Analisis Kestabilan Model Predator-Prey dengan Adanya Faktor Tempat Persembunyian Menggunakan Fungsi Respon Holling Tipe III

Predation is interaction between predator and prey, where predator preys prey. So predators can grow, develop, and reproduce. In order for prey to avoid predators, then prey needs a refuge. In this thesis, a predator-prey model with refuge factor using Holling type III response function which has three populations, i.e. prey population in the refuge, prey population outside the refuge, and predator population. From the model, three equilibrium points were obtained, those are extinction of the three populations which is unstable, while extinction of predator population and coexistence are asymptotic stable under certain conditions. The numerical simulation results show that refuge have an impact the survival of the prey.

Polinomial Pembangun dari Ideal dan Dimensi dari Kode Siklik

Dalam penelitian ini, diberikan hubungan antara ideal dan kode siklik serta sifat-sifat polinomial pembangun dari ideal dan dimensi dari kode siklik. Sifat-sifat tersebut antara lain hubungan antara polinomial pembangun dari ideal dengan polinomial monik dengan derajat terkecil di ideal, eksistensi dan ketunggalan dari polinomial pembangun dari ideal, hubungan antara polinomial pembangun dari ideal dengan pembagi monik dari , dan hubungan antara derajat dari polinomial pembangun dari ideal dan dimensi dari kode siklik.

Norms on Quotient Spaces of The 2-Inner Product Space

This paper discussed about construction of some quotients spaces of the 2-inner product spaces. On those quotient spaces, we defined an inner product with respect to a linear independent set. These inner products was derived from the -inner product. We then defined a norm which induced by the inner product in these quotient spaces.

Penyelesaian Container Stowage Problem untuk Kontainer Ukuran 20 Feet menggunakan Whale Optimization Algorithm

This paper has purpose to solve Container Stowage Problem (CSP) for 20 feet container using Whale Optimization Algorithm (WOA). CSP is a problem discussing about how to stowage a container on the ship where the purpose to minimize the unloading time. Moreover, 20 feet container is one of container types. WOA is a recently developed swarm-based metaheuristic algorithm that is based on the bubble net hunting maneuver technique of humpback whales for solving complex optimization problems. WOA had three procedures, first encircling prey, second bubble-net attacking method or exploitation phase, and third search for prey or exploration phase. WOA application program or resolving solve CSP for 20 feet container was made by using Borland C++ programming language which was implemented in three cases types of CSP data, first, the small data taking about nine containers with the number of bays, rows and tiers, respectively, are 4, 4, 4. The second and third data was medium data and big data with 62 containers and 95 containers each data, and had the number of bays, rows and tiers, respectively, are 14, 4, 5. After executing the program can be concluded the unloading time will be better if the number of whales is larger, while the number of iterations and the number of parameter control for shape of a logaritma spiral don’t affect the solution.

Hybrid Extreme Learning Machine dan Firefly Algorithm untuk Meramalkan Nilai Tukar Rupiah terhadap Dolar

Every country has a currency as a medium of exchange and the movement of its exchange rate can affect the economy of the country. In Indonesia, since the freely floating exchange rates system has been applied in August 1997, the value of rupiah currency in the foreign exchange market can change at any time. Considering the massive impacts of exchange rate fluctuation on the economy, then forecasting the exchange rate of rupiah against the US dollar is important to help Indonesia’s economic growth. The aims of this thesis is to predict the estimated exchange rate of rupiah against the US dollar in the future by using hybrid artificial neural network extreme learning machine (ELM) method and firefly algorithm (FA). In the training process, ELM-FA hybrid has a role to obtain the best weight and bias. The weight and bias that obtained will be used for forecasting and to know the success rate of the training process, the validation test process is required. Based on the implementation of program and simulation for some parameter values on the exchange rate data from Jan 2015 until Jan 2018, with four input and hidden nodes, and one output node, obtained the smallest MSE of the training is 0.000480513 with MSE of the testing is 0.0000854107. The relatively small MSE value indicates that ELM-FA network is able to recognize the data pattern well and able to predict the test data well.

Detection of Heart Abnormalities Based On ECG Signal Characteristics using Multilayer Perceptron with Firefly Algorithm-Simulated Annealing

Heart disease is one of the causes of death worldwide. Therefore, detecting heart disease is very important to reduce the increased mortality rate. One of the methods used to detect the abnormalities or disorders of the heart is to use computer assistance to determine the characteristics of an electrocardiogram. Electrocardiogram (ECG) is a test that detects and records the activity of the heart through small metal electrodes attached to the skin of one's chest, arms and legs. This test shows how fast the heart beats and whether the rhythm is stable or not. The purpose of this thesis is to apply a multi-layer perceptron model with firefly algorithm and simulated annealing in detecting cardiac abnormalities based on the ECG signal characteristics. The initial step of this research is image processing. The stages of ECG image processing are grayscale, thresholding, edge detection, segmentation and normalization processes. The results of this image processing are used as input matrices in the perceptron multilayer network training using firefly algorithm and simulated annealing. In the training process, we will get optimal weights and biases for validation tests on test data. The training data in this thesis uses 20 ECG images and in the validation test process uses 10 ECG images. The validation results in the validation test show that the accuracy in detecting heart abnormalities based on the characteristics of ECG signals using multi- layer perceptron with firefly algorithm and simulated annealing is 100%.

Penerapan Metode Learning Vector Quantization (LVQ) untuk Mendeteksi Penyalahgunaan Narkoba

Dalam penelitian ini, metode LVQ akan diterapkan untuk mendeteksi penyalahgunaan narkoba berdasarkan gejala-gejala yang dialami seseorang. Untuk mendapatkan tingkat akurasi terbaik, maka data pelatihan dan data pengujian dibagi ke dalam tiga skema pembagian data yakni 60/40, 70/30 dan 80/20. Setelah dilakukan proses pelatihan dan pengujian menggunakan metode LVQ dengan berbagai variasi nilai laju pembelajaran dan jumlah epoch, maka diperoleh tingkat akurasi terbaik sebesar 86.7 % pada skema pembagian data 70/30 dengan laju pembelajaran = 0.001 dan = 0.005.

The Dynamics of a Discrete Fractional-Order Logistic Growth Model with Infectious Disease

In this paper, we study the dynamics of a discrete fractional-order logistic growth model with infectious disease. We obtain the discrete model by applying the piecewise constant arguments to the fractional-order model. This model contains three fixed points namely the origin point, the disease-free point, and the endemic point. We confirm that the origin point is always exists and unstable, the disease-free point is always exists and conditionally stable, and the endemic point is conditionally exists and stable. We also investigate the existence of forward, period-doubling, and Neimark-Sacker bifurcation. The numerical simulations are also presented to confirm the analytical results. We also show numerically the existence of period-3 solution which leads to the occurrence of chaotic behavior.

Hybrid Jaringan Saraf Tiruan Backpropagation dengan Firefly Algorithm dan Simulated Annealing untuk Peramalan Curah Hujan di Surabaya

Indonesia mempunyai berbagai jenis iklim. Salah satu parameter iklim adalah curah hujan. Curah hujan yang dapat menjadi sumber bencana adalah curah hujan ekstrem, yaitu kondisi curah hujan yang cukup tinggi/rendah dari rata-rata kondisi normalnya. Informasi tentang peramalan curah hujan sangat berguna khususnya bagi pemerintah kota Surabaya dalam mengantisipasi kemungkinan kejadian-kejadian atau bencana yang diakibatkan oleh curah hujan ekstrem seperti, kekeringan, banjir, pohon tumbang, rusaknya fasilitas umum, dll. Tujuan dari penulisan skripsi ini adalah untuk mendapatkan nilai peramalan curah hujan di Surabaya pada bulan yang akan datang menggunakan Hybrid Jaringan Saraf Tiruan Backpropagation dengan Firefly Algorithm dan Simulated Annealing. Proses diawali dengan input dan normalisasi data, kemudian dilanjutkan dengan proses pelatihan untuk mencari bobot dan bias yang optimal. Setelah diperoleh bobot dan bias yang optimal, kemudian melakukan uji validasi, dan dilanjutkan dengan proses peramalan. Pada proses peramalan curah hujan, data yang digunakan sebanyak 120 data curah hujan bulanan dari bulan Januari 2008 hingga bulan Desember 2017 dengan ketentuan 80% data untuk pelatihan dan 20% data untuk uji validasi. Data yang digunakan, selanjutnya dilatih kemudian dicari nilai Mean Square Error (MSE) dan bobot yang optimal. Bobot optimal yang diperoleh, selanjutnya diuji dengan uji validasi untuk mengetahui seberapa baik pola yang dikenali. Berdasarkan implementasi pada data curah hujan tersebut, diperoleh nilai MSE hasil pelatihan sebesar 0.0395384228 dan nilai selisih rata-rata sebesar 3,75382. Sedangkan hasil peramalan untuk 3 bulan berikutnya yaitu bulan Januari hingga Maret 2018 berturut-turut adalah 6.1451, 8.5459, dan 7.7391.

Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate

Voter participation in general elections is an important aspect of a democratic state structure. Participation is determined by the level of public political awareness, if the level of public political awareness is low, voter participation tends to be passive (Abstinence). A mathematical model approach to voter participation in elections that has been modified to a saturated incidence rate is needed to predict voter participation in future elections. This thesis aims to analyze the stability of the equilibrium point and apply the optimal control variable in the form of an awareness campaign. In the model without control variables, we obtain two equilibriums, namely, the non-endemic equilibrium and the endemic equilibrium. Local stability and the existence of endemic equilibrium depend on the basic reproduction number (R0), where R0=bL/(g+m)m. There is voter participation in elections when R0 < 1 and the absence of voter participation in elections when R0 > 1. We also analyze the sensitivity of parameters to determine which parameters are the most influential in this mathematical model. Furthermore, the application of control variables in the mathematical model of voter participation in elections with saturated incidence rate is determined through the Pontryagin Maximum Principle method. Numerical simulation results show that providing control variables in the form of awareness campaign it is quite effective in minimize the number of the voting population who abstained from election.