Last month Yisroel Brumer wrote a Newsweek My Turn column Let's Not
Crowd Me, I'm Only a Scientist. Brumer talks about how he has
become a "social
superstar" since taking on a job at Homeland Security's Science
and Technology Directorate.
It wasn't always this way. Just a few years ago, I was a graduate
student in chemical physics, working on obscure problems involving
terms like quantum mechanics, supercooled liquids and statistical
thermodynamics. The work I was doing was fascinating, and I could have
explained the basic concepts with ease. Sure, people would sometimes
ask about my work in the same way they say "How are you?"
when you pass them in the hall, but no one, other than the occasional
fellow scientist, would actually want to know. No one wanted to hear
about a boring old scientist doing boring old science.
People want to hear only about how there's now a cell phone that plays
iTunes, or maybe about cool communications that will facilitate
emergency responses. But think about all the science that goes into
making a cell phone work. Someone had to figure out the equations of
electromagnetic waves, circuitry and myriad other scientific
details. People have to figure all that stuff out, people who could
have made more money and garnered greater prestige had they applied
their skills in fields like patent law, business or medicine.
I sympathize with the old Brumer. Even among academics, I remember the
political scientist who had the great opening line "My business is
war, and business is good", or even my friend the food scientist
who did his doctorate on starch. Much as I get excited about
the P versus NP problem and its great importance to all science and
society, trying to express these ideas to uninterested laypeople always
seems to end up with "Should I buy an Apple or a Windows machine?"
Marilyn vos Savant writes a weekly column for Parade Magazine instered into many US
papers. She's best known in
the math community for the popularization of the Monty Hall
Problem. Here is a question from her November 19th column (names added).
Carol get lost in the woods, where she ran into two campers, Alice and
Bob, who also were lost. Alice had three loaves of bread and Bob had
two loaves. They all agreed to share the bread equally. Carol was so
grateful that, when they found their way back to town, she gave the
campers $10,000 for saving her life. Alice said she should get $6,000
because she contributed 3/5 of the bread. Bob said that all had eaten
an equal amount so the campers should split the reward. To settle the
argument they visited the local wise man, a retired math
teacher. Which camper was right?
Think about the problem. Here is my short version of Marilyn's
answer.
Neither. Carol paid $10,000 for 5/3 loaves or $6000 per loaf. So Alice
gets $8,000 for her 4/3 loaves she gave up and Bob gets $2,000 for his
1/3 of a loaf.
This solution makes sense mathematically but not economically. Suppose
Alice and Bob were poor graduate students. Bob would be willing to eat
less bread and undercut the price of Alice's bread. To make this point
clearer suppose originally Alice had four loaves and Bob only one. Then
by the logic above, not only does Alice get all of Carol's $10,000 but
also $4,000 more from Bob for the 2/3 of a loaf he gets from Alice.
To do the correct math one would have to know the exact utility
functions of Alice, Bob and Carol, or set up an appropriate auction
when distributing the bread. But since the money is split after the
sharing has been done, Alice and Bob should just take $5,000 each and
be happy with it.
I have served on program committees that have entirely electronic
discussions and others that meet in person. What works better?
Logistically physical meetings have several disadvantages.
Must somehow cover travel costs of participants. Often this comes
out of the conference budget, raising registration rates.
Since traveling overseas is difficult just for a committee
meeting, physical PCs have less international participation.
Invariably some PC member misses the meeting and has substantially
less influence on the choices.
On the other hand I have heard that a physical PC meeting rewards the
PC members but allowing them to spend time together and enjoy a fine
meal.
The dynamics of physical and electronic meetings
differ. Both start by quickly accepting the strongest papers and
rejecting the weakest. In a physical meeting the remaining papers get
discussed serially. There is a tendency to
accept more often at the beginning, realizing you accept too much and
start being more stringent and bouncing back the other way towards the
end. One also spends too much time talking about the first set of
papers, leading to rushed discussions later on.
In an electronic meeting the discussion on all papers happens in
parallel. When discussion seems to go a certain way, the PC chair will
suggest acceptance and rejection and sees if someone objects. A vote
is taken for a few contentious papers. But many papers have nobody who
loves or hates them. For those the PC chair has tremendous power for
no one will object to whatever they recommend.
Both types of PCs suffer from groupthink, a tendency
for groups to
reinforce viewpoints. A PC chair also has to make sure that
everyone participates in the discussions.
My preference goes for a third approach that I have seen used in a few
conferences. The PC members send their
reviews to the PC chair who, after some emails for clarifications,
makes all the final decisions by him or herself. Simple and, with a
good PC chair, works surprisingly well.
During my Thanksgiving trip two store closings caught my eye.
The Tower Records just near Lincoln Center in New York has a going
out of business sale. I used to kill time there before going to a
concert or an opera. In fact all the Tower Records are closing down.
The small Millburn Camera Shop in New Jersey is no longer.
Both of these stores just couldn't keep up with the world of the
Internet. Tower Records made their mark by having an amazing
collection, one of the best collection of classical in the country in
their Lincoln Center store. But their collection cannot compete with
online stores like Amazon, Walmart beats them in price on the popular
CDs, not to mention the convenience of music downloads, both legal and
illegal.
The Millburn Camera Shop supported the amateur photographer with
products, advice and specialized film developing and printing
services. In high school I set up a darkroom in my basement with
equipment from the store and bought my Black and White film in
bulk from them. But as today's amateurs now have mostly gone digital,
software replaces most of the equipment and developing. Bulk film
comes in the form of a tiny media card. And so the friendly
neighborhood camera shop disappears.
It has become much easier to access music and to take and process
pictures than it ever has in the past. But I will miss the days of
browsing music and developing pictures.
An administrative note: Because of a recent large increase in comment
spam I now use CAPTCHA-type tests to leave comments. Sorry for the
inconvenience.
A graduate student complained that Indiana University requires him to
pay $60 to make a microfiche copy of his Ph.D. dissertation.
Many universities have various hidden fees they charge you just as you
are about to graduate. Usually these fees total in the $100 range, low
enough so that you just cough up and pay them as $100 doesn't mean too
much in the grand scheme of life. Still there should be some warning,
perhaps in the admissions letter.
Be aware that after you have fulfilled all the requirements, written
and successfully defended your thesis, you will not receive a
Ph.D. until you have also paid the following fees…
But why Microfiche?
Wouldn't an electronic copy of the thesis make more sense. Several
universities require a bound paper copy, partly for tradition and part
just in case the PDF files of today cannot be read by next century's
computers. I doubt the last part—there are too many PDFs
around today for us not to have a way to look at them in the future.
I was a microfiche wizard in high school. When I did reports on 20th
century history, I would go back to the original New York Times
articles to get a first hand perspective. But with the Internet and
back articles available electronically, microfiche is an aging
technology. In the past decade I've
used microfiche exactly once—to track down a box score of a
baseball game I went to long ago.
I suspect microfiche will go the way of sliderules and
typewriters. Before they die, someone (Google?) will scan in the old
microfiche and covert them to PDFs. Wouldn't it be better for the
Indiana University library to get a free high-quality PDF now instead
of an expensive scanned PDF in the future?
To recognize and honor outstanding ACM members for their achievements
in computer science and information technology and for their
significant contributions to the mission of the ACM. The ACM Fellows
serve as distinguished colleagues to whom the ACM and its members look
for guidance and leadership as the world of information technology
evolves.
Since then over 500 fellows have been named including several
theoretical computer scientists.
Becoming an ACM Fellow or Distinguished Scientist doesn't make you a
better researcher but it does give you a little more clout in the
broader CS community. Also having large numbers of Fellows and
Distinguished Scientists makes the theory community seem stronger as a
whole. So if you know of someone worthy (and eligible) for Distinction
or Fellow, go ahead and nominate them and
help give your fellow scientists and the theory community the
recognition they deserve.
The class P/poly is the
set of languages that have polynomial-size
circuit families, i.e., L is in P/poly if there is a k, a sequence of
Boolean circuits C0, C1, … where Cn
has n inputs and at most n^k gates,
such that
and all x=x1x2…xn,
x is in L iff
Cn(x1,x2,…,xn)=1.
This is a nonuniform model of computation, C27 may have no
relation whatsoever to C28.
Suppose NP is in P/poly and has a (non-uniform) circuit family that
accepts it. Karp and Lipton show that NP in P/poly implies collapses
in uniform models of computation as well.
The main result shows that if NP is in P/poly then the polynomial
hierarchy collapses to the second level, giving us evidence that NP is
not in P/poly and hope that we can prove P≠NP by showing
superpolynomial lower bounds on the circuit computing some NP
problem.
The paper also gives a general (though controversial)
definition of advice and a collapse of EXP to
Σ2p∩Π2p if
EXP is in P/poly (credited to Meyer), and similar results for PSPACE
and the Permanent.
Kannan uses Karp-Lipton to show
that some language in
Σ2p∩Π2p does
not have linear-size circuits, or more generally for every k, there is
a language Lk in
Σ2p∩Π2p that
cannot be computed by nonuniform nk-size circuits.
Later extensions to Karp-Lipton:
If NP in P/poly then the polynomial-time hierarchy collapses to S2P
⊆ ZPPNP ⊆
Σ2p∩Π2p.
(see Cai and Köbler-Watanabe)
If EXP, PSPACE or
the Permanent is in P/poly then EXP, PSPACE or
the Permanent is in MA ⊆
S2P respectively. (see Babai-Fortnow-Lund)
If NP is in BPP (in P/poly) then the polynomial-time hierarchy is
in BPP. (Zachos)
Using Kannan's proof, (1) implies that S2P does not have
nk-size circuit for any fixed k.
Can one improve (1) to show that if NP
in P/poly then the polynomial-time hierarchy collapses to MA? This
would imply MA does not have nk-size circuits for any fixed k.
New Scientist celebrates their 50 years by asking about 70
"Brilliant Minds" to
forecast the next 50 years of science. Several researchers (all well-known
though a few overrated) talk about
math and
computing including
Tim Gowers focusing
on the P versus NP problem.
This problem gets to the heart of mathematics, because mathematical
research itself has the property I have described: it seems to be
easier to check that a proof is correct than to discover it in the
first place. Therefore, if we found a solution to the P = NP problem
it would profoundly affect our understanding of mathematics, and would
rank alongside the famous undecidability results of Kurt Gödel and
Alan Turing.
I bought a Diet Pepsi yesterday and the label described a bottle top
promotion: One in six wins "Buy One Get One Free". Suppose
you drink a large amount of Diet Pepsi, what is your asymptotic
expected discount?
If you buy six bottles then you expect to have one winning bottle top
enabling you to get the next two bottles for the price of one, or
eight bottles total for the price of seven. But bottles seven and
eight have bottle tops too which may be winners. One can continue this
process and take the limit but is there a simpler argument?
Soda bottles are interchangeable, a free soda in the future can be
exchanged for your current soda. So you can assume that when you get
the "Buy One Get One Free" bottle top, your current soda is
free. That means you get one free soda from every six, a discount of
16 2/3%.
You get the same discount if the bottle top said "Buy Two
Get One Free" or simply "Get One Free". But if the
bottle top said "50% off next purchase" which seems
equivalent to the original promotion, the discount is only 8 1/3%.
The key references section of a paper points to the most similar
previous articles on the same topic that were extended, improved,
challenged, or built upon by the paper. Key references allow the
author of a research article to highlight the most closely related
previous work in the specific topic of the paper. Key references are
the natural complement of keywords.
An interesting idea. If it is used (and taken seriously) by many
authors it might help automated search systems identify important
papers in the field.
On the other hand many journals require keywords and AMS
classifications although I have rarely seen this information put to
good use. For humans a well-written "Previous Work" section
will have much greater value than just a list of references.
Key References won't become popular unless a major publisher
requires them in their journal or conference articles. Would Key
References play a useful role or just become one more thing authors
have to do to get their papers published?
Dartmouth Professor Peter Winkler visited our department yesterday and
today, the first stop of a two-week five-university tour. Winkler
gives great seminar talks and is easy to talk to about hard combinatorial
problems. Unfortunately whenever I see him he also brings very tantalizing
puzzles that you have to work hard at not thinking about, lest they
consume you. For example Love in Kleptopia
Jan and Maria have fallen in love (via the internet) and Jan wishes to
mail her a ring. Unfortunately, they live in the country of Kleptopia
where anything sent through the mail will be stolen unless it is
enclosed in a padlocked box. Jan and Maria each have plenty of
padlocks, but none to which the other has a key. How can Jan get the
ring safely into Maria's hands?
A countable number of people each have either a white hat or black hat
on their heads. Each person can see everyone's hats except their
own. Each person simultaneously announces a guess for the color of
their hat. Is there a strategy for the people so that no matter what
the arrangement of hats, only a finite number will incorrectly guess
their hat color?
The Chicago Tribune today had a few articles
on Second Life, a growing
virtual world that even has its own economic markets with its own
currency exchangable with US dollars. As the article says, Harvard Law
School taught a class in Second Life and I have heard of many other
universities in the process of establishing Second Life courses as
part of their on-line degrees. Taken to an extreme, why do we need
hundreds of graduate complexity courses taught world-wide every year
when everyone can sit in on one of a handful of the best lecturers
giving the class?
Indeed we now have the technology to have virtual seminars or even
entire conferences on-line complete with "coffee breaks",
business meetings and dance
parties. Why not even hold an established conference, like STOC or
SODA in a virtual world? The total cost would be much less than
traveling to a real-world meeting and nearly every aspect of the
conference experience could be simulated.
One advantage of a real-world conference is not so much what one can
do but what a real-world conference prevents you from doing. While
away at
STOC you can't teach your course, attend committee meetings, hold
office hours, meet with students, etc. You are forced by circumstance
to reschedule these activities and open up your calendar to see talks
and meet with your colleagues. But at a virtual meeting, can you tell
your chair you have to miss your class and the faculty meeting while
you sit at your computer, your body in your office but your mind in a
different place?
These aren't songs about loving math, these are love songs that
use math as a way to express love. There are three that I know of
(if you know more let me know).
I'm not counting THEORY
GIRL which is more of a Comp Sci song.
Lyrics are great!
Math is actually HARD!
Singing quality–they shouldn't quit their day jobs.
Video Quality–they just stand around singing.
(Actually they are grad students so its not clear they
have day jobs.)
From SQUARE ONE TV, an old PBS show about math (in a low level)
that had some nice satires and songs in it.
I watched it when I was younger (when I was 30 actually)
Lyrics are nice!
Math is easy.
Singing quality is pretty good.
Video quality–very good for content and quality.
I think this IS their day job.
Also from Square One.
Lyrics are great!
Math is easy.
Singing quality is pretty good.
Video quality–very good for content, but quality is fuzzy.
(I've got a better quality video of this in my collection.)
I think this IS their day job.
I am applying for academic jobs this year. How does one come to know
about them? Basically the only source I know is the
CRA website.
DMANET
mailing list is also helpful. [And then there is word of
mouth—but that seems to favor a privileged few.]
I think the way CRA puts ads on its website could be improved a lot. Right
now every university puts its ad in unstructured text. Now if I want to
know which university has what deadlines I have to manually sift through
their ads and the deadline could be anywhere in the text (if it's there at
all). Similarly, there are many other attributes that one might want to
use as search criteria: such as type of position being advertised, do they
need material in hard copy, or in email, or does one need to fill a
web form. I think if this were there it'd save some time.
But I think one could go further; though I understand it's probably rather
hard to implement what I am going to suggest for all sorts of reasons.
Why not make the whole process centralized. At present one has to fill up
the forms on the web for many universities which can be really painful.
And then sometimes they ask the letter writers to also fill a form.
Hard copies or emails are not much better either. What if there were a
centralized trusted server where one applicants could submit their
information along with the universities where they wanted to apply? And
then their application would be delivered to those universities. This
would save a lot of pain for everyone.
Most CS departments list their faculty positions in the CRA News and
CACM
and many job positions also get distributed over the DMANET
and
THEORYNT
mailing lists. Also check out the departmental home pages of
any university where you might have interest. Even if there is no ad
you can apply to any department by sending an email to the chair with
the usual supporting material (CV, research statement, teaching
statement and list of references), though if the department's web page
has specific instructions better to follow those. Get all your
applications submitted by December 31 no matter how late the stated
deadline.
Don't limit yourself to departments specifically mentioning theory as
they will sometimes hire in theory once they fail to find suitable
candidates in other areas. You might also consider positions overseas,
while professor positions are difficult to find in most countries,
there are more postdoc opportunities outside the US. Also consider
a broad range of universities in the US, they might have a higher
teaching load but you can still have a successful research career.
Make sure your own home page (pointed to on your CV) has on-line
versions of all your papers, contact information, CV and the rest of
your supporting material.
A standardized database for recruiting would make life
easier for all involved but don't hold your breath.
As I've mentioned before,
David Pennock, Yiling Chen and I developed a map predicting the 2006 Senate races
based on market prices from tradesports.com. So how did those
predictions go? In short you can say the markets predicted every
individual race correctly but got the senate wrong, but let us look a
little more carefully.
At about 9 AM CST on the morning of election day I made a snap
shot of the map
for a Discovery Channel Website article.
Every state colored blue was won by a democrat and every state colored
red went to a republican. But also note the 69% given to GOP
(Republican) Senate control although this election will give control
to the democrats. No outcome would have made
all the states and senate control agree with the 9 AM map.
Were the markets inconsistent? No, because the markets predict not
absolutely but probabilistically. For example, the markets gave a
probability of winning 60% for each of Virginia and Missouri and the
democrats needed both to take the senate. If these races were
independent events, the probability that the democrats take both is
36% or a 64% chance of GOP senate control assuming no other surprises.
Of course the races were not independent events and there are other
states involved making it more difficult to compare the
probabilities of the individual races with that of senate control.
So how did the markets do as predictors? Quite well as the outcome
seems quite reasonable given the markets. Other outcomes would have also
been reasonable such as the Democrats losing Virginia and the senate
remaining in republican hands, a possibility that came very close to
happening.
We plan a map with a better design and more features for the 2008
Electoral College and Senate races. Stay tuned.
For the next Complexitycast, Bill
Gasarch and I will attempt to answer reader's questions. We will pick
the best questions and answer them in the next podcast.
You can either email me your question on any topic related to this weblog or
better yet record yourself asking the question (in either MP3, WAV or
OGG) and send me the audio file.
Think of good questions for if we don't get many we'll make up our own.
There have been two important NEW results in the field of Private
Information Retrieval so its worth reviewing the field and the new
results
(Some background here).
This post is about Information-Theoretic Private Information Retrieval.
We state the problem and five results in order of discovery,
with the last two being the recent ones.
PROBLEM: A database is an n-bit string (my wife tells me
that databases are more complicated than that).
The USER wants to know the ith bit but does not want
the DB to have ANY CLUE of which bit he wanted.
EASY ANSWER: Request the ENTIRE DB. That is n bits.
QUESTION: Can we do this with substantially fewer than n bits?
ANSWER: NO if there is only one copy of the database.
NEW QUESTION: What if there are k copies of the DB?
2 DBs, O(n1/3) bits; for k≥ 4, k DBs
O(n1/k) Private Information
Retrieval,
Chor, Kushilevitz, Goldreich, Sudan, JACM-1998, (Earlier version FOCS 95)
NOTE: Introduced the field. Journal version has easy constructions. Conference
version had slightly harder poly-interpolation constructions material that are
a prelude to item (3) below.
NOTE: FOCS version has O(n1/k) result, Journal omits it
since item 2 below had already appeared.
NOTE3: k=3 gives O(n1/3)—can't use that its 3 DB's
instead of 2.
NOTE: Used Recursion. Constant is exponential. Later papers that reduced
the constant to polynomial lead the way to the next paper.
NOTE3: k=3 gives O(n1/5).
NOTE: Hard paper! Modeled 2-DB-Private Information Retrieval via
Latin Squares and then used
representation theory of finite groups to push through the lower bound.
ALL current 2-DB protocols fit the model, so lower bound is either legitimate
or will point way to other techniques. My money is on legit.
Even so, there aren't that many 2-DB protocols so who knows…
NOTE: Wins award for largest distance between GREATNESS of content
and AWFULNESS of title. I would have called it
A 3 DB O(n1/32,586,658) PIR! Really!
NOTE: Uses Mersenne primes. The number used is based on the largest
Mersenne prime known, which is 232,586,658-1. If there are
infinitely many Mersenne primes then, for infinite number of n,
get k=3, n1/loglog n-Private Information Retrieval
NOTE: Vast improvement on k=3, n1/5.25
In the constructions in items (2) and (3) above the
k-DB PIR was constructed recursively out of k'-DB PIR's
for k'<k. Hence this massive improvement for 3-DB PIRs
leads to improvements for these schemes.
PIR scheme (2): the new 3-DB PIR leads to a k-DB, O(n1/(bk-1))
where b is enormous.
PIR scheme (3): the new 3-DB PIR leads to the same asymptotic
k-DB nO(loglog k/(k log k) but with a much smaller
constant in the O-of term.
For the first 18 years of my life I never left the Eastern time
zone. Everyone I knew including all my relatives lived on the
US East coast. I never had to do time conversions.
But now as an academic living in Chicago I always need to worry about
time zones when I coordinate a phone or IM meeting or have a paper deadline. You end up remembering
some key rules: One hour to the East Coast, seven hours to Continental
Europe except for Portugal which is six hours like London, eight hours
to Israel. I always have to remind myself that California is minus two
hours not minus three. And of course there is India, currently eleven
and a half hours ahead of Chicago. Time zones are relative—your time
differences will vary.
Daylight Savings Time adds to the confusion. Europe and Israel have
similar time changes but not always changing on the same weekends. India
and China don't change their clocks and Down Under they change in the
other direction. Savings time also mean extra thinking when converting from UTC time.
Until recently Indiana didn't do savings time but since time
zones are relative, it seemed that Indiana changed from Chicago time in the
summer to New York time in the winter. Now Indiana follows daylight
savings time so most of the state is in New York time year round. I
managed to forget the change when visiting South Bend this summer and
ended up an hour late to everything.
Technology helps. You don't need to know the time zone when you
send email. I used to use the World Clock to keep
track of times in other places but now I use the nifty Time
in City feature built into Yahoo! Search.
Sometimes time zones can work to your advantage. If you are close to
deadline on a paper with a co-author in a far-away land you can each
work on the paper while the other one sleeps. This strategy never
worked with my most frequent co-author Harry Buhrman in Amsterdam. I
am an early riser and he sleeps late so we keep the same hours, seven
hours apart.
The University of Chicago wrote a press
release about the prediction market maps for the Senate and Governor races that I
created with Yahoo!'s David Pennock and Yiling Chen.
The press release led to short articles on the New
Scientist and Scientific
American web sites and a handful of other blogs. Although even
with the nice virtual ink, there was never a day more people looked at
the maps than at this weblog.
What about the elections? No senate race in Illinois but
a governor's race where I have yet to find anyone who likes
either candidate. We do have two good candidates in my congressional
district, but what difference does it make as which party has control
of the house is much more important than the views of the particular
candidate we send there.
The Illinois politician garnishing the biggest praise is not even running this
year, our junior
senator and future president.
The 2007 Federated Computing
Research Conference will bring together a large number computer
science conferences for one meeting June 8-16 in San Diego.
Here is a
run down of the FCRC theory-related conferences with submission deadlines
and links to their call-for-papers.