Rensselaer Polytechnic Institute

About: Rensselaer Polytechnic Institute is a education organization based out in Troy, New York, United States. It is known for research contribution in the topics: Terahertz radiation & Finite element method. The organization has 19024 authors who have published 39922 publications receiving 1414699 citations. The organization is also known as: RPI & Rensselaer Institute.

Cats and dogs, hair and a hero: A quintet of new milky way companions

Abstract: We present five new satellites of the Milky Way discovered in Sloan Digital Sky Survey (SDSS) imaging data, four of which were followed-up with either the Subaru or the Isaac Newton Telescopes. They include four probable new dwarf galaxies--one each in the constellations of Coma Berenices, Canes Venatici, Leo and Hercules--together with one unusually extended globular cluster, Segue 1. We provide distances, absolute magnitudes, half-light radii and color-magnitude diagrams for all five satellites. The morphological features of the color-magnitude diagrams are generally well described by the ridge line of the old, metal-poor globular cluster M92. In the last two years, a total of ten new Milky Way satellites with effective surface brightness {mu}{sub v} {approx}> 28 mag arcsec{sup -2} have been discovered in SDSS data. They are less luminous, more irregular and appear to be more metal-poor than the previously-known nine Milky Way dwarf spheroidals. The relationship between these objects and other populations is discussed. We note that there is a paucity of objects with half-light radii between {approx} 40 pc and {approx} 100 pc. We conjecture that this may represent the division between star clusters and dwarf galaxies.

Direct synthesis of long single-walled carbon nanotube strands

Abstract: Long, macroscopic nanotube strands or cables, up to several tens of centimeters in length, of aligned single-walled nanotubes are synthesized by the catalytic pyrolysis of n-hexane using an enhanced vertical floating catalyst CVD technique. The long strands of nanotubes assemble continuously from ropes or arrays of nanotubes, which are intrinsically long. These directly synthesized long nanotube strands or cables can be easily manipulated using macroscopic tools.

Data Mining and Analysis: Fundamental Concepts and Algorithms

Abstract: The fundamental algorithms in data mining and analysis form the basis for the emerging field of data science, which includes automated methods to analyze patterns and models for all kinds of data, with applications ranging from scientific discovery to business intelligence and analytics. This textbook for senior undergraduate and graduate data mining courses provides a broad yet in-depth overview of data mining, integrating related concepts from machine learning and statistics. The main parts of the book include exploratory data analysis, pattern mining, clustering, and classification. The book lays the basic foundations of these tasks, and also covers cutting-edge topics such as kernel methods, high-dimensional data analysis, and complex graphs and networks. With its comprehensive coverage, algorithmic perspective, and wealth of examples, this book offers solid guidance in data mining for students, researchers, and practitioners alike. Key features: Covers both core methods and cutting-edge research Algorithmic approach with open-source implementations Minimal prerequisites: all key mathematical concepts are presented, as is the intuition behind the formulas Short, self-contained chapters with class-tested examples and exercises allow for flexibility in designing a course and for easy reference Supplementary website with lecture slides, videos, project ideas, and more

Approximating a gram matrix for improved kernel-based learning

Abstract: A problem for many kernel-based methods is that the amount of computation required to find the solution scales as O(n3), where n is the number of training examples. We develop and analyze an algorithm to compute an easily-interpretable low-rank approximation to an n × n Gram matrix G such that computations of interest may be performed more rapidly. The approximation is of the form ${\tilde G}_{k} = CW^{+}_{k}C^{T}$, where C is a matrix consisting of a small number c of columns of G and Wk is the best rank-k approximation to W, the matrix formed by the intersection between those c columns of G and the corresponding c rows of G. An important aspect of the algorithm is the probability distribution used to randomly sample the columns; we will use a judiciously-chosen and data-dependent nonuniform probability distribution. Let || ·||2 and || ·||F denote the spectral norm and the Frobenius norm, respectively, of a matrix, and let Gk be the best rank-k approximation to G. We prove that by choosing O(k/e4) columns $${\left\|G - CW^{+}_{k}C^{T}\right\|_{\xi}} \leq \|A problem for many kernel-based methods is that the amount of computation required to find the solution scales as O(n3), where n is the number of training examples. We develop and analyze an algorithm to compute an easily-interpretable low-rank approximation to an n × n Gram matrix G such that computations of interest may be performed more rapidly. The approximation is of the form ${\tilde G}_{k} = CW^{+}_{k}C^{T}$, where C is a matrix consisting of a small number c of columns of G and Wk is the best rank-k approximation to W, the matrix formed by the intersection between those c columns of G and the corresponding c rows of G. An important aspect of the algorithm is the probability distribution used to randomly sample the columns; we will use a judiciously-chosen and data-dependent nonuniform probability distribution. Let || ·||2 and || ·||F denote the spectral norm and the Frobenius norm, respectively, of a matrix, and let Gk be the best rank-k approximation to G. We prove that by choosing O(k/e4) columns $${\left\|G - CW^{+}_{k}C^{T}\right\|_{\xi}} \leq \|G - G_{k}\|_{\xi} + \sum\limits_{i=1}^{n} G^{2}_{ii},$$ both in expectation and with high probability, for both ξ = 2,F, and for all k : 0 ≤k≤ rank(W). This approximation can be computed using O(n) additional space and time, after making two passes over the data from external storage. |_{\xi} + \sum\limits_{i=1}^{n} G^{2}_{ii},$$ both in expectation and with high probability, for both ξ = 2,F, and for all k : 0 ≤k≤ rank(W). This approximation can be computed using O(n) additional space and time, after making two passes over the data from external storage.