bio | website | regularize.wordpress.com |
---|---|---|
location | Braunschweig, Germany | |
age | 36 | |
visits | member for | 4 years |
seen | 5 hours ago | |
stats | profile views | 1,706 |
Professor at TU Braunschweig.
Area: Inverse problems, regularization theory, applied functional analysis, mathematical image processing.
Jun 5 |
comment |
How many facets can $\{\|D^T x\|_1\leq 1\}$ have?
@eins6180: Not quite. I am especially interested in the scaling in $p$ and the one constraint $\|D^Tx\|_1\leq 1$ can be formulated as $2^p$ inequalities (doing case distinction over the absolute values in the the sum). However, in the construction I did usually many of these inequalities are inactive… I also guessed that this problem may be hard but had the hope that the special construction of the polytope as a kind of distorted one-norm would make the problem simpler… |
Jun 5 |
comment |
Is this statement which relates the Fourier transform of a function to its singularities correct?
I found the formulation of $x_t$ and $y_t$ a bit confusing. Similarly to Brendan Murphy suggestion, I think a more appropriate formulation would be to use complex coordinates and investigate the function $\omega \mapsto \int_0^\omega \hat f(\Omega)\exp(t\Omega) d\Omega$ (the real and imaginary part of this are $X_t$ and $y_t$. |
Jun 5 |
revised |
How many facets can $\{\|D^T x\|_1\leq 1\}$ have?
Added an argument for the existence of $B$ and a guess for $n=2$. |
Jun 4 |
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Choice of MIP (mixed integer programming) solver
Probably you want to try out scicomp.stackexchange? I suspect that the question is a better fit over there... |
May 29 |
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Convergence of iterated stochastic matrices
Doesn't this answer a different question? I thought, the OP asked about the convergence of $\|M_n^n-M_n\|$ to zero... |
May 27 |
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Are norms intrinsically $\mathbb{R}$-valued?
I would say that norms are intrinsically $[0,\infty[$-valued. |
May 27 |
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Are norms intrinsically $\mathbb{R}$-valued?
What is a rig?$\mbox{}$ |
May 23 |
reviewed | Approve suggested edit on Defining Multiplication in Polynomials over Rings of Matrices |
May 22 |
reviewed | Edit suggested edit on $(1+\epsilon)$-injective Banach spaces, complex scalars |
May 22 |
revised |
$(1+\epsilon)$-injective Banach spaces, complex scalars
The reader should be warned first that the proof is wrong |
May 21 |
reviewed | Approve suggested edit on Exact formulas for the partition function? |
May 16 |
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Distance between probability amplitude functions
Reminds me a bit of the Hellinger distance (en.wikipedia.org/wiki/Hellinger_distance). |
May 9 |
comment |
What is the oldest open problem in mathematics?
This is not a big-list question… |
May 8 |
comment |
How many facets can $\{\|D^T x\|_1\leq 1\}$ have?
@CristóbalGuzmán Sure: both functionals are positively homogeneous, hence determined by their 1-levelset. Moreover, the set $\{\|D^Tx\|_1\leq 1\}$ is a centrally symmetric polytope, hence described by an intersection of finitely many half spaces, each of these appearing two times with opposite signs. Sets of this kind can be described as $\{\|B^Tx\|_\infty\leq 1\}$. |
May 2 |
comment |
How to correct an error in a submitted paper?
"we're all human": If you speak of authors of mathematical paper then, technically, this is not true (math.rutgers.edu/~zeilberg/ekhad.html). Speaking of, e.g., MO users I am not sure either… |
Apr 25 |
asked | How many facets can $\{\|D^T x\|_1\leq 1\}$ have? |
Apr 25 |
comment |
The Hidden Aspect of Set Theory
Regarding the reality of mathematical objects I found the chapter "Numbers and Abstraction" in Gowers' "Mathematics: A Very Short Introduction" eye opening. His point is basically: It is not of interest to mathematicians what some mathematical object is but what it does. |
Apr 21 |
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Inverse problem with a rank-1 update
I do not get what your tradeoffs are exactly... Also, what is a rank-one decomposition? |
Apr 21 |
answered | Distance between two networks |
Apr 10 |
comment |
Why quintics are Calabi-Yau?
I find the question "Why quintics are Calabi-Yau" rather cryprtic. Would you mind to give some more information? |