singular – Impossible to launch a GARCH BEKK in r

I'm trying to estimate a bivariate GARK BEKK with the mgarchBEKK R pack, but that does not work. The problem is that "H is singular

The error is:

Error in buff.par.transposed[[tmp.count + 1]]% *% as.matrix (eps[count -:
non-compliant arguments
In addition: Warning message:
In BEKK (diferenca.taxas1mo, order = c (1, 1), method = "BFGS"):
negative inverted hessie matrix element

My code is:

bekk.taxas1mo <-BEKK (diferenca.taxas1mo, order = c (1,1), method = "BFGS")

One thing that made me think is that the series I'm working on is about 1/4 zeros. Anyone know if it's a problem?

Is mgarchBEKK a good package to use?

Thank you in advance.

custom publication types – WordPress API – How to display different data in singular or plural responses

I have a "product" type custom publication that returns quite a bit of data in the API response, up to 400 publications with many nodes. Almost all data comes from advanced custom fields (I use the ACF plug-in to API to expose it).

On the 'products' page, I just need to indicate the title and the product image. Is there a way to remove all other fields when requesting all products with https://example.com/wp-json/wp/v2/productbut leave this data in place when you request a specific product with https://example.com/wp-json/wp/v2/product/123 ?

Linear algebra – How to know if a matrix is ​​poorly conditioned or singular using the system function of Eigens (or composition of LUD)?

I use the Eigensystem function and I try to determine if it is singular or poorly conditioned. I use the function as follows:

Electronic system[A]
Composition of LUD[A]

And it returns a list of eigenvalues ​​and eigenvectors, as well as the condition number last. Should the number of conditions be high or low so that we can consider that the corresponding matrix is ​​badly conditioned?

On a matrix, the condition number is $ infty $I'm sure this is badly packaged, but the other numbers are something like 14.555555, and 120.4, etc.

Singular points of nonlinear EDO

I do not know how to proceed with that. Given this non-linear ODE$$ partial_ {t} u (t, x) = cot (t) left[frac{1}{8u(t,x)}left(6u(t,x)^2-4A(x)u(t,x)+B(x)right)right]$$
for $ t in (0, pi) $, can I calculate the behavior of $ u (t, x) $ for $ t to0, pi $?

Aggressive Geometry – Calculates the Kodaira dimension of a singular hypersurface

For a smooth projective hypersurface $ H subseteq mathbb {P} ^ n $ degree $ d $ we can calculate its dimension Kodaira $ kappa (H) $, and finds
$$ kappa (H) =
begin {cases}
– infty qquad & mbox {if} d < n +1,\ 0 &mbox{if } d = n+1,\ dim H &mbox{if } d > n + 1.
end {cases} $$

And if $ H $ is not smooth? Can we say something about its Kodaira dimension, or even reasonably calculate something we can call "Kodaira dimension"?

I've never seen that canonical divisors defined on smooth varieties, so I do not know how to proceed to the singular case.

algorithms – Blind sorting of an array with a singular sort function?

I am preparing some interviews and I came across a question that really shocked me, and that did not provide me with an answer.

The premise of the question was:

You receive an unsorted A chart of size n. You are not allowed to access the table, read values ​​or compare values.

The only way you can interact with this array is to use a BlockSort () function, so that the BlockSort (index) call automatically sorts the elements within the inclusive limits of [i,i+u] for some u u arbitrary but fixed, such as u≥1.

Sort A with O ((n / u) ^ 2) calls to BlockSort.

My initial approach to this issue was to emulate bubble sorting, with the exception of blocking calls to BlockSort, so that each successive call overlaps an element of the previous call (for example, BlockSort (0, u ), BlockSort (u, 2u) .. .etc.) Then, after having iterated once in this way in the table, you end up with the global maximum at the end of the array and an unsorted array of size n-1 , and then you can solve the problem recursively.

This has a time complexity of O ((n ^ 2) / u) however.

I threw an hour or so on the problem, and I do not see how they managed to get O ((n / u) ^ 2).

Is there anything I could think of to get to the answer?

Agalgic Geometry – The p-adic Hodge Theory for Singular Projective Varieties

In the p-adic Hodge theory, there are comparison theorems linking, for example, the crystalline cohomology of the special fiber of a smooth clean family to the étale cohomology of the rigid analytical generic fiber.

The so-called rigid cohomology extends the crystalline cohomology to the case of not necessarily smooth schemes. For separate finite type schemes, rigid cohomology groups satisfy reasonable finiteness properties (as opposed to crystalline cohomology). It may not be totally unreasonable to ask the following question: if rigid cohomology is considered, does p-adic Hodge theory make sense for families of singular special fiber schemes? ?

Singular cohomology fits into symplectic cohomology

Viterbo's theorem on cotangent beams $ M = T ^ * N $ tells you in particular that singular cohomology $ H ^ * (M) $ is integrated into $ SH ^ * (M) $ via the $ c ^ * $ map. Have a variety of Weinstein (or more generally a variety of Liouville) $ M $are there any other examples when this happens?

Is it possible to create a link to a singular and specific Google search result?

I know how to link to general Google query results, but is there a way to link the user to a specific Google result?

For example: search for Google on www.website.com and show the user only the first result to click on.

If $ G $ is NOT a full-rank matrix, the minimum singular value $ sigma $ Zero?

I'm pretty sure but I have not found any proof. Is it true?