Electromigrated nanogaps: Difference between revisions

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The '''in-crowd algorithm''' is a numerical method for solving [[basis pursuit denoising]] quickly; faster than any other algorithm for large, sparse problems.<ref>See ''The In-Crowd Algorithm for Fast Basis Pursuit Denoising'', IEEE Trans Sig Proc 59 (10), Oct 1 2011, pp. 4595 - 4605, [http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5940245], demo [[MATLAB]] code available [http://molnargroup.ece.cornell.edu/files/InCrowdBeta1.zip]</ref> Basis pursuit denoising is the following optimization problem:
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<math>\min_x \frac{1}{2}\|y-Ax\|^2_2+\lambda\|x\|_1.</math>
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where <math>y</math> is the observed signal, <math>x</math> is the sparse signal to be recovered, <math>Ax</math> is the expected signal under <math>x</math>, and <math>\lambda</math> is the regularization parameter trading off signal fidelity and simplicity.
 
It consists of the following:
 
# Declare <math>x</math> to be 0, so the unexplained residual <math> r = y</math>
# Declare the active set <math>I</math> to be the empty set
# Calculate the usefulness <math>u_j = | \langle r A_j \rangle | </math> for each component in <math>I^c</math>
# If on <math>I^c</math>, no <math>u_j > \lambda</math>, terminate
# Otherwise, add <math>L \approx 25</math> components to <math>I</math>
# Solve basis pursuit denoising exactly on <math>I</math>, and throw out any component of <math>I</math> whose value attains exactly 0. This problem is dense, so quadratic programming techniques work very well for this sub problem.
# Update <math> r = y - Ax</math> - n.b. can be computed in the subproblem as all elements outside of <math>I</math> are 0
# Go to step 3.
 
Since every time the in-crowd algorithm performs a global search it adds up to <math>L</math> components to the active set, it can be a factor of <math>L</math> faster than the best alternative algorithms when this search is computationally expensive.  A theorem<ref>See ''The In-Crowd Algorithm for Fast Basis Pursuit Denoising'', IEEE Trans Sig Proc 59 (10), Oct 1 2011, pp. 4595 - 4605, [http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5940245]</ref> guarantees that the global optimum is reached in spite of the many-at-a-time nature of the in-crowd algorithm.
 
==Notes==
{{reflist}}
 
[[Category:Mathematical optimization]]
 
 
{{Mathapplied-stub}}

Latest revision as of 16:07, 10 November 2014

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Some time in 1995 an American organization called Deckers Company patented the expression UGG and started production and advertising these Australian sheepskin boots by their subsidiary UGG Australia. Given that then UGG sneakers have come to be wildly well-known amid guys and gals of all ages all over the environment. The simple fact that these footwear from Australia do not attempt to conform to any pattern pattern or procedures of fashion have caught the creativity of discerning folks close to the planet, and pretty much everybody is functioning to seize their pair of these exclusive footwear. Acceptance has its own fallout and really certainly the sector is now flush with counterfeit models of the UGG Boots. If youve decided to purchase oneself a pair of boots from UGG Australia, you must to start with be confident that you have your fingers on a pair of real UGG boots.

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