• Title/Summary/Keyword: Sparse matrix

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A Meshless Method Using the Local Partition of Unity for Modeling of Cohesive Cracks (점성균열 모델을 위한 국부단위분할이 적용된 무요소법)

  • Zi, Goangseup;Jung, Jin-kyu;Kim, Byeong Min
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.5A
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    • pp.861-872
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    • 2006
  • The element free Galerkin method is extended by the local partition of unity method to model the cohesive cracks in two dimensional continuum. The shape function of a particle whose domain of influence is completely cut by a crack is enriched by the step enrichment function. If the domain of influence contains a crack tip inside, it is enriched by a branch enrichment function which does not have the LEFM stress singularity. The discrete equations are obtained directly from the standard Galerkin method since the enrichment is only for the displacement field, which satisfies the local partition of unity. Because only particles whose domains of influence are influenced by a crack are enriched, the system matrix is still sparse so that the increase of the computational cost is minimized. The condition for crack growth in dynamic problems is obtained from the material instability; when the acoustic tensor loses the positive definiteness, a cohesive crack is inserted to the point so as to change the continuum to a discontiuum. The crack speed is naturally obtained from the criterion. It is found that this method is more accurate and converges faster than the classical meshless methods which are based on the visibility concept. In this paper, several well-known static and dynamic problems were solved to verify the method.

Recommender Systems using Structural Hole and Collaborative Filtering (구조적 공백과 협업필터링을 이용한 추천시스템)

  • Kim, Mingun;Kim, Kyoung-Jae
    • Journal of Intelligence and Information Systems
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    • v.20 no.4
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    • pp.107-120
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    • 2014
  • This study proposes a novel recommender system using the structural hole analysis to reflect qualitative and emotional information in recommendation process. Although collaborative filtering (CF) is known as the most popular recommendation algorithm, it has some limitations including scalability and sparsity problems. The scalability problem arises when the volume of users and items become quite large. It means that CF cannot scale up due to large computation time for finding neighbors from the user-item matrix as the number of users and items increases in real-world e-commerce sites. Sparsity is a common problem of most recommender systems due to the fact that users generally evaluate only a small portion of the whole items. In addition, the cold-start problem is the special case of the sparsity problem when users or items newly added to the system with no ratings at all. When the user's preference evaluation data is sparse, two users or items are unlikely to have common ratings, and finally, CF will predict ratings using a very limited number of similar users. Moreover, it may produces biased recommendations because similarity weights may be estimated using only a small portion of rating data. In this study, we suggest a novel limitation of the conventional CF. The limitation is that CF does not consider qualitative and emotional information about users in the recommendation process because it only utilizes user's preference scores of the user-item matrix. To address this novel limitation, this study proposes cluster-indexing CF model with the structural hole analysis for recommendations. In general, the structural hole means a location which connects two separate actors without any redundant connections in the network. The actor who occupies the structural hole can easily access to non-redundant, various and fresh information. Therefore, the actor who occupies the structural hole may be a important person in the focal network and he or she may be the representative person in the focal subgroup in the network. Thus, his or her characteristics may represent the general characteristics of the users in the focal subgroup. In this sense, we can distinguish friends and strangers of the focal user utilizing the structural hole analysis. This study uses the structural hole analysis to select structural holes in subgroups as an initial seeds for a cluster analysis. First, we gather data about users' preference ratings for items and their social network information. For gathering research data, we develop a data collection system. Then, we perform structural hole analysis and find structural holes of social network. Next, we use these structural holes as cluster centroids for the clustering algorithm. Finally, this study makes recommendations using CF within user's cluster, and compare the recommendation performances of comparative models. For implementing experiments of the proposed model, we composite the experimental results from two experiments. The first experiment is the structural hole analysis. For the first one, this study employs a software package for the analysis of social network data - UCINET version 6. The second one is for performing modified clustering, and CF using the result of the cluster analysis. We develop an experimental system using VBA (Visual Basic for Application) of Microsoft Excel 2007 for the second one. This study designs to analyzing clustering based on a novel similarity measure - Pearson correlation between user preference rating vectors for the modified clustering experiment. In addition, this study uses 'all-but-one' approach for the CF experiment. In order to validate the effectiveness of our proposed model, we apply three comparative types of CF models to the same dataset. The experimental results show that the proposed model outperforms the other comparative models. In especial, the proposed model significantly performs better than two comparative modes with the cluster analysis from the statistical significance test. However, the difference between the proposed model and the naive model does not have statistical significance.

An Estimation of Concentration of Asian Dust (PM10) Using WRF-SMOKE-CMAQ (MADRID) During Springtime in the Korean Peninsula (WRF-SMOKE-CMAQ(MADRID)을 이용한 한반도 봄철 황사(PM10)의 농도 추정)

  • Moon, Yun-Seob;Lim, Yun-Kyu;Lee, Kang-Yeol
    • Journal of the Korean earth science society
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    • v.32 no.3
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    • pp.276-293
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    • 2011
  • In this study a modeling system consisting of Weather Research and Forecasting (WRF), Sparse Matrix Operator Kernel Emissions (SMOKE), the Community Multiscale Air Quality (CMAQ) model, and the CMAQ-Model of Aerosol Dynamics, Reaction, Ionization, and Dissolution (MADRID) model has been applied to estimate enhancements of $PM_{10}$ during Asian dust events in Korea. In particular, 5 experimental formulas were applied to the WRF-SMOKE-CMAQ (MADRID) model to estimate Asian dust emissions from source locations for major Asian dust events in China and Mongolia: the US Environmental Protection Agency (EPA) model, the Goddard Global Ozone Chemistry Aerosol Radiation and Transport (GOCART) model, and the Dust Entrainment and Deposition (DEAD) model, as well as formulas by Park and In (2003), and Wang et al. (2000). According to the weather map, backward trajectory and satellite image analyses, Asian dust is generated by a strong downwind associated with the upper trough from a stagnation wave due to development of the upper jet stream, and transport of Asian dust to Korea shows up behind a surface front related to the cut-off low (known as comma type cloud) in satellite images. In the WRF-SMOKE-CMAQ modeling to estimate the PM10 concentration, Wang et al.'s experimental formula was depicted well in the temporal and spatial distribution of Asian dusts, and the GOCART model was low in mean bias errors and root mean square errors. Also, in the vertical profile analysis of Asian dusts using Wang et al's experimental formula, strong Asian dust with a concentration of more than $800\;{\mu}g/m^3$ for the period of March 31 to April 1, 2007 was transported under the boundary layer (about 1 km high), and weak Asian dust with a concentration of less than $400\;{\mu}g/m^3$ for the period of 16-17 March 2009 was transported above the boundary layer (about 1-3 km high). Furthermore, the difference between the CMAQ model and the CMAQ-MADRID model for the period of March 31 to April 1, 2007, in terms of PM10 concentration, was seen to be large in the East Asia area: the CMAQ-MADRID model showed the concentration to be about $25\;{\mu}g/m^3$ higher than the CMAQ model. In addition, the $PM_{10}$ concentration removed by the cloud liquid phase mechanism within the CMAQ-MADRID model was shown in the maximum $15\;{\mu}g/m^3$ in the Eastern Asia area.