Orbits of Plane Partitions of Exceptional Lie Type

For each minuscule flag variety $X$, there is a corresponding minuscule poset, describing its Schubert decomposition. We study an action on plane partitions over such posets, introduced by P. Cameron and D. Fon-der-Flaass (1995). For plane partitions of height at most $2$, D. Rush and X. Shi (2013) proved an instance of the cyclic sieving phenomenon, completely describing the orbit structure of this action. They noted their result does not extend to greater heights in general; however, when $X$ is one of the two minuscule flag varieties of exceptional Lie type $E$, they conjectured explicit instances of cyclic sieving for all heights. We prove their conjecture in the case that $X$ is the Cayley-Moufang plane of type $E_6$. For the other exceptional minuscule flag variety, the Freudenthal variety of type $E_7$, we establish their conjecture for heights at most $4$, but show that it fails generally. We further give a new proof of an unpublished cyclic sieving of D. Rush and X. Shi (2011) for plane partitions of any height in the case $X$ is an even-dimensional quadric hypersurface. Our argument uses ideas of K. Dilks, O. Pechenik, and J. Striker (2017) to relate the action on plane partitions to combinatorics derived from $K$-theoretic Schubert calculus.Comment: 25 pages, 7 figures, 3 tables. Section 5 rewritten and simplifie

Alkenylation and Allylation of Aldehydes by Using an Ni/Cr/TDAE Redox System

In 360 females, Bone mineral density (BMD) in lumbar vertebrae (L2-L4) was assessed by quantitative computed tomography (QCT), and the values obtained were compared with the frequency of vertebral transformation or fracture as assessed by lateral scan image (scanogram) by X-ray CT. A correlation was observed between the frequency of vertebral transformation (or fracture) and lumbar BMD values : BMD under 125 mg/cm(3) was observed over 90% of women with vertebral transformation, and BMD under 70mg/cm(3) was found about 50% of them. These results suggest that decrease in BMD in lumbar vertebrae leads to vertebral transformation or fracture. Thus, measurement of BMD by QCT would be very useful in predicting vertebral transformation or fractures

Applying Geographically Weighted Regression to Conjoint Analysis: Empirical Findings from Urban Park Amenities

The objective of this study is to develop spatially-explicit choice model and investigate its validity and applicability in CA studies. This objective is achieved by applying locally-regressed geographically weighted regression (GWR) and GIS to survey data on hypothetical dogrun facilities (off-leash dog area) in urban recreational parks in Tokyo, Japan. Our results show that spatially-explicit conditional logit model developed in this study outperforms traditional model in terms of data fit and prediction accuracy. Our results also show that marginal willingness-to-pay for various attributes of dogrun facilities has significant spatial variation. Analytical procedure developed in this study can reveal spatially-varying individual preferences on attributes of urban park amenities, and facilitates area-specific decision makings in urban park planning.Choice experiments, conjoint analysis, dogrun, geographically weighted regression, spatial econometrics, Research Methods/ Statistical Methods, Resource /Energy Economics and Policy,

Selective Sampling for Example-based Word Sense Disambiguation

This paper proposes an efficient example sampling method for example-based word sense disambiguation systems. To construct a database of practical size, a considerable overhead for manual sense disambiguation (overhead for supervision) is required. In addition, the time complexity of searching a large-sized database poses a considerable problem (overhead for search). To counter these problems, our method selectively samples a smaller-sized effective subset from a given example set for use in word sense disambiguation. Our method is characterized by the reliance on the notion of training utility: the degree to which each example is informative for future example sampling when used for the training of the system. The system progressively collects examples by selecting those with greatest utility. The paper reports the effectiveness of our method through experiments on about one thousand sentences. Compared to experiments with other example sampling methods, our method reduced both the overhead for supervision and the overhead for search, without the degeneration of the performance of the system.Comment: 25 pages, 14 Postscript figure