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"Multiple dirichlet series, L-functions and automorphic forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. "

"Matrix analytic methods are popular as modeling tools because they give one the ability to construct and analyze a wide class of queuing models in a unified and algorithmically tractable way. The authors present the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner. In the current literature, a mixed bag of techniques is used-some probabilistic, some from linear algebra, and some from transform methods. Here, many new proofs that emphasize the unity of the matrix analytic approach are included. The authors begin by describing several examples of quasi-birth-and-death (QBD) processes. These examples give the reader an idea of the variety of models which are hidden by the general block notation as well as reinforce some of the terminology and notation used throughout the text. These same examples are used as illustrations later. The second part of the book deals with phase-type distributions and related-point processes, which provide a versatile set of tractable models for applied probability. Part three reviews birth-and-death processes, and points out that the arguments for these processes carry over to more general processes in a parallel manner and are based on Markov renewal theory. Part four covers material where algorithmic and probabilistic reasoning are most intimately connected. In three steps, the authors take you from one of the simplest iterative procedures to the fastest, relating the successive approximations to the dynamic behavior of the stochastic process itself. The final part goes beyond simple QBDs with a sequence of short chapters where the authors discuss various extensions to the analyzed processes. Their intention is to show that the fundamental ideas extend beyond simple homogeneous QBD."

"Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. The developments in the solution of such MCs are reviewed from an algebraic point of view and possible areas for further research are indicated with an emphasis on preprocessing using reordering, grouping, and lumping and numerical analysis using block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic methods. Case studies from closed queueing networks and stochastic chemical kinetics are provided to motivate decompositional and matrix analytic methods, respectively."

"Pada tugas akhir ini akan dibahas suatu generalisasi dari distribusi Dirichlet yangdisebut Dirichlet process. Distribusi Dirichlet merupakan distribusi atas vektor,dimana elemen dari vektor tersebut merupakan bilangan-bilangan diantara 0 dan 1dan dapat dianggap sebagai nilai probabilitas. Sehingga, distribusi Dirichlet dapatdianggap sebagai distribusi atas vektor probabilitas. Sedangkan Dirichlet processdidefinisikan sebagai suatu distribusi atas probability measure atau disebut jugadengan probability set function. Untuk suatu ruang terukur  ,  B , probabilitymeasure P yang didefinisikan pada -algebra Bdisebut berdistribusi Dirichletprocess jika untuk suatu partisi terukur B1, B2, …, Bk dari , vektor random(P(B1), P(B2), …, P(Bk)) berdistribusi Dirichlet. Probability measure P tersebutdapat dianggap sebagai suatu distribusi probabilitas di . Dan untukmenghasilkan barisan variabel random yang berdistribusi P dimana P berdistribusiDirichlet process, digunakan suatu teori barisan Polya.Bentuk eksplisit dariprobability measure P yang berdistribusi Dirichlet process dijelaskan melalui theSethuraman construction of Dirichlet process. Pada tugas akhir ini, penerapan dariDirichlet process adalah dalam penentuan distribusi prior pada regresi binersemiparametrik."

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Informasi mengenai penggunaan energi listrik merupakan salah satu elemen penting dalam hal pengaturan distribusi jaringan listrik pada jaringan pintar skala kecil (smart micro grid). Selain itu informasi pemakaian energi listrik dapat membantu konsumen melakukan proses evaluasi pemakaian energi listrik untuk menekan biaya tagihan pembayaran listrik yang secara tidak langsung berpengaruh pada efisensi energi keseluruhan. Salah satu metode dalam proses pemantauan pemakaian energi listrik adalah Non-Intrusive Load Monitoring (NILM). Permasalahan utama dalam NILM adalah mengetahui peralatan-peralatan elektronik yang ada dan mengetahui konsumsi energi listrik masing-masing peralatan dengan hanya melakukan proses pengambilan data hanya dari satu titik yang terhubung dengan semua peralatan elektronik pada jaringan listrik. Berdasarkan hasil pengujian menggunakan dataset AMPds dan REDD, nilai akurasi terendah yang didapatkan adalah sebesar 96,69% pada semua pengujian yang dilakukan.

 

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Information on electricity consumption is one of the essential elements in terms of regulating the distribution of electricity in smart micro grid. Besides, information on electricity consumption can help consumers carry out an evaluation process to reduce electricity bill costs, which indirectly affect overall energy efficiency. One method in the process of monitoring electricity consumption is Non-Intrusive Load Monitoring (NILM). The main problem in NILM is electronic disaggregation equipment that exists and determines the electrical energy consumption of each appliance by merely performing the retrieval of data from only one point connected with all the electronic devices on the electrical grid. Based on the results of tests conducted using the REDD and AMPds dataset, the lowest accuracy was 96.69% for all tests performed.

 

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