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Fuzzy Topological Topographic Mapping (FTTM) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of FTTM, denoted as FTTMn, is an extension of FTTM that is arranged in a symmetrical form. The special characteristic of FTTM, namely the homeomorphisms between its components, allows the generation of new FTTM. Later, the FTTMn can also be viewed as a graph. Previously, a group of researchers defined an assembly graph and utilized it to model a DNA recombination process. Some researchers then used this to introduce the concept of tangled cords for assembly graphs. In this paper, the tangled cord for FTTM4 is used to calculate the Eulerian paths. Furthermore, it is utilized to determine the least upper bound of the Hamiltonian paths of its assembly graph. Hence, this study verifies the conjecture made by Burns et al.

The motion of solid objects or even fluids can be described using mathematics. Wind movements, turbulence in the oceans, migration of birds, pandemic of diseases and all other phenomena or systems can be understood using mathematics, i.e., mathematical modelling. Some of the most common techniques used for mathematical modelling are Ordinary Differential Equation (ODE), Partial Differential Equation (PDE), Statistical Methods and Neural Network (NN). However, most of them require substantial amounts of data or an initial governing equation. Furthermore, if a system increases its complexity, namely, if the number and relation between its components increase, then the amount of data required and governing equations increase too. A graph is another well-established concept that is widely used in numerous applications in modelling some phenomena. It seldom requires data and closed form of relations. The advancement in the theory has led to the development of a new concept called autocatalytic set (ACS). In this paper, a new form of ACS, namely, multidigraph autocatalytic set (MACS) is introduced. It offers the freedom to model multi relations between components of a system once needed. The concept has produced some results in the form of theorems and in particular, its relation to the Perron–Frobenius theorem. The MACS Graph Algorithm (MACSGA) is then coded for dynamic modelling purposes. Finally, the MACSGA is implemented on the vector borne disease network system to exhibit MACS’s effectiveness and reliability. It successfully identified the two districts that were the main sources of the outbreak based on their reproduction number, R0.

A banknote is a currency issued by a country, and it was first introduced in the 16th century. The counterfeiting of banknotes by cunning criminals became a great challenge with the current advanced technology. Forensic scientists are using chemical methods, such as Fourier transform infrared (FTIR) spectroscopy for differentiating genuine and counterfeit banknotes. However, the FTIR spectra of banknotes may require further pattern recognition analysis due to their high similarities. In this paper, a fuzzy graph-based algorithm for authentication of the FTIR spectrum, namely chemometrics fuzzy autocatalytic set (c-FACS), is used to discriminate between genuine and counterfeit hundred Ringgit Malaysian (RM100) banknotes. The results show that the genuine and counterfeit RM100 banknotes have slightly distinct patterns when analyzed using c-FACS. In addition, the results are compared with RM50 banknotes, and the results reveal that the nodes or dominant axis varies between the two banknotes. To verify the reliability of the results, the results obtained via c-FACS are compared with principal component analysis (PCA). The c-FACS showed better performances as compared to PCA in terms of time consumption and observation. Thus, the c-FACS has the ability to assist forensic investigations involving banknote counterfeiting crimes.

With the increase in users of social media websites such as IMDb, a movie website, and the rise of publicly available data, opinion mining is more accessible than ever. In the research field of language understanding, categorization of movie reviews can be challenging because human language is complex, leading to scenarios where connotation words exist. Connotation words have a different meaning than their literal meanings. While representing a word, the context in which the word is used changes the semantics of words. In this research work, categorizing movie reviews with good F-Measure scores has been investigated with Word2Vec and three different aspects of proposed features have been inspected. First, psychological features are extracted from reviews positive emotion, negative emotion, anger, sadness, clout (confidence level) and dictionary words. Second, readablility features are extracted; the Automated Readability Index (ARI), the Coleman Liau Index (CLI) and Word Count (WC) are calculated to measure the review’s understandability score and their impact on review classification performance is measured. Lastly, linguistic features are also extracted from reviews adjectives and adverbs. The Word2Vec model is trained on collecting 50,000 reviews related to movies. A self-trained Word2Vec model is used for the contextualized embedding of words into vectors with 50, 100, 150 and 300 dimensions.The pretrained Word2Vec model converts words into vectors with 150 and 300 dimensions. Traditional and advanced machine-learning (ML) algorithms are applied and evaluated according to performance measures: accuracy, precision, recall and F-Measure. The results indicate Support Vector Machine (SVM) using self-trained Word2Vec achieved 86% F-Measure and using psychological, linguistic and readability features with concatenation of Word2Vec features SVM achieved 87.93% F-Measure.

Graph theory is a well-established concept that is widely used in numerous applications such as in biology, chemistry and network analysis. The advancement in the theory of graph has led to the development of a new concept called fuzzy autocatalytic set. In this paper, a fuzzy graph-based chemometrics method, namely, chemometrics fuzzy autocatalytic set (c-FACS) is developed and applied for gelatin authentication. The issue on authenticity of gelatin has become a sensitive issue among some religious communities. Due to the matter, Fourier transform infrared (FTIR) spectra of bovine, porcine and fish gelatins are analyzed using c-FACS to identify their signatures and differences and presented in this paper. The results from the c-FACS analysis showed distinct features of each gelatin, particularly porcine. Furthermore, the new method is faster than principal component analysis (PCA) in identifying the gelatin sources.