Reducing the search space for conceptual schema transformation

In this paper we focus on the transformation of a conceptual schema into an internal schema. For a given conceptual schema, quite a number of internal schemata can be derived. This number can be reduced by imposing restrictions on internal schemata.

We present a transformation algorithm that can generate internal schemata of several types (including the relational model and the NF² model). Guidance parameters are used to impose further restrictions.

We harmonise the different types of schemata by extending the conceptual language, such that both the conceptual and the internal models can be represented within the same language.     

Uncertainty in a nested relational database model

Some database models have already been developed to deal with complex values but they have constrains that data stored is precise and queries are crisp. However, as many researchers have pointed out, there is a need to present, manipulate, and query complex and uncertain data of various non-traditional database applications such as oceanography, multimedia, meteorology, office automation systems, engineering designs, expert database systems and geographic information systems. In this paper, we present a logical database model, which is an extension of a nested relational data model (also known as an NF² data model), for representing and manipulating complex and uncertain data in databases. We also introduce a possible physical representation of such complex and uncertain values in databases and describe the query processing of the model that we discuss here.     

Moving coordinate frames for representation and visualization in four dimensions

In this paper we generalize the method of sweeping, which may be used for both object representation and object visualization, to objects in E⁴. The generalized sweeping method involves a trajectory in E⁴, and a three-dimensional cross-section orthogonal to the trajectory. Three alternatives are considered for specifying the relationship between the trajectory and the cross-section, namely the Frenet frame, modified Frenet frames, and the standard viewing-reference coordinate (VRC) frame, where each of these is generalized to the case of four dimensions. We have implemented the method using the four-dimensional VRC frame, and the method is illustrated here by means of two examples involving visualization of objects embedded in E⁴.     

Indexing animated objects using spatiotemporal access methods

We present an approach for indexing animated objects and efficiently answering queries about their position in time and space. In particular, we consider an animated movie as a spatiotemporal evolution. A movie is viewed as an ordered sequence of frames, where each frame is a 2D space occupied by the objects that appear in that frame. The queries of interest are range queries of the form, "find the objects that appear in area S between frames f_i and f_j^" as well as nearest neighbor queries such as, "find the q nearest objects to a given position A between frames f_i and f_j^". The straightforward approach to index such objects considers the frame sequence as another dimension and uses a 3D access method (such as an R-Tree or its variants). This, however, assigns long "lifetime" intervals to objects that appear through many consecutive frames. Long intervals are difficult to cluster efficiently in a 3D index. Instead, we propose to reduce the problem to a partial-persistence problem. Namely, we use a 2D access method that is made partially persistent. We show that this approach leads to faster query performance while still using storage proportional to the total number of changes in the frame evolution, What differentiates this problem from traditional temporal indexing approaches is that objects are allowed to move and/or change their extent continuously between frames. We present novel methods to approximate such object evolutions, We formulate an optimization problem for which we provide an optimal solution for the case where objects move linearly. Finally, we present an extensive experimental study of the proposed methods. While we concentrate on animated movies, our approach is general and can be applied to other spatiotemporal applications as well     

Structured Sparse Coding With the Group Log-regularizer for Key Frame Extraction

Key frame extraction based on sparse coding can reduce the redundancy of continuous frames and concisely express the entire video. However, how to develop a key frame extraction algorithm that can automatically extract a few frames with a low reconstruction error remains a challenge. In this paper, we propose a novel model of structured sparse-coding-based key frame extraction, wherein a nonconvex group log-regularizer is used with strong sparsity and a low reconstruction error. To automatically extract key frames, a decomposition scheme is designed to separate the sparse coefficient matrix by rows. The rows enforced by the nonconvex group log-regularizer become zero or nonzero, leading to the learning of the structured sparse coefficient matrix. To solve the nonconvex problems due to the log-regularizer, the difference of convex algorithm (DCA) is employed to decompose the log-regularizer into the difference of two convex functions related to the l₁ norm, which can be directly obtained through the proximal operator. Therefore, an efficient structured sparse coding algorithm with the group log-regularizer for key frame extraction is developed, which can automatically extract a few frames directly from the video to represent the entire video with a low reconstruction error. Experimental results demonstrate that the proposed algorithm can extract more accurate key frames from most SumMe videos compared to the state-of-the-art methods. Furthermore, the proposed algorithm can obtain a higher compression with a nearly 18% increase compared to sparse modeling representation selection (SMRS) and an 8% increase compared to SC-det on the VSUMM dataset.      

Handling complex and uncertain information in the ExIFO andNF2 data models

Trends in databases leading to complex objects present opportunities for representing imprecision and uncertainty that were difficult to integrate cohesively in simpler database models. In fact, one can begin at the conceptual level with a model that allows uncertainty assumptions and then transform those assumptions into a logical model having the necessary semantic foundations upon which to base a meaningful query language. Here we provide such a constructive approach beginning with the ExIFO model for expression of the conceptual design then show how the conceptual design is transformed into the logical design (for which we utilize the extended NF² logical database model). The steps are straightforward, unambiguous, and preserve the relevant information, including information concerning uncertainty     

Using a frame-based language for information retrieval

With the advent of the information society, many researchers are turning to artificial intelligence techniques to provide effective retrieval over large bodies of textual information. In the CODER system, the mission of which is to provide an environment for experiments in applying AI to information retrieval, a factual representation language (FRL) serves as a tool for knowledge engineering and experimentation. the FRL is a hybrid AI language supporting strong typing for attribute values, a frame system, and Prolog-like relational structures. Inheritance is enforced throughout, and the semantics of type subsumption and object matching are formally defined. A collection of type and object managers called the knowledge administration complex implements this common language for storing knowledge and communicating it within the system. Storage of large numbers of complete knowledge objects (statements in the language) is supported by a system of external knowledge bases. Of the three types of knowledge structures in the language, the frame facility has proven most useful in the retrieval domain. This article discusses the frame construct itself, the implementation of the relevant portions of the knowledge administration complex and external knowledge bases, and the use of frames in retrieval research. It closes with a discussion of the utility of the FRL.     

多媒体信号处理的数学理论前沿进展

深度学习模型广泛应用于多媒体信号处理领域,通过引入非线性能够极大地提升性能,但是其黑箱结构无法解析地给出最优点和优化条件。因此如何利用传统信号处理理论,基于变换/基映射模型逼近深度学习模型,解析优化问题,成为当前研究的前沿问题。本文从信号处理的基础理论出发,分析了当前针对高维非线性非规则结构方法的数学模型和理论边界,主要包括：结构化稀疏表示模型、基于框架理论的深度网络模型、多层卷积稀疏编码模型以及图信号处理理论。详细描述了基于组稀疏性和层次化稀疏性的表示模型和优化方法,分析基于半离散框架和卷积稀疏编码构建深度/多层网络模型,进一步在非欧氏空间上扩展形成图信号处理模型,并对国内外关于记忆网络的研究进展进行了比较。最后,展望了多媒体信号处理的理论模型发展,认为图信号处理通过解析谱图模型的数学性质,解释其中的关联性,为建立广义的大规模非规则多媒体信号处理模型提供理论基础,是未来研究的重要领域之一。     

基础信息层经验规则的一种表达方法

该文讨论在复杂的大型辅助决策系统中,构造智能决策规则模型的一种方法。这是一种基于决策表的知识表示方法。它在传统决策表的基础上,吸收了产生式规则、框架表示法、模糊理论、关系模型等多种方法的思想和技术,把传统决策表加以扩展,得到了一种结构性好、表达能力强、可操作性较好的智能决策表达工具,用来表示大型辅助决策系统中的复杂领域知识,将其中松散的经验规则形式化成智能决策规则模型,从而增强其结构性和可操作性,有效支持对其它信息的操作。     

Abstract data types for the logical modeling of complex data

In this paper we propose a logical data model for complex data. Our proposal extends the relational model by using abstract data types for domains specification and an extended relational algebra is also introduced. The introduction of the parameterized type Geometry(S), where S is a ground set of elements, allows the representation of complex aggregated data. As an example, we discuss how our model supports the definition of geographical DBMSs. Moreover, to show the generality of our approach, we sketch how the model can be used in the framework of statistical applications.     

Construction and optimization of CSG representations

Boundary representations (B-reps) and constructive solid geometry (CSG) are widely used representation schemes for solids. While the problem of computing a B-rep from a CSG representation is relatively well understood, the inverse problem of B-rep to CSG conversion has not been addressed in general. The ability to perform B-rep to CSG conversion has important implications for the architecture of solid modelling systems and, in addition, is of considerable theoretical interest.

The paper presents a general approach to B-rep to CSG conversion based on a partition of Euclidean space by surfaces induced from a B-rep, and on the well known fact that closed regular sets and regularized set operations form a Boolean algebra. It is shown that the conversion problem is well defined, and that the solution results in a CSG representation that is unique for a fixed set of halfspaces that serve as a ‘basis’ for the representation. The ‘basis’ set contains halfspaces induced from a B-rep plus additional non-unique separating halfspaces.

An important characteristic of B-rep to CSG conversion is the size of a resulting CSG representation. We consider minimization of CSG representations in some detail and suggest new minimization techniques.

While many important geometric and combinatorial issues remain open, a companion paper shows that the proposed approach to B-rep to CSG conversion and minimization is effective in E², In E³, an experimental system currently converts natural-quadric B-reps in PARASOLID to efficient CSG representations in PADL-2.     

The category concept: An extension to the entity-relationship model

An enhanced version of the Entity-Relationship (ER) data model called the Entity-Category-Relationship (ECR) data model is presented. The principal extension is the introduction of the concept of a category. Categories permit the grouping of entities from different entity types according to the roles they play in a relationship, as well as the representation of ISA and generalization hierarchies. The structures of the ECR data model are defined, and a graphic representation technique for their display is presented. Language operations to define and use an ECR database are defined. Two realistic examples of the use of the ECR model for database design are demonstrated. The examples show how ECR structures can be directly mapped into relational and network structures. The definition of derived relationships on an ECR database gives the power to phrase higher order recursive queries in a first order query language.     

Parallel processing of very large databases using distributed column indexes

The development and investigation of efficient methods of parallel processing of very large databases using the columnar data representation designed for computer cluster is discussed. An approach that combines the advantages of relational and column-oriented DBMSs is proposed. A new type of distributed column indexes fragmented based on the domain-interval principle is introduced. The column indexes are auxiliary structures that are constantly stored in the distributed main memory of a computer cluster. To match the elements of a column index to the tuples of the original relation, surrogate keys are used. Resource hungry relational operations are performed on the corresponding column indexes rather than on the original relations of the database. As a result, a precomputation table is obtained. Using this table, the DBMS reconstructs the resulting relation. For basic relational operations on column indexes, methods for their parallel decomposition that do not require massive data exchanges between the processor nodes are proposed. This approach improves the class OLAP query performance by hundreds of times.     

On the sensitivity of camera calibration

The orientation position errors of an object's coordinate frame are determined when the offset of image centre and lens distortion are not included in the calibration process. The orientation and position errors are [(u₀)² + (v₀)²]^0.5/f and [(u²₀+v²₀)T²_z + (u²₀T²_z + v²₀T_y²)]^0.5/f, respectively, where f is the focal length, (u₀, v₀) is the offset of image centre and (T_x T_y T_z) is the position of an object. We also obtain the following conclusions: (a) The offset of image centre has little effect on the determinations of the position and orientation of a coordinate frame; (b) the lens distortion will not dramatically change the position and orientation of a coordinate frame; (c) the scale factor has a great effect on the position of a coordinate frame, and on the accuracy of measurement; (d) the offset of image centre is more sensitive than the lens distortion on the determinations of the position and orientation of a coordinate frame. Finally, some experimental results are given to demonstrate the theoretical analysis given in this paper.     

空值环境下关系数据库的更新 Ⅰ：扩展关系模型及基本运算

本文从空值语义及更新操作的关系出发，提出了一种新的扩展关系模型，用以组织更新操作下的含有空值的关系数据库中的信息．同时，定义了这种模型下的基本关系代数运算．为实现空值环境下关系数据库的数据更新奠定了基础．     

Translating update operations from relational to object-oriented databases

In migrating a legacy relational database system to the object-oriented (OO) platform, when database migration completes, application modules are to be migrated, where embedded relational database operations are mapped into their OO correspondents. In this paper we study mapping relational update operations to their OO equivalents, which include UPDATE¹, INSERT and DELETE operations. Relational update operation translation from relational to OO faces the touchy problem of transformation from a value-based relationship model to a reference-based model and maintaining the relational integrity constraints. Moreover, with a relational database where inheritance is expressed as attribute value subset relationship, changing of some attribute values may lead to the change of the position of an object in the class inheritance hierarchy, which we call object migration. Considering all these aspects, algorithms are given mapping relational UPDATE, INSERT and DELETE operations to their OO correspondents. Our work emphasize in examining the differences in the representation of the source schema's semantics resulting from the translation process, as well as differences in the inherent semantics of the two models.     

Quartic discriminants and tensor invariants

Discusses the calculation of discriminants of polynomials. The discriminant is a function of the coefficients that indicates if the polynomial has any double roots. The discriminant Δ₄ of a homogeneous quartic f(x,w) = Ax⁴+4Bx³w+6Cx² w²+4Dxw³+Ew⁴ = 0 is Δ₄ = 27(I₃)²-(I₂)³, where I₂ = AE-4BD+3C² and I₃ = ACE-AD ²-B²E+2BCD-C³ (this is the Hilbert representation). The author shows how to write the discriminant as a tensor diagram. The discriminant of a polynomial is an example of an invariant quantity. Tensor diagrams are particularly useful to express invariant quantities. Adding a dimension moves us from the world of (1D) homogeneous polynomials to 2D homogeneous (2DH) geometry (curves in the projective plane). It is shown that a relationship exists between the possible root structures of a 4th-order polynomial and the possible degeneracies of a 3rd-order curve     

Application of the independent molecule model to elucidate the dynamics of structure I methane hydrate

Raman spectroscopy has exhibited the C–H stretch (A₁ mode) frequency ν₁ of hydrated methanes at 2915 cm⁻¹ for the 5¹² cage and 2905 cm⁻¹ for the 5¹²6² cage. These values are lower than the frequency of 2916.5 cm⁻¹ in gaseous methane. In this paper, we theoretically examine the Raman spectra observed in methane hydrate by normal mode analysis using the independent molecule model. By a breakdown of the symmetry, the four frequencies in modes A₁, E, T₂ and T₂ observed in gaseous methane are separated into nine frequencies in the hydrate. It is necessary to consider the anharmonic potential energy within methane and hydrogen bonding between methane hydrogen and water oxygen in order to get a result in qualitative agreement with experiment. The frequency in the 5¹²6² cage is shifted downward in comparison to the one in 5¹², and the frequencies in the both cages are also shifted downward compared with the frequencies in gas. Calculations are also reported for the isotopic methane (CD₄, ¹³CH₄) hydrates.     

On algorithmic rate-coded AER generation

This paper addresses the problem of converting a conventional video stream based on sequences of frames into the spike event-based representation known as the address-event-representation (AER). In this paper we concentrate on rate-coded AER. The problem is addressed as an algorithmic problem, in which different methods are proposed, implemented and tested through software algorithms. The proposed algorithms are comparatively evaluated according to different criteria. Emphasis is put on the potential of such algorithms for a) doing the frame-based to event-based representation in real time, and b) that the resulting event streams resemble as much as possible those generated naturally by rate-coded address-event VLSI chips, such as silicon AER retinae. It is found that simple and straightforward algorithms tend to have high potential for real time but produce event distributions that differ considerably from those obtained in AER VLSI chips. On the other hand, sophisticated algorithms that yield better event distributions are not efficient for real time operations. The methods based on linear-feedback-shift-register (LFSR) pseudorandom number generation is a good compromise, which is feasible for real time and yield reasonably well distributed events in time. Our software experiments, on a 1.6-GHz Pentium IV, show that at 50% AER bus load the proposed algorithms require between 0.011 and 1.14 ms per 8 bit-pixel per frame. One of the proposed LFSR methods is implemented in real time hardware using a prototyping board that includes a VirtexE 300 FPGA. The demonstration hardware is capable of transforming frames of 64/spl times/64 pixels of 8-bit depth at a frame rate of 25 frames per second, producing spike events at a peak rate of 10/sup 7/events per second.     

基于形态学的高斯模型和八邻域帧差法混合运动目标检测算法

针对视频中运动目标的提取问题,提出一种基于形态学的高斯模型和八邻域帧差法相融合的提取算法。该算法首先将视频中某些帧转化为灰度图,建立以混合高斯分布为基础的统计模型,并结合八邻域帧差法提取出运动目标的大致轮廓,然后利用自适应更新的高斯模型算法进行精确的减除,最后再进行形态学处理,从而使检测出的运动目标更加清晰完整。实验结果表明,该算法对含有低速运动物体、阴影较多的视频提取效果较好,具有很好的鲁棒性。