Yousef Saad Department Of Computer Science And Engineering

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A hypothetical calculation: [with a “naive approach”] ➤ 10 Atoms each having 14 electrons [Silicon] ➤ ... a total of 15*10= 150 particles ➤ ... Assume each coordinate will need 100 points for discretization.. ➤ ... you will get # Unknowns = 100 part.1 × 100 part.2 × · · · × 100 part.150 = 100 150 ➤ Methods based on this basic formulation are limited to a few atoms – useless for real compounds. CSE Colloquium 11/09/09 p. 8
The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to the explanation of the main features of complex atomic systems without too much computations. Dirac, 1929 ➤ In 1929 quantum mechanics was basically understood ➤ Today the “desire” to have approximate practical methods is still alive CSE Colloquium 11/09/09 p. 9
Page 1 and 2: From data-mining to nanotechnology
Page 3 and 4: ➤ Then the stock market tanked ..
Page 5 and 6: Electronic structure ➤ Quantum me
Page 7: ➤ Hamiltonian H is of the form :
Page 11 and 12: Kohn-Sham equations → nonlinear e
Page 13 and 14: The physical domain CSE Colloquium
Page 15 and 16: CHEBYSHEV FILTERING
Page 17 and 18: Chebyshev Subspace iteration - expe
Page 19 and 20: NUMERICAL LINEAR ALGEBRA IN DATA MI
Page 21 and 22: Major tool of Data Mining: Dimensio
Page 23 and 24: Linear Dimensionality Reduction Giv
Page 25 and 26: 2-D ‘reductions’: 15 10 5 0 −
Page 27 and 28: 2-D ’reductions’: 6 4 2 0 −2
Page 29 and 30: Sparse Matrices viewpoint * Joint w
Page 31 and 32: Supervised learning: classification
Page 33 and 34: A harder case: 4 3 2 1 0 −1 −2
Page 35 and 36: Fisher’s Linear Discriminant Anal
Page 37 and 38: ➤ Project set on a one-dimensiona
Page 39 and 40: Trace ratio problem * Joint work wi
Page 41 and 42: Background: The Lanczos procedure A
Page 43 and 44: Information Retrieval: Vector Space
Page 45 and 46: Common approach: Use the SVD ➤ Ne
Page 47 and 48: Polynomial filters - examples Appro
Page 49 and 50: IR: Use of the Lanczos algorithm (1
Page 51 and 52: ➤ Theory well understood: works w
Page 53 and 54: Average query times average query t
Page 55 and 56: In summary: ➤ Results comparable
Page 57 and 58: Difficulty Positions, Expressions,
Page 59 and 60:
Tests: Face Recognition Tests with
Page 61 and 62:
GRAPH-BASED METHODS
Page 63 and 64:
Example: The Laplacean eigenmaps La
Page 65 and 66:
A unified view * Joint work with Ef
Page 67 and 68:
Graph-based methods in a supervised
Page 69 and 70:
Repulsion Laplaceans * Joint work w
Page 71 and 72:
Materials informatics at work. Illu
Page 73 and 74:
Conclusion ➤ Many, many, interest
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Yousef Saad Department Of Computer Science And Engineering

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