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All Journal BIMASTER Desimal: Jurnal Matematika Jurnal SOLMA BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Matematika UNAND Jurnal Sintak STATISTIKA
Nahrul Hayati
Batam Institute Of Technology
Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Journal : Jurnal Matematika UNAND

 1 
UTILIZING DISCRETE HIDDEN MARKOV MODELS TO ANALYZE TETRAPLOID PLANT BREEDING Hayati, Nahrul; Sulistyono, Eko; Handayani, Vitri Aprilla
Jurnal Matematika UNAND Vol 13, No 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.244-256.2024

Abstract

In plant heredity, the phenotype is the result of observation that can be directly observed, while the genotype is the underlying hidden factor that underlies the expression of the phenotype. The genotype is an important aspect that needs to be understood to explain the pattern of trait inheritance and predict trait inheritance in subsequent generations. The discrete hidden Markov model is a model generated by pair of an unobserved Markov chain and an observation process. This model can be applied to tetraploid plant crosses by modeling genotypes as hidden state and phenotypes as the obeservation process. The probability of dominant phenotype in monohybrid, dihybrid and trihybrid crosses occurring over ten generations during that period is as follows 61,305%, 37,583%, and 23,041%. Furthermore, as more traits are crossed, the probability of dominant phenotype appearing within ten generations decreases. When the dominant phenotype occurs over ten generations, the same genotype can be obtained in monohybrid, dihybrid, and trihybrid crosses, which is heterozygous in the first and second generations, while from the third to the tenth generation it is homozygous dominant.
UTILIZING DISCRETE HIDDEN MARKOV MODELS TO ANALYZE TETRAPLOID PLANT BREEDING Hayati, Nahrul; Sulistyono, Eko; Handayani, Vitri Aprilla
Jurnal Matematika UNAND Vol. 13 No. 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.244-256.2024

Abstract

In plant heredity, the phenotype is the result of observation that can be directly observed, while the genotype is the underlying hidden factor that underlies the expression of the phenotype. The genotype is an important aspect that needs to be understood to explain the pattern of trait inheritance and predict trait inheritance in subsequent generations. The discrete hidden Markov model is a model generated by pair of an unobserved Markov chain and an observation process. This model can be applied to tetraploid plant crosses by modeling genotypes as hidden state and phenotypes as the obeservation process. The probability of dominant phenotype in monohybrid, dihybrid and trihybrid crosses occurring over ten generations during that period is as follows 61,305%, 37,583%, and 23,041%. Furthermore, as more traits are crossed, the probability of dominant phenotype appearing within ten generations decreases. When the dominant phenotype occurs over ten generations, the same genotype can be obtained in monohybrid, dihybrid, and trihybrid crosses, which is heterozygous in the first and second generations, while from the third to the tenth generation it is homozygous dominant.
Optimizing Classroom Allocation using Markov Chain Model for Shifted Lecture Schedules Hayati, Nahrul; Sulistyono, Eko; Utami, Bulan Purnama
Jurnal Matematika UNAND Vol. 15 No. 1 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.1.17-29.2026

Abstract

This study aims to optimize classroom allocation for shift lecture schedules at the Batam Institut of Technology (ITEBA) using a Markov chain model. Classroom utilization data from the Odd and EVen Semesters of the 2024/2025 Academic Year were analyzed by defining four classroom usage states: occupied in the morning shift and vacant in the evening shift (OV), vacant in the morning shift and occupied in the evening shift (VO), occupied in both morning and evening shifts (OO), and vacant in both morning and evening shifts (VV). State transition analysis revealed patterns in classroom allocation dynamics between semesters, while steady-state analysis projected long term utilization. The results show a steady-state probability of 74.04% for the OO state (optimal utilization), but 15.48% of classrooms remain in the VV state (chronic underutilization). Based on these findings, the study recommends a classroom consolidation strategy based on complementary patterns, implementation of a digital reservation system, and optimization of single shift usage. This study concludes that the Markov chain model provides a scientific basis for strategic decision making in educational facility management.
Co-Authors Ahmad Andrevi Alrasyidin Ananda, Serly Tri Anggraeni, Andini Setyo Arrafi, Adamsyam Auwalia, Farda Berlian Setiawaty Devikaduri, Laras Dia Cahya Wati Eko Sulistyono Eko Sulistyono Sulistyono Gusrita, Rani Handayani, Vitri Aprilla I Gusti Putu Purnaba Lilies Handayani Lunardi, Louis Nur Asikin Oktavia, Rantini Dwi Putri, Tia Aura Rani Gusrita Sabarinsyah, Sabarinsyah Sadiq Ardo Wibowo, Sadiq Ardo Sembiring, Rinawati Taufiq Rahman Utami, Arli Magfirah Utami, Bulan Purnama