Complexity Analysis of Balloon Drawing for Rooted Trees

In a balloon drawing of a tree, all the children under the same parent are placed on the circumference of the circle centered at their parent, and the radius of the circle centered at each node along any path from the root reflects the number of descendants associated with the node. Among various styles of tree drawings reported in the literature, the balloon drawing enjoys a desirable feature of displaying tree structures in a rather balanced fashion. For each internal node in a balloon drawing, the ray from the node to each of its children divides the wedge accommodating the subtree rooted at the child into two sub-wedges. Depending on whether the two sub-wedge angles are required to be identical or not, a balloon drawing can further be divided into two types: even sub-wedge and uneven sub-wedge types. In the most general case, for any internal node in the tree there are two dimensions of freedom that affect the quality of a balloon drawing: (1) altering the order in which the children of the node appear in the drawing, and (2) for the subtree rooted at each child of the node, flipping the two sub-wedges of the subtree. In this paper, we give a comprehensive complexity analysis for optimizing balloon drawings of rooted trees with respect to angular resolution, aspect ratio and standard deviation of angles under various drawing cases depending on whether the tree is of even or uneven sub-wedge type and whether (1) and (2) above are allowed. It turns out that some are NP-complete while others can be solved in polynomial time. We also derive approximation algorithms for those that are intractable in general

A Simple Model for Cavity Enhanced Slow Lights in Vertical Cavity Surface Emission Lasers

We develop a simple model for the slow lights in Vertical Cavity Surface Emission Lasers (VCSELs), with the combination of cavity and population pulsation effects. The dependences of probe signal power, injection bias current and wavelength detuning for the group delays are demonstrated numerically and experimentally. Up to 65 ps group delays and up to 10 GHz modulation frequency can be achieved in the room temperature at the wavelength of 1.3 $\mu$m. The most significant feature of our VCSEL device is that the length of active region is only several $\mu$m long. Based on the experimental parameters of quantum dot VCSEL structures, we show that the resonance effect of laser cavity plays a significant role to enhance the group delays

Artificial Intelligence and Visual Analytics: A Deep-Learning Approach to Analyze Hotel Reviews & Responses

With a growing number of online reviews, consumers often rely on these reviews to make purchase decisions. However, little is known about managerial responses to online hotel reviews. This paper reports on a framework to integrate visual analytics and machine learning techniques to investigate whether hotel managers respond to positive and negative reviews differently and how to use a deep-learning approach to prioritize responses. In this study, forty 4- and 5-star hotels in London with 91,051 reviews and 70,397 responses were collected and analyzed. Visual analyses and machine learning were conducted. The results indicate most hotels (72.5%) showing no preference to respond to positive and negative reviews. Our proposed deep-learning approach outperformed existing algorithms to prioritize responses

ELEMENTARY SCHOOL BOYS’ SOCCER KICK SKILL ANALYSIS

The purpose of this study is aimed to analyze elementary school boys’ kicking skills on the perspective of motor skills. The data is collected by Vicon Motion Analysis System (250Hz). The parameters include the compare of the instant joint angles and the time proportion during the process of the kicking toward the different kick performance groups. The participants are 36 elementary boy soccer players (age: 11.7±0.3 yrs; height: 1.42±0.13 m; weight: 37.5±13.0 kg). The subjects were divided to two groups according to the instance kicking ball speed. The result indicated that the high ball speed group players have greater extremity joint angles than the low ball speed group. No difference was found on the time proportion during the process of the kicking. We suggest that the learning of kicking skill can start with the lower speed in the beginner stage