Alashwal, H., M. E. Halaby, J. J. Crouse, A. Abdalla, and A. A. Moustafa, "The Application of Unsupervised Clustering Methods to Alzheimer's Disease.", Frontiers in computational neuroscience, vol. 13, pp. 1-9, 2019. Abstract

Clustering is a powerful machine learning tool for detecting structures in datasets. In the medical field, clustering has been proven to be a powerful tool for discovering patterns and structure in labeled and unlabeled datasets. Unlike supervised methods, clustering is an unsupervised method that works on datasets in which there is no outcome (target) variable nor is anything known about the relationship between the observations, that is, unlabeled data. In this paper, we focus on studying and reviewing clustering methods that have been applied to datasets of neurological diseases, especially Alzheimer's disease (AD). The aim is to provide insights into which clustering technique is more suitable for partitioning patients of AD based on their similarity. This is important as clustering algorithms can find patterns across patients that are difficult for medical practitioners to find. We further discuss the implications of the use of clustering algorithms in the treatment of AD. We found that clustering analysis can point to several features that underlie the conversion from early-stage AD to advanced AD. Furthermore, future work can apply semi-clustering algorithms on AD datasets, which will enhance clusters by including additional information.

Mohamed, Z., M. E. Halaby, T. Said, D. Shawky, and A. Badawi, "Characterizing Focused Attention and Working Memory Using EEG", Sensors, vol. 18, issue 11, pp. 37-43, 2018.
Halaby, M. E., "Solving MaxSAT by Successive Calls to a SAT Solver", In Proceedings of SAI Intelligent Systems Conference (IntelliSys 2016). Springer International Publishing. Pages: 428-452. DOI: https://doi.org/10.1007/978-3-319-56994-9_31. ISBN: 978-3-319-56994-9, London, UK, 2016.
Halaby, M. E., and A. Abdalla, "Fuzzy Maximum Satisfiability", 10th International Conference on Informatics and Systems (INFOS 2016), ACM ICPS, Giza, Egypt, 2016. Abstract

In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to Łukasiewicz logic. The MaxSAT problem for a set of formulae Φ is the problem of finding an assignment to the variables in Φ that satisfies the maximum number of formulae. Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem (WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have numerous applications in optimization problems that involve vagueness.

Halaby, M. E., "On the Computational Complexity of MaxSAT", ECCC (Electronic Colloquium on Computational Complexity), 2016. on_the_computational_complexity_of_maxsat.pdf

Discrete Mathematics

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