals of Sobolev functions
- 2014
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Ingår i: 10th International conference on mathematical problems in engineering, aerosace and sciences. - Melville, NY : American Institute of Physics (AIP). - 9780735412767 ; , s. 621-626
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Konferensbidrag (refereegranskat)abstract
- In various applications there appear integral equations of the first kind with a kernel which has a logarithmic singularity. The corresponding classes of well-posedness for such equations are Sobolev spaces. We prove the differentiation formulas for weighted singular integrals, which appear in such study, with the goal of its further application to integral equations.
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| 5. |
- Lundengård, Karl, et al.
(författare)
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Application of the Marquardt Least Square Method to the Estimation of Pulse Function Parameters
- 2014
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Ingår i: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014. - : AIP Publishing LLC. - 9780735412767 ; , s. 637-646
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Konferensbidrag (refereegranskat)abstract
- Application of the Marquardt least-squares method (MLSM) to the estimation of non-linear parameters of functionsused for representing various lightning current waveshapes is presented in this paper. Parameters are determined for the Pulse,Heidler’s and DEXP function representing the first positive, first and subsequent negative stroke currents as given in IEC62305-1 Standard Ed.2, and also for some other fast- and slow-decaying lightning current waveshapes. The results prove theability of the MLSM to be used for the estimation of parameters of the functions important in lightning discharge modeling.
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| 6. |
- Lundengård, Karl, et al.
(författare)
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Optimization of the determinant of the Vandermonde matrix and related matrices
- 2014
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Ingår i: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014. - : American Institute of Physics (AIP). - 9780735412767 ; , s. 627-636
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Konferensbidrag (refereegranskat)abstract
- Various techniques for interpolation of data, moment matching in stochastic applications and various methods in numerical analysis can be described using Vandermonde matrices. For this reason the properties of the determinant of the Vandermonde matrix and related matrices are interesting. Here the extreme points of the Vandermonde determinant, and related determinants, on some simple surfaces such as the unit sphere are analyzed, both numerically and analytically. Some results are also visualized in various dimensions. The extreme points of the Vandermonde determinant are also related to the roots of certain orthogonal polynomials such as the Hermite polynomials.
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| 7. |
- Malyarenko, Anatoliy, 1957-, et al.
(författare)
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The spectral expansion of the elasticity random field
- 2014
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Ingår i: AIP Conference Proceedings 1637. - : AIP Publishing LLC. - 9780735412767 ; , s. 647-655
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Konferensbidrag (refereegranskat)abstract
- We consider a deformable body that occupies a region D in the plane. In our model, the body's elasticity tensor H (x) is the restriction to D of a second-order mean-square continuous random field. Under translation, the expected value and the correlation tensor of the field H (x) do not change. Under action of an arbitrary element k of the orthogonal group O (2), they transform according to the reducible orthogonal representation k bar right arrow S-2 (S-2 (k)) of the above group. We find the spectral expansion of the correlation tensor R (x) of the elasticity field as well as the expansion of the field itself in terms of stochastic integrals with respect to a family of orthogonal scattered random measures.
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| 8. |
- Miroshnikova, Elena
(författare)
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Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted L p -spaces
- 2014
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Ingår i: 10th International conference on mathematical problems in engineering, aerosace and sciences. - Melville, NY : American Institute of Physics (AIP). - 9780735412767 ; , s. 663-672
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Konferensbidrag (refereegranskat)abstract
- In weighted space L p ( R n ,ρ), 1 < p < ∞, a new broad class of integral operators with anisotropically homogeneous kernels is investigated. For such operators boundedness theorem is proved. Also the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type is considered. For elements of the algebra symbolic calculation is constructed, the invertibility criterion is obtained in terms of operator symbol
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| 9. |
- Monsefi, Farid, et al.
(författare)
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Solution of Two-Dimensional Electromagnetic Scattering Problem by FDTD with Optimal Step Size, Based on a Semi-Norm Analysis
- 2014
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Ingår i: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014. - : American Institute of Physics (AIP). - 9780735412767 ; , s. 683-690
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Konferensbidrag (refereegranskat)abstract
- To solve the electromagnetic scattering problem in two dimensions, the Finite Difference Time Domain (FDTD)method is used. The order of convergence of the FDTD algorithm, solving the two-dimensional Maxwell’s curl equations,is estimated in two different computer implementations: with and without an obstacle in the numerical domain of the FDTDscheme. This constitutes an electromagnetic scattering problem where a lumped sinusoidal current source, as a source ofelectromagnetic radiation, is included inside the boundary. Confined within the boundary, a specific kind of AbsorbingBoundary Condition (ABC) is chosen and the outside of the boundary is in form of a Perfect Electric Conducting (PEC)surface. Inserted in the computer implementation, a semi-norm has been applied to compare different step sizes in the FDTDscheme. First, the domain of the problem is chosen to be the free-space without any obstacles. In the second part of thecomputer implementations, a PEC surface is included as the obstacle. The numerical instability of the algorithms can berather easily avoided with respect to the Courant stability condition, which is frequently used in applying the general FDTDalgorithm.
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| 10. |
- Ni, Ying, 1976-, et al.
(författare)
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Investigating the added values of high frequency energy consumption data using data mining techniques
- 2014
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Ingår i: AIP Conference Proceedings 1637 (2014). - : AIP Publishing. - 0094-243X. - 9780735412767 ; , s. 734-743
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Konferensbidrag (refereegranskat)abstract
- In this paper we apply data-mining techniques to customer classification and clustering tasks on actual electricity consumption data from 350 Swedish households. For the classification task we classify households into different categories based on some statistical attributes of their energy consumption measurements. For the clustering task, we use average daily load diagrams to partition electricity-consuming households into distinct groups. The data contains electricity consumption measurements on each 10-minute time interval for each light source and electrical appliance. We perform the classification and clustering tasks using four variants of processeddata sets corresponding to the 10-minute total electricity consumption aggregated from all electrical sources, the hourly total consumption aggregated over all 10-minute intervals during that clock hour, the total consumption over each four-hour intervals and finally the daily total consumption. The goal is to see if there are any differences in using data sets of various frequency levels. We present the comparison results and investigate the added value of the high-frequency measurements, for example 10-minute measurements, in terms of its influence on customer clustering and classification.
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