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"Pada model hidden Markov (HMM), keadaan saat ini hanya bergantung pada keadaan tepat sebelumnya tetapi tidak bergantung pada observasi tepat sebelumnya. Pada skripsi ini dibahas mengenai tipe lain dari HMM yang disebut sebagai model hidden Markov dengan keadaan yang bergantung kepada observasi( Hidden Markov Model with States Sepending on Observations atau HMMSDO). Pada HMMSDO, keadaan saat ini bergantung pada keadaan dan observasi yang terjadi tepat sebelumnya dengan barisan keadaan tetap memenuhi sifat Markov. Tiga masalah pada HMMSDO, yaitu masalah evaluasi model, optimisasi barisan keadaan, dan estimasi parameter. Pada skripsi ini akan dibahas mengenai HMMSDO, penggunaannya dalam prediksi struktur protein sekunder, beserta analisa implementasinya. Tiga prosedur dalam implementasi adalah estimasi parameter, menghitung likelihood, dan memprediksi barisan struktur protein sekunder. Hasil implementasi menunjukkan adanya pengaruhi nilai awal prosentase keakuratan prediksi dan semakin besar jumlah data training, semakin baik prosentase keakuratan yang dihasilkan. Data yang digunakan adalah data protein immunoglobin dan dapat diunduh pada http://swift.cmbi.ru.nl/gv/pdbfinder/.

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In the standard hidden Markov model (HMM), the current state depends only on the immediately preceeding state, but does not depend on the immediately preceeding observation. This skripsi presents a new type of hidden Markov model which is called hidden Markov model with states depending on observations (HMMSDO). In HMMSDO, the current state depends on the immediately preceeding state and observation, and the state sequence has Markov property. Three problems in HMMSDO, which are model evaluation, state sequence optimization, and parameter estimation.

This skripsi will gives explanation regarding HMMSDO, the implementation of it in predicting protein secondary structures, and analization of the implementation. Three procedures in the implementation are parameter estimation, computation of likelihood, and prediction of protein secondary structure. The implementation shows that initial parameter value affect the percentage accuracy of predicition and the bigger amount data training used will give better percentage accuracy of prediction. Data that is used is protein from immunoglobin and can be downloaded at http://swift.cmbi.ru.nl/gv/pdbfinder/."

"This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians—Dedekind, Euler, Gauss, Hilbert, and Weierstrass—who played major roles in the historical events described in the first four parts of the work."

"In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19thcentury. Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike."

"The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Winner of the 1983 National Book Award, The Mathematical Experience conveyed the power and beauty of its topic to a broad audience. The study version added exercises and other classroom aids. "

"Gustafson takes you from his early pioneering work in computing, through fascinating encounters with Nobel laureates and Fields medalists, to his current observations on mathematics, science and life. He tells of brushes with death, being struck by lightning, and the beautiful women who have been a part of his journey."

"Leon Ehrenpreis has been one of the leading mathematicians in the twentieth century. His contributions to the theory of partial differential equations were part of the golden era of PDEs, and led him to what is maybe his most important contribution, the Fundamental Principle, which he announced in 1960, and fully demonstrated in 1970. His most recent work, on the other hand, focused on a novel and far reaching understanding of the Radon transform, and offered new insights in integral geometry. Leon Ehrenpreis died in 2010, and this volume collects writings in his honor by a cadre of distinguished mathematicians, many of which were his collaborators."

"The scientific personalities of Luigi Cremona, Eugenio Beltrami, Salvatore Pincherle, Federigo Enriques, Beppo Levi, Giuseppe Vitali, Beniamino Segre and of several other mathematicians who worked in Bologna in the century 1861–1960 are examined by different authors, in some cases providing different view points. Most contributions in the volume are historical; they are reproductions of original documents or studies on an original work and its impact on later research. The achievements of other mathematicians are investigated for their present-day importance."