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.
|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.|
|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.|
|" 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.|
|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。|
|疾病诊断相关分组（Diagnosis Related Groups，DRG/DRGs）是一种先进的医疗支付方式，有助于医保费用的合理控制和提升医院服务管理。随着中国医疗改革的深入，DRG开始全面实施，日益重要。本文统计分析了DRG相关技术的主体、类型、时间、受理组织等专利信息，概述了涉及DRG编码的信息处理、医院管理决策支持、绩效管理和医疗收费的专利技术发展情况，对DRG的研发和实施具有现实意义。|