The problem is as follows:

$\displaystyle\min_{V}$ trace(**$V^TH^T\Phi HV$**)$\\$ s.t. $V^TV=I_d$ when $H$ is some arbitrary matrix of size $N \times M$, full column rank matrix, $V$ is a $M \times d$ matrix and $\Phi$ is $N \times N $ symmetric and positive semidefinite matrix.

When $H$ is known, the solution is given by the eigenvectors corresponding to $d$ minimum eigenvalues of $ H^T\Phi H$.

Are there any ways or techniques or ideas already solved on this in the absence of $H$? The problem may sound simple to some of you but I am sorry about that.

Thank you for your suggestions and information about the existing techniques.

]]>this message is for people who’s interesting in PRIME numbers finding algorithm , i have developed an algorithm that can find all the consecutive impair composite numbers in a given interval , we can conclude that all impairs number remaing are prime,this algorithm gives the consecutive impairs composite and then we can conclude the twin prime numbers in any interval , the algorithm has been tested and it’s so efficient.i wanted to type ]]>

I think I can show that relative to the set of all primes up to N, where N is any finite number, there is an infinite quantity of consecutive twin primes. (Adjacent pairs of twin primes). Or, to put it another way, that no finite amount of prime factors is sufficient to guarantee that there are no more consecutive pairs of twins.

My question is: Would this be trivial or interesting? I keep changing my mind, and don’t have the skills to be sure either way. Perhaps it’s easy to show this and it’s been done a thousand times. I’d be grateful if someone can set me straight. Thank you.

If there is better place to discuss this I’ll happily move there.

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I’m working on a project called Collaborating Minds, which has a lot in common with the Polymath project. Our founders followed the original Polymath project in 2009, and it shaped a lot of their thinking on online collaboration. (You can read some of their thoughts on the Polymath project and Michael Nielsen’s book here: http://www.cminds.net/2013/10/reinventing-discovery-and-collaborating-minds/)

Collaborating Minds is trying to do two things: 1) create a cloud-based platform that facilitates group problem-solving, and 2) foster a community of collaborative problem-solvers, people who who like to help and be helped, and who are willing to offer their perspective on a wide range of problems. To get a sense of what we’re doing, you can watch a short video here: http://www.cminds.net/2013/08/a-two-minute-and-12-second-introduction-to-collaborating-minds/

It would be great to hear from people who have been though Polymath and get your feedback on our model — if you think the community needs to come with the platform, any suggestions for fostering group collaboration online, or pitfalls to avoid. You can also email me at daphna@cminds.net if you prefer. Thanks in advance and let me know if there’s more information that I can provide as well!

]]>I have posted several pages on my math research project: http://theses.portonvictor.org/node/4 – feel free to add yours also.

The site is ideal for posting possible theses topics for students as well as cutting edge research for math persons. For a topic a user may mark himself as an adviser, which could help students.

Among mathematics this site is also going to list open source software proposals and whatever general utility projects.

Well, this project needs its own domain name. Please somebody donate a domain and help with hosting.

]]>*[Corrected, thanks – T.]*