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1. chinaXiv:202201.00057 [pdf]

Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

 The notion of information and complexity are important concepts in many scientific fields such as molecular biology, evolutionary theory and exobiology. Most measures of these quantities, such as Shannon entropy and related complexity measures, are only defined for objects drawn from a statistical ensemble and cannot be computed for single objects. We attempt to fill this gap by introducing the notion of a ladderpath which describes how an object can be decomposed into an hierarchical structure using repetitive elements. From the ladderpath two measures naturally emerge: the ladderpath-index and the order-index, which represent two axes of complexity. We show how the ladderpath theory can be applied to both strings and spatial patterns and argue that all systems that undergo evolution can be described as ladderpaths. Further, we discuss possible applications to human language and origins of life. The ladderpath theory provides a novel characterization of the information that is contained in a single object (or a system) and could aid in our understanding of evolving systems and the origin of life in particular.

2. chinaXiv:202105.00070 [pdf]

Subjects: Statistics >> Mathematical Statistics
Subjects: Computer Science >> Computer Application Technology
Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

 统计独立性是统计学和机器学习领域的基础性概念，如何表示和度量统计独立性是该领域的基本问题。Copula理论提供了统计相关性表示的理论工具，而Copula熵理论则给出了度量统计独立性的概念工具。本文综述了Copula熵的理论和应用，概述了其基本概念定义、定理和性质，以及估计方法。介绍了Copula熵研究的最新进展，包括其在统计学四个基本问题（结构学习、关联发现、变量选择和时序因果发现等）上的理论应用。讨论了四个理论应用之间的关系，以及其对应的深层次的相关性和因果性概念之间的联系，并将Copula熵的（条件）独立性度量框架与基于核函数和距离的相关性度量框架进行了对比。简述了Copula熵在水文学、环境气象学、生态学、化学信息学、认知神经学、计算神经学、系统生物学、生物信息学、临床诊断学、老年医学、公共卫生学、经济政策学、政治学，以及能源工程、制造工程、可靠性工程、航空工程、通信工程、测绘工程和金融工程等领域的实际应用。

3. chinaXiv:202110.00056 [pdf]

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

 The shortest path problem (SPP) is a classic problem and appears in a wide range of applications. Although a variety of algorithms already exist, new advances are still being made, mainly tuned for particular scenarios to have better performances. As a result, they become more and more technically complex and sophisticated. Here we developed a novel nature-inspired algorithm to compute all possible shortest paths between two nodes in a graph: Resonance Algorithm (RA), which is surprisingly simple and intuitive. Besides its simplicity, RA turns out to be much more time-efficient for large-scale graphs than the extended Dijkstra's algorithm (such that it gives all possible shortest paths). Moreover, RA can handle any undirected, directed, or mixed graphs, irrespective of loops, unweighted or positively-weighted edges, and can be implemented in a fully decentralized manner. These good properties ensure RA a wide range of applications.

4. chinaXiv:202109.00067 [pdf]

Subjects: Management Science >> Management Metrology
Subjects: Statistics >> Economic Statistics

 经济发展进步使得生产过程越来越复杂，复杂度指数可以反映经济及产业部门的技术进步水平。文章修正了一种基于投入产出技术的经济复杂度指数，并用于分析一个地区的产业部门及经济总体技术进步水平。实证结果表明，修正过的复杂度指数能很好地表达经济及产业部门的经济技术进步水平，比修正前的计算公式更合理。

5. chinaXiv:202108.00103 [pdf]

Subjects: Computer Science >> Other Disciplines of Computer Science

 Starting from finding approximate value of a function, introduces the measure of approximation-degree between two numerical values, proposes the concepts of "strict approximation" and "strict approximation region", then, derives the corresponding one-dimensional interpolation methods and formulas, and then presents a calculation model called "sum-times-difference formula" for high-dimensional interpolation, thus develops a new interpolation approach ? ADB interpolation. ADB interpolation is applied to the interpolation of actual functions with satisfactory results. Viewed from principle and effect, the interpolation approach is of novel idea, and has the advantages of simple calculation, stable accuracy, facilitating parallel processing, very suiting for high-dimensional interpolation, and easy to be extended to the interpolation of vector valued functions. Applying the approach to instance-based learning, a new instance-based learning method ? learning using ADB interpolation ? is obtained. The learning method is of unique technique, which has also the advantages of definite mathematical basis, implicit distance weights, avoiding misclassification, high efficiency, and wide range of applications, as well as being interpretable, etc. In principle, this method is a kind of learning by analogy, which and the deep learning that belongs to inductive learning can complement each other, and for some problems, the two can even have an effect of “different approaches but equal results” in big data and cloud computing environment. Thus, the learning using ADB interpolation can also be regarded as a kind of “wide learning” that is dual to deep learning.

6. chinaXiv:202104.00131 [pdf]

Subjects: Information Science and Systems Science >> Simulation Science and Technology

 本文证明高斯玻色采样问题和矩阵积和式计算问题一样，仍然是指数复杂度问题。对于使用有限采样时钟频率的物理光学装置，即使采样到一个有效样本都是难以完成的任务。本文提出通过高斯玻色采样来证明量子计算优越性的新方案：该方案采用量子真随机数和大型计算机相结合，用量子真随机数实现量子的内禀随机性，并使用大型计算机完成采样状态模拟和判断，从而整体无差错实现高斯玻色采样问题，完成单纯经典超级计算机无法完成的计算任务，最终证明量子计算的优越性。本文提出的行为级模拟方案，可以使用伪随机数有效仿真玻色采样问题中的大概率事件，从而可以很方便地验证物理采样装置的有效性和正确性。

7. chinaXiv:202103.00132 [pdf]

Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

 " Dempster-Shafer evidence theory, as an extension of Probability theory, is widely used in the field of information fusion due to it satisfies weaker conditions than probability theory in dealing with uncertain information. Nevertheless , the description space of the current evidence theory is only a real space, and it cannot effectively describe and process the uncertain information in the face of multidimensional characteristic data and periodic data with phase angle changes. Based on this gap , in this paper, Dempster-Shafer evidence theory is extended to the complex Dempster-Shafer evidence theory. In complex Dempster-Shafer evidence theory, mass function that used to describe the uncertain information extends from the real space to the complex space, named as complex mass function, and the modulus of the mass function indicates the degree of support for the proposition. On this basis, other basic concepts used to describe uncertainty information are also defined and discussed, such as complex belief function, complex plausibility function, etc. In order to perfect the complex Dempster-Shafer evidence theory, the complex Dempster combination rule (CDCR) is supplemented. CDCR is an extension of Dempster combination rule (CDR), which satisfies the commutative and associative laws just as CDR does, and it can degenerate into CDR under certain condition. In addition, we propose a method to generate complex mass function and apply it to target recognition. The recognized results show that compared with the mass function of the real plane, the target recognition rate can be larger by using complex mass function to describe the uncertain information.

8. chinaXiv:202102.00009 [pdf]

Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

 系统性掌握黄河流域经济发展时空格局演变规律能为整个流域高质量发展提供重要决策依据。目前，GDP是衡量经济发展格局的主要参考依据，然而GDP统计数据存在口径不统一、空间分辨率低等缺点，难以精准刻画经济发展的时空演变格局特征。夜晚灯光数据以其相对客观的特征，对其进行有效反映。本文通过对1992-2013年全国夜晚灯光数据的校正和处理，获得全国及流域夜晚灯光数据影像，进行经济空间聚合分析，以及与相关因子进行对比分析。研究结果表明：经济空间聚合高的区域分布在黄河河道附近，从黄河上游到下游，热力强度逐渐增强，并且以省会城市为核心区，向外扩散，呈现了在老的聚合点聚合度加剧的情况下，聚合区域有向周边分散的趋势；夜晚灯光数据的变化趋势与GDP的变化趋势具有一定的相似性，并且与城镇化率、人口数量、第三产比例、人均公园绿地面积、流域发展指数（Basin Development Index, BDI）具有一定的相关性；流域9省的夜晚灯光数据整体变化趋势与全国灯光数据的变化趋势基本一致，呈稳定上升的趋势，但整体值均低于全国的夜晚灯光数据，并且差距有所扩大，黄河流域高质量发展迫在眉睫。

9. chinaXiv:202101.00002 [pdf]

Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science

 本文基于邓熵提出了度量量子纠缠度的方法。分别计算纠缠态和解纠缠之后状态的最大邓熵，将两个熵之差作为纠缠度度量。用GHZ和W纠缠态作为算例给出了所提出方法的应用。