Logic, Scientific Computing, Computational Biology, Algorithms and Complexity, Information Science

1. Panel II Logic, Scientific Computing, Computational Biology, Algorithms and Complexity, Information Science Grad Visiting DayMarch 24, 2003

2. Scientific Computing Algorithms and Complexity Computational Biology Information Science Applied Logic Panel Areas and Connections

3. Artificial Intelligence Graphics Security chemistry biology Data bases vision sociology Economics Machine Learning Algorithms and Complexity Distributed Systems Computational Biology psychology Programming Languages More Connections Operations Research Scientific Computing Applied Logic Information Science

4. Panel Areas: • Applied Logic: • Bob Constanble, Dexter Kozen, Joe Halpern • Scientific Computing: • Charlie Van Loan, Steve Vavasis, Tom Coleman • Computational Biology: • Ron Elber, Golan Yona • Algorithms and Complexity: • Juris Hartmanis, John Hopcroft, Jon Kleinberg, Dexter Kozen, David Shmoys, Éva Tardos • Information Science • Bill Arms, Phoebe Sengers

5. Applied Logic @ Cornell Robert L. Constable Cornell University Grad Visiting DayMarch 24, 2003

6. Professors Robert Constable – Computer Science Joe Halpern – Computer Science Dexter Kozen – Computer Science Christoph Kreitz – Computer Science (joint with Potsdam) Anil Nerode – Mathematics Richard Shore – Mathematics (joint with MIT) Researchers Stuart Allen – Computer Science Mark Bickford – ORA

7. What Dexter Kozen does Kleene algebras ECC (Efficient Certifying Compiler)– theory: applied programming logic– practice: an implemented system Recursive types What Joe Halpern does Epistemic logic applied to:– distributed systems– security protocols Reasoning about probability What Robert Constable does Constructive type theory applied to:– program verification and synthesis– process verification and synthesis Automated reasoning with Nuprl

8. An Example of Applied Logic circa 70’s circa Now • Constructive proofs as programs • – Stamps • Constructive proofs as processes • – two-phase handshake protocol

9. Stamps Proof *T si_thm7i:{8 } . m, n:N . 3 * m + 5 * n = i|BY D 0 THENA Auto.|1. i : {8 }m, n : N. 3 * m + 5 * n = i|BY NSubsetInd 1| THEN Auto|\| 1. i: Z| 2. 0 < i| 3. 8 = i| |1 BY DTerm [1] 0 THENM DTerm [1] 0 THEN Auto \ 1. i: Z 2. 8 < i 3. m, n : N. 3 * m + 5 * n = i - 1 | BY D 3 THEN D 4 | 3. m: N4. n: N 5. 3 * m + 5 * n = i - 1 |BY Decide [n > 0] THENA Auto |\ | 6. n > 0 | | 1 BY DTerm [m + 2] 0 THENM DTerm [n – 1] 0 THEN Auto \ 6. (n > 0) | BY DTerm [m – 3] 0 THENM Dterm [n + 2] 0 THEN Auto |0  m – 3 | BY SupInf THEN Auto

10. Two-Phase Handshake Protocol The extracted message automaton is:

11. Scientific Computing @ Cornell Charlie Van Loan Cornell University Grad Visiting DayMarch 24, 2003

12. Scientific Computing Tom Coleman Charlie Van Loan Steve Vavasis Complexity Issues in Optimization Large-Scale Optimization Matrix Computations Computational Geometry Computational Finance Fast transforms

13. Connections Automatic Differentiation <---> Compilers Mesh Generation <-------------- Comp Geom / Graphics Huge Eigenproblems <----------> Network structure Subspace Computations <------> Clustering Huge/structured Ax = b <----> Machine Learning Superfast Ax = b solvers <----> Optimizing Compilers

14. Crack Propagation: Physics + Geometry + CS In the above mesh of triangles, the red crack is energetically favored over the blue crack. The mesh forces the blue crack to follow the stair-step dashed line which artificially increases the energy of fracture. (Bad) This problem persists no matter how much the mesh is refined.

15. Consider the following subdivision of a 1:2:5 triangle into five congruent subtriangles proposed by Conway and Radin Radin and Sadun showed that if this subdivision is applied recursively like this: then in the limit as the tiling is refined, all directions are equally represented.

16. Why are proteins shaped like this: Ron Elber Scientific computing at the molecular level.

17. Computational Biology @ Cornell Ron Elber Cornell University Grad Visiting DayMarch 24, 2003

18. Computational Biology • Who are we, what do we work on, and who are our collaborators? • Ron Elber, protein dynamics, folding, annotation, and evolution • Work with Steve Tanksley (Plant Breeding), David Shalloway (Molecular Biology & Genetics), Harold Scheraga (Chemistry and Chemical Biology), Jack Freed (Chemistry) • Jon Kleinberg, algorithms, genome rearrangements, evolution • Work with Susan McCouch (Plant Breeding) • David Shmoys, algorithms, genetic maps, population genetics. • Work with Steve Tanksley (Plant Breeding), Rasmus Nielsen (BSCB) • Golan Yona, Machine Learning, Protein classification, Micro arrays • Work with David Lin (Biomedical Sciences)

19. Bio-spheres in CS • Golan Yona, Klara Kedem, Paul Chew (computational geometry: structural alignments) • Ron Elber, Richard Caruana, Thorsten Joachim (Machine Learning: Protein annotation) • Ron Elber, Jon Kleinberg (Algorithms: Temperature of evolution).

20. Protein structures and sequences aremarkers of evolution: Golan Yona, Jon Kleinberg and Ron Elber AVLICKGGNMRQWASP GVLICKGGNMKQWASG AVLICKPGNMDQWASG AVFICKGGNMRQWASG ALLICKGGNMDQWASP LVLLCKGGNMRQWASP MGLYTHYRCCSQWAN CGLYTHYKCCSQFAN CGLYTHFRCCSQWAN CGLYSHYRCCSQWAN NMHKTTREWQLPICVDS DMHKTTREWQLQICVDS

21. Clustering experimentally determined protein sequences: Golan Yona

22. Determining potential sizes of protein families and “fingerprints” of connectivity (temperature): Ron Elber and Jon Kleinberg with students Catherine Grasso and Leonid Meyerguz Randomized algorithms Temperature for protein > 200 amino acids roughly constant suggesting that these clusters are evolutionary connected

23. Algorithms and Complexity @ Cornell Éva Tardos Cornell University Grad Visiting DayMarch 24, 2003

24. Algorithms and Complexity Jon Kleinberg John Hopcroft Juris Hartmanis Dexter Kozen Éva Tardos David Shmoys

25. Some Current Areas of Interest • Approximation Algorithms and Combinatorial Optimization. • Models and Algorithms for Information Access and Complex Networks. • Algorithmic Game Theory. • Complexity

26. Connections to Other Areas in CS • Artificial intelligence and machine learning: • heuristic algorithms, probabilistic models, clustering. • Databases and data mining. • Information Science: • Information Access and the Word Wide Web. • Distributed Computing: • Network Algorithms. • Computational biology. • Vision and image processing.

27. Some Current Areas of Interest wide but long What happens when individuals share a network? Algorithms for users who are selfish optimizers • Nash equilibrium: no user wants to switch paths. • Theorem: [Roughgarden-Tardos] Delay at equilibrium no worse than optimal delay with half capacity. • Properties of equilibria in other optimization problems • [Anshelevich-Dasgupta-Tardos-Wexler] network design Short, but easily congested

28. Information Science @ Cornell Jon Kleinberg Cornell University Grad Visiting DayMarch 24, 2003

29. Information Science Computer Science Cognitive Studies Applications Society HCI

30. Computer Science Faculty William Arms Graeme Bailey Claire Cardie Robert Constable Johannes Gehrke Joseph Halpern Daniel Huttenlocher Thorsten Joachims Jon Kleinberg Carl Lagoze Lillian Lee Bart Selman Eva Tardos Charles Van Loan

31. Information Retrieval: Term Vector Space TermsDocuments c1 c2 c3 c4 c5 m1 m2 m3 m4 human 1 0 0 1 0 0 0 0 0 interface 1 0 1 0 0 0 0 0 0 computer 1 1 0 0 0 0 0 0 0 user 0 1 1 0 1 0 0 0 0 system 0 1 1 2 0 0 0 0 0 response 0 1 0 0 1 0 0 0 0 time 0 1 0 0 1 0 0 0 0 EPS 0 0 1 1 0 0 0 0 0 survey 0 1 0 0 0 0 0 0 1 trees 0 0 0 0 0 1 1 1 0 graph 0 0 0 0 0 0 1 1 1 minors 0 0 0 0 0 0 0 1 1

32. Latent Semantic Indexing • term document query --- cosine > 0.9

33. Eye Tracking

34. Eye Tracking