72,368 research outputs found
Locally Learning Biomedical Data Using Diffusion Frames
Diffusion geometry techniques are useful to classify patterns and visualize high-dimensional datasets. Building upon ideas from diffusion geometry, we outline our mathematical foundations for learning a function on high-dimension biomedical data in a local fashion from training data. Our approach is based on a localized summation kernel, and we verify the computational performance by means of exact approximation rates. After these theoretical results, we apply our scheme to learn early disease stages in standard and new biomedical datasets
ROOT - A C++ Framework for Petabyte Data Storage, Statistical Analysis and Visualization
ROOT is an object-oriented C++ framework conceived in the high-energy physics
(HEP) community, designed for storing and analyzing petabytes of data in an
efficient way. Any instance of a C++ class can be stored into a ROOT file in a
machine-independent compressed binary format. In ROOT the TTree object
container is optimized for statistical data analysis over very large data sets
by using vertical data storage techniques. These containers can span a large
number of files on local disks, the web, or a number of different shared file
systems. In order to analyze this data, the user can chose out of a wide set of
mathematical and statistical functions, including linear algebra classes,
numerical algorithms such as integration and minimization, and various methods
for performing regression analysis (fitting). In particular, ROOT offers
packages for complex data modeling and fitting, as well as multivariate
classification based on machine learning techniques. A central piece in these
analysis tools are the histogram classes which provide binning of one- and
multi-dimensional data. Results can be saved in high-quality graphical formats
like Postscript and PDF or in bitmap formats like JPG or GIF. The result can
also be stored into ROOT macros that allow a full recreation and rework of the
graphics. Users typically create their analysis macros step by step, making use
of the interactive C++ interpreter CINT, while running over small data samples.
Once the development is finished, they can run these macros at full compiled
speed over large data sets, using on-the-fly compilation, or by creating a
stand-alone batch program. Finally, if processing farms are available, the user
can reduce the execution time of intrinsically parallel tasks - e.g. data
mining in HEP - by using PROOF, which will take care of optimally distributing
the work over the available resources in a transparent way
X-ray ptychography on low-dimensional hard-condensed matter materials
Tailoring structural, chemical, and electronic (dis-)order in heterogeneous media is one of the transformative opportunities to enable new functionalities and sciences in energy and quantum materials. This endeavor requires elemental, chemical, and magnetic sensitivities at the nano/atomic scale in two- and three-dimensional space. Soft X-ray radiation and hard X-ray radiation provided by synchrotron facilities have emerged as standard characterization probes owing to their inherent element-specificity and high intensity. One of the most promising methods in view of sensitivity and spatial resolution is coherent diffraction imaging, namely, X-ray ptychography, which is envisioned to take on the dominance of electron imaging techniques offering with atomic resolution in the age of diffraction limited light sources. In this review, we discuss the current research examples of far-field diffraction-based X-ray ptychography on two-dimensional and three-dimensional semiconductors, ferroelectrics, and ferromagnets and their blooming future as a mainstream tool for materials sciences
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