Principal component analyses for tree structured objects

This study is in the relatively new statistical area of Object Oriented Data Analysis, which considers general data objects (3D images, movies, etc) as the atoms of interest. The focus is on populations of tree-structured objects. Due to the highly non-Euclidean properties of the binary tree space, replacing classical analysis ideas with their counterparts in this new environment is a challenging task. Ideas analogous to Principal Component Analysis (PCA) for trees have been previously developed based on tree-lines. In this work, numerically fast (linear time) algorithms are developed for PCA based tree-lines which enable the first large scale data analysis of trees. Our analysis of tree-line PCA has lead to the invention of improved Principal Component Analyses, based on the new concepts of k-tree-lines and tree-curves. The tree-line analysis results give promising results. However, many tree-lines are required to explain most of the variation in the data. The idea of tree-curves directly targets the drawback of tree-lines. However, no polynomial-time optimal algorithm to find the optimal tree-curves exists. The heuristics developed give results that explain more variation than was observed previously. The k-tree-line study is proposed as a bridge between tree-line and tree-curve ideas. Polynomial time algorithms are sought for this group of problems. These three different proposed PCA methods are used to conduct a study to compare the three existing data sets and measure the age effect on each subpopulation within the sets. The advantages and shortcomings of each method with respect to each other are also discussed in the context of the data analysis. The motivating data set of this study is a collection of the brain vessel structures of 105 subjects. Due to the inaccuracies in scanning and tracking of these vessels, this data set is known to include a high amount of noise. A detailed visualization method is proposed in this work to spot the instances that require manual cleaning or need to be excluded

Visualizing the Structure of Large Trees

This study introduces a new method of visualizing complex tree structured objects. The usefulness of this method is illustrated in the context of detecting unexpected features in a data set of very large trees. The major contribution is a novel two-dimensional graphical representation of each tree, with a covariate coded by color. The motivating data set contains three dimensional representations of brain artery systems of 105 subjects. Due to inaccuracies inherent in the medical imaging techniques, issues with the reconstruction algo- rithms and inconsistencies introduced by manual adjustment, various discrepancies are present in the data. The proposed representation enables quick visual detection of the most common discrepancies. For our driving example, this tool led to the modification of 10% of the artery trees and deletion of 6.7%. The benefits of our cleaning method are demonstrated through a statistical hypothesis test on the effects of aging on vessel structure. The data cleaning resulted in improved significance levels.Comment: 17 pages, 8 figure

A Novel MDP Based Decision Support Framework to Restore Earthquake Damaged Distribution Systems

Electric power network expanded rapidly in recent decades due of the excessive need of electricity in every aspect of life, including critical infrastructures such as medical services, and transportation and communication systems. Natural disasters are one of the major reasons of electricity outage. It is extremely important to restore electrical energy in the shortest time possible after a disaster. This paper proposes a decision support method for electric system operators to restore electricity to the critical loads in a distribution system after an earthquake. The proposed method employs Markov Decision Process to find the optimal restoration scheme based on the Probability of Failure of critical structures determined by using the Peak Ground Acceleration values recorded by observatories and earthquake research centers during earthquakes.Comment: Presented in ISGT 201

Humic acids protective activity against manganese induced LTR (long terminal repeat) retrotransposon polymorphism and genomic instability effects in Zea mays

AbstractLong terminal repeat (LTR) retrotransposon polymorphism and genomic instability are considered to be one of the most important rearranging mechanisms under environmental stress. Triggering of this knowledge, we aimed to elucidate protective effect of humic acid (HA) on genomic instability and LTR retrotransposon polymorphism in Zea mays seeds subjected to manganese stress. REMAP (Retrotransposon-microsatellite Amplified Polymorphism) and IRAP (Inter-Retrotransposon Amplified Polymorphism) were used to define the GTS (Genomic Template Stability) levels and retrotransposon polymorphism. The results showed that all concentration used Mn led to an increase in retrotransposon polymorphism and DNA damage a reduction GTS rate showing the DNA damage. However, the treatments of humic acid (10%) together with Mn resulted as decreasing DNA damage and retrotransposon polymorphism and also increasing GTS. It can be suggested that HA applications removes the negative effects of Mn on retrotransposon polymorphism and GTS, when considering the research results

MDP based Decision Support for Earthquake Damaged Distribution System Restoration

As the society becomes more dependent on the presence of electricity, the resilience of the power systems gains more importance. This paper develops a decision support method for distribution system operators to restore electricity after an earthquake to the maximum number of customers in the minimum expected duration. The proposed method employs Markov Decision Process (MDP) to determine the optimal restoration scheme. In order to determine the probability of the field component damage due to the earthquake, the Probability of Failure ($P_f$) of structures are calculated using the Peak Ground Acceleration (PGA) values recorded by observatories and earthquake research centers during the earthquake

A principal component analysis for trees

The active field of Functional Data Analysis (about understanding the variation in a set of curves) has been recently extended to Object Oriented Data Analysis, which considers populations of more general objects. A particularly challenging extension of this set of ideas is to populations of tree-structured objects. We develop an analog of Principal Component Analysis for trees, based on the notion of tree-lines, and propose numerically fast (linear time) algorithms to solve the resulting optimization problems. The solutions we obtain are used in the analysis of a data set of 73 individuals, where each data object is a tree of blood vessels in one person's brain

A Nonparametric Regression Model With Tree-Structured Response

Highly developed science and technology from the last two decades motivated the study of complex data objects. In this paper, we consider the topological properties of a population of tree-structured objects. Our interest centers on modeling the relationship between a tree-structured response and other covariates. For tree objects, this poses serious challenges since most regression methods rely on linear operations in Euclidean space. We generalize the notion of nonparametric regression to the case of a tree-structured response variable. In addition, a fast algorithm with theoretical justification is developed. We implement the proposed method to analyze a data set of human brain artery trees. An important lesson is that smoothing in the full tree space can reveal much deeper scientific insights than the simple smoothing of summary statistics

New hybrid nano additives for thermoplastic compounding: CVD grown carbon fiber on graphene

Nano additives have unique characteristics widely used in high technology applications due to their ultrahigh mechanical and thermal properties. They are not preferred in price sensitive sectors especially in automotive applications because of their high cost. On the other hand, there is a growing interest to use graphene as a reinforcing agent in composite production. At this point, graphene platelet (GNP) produced from the recycle source was used as a template for carbon nanofiber production by using chemical vapor deposition (CVD) technique to overcome commercialization harrier. This bicomponent and novel structure is a good candidate to be used as a reinforcing agent in compound formulations. This produced hybrid additive was dispersed in thennoplastic resin by thennokinetic mixer to get homogeneous dispersion and provide strong interfacial interactions. In the current work, the outstanding properties of graphene with carbon fibers were combined into one type structure. With the further research, the number of graphene layer were adjusted in this hybrid structure to bring a new insight in graphene and its composite applications. After the fabrication of graphene and carbon fiber-based reinforcements with different graphene sources, mechanically and thermally improved Polyamide 6.6 were developed at very low loadings by a thermokinetic high shear mixer. This developed technology will utilize an innovation to produce advanced thermoplastic prepregs including graphene and its hybrid additives with high mechanical properties and increased recycling degree by decreasing manufacturing costs

Principal component analyses for tree structured objects

This study is in the relatively new statistical area of Object Oriented Data Analysis, which considers general data objects (3D images, movies, etc) as the atoms of interest. The focus is on populations of tree-structured objects. Due to the highly non-Euclidean properties of the binary tree space, replacing classical analysis ideas with their counterparts in this new environment is a challenging task. Ideas analogous to Principal Component Analysis (PCA) for trees have been previously developed based on tree-lines. In this work, numerically fast (linear time) algorithms are developed for PCA based tree-lines which enable the first large scale data analysis of trees. Our analysis of tree-line PCA has lead to the invention of improved Principal Component Analyses, based on the new concepts of k-tree-lines and tree-curves . The tree-line analysis results give promising results. However, many tree-lines are required to explain most of the variation in the data. The idea of tree-curves directly targets the drawback of tree-lines. However, no polynomial-time optimal algorithm to find the optimal tree-curves exists. The heuristics developed give results that explain more variation than was observed previously. The k-tree-line study is proposed as a bridge between tree-line and tree-curve ideas. Polynomial time algorithms are sought for this group of problems. These three different proposed PCA methods are used to conduct a study to compare the three existing data sets and measure the age effect on each subpopulation within the sets. The advantages and shortcomings of each method with respect to each other are also discussed in the context of the data analysis. The motivating data set of this study is a collection of the brain vessel structures of 105 subjects. Due to the inaccuracies in scanning and tracking of these vessels, this data set is known to include a high amount of noise. A detailed visualization method is proposed in this work to spot the instances that require manual cleaning or need to be excluded