| |
| Week 1 (June
4 - June 10) |
   |
|
Monday, |
June
4 |
9:00am |
George: An introductory
problem in ecology |
|
|
|
10:00am |
George and Giuliana: Initial meeting in Clapp
416 |
|
|
|
1:00pm |
Group meeting |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Tuesday, |
June
5 |
9:00am |
Becca:
On 3x3 swaps |
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|
|
|
Valentin: Counting checkerboards and checkerboard
units |
| |
|
|
3:00pm |
Tea |
|
|
|
3:30pm |
Tim: A recursive algorithm for counting co-occurrence
matrices |
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|
|
|
Jane and Lin:
Introduction to LaTeX |
|
Wednesday, |
June
6 |
10:00am |
Man Yu: Speeding convergence
by folding graphs |
|
|
|
1:00pm |
George: Splus demonstration |
|
|
|
3:00pm |
Tea |
|
|
|
3:30pm |
Yung-Pin: Introduction to Markov chains |
|
|
|
|
Becca and Man Yu: Folding based on column sums |
|
Thursday, |
June
7 |
10:00am |
Gregg: Counting walks
on a graph |
|
|
|
|
Yumi: Recursion relations and generating functions |
|
|
|
|
Ana: Row and column swaps (see
handout) |
|
|
|
3:00pm |
Tea |
|
|
|
3:30pm |
Group progress report: |
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|
|
Ann: Expanding coefficients |
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Sylvia: Families of expander graphs |
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|
|
|
Tim: Fill algorithm, pseudocods and baground
(download
program) |
|
|
|
|
Man Yu: On a 3x4 co-occurrence matrix and its
graph walk |
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|
|
|
Gregg: Various strategies: swapping and folding |
|
|
|
5:00pm |
REU picnic at Lower Lake fireplace |
|
|
|
7:00-8:45pm |
Foodmart van service available (canceled) |
|
Friday, |
June
8 |
10:00am |
Yung-Pin: Limiting distributions
of Markov chains |
|
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|
|
George: Motivation for the Metropolis algorithm |
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|
|
Lin and Jane: Some thoughts on checkerboards
and checkerboard units |
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|
|
3:00pm |
Tea |
|
|
|
3:15pm |
Yung-Pin: A
Markov chain through coprimality (see abstract) |
|
Saturday, |
June
9 |
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Sunday, |
June
10 |
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|
| Week 2 (June
11 - June 17) |
|
|
Monday, |
June
11 |
10:00am |
Becca & Man Yu: Row
and column swap as a group (example: 7-vertex graph) (see
handout) |
|
|
|
3:00pm |
Tea (prepared by Tim) |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Tuesday, |
June
12 |
10:00am |
Gregg and Yumi: Topology |
|
|
|
|
Tim: Return time simulation |
|
|
|
3:00pm |
Tea (prepared by Gregg and Yumi) |
|
Wednesday, |
June
13 |
10:00am |
Becca & Man Yu: Row
and column swaps grouping (see
handout) |
|
|
|
|
Valentin: Linear random walk graph |
|
|
|
|
Tim: Return time simulation (involving cliques) |
|
|
|
|
Gregg & Yumi: (An nxn case with the pattern:
r = c = (x, 1,...,1)) |
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|
Ana: Adding row and column swap edges and the
convergence rate |
|
|
|
|
Jane & Lin: Number of checkboard units and
lumpability of the chain |
|
|
|
3:00pm |
Tea (prepared by Lin and Jane) |
|
|
|
3:30pm |
Gregg: GAP demonstration |
|
Thursday, |
June
14 |
3:00pm |
Tea (prepared by
Becca) |
|
|
|
3:30pm |
Group progress report: |
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|
|
|
Yumi: The total number of matrices for a certain
pattern of row and column margins |
|
|
|
|
Ana: A proof about lumpable Markov chains (see
handout) |
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|
|
Carty: Construction of a family of expander graph |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
|
|
5:00pm |
REU picnic at Lower Lake fireplace |
|
Friday, |
June
15 |
10:00am |
Tim: A family of co-occurrence
matrices |
|
|
|
3:00pm |
Tea (prepared by Man Yu) |
|
Saturday, |
June
16 |
|
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|
Sunday, |
June
17 |
|
|
|
| Week 3 (June
18 - June 24) |
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|
Monday, |
June
18 |
10:00am |
A brief review: |
|
|
|
|
Man Yu: Various swaps and particular examples |
|
|
|
|
Valentin and Ana: Using subsets of the row and
column swap group |
|
|
|
|
Tim: Counting co-occurrence matrices; (working
on new directions) |
|
|
|
|
Yumi and Gregg: Formula for a class of square
co-occurrence matrices (see handout,
a dvi file) |
|
|
|
|
Becca: Revisit of 3x3 swaps |
|
|
|
|
Jane and Lin: Lumpability via the number of checherboard
units |
|
|
|
3:00pm |
Tea (prepared by Ben) |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Tuesday, |
June
19 |
2:00pm |
Yumi and Gregg: Investigating
patterns from summing all co-occurrence matrices |
|
|
|
|
Becca: Continuing 3x3 swaps by S-plus |
|
|
|
|
Man Yu: Looking at the transition matrices from
various lumpings |
|
|
|
|
Ana and Valentin: Lumpings not generated by subsets
of the row and column swap group |
|
|
|
|
Jane and Lin: Continuing proving the lumpability
via the number of checkerboard units |
|
|
|
|
Tim: Working on new ideas about co-occurrence
matrices |
|
|
|
3:00pm |
Tea (prepared by Sylvia) |
|
Wednesday, |
June
20 |
2:00pm |
Yumi and Gregg: A counter-example for the pattern
from summing co-occurrence matrices |
|
|
|
|
Becca: Using Splus for running 3x3 swaps |
|
|
|
|
Man Yu: Working on the transition matrices |
|
|
|
|
Jane and Lin: A counter-example for lumpability based on the number
of checkerboard units |
|
|
|
|
Valentin and Ana:: Discussing eigenvalues |
|
|
|
|
Tim: Still working on some new ideas |
|
|
|
3:00pm |
Tea (prepared by Matt) |
|
Thursday, |
June
21 |
3:00pm |
Tea (prepared by
Ann) |
|
|
|
3:30pm |
Yumi and Gregg: A simplified formula for a class of square co-occurrence
matrices |
|
|
|
|
Ana: Adding edges to a graph may increase the second largest eigenvalue
(see
handout) |
|
|
|
|
Jane and Lin: The lumpability conjecture still fails on the number
of checkerboards |
|
|
|
|
Tim: Investigating perturbed co-occurrence matrices |
|
|
|
|
Valentin: Eigenvalues of lumped chains |
|
|
|
|
Man Yu: Examples showing a lumped chain may maintain the second largest
eigenvalue (see handout) |
|
|
|
|
Becca: Using Splus for running Metropolis 3x3 swaps |
|
|
|
5:30pm |
REU picnic in the Student Center |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Friday, |
June
22 |
|
|
|
|
|
3:00pm |
Tea (prepared by Carty) |
|
|
|
3:30pm |
Group progress report: |
|
|
|
|
Jane: Checkerboard units and lumpability (see
handout) |
|
|
|
|
Becaa: 3x3 swaps of co-occurrence matrices |
|
|
|
|
Ben: Maximum order of a particular quaternion algebra |
|
Saturday, |
June
23 |
|
|
|
Sunday, |
June
24 |
|
|
|
| Week 4 (June
25 - July 1) |
|
|
Monday, |
June
25 |
2:00pm |
Tim, Becca, and Man Yu: Investigating the spectral
gap for the chains involving two alternative moves |
|
|
|
|
Ana: A closer look at the lumpings induced by subsets of row and column
swap group |
|
|
|
|
Valentin: The row and column swap group should be no simpler than the
Klein group |
|
|
|
|
Jane and Lin: Spectral analysis on the chain expanded from a lumping |
|
|
|
|
Yumi and Gregg: Considering bounds on the number of co-occurrence matrices |
|
|
|
3:00pm |
Tea (prepared by Lin) |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Tuesday, |
June
26 |
1:00pm |
Ana and Valentin: Proof of a necessary condition for lumpability |
|
|
|
|
Yumi and Gregg: Counting square co-occurrence matrices with all marginal
sums equal to 2 |
|
|
|
|
Becca: Working on an Splus program for running 3x3 swaps |
|
|
|
|
Man Yu: Investigating the spectral gaps for a chain and its Metropolized
chain |
|
|
|
|
Jane and Lin: More work on the spectral analysis on the chain expanded
from a lumping |
|
|
|
|
Tim: Writing a program investigating the spectral gap for the chains
involving two alternative moves |
|
|
|
3:00pm |
Tea (prepared by Gregg) |
|
Wednesday, |
June
27 |
2:00pm |
Man Yu: Examples for spectral analysis on various
lumped chains |
|
|
|
|
Valentin: Working on the conjecture that no row and column swap group
is simpler than the Klein group |
|
|
|
|
Jane and Lin: More spectral analysis on the chain expanded from a lumping |
|
|
|
|
Ana: Reexamining a necessary condition for lumpability |
|
|
|
|
Yumi and Gregg: A recursion relation counting square co-occurrence
matrices with all marginal sums equal to 2 |
|
|
|
3:00pm |
Tea (prepared by Yumi) |
|
Thursday, |
June
28 |
3:00pm |
Tea (prepared by Man Yu) |
|
|
|
5:00pm |
REU picnic at Lower Lake fireplace |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Friday, |
June
29 |
3:00pm |
Tea (prepared by Jane) |
|
Saturday, |
June
30 |
|
|
|
Sunday, |
July
1 |
|
|
|
| Week 5 (July
2 - July 8) |
|
|
Monday, |
July
2 |
3:00pm |
Tea (prepared by Man Yu) |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Tuesday, |
July
3 |
10:30am |
Group progress report: |
|
|
|
|
Matt: Spectral analysis of expanding regular graphs |
|
|
|
|
Valentin: Lumpability: why and how to lump, and the spectral gap of
a lumped chain |
|
|
|
|
Jane: The eigensystem of a chain expanded from a lumping |
|
|
|
|
Lin: The stationary distribution of a chain expanded from a lumping |
|
|
|
|
Man Yu: Examples for showing the spectral gaps of various lumped chains |
|
|
|
3:00pm |
Tea (prepared by Tim) |
|
Wednesday, |
July
4 |
|
Independence Day |
|
Thursday, |
July
5 |
2:00pm |
Yumi and Gregg: More investigation on the recursion
relation counting square co-occurrence matrices with a constant marginal
sum |
|
|
|
|
Becca: More work on an Splus program for running 3x3 swaps |
|
|
|
|
Man Yu: Considering co-occurrence matrices with all column sums equal
to one |
|
|
|
|
Ana: Looking at the relation between lumpability and the equality of
marginal sums of a co-occurrence matrix |
|
|
|
|
Tim: Modifying an algorithm so it can unbiasedly sample a co-occurrence
matrix |
|
|
|
|
Valentin: Proving the row and column swap group can not be simpler
than the Klein group |
|
|
|
3:00pm |
Tea (prepared by Ana) |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Friday, |
July
6 |
2:00pm |
Tim: Approximation heuristics in the field
of job-shop scheduling (see abstract) |
|
|
|
3:00pm |
Tea (prepared by Valentin) |
|
|
|
3:30pm |
George: Using the central limit theorem to count co-occurrence matrices |
|
Saturday, |
July
7 |
|
|
|
Sunday, |
July
8 |
|
|
|
| Week 6 (July
9 - July 15) |
|
|
Monday, |
July
9 |
2:00pm |
Valentin: The orbits induced by an edge-preserving
action group form a lumpable partition |
|
|
|
|
Jane and Lin: An example showing a Markov chain and its expanded chain
may not have the same stationary distribution |
|
|
|
|
Man Yu: On the transition matrix of an alternating graph walk |
|
|
|
|
Tim: Questions about a group acting on a graph |
|
|
|
|
Ana: Still working on the relation between lumpability and the equality
of marginal sums of a co-occurrence matrix |
|
|
|
|
Yumi and Gregg: Counting co-occurrence matrices by semi-standard Young
tableaux |
|
|
|
3:00pm |
Tea (prepared by Carty) |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Tuesday, |
July
10 |
2:00pm |
Man Yu and Becca: Examples for showing a different
alternating graph walk |
|
|
|
|
Jane and Lin: More work on the stationary distribution of an expanded
chain |
|
|
|
|
Valentin: On a way to lump a random walk on a graph (see
handout) |
|
|
|
|
Tim: Working on a Java program to construct the graph of co-occurrence
matrices |
|
|
|
|
Ana: On decomposing a graph into clusters |
|
|
|
|
Yumi and Gregg: More investigation on semi-standard Young tableaux |
|
|
|
3:00pm |
Tea (prepared by Sylvia) |
|
Wednesday, |
July
11 |
2:00pm |
Man Yu: More work on the spectral analysis
of the alternating chain |
|
|
|
|
Jane and Lin: A conjecture of the stationary distribution of an expanded
chain |
|
|
|
|
Tim: Working on a Java program and running the program Symmetrica |
|
|
|
|
Valentin: Some remarks on lumping |
|
|
|
3:00pm |
Tea (prepared by Sylvia) |
|
Thursday, |
July
12 |
2:00pm |
Group progress report: |
|
|
|
|
Giuliana: On automorphic forms |
|
|
|
|
Sylvia: Investigating the maximum order of quaternion algebra |
|
|
|
|
Ann: On categorical products of graphs |
|
|
|
|
Yumi: The recursion relation for counting co-occurrence matrices with
marginal sums equal to 2 |
|
|
|
|
Gregg: The bijection between the co-occurrence matrices and the semi-standard
Young tableaux |
|
|
|
|
Man Yu: Comparison of the convergence rates of different methods using
examples from 3x4 co-occurrence matrices (see
handout) |
|
|
|
3:00pm |
Tea (prepared by Sylvia) |
|
|
|
5:00pm |
REU picnic at Lower Lake fireplace |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Friday, |
July
13 |
2:00pm |
Valentin, Lin, Jane, and Ana: Investigating
the conditions that ensure a chain and its expanded chain have the same
stationary distribution |
|
|
|
|
Man Yu and Becca: More work on alternating walks |
|
|
|
|
Tim: Spectral analysis of a graph: what can we tell from the dimensionality
of an eigenspace? |
|
|
|
|
Yumi and Gregg: Counting matrices with a special form that is related
to the Catalan numbers |
|
|
|
3:00pm |
Tea (prepared by Ben) |
|
Saturday, |
July
14 |
|
|
|
Sunday, |
July
15 |
|
|
|
| Week 7 (July
16 - July 22) |
|
|
Monday, |
July
16 |
2:00pm |
Tim: Using the returning time to estimate the
number of co-occurrence matrices |
|
|
|
|
Lin, Jane, Ana, Valentin, and Becca: More thoughts on lumping a Markov
chain |
|
|
|
|
Man Yu: Examples showing an alternating chain composed of more
2x2 swaps has a smaller second largest eigenvalue modulus |
|
|
|
|
Yumi and Gregg: Using a sequence representation of a graph walk to
prove the number of matrices in a certain class is equal to the Catalan
numbers |
|
|
|
3:00pm |
Tea (prepared by Tim) |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Tuesday, |
July
17 |
1:00pm |
Yung-Pin: Probabilistic approximations for
counting co-occurrence matrices |
|
|
|
2:00pm |
George: Outline for an example-based expository paper |
|
|
|
3:00pm |
Tea (prepared by Gregg) |
|
Wednesday, |
July
18 |
3:00pm |
Tea (prepared by Yumi) |
|
Thursday, |
July
19 |
2:00pm |
Group: Preparing detailed outlines of the example-based
paper |
|
|
|
3:00pm |
Tea (prepared by Ana) |
|
|
|
3:30pm |
Yumi and Gregg: A closed form for the number of matrices with line
sums equal to 2 (see handout, a dvi
file) |
|
|
|
5:00pm |
REU picnic at Lower Lake fireplace |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Friday, |
July
20 |
2:00pm |
Group: Discussion and comments on the detailed
outlines of the example-based paper |
|
|
|
3:00pm |
Tea (prepared by Ana) |
|
Saturday, |
July
21 |
|
|
|
Sunday, |
July
22 |
|
|
|
| Week 8 (July
23 - July 27) |
|
|
Monday, |
July
23 |
2:00pm |
Finishing the first draft of the example-based
paper |
|
|
|
3:00pm |
Tea (prepared by Jane) |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Tuesday, |
July
24 |
10:00am |
REU symposium rehearsal and comment exchanges |
|
|
|
|
Taking group photos |
|
|
|
3:00pm |
Tea (prepared by Becca) |
|
|
|
3:30pm |
Discussion and comment exchanges on the draft of the example-based
paper |
|
|
|
7:00pm |
REU dinner at India House in Northampton |
|
Wednesday, |
July
25 |
noon |
Finishing revising the first draft of the example-based
paper |
|
|
|
3:00pm |
Tea (prepared by Becca) |
|
|
|
3:30pm |
Discussion on the presentation for the REU symposium |
|
|
|
4:30pm |
Discussion on the poster presentation for the Joint Math Meetings in
San Diego, 2002 |
|
Thursday, |
July
26 |
9:00am |
REU breakfast |
|
|
|
10:00am-1:30pm |
REU symposium |
|
|
|
10:05-11:25am |
Presentation One: Random walks on co-occurrence matrices |
|
|
|
|
Man Yu: Introduction, examples in ecology, and statistics associated
co-occurrence matrices |
|
|
|
|
Valentin: A graph walk on the co-occurrence matrices by 2x2 swaps |
|
|
|
|
Tim: Stationary distribution, spectral analysis, and convergence rate |
|
|
|
|
Becca: Metropolis algorithm |
|
|
|
|
Lin: General theory on lumping Markov chains |
|
|
|
|
Anna: Lumping via the group of row and column swaps |
|
|
|
|
Lin: On expanding Markov chains |
|
|
|
|
Jane: The stationary distribution of an expanding Markov chain |
|
|
|
|
Becca: On larger swaps: 3x3 swaps |
|
|
|
|
Man Yu: A numerical comparison on different methods of speeding up
the convergence rate and concluding remarks |
|
|
|
11:25-11:40am |
Break |
|
|
|
11:40am-12:50pm |
Presentation Two: Some generalizations of Ramanujan graph constructions |
|
|
|
|
Sylvia: Introduction and backgrounds |
|
|
|
|
Carty: Review of (p+1) construction by A. Lubotzky, R. Phillips, and
P. Sarnak |
|
|
|
|
Ben: Review of (p=2) construction by Chiu |
|
|
|
|
Matt: Adding random edges and investigating the consequences |
|
|
|
|
Ann: Order and maximum order |
|
|
|
|
Ann and Sylvia: Some numerical experimental results on generalized
quaternions |
|
|
|
|
Matt: On an h(q) inequality |
|
|
|
12:50-1:10pm |
Break |
|
|
|
1:10-1:35pm |
Presentation Three: Counting co-occurrence matrices |
|
|
|
|
Yumi and Gregg: Using generating functions to count co-occurrence matrices:
the general method and the special case when all marginal sums are equal
to 4 |
|
|
|
2:00pm |
Tea (prepared by Man Yu) |
|
|
|
5:00pm |
REU picnic at Lower Lake fireplace |
|
|
|
7:00-8:45pm |
Foodmart van service available |
|
Friday, |
July
27 |
2:00pm |
Final comments of the revised draft of the
example-based paper |
|
|
|
3:00pm |
Tea |