T7 vs pBAD promoter strength

Question: How do pBAD and T7 promoter strengths compare when pBAD is induced under conditions which would lead to its highest strength? Are there any papers that compare the two inducible promoter systems?
Answer: The exact numbers depend on the protein.
In my hands, I would say between the pAraBAD and a pLac-T5 you can expect some fold improvement and pAraBAD and a pT7 promoters you can expect about an order of magnitude… but there are two big caveats.
First, pET and other T7 driven plasmids do not work in K-12 strains (without the pTARA) so BL21 is generally used. BL21 is much better generally than K-12 strains (more primary metabolites cf. omics paper) for a lot of things including protein expression. The chaperone balance is difference, so you will get differences from that too —if you have used the TAKARA plasmid team you will have notice how quirky protein expression optimisation can be.
Second, if your protein has a cofactor you have a major problem. FeS clusters, PLP, heme or even O2 (for maturation of GFP, say) become rate limiting and overexpressing the protein can make it highly toxic and you might be in a bigger pickle than with a lower level promoter. In my thesis, I added pyridoxine to a pBAD expression, because it gave an improvement.
Footnote: If the expression levels are really bad, changing promoter might not be that great as the assumption of linearity might not hold.
If heterologous and not codon optimised, consider using pRARE.
If insoluble, consider using ethanol shock and the TAKARA chaperon plasmid team.
If oxygen sensitive, alas, doing expression and purification anaerobically.
Comment: thanks for taking a stab at this old question... I know that it may be difficult, but do you think you could add some links/references to some of the details you mention in your answer? We always appreciate references/links on BiologySE - and it will definitely improve the strength of your answer. Thanks!
Answer: The best reference I could find is a book chapter (available here as a .pdf) from a book on optimizing the expression of membrane proteins that argues for T7. Although they don't appear to reference a source for that specific claim, some of the references close by could be helpful. It seems as though this applies in general, not just to membrane proteins. They bring up limitations of the araBAD system as well:

However, careful studies of the araBAD promoter by Siegele et al. [20] and Giacalone et al. [21] both agreed that at subsaturating levels of l- arabinose, protein expression cultures contain a mixed population with only some of the cells expressing protein. In addition, the potential for protein overexpression is generally lower when a pBAD vector is compared to T7-mediated expression from a pET construct.
Answer: In general, T7 is stronger in producing mRNA. However, the final amount of protein produced depends on other factors like protein solubility, stability, and toxicity.
Here, https://microbialcellfactories.biomedcentral.com/articles/10.1186/1475-2859-12-26, is a study that compares T7 and other promoters for the production of few different proteins.

T7 vs pBAD promoter strength


Upgrade Required SharePoint_Config

Question: When I go to "Manage Servers in Farm" from Central Admin, I see a red alert that says "Upgrade Required" against web front end. When I run the stsadm command
stsadm.exe -o localupgradestatus

, I get the following output:
<objects>
  <object>
    <name>SharePoint_Config</name>
    <type>Microsoft.SharePoint.Administration.SPConfigurationDatabase</type>
    <level>0</level>
    <status>Needs Upgrade</status>
  </object>
</objects>

[0] content database(s) encountered.
[0] content database(s) still need upgrade or cannot be upgraded.
[0] site collection(s) are contained in the content databases.
[0] site collection(s) still need upgrade.
[1] other objects encountered, [1] of them still need upgrade or cannot be upgraded.

I Tried psconfig command :
psconfig -cmd upgrade -inplace b2b -wait

and the result was:
SharePoint Products Configuration Wizard version 15.0.4569.1503. Copyright (C) M
icrosoft Corporation 2012. All rights reserved.
The upgradebootstrap command is invalid or a failure has been encountered.
An error has occurred while validating the configuration settings.  An exception of
type System.Data.SqlClient.SqlException was thrown. Additional exception in
formation: The EXECUTE permission was denied on the object 'proc_GetProductVersions',
database 'SharePoint_Config', schema 'dbo'.

Can anyone tell me what I need to do?
Comment: Hello, did you ever get a solution for this. I'm having the same issue just with an application server running search services.
Answer: I know this is an old question, but one of mine did this too. It worked on my test server, then I got this on our production server. I may have not ran the prompt as administrator, so when I tried again in as admin it worked.

Upgrade Required SharePoint_Config


How to determine the subject and object of an object property assertion?

Question: In OWLAPI, when you get the signature of an OWLAxiom of type AxiomType.OBJECT_PROPERTY_ASSERTION, how to know which of its entities is the subject and which is the object?
Answer: Don't try to do it from the signature.  The signature is just a set, and doesn't have the information that you want.  Instead, treat it as an OWLPropertyAssertionAxiom and use the getSubject() and getObject() methods.


unitary that transforms one Hilbert space to another Hilbert space

Question: Let $H = A \otimes B$. If there exists a unitary operator $U$ that transforms the Hilbert space $H$ into another Hilbert space $H' = A' \otimes B'$ (meaning that $U$ maps each basis of $H$ to each basis of $H'$), does this imply that $U$ necessarily rotates the subsystems, i.e. mapping $A$ to $A'$ and $B$ to $B'$?
Answer: No. Suppose $A$ and $B'$ are qutrits, $A'$ and $B$ are qubits and $U$ is the SWAP unitary that sends $|ab\rangle$ to $|ba\rangle$ for every $a\in\{0,1,2\}$ and $b\in\{0,1\}$. Clearly, SWAP transforms $H=A\otimes B$ into $H'=A'\otimes B'$, but it certainly does not map $A$ to $A'$, because $\dim A=3\ne 2=\dim A'$.
Comment: Yes, it does. In this case, pick a product basis $|ab\rangle$ in $A\otimes B$ and impose the new tensor product structure $A'\otimes B'$ by _defining_ $|a'b'\rangle:=U|ab\rangle$. More formally, one way to define the tensor product is via a bilinear map $T: A\times B\ni(|a\rangle,|b\rangle)\mapsto|a\rangle\otimes|b\rangle\in A\otimes B$ which is _linearly disjoint_, i.e. sends every pair of linearly independent sets to a linearly independent set. It is a simple exercise to check that if $T$ is a linearly disjoint bilinear map then so is $U\circ T$ where $\circ$ denotes function composition.
Comment: You're definitely right. What if $\dim(A) = \dim(A')$ and $\dim(B) = \dim(B')$? I believe the statement holds in that case, is it?
Comment: Thank you for your kind answer!


Are there any other constructions of a finite field with characteristic $p$ except $\Bbb Z_p$?

Question: I mean, $\Bbb Z_p$ is an instance of $\Bbb F_p$, I wonder if there are other ways to construct a field with characteristic $p$?
Thanks a lot!
Comment: As the answers say, there are infinitely many finite fields, of different size, with characteristic $p$ for each prime $p$.  But as far as "$\mathbb{Z}_p$ is an instance of $\mathbb{F}_p$," it is the only instance; any two fields of the same finite cardinality are isomorphic.
Answer: There are also extensions of $\mathbb F_p$.  For example $\mathbb F_2[t]/(t^2 + t + 1)$ is a field with $4$ elements.  It has characteristic $2$.
You might try perusing the wikipedia page which has more examples.
Answer: For each power $p^r$ of $p$, there is a unique finite field of characteristic $p$ and size $p^r$, it is denoted by $\mathbb F_{p^r}$.
For the construction, you take an irreducible polynomial $f\in\mathbb F_p[x]$ of degree $r$. Then $\mathbb F_{p^r} \cong \mathbb F_p[x]/(f)$.
The smallest non-trivial example is $\mathbb F_4 = \mathbb F_{2^2}$. A concrete construction for it is given in the answer of Jim.
Comment: I just want to mention that the field $F_{p^r}$ is the splitting field of the polynomial $X^{p^r}-X\in F_p[X]$.
Comment: @DaveHartman: Right, thank you! In some situations, your representation is preferable, since it does not depend on the choice of the irreducible polynomial $f$.
Answer: Just to supplement the other answers: As stated in the other answers, for every prime power $p^r$, $r>0$, there is a unique (up to isomorphism) field with $p^r$ elements. There are also infinite fields of characteristic $p$, for instance if $F$ is any field of characteristic $p$ (e.g., $\mathbb Z_p$), the field $F(t)$ (the field of fractions of the polynomial ring $F[t]$, with $t$ an indeterminate), is an infinite field of characteristic $p$.
Comment: Another example of an infinite field of characteristic $p$ would be the algebraic closure of any finite field of characteristic $p$.
Comment: +1: $\Bbb F_p(t)$ is one of the simplest (if not *the* simplest) examples of a field which is not [perfect](https://en.wikipedia.org/wiki/Perfect_field).
Answer: As said in the other answers, if $P$ is an irreducible polynomial on $\mathbb{F}_p$ of degree $d$, then $k=\mathbb{F}_p[X]/ (P)$ is a field of cardinality $p^d$ and is of characteristic $p$. For a nice presentation of $k$, you can say that $k=\mathbb{F}_p(A) \subset M_d(\mathbb{F}_p)$ where $A$ is the companion matrix of $P$.
For instance, the example given by Jim becomes: $k= \left\{ \left( \begin{array}{cc} b & -a \\ a & b-a \end{array} \right) \mid a,b \in \mathbb{F}_p \right\}$.
Answer: There are two nice constructions I know, the first one is already mentioned. For every prime $p$ you can 'extend' it and construct fields with $p^n$ elements. (this depends on the fact that there are irreducible polynomials of every degree in $\mathbb{F}_p$, exercise: give some examples to show why this might be true). Then you can also take the algebraic closure of these fields and get a genuinely new field since an algebraic closed field can't be finite (you can prove this in the exact same way Euclid proved there are a infinite number of prime numbers), let's call this field $\overline{\mathbb{F}_p}$.
The second construction I know is first taking polynomials with coefficients in $\mathbb{F}_p$ i.e. $\mathbb{F}_p[x]$ and take its quotient field (as you do to construct $\mathbb{Q}$ from $\mathbb{Z}$) then get quotients of polynomials, this form a new field which contains $\mathbb{F}_p$ as a subfield (identified by the 'constant polynomials'). Let's denote this new field $\mathbb{F}_p(x)$.
One might think these two fields are isomorphic, but this post argues that it isn't the case.


Free energy in Allen-Cahn PDE

Question: I am a mathematician and I am taking a mathematical physics course. In the part of reaction-diffusion equations, there is something that I do not understand. I have been defined the Allen-Cahn equation as $$u_t=u_{xx}+u-u^3.$$ Then the professor wrote the equation as $$u_t=u_{xx}-W'(u),$$ where $$W(u)=1/4-u^2/2+u^4/4.$$ The free energy was defined as
$$ H[u]=\int_\Omega \left(\frac12 u_x^2+W(u)\right)\,\mathrm{d}x. $$
I do not understand what this free energy tries to model. I read on Wikipedia that the part $1/2\int_\Omega u_x^2\,\mathrm{d}x$ is called Dirichlet energy, but I cannot find any physical interpretation of this. Could you provide any simple explanation of $H[u]$ for a theoretical mathematician?
Comment: $H$ is minimised when $u$ satisfies the AC equation. Thus, it measures how far $u$ is from the solution to the PDE. The first term penalises the derivative, and the second one the value of $u$ itself. Physicists would say "kinetic energy" and "potential energy", although I am not sure how useful these terms are for you. Is this what you are looking for? can you clarify what exactly are you expecting answers to look like? are you perhaps asking for an explicit "real-life" situation the AC models?
Comment: @AccidentalFourierTransform Thank you for your comment. I computed $\frac{d}{dt}H[u]=-\int_\Omega u_t^2\,dx$, when $u$ satisfies AC equation. I also computed the [first variation](https://en.wikipedia.org/wiki/First_variation) of $H[u](t)$ for each $t$. In both cases, I obtained equilibria if $u_{xx}-W'(u)=0$. What do you mean by minimizing $H$? Also, the kinetic energy here has something to do with $1/2\,mv^2$? What is the mass and velocity in the Dirichlet energy? I learned that minus gradient of the potential is the force. Is this concept applicable here?
Comment: Sorry, I misread the functional $H$. My comment above is mostly wrong.
Answer: $H$ is like a potential and the system will always "roll" to smaller values of $H$ (unlike in Hamiltonian mechanics but much rather as in "gradient flows"), i.e. $H$ is a Lyapunov function of the Allen-Cahn dynamics: it decreases in time unless a stationary condition is reached. In this case, the time-evolution will try to smoothen inhomogeneities (i.e. decrease $(\partial_x u)^2$) and there will be an attraction towards the values $u=\pm 1$ (since those are the minima of $W$). Depending on the initial conditions, a minimum of $H$ may or may not be reached (If the initial data are e.g. $u(t=0,x\geq0)=1=-u(t=0,x<0)$, then the resulting solution can not reach a minimum of $H$.
A free energy is typically not simply a Lyapunov function. We understand it as a kind of Boltzmann entropy (say there is an underlying microscopic dynamics with a local detailed balance property which reduces to Allen-Cahn for macroscopic densities): the free energy counts the number of microstates that are in agreement with the observed macroscopic density profile.
Comment: Thank you for your answer. I have a question. As I said in a previous comment, equilibrium is obtained if $0=u_{xx}-W'(u)=u_{xx}+u-u^3$. We may view this as an autonomous system of ODEs $\dot{X}=Y$, $\dot{Y}=X^3-X$, and plot its dynamics on a plane with axes $X=u$ and $Y=u_x$. Let $\tilde{H}(X,Y)=Y^2/2+W(X)$ be the function inside the integral of $H$. As $X_0=\pm1$ is a minimum of $W$, then $(\pm 1,0)$ is a stable fixed point (the attraction you mentioned towards $\pm1$), by considering the Lyapunov function $V=\tilde{H}-\tilde{H}(\pm 1,0)$. My question is...
Comment: ... why $H$ is called a Lyapunov function, when actually $\tilde{H}$ (well, $V$) is the function being a Lyapunov function for a system of ODEs. Is there any concept of Lyapunov function for PDEs?
Comment: And finally, on another subject, why is the part $1/2\int_\Omega u_x^2 dx$ usually called Dirichlet energy? Where is the mass or velocity so that it could be interpreted as a kinetic energy? And why is $W$ called a potential there? Is its gradient some sort of force?
Comment: I think that in the physics community the nomer "Lyapunov function" is indeed used more broadly: In some dynamical system (in this case density profiles evolving according to Allen-Cahn) a function $f$ (domain=state space, codomain=R) is Lyapunov if it never increases in time (weaker version) or if it even has to decrease unless the system has arrived in a stationary state (=what you call equilibrium. This is a stronger version of the Lyapunov property). The Dirichlet energy is only formally analogous to kinetic energy (in that derivatives $\partial_x$ act on the field in this term).
Comment: in the term $W$ no derivatives act on the field $u$. That's why people will think and speak of this as a potential. Anyway, these are just issues of terminology and -a priori- perhaps not so important.

Free energy in Allen-Cahn PDE


How many (super)villains have managed to get into the Batcave?

Question: Having gone through a few questions asked here, it seems the Joker (Has the Joker ever been inside the Batcave?) has never been in the Batcave, but Catwoman has (Has Catwoman been to the Batcave before New 52?). It made me wonder how many other (super-) villains have managed to get into the Batcave (Silver Age)?
Comment: Technically speaking, Catwoman has been in the Batcave not only as a villain. :P
Comment: Some copy-pasting can be done from [15 Villains Who Broke Into The Batcave](https://screenrant.com/batman-rogues-villains-that-broke-into-the-batcave/), if anyone feels like it. Although, among others, _SPOILERS FOR "THE BUTTON" ARC_ Reverse-Flash _END SPOILERS_ is missing from that list.
Comment: Is it just comics? IIRC, King Tut broke into the Batcave.
Comment: I think that Ra's Al Ghul did during the Hush storyline and left a sword stabbed in a Batcave computer. Or maybe this was during "Bruce Wayne: Murderer"
Comment: Voting to close as too broad. "All media acceptable" equates to hundreds of comic serials (probably more than 10-20,000 individual issues), dozens of films, prose novels, TV shows and etc.
Comment: Better. Still really broad, but answerable.
Answer: In the LEGO multiverse in Lego Batman 2, The Joker and Lex Luthor break into the Batcave and use there anti black stuff ray to destroy a bunch of stuff.
In Batman Arkham origins Bane breaks into the Batcave and destroys Batman's computers then somehow injures Alfred and puts a boulder on top of him (the boulder bit you don't see, though its just after you return in the batwing and see the Bat-cave terminals all broken.
In the animated movie of "Batman vs Robin" the court of owls break into the Batcave and Batman and Nightwing fight them off with "quite the troubles" at not being able to stop them.
Comment: @F1Krazy - Given that it's carrying downvotes, it would probably be better to be reposted as a self-answer to a new question if OP wants to salvage it. This is what happens when people answer questions that are off-topic.
Comment: This isn't even close to being comprehensive, but then again, the question is so broad that a comprehensive answer would be almost impossible, which is why it was closed shortly after you posted this.
Comment: The edit to the question has now also invalidated this answer (it's looking for Silver Age instances, and none of these are Silver Age)


Can SharePoint search external web site?

Question: We want to search a web site (not SharePoint site) on SharePoint 2019, is it possible? The web site could be searched in Internet by Bing, Google etc.
Comment: Do you try the following answer? If you have any updates about this issue, please feel free to reply.
Answer: Yes, you can achieve that.
You can create a content source using Web sites type, then type your external web site address in the "Start Address":

After that, start a full crawl for your external content type:


Where can I find inexpensive or better yet free product images?

Question: I am wanting to build a product catalog template that can take XML and import it through InDesign to automatically style text and place product photos. The problem is I don't have a product database of photos, descriptions or prices to work from. Does anyone have ideas on where I could go to find such content? I could write the text myself but at the very least I would like the photos to be sharp and professional.
Comment: Depending on what kind of products you want to include, manufacturers, stockists may supply product photos. They often have their own image bank.
Comment: Since you don't seem to care which products are on the images, I'm guessing that it's just dummy images you need while you work on your template? If it's just for personal use why does the images have to be free? Couldn't you just "borrow" any images you find on the net and then throw them out afterwards?
Comment: I have a few goals for this project. I would like to get more practice with XML import in InDesign. So in that case I could use just any photos. But, once it is perfected I would like to be able to sell the template on a store like Creative Market. So to that end I would think that I would need royalty free stock photos.
Answer: If it's merely a template.. create a placeholder image and use that repeatedly.

The benefit of using placeholders is they show positioning and size, but do not show anything which may alter someone's perception of the overall design.
Meaning... if you use a bunch of product unrelated to a viewer, the viewer may immediately dismiss what they see as "not for me". i.e. use a bunch of gun images and someone anti-gun will not be interested. Use a collection of cosmetic images and men may not be interested. Use a bunch of children's clothing images and non-parents may not be interested, etc.
Placeholder images are agnostic and typically don't "sway" viewers because of content.
But.. I have no actual idea what you are creating or what it's purpose is.
Comment: I really need individual photos tied to unique product text so that I can properly test the xml import. If i just use the same place holder photo for everything the I wont know if the import worked properly.
Comment: You can use the same image. Just copy it 50 times in the Finder/Windows Explorer and number them 01 to 50. You'll see what image was imported by checking the links panel. The individual numbers of the file name will be reflected.


Is it an act of justice to abort an unborn child as that child would then go to heaven?

Question: On the topic of unborn/infants dying without being baptized, could one argue that, as those babies would not go to hell but instead to heaven, it is an act of mercy or justice to abort babies to "guarantee" a spot in heaven?
Comment: How is this question different from "*When someone is baptized and has all their sins forgiven, wouldn't it be appropriate to kill them immediately before they can sin again?*"?
Comment: Needs an "according to xxx" because the subject of unbaptized infants differs between denomination.  Hopefully we'd all agree this is an abhorrent idea though.
Comment: This question appears to be attempting to circumvent the rule about "asking if X or Y is a sin".
Answer: I'm sure most Christian groups will point out the gross misunderstanding of "justice" here.  Justice is "giving someone their due", in this case giving the (still) helpless baby his/her due, owing to the potential flowering of this human individual to become an adult to handle the gift of life God has given him/her since conception.
Therefore, the right understanding of justice due to babies is that we adults owe them protection while they still cannot defend themselves, not to mention that we ALL were once babies and that we were able to reach this stage (adults sufficiently mature to participate in Christianity.SE) only through the help of our parents and our society.  It is the natural sense of justice that we feel obligated to want to pass forward the gifts we have received from our parents/societies to those who need them.  This is also the principle implicit in God's rebuking the powerful in Jerusalem for neglecting those who couldn't defend themselves: the widows and the orphans.
In Christianity, "heaven" is life in the world to come.  But this question is about life in THIS world.  Justice in regards to our eligibility to enter the world to come is for God alone to confer (in this case, justice given to aborted babies to gain admittance to heaven).  But justice in regards to a human being flourishing in THIS world, God has delegated to us, which becomes part of our society's obligation to administer to those who need it.  In the Bible there are multiple instances where those who denied justice in THIS world "cry out to God", implicitly asking God to take care of society's irresponsibility.
It's not Christian justice to posit that aborted babies have received their full "due" because most likely God will admit them to heaven.  An axiom of Christian justice (supported Biblically) is that when a human is conceived, he/she immediately possesses human rights given by God alone, a gift purely from God to which not even their parents contribute (i.e. their parents don't give them this right).  Part of this right is to flourish in THIS world as well.  It's both-and, not either-or.  Therefore, the answer is a very obvious NO.
Comment: It's not justice because they have the right to live in THIS world as well.  It's **both-and**, not **either-or**.  It is an axiom of Christianity that when a human is born, they immediately possess human right given by God alone; part of this right is to flourish in this world.  Your notion of justice is not Christian.
Comment: So aborting children and guaranteeing them a spot in heaven is not justice? How come?
Comment: @uggupuggu, also, the argument is necessarily an "ends-justify-means" argument, which many would argue isn't a good argument in itself. Here's a fun point of comparison; is it okay to torture someone (inquisition-style) if it increases their chances of being saved?
Comment: Ah now I know how to reply to this argument, thanks!
Comment: @uggupuggu You're welcome.  Have a blessed day.
Comment: @GratefulDisciple. You might consider upvoting tge question since yiu deemed it worth answering and were rewarded by op
Comment: It's not justice because no one is owed salvation and even if someone were owed salvation, it isn't owed by the would-be killer to the infant in question.
Answer: No, killing babies in order to take advantage of their innocence and use their "get into heaven free card" (so to speak) would not be considered justice.  Killing the person who is killing babies to take advantage of a perceived loophole (to allow them to murder children) quite possibly would be justice.
If one believes in pre-determinism, then those children's future dates are already decided so they do not need assistance by murder before they can live out their lives.
If we are speaking in terms of free-will then you would be deny the children their right to choose their own actions which will lead them down their path.
Murder as a form of helping a person's soul would be a misinterpretation although it has been used quite often through histor.


Are mixtures of pairs of Bell states perfectly distinguishable by local operations?

Question: Consider the four Bell states
$$ |\psi^{00}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle), \hspace{2mm}
|\psi^{01}\rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle),\hspace{2mm}
|\psi^{10}\rangle = \frac{1}{\sqrt{2}}(|01\rangle + |10\rangle),\hspace{2mm}
|\psi^{11}\rangle = \frac{1}{\sqrt{2}}(|01\rangle - |10\rangle), $$
and denote by $\psi^{ij} = |\psi^{ij}\rangle\langle\psi^{ij}|$ the corresponding density matrix. If we group the Bell states into two mixed states, it is easy to see that
$$ \rho_0 = \frac{1}{2}\psi^{00} + \frac{1}{2}\psi^{01}, \quad
\rho_1 = \frac{1}{2}\psi^{10} + \frac{1}{2}\psi^{11} $$
are perfectly distinguishable by local operations and classical communication (measure in $Z$-basis locally and compare results), and similarly it is easy to see
$$ \sigma_0 = \frac{1}{2}\psi^{00} + \frac{1}{2}\psi^{10}, \quad
\sigma_1 = \frac{1}{2}\psi^{01} + \frac{1}{2}\psi^{11} $$
are perfectly distinguishable by local operations and classical communication (measure in $X$-basis locally and compare results). Is it similarly easy to see
$$ \xi_0 = \frac{1}{2}\psi^{00} + \frac{1}{2}\psi^{11}, \quad
\xi_1 = \frac{1}{2}\psi^{01} + \frac{1}{2}\psi^{10} $$
are perfectly distinguishable by local operations and classical communication? I have tried to come up with a measurement, but without success. I would appreciate any help!
Answer: The states $\sigma_0$ and $\sigma_1$ can be seen to have the form
$$\sigma_0 = N[\mathbb P(e_1+e_4) + \mathbb P(e_2+e_3)], \\
\sigma_1 = N[\mathbb P(e_1-e_4) + \mathbb P(e_2-e_3)],$$
where $N$ are normalisation constants, $\mathbb P(\psi)\equiv |\psi\rangle\!\langle\psi|$ is shorthand notation to refer to projections, and
$$
e_1\equiv |00\rangle, \quad
e_2\equiv|01\rangle, \quad
e_3\equiv|10\rangle, \quad
e_4\equiv|11\rangle.$$
If an operator is a sum (with equal weights) of two (or more) orthoprojections, it can also be written as a linear combination of said projections upon an arbitrary unitary operation.
Better said, if $A=\sum_i \mathbb P(u_i)$ with $\langle u_i,u_j\rangle=\delta_{ij}$ , then $A=\sum_i \mathbb P(Uu_i)$ for any operator $U$ that is unitary when restricted to the span of $\{u_i\}$.
In particular, this means in our case that we can write our states (ignoring normalisation constants) as
$$\sigma_0 =
  \mathbb P(\underbrace{(e_1+e_4)+(e_2+e_3)}_{=(|0\rangle+|1\rangle)\otimes(|0\rangle+|1\rangle)}) +
  \mathbb P(\underbrace{(e_1+e_4)-(e_2+e_3)}_{=(|0\rangle-|1\rangle)\otimes(|0\rangle-|1\rangle)}) \\
%= \mathbb P((|0\rangle+|1\rangle)\otimes(|0\rangle+|1\rangle))\\
\sigma_1 =
  \mathbb P(\underbrace{(e_1-e_4)+(e_2-e_3)}_{=(|0\rangle-|1\rangle)\otimes(|0\rangle+|1\rangle)}) +
  \mathbb P(\underbrace{(e_1-e_4)-(e_2-e_3)}_{=(|0\rangle+|1\rangle)\otimes(|0\rangle-|1\rangle)}).$$
So the gist is that you can find a way to write $\sigma_i$ as sum of projections over orthogonal product states.
Why is this possible at all? To better understand it, focus on $\sigma_0$. The considerations above tell us that, for any pair of complex numbers $\alpha,\beta$ with $|\alpha|^2+|\beta|^2=1$, we can write
$$\sigma_0 =
\mathbb P(\alpha(e_1+e_4) + \beta(e_2 + e_3)) +
\mathbb P(\bar\beta(e_1+e_4) - \bar\alpha(e_2 + e_3)).$$
The question is whether there are coefficients $\alpha,\beta$ such that the vectors in this projections are product states. Focusing on the first one, we are asking whethere
$$(\alpha,\beta,\beta,\alpha)^T = (a,b)^T\otimes (c,d)^T$$
for some $a,b,c,d$. While the solution is easy (and already known) in this case, let's keep things general for the sake of argument.
We can figure out when $(\alpha,\beta,\beta,\alpha)$ is a product state by computing the entropy of the corresponding reduced density matrix. Equivalently, by computing its eigenvalues. These eigenvalues are easily seen to be (again, up to multiplicative constants) $|\alpha\pm\beta|^2$, which immediately tells us that we get product states whenever $\alpha=\pm\beta$, compatibly with the solution we already knew.
So far, so good. Now with all of this in mind, let's get back to the question at hand. We can write $\xi_i$ as
$$4\xi_0 = \mathbb P(e_1+e_4) + \mathbb P(e_2-e_3) \\
= \mathbb P(\alpha (e_1+e_4) + \beta(e_2-e_3))
+ \mathbb P(\bar\beta (e_1+e_4) - \bar\alpha(e_2-e_3)), \\
4\xi_1 = \mathbb P(e_1-e_4) + \mathbb P(e_2+e_3) \\
= \mathbb P(\alpha(e_1-e_4) + \beta(e_2+e_3)) +
\mathbb P(\bar\beta(e_1-e_4) - \bar\alpha(e_2+e_3)).$$
Focusing on the first projection of $\xi_0$, we thus need to find out whether there are $\alpha,\beta$ such that $(\alpha,\beta,-\beta,\alpha)$ is a product state. The eigenvalues of its reduced density matrix can be seen to be $1\pm 2\operatorname{Im}(\alpha\bar\beta)$. We need one of these two eigenvalues to vanish, which is only possible if $\operatorname{Im}(\alpha\bar\beta)=\pm1/2$, which is the case with $\alpha=1/\sqrt2$ and $\beta=\pm i/\sqrt2$.
All this to say that we can write
$$\xi_0 =
\mathbb P((|0\rangle-i|1\rangle)\otimes(|0\rangle+i|1\rangle)) +
\mathbb P((|0\rangle+i|1\rangle)\otimes(|0\rangle-i|1\rangle)) \\
\equiv |+i\rangle\otimes|-i\rangle + |-i\rangle\otimes|+i\rangle,$$
and similarly
$$\xi_1 = |+i\rangle\otimes|+i\rangle + |-i\rangle\otimes|-i\rangle.$$
Thus the states are perfectly distinguishable measuring in the $Y$ eigenbasis and comparing results, exactly as it was the case for $\rho_i$ and $\sigma_i$ in $Z$ and $X$ bases.


Can I substitute a 10 oz bag of large marshmallows for the same weight equivalent in miniature mallows?

Question: My recipe calls for a 10 oz bag of miniature marshmallows. I only have a 10oz bag of regular marshmallows (not jet-puffed), will that work?  Thank you.
Comment: It might be worth adding a few details on the recipe to give some ideas on why the original recipe may have asked for miniature marshmallows in particular.
Comment: Depending on use, you might have to cut the large MMs into smallish pieces - which can be messy. I suggest scissors. But overall, heed @PeterJ's advice and post the recipe / intended use here. Welcome to the site!
Comment: Takes the bigger ones longer to melt, and they're a mouthfull all on their own.
Comment: possible duplicate of [What is the substitution ratio for mini marshmallows to large marshmallows?](http://cooking.stackexchange.com/questions/21763/what-is-the-substitution-ratio-for-mini-marshmallows-to-large-marshmallows)
Answer: Culinarily speaking, large marshmallows are identical ounce-for-ounce to miniature marshmallows, so for the purpose of an ingredient substitution, this should not cause you a problem. But there are a few things to consider:
Miniature marshmallows are obviously smaller… so if your recipe calls for using them whole, you may have to decide if the larger versions are appropriate for your recipe.
Miniature marshmallows are also easier to melt, so if you are adding larger pieces to a hot mixture, you may have to take extra care they are melting completely. And if you are melting them over heat, be sure the extra time required does not cause them to burn.
And just for the sake of completeness, marshmallows are also coated in corn starch to prevent them from sticking to one another. Since miniature marshmallows have a bit more surface area, you may end up with just a bit less cornstarch in your mixture. But it seems highly unlikely this will make a difference in your final product.


Do I have to use the same passport to go to Japan everytime?

Question: I have two passports. One is Hong Kong (HKSAR)passport.  One is British Citizen passport (GBR).
For both passports, they are visa exempted to enter to Japan.
My question is last month I used the British passport to go to Japan. I am going to Japan in next two weeks and I want to use the Hong Kong passport. Is it okay?
Comment: Out of curiosity what's the advantage?
Comment: @FaridNouriNeshat doesn't have to have an advantage - perhaps the British one is expired or lost.
Answer: Totally fine.  As long as you enter and exit the destination country on the same passport, it's acceptable.
There are some rules for citizens returning to their country, eg American citizens are obliged to enter the US on their American passport, but generally, as long as you arrive/exit using the same passport (And it doesn't have to be the same as last time - you might have changed citizenship in that time!), you'll be fine.
Comment: In general, is this still ok if using the second passport would mean that you're getting around restrictions about entering _too often_ in a certain period on the first one?
Comment: @TimMalone that is a very good question,  and not something I've considered.  Might be worth a new question on this site!
Comment: @fkraiem No, they actually can't.  They can *confirm* you're the same person by comparing fingerprints, but they'd need to suspect that for some other reason first.  (Identical names & birthdates, for example.)
Comment: @TimMalone Japan doesn't actually have published restrictions about how often you can enter, it's up to the discretion of the immigration officer (and, most likely, unpublished guidance).
Comment: @TimMalone - in general, it is not ok to try to get around restrictions no matter how you think they work.  It is possible that they wouldn't track the visits accurately if they were looking at entries of the passport rather than the person (if you were not talking about Japan, but somewhere which has such restrictions) - but it is also possible that they would track the person, or notice the same name and birthdate then check, and then... there would be trouble.  Better to keep track of restrictions and not violate them, even if you might have multiple passports for such shenanigans.
Comment: @TimMalone Japan has no such restrictions. And in any case, they can see that you are the same person from your fingerprints.
Comment: @jpatokal So they actually can, then...


Ribosomes and DNA in chloroplast

Question: Are there multiple copies of circular DNA and membrane bound ribosomes IN CHLOROPLAST ?
Are polysomes found in them ?
Comment: ribosomes are never membrane bound.. they are adsorbed on ER (in case of RER)
Comment: Wikipedia says the number of chloroplast DNA copies (nucleoids) drops from 100 to 15-20 as the chloroplast ages (https://en.wikipedia.org/wiki/Chloroplast_DNA#Nucleoids). No luck looking up membrane-bound ribo-/polysomes. I found lots on protein import into chloroplasts, but no export. My guess is that with many chloroplast genes migrating into the plant genome, protein flux is in rather than out (why would something the whole cell needs be made in just the chloroplast?). If you look at a list of chloroplast DNA genes, it's pretty self-contained; no proteins that would need to be exported.
Answer: The chloroplast, having multiple circular copies of its chromosome and its own tRNA and ribosome genes more resembles the bacterial systems it is descended from.  See @A.Kennard comment
Polysomes being found in bacteria frequently are single mRNA to which are attached multiple ribosomes.  This paper shows that chloroplast polysomes were observed in the mid 1960s by centrifugal sedimentation.

Ribosomes and DNA in chloroplast


Can I have a "Live" Navigator in Photoshop CC?

Question: I record my work by capturing the navigator on a second monitor at 1920x1080. This is much easier on the eye at 16x speed because the screen isn't shooting all over from zooms and panning. However, the navigator only updates when an action has finished. This means that long brush strokes add pauses to the recording.
I need a way to either modify my navigator to update during an action. Or to somehow duplicate my canvas at a different zoom level and be truly "live".
Id love to hear anyone's ideas or plugin information that might help, thanks!
Comment: do you have youtube channel?
Answer: yes, you can. Go to Window>Arrange>New Window for "abc". Now you have two windows that will  mirror each other.
You can have them side by side by going to window> arrange > two up vertical.
I think this is called Dual view photo editing.
Comment: I started to post this as well. Unfortunately, a new window will suffer from the same "only update after action" issue.


Assume $X$ and $Y$ be nonempty subsets of $R$ such that $x<y$ for every $x \in X$ and $y \in Y$. Prove that $\sup X \leq \inf Y$. Is my proof correct?

Question: We have that both sets are nonempty, by the completeness axiom, both sup and inf exist for both sets. Since $x < y$, $y$ is an upper bound for $X$ and hence by def. of sup, sup$X \le y$. So $\sup X$ is a lower bound for $Y$ and thus by def. of inf, $\sup X \leq \inf Y$.
Comment: Yes. It is correct.
Answer: That is basically a good proof, but could use some clarifications.  In particular you should try to distinguish more clearly between numbers and sets.

sup and inf do not necessarily exist for a nonempty set of real numbers.  However, it is true that a nonempty set which has an upper bound has a sup, and similarly a nonempty set which has a lower bound has an inf, and that's clearly true here.
When you say $x < y$, you're considering a single $y$ and all $x \in X$ to conclude that sup $X$ $\le y$.
Because sup $X$ $\le y$ is true for all $y \in Y$, we can also conclude that sup $X$ is a lower bound for $Y$.  It is not a lower bound for $y$: we say that sets have bounds, but numbers do not.
Answer: Actually it's enough that, given $x \in X$ there exists an $y_x \in Y$ such that $x \leq y_x$.
In fact in this case we have $supY\geq y_x \geq x \ \forall x \in X$, which implies $supY \geq sup X$.


Minimizing home heating costs

Question: I live in an old rental house with 12 foot ceilings and zero ceiling fans. I am trying to conserve as much energy as possible as heating costs are expensive. I have placed plastic on all of my windows and close doors, etc. but I am wanting to do more. My question is this, if I hang items from my ceiling, will that help keep my energy costs down? I am not sure what I would hang but almost like panels of some kind. The intent behind hanging panels from the ceiling is to help keep the heat from rising to ceiling level. My landlord is not likely to install ceiling fans. Would it make a difference even if I don't do a whole complete "drop-down" ceiling? Like, if I hang 2 or 3 panels, will that help in the slightest?
Comment: Could you clarify/give an example of  how "hanging items from the ceiling" might help lower energy costs?
Comment: This may be a better fit on [Sustainability.SE](https://sustainability.stackexchange.com/).
Comment: Negotiate with the landlord to invest in a programable thermostat and a few ceiling fans will help in reducing the heating bill. Also, turn the heat to barely low (that without the need for wearing a coat indoors) and use a portable heating device to keep warm may help too.
Answer: A suspended ceiling at a height of 2.4m is the most efficient way of saving the heating cost. Because right now most of the heat in your home goes up to the high ceiling.
If you don't have access to supplies or dry-wall (gypsum-board), you can hang a lightweight frame of boards of 4cm by 4cm lumber and cover them with plastic.
this photo is a typical suspended ceiling. If you need yu can use the space above for storage.
Comment: It is well known that hot air rises & usually the hottest region of a room is near the ceiling. Reducing the ceiling height, as this answer suggests brings the warmest zone closer to floor level, but it also reduces the amount of air that needs to be heated. Converse to this, high ceilings are a practical way to have a cooler room in a hot climate.
Comment: As this is a rental home, it is probably more likely to get the nod over a ceiling fan than a suspended ceiling. But you may try as it is a good idea.
Comment: @r13, in my area many of the rentals are rent control. meaning people pass them on to their kids in their wills.
Comment: @kamran Just serving as a reminder.

Minimizing home heating costs


Nginx redirect without a server name

Question: I'm serving a webpage from an embedded linux box that may or may not be connected to the internet. The idea is, a user enters the IP of the machine and the page comes up. I want to redirect all non-ssl urls to an ssl url (https). Every example I've found uses $server_name or $host in the return line of the nginx configuration. The problem for me is that the IP of the machine might change and editing the nginx config file every time is not an option. I've tried setting the server_name to _ to no avail. What does work is if I set server_name to the current IP of the machine. Then, if I type in 192.168.1.196 it redirects to https://192.168.1.196/dashboard, which is what I want. Unfortunately this will not work in production, since as mentioned the IP may change. My current nginx config is below.
server {
    listen       80;
    #server_name  _;
    #server_name 192.168.1.196;
    ssl_certificate server.crt;
    ssl_certificate_key private.pem;
    ssl_protocols TLSv1 TLSv1.1 TLSv1.2;
    ssl_ciphers HIGH:!aNULL:!MD5;
    autoindex on;
    return 302 https://$server_name/dashboard;

    location /dashboard {
        alias build;
        index index.html;
    }
}

Comment: Can  you provide some more details about your configuration files, directories, and possibly a curl command output?
Answer: Then it's $host that you want to use, because this is what contains the Host: header that the browser supplied.
Comment: Tried this, does not redirect.
Comment: Then you should start from there and try to figure out why.
Comment: I've been trying to figure out why for the past few hours, that's why I came here.

Nginx redirect without a server name


Change labels on 'Nickname' and 'Biographical Info' in user-edit.php

Question: For a project I'm working on, I want to change the labels of the 'Nickname' and 'Biographical Info' fields on edit profile (user-edit.php) page in the dashboard. I still want to use those fields as they are, I only want to change the labels. Anyone know of a function that can do this?
Answer: Every string goes through translate(), which uses the gettext filter. This mean you can try something like this:
add_filter( 'gettext', 'wpse6096_gettext', 10, 2 );
function wpse6096_gettext( $translation, $original )
{
    if ( 'Nickname' == $original ) {
        return 'Funny name';
    }
    if ( 'Biographical Info' == $original ) {
        return 'Resume';
    }
    return $translation;
}

It's probably even more efficient if you only call the add_filter when you are on the user-edit.php page (see the admin_head-user-edit.php hook or something like that).
Answer: I am late with answer, but here is my take anyway. Slight differences and that selective filter add.
add_action('admin_head-user-edit.php', 'setup_user_edit');

function setup_user_edit() {

    add_filter('gettext', 'change_profile_labels');
}

function change_profile_labels($input) {

    if ('Nickname' == $input)
        return 'Nickname replacement';

    if ('Biographical Info' == $input)
        return 'Biographical Info replacement';

    return $input;
}

Comment: You'll want `admin_head-profile.php` as well.
Comment: Thanks! This works...almost. It changes the labels when an admin is viewing another user but it doesn't change the labels when a user is editing their own profile. Is there a different function to use other than 'admin_head-user-edit.php'
Comment: @John Chandler `admin_head-user-edit.php` is not a function, but hook with dynamically generated name. So if you want this to run on more pages, hook it to more `admin_head-`hooks, appending suffixes accordingly.
Comment: Thx. Still getting used to work with functions and learning all the language.


How to dynamically create and position a textbox in javascript?

Question: I would like to dynamically create a text box then dynamically position the text box.  I have been able to dynamically create the text box with no problem but I have not been able to figure out how to position it.  Any suggestions?
Comment: Please try to make your question titles meaningful. "Javascript question" is not going to be of much use to someone searching the archives.
Answer: Set the "top" and "left" positions? You may also need to set the "position" property to be "relative" or "absolute", depending on what you want to do.
Answer: var box = document.createElement('input'); // creates the element

box.style.position = 'absolute';  // position it
box.style.left = '100px';
box.style.top = '100px';

document.body.appendChild(box); // add it as last child of body elemnt

If you want to add it somewhere else in the document hierarchy you have to find the parent using getElementById and use that elements appendChild function.
Answer: Position where?
Are you trying to position at some specific point or inside some other element?
Try using position: absolute either in the CSS for your textbox class or use the style property on the object in the DOM.
Answer: There's a trick to positioning elements using javascript:
var el = document.getElementById('myelementID');
el.style.left = 10 + "px";
el.style.top = 10 + "px";

Note the ' + "px"' part of that.  You need to make sure the expression is a string with units before the assignment takes place or it won't work reliably.  You can also use the offsetTop and offsetLeft properties instead of the style, but the "string with units" rule still applies.
Comment: You also need to set the 'position' property to 'absolute', otherwise the 'left'/'top' properties won't do anything.
Comment: I was figuring he'd already done that, but yes, that is necessary as well.


Subclassed ForeignKey field not created for model

Question: I've been looking at Marty Alchin's Apress book 'ProDjango' and I've run into an issue with the last chapter (chapter 11). I'm a relative noob at Python and Django, and although I've tried searching around I can't put my finger on something similar through this and other forums. I have seen Is Pro Django book still relevant? on this site but doesn't answer any specific questions.
The problem revolves around the trying to create a mechanism to track changes - a history of additions, changes and deletions. The first step is creating a user field on models you want to track. In the example project he has created a specialised ForeignKey field hard-coded to relate to Django's built-in 'User' model:
from django.db import models
from django.contrib.auth.models import User

class CurrentUserField(models.ForeignKey):
    def __init__(self, **kwargs):
        super(CurrentUserField, self).__init__(User, null=True, **kwargs)

There is also a 'contrib_to_class() method later. The class is in a seperate models.py file from the models to which is to be applied.
The use, as I understand, is to add a new field referencing this new field class in your model:
e.g.
class SimpleModel(models.Model):
    a_user = CurrentUserField()

But the problem is that when I syncdb the field is nowhere to be found, a 'FieldError' is the usual result trying to access it.
There are many other elements in the book's solution that I haven't tried to copy here, but this is the first and fundamental part.
I'm guessng that changes in Django and/or Python itself are responsible here. Has anyone any pointers?
Thanks.
EDIT: Given the class below in registration.py which is the current_user folder. This is also where you find the models.py holding the CurrentUserField class. The InformationRequest models has:
user = CurrentUserField()

as its last field. All imports are present and appear correct.
class FieldRegistry(object):
    _registry = {}

    def add_field(self, model, field):
        reg = self.__class__._registry.setdefault(model, [])
        reg.append(field)

    def get_fields(self, model):
        return self.__class__._registry.get(model, [])

    def __contains__(self, model):
        return model in self.__class__._registry

In [1]: from current_user.registration import FieldRegistry

In [2]: from inforequest.models import InformationRequest

In [3]: registry = FieldRegistry()

In [4]: registry.add_field(InformationRequest, InformationRequest._meta.get_field('user'))
---------------------------------------------------------------------------
FieldDoesNotExist                         Traceback (most recent call last)
<ipython-input-4-6fcbbdcae066> in <module>()
----> 1 registry.add_field(InformationRequest, InformationRequest._meta.get_field('user'))

/usr/local/lib/python2.7/dist-packages/django/db/models/options.pyc in get_field(self, name, many_to_many)
    353             if f.name == name:
    354                 return f
--> 355         raise FieldDoesNotExist('%s has no field named %r' % (self.object_name, name))
    356
    357     def get_field_by_name(self, name):

FieldDoesNotExist: InformationRequest has no field named 'user'

Trying to look at the admin generates "Unknown field(s)..."
Comment: Please show the exact error message you are getting including the traceback.
Answer: I think I've found an answer to my question: django-simple-history (https://django-simple-history.readthedocs.org/en/latest/), inasmuch it provides part of solution I was trying to achieve and apparently it was built on Marty Alchin's code in Pro Django.


Why is some racemisation possible in Sn2 reaction?

Question: Partial racemisation is known to occur in Sn1 reactions, but why does Sn2 reaction also show little racemisation?
Comment: Because it's not really a binary thing - real processes are somewhere in between $\mathrm{S_N1}$ and $\mathrm{S_N2}$.
Comment: Your question is a potentially good one, but the way of asking it can be many times better. Please include supporting resources, your research work and the source from where you read it. As such, your question is too vague to be answered.
Answer: If this is a question you've been asked to answer, it is a poor one. SN2  reactions (as they are generally understood) don't show racemisation at all, but some reactions are a mixture of SN1 and SN2 as outlined by Mithoron.
That said, I recently read this paper which blew my mind a little:
Backside versus Frontside SN2 Reactions of Alkyl Triflates and Alcohols
It leads to a more general point: should we think of SN2 reactions in terms of kinetics (i.e. second order nucleophilic substitutions) or mechanistically (i.e. backside attack into a low-lying σ*)? It so happens that the two definitions usually correspond, but I suppose this isn't necessarily the case.
But I'm certain the answer they were looking for was "because it does SN1 too, a bit".


Why does positronium decay into 2 photons more often than into 3 photons?

Question: I cannot find the answer to the above question.
I know that para-positronium is created with a probability of $25\%$ and decays into 2 photons, while ortho-positronium is created with a probability of $75\%$ and decays into 3 photons.
I also know that ortho-positronium has a way longer life time than para-positronium. This, in my understanding, should not affect the number of decays per time, but just means that the ortho-positronium will decay LATER into three photons. But in the end there should be $75\%$ 3-photon-decays and $25\%$ 2-photon-decays. But in reality 2-photon-decay happens about 300 times more often than 3-photon-decay.
What information am I missing?
Thank you!
Comment: What source says the 2-photon decay is more common? In astrophysical studies of the ISM, it is well known that 25% of Ps decays via the 511 keV line rather than the 3$\gamma$ continuum. Deviations from this are due to instances where Ps did not form from nice radiative recombination $e^+ + e^- \to \mathrm{Ps} + \gamma$ of slow-moving leptons, or from cases where a third body was involved in the decay somehow.
Comment: The title and the text do not match. My initial guess is that para-positroniums can emit a single photon and turn into an ortho-positronium. Then the ortho-positronium will decay and we will detect its photons and measure their wavelength.
Comment: Thank you! Why do title and text not match? I don't see how this is the answers to why there are more 2-photon-decays than 3-photon-decays. Could you please elaborate?
Comment: "But in reality 2-photon-decay happens about 300 times more often than 3-photon-decay" But in the title you are asking the opposite! $$  $$If my guess turn out to be correct, then it follows smoothly that the number of 2-photon decays should be more than the 3-photon ones.
Comment: You are right sorry, I will edit the title.
Comment: Is Furrys' theorem relevant here?
Answer: Let us start with the wiki article:

The singlet state with antiparallel spins (S = 0, Ms = 0) is known as para-positronium (p-Ps) and denoted 1S0. It has a mean lifetime of 125 picoseconds and decays preferentially into two gamma quanta with energy of 511 keV each (in the center of mass frame). Detection of these photons allows for the reconstruction of the vertex of the decay and is used in the positron emission tomography. Para-positronium can decay into any even number of photons (2, 4, 6, ...), but the probability quickly decreases as the number increases

It is called conservation of angular momentum. An even number of photons allow to match the S=0 M_s=0 angular momentum. Two photons can add up to spin either 0 or 2 as each carries a spin of 1. The 0 matches the quantum numbers of para positronium.

The triplet state with parallel spins (S = 1, Ms = −1, 0, 1) is known as ortho-positronium (o-Ps) and denoted 3S1. The triplet state in vacuum has a mean lifetime of 142.05±0.02 ns[2] and the leading mode of decay is three gamma quanta

Because with three gammas one can match the S=1 angular momentum quantum numbers.
One has to remember that electrons and positrons annihilate to two gammas when not in a bound state as in positronium. The ground state at S=0 has a probability of electrons and positrons to be found at the center of each other and annihilate. The closer to the ground state the shorter the lifetime of the bound system.
Answer: I'm afraid the responses so far are either misleading or do not answer the question.
In fact in a dense medium a positron when it forms the longer lived ortho-positronium can "pick-up" an electron from an adjacent atom and then decay into 2 x 511 keV photons long before the 3-photon ortho-positronium state would have decayed.   Look up "pick-up effect".
Answer: Jezstarski is mostly correct,
The para-positronium (p-PS) state ends up being the main mode of annihilation of positronium (PS). Positrons can annihilate in at least eight different ways but once ortho-positronium (o-PS) forms in a void/vacuum, it has additional time to undergo another mode of annihilation.
P-PS annihilates in under 125 picoseconds.
O-PS annihilates at or less than 142 nanoseconds (vacuum).
A consequence of this long lived lifetime is "pick-off" (the correct term) annihilation where an opposite spin electron from some surrounding material will annihilate in para-orientation before the ortho-bound electron can collapse and annihilate with the positron.
Source: Member of the Positron Science Lab at UMKC.


Presenting non-significant results at a conference?

Question: Recently got accepted for a poster presentation based on a pre-registered abstract. However, all the results are non-significant (after running the analysis) and I can't help but feel slightly disappointed. Has anyone faced a similar issue and presented non-significant results at the conference? :( How often does one see non-significant results at a conference? It sucks to think that this disappointment will be blown up to poster size for all to see.
Comment: Well, that just means that your null-hypothesis *cannot be rejected with the exceptional set your chose*. If your exceptional low probability set was a decent one, it merely means that it may be true after all and the alternative has not enough ground for validation. That is a perfectly valid outcome of a statistical study and you should be always ready for it. Whether it is worth reporting depends solely on whether the question was worth investigating in the first place. If it was, yes, the negative result should be made public and has equal value with a positive one.
Answer: Publication bias is a huge problem in academic publishing right now.
In summary, if a field uses null-hypothesis significance testing with some arbitrary threshold (say, p<0.05) for significance, and only significant results are published because the field is only interested in significant results (impacting publishing decisions both by authors choosing what to submit and venues choosing what to publish), many (and possibly most) published significant results are actually showing effects that are not real or exaggerated sizes of the actual effects.
A high-quality study is high-quality whether or not the result is significant. You should design studies where either a significant or non-significant result is interesting (one key aspect of this is designing studies to be large enough that non-significant results are interesting).
Think about what is interesting about your non-significant result, and know that it is honorable and methodologically far better to present such results rather than hide them in a cabinet.
Comment: Evidence contrary to the hypothesis is just as valuable as any other.
Comment: @Buffy The biggest problem is with underpowered studies where no individual study provides useful evidence in *any* direction, yet where a sufficient number of such studies are performed such that those that spuriously provide evidence of a particular hypothesis get published as evidence of interesting large effects.
Comment: "You should design studies where either a significant or non-significant result is interesting" - I can not stress it enough how important this step is for a research career. Almost an open secret of the academic world: for some reason, everyone seems to teach how to design a *correct* study, but almost never a *good* one.
Answer: If your method was promising but turned out not to work, explain both the promise and the failure in your poster.
Related: What to do when you spend several months working on an idea that fails in a masters thesis?


Is it possible to deploy multiple Mobile Tractor Units?

Question: Is it possible in eve online with the upcoming rubicon changes to deploy multiples of the new mobile tractor unit deployable structures?
Comment: That is pretty much speculation as far as i know. Unless the dev's made a clear statement about this which i can't find with a quick search.
Comment: Please do not ask questions about unreleased patches and content. Even in a case like this where you can preview the patch on a test server, it is likely that what's being tested there and what will be released will differ.
Answer: According to the Rubicon patch notes a mobile tractor unit cannot be deployed:

within 40km of a control tower
within 50km of a gate or station
within 5000m of another mobile tractor unit

As such it should be possible to deploy multiple mobile tractor units at the same time (assuming sufficient cargo space to carry them + your loot as each tractor unit takes up 100m3)
Edit:
Having been on the test server and checked them out I can confirm that multiple tractor units can definitely be deployed together but, at least on the current test server build, will have a tendency to play tug-of-war with wrecks due to their required minimum separation.
Answer: Salvaging is made easier with a noctis plus MTU.  Simply deploy the mtu's in each pocket and follow w/ your salvager...Parking the salvager next to the MTU.  No need to loot (as all loot is in one can) and all wrecks are all in one tidy lump removing the need for tractor beams and freeing up room for more salvagers.  I can target 9 wrecks at a time, I have 7 salvagers and 1 tractor making quick work of it all.
Answer: Multiple mobile tractor units can be deployed but they must be 5000 meters away from each other.  There is a problem though.  The mobile tractor units by default will tractor the wrecks or containers closest to them.  So if you put one mobile tractor unit down then go 5000 meters and put another one down.  They will tractor each others already looted wrecks and disregard the other wrecks that are farther away.
Comment: Yeah I've noticed that. However I did also notice that the autolooting still works as long as the unit touches the wreck, which is the primary reason I wanted the unit. I run a salvage alt so usually I tractor the wrecks in with the noctis, salvage with drones and let the tractor unit gather the loot to scoop in one go.


Change code segment with disassemblers like IDA

Question: Do disassemblers like IDA or Ghidra change write rules on code segment of a process to change instructions? For example one can place NOP instead of a function call, so it should have RWX instead only RX bits
Answer: IDA and Ghidra create their own database files to store information about the binary (.idb and .gbf respectively). While binary editing is possible, it does not affect the binary's or its database's segment permissions.
For example, to check segment permissions in a PE executable with IDA, go to the beginning of a section in assembly text view:
Answer: I think you are mistaking analysis of a binary file with the file itself.
Sections can have permissions once in memory (because it will be mapped to physical pages that can have specific RWX permissions), but as long as your file is a file on disk, you should be able to edit its content the same way you edit a text file : get a file descriptor by opening the file with your OS API, read/writing it, close the file descriptor.
As stated by previous answer from mimak, IDA got its own database, and editing anything within IDA will only update the database, unless you explicitly ask IDA to write changes to the file (which you can do with File->Patches->apply patches to input file) ; in which case IDA will probably open your file on disk, read/write it, and close it.


Algorithm/Technique for Steganography

Question: What is the most used Algorithm/Technique in Steganography? I made some research about the algorithm/technique and I think Least Significat Bit(LSB) is the most used algorithm, is there any more efficient algorithm/technique that can be use for Steganography aside from LSB?
Comment: The be truly on-topic here, I think steganography must be per [Kerchoffs's principle](http://en.wikipedia.org/wiki/Kerckhoffs%27s_principle); that is, there must be a _public_ algorithm with a secret key involved (at least on the decoding end) allowing to determine if there is steganographically encoded data, and decipher it. There are a few techniques for this, using still image, video, sound, even code..., in various formats, as the carrying medium; and making it seriously hard to demonstrate without the key that any content is embedded. I hope someone will have time to give pointers.
Comment: Some of the steganography schemes listed at http://crypto.stackexchange.com/questions/6058/any-efficient-text-based-steganographic-schemes are more efficient, in the sense of requiring a smaller file to send the same number of ciphertext bits.
Answer: I'm assuming you're referring only to static image manipulation, as that's the common fear these days (terrorists are hiding data in eBay images!)  But it's a mistake to think that images are the only potential carriers of hidden data.  Data can hide wherever information moves, including audio files, DNS requests, TCP port knocking, error codes, URLs, Unicode, spam, anywhere.
LSB is often used in stego demonstrations because it's a simple and understandable example of the idea, but it has a lot of weaknesses that make it less than perfect for real world use.  For one thing, it works directly on bitmaps, but not compressed images.  If the message is short and modifies only the first half of the picture, the top of the image will have a "static" appearance that magically cleans up in the bottom half.  Also, BMPs may themselves be suspicious, as most people use compressed formats such as JPG or PNG.
Using LSB on an ordinary GIF would give you crazy incorrect colors, but you could use a modified palette with 128 duplicated colors to hide the data invisibly.
Both of these are easy experiments to perform and demonstrate to an audience.  You can show them a before and after picture.  You can show them a photo of a clear blue sky over the ocean, then mar the top third with an LSB stego message.  Then show them how a photo of a forest of autumn leaves or a field of wheat makes the effects of LSB stego almost invisible.  Show them how LSB messes with GIF images, then show them a reduced palette image followed by the same image with an LSB stego message.
Messing with JPEG and TIFF formats is technically much more difficult, but in the real world would probably do a better job of remaining hidden.  But they're still detectable to someone looking for them.  Each camera and image manipulation software package uses a custom "quantization table" that says how a block of pixels will be encoded.  Canon's are distinct from Nikon's.  Both are distinct from Adobe's, GIMP's, ImageMagick's, etc.  If your image has some quantized blocks that match those from Canon, but others that aren't recognizable, an eavesdropper might determine it was tampered with.  For a start to more information, see http://www.imagemagick.org/Usage/quantize/
A long time ago, the program OutGuess did a good job at spotting steganographically altered images encoded in many different image formats, but as far as I know the author never released the source.
Comment: You're right in saying that lossy formats like JPG are not suitable, but [PNG](http://bit.ly/LCg73) is actually a (typically) lossless bitmap format, ideal for steganography - and it's used very commonly on the internet - unlikely to draw attention.  The 'static' you refer to would not appear if you're only modifying the LSB.  Modifying even the 2nd or 3rd least significant bits would only result in a difference that is difficult to discern with the human eye (depending on the image).  Also, it's common to space out encoded information uniformly across an image, so as to be less conspicuous.
Comment: @hunter, I've seen data LSB stegoed into lossless (bitmap) images, and visibility depends entirely on the subject of the picture.  The example I gave above of a clear blue sky was of a real example, and the artifacts in it were painfully visible.  If you're going to try it, you'll have to figure out which bytes should have LSBs modified.  Even then, a picture with LSB modifications has a different statistical profile than an un-stegoed picture, and they are detectable.
Comment: Of course, there are lots variables, and results are subjective to the image.  However, I've created my own steganographic app and modifying the LSB does not result in a discernable change to the image, even on flat-color such as a blue sky.  Assume each pixel contains 3 color values, R, G and B.  Each value is between 0 and 255.  Modifying the LSB *might* (assuming the value you're encoding is 1 or 0) result in a change of 1.  You're not going to notice a change of 1/255, especially when it's only in 1 of the 3 color channels. Of course, I'm talking about visual inspection, not computational.
Answer: Your question is really too general - and perhaps off-topic, as steganography is quite a different field to cryptography.
That being said, the answer to your question really depends on many things.  Steganography is the art of hiding information in plain-sight.  This information could be hidden in either; analogue or digital media, on the internet or in a newspaper, text or photos (or many other file-types like audio or video files, to name a few).
Information can be encoded into the pixels of an image, hidden in the metadata of a file, published in the classified-announcements section of a newspaper, etc.
You're asking about efficient techniques, but efficiency is relative to requirements.  What are you trying to achieve?  How much data are you trying to hide?  In what medium?  Might the people you're hiding information from know your protocols?
Encoding information in the least significant bit of pixel data is a common approach, yes, but keep in mind that Steganography works because it's esoteric.  It provides (perceived) security because the information being hidden is not apparent to the majority of people who see it.  Using the most common techniques might result in the easy discovery of your protocol.  Unlike cryptography, you don't really have to play by the rules when using steganography, so you should get creative and experiment with your own protocols.
One alternative to LSB is to encode a hex encoded message into the alpha channel of a PNG image.  Assuming the alpha value of all pixels in a png file is 255 (fully opaque), offsetting this constant value by a value between 0 and 16 (possible values in hex encoding) would not be perceivable by the human eye, but is a clean and deterministic approach to hiding data.
Comment: There's also a lot more to steganography, including: it needs to be resistant to statistical analysis on the carrier (your alpha value scheme would instantly fail here), and it needs to be resistant to transformations, meaning the payload should be able to be preserved to some extent if the image ends up compressed, resized, or otherwise altered on a reasonable scale (probably via redundancy). But it depends how much secrecy you really need. Ultimately, given enough samples and a specific carrier distribution, any steganographic scheme can be detected, you want to make it very hard to do so.

Algorithm/Technique for Steganography


Automate File Upload using Selenium Webdriver C# on ASP.NET file upload control

Question: I have a ASP.NET file upload control which opens a window when you click the upload button to select the file you want to upload. But the problem is that the webdriver cant recognize the window and therefore cant select the file to be uploaded.
I have found numerous solutions in the stackoverflow which use sendkeys to enter the path of file. I think that works when you have html file upload control. In my case I have the ASP.NET file upload control and it doesn not have a text box where i can enter the file path using sendkeys.
how do i solve this?? Any suggestions ?
Answer: You can use the Windows Automation library to identify windows. UIspy can be used to identify the properties of a window. Add the System.Windows.Automation reference to your project.


Defining aliases for keywords in Python

Question: I want to use Spanish instead of English to program in Python. How to define aliases for keywords such as if and for?
Comment: You can't unless you write your own interpreter in Spanish :)
Comment: You don't. And if you somehow managed to do it, then you would not be able to get help from non-Spanish speakers, and it will also be harder for you to work on international projects in the future.
Comment: It's a subtle distinction: Python is not English, but rather a separate language whose tokens happen to coincide with English words. A language with tokens that coincide with Spanish instead is not Python, but some other language.
Comment: Sure you can, just modify the statement's names in the grammar file included in Python source, and recompile Python. But this is a rather bad idea.
Comment: @chepner if Python had macro support (bad idea IMHO) then would be even subtler distinction
Answer:
You don't. "if" and "for" are hardcoded parts of Python. You could write your own programming language or a translator but you can't do what you are asking for in real Python (you could in Lisp or in C/C++ using macros).
More importantly, programming is done in English. It's not necessarily fair, but that is the way it is. All the documentation is in English and so are the the methods from all the libraries. From ESR: "that English is the working language of the hacker culture and the Internet, and that you will need to know it to function in the hacker community." and  "Linus Torvalds, a Finn, comments his code in English (it apparently never occurred to him to do otherwise). His fluency in English has been an important factor in his ability to recruit a worldwide community of developers for Linux. It's an example worth following."
Comment: @ArtB You never know the future of a project and who has to maintain it in a few years
Comment: @Morwenn I use American English for code because it's more concise and tends to be consistent with 3rd party libraries. In comments the two are similar enough that it doesn't really matter.
Comment: I've always commented in English, too. Using local language is counterproductive (esp if it didn't import all technical terms related to CS and programming, or did but nobody knows them anyway).
Comment: I think it depends on the fluency of the developers. If all the developers are Chinese and their English is poor, then their English comments would have no value over Chinese comments. If the project is internal then there is no reason not to IMHO.
Comment: A new problem arises: English or American English?
Answer: If you are fine to have iPython as a dependency, you might have a look at Custom input transformation — IPython 3.2.1 documentation.
Basically, ipython is already preprocessing anything that is given to the prompt, and it allows code to specify more transformations in the various compilation steps it handles before passing it to the python interpreter itself.
At first glance, the most approriate transformer for transforming reserved keywords is TokenInputTransformer.wrap().
Answer: in general this is not possible (easily). you can look at http://en.wikipedia.org/wiki/Non-English-based_programming_languages to see what others did previously and especially have a look at the projects that translated python to russian/chinese and determine how much work that was (a lot) and if it is worth to do it for spanish (probably not).
Answer: I think you're required to re-compile Python and do your changes by yourself. Anyway, this is a general discussion about it:
http://www.python.org/dev/peps/pep-0306/
(No te queda otra tío :)...)
Comment: And by doing that, you're making your own fork of Python that's incompatible with 100% of Python code out there. Good job. (Don't do this, PEP306 is a guide for core developers.)
Comment: I'm just answering his question, not evaluating if it's the right way to develop or not.

Defining aliases for keywords in Python


Quantum Annealing vs Quantum Monte Carlo: can QMC do all that QA can?

Question: I'm working on an essay about quantum technology, and the connection between the annealing algorithm and quantum computing hardware is an important transition in the text. I'd like to know if there is an advantage to running quantum annealing on a quantum device, over implementing the quantum Monte Carlo method (path-integral MC, if I got it right) to simulate QA. I mean, advantages other than those from quantum computing, e.g.parallel information processing. Are there problems that QA can solve better than QMC?
Comment: I think this older paper by Matt Hastings addresses exactly the question you are asking: https://arxiv.org/abs/1302.5733
Answer: First of all, quantum annealing is an concept of quantum computing which allows to solve only binary optimization problems, while quantum Monte Carlo is an algorithm which is run on gate-based universal quantum computers. However, there are algorithms (VQE or QAOA) running on the universal quantum computer and simulating quantum annealers.
A 'commercial' example of quantum annealer is a processor produced by D-Wave Systems. An example of gate-based processor is IBM quantum.
Concerning the speed-up provided by each of the algorithms. Quantum Monte Carlo provides quadratic speed-up in comparison with classical Monte Carlo (i.e. to get some accuracy of result we need $n$ operations on a classical computer, while only $\sqrt{n}$ ops. on a quantum computer. In case of quantum annealing, there is no proved speed-up over classical binary optimization, however, for some optimization tasks an empirical evidences reveal better performance of the quantum approach.
Lastly, lets have a look at the tasks which QA and QMC can solve. As mentioned above, QA is used for binary optimization problems or any other other tasks which can be expressed as a binary optimization problem. QMC is used for simulation of time evolution of a phenomena described by a statistical distribution, e.g. time development of share price or many other financial markets phenomenons. Of course, QMC is also used in modeling statistical phenomena in physics, e.g. finding thermodynamics equilibrium. So, you can see that each approach is intended for different type of task.
Comment: I thought quantum Monte Carlo was a *classical* heuristic that was *informed by* quantum mechanics, and it wasn't a gate-based quantum algorithm, no?
Comment: @MarkS: In QA you have a classical optimization cycle, so QA algorithms are hybrid, i.e. those you call quantum mechanics informed. However, QMC is purely quantum computing algorithm utilizing gate-based model.
Comment: @MarkS: A paper on QMC implementation on IBM Q: https://www.nature.com/articles/s41534-019-0130-6


What should I look for or look out for in a publishing deal?

Question: I have a manuscript ready to go for a book on Information Management and I'm about to start approaching publishers. As I do, what should I be looking for in a publishing deal? What should I be looking out for?
Answer: What kind of book are you writing? Is it a paperback or an e-book?
The two are very different today. I have less experience with paperbacks though the journalists I work with tell me they are a very long process and much more difficult to find publishers for. It's about a year for the whole process and what you should look for is a publisher who is:

responsiveness
good at editing? (one of my colleagues found a bunch of typos in the second to last edit before printing which caused her a lot of panic, as well as poorly organized index that did not make sense)
whether they will give you an advance?
does your publisher have good contacts to help you arrange book tours and other promotions?
how many revisions they are willing to go through and how many times will they patiently change the cover and title?
of course, how much revenue do you get off sales, how do the royalties work?
are there chances for sequels or other projects related? (e.g. will they build a website to help you promote...)
will they help you find a designer for the book cover?
what are your rights? This is maybe the most important because you must be very clear what your right is to republish the contents of your book (if they decide to publish a revision to update it, what happens? Do you have the rights to translations? etc...)

For e-books, things can be simpler. You can self-publish if you don't find a publisher. This is a choice many authors take in the Kindle, iBooks, Google Play stores. In this case, the barriers for entry are much lower. The main things you need to worry about are:

What's the turnaround time? Apple is famous for a much longer lead time so you need to take it into a account if you're trying to release on all platforms at the same time
formatting issues

I've heard from newspapers printing e-books that it is very possible to self-publish so you don't have to pay a company to do this for you if you need to cut costs.
Comment: This is so amazing, thank-you. I'm thinking of going down the paperback path - I'll give it a bit of a rethink though
Comment: Seriously consider ebooks; if you get a following in ebook you can use the earnings to sustain you while you hop from one publishing house to another in NYC to find a publisher.
Answer: Frankly, if this is your first book, and you are not already famous, I would not be too picky. Take any deal that does not include selling your daughter into slavery.
Getting your first book published by a major publisher is very, very difficult. You don't want to reject a decent deal in hopes of finding something better, because the odds are, you won't find something better.
Once you've had one book published, THEN you are in a position to negotiate.
It's like getting your first job. You don't go to the fast food place demanding a corner office, chauffeured limo, and 12 weeks vacation. You accept minimum wage and a paper hat. Once you've been working a few years and have some experience, then you are in a position to make demands.
Comment: I agree with Jay. It is so challenging that many famous journalists have abandoned the paper publishing route in favor of blogging or ebook publishing (seriously, sometimes blogging might get you the audience you want even if it's not as "satisfying").


How to proceed if I get current/vibration after meditation?

Question: After exercise, when I concentrated on my heart I used to feel my hands becoming warm, but that was the only response I ever got from meditation and it did not last long. But I recently tried kapalbhati and felt a sort of very light current in head. I tried focusing on that and increased in many sessions of kapalbhati. Now current has spread around my both hands, chest and head, and it lingers for hours, I know kapalbhati is hatha yoga, but is this some sort of explaination for this current? and advice me any buddhist practice to proceed from here
P.s. I also feel my face, hands and chest lightly vibrating. This finger and phone shaking even as I type right now.
Comment: I'd vote to close this as it is unrelated to Buddhist practice.
Comment: Why not just answer that it's not Buddhist practice? Then we could filter the questions that aren't relative enough and people would have examples of what not to ask.
Comment: Kapalabhati is a practice from hatha yoga.  I don't having closing rights on this account.
Comment: I'm voting to close this question as off-topic because Kapalbhati is not Buddhist
Answer: kapalbhati and hatha yoga have nothing to do with buddhism so ask the same question here https://hinduism.stackexchange.com/ or on reddit
People who talk about vibrations are people who do ''insight practice'' and they say their unpleasant vibrations disappear once they stop their ''insight practice'', so stop practicing whatever you have been doing.
Answer: electrical feeling current, hydraulic sensations,  vibration, are a universal part of meditation phenomena whether you're practicing buddhist, hindu, christian mystic meditation.
In the suttas, for example, the Buddha talks about it here in SN 54.7:
http://lucid24.org/sn/sn54/index.html
and here in MN 62
http://lucid24.org/mn/mn062/index.html
(in more abstract terms of fire and wind element)
All of these phenomena are a natural part of relaxation, pacification (passaddhi) awakening factor. It's described in hundreds of suttas as part of the 7 awakening factors:
http://lucid24.org/sted/7sb/allref/index.html
If your energy channels are blocked, then you get vibrations that hurt, are un comfortable, make your body shake as described in SN 54.7. But if you persist in your meditation assiduously every day, then the energy channels will open up and the currents of energy that loop around the body will smooth out, and you'll experience piti and sukha (rapture and pleasure).
Here's the big secret about the underlying principle of how this all works that the suttas don't explain. If you want to advance beyond first jhana, you'll need to maintain celibacy purely (no sex, no masturbation, no lustful thoughts period), and charge up your jhana battery through noble silence (second jhana quality of samadhi, stopping the thinking mind).
Just like if you want to get rich, you have to make money and not spend more money than you make. If you talk and think a lot, you'll be draining your jhana battery, it will never charge up. If you're having sexual activity, it drains the jhana battery much faster and harder. So lay people who have lots of sexual activity, will never realistically get better than low quality first jhana. If they meditate a lot and have a lot of sex, what is the most likely result is the meditation will have lots of shaking, vibration, pain, and disturbing emotions, psychosis.


Android project jar file missing after pushing to github

Question: I added the Google Gson jar file to my Android project by copying and pasting the gson-2.2.4 jar file to the libs folder and then right clicked on the Jar file and then select Build Path > Add to Build Path(I followed this tutorial). Then everything worked fine for me with this jar file, but after pushing to github, when my friends pulling this project, they said that all code relevant to that Gson jar file shows errors. How could I fix this?
Answer: Problem 1 : Jar doesnt exist. You probably forgot to add, commit and push your changes to github after adding the jar.
Problem 2 : Jar exists but unrecognised. Ask your friends to remove the existing library from java build path using project properties and add again.
Answer: You can create a library project which contains the jar file, and then add this library to your project.
Create library project in eclipse:
File->New->Android application project->Next->Check Mark this porject as a library,
uncheck Create custom launcher icon and Create activity->Finish
Add the library to your project:
Right click your project->Properties->Android->Add->Select the library project you created
->Apply->OK
After finishing these two, you should be able to use Gson, and when pushing your project,
remember to push the library project as well.
Comment: As you said its working fine but " push the library project as well",When i try to push the library project it shows the same error...How to push the support library(gson) to github?


What is SIP trunking?

Question: Can someone explain to me in plain English what SIP trunking is, please?  I've read about it on Google, but I don't really grasp it yet.  Does it allow a VoIP call to be placed outside of the LAN?  So if you had Asterisk setup as the PBX, then IP calls could be made outside of the network?  Am I close or am I just saying stupid words?
Answer: SIP trunking is connecting the PBX to the regular public telephone network using an Internet connection. It means you can connect an organisational telephone system to the outside world without needing to run voice communications lines, only requiring an Internet connection.
It allows you to make/receive telephone calls from within your phone system to/from the rest of the world, just as if your phone system was connected directly to the regular telephone network.
Answer: You also need to be aware that "SIP" on it's own can & will be used for Telephone Handsets that connect to an old telephone system that can then push the call out via analogue. (wired telephone lines or ISDN - digital lines)
SIP Trunking can as rightly stated be from a telephone system or it could just be a single phone physical or virtual softphone using a SIP trunk to make outside calls (slight over-kill), but certainly possible.

What is SIP trunking?


Rigorous Textbook for Introduction to Complex Numbers/Analysis?

Question: Does anybody know where I can find a rigorous textbook on developing complex numbers/analysis?  I'm currently working through Needham's Visual Complex Analysis, which is interesting but non-rigorous.  I would like to supplement that text.  Thanks.
Comment: I like [Stein & Shakarchi](http://www.amazon.com/Complex-Analysis-Princeton-Lectures-No/dp/0691113858). Also see [this](http://math.stackexchange.com/q/160132/4583) and [this](http://math.stackexchange.com/q/30749/4583).
Comment: The classic text by [A. I. Markushevich](http://www.amazon.com/Theory-Functions-Complex-Variable-Edition/dp/082183780X/ref=sr_1_sc_1?ie=UTF8&) is very good and easy to read. (Which is all the more impressive given that it is translated from Russian!)
Comment: Possible duplicate of http://math.stackexchange.com/questions/160132/complex-analysis-book and http://math.stackexchange.com/questions/30749/what-is-a-good-complex-analysis-textbook.
Answer: L. Ahlorfs's Complex Analysis is widely accepted as a good textbook. Also, Rudin's Real and Complex Analysis, though a bit dated, is certainly rigorous enough.
Answer: I love-hate Complex Analysis by Bak and Newman, in the same way that a cat love-hates its human.
Answer: The book of Lavrent'ev and Shabat (Methods of complex functions) is very good but it seems there is no English translation. A book by Shabat, Introduction to complex analysis has been translated and published by AMS (it has a second volume on functions of several variables).
Comment: I used Shabat's excepts on my complex analysis class, but although I searched I couldn't find the whole book. Is there any reference to it around?
Answer: For rigor and extensive discussion it is hard to beat Remmert's classic Theory of Complex Functions  (Graduate Texts in Mathematics)(v. 122).
For clarity of concept Gamelin's text is hard to beat. Although, he seems to think we teach harmonic analysis in calculus III. Sadness. It's nicely written. I found the introduction of complex-valued line-integrals and complex-Green's theorem a bit different than what I saw elsewhere. It provides a nice path to interesting results. Moreover, the whole reason I used the text to start with was that a practicing analyst recommended it. So, the criticism of lacking rigor rings hollow in my estimation. I'm sure there is a more rigorous book, but, surely there are less as well. I thought it struck a nice balance.
Another deep text that is a good second book in complex analysis is by Freitag and Busam. I emphasize, second book you read, not the first. His second volume is on modular forms and there is a truckload of gory details on Gamma functions and other sundry analytic number theory bent topics.
Comment: Or, putting unnecessary politeness aside, Gamelin's book simply lacks *any* rigour and can be superconfusing for those who see complex functions for the first time.
Comment: This is quite strange to see Gamelin's textbook as an answer for a request for a *rigorous* book.
Comment: @Artem care to elaborate? I am curious, what is the criticism. Style, or substance? Both? A link to a critical review would suffice. Thanks!
Comment: Gamelin's book appeals too much to intuition and uses too much hand waving to be advised as a rigorous textbook. This is, of course, my personal opinion (which is shared by many, e.g., reviewers on Amazon)
Answer: This is the clearest presentation I have seen. And since it's Dover, it is a bargain. The proofs are detailed, replete with pictures, and very accessible. Plus numerous examples. Flanigan's "Complex Variables."
http://www.amazon.com/Complex-Variables-Dover-Books-Mathematics/dp/0486613887
Answer: To add to @adhalanay's recommendation, unfortunately, Shabat's Volume 1 has not been translated. As if on purpose, nothing in English comes close to those books in terms of the beautiful balance of theory and applications. For just theory, Markushevich is by far the best I've seen, and luckily has been translated into English. However, it is pretty long and slow and probably a little too technical for applications. Lavrentiev&Shabat has been translated into several languages like German and Spanish though.


How to join maximum values from a polygons layer to other gridded polygons layer in QGIS?

Question: I have two overlapping SHPs. One is with two noncontinous polygons - values 0 is blue and 1 is green. Now I have 9 meters grid for the same area, but I need to "fill" the grid with values from previsous shapefile - not by averaged, but by maximum value (it means when one small polygon with value 1 is underlaying the grid, then the whole grid cell has new value 1).  Below is the picture. I'm afraid all this spatial join tools does it only by averaged values.
Answer: Look at the answer here:  How to get the "Join attributes by location" features on a QGIS Mac version    . Use the Join by Location (Summary) tool . you can find it in the Processing Toolbox.
Answer: First create a virtual field (using Field Calculator), use the tools in there to populate the virtual field with "Max(##)" values.
The do a spatial join attributes.


Does PostgreSQL PDPG support Yakkety (Ubuntu 16.10)?

Question: The official repository does not have Yakkety (16.10 packages). It seems it stops at Xenial.
Answer: PostgreSQL's PDPG only creates separate packages for LTS releases, however it seems to suggest that it should work in the FAQ

I am using a non-LTS release of Ubuntu
  Non-LTS releases of Ubuntu are only added to the repository if the packages from the latest LTS release are incompatible with the release in question. Using the latest LTS release instead generally works, unless library dependencies cannot be fulfilled, in which case we will provide updated packages for the non-LTS release.

I'm a little hesitant to spring for generally works, but there you have it.
So do not run the suggested command,
sudo sh -c 'echo "deb http://apt.postgresql.org/pub/repos/apt/ $(lsb_release -cs)-pgdg main" > /etc/apt/sources.list.d/pgdg.list'

Instead, run
sudo sh -c 'echo "deb http://apt.postgresql.org/pub/repos/apt/ xenial-pgdg main" > /etc/apt/sources.list.d/pgdg.list'

Warning, I wasn't not able to get this to work... Installing postgis failed.
 postgresql-9.6-postgis-2.3 : Depends: libgdal1i (>= 1.9.0) but it is not installable
                              Recommends: postgresql-contrib-9.6 but it is not going to be installed

Ubuntu 16.10 does not ship with libgdal1i, it ships with libgdal20 and libgdal-dev which uses 2.1.1. Bug filed here
Comment: This has just been resolved by the addition of zesty (17.04). Sorry for the lack of earlier response.