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20 pages, 6737 KiB

Open AccessArticle

Persistent Homology-Based Machine Learning Method for Filtering and Classifying Mammographic Microcalcification Images in Early Cancer Detection

by Aminah Abdul Malek, Mohd Almie Alias, Fatimah Abdul Razak, Mohd Salmi Md Noorani, Rozi Mahmud and Nur Fariha Syaqina Zulkepli

Cancers 2023, 15(9), 2606; https://doi.org/10.3390/cancers15092606 - 4 May 2023

Cited by 8 | Viewed by 2909

Abstract

Microcalcifications in mammogram images are primary indicators for detecting the early stages of breast cancer. However, dense tissues and noise in the images make it challenging to classify the microcalcifications. Currently, preprocessing procedures such as noise removal techniques are applied directly on the [...] Read more.

Microcalcifications in mammogram images are primary indicators for detecting the early stages of breast cancer. However, dense tissues and noise in the images make it challenging to classify the microcalcifications. Currently, preprocessing procedures such as noise removal techniques are applied directly on the images, which may produce a blurry effect and loss of image details. Further, most of the features used in classification models focus on local information of the images and are often burdened with details, resulting in data complexity. This research proposed a filtering and feature extraction technique using persistent homology (PH), a powerful mathematical tool used to study the structure of complex datasets and patterns. The filtering process is not performed directly on the image matrix but through the diagrams arising from PH. These diagrams will enable us to distinguish prominent characteristics of the image from noise. The filtered diagrams are then vectorised using PH features. Supervised machine learning models are trained on the MIAS and DDSM datasets to evaluate the extracted features’ efficacy in discriminating between benign and malignant classes and to obtain the optimal filtering level. This study reveals that appropriate PH filtering levels and features can improve classification accuracy in early cancer detection. Full article

(This article belongs to the Special Issue Artificial Intelligence and Machine Learning in Precision Oncology)

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10 pages, 261 KiB

Open AccessArticle

Orbit Growth of Shift Spaces Induced by Bouquet Graphs and Dyck Shifts

by Azmeer Nordin and Mohd Salmi Md Noorani

Mathematics 2021, 9(11), 1268; https://doi.org/10.3390/math9111268 - 1 Jun 2021

Cited by 2 | Viewed by 2133

Abstract

For a discrete dynamical system, the prime orbit and Mertens’ orbit counting functions describe the growth of its closed orbits in a certain way. The asymptotic behaviours of these counting functions can be determined via Artin–Mazur zeta function of the system. Specifically, the [...] Read more.

For a discrete dynamical system, the prime orbit and Mertens’ orbit counting functions describe the growth of its closed orbits in a certain way. The asymptotic behaviours of these counting functions can be determined via Artin–Mazur zeta function of the system. Specifically, the existence of a non-vanishing meromorphic extension of the zeta function leads to certain asymptotic results. In this paper, we prove the asymptotic behaviours of the counting functions for a certain type of shift spaces induced by directed bouquet graphs and Dyck shifts. We call these shift spaces as the bouquet-Dyck shifts. Since their respective zeta function involves square roots of polynomials, the meromorphic extension is difficult to be obtained. To overcome this obstacle, we employ some theories on zeros of polynomials, including the well-known Eneström–Kakeya Theorem in complex analysis. Finally, the meromorphic extension will imply the desired asymptotic results. Full article

(This article belongs to the Section C2: Dynamical Systems)

13 pages, 1155 KiB

Open AccessArticle

An Early Warning System for Flood Detection Using Critical Slowing Down

by Syed Mohamad Sadiq Syed Musa, Mohd Salmi Md Noorani, Fatimah Abdul Razak, Munira Ismail, Mohd Almie Alias and Saiful Izzuan Hussain

Int. J. Environ. Res. Public Health 2020, 17(17), 6131; https://doi.org/10.3390/ijerph17176131 - 24 Aug 2020

Cited by 4 | Viewed by 3522

Abstract

The theory of critical slowing down (CSD) suggests an increasing pattern in the time series of CSD indicators near catastrophic events. This theory has been successfully used as a generic indicator of early warning signals in various fields, including climate research. In this [...] Read more.

The theory of critical slowing down (CSD) suggests an increasing pattern in the time series of CSD indicators near catastrophic events. This theory has been successfully used as a generic indicator of early warning signals in various fields, including climate research. In this paper, we present an application of CSD on water level data with the aim of producing an early warning signal for floods. To achieve this, we inspect the trend of CSD indicators using quantile estimation instead of using the standard method of Kendall’s tau rank correlation, which we found is inconsistent for our data set. For our flood early warning system (FLEWS), quantile estimation is used to provide thresholds to extract the dates associated with significant increases on the time series of the CSD indicators. We apply CSD theory on water level data of Kelantan River and found that it is a reliable technique to produce a FLEWS as it demonstrates an increasing pattern near the flood events. We then apply quantile estimation on the time series of CSD indicators and we manage to establish an early warning signal for ten of the twelve flood events. The other two events are detected on the first day of the flood. Full article

(This article belongs to the Special Issue Managing Disaster Risk in a Changing World)

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17 pages, 3259 KiB

Open AccessArticle

Cluster Analysis of Haze Episodes Based on Topological Features

by Nur Fariha Syaqina Zulkepli, Mohd Salmi Md Noorani, Fatimah Abdul Razak, Munira Ismail and Mohd Almie Alias

Sustainability 2020, 12(10), 3985; https://doi.org/10.3390/su12103985 - 13 May 2020

Cited by 13 | Viewed by 2897

Abstract

Severe haze episodes have periodically occurred in Southeast Asia, specifically taunting Malaysia with adverse effects. A technique called cluster analysis was used to analyze these occurrences. Traditional cluster analysis, in particular, hierarchical agglomerative cluster analysis (HACA), was applied directly to data sets. The [...] Read more.

Severe haze episodes have periodically occurred in Southeast Asia, specifically taunting Malaysia with adverse effects. A technique called cluster analysis was used to analyze these occurrences. Traditional cluster analysis, in particular, hierarchical agglomerative cluster analysis (HACA), was applied directly to data sets. The data sets may contain hidden patterns that can be explored. In this paper, this underlying information was captured via persistent homology, a topological data analysis (TDA) tool, which extracts topological features including components, holes, and cavities in the data sets. In particular, an improved version of HACA was proposed by combining HACA and persistent homology. Additionally, a comparative study between traditional HACA and improved HACA was done using particulate matter data, which was the major pollutant found during haze episodes by the Klang, Petaling Jaya, and Shah Alam air quality monitoring stations. The effectiveness of these two clustering approaches was evaluated based on their ability to cluster the months according to the haze condition. The results showed that clustering based on topological features via the improved HACA approach was able to correctly group the months with severe haze compared to clustering them without such features, and these results were consistent for all three locations. Full article

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19 pages, 837 KiB

Open AccessArticle

Orbit Growth of Periodic-Finite-Type Shifts via Artin–Mazur Zeta Function

by Azmeer Nordin and Mohd Salmi Md Noorani

Mathematics 2020, 8(5), 685; https://doi.org/10.3390/math8050685 - 1 May 2020

Cited by 4 | Viewed by 2070

Abstract

The prime orbit and Mertens’ orbit counting functions describe the growth of closed orbits in a discrete dynamical system in a certain way. In this paper, we prove the asymptotic behavior of these functions for a periodic-finite-type shift. The proof relies on the [...] Read more.

The prime orbit and Mertens’ orbit counting functions describe the growth of closed orbits in a discrete dynamical system in a certain way. In this paper, we prove the asymptotic behavior of these functions for a periodic-finite-type shift. The proof relies on the meromorphic extension of its Artin–Mazur zeta function. Full article

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19 pages, 337 KiB

Open AccessArticle

On Fixed Point Results in G_b-Metric Spaces

by Hassen Aydi, Dušan Rakić, Asadolah Aghajani, Tatjana Došenović, Mohd Salmi Md Noorani and Haitham Qawaqneh

Mathematics 2019, 7(7), 617; https://doi.org/10.3390/math7070617 - 11 Jul 2019

Cited by 21 | Viewed by 4701

Abstract

The purpose of this paper is to consider various results in the context of G

_{b}

-metric spaces that have been recently published after the paper (Aghajani, A.; Abbas, M.; Roshan, J.R. Common fixed point of generalized weak contractive mappings in partially ordered [...] Read more.

The purpose of this paper is to consider various results in the context of G

_{b}

-metric spaces that have been recently published after the paper (Aghajani, A.; Abbas, M.; Roshan, J.R. Common fixed point of generalized weak contractive mappings in partially ordered G

_{b}

-metric spaces. Filomat 2014, 28, 1087–1101). Our new results improve, complement, unify, enrich and generalize already well known results on G

_{b}

-metric spaces. Moreover, some coupled and tripled coincidence point results have been provided. Full article

(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)

13 pages, 800 KiB

Open AccessArticle

New Fixed Point Results for Modified Contractions and Applications

by Hüseyİn Işık, Hassen Aydi, Mohd Salmi Md Noorani and Haitham Qawaqneh

Symmetry 2019, 11(5), 660; https://doi.org/10.3390/sym11050660 - 11 May 2019

Cited by 4 | Viewed by 2034

Abstract

In this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. [...] Read more.

In this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. As applications of the results obtained, some new fixed point theorems are presented for graph-type contractions. Furthermore, sufficient conditions are discussed to ensure the existence underlying various approaches of a solution for a functional equation originating in dynamic programming. Full article

13 pages, 772 KiB

Open AccessArticle

Fixed Point Results for Multi-Valued Contractions in b−Metric Spaces and an Application

by Haitham Qawaqneh, Mohd Salmi Md Noorani, Wasfi Shatanawi, Hassen Aydi and Habes Alsamir

Mathematics 2019, 7(2), 132; https://doi.org/10.3390/math7020132 - 1 Feb 2019

Cited by 83 | Viewed by 4204

Abstract

In this paper, by characterizing a weak contractive condition based on using

C -

functions and

α -

admissible multi-valued mapping of type S, we present some fixed point results for

(α, F) -

admissible multi-valued mappings in the [...] Read more.

In this paper, by characterizing a weak contractive condition based on using

C -

functions and

α -

admissible multi-valued mapping of type S, we present some fixed point results for

(α, F) -

admissible multi-valued mappings in the setting of

b -

metric spaces. Some examples and an application are added in order to show the reliability of our obtained results. Our results amend, unify, and generalize some existing results in the literature. The scientific novelty of our main results is to take new contraction self-mappings in

b -

metric spaces for multi-valued mappings. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)

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