A Generalization of the AL method for Fair Allocation of Indivisible Objects

We consider the assignment problem in which agents express ordinal preferences over $m$ objects and the objects are allocated to the agents based on the preferences. In a recent paper, Brams, Kilgour, and Klamler (2014) presented the AL method to compute an envy-free assignment for two agents. The AL method crucially depends on the assumption that agents have strict preferences over objects. We generalize the AL method to the case where agents may express indifferences and prove the axiomatic properties satisfied by the algorithm. As a result of the generalization, we also get a $O(m)$ speedup on previous algorithms to check whether a complete envy-free assignment exists or not. Finally, we show that unless P=NP, there can be no polynomial-time extension of GAL to the case of arbitrary number of agents

PENGEMBANGAN MEDIA PEMBELAJARAN MODUL PADA MATA DIKLAT PENGUKURAN UNTUK MENINGKATKAN PRESTASI BELAJAR SISWA KELAS X DI SMK N 2 DEPOK, SLEMAN

Penelitian ini bertujuan untuk membuat modul pada mata diklat pengukuran langsung, mengetahui kelayakan modul pada mata diklat pengukuran langsung, dan mengetahui pengaruh penerapan modul pada mata diklat pengukuran langsung terhadap prestasi belajar siswa kelas X Jurusan Teknik Mesin SMK N 2 Depok, Sleman. Penelitian ini adalah jenis penelitian pengembangan (Research and Development) dengan analisis deskriptif kuantitatif. Tahapan pembuatan modul penggunaan alat ukur linier langsung diawali dari observasi ke objek penelitian, merencanakan pengembangan modul, pengembangan modul, uji coba kelompok kecil (responden 10 siswa), revisi pertama, uji coba luas (responden 53 siswa dan 1 guru), revisi kedua, penerapan modul (32 siswa melakukan pembelajaran dengan menggunakan modul), dan revisi terakhir. Modul yang sudah jadi, kemudian dilakukan validasi meteri dan media oleh tiga ahli. Penskoran hasil dari validasi materi, validasi media, validasi soal pre dan post tes, respon siswa pada uji coba kelompok kecil dan uji coba luas serta respon guru terhadap pengembangan modul, dan respon siswa terhadap proses pembelajaran modul dihasilkan dengan menggunakan skala likert. Pada analisis dari penerapan pembelajaran modul menggunakan uji t (t-test). Analisis ini untuk mengetahui selisih nilai rata-rata dari peningkatan prestasi belajar siswa kelas X-A menggunakan metode ceramah dan kelas X-B menggunakan pembelajaran modul di SMK Negeri 2 Depok, Sleman. Hasil penelitian ini adalah proses pengembangan media pembelajaran modul penggunaan alat ukur linier langsung yang diawali pada tahapan studi pendahuluan, pengembangan modul, dan uji efektivitas modul. Modul yang sudah dikembangkan secara keseluruhan dikategorikan baik, sehingga modul mata diklat pengukuran linier langsung dapat digunakan sebagai buku panduan belajar, khususnya bagi siswa dan guru. Modul yang sudah dinilai baik kemudian diterapkan kepada siswa. Hasil pembelajaran modul yaitu adanya peningkatan prestasi belajar siswa pada mata diklat pengukuran langsung, khususnya sub bab mikrometer sesudah diberikan media pembelajaran modul. Berdasarkan hasil nilai rerata post tes pada pembelajaran modul (kelas X-B) adalah 83,37. Sedangkan, nilai rerata post tes menggunkan metode ceramah (kelas X-A) adalah 79,03. Perbedaan selisih rata-rata nilai post tes dari kedua kelas terjadi peningkatkan nilai kelas X-B lebih besar daripada nilai kelas X-A (kelas X-B > kelas X-A)

Joint Haplotype Assembly and Genotype Calling via Sequential Monte Carlo Algorithm

Genetic variations predispose individuals to hereditary diseases, play important role in the development of complex diseases, and impact drug metabolism. The full information about the DNA variations in the genome of an individual is given by haplotypes, the ordered lists of single nucleotide polymorphisms (SNPs) located on chromosomes. Affordable high-throughput DNA sequencing technologies enable routine acquisition of data needed for the assembly of single individual haplotypes. However, state-of-the-art high-throughput sequencing platforms generate data that is erroneous, which induces uncertainty in the SNP and genotype calling procedures and, ultimately, adversely affect the accuracy of haplotyping. When inferring haplotype phase information, the vast majority of the existing techniques for haplotype assembly assume that the genotype information is correct. This motivates the development of methods capable of joint genotype calling and haplotype assembly. Results: We present a haplotype assembly algorithm, ParticleHap, that relies on a probabilistic description of the sequencing data to jointly infer genotypes and assemble the most likely haplotypes. Our method employs a deterministic sequential Monte Carlo algorithm that associates single nucleotide polymorphisms with haplotypes by exhaustively exploring all possible extensions of the partial haplotypes. The algorithm relies on genotype likelihoods rather than on often erroneously called genotypes, thus ensuring a more accurate assembly of the haplotypes. Results on both the 1000 Genomes Project experimental data as well as simulation studies demonstrate that the proposed approach enables highly accurate solutions to the haplotype assembly problem while being computationally efficient and scalable, generally outperforming existing methods in terms of both accuracy and speed. Conclusions: The developed probabilistic framework and sequential Monte Carlo algorithm enable joint haplotype assembly and genotyping in a computationally efficient manner. Our results demonstrate fast and highly accurate haplotype assembly aided by the re-examination of erroneously called genotypes.National Science Foundation CCF-1320273Electrical and Computer Engineerin