scholarly journals The implication problem for ‘closest node’ functional dependencies in complete XML documents

2012 ◽  
Vol 78 (4) ◽  
pp. 1045-1098 ◽  
Author(s):  
M.W. Vincent ◽  
J. Liu ◽  
M. Mohania
Keyword(s):  
Functional Dependencies ◽  
Xml Documents ◽  
Implication Problem

Towards a Normal Form and a Query Language for Extended Relations Defined by Regular Expressions

2016 ◽  
Vol 27 (2) ◽  
pp. 27-48
Author(s):  
András Benczúr ◽  
Gyula I. Szabó
Keyword(s):  
Normal Form ◽  
Data Base ◽  
Data Model ◽  
Query Language ◽  
Xml Schema ◽  
Relational Model ◽  
Regular Expressions ◽  
Functional Dependencies ◽  
Decision Algorithm ◽  
Implication Problem

This paper introduces a generalized data base concept that unites relational and semi structured data models. As an important theoretical result we could find a quadratic decision algorithm for the implication problem of functional and join dependencies defined on the united data model. As practical contribution we presented a normal form for the new data model as a tool for data base design. With our novel representations of regular expressions, a more effective searching method could be developed. XML elements are described by XML schema languages such as a DTD or an XML Schema definition. The instances of these elements are semi-structured tuples. A semi-structured tuple is an ordered list of (attribute: value) pairs. We may think of a semi-structured tuple as a sentence of a formal language, where the values are the terminal symbols and the attribute names are the non-terminal symbols. In the authors' former work (Szabó and Benczúr, 2015) they introduced the notion of the extended tuple as a sentence from a regular language generated by a grammar where the non-terminal symbols of the grammar are the attribute names of the tuple. Sets of extended tuples are the extended relations. The authors then introduced the dual language, which generates the tuple types allowed to occur in extended relations. They defined functional dependencies (regular FD - RFD) over extended relations. In this paper they rephrase the RFD concept by directly using regular expressions over attribute names to define extended tuples. By the help of a special vertex labeled graph associated to regular expressions the specification of substring selection for the projection operation can be defined. The normalization for regular schemas is more complex than it is in the relational model, because the schema of an extended relation can contain an infinite number of tuple types. However, the authors can define selection, projection and join operations on extended relations too, so a lossless-join decomposition can be performed. They extended their previous model to deal with XML schema indicators too, e.g., with numerical constraints. They added line and set constructors too, in order to extend their model with more general projection and selection operators. This model establishes a query language with table join functionality for collected XML element data.

An optimized approach for extracting approximate functional dependencies in XML documents

2006 ◽  
Vol 11 (1) ◽  
pp. 127-132
Author(s):  
Shi Lei ◽  
Yang Xiao-chun ◽  
Yu Ge ◽  
Wang Bin ◽  
Zhou Hua-hui
Keyword(s):  
Functional Dependencies ◽  
Xml Documents

scholarly journals Integrity Constraints Revisited: From Exact to Approximate Implication

2022 ◽  
Vol Volume 18, Issue 1 ◽  
Author(s):  
Batya Kenig ◽  
Dan Suciu
Keyword(s):  
Linear Inequality ◽  
Measure Theory ◽  
Probability Distributions ◽  
Integrity Constraints ◽  
Functional Dependencies ◽  
Data Dependencies ◽  
Relaxation Problem ◽  
Implication Problem ◽  
Schema Design ◽  
Degree Of Satisfaction

Integrity constraints such as functional dependencies (FD) and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate probability distributions. The implication problem studies whether a set of constraints (antecedents) implies another constraint (consequent), and has been investigated in both the database and the AI literature, under the assumption that all constraints hold exactly. However, many applications today consider constraints that hold only approximately. In this paper we define an approximate implication as a linear inequality between the degree of satisfaction of the antecedents and consequent, and we study the relaxation problem: when does an exact implication relax to an approximate implication? We use information theory to define the degree of satisfaction, and prove several results. First, we show that any implication from a set of data dependencies (MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most quadratic in the number of variables; when the consequent is an FD, the factor can be reduced to 1. Second, we prove that there exists an implication between CIs that does not admit any relaxation; however, we prove that every implication between CIs relaxes "in the limit". Then, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Finally, we show how some of the results in the paper can be derived using the I-measure theory, which relates between information theoretic measures and set theory. Our results recover, and sometimes extend, previously known results about the implication problem: the implication of MVDs and FDs can be checked by considering only 2-tuple relations.

scholarly journals On the Discovery of Semantically Meaningful SQL Constraints from Armstrong Samples: Foundations, Implementation, and Evaluation

2021 ◽  
Author(s):  
◽  
Van Tran Bao Le
Keyword(s):  
Database Design ◽  
Design Tool ◽  
Relational Model ◽  
Functional Dependencies ◽  
Data Dependencies ◽  
Design Choice ◽  
Implication Problem ◽  
Finite Set ◽  
Current Design ◽  
Class C

<p>A database is said to be C-Armstrong for a finite set Σ of data dependencies in a class C if the database satisfies all data dependencies in Σ and violates all data dependencies in C that are not implied by Σ. Therefore, Armstrong databases are concise, user-friendly representations of abstract data dependencies that can be used to judge, justify, convey, and test the understanding of database design choices. Indeed, an Armstrong database satisfies exactly those data dependencies that are considered meaningful by the current design choice Σ. Structural and computational properties of Armstrong databases have been deeply investigated in Codd’s Turing Award winning relational model of data. Armstrong databases have been incorporated in approaches towards relational database design. They have also been found useful for the elicitation of requirements, the semantic sampling of existing databases, and the specification of schema mappings. This research establishes a toolbox of Armstrong databases for SQL data. This is challenging as SQL data can contain null marker occurrences in columns declared NULL, and may contain duplicate rows. Thus, the existing theory of Armstrong databases only applies to idealized instances of SQL data, that is, instances without null marker occurrences and without duplicate rows. For the thesis, two popular interpretations of null markers are considered: the no information interpretation used in SQL, and the exists but unknown interpretation by Codd. Furthermore, the study is limited to the popular class C of functional dependencies. However, the presence of duplicate rows means that the class of uniqueness constraints is no longer subsumed by the class of functional dependencies, in contrast to the relational model of data. As a first contribution a provably-correct algorithm is developed that computes Armstrong databases for an arbitrarily given finite set of uniqueness constraints and functional dependencies. This contribution is based on axiomatic, algorithmic and logical characterizations of the associated implication problem that are also established in this thesis. While the problem to decide whether a given database is Armstrong for a given set of such constraints is precisely exponential, our algorithm computes an Armstrong database with a number of rows that is at most quadratic in the number of rows of a minimum-sized Armstrong database. As a second contribution the algorithms are implemented in the form of a design tool. Users of the tool can therefore inspect Armstrong databases to analyze their current design choice Σ. Intuitively, Armstrong databases are useful for the acquisition of semantically meaningful constraints, if the users can recognize the actual meaningfulness of constraints that they incorrectly perceived as meaningless before the inspection of an Armstrong database. As a final contribution, measures are introduced that formalize the term “useful” and it is shown by some detailed experiments that Armstrong tables, as computed by the tool, are indeed useful. In summary, this research establishes a toolbox of Armstrong databases that can be applied by database designers to concisely visualize constraints on SQL data. Such support can lead to database designs that guarantee efficient data management in practice.</p>

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

scholarly journals CRISPRi enables isoform-specific loss-of-function screens and identification of gastric cancer-specific isoform dependencies

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Rebecca Davies ◽  
Ling Liu ◽  
Sheng Taotao ◽  
Natasha Tuano ◽  
Richa Chaturvedi ◽  
...  
Keyword(s):  
Gastric Cancer ◽  
Functional Dependencies ◽  
Loss Of Function ◽  
Genetic Screens ◽  
Transcript Isoforms ◽  
Specific Loss ◽  
Current Loss ◽  
Specific Transcript ◽  
Multiple Promoters ◽  
Poor Patient

Abstract Introduction Genes contain multiple promoters that can drive the expression of various transcript isoforms. Although transcript isoforms from the same gene could have diverse and non-overlapping functions, current loss-of-function methodologies are not able to differentiate between isoform-specific phenotypes. Results Here, we show that CRISPR interference (CRISPRi) can be adopted for targeting specific promoters within a gene, enabling isoform-specific loss-of-function genetic screens. We use this strategy to test functional dependencies of 820 transcript isoforms that are gained in gastric cancer (GC). We identify a subset of GC-gained transcript isoform dependencies, and of these, we validate CIT kinase as a novel GC dependency. We further show that some genes express isoforms with opposite functions. Specifically, we find that the tumour suppressor ZFHX3 expresses an isoform that has a paradoxical oncogenic role that correlates with poor patient outcome. Conclusions Our work finds isoform-specific phenotypes that would not be identified using current loss-of-function approaches that are not designed to target specific transcript isoforms.

Algorithms for the discovery of embedded functional dependencies

2021 ◽  
Author(s):  
Ziheng Wei ◽  
Sven Hartmann ◽  
Sebastian Link
Keyword(s):  
Functional Dependencies
Sign in / Sign up

Export Citation Format

Share Document