Blockchain: A Graph Primer

Bitcoin and its underlying technology Blockchain have become popular in recent years. Designed to facilitate a secure distributed platform without central authorities, Blockchain is heralded as a paradigm that will be as powerful as Big Data, Cloud Computing and Machine learning. Blockchain incorporates novel ideas from various fields such as public key encryption and distributed systems. As such, a reader often comes across resources that explain the Blockchain technology from a certain perspective only, leaving the reader with more questions than before. We will offer a holistic view on Blockchain. Starting with a brief history, we will give the building blocks of Blockchain, and explain their interactions. As graph mining has become a major part its analysis, we will elaborate on graph theoretical aspects of the Blockchain technology. We also devote a section to the future of Blockchain and explain how extensions like Smart Contracts and De-centralized Autonomous Organizations will function. Without assuming any reader expertise, our aim is to provide a concise but complete description of the Blockchain technology.Comment: 16 pages, 8 figure

Decision Stream: Cultivating Deep Decision Trees

Various modifications of decision trees have been extensively used during the past years due to their high efficiency and interpretability. Tree node splitting based on relevant feature selection is a key step of decision tree learning, at the same time being their major shortcoming: the recursive nodes partitioning leads to geometric reduction of data quantity in the leaf nodes, which causes an excessive model complexity and data overfitting. In this paper, we present a novel architecture - a Decision Stream, - aimed to overcome this problem. Instead of building a tree structure during the learning process, we propose merging nodes from different branches based on their similarity that is estimated with two-sample test statistics, which leads to generation of a deep directed acyclic graph of decision rules that can consist of hundreds of levels. To evaluate the proposed solution, we test it on several common machine learning problems - credit scoring, twitter sentiment analysis, aircraft flight control, MNIST and CIFAR image classification, synthetic data classification and regression. Our experimental results reveal that the proposed approach significantly outperforms the standard decision tree learning methods on both regression and classification tasks, yielding a prediction error decrease up to 35%

Age- and Gender-Related Differences in the Geometric Properties and Biomechanical Significance of Intracortical Porosity in the Distal Radius and Tibia

Cortical bone contributes the majority of overall bone mass and bears the bulk of axial loads in the peripheral skeleton. Bone metabolic disorders often are manifested by cortical microstructural changes via osteonal remodeling and endocortical trabecularization. The goal of this study was to characterize intracortical porosity in a cross-sectional patient cohort using novel quantitative computational methods applied to high-resolution peripheral quantitative computed tomography (HR-pQCT) images of the distal radius and tibia. The distal radius and tibia of 151 subjects (57 male, 94 female; 47 ± 16 years of age, range 20 to 78 years) were imaged using HR-pQCT. Intracortical porosity (Ct.Po) was calculated as the pore volume normalized by the sum of the pore and cortical bone volume. Micro–finite element analysis (µFE) was used to simulate 1% uniaxial compression for two scenarios per data set: (1) the original structure and (2) the structure with intracortical porosity artificially occluded. Differential biomechanical indices for stiffness (ΔK), modulus (ΔE), failure load (ΔF), and cortical load fraction (ΔCt.LF) were calculated as the difference between original and occluded values. Regression analysis revealed that cortical porosity, as depicted by HR-pQCT, exhibited moderate but significant age-related dependence for both male and female cohorts (radius ρ = 0.7; tibia ρ = 0.5; p < .001). In contrast, standard cortical metrics (Ct.Th, Ct.Ar, and Ct.vBMD) were more weakly correlated or not significantly correlated with age in this population. Furthermore, differential µFE analysis revealed that the biomechanical deficit (ΔK) associated with cortical porosity was significantly higher for postmenopausal women than for premenopausal women (p < .001). Finally, porosity-related measures provided the only significant decade-wise discrimination in the radius for females in their fifties versus females in their sixties (p < .01). Several important conclusions can be drawn from these results. Age-related differences in cortical porosity, as detected by HR-pQCT, are more pronounced than differences in standard cortical metrics. The biomechanical significance of these structural differences increases with age for men and women and provides discriminatory information for menopause-related bone quality effects. © 2010 American Society for Bone and Mineral Research