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Logic, Scientific Computing, Computational Biology, Algorithms and Complexity, Information Science Grad Visiting Day March 24, 2003 Panel II

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

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More Connections Information Science Algorithms and Complexity Computational Biology Scientific Computing Applied Logic Economics visionData basesGraphicsbiologychemistrySecurityMachine Learning Distributed Systems Programming Languages Artificial Intelligence Operations Research psychology sociology

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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

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Robert L. Constable Cornell University Applied Logic @ Cornell Grad Visiting Day March 24, 2003

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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

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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

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

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*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: N 4. 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 Stamps Proof

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Two-Phase Handshake Protocol The extracted message automaton is:

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Charlie Van Loan Cornell University Scientific Computing @ Cornell Grad Visiting Day March 24, 2003

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

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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

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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. Crack Propagation: Physics + Geometry + CS

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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.

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

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Ron Elber Cornell University Computational Biology @ Cornell Grad Visiting Day March 24, 2003

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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)

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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).

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

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Clustering experimentally determined protein sequences: Golan Yona

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

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Éva Tardos Cornell University Algorithms and Complexity @ Cornell Grad Visiting Day March 24, 2003

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

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

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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.

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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 Some Current Areas of Interest wide but long Short, but easily congested

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Jon Kleinberg Cornell University Information Science @ Cornell Grad Visiting Day March 24, 2003

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Society Cognitive Studies HCI Computer Science Applications Information Science

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Computer Science Faculty William Arms Graeme Bailey Claire CardieRobert Constable Johannes GehrkeJoseph Halpern Daniel HuttenlocherThorsten Joachims Jon KleinbergCarl Lagoze Lillian LeeBart Selman Eva TardosCharles Van Loan

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Information Retrieval: Term Vector Space Terms Documents c1c2c3c4c5m1m2m3m4 human100100000 interface101000000 computer110000000 user011010000 system011200000 response010010000 time010010000 EPS001100000 survey010000001 trees000001110 graph000000111 minors000000011

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Latent Semantic Indexing term document query --- cosine > 0.9

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Eye Tracking

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