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

Adaptive Circuit Learning of Born Machine: Towards Realization of Amplitude Embedding and Data Loading

With the progress in the quantum algorithm in recent years, much of the existing literature claims the exponential quantum advantage against their classical counterpart. However, many of these successes hinge on the assumption that arbitrary states can be efficiently prepared in quantum circuits. In reality, crafting a circuit to prepare a generic $n$-qubit quantum state demands an operation count on the order of $\mathcal{O}(2^n)$, which is prohibitively demanding for the quantum algorithm to demonstrate its advantage against the classical one. To tackle this data-loading problem, numerous strategies have been put forward. Nonetheless, most of these approaches only consider a very simple and easy-to-implement circuit structure, which has been shown to suffer from serious optimization issues. In this study, we harness quantum circuits as Born machines to generate probability distributions. Drawing inspiration from methods used to investigate electronic structures in quantum chemistry and condensed matter physics, we present a novel algorithm "Adaptive Circuit Learning of Born Machine" (ACLBM) that dynamically expands the ansatz circuit. Our algorithm is tailored to selectively integrate two-qubit entangled gates that best capture the complex entanglement present within the target state. Empirical results underscore the proficiency of our approach in encoding real-world data through amplitude embedding, demonstrating not only compliance with but also enhancement over the performance benchmarks set by previous research.Comment: 14 pages, 11 figures, 1 tabl

Rega-Net:Retina Gabor Attention for Deep Convolutional Neural Networks

Extensive research works demonstrate that the attention mechanism in convolutional neural networks (CNNs) effectively improves accuracy. But little works design attention mechanisms using large receptive fields. In this work, we propose a novel attention method named Rega-net to increase CNN accuracy by enlarging the receptive field. Inspired by the mechanism of the human retina, we design convolutional kernels to resemble the non-uniformly distributed structure of the human retina. Then, we sample variable-resolution values in the Gabor function distribution and fill these values in retina-like kernels. This distribution allows important features to be more visible in the center position of the receptive field. We further design an attention module including these retina-like kernels. Experiments demonstrate that our Rega-Net achieves 79.963\% top-1 accuracy on ImageNet-1K classification and 43.1\% mAP on COCO2017 object detection. The mAP of the Rega-Net increased by up to 3.5\% compared to baseline networks

A Global Method for a Two-Dimensional Cutting Stock Problem in the Manufacturing Industry

A two-dimensional cutting stock problem (2DCSP) needs to cut a set of given rectangular items from standard-sized rectangular materials with the objective of minimizing the number of materials used. This problem frequently arises in different manufacturing industries such as glass, wood, paper, plastic, etc. However, the current literatures lack a deterministic method for solving the 2DCSP. However, this study proposes a global method to solve the 2DCSP. It aims to reduce the number of binary variables for the proposed model to speed up the solving time and obtain the optimal solution. Our experiments demonstrate that the proposed method is superior to current reference methods for solving the 2DCSP

Acceptance Of Qr Code In Taiwan: An Extension Of The Technology Acceptance Model

The development and application of QR code is quite advanced in Japan and Korea; in contrast, at the time when the QR code was introduced in Taiwan, lack of mobile phone support and the limited applications of QR code meant that it was not immediately popularized. In recent years, the growing popularity of smart phones has enhanced the various applications of QR code, not only providing the information to the user, but also performing navigation, marketing and ticketing functions, to name a few. This study is based on the Technology Acceptance Model, with Social Influence, Facilitating Conditions, Awareness Knowledge, Operation Knowledge and Price as the usage factors, and by verifying the structural modelling through public surveys and analyzing the importance of the Acceptance Model and other influences of users in Taiwan as the driving factors in incorporating QR code applications in the government, telecommunication carrier and business spheres