Mean field equations, hyperelliptic curves and modular forms: II

A pre-modular form $Z_n(\sigma; \tau)$ of weight $\tfrac{1}{2} n(n + 1)$ is introduced for each $n \in \Bbb N$, where $(\sigma, \tau) \in \Bbb C \times \Bbb H$, such that for $E_\tau = \Bbb C/(\Bbb Z + \Bbb Z \tau)$, every non-trivial zero of $Z_n(\sigma; \tau)$, namely $\sigma \not\in E_\tau[2]$, corresponds to a (scaling family of) solution to the mean field equation \begin{equation} \tag{MFE} \triangle u + e^u = \rho \, \delta_0 \end{equation} on the flat torus $E_\tau$ with singular strength $\rho = 8\pi n$. In Part I (Cambridge J. Math. 3, 2015), a hyperelliptic curve $\bar X_n(\tau) \subset {\rm Sym}^n E_\tau$, the Lam\'e curve, associated to the MFE was constructed. Our construction of $Z_n(\sigma; \tau)$ relies on a detailed study on the correspondence $\Bbb P^1 \leftarrow \bar X_n(\tau) \to E_\tau$ induced from the hyperelliptic projection and the addition map. As an application of the explicit form of the weight 10 pre-modular form $Z_4(\sigma; \tau)$, a counting formula for Lam\'e equations of degree $n = 4$ with finite monodromy is given in the appendix (by Y.-C. Chou).Comment: 32 pages. Part of content in previous versions is removed and published separately. One author is remove

Microfluidic Mixing: A Review

The aim of microfluidic mixing is to achieve a thorough and rapid mixing of multiple samples in microscale devices. In such devices, sample mixing is essentially achieved by enhancing the diffusion effect between the different species flows. Broadly speaking, microfluidic mixing schemes can be categorized as either “active”, where an external energy force is applied to perturb the sample species, or “passive”, where the contact area and contact time of the species samples are increased through specially-designed microchannel configurations. Many mixers have been proposed to facilitate this task over the past 10 years. Accordingly, this paper commences by providing a high level overview of the field of microfluidic mixing devices before describing some of the more significant proposals for active and passive mixers

Water Resources Management in Practices at National Pingtung University of Science and Technology Campus

NPUST was the top Taiwan university for the 9th consecutive year on the UI GreenMetric World University Ranking, and placed 27th out of 1,050 schools from 85 countries. This achievement is the result of our commitments to sustainable development. NPUST has been building green transportation for carbon and air pollution reduction, green energy system for effective use of electricity generated by renewable energy, and campus waste water recycling system for the goal of zero discharge. We also implement policies on waste reduction and waste sorting and recycling, as well as encourage planting in school campus. The practice of water resources management is crucial in various aspects that contribute to this sustainable campus. The sustainable management strategies include water consumption management, water conservation and water saving, and water recycling management. In this paper, we are going to share our practical experience in waste water treatment, recycling system set-up, waste water reuse, sustainable development for water resources and how we implement the policies on water saving at campus and spread water resources knowledge. The information is prov

THE EFFECTS Of VOLLEYBALL ATTACKING ON SCORE POINTS: A CASE STUDY OF 2014 TVL IN TAIWAN

Volleyball is a sport in which team tactical and players' attacking skills determine to score points. Therefore, an effective team tactical is achieved by main spikers' and middle blockers' skills. To name but a few, delayed spike, open spike and back-row spike are main spikers' skills, yet quick spike, and individual time difference attack are associated with middle blockers'. Under this aspect, a case study of male teams of Taiwan Top Volleyball League (TVL) was yield out, which aimed at exploring the effects of team tactical and players attacking skills on score points. The results indicated that the attacking point ratio of main spikers and middle blockers in the champion team was higher than others. This was because the middle blockers gave cover to main spikers as attacking. By doing so, it promoted point ratio to main spikers. Furthermore, it found that to strengthen main spikers and middle blockers' skills would increase team's attacking point ratio

Distributed Training Large-Scale Deep Architectures

Scale of data and scale of computation infrastructures together enable the current deep learning renaissance. However, training large-scale deep architectures demands both algorithmic improvement and careful system configuration. In this paper, we focus on employing the system approach to speed up large-scale training. Via lessons learned from our routine benchmarking effort, we first identify bottlenecks and overheads that hinter data parallelism. We then devise guidelines that help practitioners to configure an effective system and fine-tune parameters to achieve desired speedup. Specifically, we develop a procedure for setting minibatch size and choosing computation algorithms. We also derive lemmas for determining the quantity of key components such as the number of GPUs and parameter servers. Experiments and examples show that these guidelines help effectively speed up large-scale deep learning training

Genetic algorithm integrated with artificial chromosomes for multi-objective flowshop scheduling problems

a b s t r a c t Recently, a wealthy of research works has been dedicated to the design of effective and efficient genetic algorithms in dealing with multi-objective scheduling problems. In this paper, an artificial chromosome generating mechanism is designed to reserve patterns of genes in elite chromosomes and to find possible better solutions. The artificial chromosome generating mechanism is embedded in simple genetic algorithm (SGA) and the non-dominated sorting genetic algorithm (NSGA-II) to solve single-objective and multiobjective flowshop-scheduling problems, respectively. The single-objective problems are to minimize the makespan while the multi-objective scheduling problems are to minimize the makespan and the maximum tardiness. Extensive numerical studies are conducted and the results indicate that artificial chromosomes embedded with SGA and NSGAII are able to further speed up the convergence of the genetic algorithm and improve the solution quality. This promising result may be of interests to industrial practitioners and academic researchers in the field of evolutionary algorithm or machine scheduling

Structured LDPC codes with low error floor based on PEG Tanner graphs

Abstract-Progressive edge-growth (PEG) algorithm was proven to be a simple and effective approach to design good LDPC codes. However, the Tanner graph constructed by PEG algorithm is non-structured which leads the positions of 's of the corresponding parity check matrix fully random. In this paper, we propose a general method based on PEG algorithm to construct structured Tanner graphs. These hardware-oriented LDPC codes can reduce the VLSI implementation complexity. Similar to PEG method, our CP-PEG approach can be used to construct both regular and irregular Tanner graphs with flexible parameters. For the consideration of encoding complexity and error floor, the modifications of proposed algorithm are discussed. Simulation results show that our codes, in terms of bit error rate (BER) or packet error rate (PER), outperform other PEG-based LDPC codes and are better than the codes in IEEE 802.16e

Indoxyl Sulfate-Induced Oxidative Stress, Mitochondrial Dysfunction, and Impaired Biogenesis Are Partly Protected by Vitamin C and N-Acetylcysteine

Indoxyl sulfate (IS) contributes to oxidative stress and endothelial dysfunction in chronic kidney disease patients. However, the role of mitochondria in IS-induced oxidative stress is not very clear. In this study, we examined whether mitochondria play a pivotal role in modulating the effects of antioxidants during IS treatment. In the context of human umbilical vein endothelial cells, we found that IS had a dose-dependent antiproliferative effect. In addition, we used flow cytometry to demonstrate that the level of reactive oxygen species increased in a dose-dependent manner after treatment with IS. High doses of IS also corresponded to increased mitochondrial depolarization and decreased mitochondrial DNA copy number and mitochondrial mass. However, these effects could be reversed by the addition of antioxidants, namely, vitamin C and N-acetylcysteine. Thus, our results suggest that IS-induced oxidative stress and antiproliferative effect can be attributed to mitochondrial dysfunction and impaired biogenesis and that these processes can be protected by treatment with antioxidants