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1. 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.

2. chinaXiv:202001.00045 [pdf]

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.

3. chinaXiv:201705.00837 [pdf]

Subjects: Energy Science >> Energy Science （General）

 河盆地有无天然气一直是地学界研究的热点问题之一，而该问题的关键是有无气源岩的存在。为进一步评价因缺乏有效烃源岩而停顿多年的渭河盆地的油气地质前景，结合区域地质背景，通过二维地震反射特征、地热井伴生气及油气化探的CH4、CO2碳同位素数据和钻探成果综合分析，认为渭河盆地深部残留有晚古生代含煤地层：①二维地震反射剖面揭示，渭河盆地深部发育类似鄂尔多斯盆地石炭系—二叠系煤系地层特有的强反射特征（T9），对应于太原组9#、8#和山西组4#、3#主力煤层反射；②地热井伴生气及油气化探样品中δ13CH4在-24.5‰ ~ -40.2‰之间，属于煤型热解—裂解气，大多数样品δ13 Cco2＜-10‰，属有机成因气；③渭参3井揭示盆内存在上古生界二叠系石盒子组，推测下部存在山西组和太原组地层；④渭河盆地在晚古生代为大华北克拉通的一部分，沉积有煤系地层，三叠纪末期开始遭受一定的隆升剥蚀，至新生代渭河断陷盆地开始形成，盆地周缘发生大规模隆升剥蚀，而渭河盆地内这一时期接受了巨厚沉积，前新生代地层（上古生代煤系地层等）得以保存和深埋，即构造演化的差异造成了不同构造单元地层剥蚀和残留程度的差异。综合认为晚古生代煤系地层甚至更晚层位存在于渭河盆地的西安凹陷、固市凹陷和咸渭凸起的部分区域。渭河盆地晚古生代含煤地层可作为油气及氦气载体气的气源岩，为渭河盆地油气及富氦天然气勘探提供了物质基础，同时可为鄂尔多斯周缘断陷盆地群油气资源调查提供借鉴。