1. chinaXiv:202005.00043 [pdf]

DEED: A general quantization scheme for saving bits in communication

Tian Ye; Peijun Xiao; Ruoyu Sun
Subjects: Mathematics >> Control and Optimization.

Quantization is a popular technique to reduce communication in distributed optimization. Motivated by the classical work on inexact gradient descent (GD) \cite{bertsekas2000gradient}, we provide a general convergence analysis framework for inexact GD that is tailored for quantization schemes. We also propose a quantization scheme Double Encoding and Error Diminishing (DEED). DEED can achieve small communication complexity in three settings: frequent-communication large-memory, frequent-communication small-memory, and infrequent-communication (e.g. federated learning). More specifically, in the frequent-communication large-memory setting, DEED can be easily combined with Nesterov's method, so that the total number of bits required is $ \tilde{O}( \sqrt{\kappa} \log 1/\epsilon )$, where $\tilde{O}$ hides numerical constant and $\log \kappa $ factors. In the frequent-communication small-memory setting, DEED combined with SGD only requires $\tilde{O}( \kappa \log 1/\epsilon)$ number of bits in the interpolation regime. In the infrequent communication setting, DEED combined with Federated averaging requires a smaller total number of bits than Federated Averaging. All these algorithms converge at the same rate as their non-quantized versions, while using a smaller number of bits.

submitted time 2020-06-16 Hits5951， Downloads611， Comment 0

2. chinaXiv:202004.00005 [pdf]

金融科技中支持区块链生态系统的一般共识博弈框架

袁先智
Subjects: Mathematics >> Applied Mathematics
Subjects: Information Science and Systems Science >> Other Disciplines of Information Science and Systems Science

本文的目的是建立区块链生态系统中采矿池博弈共识均衡的一般框架，特别是在区块链生态系统中，通过使用一个新的概念“共识博弈（Consensus Game）”，解释与挖掘差距（Gap Games）博弈行为相关的共识均衡存在的意义上的稳定性，这里，区块链生态系统主要是指应用2008年中本聪（Nakamoto）所提出的“工作证明”(Proof of Work) 这一关键共识，将区块链工作的费用、报酬机制和采矿权三类不同因素考虑在内的经济活动。 为了做到这一点，我们首先概述了采矿池游戏共识均衡的一般存在性是如何表述的，然后通过区块链共识框架下共识均衡的存在性来解释比特币缺口博弈 (Gap博弈) 稳定性，然后利用博弈论中矿工的利润函数作为收益，建立了一般矿业缺口博弈一致均衡的一般存在性结果。作为应用，建立了缺口博弈 (Gap博弈)一致均衡的一般存在性结果，这不仅有助于我们在区块链生态系统的一般框架下断言缺口博弈 (Gap博弈) 的一般稳定性的存在性，但也让我们能够说明在研究采矿池博弈时的一些不同现象，这些现象可能是由于采矿者的(Gap博弈)行为与嵌入比特币经济学的情景造成的。 我们对区块链生态系统挖掘缺口博弈稳定性的解释研究表明，共识均衡的概念可能对共识经济学基础理论的发展起到重要作用

submitted time 2020-03-31 Hits5847， Downloads554， Comment 0

3. chinaXiv:202003.00055 [pdf]

近似稀疏的低秩张量填充

喻高航; 郑伟东; 胡文玉
Subjects: Mathematics >> Computational Mathematics.

针对目前大多数的低秩张量填充(LRTC)模型存在过度稀疏而导致数据的细微特征被忽略的现象, 本文借助框架变换和低秩矩阵分解, 提出了一个基于近似稀疏的低秩张量填充(AS-LRTC) 模型, 进一步设计了块逐次上界极小化(BSUM) 算法求解该模型. 在一定条件下可以证明该算法的收敛性, 大量的实验结果表明本文提出的算法比现有一些经典算法有明显的优势.

submitted time 2020-03-16 Hits6055， Downloads540， Comment 0

4. chinaXiv:202002.00066 [pdf]

新型冠状病毒肺炎疫情的动力学分析和预测

诸葛昌靖; 张东艳; 杨武岳; 彭梁榕; 洪柳
Subjects: Mathematics >> Modeling and Simulation

基于经典动力学模型和模型参数自动优化算法, 本文分析了全国当前累计确诊感染病例数大于100（截止到2020年2月16日）的24个省市自治区, 以及湖北省除神农架以外的16个地市从2020年1月20日至2月16日的累计确诊病例数, 并对相应省市地区疫情可能的结束时间和总感染人数的进行了长期预测. 我们的研究表明, 在目前严防严控措施下, 全国大部分省市的疫情将于2月底前基本结束, 而湖北省内疫情也有望于3月中旬结束, 但是武汉市的疫情可能要持续到4月初. 通过对比公开数据与预测值, 我们建议加强对黑龙江、河北、江西、安徽、贵州和四川六省, 以及湖北省内武汉、荆州、鄂州、随州、天门和恩施六个地市的的监控, 以防疫情死灰复燃. 此外, 分析结果提示, 在疫情发展前期, 天津、河北、重庆、四川、海南和广西等省, 以及湖北省下辖多个地市可能存在着聚集性感染, 这有待于疫后进一步的流行病学调查确认.

submitted time 2020-02-25 Hits13403， Downloads1194， Comment 0

5. chinaXiv:202002.00021 [pdf]

关于新型冠状病毒感染人数的预测研究

吴宇宸
Subjects: Mathematics >> Mathematics （General）

2019年12月，新型冠状病毒肺炎(NCP，又称2019-nCoV)疫情从武汉开始爆发,几天内迅速传播到全国乃至海外，对我国的工农业生产和人民生活产生了重要影响。科学有效掌控疫情发展对疫情防控至关重要。本文基于中国卫健委及湖北省卫健委每日公布的累计确诊数，采用逻辑斯蒂模型对数据进行了拟合，以期给该疾病的防控治提供科学依据。通过公布的疫情数据，我们反演了模型的参数，进而有效地模拟了目前疫情的发展，并预测了疫情未来的趋势。我们预测，湖北省疫情还要持续至少2周，而在全国其他地区，疫情可望1周左右达到顶峰。

submitted time 2020-02-18 Hits16490， Downloads2107， Comment 0

6. chinaXiv:202001.00045 [pdf]

Approximation-Degree-Based Interpolation: A New Interpolation Method

廉师友
Subjects: Mathematics >> Numerical Analysis

This paper introduces the measure of approximate-degree and the concept of approximate-degree function between numerical values, thus developing a new interpolation method —— approximation-degree-based interpolation, i.e., AD interpolation. One-dimensional AD interpolation is done directly by using correlative interpolation formulas; n(n>1)-dimensional AD interpolation is firstly separated into n parallel one-dimensional AD interpolation computations to do respectively, and then got results are synthesized by Sum-Times-Difference formula into a value as the result value of the n-dimensional interpolation. If the parallel processing is used, the efficiency of n-dimensional AD interpolation is almost the same as that of the one-dimensional AD interpolation. Thus it starts a feasible and convenient approach and provides an effective method for high-dimensional interpolations. Furthermore, if AD interpolation is introduced into machine learning, a new instance-based learning method is expected to be realized.

submitted time 2019-12-29 Hits9292， Downloads470， Comment 0

7. chinaXiv:201911.00099 [pdf]

滑动均值聚类

何沧平; 孟令霞
Subjects: Mathematics >> Computational Mathematics.

本文提出一个名为滑动均值的聚类算法，尝试替代常用的k均值算法。滑动均值能处理大量的样本，自行决定类别数量，用混洗样本来避免出现很差的中心点，能够中途裁减类别数量，聚类效果显著好于k均值。在鸢尾花数据和手写数字数据上，滑动均值的聚类效果比k均值分别高9.93%和5.17%。

submitted time 2019-11-26 Hits11392， Downloads715， Comment 0

8. chinaXiv:201911.00094 [pdf]

Copositivity for 3rd order symmetric tensors and applications

刘佳蕊; 宋义生
Subjects: Mathematics >> Mathematical Physics

The strict opositivity of 4th order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) opositivity of 4th order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided that several analytically sufficient conditions for the copositivity of 3th order 2 dimensional (3 dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th order tensors, the analytically sufficient conditions of copositivity are proved for 4th order 2 dimensional and 3 dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for $\mathbb{Z}_3$ scalar dark matter.

submitted time 2019-11-23 Hits12076， Downloads634， Comment 0

9. chinaXiv:201910.00071 [pdf]

Sparse Representation Based Efficient Radiation Symmetry Analysis Method for Cylindrical Model of Inertial Confinement Fusion

张雁峰
Subjects: Mathematics >> Modeling and Simulation

Radiation symmetry evaluation is critical to the laser driven Inertial Confinement Fusion (ICF), which is usually done by solving a view-factor equation model. The model is nonlinear, and the number of equations can be very large when the size of discrete mesh element is very small to achieve a prescribed accuracy, which may lead to an intensive equation solving process. In this paper, an efficient radiation symmetry analysis approach based on sparse representation is presented, in which, 1) the Spherical harmonics, annular Zernike polynomials and Legendre-Fourier polynomials are employed to sparsely represent the radiation flux on the capsule and cylindrical cavity, and the nonlinear energy equilibrium equations are transformed into the equations with sparse coefficients, which means there are many redundant equations, 2) only a few equations are selected to recover such sparse coefficients with Latin hypercube sampling, 3) a Conjugate Gradient Subspace Thresholding Pursuit (CGSTP) algorithm is then given to rapidly obtain such sparse coefficients equation with as few iterations as possible. Finally, the proposed method is validated with two experiment targets for Shenguang II and Shenguang III laser facility in China. The results show that only one tenth of computation time is required to solve one tenth of equations to achieve the radiation flux with comparable accuracy. Further more, the solution is much more efficient as the size of discrete mesh element decreases, in which, only 1.2% computation time is required to obtain the accurate result.

submitted time 2019-10-23 Hits10154， Downloads506， Comment 0

10. chinaXiv:201910.00074 [pdf]

基于线性模型平均估计的置信区间

王苗苗
Subjects: Mathematics >> Statistics and Probability

已有的关于模型平均估计渐近分布理论的研究多是基于局部误设定的假设,[1] 是其中开创性的且最著名的文章之一. 虽然利用局部误设定的假设可以证明模型平均估计渐近分布理论, 但是 [2] 等对此假设提出了不合理性质疑和解释. 本文我们研究[1]中的置信区间估计方法. 证明了在一般参数设定下, 虽然 [1]中的渐近分布理论不一定成立, 但是关于不确定参数的线性函数的置信区间在正态分布误差、线性回归模 型下是有效的, 即置信区间的覆盖率趋于预设定的名义水平. 我们通过模拟研究进一步验证了理论结果.

submitted time 2019-10-14 Hits10297， Downloads561， Comment 0