PPT-Clustering and Phase Transitions on a

Neutral Landscape Adam D Scott Center for Neurodynamics Department of Physics amp Astronomy University of Missouri St Louis APS March Meeting 2012 Boston MA 22712 Acknowledgments. www.ntocc.org September 2008 Update Transitions of Care Measures Paper by the NTOCC Measures Work Group, 2008
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\t\r\f\f\t\b\t\b\tt present, The Structure and Dynamics of Solids. 4. . Phase Transitions & Crystal . Growth. 1. st. Order Phase Transitions. Ehrenfest classification:. Discontinuity in the 1. st. derivative of Gibbs free energy. VO2 – Nikita Butakov. Mott vs. Mott-Hubbard Transitions. Role of Lattice vs. Electronic Subsystems. Presence of intermediary phases. Trigger-dependent excitation pathways. Electron/hole doping. Heating. The Structure and Dynamics of Solids. 3. Ferroelectricity and Phase Transitions . Perovskites – ABO. 3. Classic example – . Ba. Ti. O. 3. which exhibits ferroelectricity. Figure adapted from Callister, Materials science and engineering, 7. Leo . Lamontagne. MATRL286K. December 10. th. , 2014. Intro to Nuclear Magnetic Resonance . 2. Element specific technique utilizing nuclear spins of atoms. Nuclear spins are aligned in a magnetic field and pulsed with a radio frequency causing spins to . Lecture outline. Distance/Similarity between data objects. Data objects as geometric data points. Clustering problems and algorithms . K-means. K-median. K-center. What is clustering?. A . grouping. of data objects such that the objects . Giuseppe M. Mazzeo. joint work with Elio Masciari and Carlo Zaniolo. Why a new clustering algorithm?. U. 2. -Clubs offers major advantages over current clustering algorithms. Totally unsupervised. Significantly faster. issue in . computing a representative simplicial complex. . Mapper does . not place any conditions on the clustering . algorithm. Thus . any domain-specific clustering algorithm can . be used.. We . What is clustering?. Why would we want to cluster?. How would you determine clusters?. How can you do this efficiently?. K-means Clustering. Strengths. Simple iterative method. User provides “K”. Unsupervised . learning. Seeks to organize data . into . “reasonable” . groups. Often based . on some similarity (or distance) measure defined over data . elements. Quantitative characterization may include. Mott vs. Mott-Hubbard Transitions. Role of Lattice vs. Electronic Subsystems. Presence of intermediary phases. Trigger-dependent excitation pathways. Electron/hole doping. Heating. Structural distortions. Lecture outline. Distance/Similarity between data objects. Data objects as geometric data points. Clustering problems and algorithms . K-means. K-median. K-center. What is clustering?. A . grouping. of data objects such that the objects . Log. 2. transformation. Row centering and normalization. Filtering. Log. 2. Transformation. Log. 2. -transformation makes sure that the noise is independent of the mean and similar differences have the same meaning along the dynamic range of the values.. Randomization tests. Cluster Validity . All clustering algorithms provided with a set of points output a clustering. How . to evaluate the “goodness” of the resulting clusters?. Tricky because .