Hierarchical interpolative factorization for elliptic operators: differential equations

This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an approximate generalized LU/LDL decomposition that facilitates the efficient inversion of the discretized operator. HIF-DE is based on the multifrontal method but uses skeletonization on the separator fronts to sparsify the dense frontal matrices and thus reduce the cost. We conjecture that this strategy yields linear complexity in 2D and quasilinear complexity in 3D. Estimated linear complexity in 3D can be achieved by skeletonizing the compressed fronts themselves, which amounts geometrically to a recursive dimensional reduction scheme. Numerical experiments support our claims and further demonstrate the performance of our algorithm as a fast direct solver and preconditioner. MATLAB codes are freely available.Comment: 37 pages, 13 figures, 12 tables; to appear, Comm. Pure Appl. Math. arXiv admin note: substantial text overlap with arXiv:1307.266

Hierarchical interpolative factorization for elliptic operators: integral equations

This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization takes the form of an approximate generalized LU decomposition that permits the efficient application of the discretized operator and its inverse. HIF-IE is based on the recursive skeletonization algorithm but incorporates a novel combination of two key features: (1) a matrix factorization framework for sparsifying structured dense matrices and (2) a recursive dimensional reduction strategy to decrease the cost. Thus, higher-dimensional problems are effectively mapped to one dimension, and we conjecture that constructing, applying, and inverting the factorization all have linear or quasilinear complexity. Numerical experiments support this claim and further demonstrate the performance of our algorithm as a generalized fast multipole method, direct solver, and preconditioner. HIF-IE is compatible with geometric adaptivity and can handle both boundary and volume problems. MATLAB codes are freely available.Comment: 39 pages, 14 figures, 13 tables; to appear, Comm. Pure Appl. Mat

Butterfly Factorization

The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the matrix and its adjoint are available or the entries of the matrix can be sampled individually. For an $N \times N$ matrix, the resulting factorization is a product of $O(\log N)$ sparse matrices, each with $O(N)$ non-zero entries. Hence, it can be applied rapidly in $O(N\log N)$ operations. Numerical results are provided to demonstrate the effectiveness of the butterfly factorization and its construction algorithms

Benefits and costs of legalized gaming in Penghu as perceived by Taiwanese people

This study evaluates attitudes and perceptions of residents in Penghu County and the main island of Taiwan regarding benefits and costs of legalized gaming in Penghu County. Surveys were conducted by using convenient sampling in both Taiwan\u27s main island and Penghu County. Results indicate residents in Penghu and residents in Taiwanese have no significant difference in supporting legalized gaming. Residents in both locations show a positive attitude toward the legalized gaming based on the mean score from the test. Results also indicate that there are three socio-demographic groups have significantly different opinions in supporting legalized gaming. Results also point out the impacts that those three groups are concerned about regarding benefits and costs of legalized gaming. In addition, results may provide the Taiwanese Government some directions for improving residents\u27 perceptions toward the benefits and costs of legalized gaming once the Taiwanese Government decides to use legalized gaming as a means to improve the community\u27s economy and tourism development

Causes and Consequences of Roost Switching by the Bat Myotis formosus (V espertilionidae)

Group living is widespread among animals. Theory predicts that animals should aggregate if the benefits associated with group living outweigh the costs. Benefits associated with group living could arise passively (e.g. aggregate independently to exploit a patchily distributed resource) or actively (e.g. cooperation). Some forest-dwelling bat species switch roosts frequently, but maintain an association among specific individuals, and therefore are fission-fusion societies, the temporary splitting of colonies into several subgroups. Normally, movements between alternative roosts are costly. Fission-fusion societies might overcome the costs by providing benefits associated with large subgroup size or cooperation. In addition, sociality could influence the movements of individuals within and between social groups and affect the gene flow. However, our understanding about the underlying causes and effects of fission-fusion behaviour is still lacking. I used both direct behavioural observation and indirect molecular analysis to study the roosting behaviour and sociality of Aiyotis formosus. In my study area, M. formosus used two different types of day roosts in summer, houses and foliage, which were extremely different in availability, permanency, and space. I found the roost type affected roosting behaviour of bats. In general, roost switching frequency of foliage- roosting Myotis formosus was high and associated with intrinsic and environmental factors. Myotis formosus in large subgroups switched roosts less frequently than those living in smaller subgroups. Bats were faithful to specific roosting areas, and the nonrandom association between individuals indicated that they live in a fission-fusion society and switched roosts to enhance social interaction. Reproductive status also in affected the association pattern and roost switching frequency of foliage-roosting M formosus while the similarity in genetic relatedness or matrilineal relationship did not facilitate association between individuals. Benefits associated with cooperation or clustering as well as female philopatry are possible reasons for the fission-fusion society of M. formosus. The molecular data based on the contrasted pattern found from the biparentally inherited nuclear microsatellite markers and maternally inherited mitochondrial DNA markers also suggest that gene flow between colonies is male- mediated, while females appeared to show high fidelity to a small roosting area. Behaviourally, the male-mediated gene flow among bat colonies might occur by male dispersal and/or mating outside the colony, including swarming sites, hibemacula, or on the migration route. However, the details about the mating of this species are still unknown

Parental Involvement of Chinese International Students in Regards to Their Children’s School Selection and Communication with Teachers

This research explores two broad areas in relation to the experiences of international students located in Ontario. The first area explores how international students, who are also parents, selected schools for their children. The second area explores how they communicated with their child’s teacher. Six participants were recruited to participate in this study. Data was collected through semi-structured interviews. This small-scale study reveals that participants considered five key factors when selecting schools for their children, including peers’ family background, school ranking, language of instruction, impression of the teachers and school staff, and parents’ religious background. These factors are shaped by the Chinese culture, the participants’ class identity, and their anxiety towards their children’s future. In relation to the second area explored in this study, participants communicated with teachers in different ways with a preference of written form. More parent-teacher communication took place among participants who had younger children or children with behavioural issues. Participants viewed attending parent-teacher meeting as their responsibility. Their expectations of parent-teacher communication were to obtain information about their children’s school performance and to share their parental concerns and care. The major challenges in parent-teacher communication included unfamiliarity of the schooling system and cultural differences. Suggestions were given to the universities so that they will fully address the needs of such a unique group of graduate students

Myofibrillar protein degradation patterns and structural changes in skeletal muscle from electrically stimulated Bos taurus and Bos indicus crossbred cattle

Degradation of titin, nebulin, desmin and troponin-T, structural changes in nonstimulated (NS) and electrically stimulated (ES) bovine skeletal muscle and comparison of these changes in Angus x Jersey (AxJ) cattle (Bos taurus cross) with the changes in Brahman x Simmental (BxS) cattle (Bos indicus cross) were determined. Myofibrils for SDS-PAGE and Western blots and intact muscle samples for transmission electron microscopy were prepared at 0, 1, 3, 7, 14 and 28 days postmortem (PM). In SDS-PAGE, ES slightly accelerated the degradation of intact titin (T1 band), nebulin, desmin and troponin-T in AxJ samples. In Western blots of AxJ samples, ES enhanced T1 degradation, the appearance of a 38 kDa desmin degradation product and the accumulation of the 30 kDa polypeptide but had no detectable affect on nebulin degradation. Both SDS-PAGE and Western blots of BxS samples showed that ES had no effect on degradation of T1, nebulin, desmin and troponin-T but slightly enhanced the accumulation of the 30 kDa polypeptide. These four proteins were degraded faster in AxJ than in BxS samples. ES accelerated the appearance of wide I-band fractures and increased the frequency of narrow I-band fractures in all samples and of intermediate and wide I-band fractures through day 7 in AxJ samples. In BxS samples, ES accelerated the appearance and frequency of all three types of I-band fractures through 14 days PM. All three types of I-band fractures were seen sooner in NS AxJ than in NS BxS samples. The frequency of all types of I-band fractures was greater in all AxJ than in all BxS samples. Twice as many intermediate and wide I-band fractures were present at 3, 7, 14 and 28 days in AxJ as in BxS samples. Z-line degradation occurred but was unaffected by ES or by breed. In conclusion, ES slightly accelerated the degradation of titin, nebulin, desmin and troponin-T in AxJ samples only and accelerated the appearance of wide I-band fractures in AxJ samples. ES caused all three types of I-band fractures to appear sooner in BxS than in NS BxS samples