Logic, Scientific Computing, Computational Biology,
Algorithms and Complexity, Information Science
Grad Visiting DayMarch 24, 2003
Panel II
Panel Areas and Connections
Algorithms and Complexity
Computational Biology
Scientific Computing
Applied Logic
Information Science
More Connections
Information Science
Algorithms and Complexity
Computational Biology
Scientific Computing
Applied Logic
Economics
vision
Data bases
Graphics
biologychemistrySecurity
Machine Learning
Distributed Systems
Programming Languages
Artificial Intelligence
Operations Research
psychology
sociology
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
Robert L. Constable
Cornell University
Applied Logic @ Cornell
Grad Visiting DayMarch 24, 2003
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
What Dexter Kozen doesKleene algebras
ECC (Efficient Certifying Compiler)
– theory: applied programming logic
– practice: an implemented system
Recursive types
What Joe Halpern doesEpistemic logic applied to:
– distributed systems
– security protocols
Reasoning about probability
What Robert Constable doesConstructive type theory applied to:
– program verification and synthesis
– process verification and synthesis
Automated reasoning with Nuprl
• Constructive proofs as programs
– Stamps
• Constructive proofs as processes
– two-phase handshake protocol
An Example of Applied Logic
circa 70’s
circa Now
*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
Two-Phase Handshake Protocol
1 2 1 2 1 2: , : . : .(( ( )& ( )& )s sSpec e e E r E send e send e e e
1 2( ( )& ))rcv r e r e
The extracted message
automaton is::x TState
: truerdy BState initially
: ( ) ( , );rdysend true send val x action precondition effect
: fdy er als( ) :rcv ack truerdy action effect
[ , ]send rcv rdyframe only effect
[ ]sendframe only sends
Charlie Van Loan
Cornell University
Scientific Computing @ Cornell
Grad Visiting DayMarch 24, 2003
Tom ColemanSteve Vavasis
Charlie Van Loan
Large-Scale Optimization
Computational Geometry
Matrix Computations
Complexity Issues in Optimization
Computational Finance Fast transforms
Scientific Computing
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
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
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.
Ron Elber
Scientific computing at themolecular level.
Why are proteins shaped like this:
Ron Elber
Cornell University
Computational Biology @ Cornell
Grad Visiting DayMarch 24, 2003
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)
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).
Protein structures and sequences aremarkers of evolution: Golan Yona, Jon Kleinberg
and Ron Elber
MGLYTHYRCCSQWANCGLYTHYKCCSQFANCGLYTHFRCCSQWANCGLYSHYRCCSQWAN
AVLICKGGNMRQWASPGVLICKGGNMKQWASGAVLICKPGNMDQWASGAVFICKGGNMRQWASGALLICKGGNMDQWASPLVLLCKGGNMRQWASP
NMHKTTREWQLPICVDSDMHKTTREWQLQICVDS
Clustering experimentally determined protein sequences: Golan Yona
Determining potentialpotential sizes of protein families and “fingerprints” of connectivity (temperature):
Ron Elber and Jon Kleinberg with students Catherine Grasso and Leonid Meyerguz
10010
Temperature for protein > 200 amino acids roughly constantsuggesting that these clusters are evolutionary connected
Randomized algorithms
Éva Tardos
Cornell University
Algorithms and Complexity @ Cornell
Grad Visiting DayMarch 24, 2003
Algorithms and Complexity
Juris Hartmanis John Hopcroft Jon Kleinberg
Dexter Kozen David Shmoys Éva Tardos
Some Current Areas of Interest
• Approximation Algorithms and Combinatorial Optimization.
• Models and Algorithms for Information Access and Complex Networks.
• Algorithmic Game Theory.
• Complexity
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.
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 Interestwide but long
Short, but easily congested
Jon Kleinberg
Cornell University
Information Science @ Cornell
Grad Visiting DayMarch 24, 2003
SocietyCognitiveStudies HCI
Computer Science
Applications
Information Science
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
Information Retrieval: Term Vector Space
Terms Documents
c1 c2 c3 c4 c5 m1 m2 m3 m4human 1 0 0 1 0 0 0 0 0interface 1 0 1 0 0 0 0 0 0computer 1 1 0 0 0 0 0 0 0user 0 1 1 0 1 0 0 0 0system 0 1 1 2 0 0 0 0 0response 0 1 0 0 1 0 0 0 0time 0 1 0 0 1 0 0 0 0EPS 0 0 1 1 0 0 0 0 0survey 0 1 0 0 0 0 0 0 1trees 0 0 0 0 0 1 1 1 0graph 0 0 0 0 0 0 1 1 1minors 0 0 0 0 0 0 0 1 1
Latent Semantic Indexing
• term
document
query
--- cosine > 0.9
Eye Tracking
Eye Tracking