Spectral renormalization group theory on networks

Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second order phase transitions call for special techniques. We set up a renormalization group scheme by expanding an arbitrary scalar field living on the nodes of an arbitrary network, in terms of the eigenvectors of the normalized graph Laplacian. The renormalization transformation involves, as usual, the integration over the more "rapidly varying" components of the field, corresponding to eigenvectors with larger eigenvalues, and then rescaling. The critical exponents depend on the particular graph through the spectral density of the eigenvalues.Comment: 17 pages, 3 figures, presented at the Continuum Models and Discrete Systems (CMDS-12), 21-25 Feb 2011, Saha Institute of Nuclear Physics, Kolkata, Indi

Improvement Of Protein Function Prediction Using Structural Information And Peptide Classification Using Syntactic Transition Probabilities

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2009Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2009Biyolojik dizi analizi, nükleotid ve amino asit dizilerinin evrimsel, yapısal ve işlevsel özelliklerini ortaya çıkarmayı amaçlar. İkili hizalama algoritmaları, biyolojik dizi analizinde yoğun olarak kullanılan araçlardır. Bu çalışmada; standart ikili hizalama algoritmalarının bir derlemesini sunmak, Oommen ve Kashyap ın tanımladığı dizi geçiş olasılığını bir biyolojik dizi benzerlik ölçütü olarak tanıtmak, yapısal bilginin protein işlev kestiriminin başarısını nasıl arttırdığını göstermek, Oommen ve Kashyap ın dizi geçiş olasılığını, iki peptit sınıflandırma problemi üzerine standart dizi benzerlik ölçütleriyle kıyaslamak, ve gereken dizi analiz araçlarını bir bilgisayar yazılımı olarak gerçeklemek amaçlanmıştır. Çalışmanın deneysel kısmının ilk aşamasında, ikincil yapı dizilerini amino asit dizisi hizalamalarıyla birlikte kullanmanın moleküler işlev kestirim başarısını arttırdığını açıkça ortaya koymuştur. Buna karşılık kestirilmiş ikincil yapıların kestirime herhangi bir katkısının olmadığı gözlenmiştir. İkinci olarak, dizi geçiş olasılıkları, sınıflandırıcıya sunulan nitelikler olarak, standart genel hizalama puanları ile kıyaslanmıştır. Sınıflandırma başarısı ölçümleri, dizi geçiş olasılıklarının genel hizalama puanlarından çok daha iyi nitelikler sağladığını şüpheye yer bırakmayacak şekilde ortaya koymuştur. Önerilen yöntem ayrıca aynı veri kümeleri üzerinde uygulanmış önceki yöntemlerin neredeyse hepsinden daha başarılı olarak genel kabul görmüş peptit benzerlik ölçütü olmaya aday olduğunu kanıtlamıştır.Biological sequence analysis deals with nucleotide and amino acid sequences, aiming to expose their evolutionary, structural and functional properties. This study intends to provide a review of well known pairwise alignment methods, to introduce the syntactic transition probability of Oommen and Kashyap as a biological sequence similarity metric, to demonstrate how the structural information improves protein function prediction, to compare syntactic transition probability of Oommen and Kashyap with standard sequence similarity metrics on two peptide classifaction problems, and to implement necessary sequence analysis tools as a computer software. In the first part of the experiments, the results clearly indicate that the use of secondary structure sequences along with amino acid sequence alignments improves molecular function prediction performance, while the use of predicted secondary structures does not. In the second part, syntactic transition probabilities are compared with standard global alignment scores as being features fed into a machine learning classifier. The classification performance measurements undoubtedly proved that syntactic transition probabilities are much better features than global alignment scores for peptides.Yüksek LisansM.Sc

On utilizing optimal and information theoretic syntactic modeling for peptide classification

Syntactic methods in pattern recognition have been used extensively in bioinformatics, and in particular, in the analysis of gene and protein expressions, and in the recognition and classification of bio-sequences. These methods are almost universally distance-based. This paper concerns the use of an Optimal and Information Theoretic (OIT) probabilistic model [11] to achieve peptide classification using the information residing in their syntactic representations. The latter has traditionally been achieved using the edit distances required in the respective peptide comparisons. We advocate that one can model the differences between compared strings as a mutation model consisting of random Substitutions, Insertions and Deletions (SID) obeying the OIT model. Thus, in this paper, we show that the probability measure obtained from the OIT model can be perceived as a sequence similarity metric, using which a Support Vector Machine (SVM)-based peptide classifier, referred to as OIT-SVM, can be devised. The classifier, which we have built has been tested for eight different "substitution" matrices and for two different data sets, namely, the HIV-1 Protease Cleavage sites and the T-cell Epitopes. The results show that the OIT model performs significantly better than the one which uses a Needleman-Wunsch sequence alignment score, and the peptide classification methods that previously experimented with the same two datasets

Hayvancılık alanında bootstrap tekniğinin bir uygulaması: Yumurta sarı rengi Örneği]

In this study, it was aimed to introduce the Bootstrap technique and to reveal the relationship between measurements of yolk color fan grades and digital colorimeter that is used for determining the yellow color of egg by utilizing this technique. For this purpose, a total of 1350 samples of 15 color grades of Roche yolk color fan and L* (lightness), a* (redness), b* (yellowness) values in the same samples were compared. The means, standard errors and confidence intervals for each color parameters of fan grades have been demonstrated by the Bootstrap technique. The grades of Roche yolk color fan in terms of L* values have been divided into 10 groups (P < 0.01), while only divided into 9 groups in terms of b* values (P < 0.01). According to the means of Redness (a*), all of the Roche yolk color fan grades (15 grades) have been determined as independent from each other (P < 0.01). With the Bootstrap method, the standard error values of means were decreased by 42.03%, 35.38% and 30.24%, respectively, and the confidence intervals were narrowed by the ratio of 42.03%, 35.38% and 30.24%, respectively. The results of the study were compared with the results of the study that was conducted by using Roche yolk color fan which is cheaper but less reliable and by using digital colorimeter method which is expensive but reliable