Sanda Bujacic Babic
@math.uniri.hr
Faculty of Mathematics, University of Rijeka
Assistant Professor
RESEARCH, TEACHING, or OTHER INTERESTS
Algebra and Number Theory, Applied Mathematics, Theoretical Computer Science
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Tajana Ban Kirigin and Sanda Bujačić Babić
MDPI AG
Directed and weighted graphs can be used for many real-world applications to model and analyse the quality and structure of communication within the system, the distribution and flow of information, and various resources, dependencies, resilience, etc. On social media platforms, for example, highly networked members, so-called influencers, disseminate information, opinions and trends to their followers, who in turn increase the popularity of the influencers through likes and comments. Both types of interaction have a major influence on discussions and activities in the social network. To identify the nodes with the highest integration and interconnectivity within the neighbourhood subnetwork, we introduce the Directed Semi-Local Integration (DSLI) centrality measure for directed and weighted graphs. This centrality measure evaluates the integration of nodes assessed by the presence of connection, the strength of links, the organisation and optimisation of inbound and outbound interconnectivity, and the redundancy in the local subnetwork, and provides a stronger differentiation of the importance of nodes than standard centrality measures. Thus, DSLI has the potential to be used for analysing the degree of integration for the uptake and dissemination of resources in complex networks in many different contexts.
Tajana Ban Kirigin, Sanda Bujačić Babić, and Benedikt Perak
MDPI AG
We present a graph-based method for the lexical task of labeling senses of polysemous lexemes. The labeling task aims at generalizing sense features of a lexical item in a corpus using more abstract concepts. In this method, a coordination dependency-based lexical graph is first constructed with clusters of conceptually associated lexemes representing related senses and conceptual domains of a source lexeme. The label abstraction is based on the syntactic patterns of the x is_a y dependency relation. For each sense cluster, an additional lexical graph is constructed by extracting label candidates from a corpus and selecting the most prominent is_a collocates in the constructed label graph. The obtained label lexemes represent the sense abstraction of the cluster of conceptually associated lexemes. In a similar graph-based procedure, the semantic class representation is validated by constructing a WordNet hypernym relation graph. These additional labels indicate the most appropriate hypernym category of a lexical sense community. The proposed labeling method extracts hierarchically abstract conceptual content and the sense semantic features of the polysemous source lexeme, which can facilitate lexical understanding and build corpus-based taxonomies.
Tajana Ban Kirigin, Sanda Bujačić Babić, and Benedikt Perak
MDPI AG
Numerous centrality measures have been introduced as tools to determine the importance of nodes in complex networks, reflecting various network properties, including connectivity, survivability, and robustness. In this paper, we introduce Semi-Local Integration (SLI), a node centrality measure for undirected and weighted graphs that takes into account the coherence of the locally connected subnetwork and evaluates the integration of nodes within their neighbourhood. We illustrate SLI node importance differentiation among nodes in lexical networks and demonstrate its potential in natural language processing (NLP). In the NLP task of sense identification and sense structure analysis, the SLI centrality measure evaluates node integration and provides the necessary local resolution by differentiating the importance of nodes to a greater extent than standard centrality measures. This provides the relevant topological information about different subnetworks based on relatively local information, revealing the more complex sense structure. In addition, we show how the SLI measure can improve the results of sentiment analysis. The SLI measure has the potential to be used in various types of complex networks in different research areas.
Tajana Ban Kirigin, Sanda Bujačić Babić, and Benedikt Perak
MDPI AG
This paper describes a graph method for labeling word senses and identifying lexical sentiment potential by integrating the corpus-based syntactic-semantic dependency graph layer, lexical semantic and sentiment dictionaries. The method, implemented as ConGraCNet application on different languages and corpora, projects a semantic function onto a particular syntactical dependency layer and constructs a seed lexeme graph with collocates of high conceptual similarity. The seed lexeme graph is clustered into subgraphs that reveal the polysemous semantic nature of a lexeme in a corpus. The construction of the WordNet hypernym graph provides a set of synset labels that generalize the senses for each lexical cluster. By integrating sentiment dictionaries, we introduce graph propagation methods for sentiment analysis. Original dictionary sentiment values are integrated into ConGraCNet lexical graph to compute sentiment values of node lexemes and lexical clusters, and identify the sentiment potential of lexemes with respect to a corpus. The method can be used to resolve sparseness of sentiment dictionaries and enrich the sentiment evaluation of lexical structures in sentiment dictionaries by revealing the relative sentiment potential of polysemous lexemes with respect to a specific corpus. The proposed approach has the potential to be used as a complementary method to other NLP resources and tasks, including word disambiguation, domain relatedness, sense structure, metaphoricity, as well as a cross- and intra-cultural discourse variations of prototypical conceptualization patterns and knowledge representations.
S. Bujacic Babic and K. Nabardi
Mathematical Notes
In this paper we deal with some Diophantine equations and present infinitely many positive integer solutions for each one of them. 2010 Mathematics Subject Classification: 11D45; 11D25
Sanda Bujačić Babić
Croatian Academy of Sciences and Arts
Sanda Bujačić
Springer Science and Business Media LLC
Sanda Bujačić
Mathematical Notes
In this paper we are dealing with the problem of the existence of two divisors of $(n^2+1)/2$ whose sum is equal to $\\delta n+\\varepsilon$, in the case when $\\delta$ and $\\varepsilon$ are even, or more precisely in the case in which $\\delta\\equiv\\varepsilon+2\\equiv0$ or $2 \\pmod{4}$. We will completely solve the cases $\\delta=2, \\delta=4$ and $\\varepsilon=0$.
RECENT SCHOLAR PUBLICATIONS
MOST CITED SCHOLAR PUBLICATIONS
Publications
Tajana Ban Kirigin, Sanda Bujačić Babić, Benedikt Perak, Graph-Based Taxonomic Semantic Class Labeling Future Internet 2022 - 14 (12),
Ban Kirigin, Tajana; Bujačić Babić, Sanda; Perak, Benedikt, Semi-Local Integration Measure of Node Importance, Mathematics, 10(3), (2022), 405; - 10 1-16,
Ban Kirigin, Tajana; Bujačić Babić, Sanda; Perak, Benedikt, Lexical Sense Labeling and Sentiment Potential Analysis using Corpus-Based Dependency Graph, Mathematics, 9(12), (2021), 1449; 1-22 - 9 1-22,
Bujačić Babić, Sanda, Nabardi, Kamran, On Some Diophantine Equations, Miskolc Mathematical Notes - 1-11,
Bujačić, Sanda, Two divisors of (n^2+1)/2 summing up to δn + δ ± 2, δ even, Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti - 22 39 - 61,
Bujačić, Sanda, A variation of a congruence of Subbarao for n=2^α*5^β, α, β>=0, Periodica Mathematica Hungarica - 75 66 - 79,
S. Bujačić, A. Filipin, Linear Forms in Logarithms, Springer-Verlag, Berlin, Jörn Steuding editor - 1-59
Bujačić, Sanda, Two divisors of (n^2+1)/2 summing up to δn+ε, for δ and ε even, Miskolc Mathematical Notes - 15 333-344,