A survey on HHL algorithm: From theory to application in quantum machine learning

The Harrow-Hassidim-Lloyd (HHL) algorithm is a method to solve the quantum linear system of equations that may be found at the core of various scientific applications and quantum machine learning models including the linear regression, support vector machines and recommender systems etc. After reviewing the necessary background on elementary quantum algorithms, we provide detailed account of how HHL is exploited in different quantum machine learning (QML) models, and how it provides the desired quantum speedup in all these models. At the end, we briefly discuss some of the remaining challenges ahead for HHL-based QML models and related methods.     

Haezendonck–Goovaerts risk measure with a heavy tailed loss

Recently Haezendonck–Goovaerts (H–G) risk measure has received much attention in (re)insurance and portfolio management. Some nonparametric inferences have been proposed in the literature. When the loss variable does not have enough moments, which depends on the involved Young function, the nonparametric estimator in Ahn and Shyamalkumar (2014) has a nonnormal limit, which challenges interval estimation. Motivated by the fact that many loss variables in insurance and finance could have a heavier tail such as an infinite variance, this paper proposes a new estimator which estimates the tail by extreme value theory and the middle part nonparametrically. It turns out that the proposed new estimator always has a normal limit regardless of the tail heaviness of the loss variable. Hence an interval with asymptotically correct confidence level can be obtained easily either by the normal approximation method via estimating the asymptotic variance or by a bootstrap method. A simulation study and real data analysis confirm the effectiveness of the proposed new inference procedure for estimating the H–G risk measure.     

随机算子方程随机解的若干存在性定理

自提出随机拓扑度和随机不动点指数概念以来,随机拓扑度和随机不动点指数理论已成为研究随机非线性算子的一种基本方法,建立了许多新的定理。利用随机不动点指数理论,研究了不同边界条件下的随机算子方程随机解的存在性,得到了若干新的结果,所得结果推广了相关文献中的部分结果     

A chaotic maps-based authenticated key agreement protocol with strong anonymity

In wireless communication environments, the authenticated key agreement with user anonymity is important. Recently, many chaotic maps-based anonymous authenticated key agreement protocols have been proposed. Tseng et al. applied Chebyshev chaotic maps to propose an anonymous key agreement protocol. Unfortunately, Niu et al. demonstrated that Tseng et al.’s protocol cannot protect the user anonymity and it suffers from insider attacks. Xue et al. improved Tseng et al.’s protocol. However, we have found that their improved protocol still cannot provide strong anonymity and it is vulnerable to the man-in-the-middle attack. To remove these weaknesses, we have proposed a novel chaotic maps-based authenticated key agreement protocol. The proposed protocol cannot only resist these attacks, but also provide strong anonymity.     

规模生猪养殖液态生物质资源循环开发仿真分析

对银河杜仲基于沼气工程的液态生物质资源的循环开发进行仿真分析。根据历史数据和公司五年、十年发展规划,使用基于反馈调控参数的入树逐步建模法,构建7棵入树仿真模型;通过仿真定量揭示公司规划实施过程中将产生大量废弃物类生物质,沼气工程对废弃物开发产生的沼液和沼气中含大量的生物质能;为此,基于仿真结果及系统反馈结构,提出促进消除环境与猪肉产品双污染,实现绿色安全猪肉生产和改善环境双重目标的三条管理对策,并进行初步实施。     

Z—P—S空间中一类新的不动点定理

利用概率度量空间中A—proper映射拓扑度的基本性质,在投影完备的Z—P—S空间中研究了非线性映射的不动点问题,得到了一些新的结果．     

Distribution of the units digit of primes

A sequence is formed by the units digit of consecutive prime numbers. The sequence is not random. To visualize the non-randomness of the sequence, we utilize a method put forward by Hao et al. [Chaos, Solitons & Fractals 11 (2000) 825]. A fractal-like structure is observed.     

绿色产品零售企业与市场消费者策略选择演化分析

线上线下结合营销模式有效缓解了流通渠道不畅和营销方式单一的问题,进而促进绿色产品消费。在相关假设的基础上,通过构建绿色产品零售企业和市场消费者的演化博弈模型,重现博弈主体的动态演进过程。研究结果表明,在线上线下结合营销模式中,绿色产品零售企业与消费者演化博弈系统存在两个可能的均衡状态,分别是O{维持传统营销策略,使用传统渠道购买产品}、C{建立线上营销策略,使用线上渠道购买产品}。演化博弈系统的演进受到9个相关因素的干扰,这些因素通过影响博弈主体的收益、成本及潜在的风险损失等发生作用。在理论推导的基础上,以被调研的A绿色产品零售企业为样本进行数值模拟,验证理论推导的正确性,给出上述影响因素的作用强度。     

TBAI-mediated regioselective 5-exo-dig iodinative oxocyclization of 2-alkynylbenzamides for the synthesis of isobenzofuran-1-imines and isobenzofurans

Alkyne-based regioselective functionalization is an important transformation method for the synthesis of a wide variety of organic products. In this work, a regioselective TBAI-mediated oxidative 5-exo-dig iodo-oxycyclization of 2-alkynylbenzamide is used for the synthesis of various isobenzofuran derivatives with excellent functional group tolerance and high reaction efficiency. We hypothesized that using water in a mixed solvent could change the reaction pathway and realize a high reaction regioselectivity. Furthermore, the application of the developed procedure was demonstrated by the synthesis of phthalazin-1(2H)-one and aryl-substituted isobenzofurans.     

氢化物发生-银盐分光光度法测定中草药中砷的含量

采用氢化物发生-银盐分光光度法对中草药中溶解态砷的含量进行了测定。结果表明,砷标准曲线的回归方程为C=1．4474 A-0．0087,r=0．99,在0～0．4μg/mL的范围内,线性关系良好。对5种样品进行了回收实验,回收率为92．4％-102．6％,相对标准偏差为1．26％-2．43％。该法简单、快速、灵敏、准确。