Judul: Analisis Gerombol Dua Tahap untuk Penentuan Koleksi Inti Tanaman Ubi Kayu.
Abstrak: Cassava is a tropical plant that has many uses, such as food, animal feed, ethanol’s raw material, and can also be utilized in the field of industry. According to the collection of cassava, naturally there are some accessions which has similar characteristics, therefore the selection of core collection is needed to be done to make the utilization easier.The objective of this research was to determine the core collection of cassava using two step clusters analysis and to evaluate the goodness of the core collection. Two step clusters analysis is used because the observe variables contain two type of variables that is numeric and categoric. The result of two step clustering formed two optimum clusters. However, stratified random sampling in four clusters has MD% and VD% value smaller than MD% and VD% value of two clusters.
Keyword: Bogor Agricultural University (IPB), VD%, two step cluster analysis, MD%, evaluation of the core colllection, core collection, cassava

Judul: Cluster Analysis for Creating a Core Collection of Cassava (Manihot esculenta C.) Germplasm
Abstrak: anihot esculenta C.) Germplasm. Advised by ASEP SAEFUDDIN dan SUTORO Cassava that are locally often called as tapioca, sampeu, cassava is Manihot esculenta Crantz species, from the family Euphorbiaceae, originally from Brazil, the Amazon region. The development of cassava needs upgrading to improve the productivity of cassava. Its productivity can be enhanced by the presence of plant breeding. Genetic variability of germplasm is needed to produce superior varieties. Although there is an increase in the number of germplasm accessions in gene bank, there is no corresponding increase in their use by crop improvement scientists, indicating that collection were not being used their full potential. This is due to the lack of funding for research and limited human resources. Therefore, to solve the problems, developing core collection is necessary. Core collection is a germplasm sample in the range that exists in the entire collection. Statistical methods used in the core collection are clustering and allocation sampling. Therefore breeders need same indicates for creating core collection. The first index refers to the average of absolute differences between variances across all of the characteristic in the core and entire collections relative to the means in entire collection, MD%. The other index is the average of the absolute differences between variances across all of the characteristic in the core and entire collections relative to the variances in entire collection, VD%. The result shows that the two allocation sampling methods are good enough to construct core collection. However, stratified random sampling always has higher value than two stage random sampling for all evaluation of parameters.
Keyword: core collection, cassava germplasm, cluster analysis, MD (%), VD (%)

Judul: Konstruksi Persamaan Friedmann Alam Semesta Friedmann-Lemaitre-Robertson-Walker Termodifikasi Materi Gelap Superfluida
Abstrak: Kosmologi merupakan salah satu objek kajian dari teori relativitas umum. Salah satu model dalam kosmologi adalah model kosmologi Friedmann. Model kosmologi Friedmann dibangun berdasarkan asumsi bahwa materi dan energi terdistribusi secara homogen dan isotropik di alam semesta. Teori relativitas umum dapat dimodifikasi melalui pendekatan teori materi gelap superfluida (MGS). Persamaan medan Einstein untuk teori MGS dapat dirumuskan melalui prinsip aksi dengan memodifikasi Lagrangian pada aksi teori MGS. Selanjutnya dengan memilih metrik Friedmann-Lemaitre-Robertson-Walker (FLRW) datar dengan indeks kurvatur sama dengan nol, dapat dibangun suatu bentuk persamaan Friedmann yang dimodifikasi teori MGS.
Keyword: kosmologi, teori materi gelap superfluida, persamaan medan Einstein, metrik FLRW, persamaan Friedmann.