Piotr Migdal
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Registered User
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A PhD student in Theoretical Quantum Optics at ICFO.
Alumnus of Physics and Mathematics at the University of Warsaw. Interested in quantum optics & quantum information, applied optics and mathematical modeling in psychology.
Dedicated to education of gifted schoolchildren (as both tutor and organizer). In free time enjoys photography, hiking and psychology (esp. cognitive science).
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2h |
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Upper bound on the difference between two elements of the Fiedler vector (a particular eigenvector of a graph Laplacian) I am afraid that it might be hard. Even for a circular graph with the same weights you get $|v_{0}-v_{n/2}|^2 = 4/n$ (for even $n$ and a particular Fielder vector), even though there are not connected ($W_{ij}=0$) and are laying on the opposite side of the graph. |
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3h |
answered | How to cite a sequence from The On-Line Encyclopedia of Integer Sequences (OEIS)? |
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22h |
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How to cite a sequence from The On-Line Encyclopedia of Integer Sequences (OEIS)? That said, the question is "what to do?" in a practical case, where I can write a line of a reference (as for other articles and books). |
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22h |
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How to cite a sequence from The On-Line Encyclopedia of Integer Sequences (OEIS)? In theory, a (hidden) inline may be a good option (to make it clear, self-contained and as now we don't need to pay for paper and ink). Sure, for it is also a boon to archeologists discovering our civilization. I am aware of some dangers (even the previous (i.e. research.att.com/~njas/sequences) link to OEIS is not working), but otherwise numbering seems to be consistent and I want to provide only a reference, not use it as a detailed argument. |
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1d |
asked | How to cite a sequence from The On-Line Encyclopedia of Integer Sequences (OEIS)? |
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May 14 |
awarded | ● Organizer |
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May 14 |
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Upper bound on joint Renyi entropy Related: mathoverflow.net/questions/116864/… |
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May 14 |
revised |
Upper bound on joint Renyi entropy edited tags |
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May 8 |
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Nth root of a matrix as an analytic function? @Federico So, you have my thanks in arxiv.org/abs/1305.1506. |
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Mar 18 |
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Invariants of a set of real unit vectors in 3d space, under SO(3) @Robert I know how to generate invariants of a given degree (see e.g. (2.1) from arxiv.org/quant-ph/0001116, referring back to Weyl's "The Classical Groups"). What is hard (as you said) is looking for relations between them. Also, I don't even know what is the minimal $k$ such that the ring of invariants is generated by polynomials of degree $\leq k$ (do you know or have any pointers?). But, as I understand, my specific case does not simplify the problem too much. For the dimension I know that one can use Molien series (but in my case one can check by hand that it is $2n-3$). |
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Mar 18 |
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Invariants of a set of real unit vectors in 3d space, under SO(3) @Robert In particular there seem to be sth like a set of symmetric polynomials in $\vec{v}_i\cdot\vec{v}_j$... |
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Mar 18 |
revised |
Invariants of a set of real unit vectors in 3d space, under SO(3) tags changed |
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Mar 18 |
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Invariants of a set of real unit vectors in 3d space, under SO(3) @Robert The story is that I'm working on quantum information. There a relation of permutation-symmetric state for n qubits (n two-dimensional complex vectors) to n points on 2d real sphere is called "Majorana's stellar representation" (it is basically: sym. subspace for d=2 -> polynomial -> factorization). (I should have said what I know, excuse me for that.) Such relation is specific to d=2 case; so I thought that maybe in this specific case there is an easier way to calculate invariants (clearly, there is at least an easy way to find some invariants). |
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Mar 2 |
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Relation between the eigenspace of a covariance matrix and eigenspace of correlation matrix Well, it's not the result yet. I don't know how one can squeeze out of it, besides for looking at smallest and largest $\sigma_{X_i}$. |
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Feb 27 |
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Relation between the eigenspace of a covariance matrix and eigenspace of correlation matrix As you see, $\Sigma = D R D$, where $D = \text{diag}(\sigma_{X_1}, \ldots \sigma_{X_n})$. |
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Feb 25 |
revised |
Nth root of a matrix as an analytic function? added 55 characters in body |
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Feb 25 |
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Nth root of a matrix as an analytic function? It was my initial thought, but in my case I cannot make such an assumption. |
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Feb 24 |
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Nth root of a matrix as an analytic function? However, it is not as simple - I cannot assume that the matrix is diagonalizable; so any function which just maps eigenvalues to their roots won't work. Take as a counterexample $A = [[1, 1], [0, 1]]$ and $f(z)=z$ (sure, another polynomial works for this $A$). |
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Feb 24 |
revised |
Nth root of a matrix as an analytic function? deleted motivation as it is not relevant anymore |
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Feb 24 |
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Nth root of a matrix as an analytic function? Yes, I'm fine with coefficients depending on the matrix. I don't know why I overlooked this solution. |
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Feb 24 |
asked | Nth root of a matrix as an analytic function? |
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Jan 22 |
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LU decomosition for ill-condition matrixes Mary: 1) Is it a 5x5 matrix (brackets are confusing)? 2) What do you mean by "ill-condition matrix"? 3) What do you mean by "suitable" decomposition? That is, what is your final goal? |
