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InPrime: Indonesian Journal Of Pure And Applied Mathematics

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Published by Universitas Islam Negeri Syarif Hidayatullah Jakarta

ISSN : 26865335 EISSN : 27162478 DOI : 10.15408/inprime

Core Subject : Science, Education,

Computer Science & IT Mathematics

InPrime: Indonesian Journal of Pure and Applied Mathematics is a peer-reviewed journal and published on-line two times a year in the areas of mathematics, computer science/informatics, and statistics. The journal stresses mathematics articles devoted to unsolved problems and open questions arising in chemistry, physics, biology, engineering, behavioral science, and all applied sciences. All articles will be reviewed by experts before accepted for publication. Each author is solely responsible for the content of published articles. This scope of the Journal covers, but not limited to the following fields: Applied probability and statistics, Stochastic process, Actuarial, Differential equations with applications, Numerical analysis and computation, Financial mathematics, Mathematical physics, Graph theory, Coding theory, Information theory, Operation research, Machine learning and artificial intelligence.

Arjuna Subject : Matematika - Matematika Terapan

Articles 67 Documents

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Some Notes on Relative Commutators Masoumeh Ganjali; Ahmad Erfanian
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Let G be a group and α ϵ Aut(G). An α-commutator of elements x, y ϵ G is defined as [x, y]α = x-1y-1xyα. In 2015, Barzegar et al. introduced an α-commutator of elements of G and defined a new generalization of nilpotent groups by using the definition of α-commutators which is called an α-nilpotent group. They also introduced an α-commutator subgroup of G, denoted by Dα(G) which is a subgroup generated by all α-commutators. In 2016, an α-perfect group, a group that is equal to its α-commutator subgroup, was introduced by authors of this paper and the properties of such group was investigated. They proved some results on α-perfect abelian groups and showed that a cyclic group G of even order is not α-perfect for any α ϵ Aut(G). In this paper, we may continue our investigation on α-perfect groups and in addition to studying the relative perfectness of some classes of finite p-groups, we provide an example of a non-abelian α-perfect 2-group.

Partially Ordered Group of the 2×2 Symmetric Matrices Irmatul Hasanah
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 2 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractThis paper deals with the partially ordered group of the 2×2 symmetric matrices. A matrix is defined to be a positive if each entry of the matrix is positive. With the characterization of the 2×2 symmetric matrix, we construct the positive cone such that the set of the matrices constructs partially ordered group.Keywords: Symmetric Matrix, Group-Ordered, Positive Cone. AbstrakArtikel ini membahas grup terurut parsial pada matriks simetri berukuran 2×2. Suatu matriks dikatakan positif jika setiap entri pada matriks bernilai positif. Melalui karakteristik dari matriks simetri, akan dikonstruksi sebuah positif cone sehingga matriks simetri berukuran 2×2 merupakan grup terurut parsial.Kata kunci: Matriks Simetri, Grup Terurut, Positif Cone.

Sequential Topic Modelling: A Case Study on Indonesian LGBT Conversation on Twitter Arsy Arslina; Muhaza Liebenlito
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 1 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractAs a country with the largest Muslim population in the world, the Lesbian, Gay, Bisexual, and Transgender (LGBT) issue in Indonesia has always been a hot topic to investigate. Social media such as Twitter is normally the main media where people normally discuss this LGBT topic. In this paper, we collect 18,552 tweets dated from 2015 up to 2018 to analyze the dynamics of the LGBT conversation among Indonesian peoples. In this research, we will explore the main topic of the LGBT conversation using Linear Discriminant Analysis (LDA). LDA is one of the most popular methods of soft clustering. This technique is effective to identify latent topic information (hidden) in a collection of big data using a bag of words approaches that treat every document as a vector of total words and is represented as a probability distribution on several topics. The result shows that there are seven main categories that people normally talked about regarding LGBT i.e. politics, religion, government, ethics, nationality, culture, and technology. Looking at the topic probability distributions on each semester we found that it is generally homogenous. An exception occurs during the government election period where politic tends to have a significantly higher probability. In other words, we have found that there is a tendency that LGBT issues are used in Indonesian politics.Keywords: LGBT; politics; topic modeling; twitter. AbstrakSebagai negara dengan penduduk muslim terbesar di dunia, isu mengenai Lesbian, Gay, Bisexual, dan Transgender (LGBT) di Indonesia adalah isu sensitif yang senantiasa menarik untuk diteliti. Media sosial seperti twitter adalah salah satu media yang biasa digunakan masyarakat untuk mendiskusikan tentang topik LGBT ini. Penelitian ini menggunakan 18.552 tweet tahun 2015 – 2018 dikumpulkan untuk melihat perbedaan pola perbincangan dari waktu ke waktu. Dalam penelitian ini, eksplorasi topik utama perbincangan LGBT dianalisis menggunakan metode Linear Discriminant Analysis (LDA). LDA adalah metode yang paling populer dalam soft clustering. Teknik ini efektif untuk mengidentifikasi informasi topik laten (tersembunyi) dalam koleksi dokumen besar menggunakan pendekatan bag of words yang memperlakukan setiap dokumen sebagai vektor jumlah kata dan direpresentasikan sebagai distribusi probabilitas atas beberapa topik, sementara setiap topik direpresentasikan sebagai distribusi probabilitas atas sejumlah kata. Hasil menunjukkan bahwa terdapat tujuh topik dominan yang sering muncul pada perbincangan tentang LGBT, yaitu politik, agama, pemerintahan, keasusilaan, kewarganegaraan, budaya dan teknologi. Pada kategori ini kemudian distribusi probabilitas topik dihitung dan dianalisa pada setiap semesternya. Hasilnya menunjukkan bahwa ada kecenderungan distribusi topik seragam, kecuali pada masa-masa pergantian pemerintahan dimana kategori politik cenderung meningkat secara signifikan. Dengan kata lain, ada kecenderungan bahwa isu LGBT dikaitkan dengan kehidupan perpolitikan di Indonesia.Kata kunci: LGBT, politik, topic modelling, twitter.

Classification of Tuberculosis and Pneumonia in Human Lung Based on Chest X-Ray Image using Convolutional Neural Network Muhaza Liebenlito; Yanne Irene; Abdul Hamid
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 1 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractIn this paper, we use chest x-ray images of Tuberculosis and Pneumonia to diagnose the patient using a convolutional neural network model. We use 4273 images of pneumonia, 1989 images of normal, and 394 images of tuberculosis. The data are divided into 80% as the training set and 20% as the testing set. We do the preprocessing steps to all of our images data, such as resize, converting RGB to grayscale, and Gaussian normalization. On the training dataset, the sampling technique used is undersampling and oversampling to balance each class. The best model was chosen based on the Area under Curve value i.e. the area under the curve of Receiver Operating Characteristics. This method shows that the best model obtains when trains the training dataset using oversampling. The Area under Curve value is 0.99 for tuberculosis and 0.98 for pneumonia. Therefore, this best model succeeds to identify 86% true for tuberculosis and 96% true for pneumonia.Keywords: chest X-ray images; tuberculosis; pneumonia; convolutional neural network. AbstrakPada penelitian ini memanfaatkan data citra chest x-ray penderita penyakit tuberculosis dan pneumonia. Model convolutional neural network digunakan untuk membantu mendiagnosis kedua penyakit ini. Data yang digunakan masing-masing sudah dilabeli sebanyak 4273 citra pneumonia, 1989 citra normal dan 394 citra tuberculosis. Data tersebut dibagi menjadi 80% himpunan data latih dan 20% data uji. Himpunan data tersebut telah melalui 3 tahap prepocessing yaitu resize citra, merubah citra RGB menjadi grayscale dan standarisasi gausian pada citra. Pada data latih dilakukan teknik sampling berupa undersampling dan oversampling data untuk menyeimbangkan data latih antar kelas. Model terbaik dipilih berdasarkan nilai Area under Curve yaitu luas daerah di bawah kurva Receiver Operating Chracteristics. Hasil menunjukkan bahwa model terbaik dihasilkan ketika dilatih menggunakan data latih hasil oversampling dengan nilai Area under Curve kelas tuberculosis sebesar 0,99 dan nilai Area under Curve kelas pneumonia sebesar 0,98. Oleh karena itu, model terbaik ini mampu mengindentifikasi sebanyak 86% penyakit tuberculosis dan 96% penyakit pneumonia.Kata Kunci: citra chest X-ray; penyakit infeksi paru; pengolahan citra digital Convolutional Neural Network.

Fit of the 2011 Indonesian Mortality Table to Gompertz's and Makeham's Law using Maximum Likelihood Estimation Dino Agustin Putra; Nina Fitriyati; Mahmudi Mahmudi
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 2 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractThis research discusses the estimation of the parameters for Gompertz’s law and Makeham’s law using the Maximum Likelihood Estimation method. A numerical approach to estimate the parameters of Gompertz’s law is the Newton-Raphson method. In the Makeham’s law, we use the Lagrange multiplier method to solve constraints of 0.001<A<0.003, 10^(-6)<B<10^3 and 1.075<C<1.115, and Broyden as a method to estimate the parameter numerically. The estimation result shows that parameter B converges to 0.005749 and parameter C converges to 1.024738 in the Gompertz’s law. In the Makeham’s law, the estimated parameters that satisfied the constraints are A converges to 0.00300344, B converges to 0.0002716465, and C converges to 1.113395. Based on the Average Relative Error (ARE) that calculated from the estimated for px, the 2011 Indonesian Mortality Table (the 2011 TMI) for men and for women are more accurate when approached using the Gompertz’s law than the Makeham’s law. The estimated for px uses the Gompertz’s law are very close to the px at the 2011 TMI (with Absolute Percentage Errors of less than 1%) at age intervals, for men: 0 – 10 years, 10 – 20 years, 20 – 30 years, and 60 – 70 years, and for women: 0 – 10 years, 10 – 20 years, and 70 – 80 years.Keywords: parameter estimation; Newton-Raphson method; Broyden method; Lagrange Multiplier method. AbstrakPenelitian ini membahas mengenai estimasi parameter hukum mortalitas Gompertz’s dan hukum mortalitas Makeham’s menggunakan metode Maximum Likelihood Estimation. Pendekatan numerik untuk estimasi parameter hukum mortalitas Gompertz dilakukan menggunakan metode Newton-Raphson. Untuk mengatasi syarat batas 0.001<A<0.003, 10^(-6)<B<10^3 dan 1.075<C<1.115, pada estimasi parameter hukum mortalita Makeham digunakan metode pengali Lagrange dan pendekatan numerik metode Broyden. Hasil estimasi menunjukkan bahwa parameter B konvergen ke 0,005749 dan parameter C konvergen ke 1,024738 pada hukum mortalitas Gompertz. Pada hukum mortalitas Makeham’s, hasil estimasi parameter yang memenuhi syarat batas adalah nilai A konvergen ke 0,00300344, B konvergen ke 0,0002716465, dan C konvergen ke 1,113395. Berdasarkan nilai Average Relative Error (ARE) yang dihitung untuk estimasi , Tabel Mortalita Indonesia (TMI 2011) untuk pria dan untuk wanita lebih sesuai jika didekati menggunakan hukum Gompertz daripada hukum Makeham. Estimasi menggunakan pendekatan hukum Gompertz berada sangat dekat dengan nilai pada TMI 2011 (dengan Mean Absolute Percentage Error kurang dari 1%) pada interval usia, untuk pria: 0 – 10 tahun, 10 – 20 tahun, 20 – 30 tahun, dan 60 – 70 tahun, dan untuk wanita: 0 – 10 tahun, 10 – 20 tahun, dan 70 – 80 tahun.Kata kunci: estimasi parameter; metode Newton-Raphson; metode Broyden; metode Pengali Lagrange.

World Gold Price Forecast using APARCH, EGARCH and TGARCH Model Yanne Irene; Madona Yunita Wijaya; Aisyah Muhayani
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractInvestment is a process of investing money for profit or material result. One investment commodity is gold. Gold is a precious metal in which the value tends to fluctuate over time. This indicates that there is a non-constant variance called heteroscedasticity. The appropriate time-series model to solve this heteroscedasticity problem is ARCH/GARCH. However, this model can't be applied for the financial cases that have an asymmetric effect (the downward and increase tendency in the level of volatility when returns rise and vice versa). Therefore, in this research, we forecast the world gold prices using APARCH, EGARCH, and TGARCH methods. We use the monthly world gold price data from June 1993 until May 2018. The result shows that the best-fitted model to forecasting the world gold prices is EGARCH (1.1). This model has the smallest error than the other models with a Mean Absolute Percentage Error (MAPE) value of 4.66%.Keywords: return; volatilities; heteroscedasticity; asymmetric effect; APARCH; EGARCH; TGARCH. AbstrakInvestasi adalah proses menginvestasikan uang untuk keuntungan atau hasil material. Salah satu komoditas investasi adalah emas. Emas adalah logam mulia yang nilainya cenderung berfluktuasi dari waktu ke waktu. Ini menunjukkan bahwa ada varian non-konstan yang disebut heteroskedastisitas. Metode deret waktu yang tepat untuk menyelesaikan masalah ini adalah ARCH/GARCH. Namun model ini tidak dapat digunakan untuk kasus keuangan yang memiliki efek asimetris (kecenderungan menurun dan meningkatnya volatilitas ketika nilai return naik dan sebaliknya). Oleh karena itu, dalam penelitian ini, kami memprediksi harga emas dunia menggunakan metode APARCH, EGARCH, dan TGARCH dengan data harga emas dunia bulanan pada bulan Juni 1993 - Mei 2018. Hasilnya menunjukkan bahwa, di antara ketiga metode itu, model terbaik untuk memprediksi harga emas dunia adalah EGARCH (1.1) dengan nilai Mean Absolute Percentage Error (MAPE) sebesar 4,66%.Kata kunci: return; volatilitas; heteroskedastisitas; efek asimetris; APARCH; EGARCH; TGARCH.

Calculation and Management of Premium Funds in Sharia Insurance based on Langevin Type Model of Return on Investment Khusnul Khotimah; Mahmudi Mahmudi; Nina Fitriyati
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 2 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractThis research discusses the calculation of the premium of term life-insurance based on sharia principles. The difference between the conventional method and the sharia principle is in the concept of interest rates. In this research, the concept of interest in the conventional method is replaced by the Return on Investment (ROI) that changes stochastically following the Langevin type model. The Monte-Carlo simulation is applied to generate the ROI with some initial values. On the mechanism of premium management, we apply the system without a saving element and the Al-Mudharabah relationship where the participants will get a sharing-profit of the operating surplus if they don’t make a claim until the end of the agreement period. We assume that the administrative expenses only charged in the first year. Therefore, the operating surplus will be greater after the first year. In addition, we do 20 times of Monte–Carlo simulations to generate the ROI with initial value are 7.5%, 9%, and 10%. The result shows that the annual premiums become smaller when the ROI become greater and vice versa. This is because the company get a smaller return when the initial of ROI is small. So the annual premium will be greater. The annual premium for male participants is greater than women because the rate of death of men is greater than women. The other factors that make the annual premium more expensive are length of the agreement and greater compensation.Keywords: Langevin type model, stochastic differential equation, system without a saving element, Al-Mudharabah principle, Monte–Carlo simulation. AbstrakPenelitian ini membahas mengenai perhitungan dana premi asuransi jiwa berjangka berdasarkan prinsip–prinsip syariah. Perbedaan antara metode konvensional dengan prinsip syariah adalah pada konsep tingkat bunga. Pada penelitian ini, konsep bunga digantikan dengan nilai Return on Investment (ROI) yang berubah secara stokastik mengikuti model tipe Langevin. Simulasi Monte–Carlo diterapkan untuk membangkitkan nilai ROI menggunakan beberapa nilai awal. Pada mekanisme pengelolaan dana premi, kami menerapkan sistem tanpa unsur tabungan dan hubungan Al-Mudharabah dimana peserta akan mendapatkan bagi hasil atas surplus operasional jika peserta tersebut tidak melakukan klaim sampai akhir masa perjanjian. Kami mengasumsikan bahwa biaya administrasi hanya dibebankan pada tahun pertama. Sehingga surplus operasional akan menjadi lebih besar setelah tahun pertama. Selain itu, kami melakukan 20 kali simulasi Monte–Carlo untuk membangkitkan ROI dengan nilai awal 7.5%, 9%, dan 10%. Hasil menunjukkan bahwa premi tahunan akan semakin kecil jika nilai awal dari ROI membesar dan sebaliknya. Hal ini disebabkan oleh keuntungan perusahaan yang kecil jika nilai awal ROI semakin kecil sehingga premi tahunan haruslah lebih besar. Premi tahunan untuk peserta laki-laki cenderung lebih besar daripada premi tahunan peserta wanita. Hal ini karena tingkat kematian laki-laki lebih tinggi daripada wanita. Faktor lain yang membuat premi tahunan lebih besar adalah lamanya masa kontrak asuransi dan kompensasi yang semakin besar.Kata kunci: Model tipe Langevin, persamaan diferensial stokastik, sistem tanpa unsur tabungan, prinsip Al-Mudharabah, simulasi Monte–Carlo.

Prediction of The Number of Ship Passengers in The Port of Makassar using ARIMAX Method in The Presence of Calender Variation Laili Nahlul Farih; Irma Fauziah; Madona Yunita Wijaya
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 1 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractIndonesia is an archipelago with the largest Muslim population in the world. Every year, Indonesian people have a tradition of meeting relatives in other areas or take a vacation on Eid al-Fitr. People use different modes of transport to travel such as air, water, and land transport. Port plays a role in supporting water transportation because it is a knot of inter-regional relations. The celebration of Eid al-Fitr moves forward by about 11 days every year. The purpose of this thesis is to make an estimate of the total departure of ship passengers in the main port of Makassar using the ARIMAX method with the effects of calendar variations. The ARIMAX method is a method that can be used when there are exogenous variables, where in this case the exogenous variable is in the form of variable dummy wich is Eid holidays. These forecasting results show that the ARIMAX method has a relatively small accuracy with the MAPE value of .Keywords: water transportation; calendar variations effects; Eid Al-Fitr. AbstrakIndonesia merupakan negara kepulauan dengan mayoritas muslim terbesar didunia. Setiap tahun masyarakat Indonesia memiliki tradisi bertemu sanak saudara di daerah lain ataupun berlibur pada hari raya Idul Fitri. Jalur transportasi yang digunakan yaitu melalui darat, udara dan laut. Pelabuhan memiliki peran yang sangat penting dalam mendukung transportasi laut karena menjadi titik simpul hubungan antar daerah. Perayaan hari raya Idul Fitri dalam setiap tahun mengalami pergeseran 11 hari. Tujuan penulisan skripsi ini adalah untuk membuat prakiraan total keberangkatan penumpang kapal di Pelabuhan Utama Makassar menggunakan metode ARIMAX dengan efek variasi kalender. Metode ARIMAX merupakan metode yang dapat digunakan ketika data tersebut menggunakan variable eksogen, dimana dalam kasus ini variable eksogennya berupa variable dummy libur hari raya idul fitri. Hasil peramalan ini menunjukan bahwa metode ARIMAX memiliki tingkat akurasi yang lebih baik dibandingkan ARIMA musiman dengan nilai MAPE sebesar 14,08%.Kata Kunci: transportasi air; efek variasi kalender, Hari Raya Idul Fitri.

Application of Mathematical Models Two Predators and Infected Prey by Pesticide Control in Nilaparvata Lugens Spreading in Bantul Regency Irham Taufiq; Denik Agustito
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 1 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractIn this paper, we develop a mathematical model to analyze interactions between planthopper pests as prey and menochilus sexmaculatus and mirid ladybug as two predators where prey is controlled by pesticides. The interaction between predator and prey is modeled using the Holling type II response function. The predator and prey growth are modeled using a logistic function. From this model, we obtain eight equilibrium points. The three of these equilibrium points are analyzed using linearization and locally asymptotically stable. We simulate this model using data to predict the dynamics of planthopper population and its predators. Simulation result shows that all of these populations will survive because they are influenced by pesticide control and predation rates.Keywords: control of pest; predator-prey model; the Holling type II; the logistic function. AbstrakPada penelitian ini, kami membangun model matematika untuk menganalisis interaksi antara hama wereng sebagai mangsa (prey) dan menochilus sexmaculatus dan mirid ladybug sebagai dua pemangsa (predator) dimana mangsa dikontrol oleh pestisida. Interaksi antara predator dan prey dimodelkan menggunakan fungsi respon Holling tipe II sedangkan pertumbuhan predator dan prey dimodelkan menggunakan fungsi logistik. Dari model tersebut diperoleh delapan titik ekuilibrium. Tiga titik ekuilibrium dari titik-titik equilibrium tersebut dianalisis menggunakan metode linierisasi dan bersifat stabil asimtotik lokal. Kemudian model ini diaplikasikan pada data. Untuk memudahkan interpretasi antara mangsa dan dua pemangsa dilakukan simulasi numerik untuk memprediksikan dinamika populasi wereng dan predatornya. Hasil simulasi menunjukkan bahwa semua populasi tersebut akan bertahan hidup karena dipengaruhi oleh kontrol pestisida dan tingkat pemangsaan.Kata Kunci: kontrol pestisida; model predator-prey; Holling tipe II; fungsi logistik.

Protein Clustering in Formation of Falciparum Plasmodium using Soft Regularized-Markov Clustering Algorithm Hafizh Amrullah; Syamsuddin Wisnubroto
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 2 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

AbstractProtein has an important role in our life. Every protein interacts with other proteins, DNA, and other molecules. It forms a very large protein interaction networks. We need clustering method to analyze it. Soft Regularized Markov Clustering (SR-MCL) algorithm is one of clustering method to reduce the weakness of Regularized Markov Clustering and Markov Clustering. In this research, SR-MCL will be applied using OpenMP. In every thread, SR-MCL is run using inflation parameter r = 2, 3, and 4. The simulation results show that, based on the fastest execution time and the smallest iteration, the parameter r = 2 produces the best cluster with 40 iterations and execution time is 613 seconds. The cluster centers obtained are 49 clusters with the largest cluster center is the XPO1 protein that interacts with 662 proteins, and 17 protein pairs that interact with each other. Therefore, the XPO1 is a very influential protein in Plasmodium Falciparum.Keywords: SR-MCL Algorithm, Protein Interaction Network, Plasmodium Falciparum. AbstrakProtein memiliki peranan yang sangat penting dalam kehidupan. Setiap protein berinteraksi dengan protein-protein lain, DNA, dan molekul-molekul lainnya, sehingga terbentuklah jaringan interaksi protein yang berukuran sangat besar. Untuk memudahkan dalam menganalisisnya, diperlukan metode clustering. Algoritma Soft Regularized Markov Clustering (SR-MCL) yang merupakan pengembangan metode clustering untuk mengurangi kelemahan dari Regularized Markov Clustering dan Markov Clustering. Pada penelitian ini, SR-MCL akan diterapkan menggunakan OpenMP, yaitu setiap thread menjalankan SR-MCL dengan parameter inflasi r = 2, 3, dan 4. Hasil simulasi menunjukkan bahwa, berdasarkan waktu eksekusi tercepat dan iterasi terkecil, cluster terbaik diperoleh ketika r = 2 yang menghasilkan 40 iterasi dengan waktu eksekusi 613 detik. Pusat cluster adalah protein XPO1 yang berinteraksi dengan 662 protein dan 17 pasangan protein yang saling berinteraksi satu dengan lainnya. Oleh karena itu, protein XPO1 adalah protein yang sangat berpengaruh dalam pembentukan Plasmodium Falciparum.Kata kunci: Algoritma SR-MCL, Jaringan Interaksi Protein, Plasmodium Falciparum.

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Editorial Address Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah Jl. Ir H. Juanda No.95, Cemp. Putih, Kec. Ciputat, Kota Tangerang Selatan, Banten 15412

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Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah Jl. Ir H. Juanda No.95, Cemp. Putih, Kec. Ciputat, Kota Tangerang Selatan, Banten 15412

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