1. Using Dynamic Quantum Clustering to Analyze Structure of Hierarchically Heterogeneous Samples at the Nanoscale Allison Hume Mentor: Marvin Weinstein

2. Problem: Interface of materials Sample data: Roman pottery – Red and Black colors are from different iron oxides Similar problems: – Lithium-ion batteries – Catalyst breakdown http://touritaly.org/tours/capua/museum.htm

3. Data X-ray Absorption Near Edge Structure (XANES) for each pixel: 30nm resolution Large field of view: half a million data points Can DQC be used for this data? Spectrum of a pixel Florian Meirer, ProtoSig1_a1_Clustering_Analysis_report_v2

4. Singular Value Decomposition Original Curve

5. Singular Value Decomposition Curve Reconstructed from first N Components N = 5

6. Singular Value Decomposition Curve Reconstructed from first N Components N = 30

7. Singular Value Decomposition N = 70 Curve Reconstructed from first N Components

8. Singular Value Decomposition N = 146 Curve Reconstructed from first N Components

9. DQC: Modeling the Data Each data point is a 5-dimensional Gaussian Data set is sum of Gaussians: M. Weinstein, D. Horn. Dynamic quantum clustering: a method for visual exploration of structures in data. Physical Review E 2009 (80) 066117.

10. DQC: a QM Problem Composite function is ground state of Hamiltonian Define potential according to time- independent Schrodinger equation: M. Weinstein, D. Horn. Dynamic quantum clustering: a method for visual exploration of structures in data. Physical Review E 2009 (80) 066117.

11. Clustering Process:

12. Data collapses into clumps and strands

13. Clustering Process: Data collapses into clumps and strands

14. Clustering Process: Some strands collapse to points, others remain

15. Clustering Process: Some strands collapse to points, others remain

16. Clustering Process: Separation continues

17. Clustering Process: Separation continues

18. Clustering Process: Separation continues

19. Identifying Clusters

20. Recreate the Picture F. Meirer, Y. Liu, A. Mehta. Mineralogy and morphology at nanoscale in hierarchically heterogeneous materials. June 24, 2011.

21. Spectra Iron phases Hercynite phases Hematite

22. Importance of Sub-clustering Sub-clusters of blue show big difference in shape – revealing the existence of Iron

23. Conclusion

24. Special Thanks to: Marvin Weinstein Apurva Mehta David Horn Florian Meirer Yijin Liu DOE & SLAC Steve Rock & SULI Program

25. DQC vs. Gradient Descent D. Horn, A. Gottlieb. Algorithm for Data Clustering in Pattern Recognition Problems Based on Quantum Mechanics. Physical Review Letters 2001 (88) 018702.