Suppose I have n auctions and m bidders where m >= n. A bidder can only place bids in one auction but each auction can have multiple bidders. The auctions are probabilistic (i.e. bids are random variables with some arbitrary and probably continuous distribution) and the bidders have different valuations for each auction. Furthermore, while each auction has only one type of item, it does have k of these items where k is potentially random (no diminishing marginal utility for any of the items.)
How do I choose the assignment of bidders to auctions so that I maximize expected revenue across all auctions given 1) valuations of bidders for each item and 2) the distributions of k for all auctions?
Showing posts with label math. Show all posts
Showing posts with label math. Show all posts
Saturday, August 8, 2009
Sunday, May 24, 2009
Whitney Music Box
Click here to enlarge your penis
Damn that's beautiful. It's basically a visualization of integers and divisibility. Every time a group of dots crosses the white line, they share a common divisor, which would be the dot on the outside. Getting it to be a visualization of the real numbers (>= 1) would be interesting. Each point takes 1/n time units to go around once, assuming the outer dot (1) takes 1 time unit to go around once.
So what you would have is a space of functions: x = r cos n*t/2pi and y = r sin n*t/2pi where t is time, n is the number, and r is the radius of the circle that n goes around. Whitney's music box makes the intervals more or less equidistant... but man that's not mathematically elegant since you would need an infinitely long line to describe the real numbers. What would be nice is a function that converges to 1 at 0 and 0 at infinity. x = r(n) and y = r(n) should form a nice little spiral. 1/a^n works pretty well though it converges to 0 really freaking fast.
I don't know much Mathematica or whatever graphing package you kids are using these days... but it'd be pretty cool to see this in 3-d (taking time as another dimension.) Each of the functions would plot a spiral through time, but the space of functions would plot an infinite number of spirals, each spiraling at a different rate, with different distances from the origin line (where n = infinity.)
I wish I knew more topology.
http://www.coverpop.com/whitney/index.php?var=v12
Also pretty cool. Obviously, no two dots are ever on the white line at the same time.
Damn that's beautiful. It's basically a visualization of integers and divisibility. Every time a group of dots crosses the white line, they share a common divisor, which would be the dot on the outside. Getting it to be a visualization of the real numbers (>= 1) would be interesting. Each point takes 1/n time units to go around once, assuming the outer dot (1) takes 1 time unit to go around once.
So what you would have is a space of functions: x = r cos n*t/2pi and y = r sin n*t/2pi where t is time, n is the number, and r is the radius of the circle that n goes around. Whitney's music box makes the intervals more or less equidistant... but man that's not mathematically elegant since you would need an infinitely long line to describe the real numbers. What would be nice is a function that converges to 1 at 0 and 0 at infinity. x = r(n) and y = r(n) should form a nice little spiral. 1/a^n works pretty well though it converges to 0 really freaking fast.
I don't know much Mathematica or whatever graphing package you kids are using these days... but it'd be pretty cool to see this in 3-d (taking time as another dimension.) Each of the functions would plot a spiral through time, but the space of functions would plot an infinite number of spirals, each spiraling at a different rate, with different distances from the origin line (where n = infinity.)
I wish I knew more topology.
http://www.coverpop.com/whitney/index.php?var=v12
Also pretty cool. Obviously, no two dots are ever on the white line at the same time.
Saturday, February 14, 2009
Meh?
So I had what some might call a moment of clarity last night while throwing back that disgusting shot of scotch Luke ordered. I took a penetrating look at my life and realized that.... I am at heart an applied math person, not a pure math person.
I just find it a lot easier when problems are related back to concrete, real world situations. That's not to say I don't enjoy thinking abstractly. I just prefer diving into the abstract with a bungee cord instead of a parachute.
After that my rearranged hierarchy of math interests would be:
1. Complex systems
2. Probability and the non-artsy parts of statistics
3. Mathematics of structure (topology and geometry)
4. Theory of computation
5. Everything else
#1 completely dominates everything else (I would spend all my time on it if work didn't force me to focus more on #2 and #4,) so I'll elaborate a bit.
In the first half of the 20th century, we thought we had figured shit out. We thought that with the math we had, we could understand and potentially control things like: weather, the economy, and the human mind. Epic fail.
The math we have now is very much focused on studying fundamentally simple things... things that have nice properties like symmetry. Unfortunately, when you have a large number of agents following even a simple set of rules, crazy shit happens on the global level. For example, we have a very good understanding of particle interactions... but we might never be able to fully understand weather.
Well anyways...
I thought this was a pretty appropriate Valentine's Day entry. Math is my greatest unrequited love, which is saying a lot given my history of unrequited love. I enjoy the beauty and elegance of math, but I don't really have what it takes (intelligence, commitment and focus) to be a real mathematician. All I can do is sit by the side lines and skim papers that I only understand superficially.
Frowntown.
I just find it a lot easier when problems are related back to concrete, real world situations. That's not to say I don't enjoy thinking abstractly. I just prefer diving into the abstract with a bungee cord instead of a parachute.
After that my rearranged hierarchy of math interests would be:
1. Complex systems
2. Probability and the non-artsy parts of statistics
3. Mathematics of structure (topology and geometry)
4. Theory of computation
5. Everything else
#1 completely dominates everything else (I would spend all my time on it if work didn't force me to focus more on #2 and #4,) so I'll elaborate a bit.
In the first half of the 20th century, we thought we had figured shit out. We thought that with the math we had, we could understand and potentially control things like: weather, the economy, and the human mind. Epic fail.
The math we have now is very much focused on studying fundamentally simple things... things that have nice properties like symmetry. Unfortunately, when you have a large number of agents following even a simple set of rules, crazy shit happens on the global level. For example, we have a very good understanding of particle interactions... but we might never be able to fully understand weather.
Well anyways...
I thought this was a pretty appropriate Valentine's Day entry. Math is my greatest unrequited love, which is saying a lot given my history of unrequited love. I enjoy the beauty and elegance of math, but I don't really have what it takes (intelligence, commitment and focus) to be a real mathematician. All I can do is sit by the side lines and skim papers that I only understand superficially.
Frowntown.
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