Murray's law has been generalized to provide morphometric relationships among various subtrees as well as between a feeding segment and the subtree it perfuses. The equivalent resistance of each subtree is empirically determined to be proportional to the cube of a subtree's cumulative arterial length (L) and inversely proportional to a subtree's arterial volume (V) raised to a power of approximately 2.6. This relationship, along with a minimization of a cost function, and a linearity assumption between flow and cumulative arterial length, provides a power law relationship between V and L. These results, in conjunction with conservation of energy, yield relationships between the diameter of a segment and the length of its distal subtree. The relationships were tested based on a complete set of anatomical data of the coronary arterial trees using two models. The first model, called the truncated tree model, is an actual reconstruction of the coronary arterial tree down to 500 microm in diameter. The second model, called the symmetric tree model, satisfies all mean anatomical data down to the capillary vessels. Our results show very good agreement between the theoretical formulation and the measured anatomical data, which may provide insight into the design of the coronary arterial tree. Furthermore, the established relationships between the various morphometric parameters of the truncated tree model may provide a basis for assessing the extent of diffuse coronary artery disease.

The advent of social media and its prosperity enable users to share their opinions and views. Understanding users' emotional states might provide the potential to create new business opportunities. Automatically identifying users' emotional states from their texts and classifying emotions into finite categories such as joy, anger, disgust, etc., can be considered as a text classification problem. However, it introduces a challenging learning scenario where multiple emotions with different intensities are often found in a single sentence. Moreover, some emotions co-occur more often while other emotions rarely coexist. In this paper, we propose a novel approach based on emotion distribution learning in order to address the aforementioned issues. The key idea is to learn a mapping function from sentences to their emotion distributions describing multiple emotions and their respective intensities. Moreover, the relations of emotions are captured based on the Plutchik's wheel of emotions and are subsequently incorporated into the learning algorithm in order to improve the accuracy of emotion detection. Experimental results show that the proposed approach can effectively deal with the emotion distribution detection problem and perform remarkably better than both the state-of-theart emotion detection method and multi-label learning methods.

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Patients with a partial fetal-type PCA could be more prone to develop ischemic strokes.