dataesr/scientific-paragraphs-categorization huggingface dataset:
A. Data model In the following, we are interested in fuzzy graph databases where nodes and edges can carry data (e. g. keyvalue pairs in attributed graphs, see Section II-A). So, we first propose an extension of the definition of a fuzzy graph into that of a fuzzy data graph. Definition 1 (Fuzzy data graph): Let E be a set of labels. A fuzzy data graph G is a quadruple (V, R, κ, ζ), where V is a finite set of nodes (each node n is identified by an id, also denoted by n. id), R = e∈E {ρ e : V × V → [0, 1]} is a set of labeled fuzzy edges between nodes of V , and κ (resp. ζ) is a function assigning a data value, e. g. a set of key-value pairs, to nodes (resp. edges) of G. A fuzzy data graph may contain both fuzzy edges and crisp edges as a fuzzy edge with a degree of 0 or 1 can be considered as crisp.
Along the same line, a crisp data graph is simply a special case of fuzzy data graph (where ρ e : V × V → {0, 1} for all e ∈ E). We then only deal with fuzzy edges and data graph in the following. In the following, a graph database is meant to be a fuzzy data graph. The following example illustrates this notion. Example 1: Fig. 2  is an example of fuzzy data graph inspired of data stemming from DBLP 1 , with some fuzzy edges (with a corresponding degree in brackets), and crisp ones (equivalent to a corresponding degree of 1). In this 1 http://www. informatik. uni-trier. de/ ∼ ley/db/ example, the degree associated with A -contributor-> B is the proportion of journal papers co-written by A and B, over the total number of journal papers written by B. In this example, the degree is based on a simple statistical notion, which can be made subtler by fuzzy operations or by the integration of expert knowledge.
B. Algebra We now move to the definition of a graph algebra allowing the definition of flexible queries, for handling fuzzy or crisp graph databases. Along the lines of relational algebra, the algebra could be the core of a practical language and serve as a basis for describing and optimizing underlying query execution plans. The algebra is partly inspired from graph pattern queries of  [24]  and from the crisp algebra proposed in  [5]. The basic unit of information is the graph. The first operator is the selection, which is based on the concept of fuzzy graph pattern, an extension of the crisp graph pattern notion defined in  [24]  shown to have good properties for a practical implementation. We first introduce the notion of a fuzzy regular expression subsequently used for defining a fuzzy graph pattern.
e ∈ E) then µ exp (p) = 1 else µ exp (p) = 0. • If exp is of the form f 1 •f 2. Let P Example 2: The paths represented in Fig. 4  are some paths from the graph database depicted in Fig. 2. • Expression e 1 = creator • contributor + is a fuzzy regular expression. All paths p i (i ∈ [1. We then introduce the notion of a fuzzy graph pattern, which is a directed crisp graph with conditions on nodes and edges, types on nodes, and where edges are labeled by fuzzy regular expressions that denote paths. Definition 4 (Fuzzy graph pattern): Let F be a set of fuzzy terms. A fuzzy graph pattern is defined as a sextuple P = (V P , E P , f path e , f cond n , f cond e , f type n ) where • V P is a finite set of nodes; • E P ⊆ V P × V P is a finite set of edges where (u, u ) denotes an edge from u to u ; • f path e is a function defined on E P s.
CYPHER  [25]  is an intuitive query language inspired from ASCII-art for graph representation, implemented in the Neo4j (crisp) graph database management system  [15]. A fuzzy graph pattern expressed à la CYPHER consists of a set of expressions of the form (n1:Type1)-[exp]->(n2:Type2) or (n1:Type1)-[e:label]->(n2:Type2) where n1, n2 are node variables, e is an edge variable, label is a label of E, exp is a fuzzy regular expression, and Type1 and Type2 are node types. Such an expression denotes a path satisfying a fuzzy regular expression (that is simple in the second form) going from a node of type Type1 to a node of type Type2. All its arguments are individually optional, so the merest form of an expression is ()-[]->() denoting a path made of two nodes connected by any edge. Conditions on attributes are expressed on node and edges variables in a W H E R E clause.
75 (as µ short (Length(p)) = µ short (1. 72) = 1), µ P (g 2 ) = 0. 5 (as µ short (Length(p)) = µ short (4) = 0. 5), µ P (g 3 ) = 0. 33 (as µ short (Length(p)) = µ short (4. 33) = 0. 33), µ P (g 4 ) = 0. 75 (as µ short (Length(p)) = µ short (3. 33) = 0. 83) and µ P (g 5 ) = 0. 5 (as µ short (Length(p)) = µ short (4) = 0. 5). Let us now move to the definition of the fuzzy operators and expressions of the algebra. Even if the graph database contains a single graph, a query may return a set of graphs as several subgraphs may match a pattern as shown in Example 3. Graphs of a set do not necessarily have the same structure. A satisfaction degree is associated with each graph. A set of pairs graph , degree is nothing but a fuzzy set of graphs. Hence, each operator of the algebra takes one or more (depending on the arity of the operation) fuzzy set(s) of graphs as an input and generates a fuzzy set of graphs as an output.
All of the operators of the algebra operate in closed form. Applying an operation to the whole initial database means applying the operation to the singleton { DB , 1 }. Expressions of the algebra are defined inductively as usual: (i) a (fuzzy) graph database DB is an expression of the algebra, and (ii) if e 1 , • • • , e n are expressions and O is an operator of arity n then O(e 1 , • • • , e n ) is an expression of the algebra. Definition 6 (Selection operator): The selection operator σ takes as an input a fuzzy graph pattern P and a fuzzy set G of graphs. It returns a fuzzy set composed of all subgraphs of G that match the fuzzy graph pattern. σ P (G) = { s , min(d, µ P (s)) | µ P (s) > 0} where s is a subgraph of g s. t. g , d ∈ G. In case of duplicates (a same graph appearing with several satisfaction degrees), the highest satisfaction degree is kept.
Example 5: Fig. 6  is the answer of σ P (DB) where P is the pattern of Example 3 and DB is the database of Fig. 2. Definition 7 (Alpha-cut operator): This operation performs an α-cut on a fuzzy relation of a graph (cf. section III-2). The alpha-cut operator Cut takes as input a fuzzy set of graphs G, a label e ∈ E and a degree α ∈ [0 + , 1]. It produces a fuzzy set of graphs defined as follows: Cut e,α (G) = { (V, R , κ, ζ) , d | (V, R, κ, ζ) , d ∈ G} where R = {ρ l | ρ l ∈ R and l = e} ∪ {ρ α e }. Note that the alpha-cut is seen here as an operation that "updates" the ρ e relation by performing an α-cut on it, and so makes ρ e crisp instead of fuzzy. It keeps the data embedded in edges labeled by e. Definition 8 (Projection operators): The projection operation "on edges", Π edges , removes relations from a graph.
V. TOWARDS A FLEXIBLE QUERY LANGUAGE The algebra constitutes the basis of a query language called FUDGE implementing the selection operator, in which fuzzy preferences appear. A FUDGE query is composed of: As a proof-of-concept of our approach, we developed a software prototype for evaluating FUDGE queries. The FUDGE prototype, downloadable at www-shaman. irisa. fr/fudge-prototype, is based on the Neo4j system  [15]  that implements the CYPHER (crisp) query language. We extended then interactive Neo4j REPL Console Rabbithole  [26]. We decided to use a crisp graph database management system for implementing the FUDGE query evaluator. This allows not only to access all the functionalities offered by the query language of the crisp engine, but also not to have to implement a whole query evaluator engine.
Then two problems arise. The first problem is to model a fuzzy graph database into a crisp graph database. This can be done in the crisp property graphs model. In a crisp property graph, a set of properties, where a property is a keyvalue pair, can be bound to a node or an edge. Properties usually denote embedded data and meta-data for nodes, and properties of the relation for edges. A relation ρ e (x, y) of a  Thus, the crisp property graph representation can simulate the fuzzy one by attaching to each edge of the property graph a supplementary property called fdegree carrying the degree value of the relations (supposing that fdegree now becomes a reserved keyword of the system). If needed, a similar mechanism allows to turn crisp nodes into fuzzy ones. The second problem is the evaluation of a FUDGE query that we dealt with by translating FUDGE queries into CYPHER crisp ones.
We implemented two modules: a module allowing the transcription of a FUDGE query into a (crisp) CYPHER one, which is then sent to the classical Neo4j query evaluation engine, and another module allowing the calculation of the satisfaction degree associated with each answer returned by the engine. Fig. 7  illustrates this architecture. Fig. 8  presents a screenshot of the software. As several models have been proposed to represent data having an implicit or explicit graph structure (see  [12]  for an overview of these models), literature includes a variety of query languages for graphs. Authors of  [12] ,  [27]  and  [11]  propose complementary surveys of graph query languages defined in the past 25 years, including languages for querying graph-based object databases, semi-structured data, social networks and semantic web data.
Reference  [11]  focuses on theoretical query languages for graph databases, and emphasizes that graph database management systems still lack query languages with a clear syntax and semantics. Our work goes towards filling this gap. Functionalities that should be offered by a language for querying the topology of a crisp graph database are exhibited in  [28] ,  [8] ,  [7] ,  [9] ,  [29] ,  [27]. We summarize these (nonexclusive) functionalities hereafter, focusing on selection statements of the DML part of the language. Given a graph data G, Adjacency queries test node adjacency eg. check whether two nodes are adjacent, list all neighbors of a node; Given a vertex, Reachability queries search for topologically related vertices in G, where vertices are reachable by a fixed-length path, a regular simple path or a shortest path; Pattern matching queries look for all subgraphs of G that are isomorphic to a given graph pattern; Data queries specify conditions on the data embedded in G.
Our algebra for fuzzy graph database expresses some flexible adjacency, reachability (as a rooted path is a special case of graph pattern), pattern matching and data queries on fuzzy and crisp graph databases. As a satisfaction degree is attached to each answer, rank-ordering them is straightforward. Concerning flexible querying,  [21]  discusses different types of fuzzy preference criteria that appear relevant in the context of graph databases, without getting into the detail of how to express them using a formal query language. There are three main approaches allowing a flexible querying of graph databases: (i) keyword-based query approaches that completely ignore the data schema (see eg. [30] ), which lack expressiveness for most querying use cases  [31]  ; (ii) approaches that, given a "crisp" query, propose approximate answers, for instance by the implementation of a query relaxation or a approximate matching mechanism (see eg.
[32] ,  [33]  or  [31] ); (iii) approaches allowing the user to introduce flexibility when formulating the query. Our approach belongs to this latter family for which many contributions concern the flexible extension of XPath  [34] ,  [35] ,  [36]  for querying semi-structured data (data trees). Such navigational languages behave well for querying graph databases  [37]  but no flexible extension was proposed in this specific case. A work somewhat close to ours is  [38]  where authors propose a flexible extension of SPARQL allowing to introduce fuzzy terms and relations into the query language. A proof-of-concept implementation is proposed. This work only considers crisp graph databases, through.
VII. CONCLUSION In this paper, we define a notion of fuzzy graph database and a fuzzy algebra for querying fuzzy and crisp graph databases in a flexible way. This algebra, based on fuzzy set theory and the notion of a fuzzy graph, consists of a data model and a family of operators that make it possible to express preferences on i) the data embedded in the graph and ii) the structure of the graph. We also introduce a language based on the algebra, with a proof-of-concept implementation of this language. This language could be extended with new features. Interesting ones based on ordering and counting capabilities concern the distance, and indegree, outdegree or centrality of nodes. The other operators of the algebra could also be implemented.
Namely the secularization, politicization, economization and mediatization of society will therefore be re-conceptualized in terms of hypotheses and tested against the results of a Google Ngram Viewer analysis of the most frequent function system references in the Google Books corpus for the year 1800 through 2000. The results not only show that the importance of individual function systems changes over time and across language areas, but also give reason to believe that at least one of the four mentioned trends is an intellectual artifact rather than a true fact.
Despite the fact that web search engines are said to return word frequency estimates that are highly consistent with established methods  (Blair et al. , 2002) , the problem with Internet word frequency analyses is that the analysis of this most recent media hardly allows for long-term trend analyses. Hence, the present discussion of popular trends in functional differentiation analyses changes the frequency distributions of function system references in the second largest available text data collection. Since its start in 2004, the Google Books project has digitalized some 15 million of the estimated 115 million books ever published. In 2007, a Harvard research team  (Michel et al. , 2011)  recognized the research potential of the Google Books corpus, performed considerable quality checks, and finally reported the compilation of a representative corpus of more than five million books or 500 billion words covering seven language areas and a time span of 600 years.
The development of this enormous data soon raised hopes of a golden age of digital humanities  (Johnson, 2010) , which would open up new types of historical knowledge  (Ophir, 2010) , as it has already given birth to the discipline of culturomics as "the application of high-throughput data collection and analysis to the study of human culture"  (Michel et al. , 2011:181). The access to the Google Books corpus is facilitated by the Google Ngram Viewer -an open-access interface that allows for trending  (Manovich, 2012)  in terms of the production of customized time-series plots for entered search terms. Such, the Google Ngram Viewer can be used to re-present well-known information in a compact and intuitive way (Figure  2 ). In relation to the German language area, figure  2  illustrates how the importance of the concepts of Germany, England, France, and the USA varied between the year 1800 and 2000.
Contrasting the German and the English distribution of the concepts of money (blue), power (red), and love (green) we find that love and money started to feature common characteristic in the English context as of the late 1940s, while love seems to be closer to power than to money in the German context, if at all. Far from representing proof for anything, the presented evidence can, nonetheless, be considered a reason for further research. In some cases, a Google Ngram View might even be used for validity tests of more or less prominent hypotheses (Figure  5 6 7 ). For example, regionalization is sometimes said to be an effect of globalization  (Kacowicz, 1999; Amin, 1999). The Google Ngram View of the respective concepts, however, does not support this idea. Rather, we find evidence for the opposite effect, being that in all the three language areas, the concept of regionalization enjoyed a modest popularity before globalization boomed, which is most evident in the French case, which featured a noticeable trend in regionalization between 1960 and 1975.
It is not until the mid 1980s (US-American English) or the early 1990s (British English, French, German), respectively, that the globalization discourse reached the level of the respective regionalization discourses. Moreover, the findings suggest that the globalization discourse could have had its origins in the French discourse and the largest impact on the German discourse. Testing its own hypotheses, the present article will focus on the analysis of trends in the English, French, and German Google Books 1-gram corpora 1800-2000. 10 Due to the sheer size of the databases concerned, further in-depth analyses will be conducted using the Google Million, an English-language corpus of only one million words designed to fulfill the same representativeness requirements as the larger English version(s), however, with improved handling characteristics.
In this setting, the null hypothesis will be rejected in favor of the alternative hypothesis (H1) when the time-series plots produced by the Google Ngram Viewer feature an unequal distribution of the occurrence frequencies of all function system designations. Moreover, the plots will be analyzed with regard to variations of occurrences in the course of time (H1. 1) and across cultures (H1. 2). The hypotheses H2. 1-2. 4 will be weakly confirmed if the output of the Google Ngram Viewer query supports the respective trend assumptions in at least two out of three language areas. In concrete terms, the plots should display a decrease in the importance of religion (H2. 1: secularization) as well as an increase in the importance of policy (H2. 2: politicization), the economy (H2. 3: economization), and the media (H2.
4: mediatization), respectively. A strong confirmation would, moreover, call for (the loss of) a dominant position in the texture of function system references for all language areas. Meeting concerns that the function system designations might not represent the most frequent function system reference in the corpus, the Top 2000 1-grams of the Google Million corpus will be scanned for further function system references. The list of the ten most frequent references to function systems relevant to the hypotheses H2. 1-2. 4 will also be entered into the Google Ngram Viewer and the result compared to the outcome of the query for the names of the function systems.
RESULTS RELOADED In order to re-test the hypotheses, in particular H2. 3 and 2. 4, the present article presents the results of an additional analysis of the English Google Million corpus (only, as other corpora proved unmanageable with the available hardware). First, the 10 separate fractions of this user-friendlier corpus were merged to a 8GB SPSS file. The corpus was then transformed into a ranked word frequency list of books published between 1800 and 2000. The 2,000 most frequent entries of this list were, thereupon, qualitatively analyzed for their function system references. As a first result, some 230 words with a clear function system reference were identified. The only function system missing among the 2,000 most important words of the corpus was sport, with the designation itself as the first reference ranking far beyond the 6,000th position.
DISCUSSION The first striking finding of the presented analyses is that the Google Ngram Views of functional differentiation actually react to history, which is true with regard to both the interregional and the regional level. On the one hand, all language areas display a decline of religion as well as clear evidence of the impact of Black Friday on the takeoff of policy and the economy. On the other hand, the results also reflect particularities related to the histories of the individual languages areas: The German time-series plot (Figure  10 ) displays a veritable program change for an entire language area from a realm of priests, poets, and philosophers to a national economy. This politico-economic campaign started soon after the death of Karl Marx, which is considerably earlier then in the other two cases.
LIMITATIONS AND FUTURE RESEARCH QUESTIONS One of the most serious limitations of the Google Ngram Viewer is that it allows for casesensitive queries in ngram only. Ngrams can, consequently, not be bundled into one single graph, just as the queries cannot be for lemmas. 14  To compensate for this circumstance, the ten of word selection biases. Hence, it is admitted that the word selection has an important impact on the results, e. g. if the function system names were replaced by the corresponding adjectives, then the politico-economic twin-star would actually dominate (Figure  15 ). Such a focus on the adjectives, however, did not prove reasonable because it would have brought considerable problems related to the comprehensive flexion of adjectives common in both the French and the German language, given that the Ngram Viewer does not allow for graph bundling.
Moreover, the Internet corpus does allow for research within the sample period of several hundred years. Further research limits are, as a matter of course, related to restricted language competences and the corpus data size. In fact, it would be best to compare all language areas and analyze 2-or more-grams, e. g. with regard to word co-occurrences, in order to get much deeper context-information. Future research on "Big Data"  (Boyd & Crawford, 2012)  in general and the present topic in particular could, therefore, call upon international cooperation and access to more powerful computer resources. Future expeditions in the corpus might then not only open up further and more snapshots of trends in functional differentiation, but also allow for an answer to the question of whether or not functional differentiation is indeed a master trend in present societies.
10 The data from 1500-1800 is likely to feature biases due to insufficient sample sizes: "The oldest works were published in the 1500s. The early decades are represented by only a few books per year, comprising several hundred thousand words. By 1800, the corpus grows to 98 million words per year; by 1900, 1. 8 billion; and by 2000, 11 billion"  (Michel et al. , 2011:176). The abbreviation ppm represents "parts per million", i. e. the relative word frequency per million words in the Google Book corpus in 2000. The unit per million is used to avoid longer chains of digits after the decimal point. The most common English words account for 45,000ppm (4. 5%: the), 30,000ppm (3%: of) and 23,000ppm (2. 3%: and). Time, the most frequent noun in the Google Million corpus, has an appearance of 1,300ppm.
Equally famous in bioinformatics is the "Smith-Waterman" algorithm for finding most conserved sub-sequences in genes and proteins  [4] , also refered to as the "local similarity" algorithm. It is derived from string edit distance by allowing the algorithm to skip prefixes and suffixes of both sequences free of charge. Except for minimizing distance (which makes no sense with local similarity), local similarity comes with the same variants as global string edit distance. Then, there are hybrids of both algorithms: Matching a complete sequence to a sub-sequence of a longer one, or "free shift" alignment, where one sequence may be displaced with respect to the other, but else, a global distance or similarity is sought. When searching sequence databases, one of the two inputs may be fixed, giving rise to a (potentially faster) matching algorithm.