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