Sharp bounds for harmonic numbers

In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\in\mathbb{N}$, the double inequality -\frac{1}{12n^2+{2(7-12\gamma)}/{(2\gamma-1)}}\le H(n)-\ln n-\frac1{2n}-\gamma<-\frac{1}{12n^2+6/5} is valid, with equality in the left-hand side only when $n=1$, where the scalars $\frac{2(7-12\gamma)}{2\gamma-1}$ and $\frac65$ are the best possible.Comment: 7 page

MEDOE: A Multi-Expert Decoder and Output Ensemble Framework for Long-tailed Semantic Segmentation

Long-tailed distribution of semantic categories, which has been often ignored in conventional methods, causes unsatisfactory performance in semantic segmentation on tail categories. In this paper, we focus on the problem of long-tailed semantic segmentation. Although some long-tailed recognition methods (e.g., re-sampling/re-weighting) have been proposed in other problems, they can probably compromise crucial contextual information and are thus hardly adaptable to the problem of long-tailed semantic segmentation. To address this issue, we propose MEDOE, a novel framework for long-tailed semantic segmentation via contextual information ensemble-and-grouping. The proposed two-sage framework comprises a multi-expert decoder (MED) and a multi-expert output ensemble (MOE). Specifically, the MED includes several "experts". Based on the pixel frequency distribution, each expert takes the dataset masked according to the specific categories as input and generates contextual information self-adaptively for classification; The MOE adopts learnable decision weights for the ensemble of the experts' outputs. As a model-agnostic framework, our MEDOE can be flexibly and efficiently coupled with various popular deep neural networks (e.g., DeepLabv3+, OCRNet, and PSPNet) to improve their performance in long-tailed semantic segmentation. Experimental results show that the proposed framework outperforms the current methods on both Cityscapes and ADE20K datasets by up to 1.78% in mIoU and 5.89% in mAcc.Comment: 18 pages, 9 figure

Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation

Machine learning has been successfully applied to improve the efficiency of Mixed-Integer Linear Programming (MILP) solvers. However, the learning-based solvers often suffer from severe performance degradation on unseen MILP instances -- especially on large-scale instances from a perturbed environment -- due to the limited diversity of training distributions. To tackle this problem, we propose a novel approach, which is called Adversarial Instance Augmentation and does not require to know the problem type for new instance generation, to promote data diversity for learning-based branching modules in the branch-and-bound (B&B) Solvers (AdaSolver). We use the bipartite graph representations for MILP instances and obtain various perturbed instances to regularize the solver by augmenting the graph structures with a learned augmentation policy. The major technical contribution of AdaSolver is that we formulate the non-differentiable instance augmentation as a contextual bandit problem and adversarially train the learning-based solver and augmentation policy, enabling efficient gradient-based training of the augmentation policy. To the best of our knowledge, AdaSolver is the first general and effective framework for understanding and improving the generalization of both imitation-learning-based (IL-based) and reinforcement-learning-based (RL-based) B&B solvers. Extensive experiments demonstrate that by producing various augmented instances, AdaSolver leads to a remarkable efficiency improvement across various distributions

State Sequences Prediction via Fourier Transform for Representation Learning

While deep reinforcement learning (RL) has been demonstrated effective in solving complex control tasks, sample efficiency remains a key challenge due to the large amounts of data required for remarkable performance. Existing research explores the application of representation learning for data-efficient RL, e.g., learning predictive representations by predicting long-term future states. However, many existing methods do not fully exploit the structural information inherent in sequential state signals, which can potentially improve the quality of long-term decision-making but is difficult to discern in the time domain. To tackle this problem, we propose State Sequences Prediction via Fourier Transform (SPF), a novel method that exploits the frequency domain of state sequences to extract the underlying patterns in time series data for learning expressive representations efficiently. Specifically, we theoretically analyze the existence of structural information in state sequences, which is closely related to policy performance and signal regularity, and then propose to predict the Fourier transform of infinite-step future state sequences to extract such information. One of the appealing features of SPF is that it is simple to implement while not requiring storage of infinite-step future states as prediction targets. Experiments demonstrate that the proposed method outperforms several state-of-the-art algorithms in terms of both sample efficiency and performance

Silk Fibroin/Polyvinyl Pyrrolidone Interpenetrating Polymer Network Hydrogels

Silk fibroin hydrogel is an ideal model as biomaterial matrix due to its excellent biocompatibility and used in the field of medical polymer materials. Nevertheless, native fibroin hydrogels show poor transparency and resilience. To settle these drawbacks, an interpenetrating network (IPN) of hydrogels are synthesized with changing ratios of silk fibroin/N-Vinyl-2-pyrrolidonemixtures that crosslink by H2O2 and horseradish peroxidase. Interpenetrating polymer network structure can shorten the gel time and the pure fibroin solution gel time for more than a week. This is mainly due to conformation from the random coil to the β-sheet structure changes of fibroin. Moreover, the light transmittance of IPN hydrogel can be as high as more than 97% and maintain a level of 90% within a week. The hydrogel, which mainly consists of random coil, the apertures inside can be up to 200 μm. Elastic modulus increases during the process of gelation. The gel has nearly 95% resilience under the compression of 70% eventually, which is much higher than native fibroin gel. The results suggest that the present IPN hydrogels have excellent mechanical properties and excellent transparency.This work was supported by The National Key Research and Development Program of China (Grant No. 2017YFC1103602), National Natural Science Foundation of China (Grant No. 51373114, 51741301), PAPD and Nature Science Foundation of Jiangsu, China (Grant No. BK20171239, BK20151242).info:eu-repo/semantics/publishedVersio

Customer Behavior Survery for Cultural and Creative Park in Taiwan

Cultural and Creative Park is a recreational campus which usually consists of exhibition, gallery, show room, movie theater, and multi-function facilities to provide the cultural activities. Besides, in the Cultural and Creative Park, restaurants, coffee shops, bookstores, gift shops, and other business units are nearby. How to improve the customer experience in the Cultural and Creative Park is an important research question for the managerial division to promote culture industries. In this research, the questionnaires were developed and performed in one of creative park in Taipei, Taiwan to study customer behavior. This paper addresses the survey result and the insights revealed from the survey