I have a math question

[Dari]

My boss gave me an economic research paper for me to summarize for him. But it has a type of math I do not understand. And I have until Monday to do so. Anyone here can show me a path to understanding the Hessian of heat kernel? At the cut locus. Is it a branch of stochastic processes? I've never heard it about it before when I took that class. Or is it in differential geometry? If so, what's a good book to get? I cannot even find a wiki page on this subject.

EDIT: Sorry, it's cut locus, not Locus Point. Been watching season 2 of The Wire.

 

[disappoint]

A Dari math thread is something I had feared far more than the charlatan doomsday proclamations about CERN making black holes and ending us all with the LHC. Don't worry humans I'll protect you.

Dari: NO

 

[Hacp]

Hessian : http://en.wikipedia.org/wiki/Hessian_matrix
Heat Kernel: http://en.wikipedia.org/wiki/Heat_kernel

Hessian of Heat Kernel is then taking the second order derivative of some heat kernel h(t,x,y). No idea what a cut locus is.

 

[JManInPhoenix]

Hessian : http://en.wikipedia.org/wiki/Hessian_matrix
Heat Kernel: http://en.wikipedia.org/wiki/Heat_kernel

Hessian of Heat Kernel is then taking the second order derivative of some heat kernel h(t,x,y). No idea what a cut locus is.

That looks like something I did in a discrete mathematics course in college years ago. About a week after that course, I completely forgot how to do any of it (actually just learned enough to pass the tests, I didnt really "learn" it).

 

[Dari]

Hessian : http://en.wikipedia.org/wiki/Hessian_matrix
Heat Kernel: http://en.wikipedia.org/wiki/Heat_kernel

Hessian of Heat Kernel is then taking the second order derivative of some heat kernel h(t,x,y). No idea what a cut locus is.

heat equation is pde. Cut locus I have no idea. Googling hessian of heat kernel at cut locus yields something entirely different. Maybe an abstract generalization of something commonly known.

 

[KLin]

42

 

[Schmide]

This seems to be a great explanation of it.

http://www.lems.brown.edu/vision/Presentations/Wolter/index.html

esp http://www.lems.brown.edu/vision/Presentations/Wolter/figs2.html

The only place I've seen Hessian matrices used is in image edge detection.

 

[Printer Bandit]

Seriously, some math is so abstract, people could just be making that shit up and no one would even know.

 

[Dari]

This seems to be a great explanation of it.

http://www.lems.brown.edu/vision/Presentations/Wolter/index.html

esp http://www.lems.brown.edu/vision/Presentations/Wolter/figs2.html

The only place I've seen Hessian matrices used is in image edge detection.

Thank you extremely much. Now I have something to work with.

 

[yllus]

What kind of weird company do you work for that they have amateurs doing economic analysis (or at least summaries of them)?

 

[JEDIYoda]

What kind of weird company do you work for that they have amateurs doing economic analysis (or at least summaries of them)?

Those so called amateurs obviously know more than you do about the subject...enlighten us most wise one.....

 

[Dari]

What kind of weird company do you work for that they have amateurs doing economic analysis (or at least summaries of them)?

This is outside our purview. If anything this probably interested him but he did not understand it and asked me to summarize it for him. I'm guessing this came out of a journal somewhere or someone he knew worked on it. The math is difficult but this is how it is with economics. Mathematicians or Statisticians invent something then physicists and economists apply it to their respective literature.

 

[Fenixgoon]

well, your heat kernel is a solution to a differential equation.

the hessian matrix is just a matrix of partial differentials.

1,1 = d2F/dx2
2,2 = d2F/dy2

1,2 and 2,1 are equal since mixed partial derivatives are identical.

pretty straightforward actually, as long as you know how to differentiate.

 

[Dari]

Been meaning to update this but the answer lies in differential geometry. The cut locus, in layman's term is the polar opposite of where a point is on a sphere.

 

[SKORPI0]

ANALYSIS OF THE CUT LOCUS VIA THE HEAT KERNEL (pdf-13 pages)

Abstract.
We study the Hessian of the logarithm of the heat kernel to see
what it says about the cut locus of a point. In particular, we show that the
cut locus is the set of points at which this Hessian diverges faster than
t
−
1
as
t

0. In addition, we relate the rate of divergence to the conjugacy and
other structural properties.

 

[Dari]

ANALYSIS OF THE CUT LOCUS VIA THE HEAT KERNEL (pdf-13 pages)

Thanks but where were you one month ago?

 

[brianmanahan]

A Dari math thread is something I had feared far more than the charlatan doomsday proclamations about CERN making black holes and ending us all with the LHC. Don't worry humans I'll protect you.

Dari: NO

DARI DONT DO IT /pleads

 

[Schmide]

Been meaning to update this but the answer lies in differential geometry. The cut locus, in layman's term is the polar opposite of where a point is on a sphere.

I would say in layman's terms - A cut locus is the arcs equally distant from 2 points projected onto a line for the purpose of producing a geodesic shape.

 

[MongGrel]

And then the earth explodes.

:biggrin:

 

[Printer Bandit]

what does geometry have to do with economics?

 

[brianmanahan]

what does geometry have to do with economics?

dari is the glue that joins all things together

 

[Dari]

what does geometry have to do with economics?

That's like asking what does mathematics have to do with econ. ..

 

[EliteRetard]

Since this thread came up again I'm going to pretend I knew the answer all along...because I'm a smart smart man. Best part is, none of you will know what's true or false.

 

[shortylickens]

An ice cream shop sees 212 customers during its 12 hour work day.

What is the likelihood that 5 customers will walk thru the door in the next 8 minutes?

 

[EliteRetard]

An ice cream shop sees 212 customers during its 12 hour work day.

What is the likelihood that 5 customers will walk thru the door in the next 8 minutes?

They actually ran out of ice cream, so I couldn't get my pie-shake.