Classification of knowledge graph completeness measurement techniques

At present,although knowledge graphs have been widely used in various fields such as recommendation systems,question and answer systems,and intelligent search,there are always quality problems such as knowledge omissions and errors.Quality assessment and control,as an important means to ensure the quality of knowledge,can make the applications based on knowledge graphs more complete and more accurate by reasonably assessing the knowledge graphs and fixing and improving the quality problems at the same time.Therefore,as an indispensable part of the knowledge graph construction process,the results of quality assessment and control determine the usefulness of the knowledge graph.Among them,the assessment and enhancement of completeness,as an important part of the assessment and control phase,determine whether the knowledge graph can fully reflect objective phenomena and reveal potential connections among entities.In this paper,we review specific techniques of completeness assessment and classify completeness assessment techniques in terms of closed world assumptions,open world assumptions,and partial completeness assumptions.The purpose of this paper is to further promote the development of knowledge graph quality control and to lay the foundation for subsequent research on the completeness assessment of knowledge graphs by reviewing and classifying completeness assessment techniques.

How to implement a knowledge graph completeness assessment with the guidance of user requirements

In the context of big data, many large-scale knowledge graphs have emerged to effectively organize the explosive growth of web data on the Internet. To select suitable knowledge graphs for use from many knowledge graphs, quality assessment is particularly important. As an important thing of quality assessment, completeness assessment generally refers to the ratio of the current data volume to the total data volume.When evaluating the completeness of a knowledge graph, it is often necessary to refine the completeness dimension by setting different completeness metrics to produce more complete and understandable evaluation results for the knowledge graph.However, lack of awareness of requirements is the most problematic quality issue. In the actual evaluation process, the existing completeness metrics need to consider the actual application. Therefore, to accurately recommend suitable knowledge graphs to many users, it is particularly important to develop relevant measurement metrics and formulate measurement schemes for completeness. In this paper, we will first clarify the concept of completeness, establish each metric of completeness, and finally design a measurement proposal for the completeness of knowledge graphs.

Strong Completeness of Medium Logic System

The strong completeness of medium logic system is discussed. The following results are proved： medium propositional logic system MP and its extension MP^＊ are strong complete; medium predicate logic system MF and its extensions （MF^＊ and ME^＊ ） are not strong complete; and generally, ff a consistent formal system is not strong complete, then any consistent extensions of this forreal system are not strong complete either.

Completeness of Eigenfunction Systems for Off-Diagonal Infinite-Dimensional Hamiltonian Operators

For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity

The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.

THE HAMILTONIAN SYSTEM AND COMPLETENESS OF SYMPLECTIC ORTHOGONAL SYSTEM

In this paper, a new Banach space ZH is defined, and it is proved that there is completeness of eigenfunction system (symplectic orthogonal system) of a class of Hamiltonian system in ZH space. We have also proved the following results: ZH space can be continuously imbedded to L-2[0,1] X L-2[0,1], but ZH not equal L-2[0,1] X L-1[0,1].

Research on completeness of earthquake data in the Chinese mainland（Ⅱ）──The regional distribution of the beginning years of basically complete earthquake data

Based on the concrete conditions of earthquake data in the west of China, East China and SOuth China, we studied the completeness of data in these regions by suitable methods to local conditions. Otherwise, we roughly estimated monitoring capability of local networks in China since 1970 and some outlying regions where the data is lack. Finally, we gave the regional distribution of the beginning years since which the data for different magnitude intervals are largely complete in the Chinese mainland.

On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.

Completeness of system of root vectors of upper triangular infinitedimensional Hamiltonian operators appearing in elasticity theory

This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.

Super Resolution Perception for Improving Data Completeness in Smart Grid State Estimation

The smart grid is an evolving critical infrastructure,which combines renewable energy and the most advanced information and communication technologies to provide more economic and secure power supply services.To cope with the intermittency of ever-increasing renewable energy and ensure the security of the smart grid,state estimation,which serves as a basic tool for understanding the true states of a smart grid,should be performed with high frequency.More complete system state data are needed to support high-frequency state estimation.The data completeness problem for smart grid state estimation is therefore studied in this paper.The problem of improving data completeness by recovering highfrequency data from low-frequency data is formulated as a super resolution perception(SRP)problem in this paper.A novel machine-learning-based SRP approach is thereafter proposed.The proposed method,namely the Super Resolution Perception Net for State Estimation(SRPNSE),consists of three steps:feature extraction,information completion,and data reconstruction.Case studies have demonstrated the effectiveness and value of the proposed SRPNSE approach in recovering high-frequency data from low-frequency data for the state estimation.

ON THE DEGREE OF COMPLETENESS OF CRYPTOGRAPHIC FUNCTIONS

This paper discusses the degree of completeness of cryptographic functions, which is one of the cryptographic criteria should be considered in the design of stream ciphers. We establish the relationships between the degree of completeness and other cryptographic criteria. For resilient Boolean functions, a method to enhance the degree of completeness is proposed, while the nonlinearity and the algebraic degree do not decrease. Moreover, two constructions of resilient functions are provided, which have optimal degree of completeness, high nonlinearity, and high algebraic degree.

Completeness Analysis of the Historical Earthquake Catalogue in China

The historical earthquake catalogue of China has lasted more than 3000 years,and most of its data are inferred from historical records.The earthquake catalogue in earlier times is not complete owing to various reasons,so some events are lost.This paper estimates the loss rate of earthquakes with various magnitudes in the historical earthquake catalogue for different time intervals quantitatively by using the Gutenberg-Richter formula and modern instrumental records,which will provide the references for statistic research in seismicity.

GLOBAL WEAK SHARP MINIMA AND COMPLETENESS OF METRIC SPACE

A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris' result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.

Research on the completeness of earthquake data in the Chinese mainland（I）──North China

In terms of the temporal-spatial distribution features of earthquakes, we study the completeness of historical data in North China where there is the most plenty historical data and with the longest record history by some meth ods of analysis and comparison. The results are obtained for events with Ms≥4 are largely complete since 1484 in North China (except Huanghai sea region and remote districts, such as Nei Mongol Autonomous region), but quakes with Ms≥6 are largely complete since 1291 in the middle and lower reaches of the Yellow River.

A NOTE ON THE COMPLETENESS OF HU HAI-CHANG’S SOLUTION

In this paper it is showed that Hu Hai-chang's solution for the isotropic is complete in case of regions convex in z-direction.

ON THE COMPLETENESS OF THE GENERALIZED AXISYMMETRIC STOKES FLOW EQUATION

This paper defines new kinds of functions——the conjugate axisymmetric poteptial functions. With the aid of them, we can prove the completeness of the solutions of the generalized axisymmetric Stokes flow equation without the condition on the convexity of the domain.

The Completeness of Cone Metric Spaces

Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.

Completeness Problem of the Deep Neural Networks

Hornik, Stinchcombe & White have shown that the multilayer feed forward networks with enough hidden layers are universal approximators. Roux & Bengio have proved that adding hidden units yield a strictly improved modeling power, and Restricted Boltzmann Machines (RBM) are universal approximators of discrete distributions. In this paper, we provide yet another proof. The advantage of this new proof is that it will lead to several new learning algorithms. We prove that the Deep Neural Networks implement an expansion and the expansion is complete. First, we briefly review the basic Boltzmann Machine and that the invariant distributions of the Boltzmann Machine generate Markov chains. We then review the θ-transformation and its completeness, i.e. any function can be expanded by θ-transformation. We further review ABM (Attrasoft Boltzmann Machine). The invariant distribution of the ABM is a θ-transformation;therefore, an ABM can simulate any distribution. We discuss how to convert an ABM into a Deep Neural Network. Finally, by establishing the equivalence between an ABM and the Deep Neural Network, we prove that the Deep Neural Network is complete.

Completeness and Timeliness of Hepatitis B Vaccination in Preschool Children: Determinants for Good and Timely Uptake in Libreville, Gabon

Background: Gabon is endemic for hepatitis B, but they have still not reached the WHO goal for Hepatitis B vaccination coverage. We aimed to determine the rate of completeness and timeliness of hepatitis B vaccination among children under 15 years of age in Libreville. Methods: Cross-sectional study conducted over 9 months, including children randomly selected from vaccination centres, nurseries and kindergartens. We collected data on the child, socio-economic characteristics of the families, and dates of administration of hepatitis B vaccines. We determined the compliance of the vaccination dates according to the vaccination start pattern. Results: We included 453 children, of whom 236 were girls, for a sex ratio of 0.92. A total of 87% (95% CI [83.9% - 90.1%]) of children had started and completed their 3 doses of vaccine before the 12th month of age. 149 subjects had received their 3 doses on time according to the original vaccination schedule, i.e. 32.9% (95% CI [28.6% - 37.2%]). Factors significantly associated with completeness were vaccination in a public centre OR = 114 [47.2 - 347] p st dose OR = 3 [1.6 - 5.5] p < 0.001. Age at first dose was the predictor of timeliness aOR = 1.3 (95% CI [1.2 - 1.5] p 0.001). Conclusion: The respect for the vaccination deadlines is insufficient in our context, solutions exist to improve this situation.