Attribute tuple

The unique attribute means that no other object of this owner type has the same attribute value, unique can apply to a tuple of attributes. 

In this appendix, basic theorems on differential inequalities are stated and interpreted. The main theorem is usually attributed to Kamke [Ka] but the work of Muller [Mii] is prior. A more general version due to Burton and Whyburn [BWh] is also needed. We follow the presentation in Coppel [Co, p. 27] and Smith [S2 S6j. The nonnegative cone in R", denoted by R , is the set of all n-tuples with nonnegative coordinates. One can define a partial order on R" by < x if x—R". Less formally, this is true if and only if < x, for ail i. We write x < if x, < )>/ for all i. The same notation will be used for matrices with a similar meaning. 

The product of several exponentiations, i.e., a t-tuple exponentiation g- as in Definition 8.1, can be computed more efficiently than by computing all the products separately and multiplying them. In the following, small tuples are often used, e.g., with /i = 3. In such cases, the simplest technique (attributed to Shamir in [ElGa85]) is an extension of the square-and-multiply algorithm that evaluates exponents from left to right After each squaring, the intermediate result is multiplied with a product where h,- is the appropriate bit of x,-. A table with the 2 ... 

Contextual attribute correspondences can be modeled with similarity matrices. An entry in the similarity matrix Mjj is extended to be a tuple v,c), where v e [0,1] is a similarity value and c is a context as defined above. This modeling allows a smooth extension of contextual attribute correspondences to matcher ensembles [Domshlak et al. 2007 He and Chang 2005], in which matchers are combined to improve the quality of the outcome of the matching process. For example, Do et al. [2002] and Domshlak et al. [2007] proposed several ways to combine similarity matrices, generated by different matchers, into a single matrix. Such combination, which was based solely on aggregating similarity scores, can be extended... 

Contextual and by-tuple probabilistic attribute correspondences seem to be complementary. A by-tuple probabilistic attribute correspondence represents a situation in which there is uncertainty as to whether a given tuple should be interpreted using one correspondence or the other. Contextual attribute correspondences models exactly such knowledge. Therefore, By-tuple probabilistic attribute correspondence is needed whenever no information regarding the contextual attribute correspondence is available. Whenever contextual attribute correspondence is gathered automatically, using statistical methods as described in Sect. 3.2, another layer of uncertainty is added to the modeling. Therefore, contextual attribute correspondences should also be extended to provide probabilistic alternative versions. 

A pair of instances Ds and Dr satisfies a relation mapping m if for every source tuple ts e Ds, there exists a target tuple tt e Dt, such that for every attribute correspondence (s, t) e m, the value of attribute s in ts is the same as the value of attribute t in tt. 

On the two tuples generated by chasing the tgds, Company (23, Yahoo., YHOO), Company (N2, Yahoo., YHOO), chasing the egd equates N2 to the constant 23, based on the same value for the symbol attribute, YHOO. Chasing the egds returns the canonical universal solution in Fig. 5.3b. Notice how the canonical universal solution is not the core universal solution, which in turn is represented in Fig. 5.3c. 

Moreover the user can specify if tuple fields are converted to attributes, instead of elements, the ordering of sequences, as well as other details of the conversion process. 

The tables are formally called relations, referring to the mathematical set theory used in the original work on relational databases.1 In database theory, rows are called tuples and columns are called attributes of a tuple. The focus of this book is practical, so the common terms table, row, and column are used. The detail of using the SQL language to perform these operations is left to a later chapter of this book. 

Partially ordered sets can be visualized through Hasse diagrams, which are quite useful if not too many objects are included. Let a and b be two elements of the object set E. Each object is characterized by a set of attributes. The relation < between a and b is valid, if and only if this relation holds for ah attributes of a and b. In other words a < b, if all components of the tuple of a are smaller or equal to the corresponding component of the tuple of b. With help of the notation qj(i) with i the index for any element of E, and j as index for any attribute of IB we give a formula ... 

Attributes are -in the case of the object x denoted as q(l,x), q(2,x),...,q(m,x) and often written as a tuple q(x). We avoid the term vector, because the properties of a linear space are not needed in the HDT. Often the properties are gathered to a set without reference to actual values realized by the objects. This set of properties is called an information base IB. If METEOR is to be applied, often subsets of IB are needed. 

To the user, the relational database consists of a collection of tables (or relations in the formal language of the model). Each table may be thought of as a matrix of values divided into rows and columns. Each row represents a record and is referred to as a tuple in the model. Each column is a field and is called an attribute in the model. Below are some simple tables for Employee and Department. 

The relational model is a modification of the individual record model that limits its data structures and thereby provides a mathematical basis for operation on records. Data structures in a relational database may consist only of relations, or field sets that are related. Every relation may be considered as a table. Each row in the table is a record or tuple. Every column in each table or row is a field or attribute. Each field or attribute has a domain that defines the admissible values for that field. 

Rule induction uses a number of specific beliefs in the form of database tuples as evidence to support a general belief that is consistent with these specific beliefs. A collection of tuples in the database may form a relation that is defined by the values of particular attributes, and relations in the database form the basis of rules. Evidence from within the database in support of a rule is thus used to induce a rule which may be generally applied. 

Rules tend to be based on sets of attribute values, partitioned into an antecedent and a consequent. A typical if then rule, of the form if antecedent = true, then consequent = true, is given by if a male employee is aged over 50 and is in a management position, then he will hold an additional pension plan. Support for such a rule is based on the proportion of tuples in the database that have the specified attribute values in both the antecedent and the consequent. The degree of confidence in a rule is the proportion of those tuples that have the specified attribute values in the antecedent, which also have the specified attribute values in the consequent. 

The relational data model makes available one single data type, referred to as a relation. Informally, a relation can be thought of as a table, with each row corresponding to an instance of the application concept modeled by that relation and each column corresponding to the values of a property that describes the instances. Rows are referred to as tuples and column headers as attributes. More formal definitions now follow. 

Key Constraint Every relation has a designated attribute (or a concatenation thereof) which acts as the primary key for the relation in the sense that the value of its primary key identifies the tuple uniquely. 

A ) is a subset of the Cartesian product of the domains of the attributes that characterize R. Thus, a relation instance of degree n is a set, each element of which is an /i-tuple of the form v, ..., Vn) such that... 

Since there are no duplicate elements in a set, each tuple in a relation instance is unique. In other words, the concatenation of all the attributes is always a candidate key for the relation. 

As a consequence of the central role that relations retain in object-relational data models, one crucial difference with respect to the object-oriented case is that the role played by object identity is relaxed to an optional, rather than mandatory, feature. Thus, an object-relational DBMS stands in an evolutionary path regarding relational ones, whereas object-oriented ones represent a complete break with the relational approach. In this context, notice that while a tuple of type constructor may allow a relation type to be supported, each tuple will have an identity, and attribute names will be explicitly needed to retrieve and interact with values. 

SQL can also express insertions, deletions and updates, as indicated in Fig. 7. Note in Fig. 7 that on insertion it is possible to omit null values by listing only the attributes for which values are being supplied. Note also that the order of insertion in Fig. 7 matters, since referential integrity constraints would otherwise be violated. Finally, note that, because of cascading deletions, the final statement will also delete all tuples in DNA sequence that refer to the primary key of the tuple being explicitly deleted in organism. 

SQL also supports aggregations (e.g., COUNT and AVG, which, respectively, count the number of tuples in a result and compute the average value of a numeric attribute in the result), groupings, and sorting. 

Evaluating a WSN, which may be considered a distributed database and that each sensor node is, in essence, a tuple of a relation, where the completeness of the tuple could be measured, that is, if all the data that could be collected by the sensor node was actually made available. Another set of metrics, for the same dimension, could be for the attribute, in which it would be possible to verify that all the sensor nodes have executed the collection of a special physical quantities, and with this, inferred the quantity of nodes that are active in the relation. Furthermore, a third set of metrics for the same dimension could be executed for the complete relation, in which all the values of the relations would be evaluated by their existence or inexistence. 

Since attribute values can be either naturally ordered, such as the set of integers, or unordered, such as the set of labels red, green, blue, etc., the RST approach has considerable descriptive power. Lastly, the ordered pair a,vl) is called a descriptor in an information system, which is defined by the 3-tuple IS=(Xv4,V), where each of the terms is defined earlier. 

The major development in the JCAMP-DX file structure in version 5.0 is the use of the n-tuple form. This version is. still in the draft form, and the same restrictions apply to its implementation as are stated for the NMR version 5.01 in Section 2.4.3 above. In a file built to this format the DATACLASS= NTUPLES. There follows an attribute table... 

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