Fusion Rings over Drinfeld Doubles

We prove an explicit formula for the fusion rules in $\mathrm{Rep}_f D(G)$ for any finite group $G$ in terms of character inner products. This formula was proved in a special case by Goff. We generalized it to the present form. An even more general result is stated without explicit proof in a paper by Mason and Goff. Here, we give two different proofs, one by character manipulations and the other one by using Mackey theory. Using this formula, we show that $\mathrm{Rep}_f D(G)$ is multiplicity free for two infinite families of finite groups: the Dihedral groups and the Dicyclic groups. In fact, we will compute all fusion rules in these categories. Multiplicity freeness is a desired property for modular tensor categories, since it greatly simplifies the computation of $F$-matrices. Furthermore, we observe that the fusion rules for Dihedral groups $D_{2n}$ with $n$ odd are extremely similar to the fusion rules of Type $B$ level $2$ fusion algebras of Wess-Zumino-Witten conformal field theories.Comment: 22 page

LIGNIN-DERIVED CARBON AND NANOCOMPOSITE MATERIALS FOR ENERGY STORAGE APPLICATIONS

With a growing demand for electrical energy storage materials, lignin-derived carbon materials have received increasing attention in recent years. As a highly abundant renewable carbon source, lignin can be converted to a variety of advanced carbon materials with tailorable chemical, structural, mechanical and electrochemical properties through thermochemical conversion (e.g. pyrolysis). However, the non-uniformity in lignin structure, composition, inter-unit linkages and reactivity of diverse lignin sources greatly influence lignin fractionation from plant biomass, the pyrolysis chemistry, and property of the resulting carbon materials. To introduce a better use of lignocellulosic biomass to biofuels and co-products, it is necessary to find novel ways to fractionate lignin and cellulose from the feedstock at high efficacy and low cost. Deep eutectic solvent (DES) was used to extract lignin from high lignin-content walnut and peach endocarps. Over 90% sugar yields were achieved during enzymatic hydrolysis of DES pretreated peach and walnut endocarps while lignins were extracted at high yields and purity. The molecular weights of the extracted lignin from DES pretreated endocarp biomass were significantly reduced. The native endocarp lignins were SGH type lignins with dominant G-unit. DES pretreatment decreased the S and H-unit which led to an increase in condensed G-units, which may contribute to a higher thermal stability of the isolated lignin. Lignin slow pyrolysis was investigated using a commercial pyrolysis–GC/MS system for the first time to link pyrolysis chemistry and carbon material properties. The overall product distributions, including volatiles and solid product were tracked at different heating rates (2, 20, 40 ℃/min) and different temperature regions (100-200, 200-300 and 300-600 ℃). Results demonstrate that changes in reaction chemistry as a factor of pyrolysis conditions led to changes in yield and properties of the resulting carbon materials. Physical and chemical properties of the resulting carbon material, such as porosity, chemical composition and surface functional groups were greatly affected by lignin slow pyrolysis temperature and heating rate. Lignin-derived activated carbons (AC) were synthesized from three different lignin sources: poplar, pine derived alkaline lignin and commercial kraft lignin under identical conditions. The poplar lignin-derived ACs exhibited a larger surface area and total mesopore volume than softwood lignin-derived AC, which contribute to a larger electrochemical capacitance over a range of scan rates. The presence of oxygen-containing functional groups in all lignin-derived ACs, which participated in redox reaction and thus contributed to an additional pseudo-capacitance. By delineating the carbonization and activation parameters, results from this study suggest that lignin structure and composition are important factors determining the pore structure and electrochemical properties of the derived carbon materials. A 3-dimensional, interconnected carbon/silicon nanoparticles composite synthesized from kraft lignin (KL) and silicon nanoparticles (Si NPs) is shown to have a high starting specific capacity of 2932 mAh/g and a retaining capacity of 1760 mAh/g after 100 cycles at 0.72 A/g as negative electrode in a half-cell lithium-ion battery (LIB) test. It was found the elemental Si and C of the C/Si NPs were most likely linked via Si-O-C rather than direct Si-C bond, a feature that helps to alleviate the mechanical degradation from Si volume change and assure a sound electronic and ionic conductivity for enhanced electrochemical performance. EGA-MS and HC-GC/MS analyses suggest that the interaction of the Si, O and C can be tailored by controlling pyrolysis conditions. This study systematically investigated the interconnecting aspects among lignin source, pyrolysis chemistry, characteristics of the derived carbon materials and electrochemical performance. Such knowledge on the processing-structure-function relationships serves as a basis for designing lignin-based carbon materials for electrochemical energy storage applications

Automatic Brain Tumor Segmentation using Cascaded Anisotropic Convolutional Neural Networks

A cascade of fully convolutional neural networks is proposed to segment multi-modal Magnetic Resonance (MR) images with brain tumor into background and three hierarchical regions: whole tumor, tumor core and enhancing tumor core. The cascade is designed to decompose the multi-class segmentation problem into a sequence of three binary segmentation problems according to the subregion hierarchy. The whole tumor is segmented in the first step and the bounding box of the result is used for the tumor core segmentation in the second step. The enhancing tumor core is then segmented based on the bounding box of the tumor core segmentation result. Our networks consist of multiple layers of anisotropic and dilated convolution filters, and they are combined with multi-view fusion to reduce false positives. Residual connections and multi-scale predictions are employed in these networks to boost the segmentation performance. Experiments with BraTS 2017 validation set show that the proposed method achieved average Dice scores of 0.7859, 0.9050, 0.8378 for enhancing tumor core, whole tumor and tumor core, respectively. The corresponding values for BraTS 2017 testing set were 0.7831, 0.8739, and 0.7748, respectively.Comment: 12 pages, 5 figures. MICCAI Brats Challenge 201

Creating New Rural Communitas: The Case of China Taiwan’s Rural Regeneration

Traditional sociological theory explains that a rural community is an enclosed unit. China’s fast modernization and urbanization, however, display a rather different phenomenon, where rural communities are changing into open communities, which face the dual task of rebuilding internal relations and expanding external resources. Based on this background and practical cognition, the theoretical framework of the ‘new rural communitas’ is proposed, which expands the common enclosed relationships in traditional rural communities into new, open co-construction relationships with endogenous power as core, government power as support, and social power as coordination, emphasizing the full cooperation of these three types of power. On the basis of the theory, this article employs the practice of the rural regeneration policy in Taiwan as an empirical case, and analyzes how these three types of power affect and cooperate with each other. Furthermore, interviews have been conducted with local community members, government officers, and social participants in three communities in Taiwan to give examples of three different types of new rural communitas. Finally, several suggestions toward constructing new rural communitas are discussed.   Abstrak. Teori tradisional dalam sosiologi menjelaskan bahwa komunitas perdesaan adalah unit yang tertutup. Modernisasi dan urbanisasi cepat yang terjadi di China menampilkan fenomena yang sedikit berbeda, dimana komunitas perdesaan berubah menjadi komunitas yang terbuka yang menghadapi tugas ganda membangun kembali hubungan internal dan memperluas sumber daya eksternal. Berdasarkan latar belakang dan kognisi praktis ini, kerangka teoritis ‘komunitas perdesaan baru’ diusulkan, sehingga dapat memperluas hubungan tertutup bersama dalam komunitas perdesaan tradisional menjadi hubungan ko-kontruksi baru yang terbuka dengan kekuatan endogen sebagai inti, kekuatan pemerintah sebagai pendukung, dan kekuasaan social sebagai koordinasi serta menekankan kerjasama penuh dari ketiga jenis kekuasaan tersebut. Berdasarkan teori tersebut, artikel ini menggunakan praktik kebijakan regenerasi perdesaan di Taiwan sebagai kasus empiris, dan menganalisis bagaimana ketiga jenis kekuasaan ini saling mempengaruhi dan bekerja sama. Selanjutnya, wawancara telah dilakukan dengan anggota masyarakat setempat, pejabat pemerintah, dan peserta sosial di tiga komunitas di Taiwan untuk memberikan contoh tiga jenis komunitas perdesaan baru yang berbeda. Akhirnya, beberapa  saran untuk membangun komunitas perdesaan baru juga dibahas.   Kata kunci. Komunitas perdesaan, komunitas, regenerasi perdesaan, Cina, Taiwan

A summary of the research on tourism public service system in ancient cities and towns in China

This paper collates and analyzes the ancient town tourism, tourism public service, ancient town tourism public service system and relevant research literature. It is found that Chinese scholars have begun to try to systematically study the ancient town tourism public service system, but the research on China’s ancient town tourism public service system has some problems, such as narrow research scope, theoretical research lagging behind practice, and then puts forward the direction that needs to be discussed in depth in the future.

Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations

Deep-learning has proved in recent years to be a powerful tool for image analysis and is now widely used to segment both 2D and 3D medical images. Deep-learning segmentation frameworks rely not only on the choice of network architecture but also on the choice of loss function. When the segmentation process targets rare observations, a severe class imbalance is likely to occur between candidate labels, thus resulting in sub-optimal performance. In order to mitigate this issue, strategies such as the weighted cross-entropy function, the sensitivity function or the Dice loss function, have been proposed. In this work, we investigate the behavior of these loss functions and their sensitivity to learning rate tuning in the presence of different rates of label imbalance across 2D and 3D segmentation tasks. We also propose to use the class re-balancing properties of the Generalized Dice overlap, a known metric for segmentation assessment, as a robust and accurate deep-learning loss function for unbalanced tasks