COVID-19 is a type of an infectious disease that is caused by the new coronavirus. The spread of COVID-19 needs to be suppressed because COVID-19 can cause death, especially for sufferers with congenital diseases and a weak immune system. COVID-19 spreads through direct contact, wherein the infected individual spreads the COVID-19 virus through cough, sneeze, or close contacts. Predicting the number of COVID-19 sufferers becomes an important task in the effort to curb the spread of COVID-19. Artificial neural network (ANN) is the prediction method that delivers effective results in doing this job. Backpropagation, a type of ANN algorithm, offers predictive problem solving with good performance. However, its performance depends on the optimization method applied during the training process. In general, the optimization method in ANN is the gradient descent method, which is known to have a slow convergence rate. Meanwhile, the Fletcher–Reeves method has a faster convergence rate than the gradient descent method. Based on this hypothesis, this paper proposes a prediction model for the number of COVID-19 sufferers in Malang using the Backpropagation neural network with the Fletcher–Reeves method. The experimental results show that the Backpropagation neural network with the Fletcher–Reeves method has a better performance than the Backpropagation neural network with the gradient descent method. This is shown by the Means Square Error (MSE) resulting from the proposed method which is smaller than the MSE resulting from the Backpropagation neural network with the gradient descent method.

This article discusses about some properties which are equivalent between a finitely generated module over PID and a finitely generated module over a valuation domain. This can be done by considering a finitely generated module over a DVR. Although in general a PID is not a valuation domain or vice versa, these equivalence of some properties will be valid. It is because a DVR is a PID and a valuation domain at the same time. Those the equivalent properties in a finitely generated module over DVR are related with the decomposition of the module and the height of an element in that module.<strong></strong>

The number of claims plays an important role the profit achievement of health insurance companies. Prediction of the number of claims could give the significant implications in the profit margins generated by the health insurance company. Therefore, the prediction of claim submission by insurance users in that year needs to be done by insurance companies. Machine learning methods promise the great solution for claim prediction of the health insurance users.  There are several machine learning methods that can be used for claim prediction, such as the Naïve Bayes method, Decision Tree (DT), Artificial Neural Networks (ANN) and Support Vector Machine (SVM). The previous studies show that the SVM has some advantages over the other methods. However, the performance of the SVM is determined by some parameters. Parameter selection of SVM is normally done by trial and error so that the performance is less than optimal. Some optimization algorithms based heuristic optimization can be used to determine the best parameter values of SVM, for example Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). They are able to search the global optimum, easy to be implemented. The derivatives aren’t needed in its computation. Several researches show that PSO give the better solutions if it is compared with GA. All particles in the PSO are able to find the solution near global optimal. For these reasons, this article proposes the health claim insurance prediction using SVM with PSO. The experimental results show that the SVM with PSO gives the great performance in the health claim insurance prediction and it has been proven that the SVM with PSO give better performance than the SVM standard.

COVID-19 merupakan penyakit menular yang diakibatkan oleh infeksi virus corona baru. Penyakit ini sangat berbahaya dan menyebabkan kematian terutama bagi penderita yang memilki penyakit bawaan atau yang memiliki imunitas rendah. Penyebaran penyakit ini melalui melalui percikan-percikan dari hidung atau mulut yang keluar saat orang yang terinfeksi COVID-19 batuk, bersin atau berbicara. Prediksi jumlah penderita COVID-19 menjadi sangat penting untuk dilakukan dalam pencegahan dan penanggulangan penyebaran penyakit ini. Jaringan syaraf tiruan backpropagation merupakan salah metode yang dapat digunakan untuk menyelesaikan masalah prediksi dengan hasil yang baik, tetapi kinerjanya dipengaruhi oleh metode optimisasi yang digunakan saat pelatihan. Pada umumnya metode optimisasi yang digunakan adalah metode gradient descent, tetapi metode ini memiliki konvergensi yang lambat. Metode Conjugate Gradient memiliki konvergensi yang sangat baik jika dibandingkan dengan metode gradient descent. Pada tulisan ini akan dibahas bagaimana membuat model prediksi jumlah penderita COVID-19 di Kota Malang menggunakan jaringan syaraf backprogation dan metode conjugate gradient. Hasil eksperimen menunjukan bahwa model prediksi ini memperoleh hasil yang baik jika dibandingkan jaringan syaraf tiruan yang dioptimasi dengan metode gradient descent.

AbstrakDefinisi ring valuasi sangat erat kaitannya dengan pemetaan valuasi pada lapangan hasil bagi dari ring tersebut. Oleh karena itu, definisi ring valuasi diskrit jika dikaitkan dengan adanya pemetaan valuasi merupakan ring yang value groupnya isomorfik dengan himpunan bilangan bulat (Matsumura [2]). Akan tetapi Piotr, Askar [3] menyebutkan bahwa suatu ring merupakan ring valuasi diskrit jika memenuhi tiga kondisi tertentu. Makalah ini akan membahas ekivalensi dari dua definisi tersebut. Kata kunci: pemetaan valuasi, ring valuasi diskrit, value group. AbstractDefinition of valuation ring is closely related with the existence of valuation mapping on field of fraction of that ring. Therefore, the definition of discrete valuation ring is a ring which value group is isomorphic with a set of integers (Matsumura [2]). However, Piotr, Askar [3] state that a discrete valuation ring is a ring which satisfies certain three conditions. This paper discusses about the equivalence of those definitions.