-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathsymbols.tex
151 lines (104 loc) · 12.3 KB
/
symbols.tex
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Text symbols.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\YOURPRODUCT/{\textsf{YOURproduct}} % use YOURPRODUCT as \YOURPRODUCT/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Symbols.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% A group (the group is specified in the sort field)
\newcommand*{\Agroupname}{Basics}
\newglossaryentry{symnatural}{sort={AAsymnatural},name=\ensuremath{\mathbb{N}},symbol=\ensuremath{\mathbb{N}},type={symbols},description={Set of natural numbers}}
\newcommand{\symnatural}{{\glssymbol{symnatural}}}
\newglossaryentry{symreal}{sort={ABsymreal},name=\ensuremath{\mathbb{R}},symbol=\ensuremath{\mathbb{R}},type={symbols},description={Set of real numbers}}
\newcommand{\symreal}{{\glssymbol{symreal}}}
\newglossaryentry{symcomplex}{sort={ACsymcomplex},name=\ensuremath{\mathbb{C}},symbol=\ensuremath{\mathbb{C}},type={symbols},description={Set of all complex numbers}}
\newcommand{\symcomplex}{{\glssymbol{symcomplex}}}
\newglossaryentry{symand}{sort={ADsymand},name=\ensuremath{\wedge},symbol=\ensuremath{\wedge},type={symbols},description={Logical conjunction}}
\newcommand{\symand}{{\glssymbol{symand}}}
\newglossaryentry{symor}{sort={AEsymor},name=\ensuremath{\vee},symbol=\ensuremath{\vee},type={symbols},description={Logical, inclusive disjunction}}
\newcommand{\symor}{{\glssymbol{symor}}}
\newglossaryentry{symnot}{sort={AFsymnot},name=\ensuremath{\neg},symbol=\ensuremath{\neg},type={symbols},description={Logical negation}}
\newcommand{\symnot}{{\glssymbol{symnot}}}
%% B group (the group is specified in the sort field)
\newcommand*{\Bgroupname}{Relational Algebra}
% this is the definition of a symbol entry, note that glossaryentry is defined; for convenience using a newcommand, glssymbol is printed
% see also the use of \ensuremath
\newglossaryentry{relation}{sort={BArelation},name=\ensuremath{\mathcal{R}},symbol=\ensuremath{\mathcal{R}},type={symbols},description={A relation. Sometimes with subscript, e.g., \( \relation_{\mathtt{name}} \) to specify name or index.}}
\newcommand{\relation}{\glssymbol{relation}}
\newglossaryentry{rankedrel}{sort={BBrankedrelation},name=\ensuremath{\relation^{O}},symbol=\ensuremath{\relation^{O}},type={symbols},description={A ranked, relation that exhibits a partial ordering of elements induced by \( O \). Sometimes used with subscript, e.g., \( \rankedrel_{\mathtt{name}} \) to specify name or index.}}
\newcommand{\rankedrel}{\glssymbol{rankedrel}}
\newglossaryentry{domain}{sort={BCdomain},name=\ensuremath{\mathcal{D}},symbol=\ensuremath{\mathcal{D}},type={symbols},description={A data domain of a relation. Sometimes with subscript, e.g., \(\domain_{\mathtt{name}}\), to specify name or index.}}
\newcommand{\domain}{\glssymbol{domain}}
\newglossaryentry{attribute}{sort={BDattribute},name=\ensuremath{\mathcal{A}},symbol=\ensuremath{\mathcal{A}},type={symbols},description={An attribute of a relation, i.e., a tuple \((\mathtt{name}, \domain)\). Sometimes with subscript to specify name or index.}}
\newcommand{\attribute}{\glssymbol{attribute}}
\newglossaryentry{attributep}{sort={BEattributep},name=\ensuremath{\mathcal{A}^{*}},symbol=\ensuremath{\mathcal{A}^{*}},type={symbols},description={An attribute that acts as a primary key.}}
\newcommand{\attributep}{\glssymbol{attributep}}
\newglossaryentry{attributef}{sort={BFfattributef},name=\ensuremath{\overline{\mathcal{A}}},symbol=\ensuremath{\overline{\mathcal{A}}},type={symbols},description={An attribute that acts as a foreign key.}}
\newcommand{\attributef}{\glssymbol{attributef}}
\newglossaryentry{tuple}{sort={BGtuple},name=\ensuremath{t},symbol=\ensuremath{t},type={symbols},description={A tuple \( \tuple \in \relation \) of attribute values \( a_i \in \domain_i \). Sometimes with subscript to specify the index of the tuple in \( \relation \).}}
\newcommand{\tuple}{\glssymbol{tuple}}
\newglossaryentry{domainset}{sort={BHdomainset},name=\ensuremath{\mathbb{D}},symbol=\ensuremath{\mathbb{D}},type={symbols},description={The set system of all data domains \( \domain \) supported by a \acrshort{dbms}.}}
\newcommand{\domainset}{\glssymbol{domainset}}
\newglossaryentry{schema}{sort={BIschema},name=\ensuremath{\mathtt{SCH}},symbol=\ensuremath{\mathtt{SCH}},type={symbols},description={The schema of a relation \( \relation \), i.e., all attributes \(\schema (\relation) = (\attribute_1, \attribute_2, \ldots, \attribute_N)\) that make up \(\relation \).}}
\newcommand{\schema}{\glssymbol{schema}}
\newglossaryentry{selection}{sort={BJselection},name=\ensuremath{\sigma},symbol=\ensuremath{\sigma},type={symbols},description={The unary selection operator used to filter a relation \(\relation \). Usually printed with a subscript to describe the Boolean predicate \( S \), e.g. \( \selection_{S} \).}}
\newcommand{\selection}{\glssymbol{selection}}
\newglossaryentry{projection}{sort={BKprojection},name=\ensuremath{\pi},symbol=\ensuremath{\pi},type={symbols},description={The unary projection operator used to restrict the attributes \( \attribute \) of a relation \( \relation \). Usually used with subscript to list the projection attributes \( P \), e.g., \( \projection_{\attribute_1,\attribute_2} \).}}
\newcommand{\projection}{\glssymbol{projection}}
\newglossaryentry{rename}{sort={BLrename},name=\ensuremath{\rho},symbol=\ensuremath{\rho},type={symbols},description={The unary rename operator used to rename the attributes \( \attribute \) of a relation \( \relation \). Usually used with subscript to list the rename operations, e.g., \( \rename_{\attribute_1 \rightarrow \attribute_2} \).}}
\newcommand{\rename}{\glssymbol{rename}}
\newglossaryentry{order}{sort={BMorder},name=\ensuremath{\omega},symbol=\ensuremath{\omega},type={symbols},description={The binary sort operator used to construct a ranked relation \( \rankedrel \). Usually printed with a subscript to list order attributes \( O \), e.g., \( \order_{\attribute_1 \uparrow,\attribute_2 \downarrow} \).}}
\newcommand{\order}{\glssymbol{order}}
\newglossaryentry{limit}{sort={BNlimit},name=\ensuremath{\lambda},symbol=\ensuremath{\lambda},type={symbols},description={The unary k-selection operator restricts \( \relation \) to the first \( k \) tuples. Usually printed with a subscript to define \( k \), e.g., \( \limit_{k} \).}}
\newcommand{\limit}{\glssymbol{limit}}
\newglossaryentry{aggregation}{sort={BOlimit},name=\ensuremath{\gamma},symbol=\ensuremath{\gamma},type={symbols},description={The unary aggregation operator.}}
\newcommand{\aggregation}{\glssymbol{aggregation}}
\newglossaryentry{group}{sort={BPgroup},name=\ensuremath{\gamma},symbol=\ensuremath{\gamma},type={symbols},description={The unary group operator aggregates tuples in \( \relation \). Usually printed with a subscript to list the group attributes \( G \), e.g., \( \group_{G} \).}}
\newcommand{\group}{\glssymbol{group}}
%% C group (the group is specified in the sort field)
\newcommand*{\Cgroupname}{Multimedia Retrieval}
\newglossaryentry{symmediacol}{sort={CAsymmediacol},name=\ensuremath{\mathbb{O}},symbol=\ensuremath{\mathbb{O}},type={symbols},description={The media collection domain \(\symmediacol = \lbrace o_1, o_2 , \ldots, o_N \rbrace \)}}
\newcommand{\symmediacol}{\glssymbol{symmediacol}}
\newglossaryentry{symfeatures}{sort={CBsymfeatures},name=\ensuremath{\mathbb{F}},symbol=\ensuremath{\mathbb{F}},type={symbols},description={The feature domain \(\symfeatures = \lbrace f_1, f_2, \ldots f_M \rbrace \)}}
\newcommand{\symfeatures}{\glssymbol{symfeatures}}
\newglossaryentry{symfeaturetransform}{sort={CCsymfeaturetransform},name=\ensuremath{\mathfrak{t}},symbol=\ensuremath{\mathfrak{t}},type={symbols},description={Feature transformation function \(\symfeaturetransform \colon \symmediacol \rightarrow \symfeatures \)}}
\newcommand{\symfeaturetransform}{\glssymbol{symfeaturetransform}}
\newglossaryentry{symdist}{sort={CDsymdist},name=\ensuremath{\mathfrak{d}},symbol=\ensuremath{\mathfrak{d}},type={symbols},description={Dissimilarity or distance function \(\symdist \colon \symfeatures \times \symfeatures \rightarrow \symreal \)}}
\newcommand{\symdist}{\glssymbol{symdist}}
\newglossaryentry{symsim}{sort={CEsymsim},name=\ensuremath{\mathfrak{s}},symbol=\ensuremath{\mathfrak{s}},type={symbols},description={Similarity function \(\symsim \colon \symfeatures \times \symfeatures \rightarrow [0, 1.]\)}}
\newcommand{\symsim}{\glssymbol{symsim}}
\newglossaryentry{symcorr}{sort={CFsymcorr},name=\ensuremath{\mathfrak{c}},symbol=\ensuremath{\mathfrak{c}},type={symbols},description={A correspondence function \(\symcorr \colon \symreal \rightarrow [0, 1]\)}}
\newcommand{\symcorr}{\glssymbol{symcorr}}
%% C group (the group is specified in the sort field)
\newcommand*{\Dgroupname}{System Model}
\newglossaryentry{symdfc}{sort={DAsymdfc},name=\ensuremath{\hat{\mathfrak{d}}},symbol=\ensuremath{\hat{\mathfrak{d}}},type={symbols},description={A \acrshort{dfc} $\symdfc \colon \domain_f \times \domain_f \times \domain_{1} \ldots \times \domain_{N} \to \symreal$, which is a generalisation of a distance or dissimilarity function.}}
\newcommand{\symdfc}{\glssymbol{symdfc}}
\newglossaryentry{symindex}{sort={DEsymindex},name=\ensuremath{\mathcal{I}},symbol=\ensuremath{\mathcal{I}},type={symbols},description={An index \( \symindex_{I} \) on relation \( \relation \) indexing attributes \( I \subset \schema(\relation) \)}}
\newcommand{\symindex}{\glssymbol{symindex}}
\newglossaryentry{symop}{sort={DFsymop},name=\ensuremath{\mathtt{OP}},symbol=\ensuremath{\mathtt{OP}},type={symbols},description={A (relational) database operation, typically acting on a relation \( \relation \).}}
\newcommand{\symop}{\glssymbol{symop}}
\newglossaryentry{symplan}{sort={DGsymplan},name=\ensuremath{\mathcal{P}},symbol=\ensuremath{\mathcal{P}},type={symbols},description={A query execution plan, i.e., a concatenation of \( N \) operators \(\mathtt{OP}_1 \circ \mathtt{OP}_2, \ldots \circ \mathtt{OP}_N \).}}
\newcommand{\symplan}{\glssymbol{symplan}}
\newglossaryentry{symtrans}{sort={DHsymtrans},name=\ensuremath{\mathcal{T}},symbol=\ensuremath{\mathcal{T}},type={symbols},description={A transaction, which is used to executed multiple queries. Subscript is typically used to indicate a point in time, e.g., \( \symtrans_1 \).}}
\newcommand{\symtrans}{\glssymbol{symtrans}}
\newglossaryentry{symsnap}{sort={DIsymsnap},name=\ensuremath{\mathcal{S}},symbol=\ensuremath{\mathcal{S}},type={symbols},description={A consistent snapshot of the database and all objects it contains (e.g., relations and indexes). Subscript is typically used to indicate a point in time, e.g., \( \symsnap_1 \).}}
\newcommand{\symsnap}{\glssymbol{symsnap}}
\newglossaryentry{symchangeop}{sort={DJsymchangeop},name=\ensuremath{\mathtt{OP}_c},symbol=\ensuremath{\mathtt{OP}_c},type={symbols},description={A change operation \( \mathtt{OP}_c(\relation, \cdot)\), which can either be an insert, update or delete.}}
\newcommand{\symchangeop}{\glssymbol{symchangeop}}
\newglossaryentry{symchange}{sort={DKsymchange},name=\ensuremath{\mathcal{C}},symbol=\ensuremath{\mathcal{C}},type={symbols},description={A change on relation \( \relation \) with \( \symchange = (\symchangeop, \relation, t, t^{\prime})\).}}
\newcommand{\symchange}{\glssymbol{symchange}}
\newglossaryentry{symwritem}{sort={DLsymwritem},name=\ensuremath{\mathtt{WRITEM}},symbol=\ensuremath{\mathtt{WRITEM}},type={symbols},description={A write model function that determines if a change \( \symchange \) can be propagated to an index \( \symindex \).}}
\newcommand{\symwritem}{\glssymbol{symwritem}}
\newglossaryentry{symfailm}{sort={DMsymfailm},name=\ensuremath{\mathtt{FAILM}},symbol=\ensuremath{\mathtt{FAILM}},type={symbols},description={A failure model function that adjusts the state of an index \( \symindex \) for a change \( \symchange \).}}
\newcommand{\symfailm}{\glssymbol{symfailm}}
\newglossaryentry{symrebuild}{sort={DNsymrebuild},name=\ensuremath{\mathtt{REBUILD}},symbol=\ensuremath{\mathtt{REBUILD}},type={symbols},description={A rebuild function that can rebuild the index \( \symindex \) based on primary data in \( \relation \) .}}
\newcommand{\symrebuild}{\glssymbol{symrebuild}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math Symbols.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator*{\argmax}{argmax}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Image.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand*{\pin}{\includegraphics[height=\heightof{M}]{figures/pin}}