unity – Mirror Networking; Instantiating Level Prefab That Has Network Identities as Children Objects

I am trying to instantiate level prefabs and level prefabs has some networked objects in them. For the networked objects i need to call NetworkServer.Spawn, but i simply want to instantiate a level prefab. If i just instantiate the level prefab, all the children that has network identities won’t be initialized. Since inherited network identities not avaible i can’t put network identity to the level prefab and then call NetworkServer.Spawn for the level prefab. What should be the proper way for this situation ?

forms – How can I deal with diverse gender identities in user profiles?

I was having a discussion with my housemate who is a data analyst by trade, and the conclusion that we came to is that there are two sensible options here, depending on the amount of work you personally want to do (we’re assuming here that the collection of gender data is actually useful to you, rather than simply of interest in which case it is almost always better to leave it out).

The simple option is to have three or four discrete options: Female, Male, Other, and possibly Prefer not to say. In my experience, this is the most acceptable option for gathering data while being both simple and inclusive – it acknowledges that there are people who don’t fit the gender binary, allows users to select a different option, and doesn’t overload your cisgendered users with lots of options. It also allows people to completely opt out if they really don’t want to answer (the standard objection is that it’ll negatively impact your data collection, but in practice it probably doesn’t make much of a difference). Note that if gender identity is particularly important to your application, then this may not be the most sensible or inclusive option.

The ideal but more complex option is to have a textbox and suck it up – it’s a data sanitisation problem. A simple find/replace on your dataset will be able to lump your users into a group of man/male/boy responses, a group of woman/female/girl responses, and a group of assorted other responses. Crucially if you’re doing demographic analysis, whatever is left over probably isn’t statistically significant at an individual level so in your analysis it is acceptable to put them in an internal Other category. You can then preserve that minority data for further study should you find you need it.

Alternatively, as noted in the comments, it may be possible to combine the two approaches. Once a user selects your Other option, you could then display a text box which allows them to specify their gender identity exactly. This has the benefit of minimising cognitive load on cisgendered users while also capturing specific minority data. The downsides are that you may still run into issues sanitising this data to make it useful, and your form must be able to handle revealing a hidden element.


Gender is the correct label for this field, from a descriptive point of view and from a data collection point of view. You’d be surprised how many people think it’s hilarious to answer Sex: with “Yes please”.

If you choose to go with the simple dropdown/radio button approach, then Other is probably the most appropriate label for the third group. It is easily understandable, and non-exclusive in terms of what it might represent. Transgender is probably not an appropriate label here unless you include additional ones because it excludes people outside the binary who are not transgender or who do not view the label as appropriate for them, and it doesn’t actually tell you the respondent’s gender (transgender just tells you their gender is not the same as their assigned sex at birth). The problem with the use of the word “other” is that it is exclusionary and can potentially feel like the user is being shoved into a box of leftovers – not an ideal experience! For that reason, a text box is probably preferred if you want to make sure you’re being inclusive.

Think Outside The Box mirrors these recommendations and has some other interesting guidelines for form construction.

What does it mean that Ikev1 (IPSec) protects peer identities in main mode?

Does it mean that the source IP is replaced with something else (like if in IP spoofing) so intermediate routers don’t know who is sending the packet?

dg.differential geometry – Proving some identities about the time derivative of the k-th covariant derivatives of scalar curvature under normalized Ricci flow on surfaces

I’m trying to prove the following identities (under the normalized Ricci flow on surfaces, on which $partial_t g = (r-R)g$ holds true, where $r$ denotes the average scalar curvature and has the same sign as the Euler characteristic):

$$
frac{partial}{partial t}left(nabla^{k} Rright)=Delta nabla^{k} R-rleft(nabla^{k} Rright)+sum_{j=0}^{lfloor k / 2rfloor}left(nabla^{j} Rright) otimes_{g}left(nabla^{k-j} Rright)
$$

$$
begin{array}{l}
frac{partial}{partial t}(|nabla^k R |^2) =Deltaleft|nabla^{k} Rright|^{2}-2left|nabla^{k+1} Rright|^{2}-(k+2) rleft|nabla^{k} Rright|^{2}
+left(nabla^{k} Rright) otimes_{g}left(sum_{j=0}^{lfloor k / 2rfloor}left(nabla^{j} Rright) otimes_{g}left(nabla^{k-j} Rright)right)
end{array}
$$

where by $A otimes_g B$ we refer to any tensor field which is a finite linear combination of contractions and metric contractions of the tensor product $A otimes B$. Now, I’ve already proven that the following hold:

$$partial_{t} nabla R=Delta nabla R+frac{3}{2} R nabla R-r nabla R$$
$$
nabla^{n} Delta R-Delta nabla^{n} R=sum_{j=0}^{lfloor n / 2rfloor}left(nabla^{j} Rright) otimes_{g(t)}left(nabla^{n-j} Rright)
$$

$$
begin{array}{c}
nabla^{n} R^{2}=displaystyle{sum_{j=0}^{lfloor n / 2rfloor}left(nabla^{j} Rright) otimes_{g(t)}left(nabla^{n-j} Rright) }\
left(frac{partial}{partial t} Gammaright) otimes_{g(t)}left(nabla^{j} Rright)=(nabla R) otimes_{g(t)}left(nabla^{j} Rright)
end{array}
$$

$$
frac{partial}{partial t}left(nabla_{k_{1}} nabla_{k_{2}} ldots nabla_{k_{n}} Rright)=nabla_{k_{1}}left{partial_t nabla_{k_{2}} ldots nabla_{k_{n}} Rright}-sum_{l=2}^{n}left(partial_{t} Gamma_{k_{1} k_{l}}^{m}right) nabla_{k_{2}} ldots nabla_{k_{l-1}} nabla_{m} ldots nabla_{k_{n}} R
$$

So, to prove the first formula for the evolution of $nabla^k R$, I used recursive applications of this last identity just above, but I’d like someone to check my work. I noticed there would be terms of the form:

begin{align*}
nabla_{k_1} cdots nabla_{k_{n-1}}(partial_t nabla_{k_n} R) &= nabla_{k_1} cdots nabla_{k_{n-1}}(Delta nabla_{k_n}R + frac{3}{2} R nabla_{k_n} R – r nabla_{k_n R}) \
&= nabla_{k_1} cdots nabla_{k_{n-1}} ( nabla_{k_n} Delta R + Sigma + frac{3}{2} R nabla_{k_n} R – r nabla_{k_n R} )\
&=nabla^k Delta R + Sigma – r(nabla^{k} R) \
&=Delta nabla^k R + Sigma – r(nabla^k R)
end{align*}

where by $Sigma$ I’m denoting $displaystyle{sum_{j=0}^{lfloor k / 2rfloor}left(nabla^{j} Rright) otimes_{g}left(nabla^{k-j} Rright)}$ to avoid taking up too much space. The remaining terms are of the form:

$$ begin{aligned}
&left(partial_{t} Gammaright) otimes nabla^{k-1} R=nabla R otimes nabla^{k-1} R=Sigma\
&nabla^r(partial_t Gamma) otimes nabla^{k-r-1} R = nabla^{r+1}R otimes nabla^{k-r-1}R = Sigma end{aligned}
$$

and so we have proved the first identity. But I didn’t manage to prove the second one. We have:

$$begin{aligned}
frac{partial}{partial t}left|nabla^{k} Rright|^{2} &= frac{partial}{partial t}left(g^{i_1 p_1} cdots g^{i_k p_k} nabla_{i_1} cdots nabla_{i_k} R nabla_{p_1} cdots nabla_{p_k} Rright) \
&=(R-r)k |nabla^k R |^2 + 2 langle nabla^k R, partial_t(nabla^k R) rangle
end{aligned}
$$

and since

begin{align*}
2 langle nabla^k R, partial_t(nabla^k R) rangle &= 2 langle nabla^k R, Delta nabla^k R + Sigma – r nabla^k R rangle \
&=2 langle nabla^k R, Delta nabla^k R rangle + 2 langle nabla^k R, Sigma rangle – 2r |nabla^k R|^2
end{align*}

We’re then left to prove that:

$$2 langle nabla^k R, Delta nabla^k R rangle = -kR |nabla^k R|^2 + Delta |nabla^k R|^2 – 2 |nabla^{k+1} R|^2$$

but I’ve been stuck on this one for a while. I’d really appreciate some help on this! Thanks in advance.

fourier analysis – Approximate Identities on the Unit Disk and going beyond a power series’ radius of convergence

Let $left{ a_{n}right} _{ngeq0}$ be a bounded sequence of complex numbers, so that the power series $fleft(zright)=sum_{n=0}^{infty}a_{n}z^{n}$ has a radius of convergence $geq1$. Additionally, suppose that $fleft(0right)neq0$, and that $fleft(omegaright)=0$ for some complex number $omega$ with $0<left|omegaright|<1$. Let $nu$ be a positive non-integer real number and let $g_{nu}left(zright)=left(fleft(zright)right)^{1/nu}$. Since $f$ is non-vanishing at $z=0$, $g_{nu}left(zright)$ has a power series expansion: $$g_{nu}left(zright)=sum_{n=0}^{infty}a_{n}left(frac{1}{nu}right)z^{n}$$ with a radius of convergence $r_{nu}inleft(0,1right)$. In particular, thanks to the zero of $f$ at $omega$, we have that $r_{nu}<left|omegaright|$.

Next, let: $$g_{nu,r}left(tright)=left(fleft(re^{2pi it}right)right)^{1/nu}$$

Since $f$ is holomorphic on the open unit disk, $g_{nu,r}in L^{p}left(mathbb{R}/mathbb{Z}right)$ for all $pinleft(1,inftyright)$ and all $rinleft(0,1right)$.

Now, let $left{ K_{r}right} _{r>0}$ be a family of good kernels/an approximate identity on $mathbb{R}/mathbb{Z}$ (ex: $K_{r}left(tright)=P_{r}left(tright)=sum_{ninmathbb{Z}}r^{left|nright|}e^{2npi it}$, the Poisson Kernel), and consider the integral: $$left(K_{rho}*g_{nu,r}right)left(tright)=int_{0}^{1}K_{rho}left(t-xright)g_{nu,r}left(xright)dx$$

Because of the integrability of $g_{nu,r}$ for each $rinleft(0,1right)$, the approximate identity property of the $K_{rho}$s guarantees that $lim_{rhouparrow1}left(K_{rho}*g_{nu,r}right)left(tright)=g_{nu,r}left(tright)$ for almost every $tinmathbb{R}/mathbb{Z}$ (in particular, the limit exists for every $t$ at which $g_{nu,r}$ is continuous). When $r<r_{nu}$, the power series of $g_{nu,r}$ gives us an absolutely convergent Fourier series for $g_{nu,r}$: $$g_{nu,r}left(xright)=sum_{n=0}^{infty}a_{n}left(frac{1}{nu}right)r^{n}e^{2npi ix},textrm{ }forall xinmathbb{R},textrm{ }forallleft|rright|<r_{nu}$$ consequently, we can compute $left(K_{rho}*g_{nu,r}right)left(tright)$ term-by term using this series representation, and hence (writing $eleft(tright)=e^{2npi it}$): $$left|rright|<r_{nu}Rightarrow g_{nu,r}left(tright)=lim_{rhouparrow1}left(K_{rho}*g_{nu,r}right)left(tright)=lim_{rhouparrow1}sum_{n=0}^{infty}a_{n}left(frac{1}{nu}right)r^{n}left(K_{rho}*eright)left(tright)$$ for all $t$ at which $g_{nu,r}$ is continuous. However, when $left|rright|>r_{nu}$, the series for $g_{nu,r}$ fails to converge, and as such, the right-most of the above equalities no longer holds. That is, if we think of the limit: $$lim_{rhouparrow1}sum_{n=0}^{infty}a_{n}left(frac{1}{nu}right)r^{n}left(K_{rho}*eright)left(tright)$$ as a generalization of the abel method of summing divergent series (with respect to the parameter $rho$), while $lim_{rhouparrow1}left(K_{rho}*g_{nu,r}right)left(tright)$ still equals $g_{nu,r}left(tright)$ almost everywhere, this equality does not appear to be realizable as an abel-style summation of a divergent series.

All that being said, I have two questions:

(I) Let $rinleft(r_{nu},1right)$, so that $fleft(zright)$‘s power series about $z=0$ converges for $left|zright|=r$, but $g_{nu}left(zright)$‘s power series about $z=0$ diverges for all $left|zright|=r$. Under these hypotheses, as discussed above, the limit $lim_{rhouparrow1}left(K_{rho}*g_{nu,r}right)left(tright)$ exists for almost every $t$. Is there a way to express the value of the limit (when it converges to $g_{nu,r}$) in terms of power series coefficents of $g_{nu,r}$ (maybe expanded about some point other than $0$), or something similar? Here, case I’m most interested in is when $K_{rho}=P_{rho}$, the Poisson Kernel. So understanding that particular situation is paramount, though information about the more general case would also be desirable.

(II) The Parseval-Gutzmer formula establishes the identity: $$int_{0}^{1}left|sum_{n=0}^{infty}c_{n}left(re^{2npi it}right)^{n}right|^{2}dt=sum_{n=0}^{infty}left|c_{n}right|^{2}r^{2n}$$ for all $rgeq0$ which are less than the radius of convergence of the power series $sum_{n=0}^{infty}c_{n}z^{n}$. For our function $fleft(zright)$, this gives: $$int_{0}^{1}left|fleft(re^{2pi it}right)right|^{2/nu}dt=sum_{n=0}^{infty}left|a_{n}left(frac{1}{nu}right)right|^{2}r^{2n},textrm{ }forall rinleft(0,r_{nu}right)$$ where, recall, $r_{nu}$ is the radius of convergence of the power series of $f^{1/nu}left(zright)$ about $z=0$. Since $tmapsto f^{1/nu}left(re^{2pi it}right)$ is bounded for all $rinleft(0,1right)$, however, the left-hand side of this identity exists even for $rinleft(r_{nu},1right)$. Is there a way to “correct”/alter the right-hand side of the identity so as to extend it to all $rinleft(0,1right)$? And if so, how would one do this?

co.combinatorics – Combinatorics and geometry underlying a refined Pascal matrix/Newton identities

The partition polynomials of OEIS A263633 give the coefficients of the power series/o.g.f of the multiplicative inverse (reciprocal) of a power series/o.g.f. and so give the Newton identities for transforming between complete homogeneous symmetric polynomials/functions and elementary symmetric polynomials/functions. Certain Koszul duals are related to this.

The algebraic combinatorics of the complementary reciprocal of a Taylor series/e.g.f. is governed by the antipode/refined Euler characteristic classes of the permutahedra or, equivalently, by surjective mappings, so I have an indirect geometric combinatorial interpretation of ‘scaled’ versions of the Newton identities, but I’m looking for more direct interpretations.

What combinatoric/geometric structures are enumerated by the integer coefficients of these partition polynomials for conversion of an o.g.f. into a reciprocal o.g.f.?

fa.functional analysis – Doubt from a paper on approximate identities

I am currently reading this paper on approximate identities of Ternary Banach algebras. Assume that $(A, (.,.,.))$ is a ternary Banach algebra. A bounded net $(e_{alpha}, f_{alpha})$ is said to be left-bounded approximate identity for $A$ if $lim_{alpha}(e_{alpha}, f_{alpha},a)=a$ for all $a in A$. Can someone clarify my following doubts from the same paper:

What is the definition of bounded net? Also at many places in the same paper for instance in Theorem $2.2$, the product $e_{alpha}f_{alpha}$ is used. What is the meaning of product in ternary Algebra?

All these doubts are not explained in paper. Thank you very much in advance!

Get identities of authors of wordpress.com websites?

How can I found out the real identities of authors of wordpress.com websites?

For example, there is a wordpress.com website which seems to be involved in terrorist activities:

https://staatsterrorlive.wordpress.com

I have tried with several domain tools but got only the data of wordpress.com itself.

domain-driven design: can entity identities be written in a DDD world?

When designing entities, I instinctively put their identities as read-only properties.

class MyEntity
{
    MyEntity(Id id) { Id = id; }

    Id { get; }
}

But I wonder, can identity be a property of writing?
Should we consider the controller / pointer itself to be part of the identity or not?

I did not work with Entity framework, but it seems that they expose identities as properties of writing.
Do you see any problem with this fact?

Hyperledger tissue nodeOU not activated. Identities cannot be distinguished

When I try to approve a chaincode package, a timeout error appears.
Peer records show the following warnings. Although I have the config.yaml file in the MSP directory with NodeOUs enabled for true, it says NodeOus not enabled. Can anyone help me solve this problem? I use Hyperledger Fabric 2.0 binaries.
identity 0 does not satisfy principal: The identity is not a [PEER] under this MSP [org1MSP]: NodeOUs not activated. Cannot tell apart identities.

bric"],"L-ST-C":"[]-[]-[US]","MSP":"org1MSP","OU":["peer"]} isn't eligible for channel twoorgschannel : implicit policy evaluation failed - 0 sub-policies were satisfied,
but this policy requires 1 of the 'Readers' sub-policies to be satisfied```