In this paper, we present a Bound states in the continuum (BIC) metamaterial heterogeneous structures based on coupled mode theory. We find more general physical parameters to represent BIC, which are resonant frequencies and corresponding phases of structures. Therefore, BIC comes from equal value not only for homogeneous Meanwhile, if one structure's frequency phase vary by varying geometry, ...

We develop a closed form asymptotic for­ mula to compute the marginal likelihood of data given a naive Bayesian network model with two hidden states and binary features. This formula deviates from the standard BIC score. Our work provides a concrete example that the BIC score is generally not valid for statistical models that belong to a stratified exponential family. This stands in contrast to...

Bayesian Information Criterion (BIC) is a promising method for detecting the number of clusters. It is often used in model-based clustering in which a decisive first local maximum is detected as the number of clusters. In this paper, we re-formulate the BIC in partitioning based clustering algorithm, and propose a new knee point finding method based on it. Experimental results show that the pro...

In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation (SCAD) penalty (Fan and Li, 2001) and the adaptive LASSO penalty (Zou, 2006) have been proposed in literature. In this article, we establish the result that ...

The Bayesian Information Criterion (BIC) is widely used for variable selection in mixed effects models. However, its expression is unclear in typical situations of mixed effects models, where simple definition of the sample size is not meaningful. We derive an appropriate BIC expression that is consistent with the random effect structure of the mixed effects model. We illustrate the behavior of...

The purpose of this study is to evaluate the degree of osseointegration of resorbable blasting media (RBM) surface implants retrieved from humans. Three implants in the mandibular molar region that were surface-treated with RBM were retrieved from two patients. The implants were used to manufacture specimens in order to measure the bone-implant contact (BIC) ratio. The BIC ratios of the three i...

One difficult problem we are often faced with in clustering analysis is how to choose the number of clusters. In this paper, we propcse to choose the number of clusters by optimizing the Bq2yesian information criterion (BIC), a model selection criierion in the statistics literature. We develop a termination criterion for the hierarchical clustering methods which optimizes the BIC criterion in a...