Why are von Neumann algebras important in quantum physics?

Question: At the moment I am studying operator algebras from a mathematical point of view. Up to now I have read and heard of many remarks and side notes that von Neumann algebras ($W^*$ algebras) are important in quantum physics. However I didn't see where they actually occur and why they are important. So my question is, where do they occur and what's exactly the point why they are important.
Comment: Mainly when one goes to quantum field theory. As long as you stay within the domain of ordinary quantum mechanics, i.e. a finite number of degrees of freedom, you can handle everything with Hilbert spaces and operators acting on Hilbert spaces. Once you have an infinite amount of degrees of freedom, you usually have several inequivalent Hilbert space representations of the action of the operators. This justifies a direct study of the operator algebras.
Comment: Perhaps you ought to take a look at the connection between Connes' Embedding Conjecture concerning $II_1$ factors and Tsirelson's Problem concerning quantum correlation functions of bipartite systems.
Answer: as already mentioned, von Neumann algebras are at the heart of axiomatic approaches to quantum field theory and statistical mechanics, classical references to these topics are for the former (there are a lot more, of course)

Hellmut Baumgärtel: "Operatoralgebraic Methods in Quantum Field Theory".

and for the latter

Ola Bratteli and Derek W. Robinson: "Operator algebras and quantum statistical mechanics." (two volumes).

The basic idea is that the observables of a physical theory should have some algebraic structure, for example it should be possible to scale them, that is measure c*A instead of A. Even more, one should be able to measure any (measurable, no pun intended) function of any observable A, which is possible if A is a memeber of a von Neumann algebra by Borel functional calculus. The philosophy of axiomatic quantum field theory in the sense of Haag-Kastler is therefore that a specific QFT is specified by a net of von Neumann algebras fulfilling a specific set of axioms, and that everything else can be deduced from this net of algebras (for an example see the page on the nLab here).
As Lubos pointed out, this ansatz has been very succesful in proving a lot of model indepenent insights/theorems, like the PCT and spin/statistics theorem, but has not been successful in describing the standard model, as far as I know it is not possible to use this ansatz to calculate any number that could be compared to any experiment, which puts some criticism of string theory along these lines into perspective.
On the other hand, it is possible to derive the Unruh effect and Hawking radiation using this framework in a much more rigorous fashion than it was done by the original authors, for more details see Robert M. Wald: "Quantum field theory in curved spacetime and black hole thermodynamics." (Although somewhat outdated, this is still a good place to start.)
Two striking results where the deep connection between physical intuition and the (deep) mathematical theory of von Neumann algebras is visible involve the modular group of von Neumann algebras with a separating and cyclic vector:

the characterization of KMS states in statistical mechanics,
the Bisognano-Wichmann theorem connecting the automorphism of the modular group to the representation of the Lozentz group, for more ideas using modular theory see the paper "Modular theory for the von Neumann algebras of Local Quantum Physics" by Daniele Longo on the arXiv.

The Bisognano-Wichmann theorem says that under specific conditions the modular group (of the von Neumann algebra associated with a wedge region in Minkowski space) coincides with the Lorentz boosts (that map the wegde onto itself), so here we have a very nontrivial connection of a mathematical object obtained from the structure theory of von Neumann algebras (modular theory) with an object coming from special relativity (a representation of the Lorentz group).
Answer: [Once again reading @Lubos' answer sparked these memories in my mind. Thanks for the inspiration @Lubos :)]
@student - everything @Lubos says in this answer is valid. Given that von Neumann algebras are an exotic beast at present as far as their application in physics is concerned, I do know of three cases where they have had significant direct or indirect influence on theoretical physics.

The entire program of knot theory and manifold invariants etc - as represented in Witten's work on TQFT's (topological quantum field theories) - owes in large part to Vaugh Jones' discovery of a knot invariant known as (obviously) the Jones Polynomial. I know only the vague outline of how he was led to this discovery but I do know that it happened in the course of his investigations on a particular class (type III?) of von Neumann algebras.

Connes' non-commutative geometry program also has its roots in the study of von Neumann's algebras if I'm not mistaken. Non-commutative geometry is coming of age with a large number of applications ranging from methods of unifying the Standard Model particles to understanding the quantum hall effect. NCG also arises naturally in string inspired models of cosmology and inflation, [Reference]

Finally, Connes and Rovelli  put forward the intriguing "thermal time hypothesis" in order to try to resolve some of the dilemmas regarding the notion of "time" evolution and dynamics which arise in theories of quantum gravity where the Hamiltonian is a pure constraint - as is the case in the "Canonical Quantum Gravity" program. Their construction rests on a certain property of von Neumann algebras. To quote from their abstract:

... we propose ... that in a generally covariant quantum theory the physical time-flow is not a universal property of the mechanical theory, but rather it is determined by the thermodynamical state of the system ("thermal time hypothesis"). We implement this hypothesis by using a key structural property of von Neumann algebras: the Tomita-Takesaki theorem, which allows to derive a time-flow, namely a one-parameter group of automorphisms of the observable algebra, from a generic thermal physical state. We study this time-flow, its classical limit, and we relate it to various characteristic theoretical facts, as the Unruh temperature and the Hawking radiation.

Of course these are all rather specific and esoteric sounding applications so as @Lubos' noted, vNA's are far more being ubiquitous in theoretical physics.
Comment: Well, the thing is, the language of von Neumann algebras and C*-algebras allows to formalize a lot of the concepts that people doing quantum statistical physics and quantum field theory use daily but in a sloppy way. But the price to pay is a high level of abstraction, sometimes a loss of clarity even. Especially, the geometric picture gets lost when one goes to algebraic formulations. But people like Connes are trying to bridge the gap.
Comment: Vaugh*an* Jones.
Answer: Your impression that the von Neumann algebras are not being talked about by the physicists is entirely valid. The operators on the Hilbert space may perhaps satisfy the definition of a von Neumann algebra, but it doesn't make the specific results from this portion of maths useful in physics. The von Neumann algebras are not linked to any "specific piece" of interesting knowledge or mechanisms that physicists have to learn.
An exception was algebraic or axiomatic quantum field theory which liked to talk about the von Neumann algebra but it has eventually become a fringe subdiscipline of theoretical physics. AQFT doesn't really work - it is not compatible with the most recent 40 years of fundamental physical insights about quantum field theory, such as the Renormalization Group. So the particular "focus" of the von Neumann algebra - in comparison with any algebra of operators on a linear space - are unlikely to be relevant for some important insights.
Aside from quantum field theory, the notion of von Neumann algebras is also sometimes mentioned by physicists who study statistical physics and other fields but I think it is correct to say that only physicists who have gone through some math education in the past may be seen to "spontaneously" start to use the concept of von Neumann algebras. The algebras have surely not become a standard topic of undergraduate or graduate courses directed at theoretical physicists and I think that even most top theoretical physicists don't exactly know what the algebras are and aren't.
Clearly, John von Neumann who introduced them would think that they would become much more important in physics in those 80 years than they have become. Von Neumann may be counted as one of the founding fathers of quantum mechanics; among these fathers, he was clearly the most mathematical (abstract) one and many of his hints simply didn't become standard. That's also true for some other concepts he introduced to quantum mechanics, including quantum logic. Still, he was a smart guy.
Comment: Joe, you are aware that claiming that von Neumann had a baleful influence on operator algebras is completely ridiculous. Although I've heard you cast aspersions at various mathematicians in the past but, honestly, von Neumann???
Comment: von Neumann had a baleful influence on every aspect of applied maths he ever touched: QM, QFT, economics, game theory, computers (where he perjured himself to break Mauchley's patent), and operator algebras... when you compare his achievment with those of Weyl or Wiener (or Weil) you see he just had a desire to avoid competing or communicating with his equals.... Weyl at least tried to do physics, and took the risk of appearing silly and making mistakes... Weyl's mistakes (gauge field theory! the Weyl Eq.) are more valuable than von Neumann's correct sterility...
Comment: He risked making mistakes, but not everything where he took that risk turned out to be wrong. the risk paid off: The Weyl equation was for a long time thought a mistake, since it violated parity-symmetry. Now we know that parity symmetry is not true, and we realise that Wey's equation is valid for some kinds of particles.
He invented gauge-field theory in order to unify gravity with electromagnetism, and its now thought a mistake. But his method, gauge-fields is now very important, for other purposes. That risk paid off even though his immediate intention was a mistake.
Comment: @josephf.johnson, could you exlpain why <> ?
Comment: I am not ignorant about it. I explained why it was a dead end and it has zero value according to contemporary physics.
Comment: @JonBannon - How odd is that? I thought I read on their profile that they were a mathematician. Now, they spelled it oddly, for sure (S-T-R-I-N-G-T-H-E-O-R-I-S-T), but they definitely said they were a mathematician.
Comment: I don't think Weyl's hypothesis on gauge field theory was a mistake, in the sense that there is no logical contradiction or blunder in his theory. It just doesn't describe the reality. You propose a hypothesis, and it is refuted by experiments. This is how science progresses.
Comment: But some people may see that a hypothesis has been falsified (or confirmed) vastly earlier than others.
Answer: It seems to be a good time to bring this topic up to date, at least on an increasingly active development in the field of condensed matter physics, since this discussion is part of a very few on the topic of Von Neumann Algebra.
I insist that the topic mentioned is a current effort, and nothing has been brought to conclusion yet. However, for students/researchers interested in trying to answer question of mathematical physics using Von Neumann algebra, this is certainly a promising direction to follow, and hence important to mention already at this stage.
To begin with, let us recall briefly why the operator algebraic framework of quantum statistical mechanics is an important part of physics: the concept of phase and phase transition is a well defined mathematical phenomenon only in the thermodynamic limit. For instance, recall that a "spontaneous symmetry breaking" of an Ising model is always assumed to be "in the thermodynamic limit", because the two phases "all up" and "all down", have to be separated by an infinite energy gap, so that one is sure that no local operator (meaning no operator acting on finitely many spins) can switch from one state to the other. However in quantum mechanics, these broader terms of "symmetry breaking" and "phase" or "sector" are very often employed in a relaxed manner. The reason for this is that an infinite dimensional Hilbert space (for instance an infinite 2D lattice of spins) is an object requiring the tools of algebraic quantum statistical mechanics, in which states are no longer simply vector in a Hilbert space. Usually, researcher can avoid using this framework by explicitly finding a bound of some quantity like energy, depending on the size of the system, and making the size grow to "infinity". A lot of very rigorous and pioneering results have been found as such.
This being recalled, as it is commonly known in the entire quantum physics community now, classification of quantum phases of matter is a very active and challenging domain. Among the classes of phases are non invertible phases, commonly referred to as topological order, for which the mathematical framework is already known to be category theory. It has been the subject of massive attention in the past 20 years. However, like any quantum phase, to be mathematically well defined a topological ordered phase need to be studied in the thermodynamic limit and a classification of these phases is a mathematically complicated task: they are interacting long ranged entangled  phases and finding an "index" (a robust mathematical quantity that distinguish phases) seem to require to work directly in the thermodynamic limit. This method has been very successful and straightforward (non ambiguous) in the last couple of years to classify symmetry protected phases (SPT), see for instance https://arxiv.org/abs/2111.07335 for a very comprehensible case of SPT. It has recently been brought forward (but in fact assumed from the beginning by a small community of researchers) that the classification of topological order should also be successful in the operator algebraic Framework, where the super-selection sectors, as defined here http://nlab-pages.s3.us-east-2.amazonaws.com/nlab/show/DHR+superselection+theory , are expected to be the essential object, and to show rigorously the appearance of braided tensor categories. In this active effort of research, Von Neumann algebra plays an important role: https://arxiv.org/abs/1608.02618. In this same direction, the topological entanglement entropy is thought to be rigorously defined thanks to the Jones index: https://arxiv.org/abs/2106.15741. This is not so surprising to see V. Jones' work appear here, since topological order and topological entanglement entropy are, at this point, derived only from topological quantum field theory arguments, in which Jones' work on knots is central.
Answer: It depends on the viewpoints. von Neumann algebras are a technical tool of crucial mathematical relevance in quantum theory. Whether or not  they have physical relevance is a different issue.
The reason for their technical relevance is the following: They are structures which embody both  the algebraic and topological features of all manipulations of Quantum Theory in Hilbert space. The topological aspect is in particular relevant: von Neumann algebras are closed exactly with respect to the topologies used in spectral theory and the permitted operations are continuous with respect to them. For instance if an observable belongs, or is affilitated, to a von Neumann algebra, then its spectral measure does and all (Borel) functions of that observable do.
So, technically speaking, the structure of von Neumann algebra is the best for all mathematical  descriptions or manipulations that  Quantum Theory (Quantum Mechanics and Quantum Field Theory)  needs in its Hilbert space formulation. They also permit to go behind and beyond some basic postulates  of QM and to extend them. For instance, the fact that composite systems are formalized in terms of the tensor product can be proved here,  using a more general definition of independent subsystems, under suitable hypotheses (in QFT, independence does not automatically imply the use of the tensor product as is well known dealing with type-III factors).
What is the physical weakness of a formalisation relying on von Neumann algebras? It  is easy to understand: As soon as we assume that  the physical observables of a quantum system are (exactly) the operators which belong or are affiliated to a certain von Neumann algebra (determined by the quantum system), we are assuming an incredibly strong postulate which does not have a justification and it cannot be controlled. In the practice, it is evidently false that every self-adjoint operator in a Hilbert space is an observable. Though, when dealing with systems without superselection rules or a non-abelian Gauge group, the relevant von Neumann algebra contains (as affiliated operators at list)  every selfadjoint operator in the Hilberts space.
There is no general way in QT to associate an experimental  measurement procedure to a arbitrarily given selfadjoint operator, so the postulate cannot be even checked. Think of $P^2+X^2$ when we are able to measure the position $X$ and the momentum $P$: If $P^2/2m+kX^2/2$ is the Hamiltonian of the system we know how to measure it, but if it is not, how we can measure it? (For instance the Hamiltonian may be $P^2/2m+ cX^4$.)
Another example is the Newton-Wigner position operator: it is clearly unphysical since, when assuming the standard ideal formulation of the collapse of the state, it does not satisfy basic requirements about causality. However it can be constructed with the basic observables of the considered elementary particle (in Wigner's sense) and it belongs to the von Neumann algebra generated by them.  This example is important because we have here a self-adjoint operator which cannot define an observable though there is no superselction rule o Gauge group to justify this fact.
(A few,  very personal, words about von Neumann are in my view necessary, since I read some negative comments quite inappropriate in my view. In my opinion he was one of the most outstanding applied and pure mathematicians of human kind. He can be compared with a very  small number of other mathematicians, like Archimedes, for his productivity and relevance and influential ideas  in an incredibly large and spread  fields of pure and especially applied mathematics. Maybe he was not a pleasant person, with personal opinions I cannot say to share. However his book on mathematical foundations of QM contains exceptionally  deep ideas, some of them completely understood only in this century: all modern view on quantum measurement relies in particular upon ideas by von Neumann, some of them already present in that book. )
Comment: Yes that is the point! If it is not the energy, generally speaking, there is no way to measure it. I mean: there is no suggestion in the formalism about a measurement procedure...
Comment: Not only, it depends and what you control in the laboratory. You can define observables in term of tests YES/NO using for instance detectors...
Comment: The problem with deBrogle-Bohm theory is that it is difficult to extend it into the relativistic realm. The number of particle is **not** an observable, it is *a priori* given, as far as I know. However I am not an expert...
Comment: "*If seems awkward that we're defining nature in terms of what our macroscopic apparatuses can measure*" this is the statndard claim of Copenhagen interpretation. Once more von Neumann was deeper. In his measurement scheme both the apparatus and the system (and the probe) are quantum. This is also the modern viewpoint on quantum information. Have a look at "No information without Disturbance: quantum limitations of measurement " by P. Busch  https://arxiv.org/abs/0706.3526
Comment: Perhaps we can measure $P^2+\frac{X^2}{4}$, assuming it is the energy. The electron with this energy can be made to emit a photon and we can measure the photon's energy. But we cannot measure this operator if it's not the energy, but just a random Self Adjoint operator.
Comment: Indeed. I feel very uncomfortable by this fact about quantum mechanics. There is nothing to determine the observables. Perhaps we could say that observables are generators of the Poincaire algebra?
Comment: Pilot wave theory does provide some consolation to this by saying that position is the only fundamental observable, and all other measurements are derived from position measurements
Comment: They have got two popular solutions: One is to say that the wavefunctional is the "pilot" and the field configuration is the "particle". The other is to use a stochaistic model to account for particle number changes. Both solutions are very awkward imo....If only there was some mathematical explanation of which operators are observables. If seems awkward that we're defining nature in terms of what our macroscopic apparatuses can measure.
Comment: Thanks! I will look it up. I was of the opinion that the information theory interpretation still needs some rigorous definition of the "agent" that holds the information. I still think that it's the leading interpretation of quantum mechanics.
Answer: Von Neumann algebras help understanding how physical properties of quantum systems evolve when more and more degrees of freedom are added.
To put it simply, if one builds a large quantum system by assembling $N$ elementary systems (e.g. qubits or spins 1/2), the resulting Hilbert state space $H_N$ is the tensor product of these $N$ 2D elementary Hilbert spaces. Its dimension is $2^N$. Now if one takes the $N\rightarrow \infty$ limit to model a macroscopic quantum system, the complete Hilbert space has an uncountable dimension which means it is non-separable.
There is however a theorem by von Neumann (let's call it the "sectorisation theorem") that tells that this huge Hilbert space is the direct sum of (uncountable many) separable subspaces. Each of these separable subspaces are generated by a reference vector in the complete Hilbert space (say all qubits in $|1\rangle$) and all the states obtained by changing a finite number of elementary states in the reference state.
Each reference state defines a classical sector, and one can show a number of properties on them by using von Neumann algebra concepts. In particular, there is a spontaneous decoherence mechanism that does not involve information loss to the system environment, that emerges from these properties.
This allows understanding what can be quantum and what can't. In particular it gives an explanation of the quantum/classical boundary from within the quantum formalism.
You can find more on this in arxiv/2209.01463


PnP Partner Pack 2.0 - Value cannot be null. Parameter name: certificate

Question: I am setting up the PnP Partner Pack 2.0 but getting an error 'Value cannot be null. Parameter name: certificate'. I have followed the all steps and made sure to avoid below possible errors. Can you please guide me if I am missinng anything?

Reply URL with trailing slash "/"
Permissions to other applications(SharePoint Online and Azure Graph)
Certificate Keycredentials in manifest
Captured the Thumbprint using powershell
Client Id, Secret and Storage keys in web.config
Uncehcked the option "Enable Organizational Authentication" during the deployment
Certificate in Azure Web app and the WEBSITE_LOAD_CERTIFICATES in app settings
Answer:
Make sure that in app settings of your Web App, the value of WEBSITE_LOAD_CERTIFICATES is set to *
Make sure that the App Service Plan of your Web App is at least Basic (not free)


Timing of saying "Adonai sefatai tiftach" at beginning of Amidah

Question: When does one say the 6 words starting with Adonai sefatai tiftach? Does one say it before taking three steps back, during taking the three steps back, after taking the three steps back but before walking forward, during walking forward, after walking forward?
Comment: Hey @eliyahu12, welcome to Mi Yodeya, and thanks for your interesting question! I've added a tag to your question, to make it easier for people who know what they're talking about to find your question. Hope to see you around the site!
Answer: From the Sefer Ishei Yisreol perek 23:13,14 on pg 228 it seems the proper action is to take three steps back(if thats your minhag(The Steipler did not) then take three steps forward and then say this phrase before saying shmoneh esrei. The phrase is considered a part of shmoneh esrei and not just an introduction( see Levush siman 111:1, and Igros Moshe Chelek 5:24:8 where he goes through a long discussion about this phrase and the importance of it.)


How to use a key listener?

Question: Ok, at the moment I am working on adding motors to a lego tank that I have. I have one servo in the front to steer and another motor in the rear that will make it go forwards and backwards. i have them both hooked up to a pwm controller from adafruit. I have used their python library and I have some code to move the motors. Now I just am wondering how I can make it so that when the program is running if I hit "w" it will go forward, no having to press enter. Sorry if this seems like a simple problem, I am a beginner programmer.
Comment: You'll probably get better help if you rephrase this in terms of code (like, show the code, refer to the library docs, etc) and *ask on a python forum*.
Comment: Using Lego to learn to program is awesome, that's how they taught us at uni, and it works a treat. If you can link me to the man page I'd be more than happy to have a crack at it for you.
Answer: The full answer is here:
  https://stackoverflow.com/questions/292095/polling-the-keyboard-in-python
The short answer is:
import sys
import select

def heardEnter():
    i,o,e = select.select([sys.stdin],[],[],0.0001)
    for s in i:
        if s == sys.stdin:
            input = sys.stdin.readline()
            return True
    return False

You will need to generalize this for steering.  sys.stdlin.readline is looking to read everything up to the enter key (newline)  You probably just want to do sys.stdin.read(1) to get a single keystroke.

How to use a key listener?


PHP ODBC MDB Access on a Cloud Server

Question: Hopefully quick question....
I have a .MDB file stored on my webserver and I'm trying to connect to it.
I have no way of "registering" it with a name in ODBC.
Is the only way to connect to it by specifying the absolute page of the .mdb file?

$mdbFilename = "./db/Scora.mdb";
  $connection =
  odbc_connect("Driver={Microsoft Access
  Driver
  (*.mdb)};Dbq=$mdbFilename","","");
if (!$connection) {   echo "Couldn't
  make a connection!";  }
$sql = "SELECT ID FROM
  ScoraRegistrations"; $sql_result =
  odbc_prepare($connection,$sql);
  odbc_execute($sql_result);
  odbc_result_all($sql_result,"border=1");
  odbc_free_result($sql_result);
  odbc_close($connection);

It never connects.
Any thoughts?
Answer:
try an absolute filename.
see if the mdb driver is installed on your server. If it's a unix server, chances are ... low.

PHP ODBC MDB Access on a Cloud Server


Tag Wiki and Access to Moderator Tools

Question: This is a bit odd... Since hitting the 10K rep, I've tried to help out the mods with edit approvals and the like and that appears to include tag wiki edits. The odd thing is, I don't have normal editing capability for tag wiki. This strikes me as an odd hole in the process... I can approve edits but can't make them? Any ideas?
Comment: This is no answer, but "Edit all tag wikis" is part of the 20k "Trusted User" privs. http://photo.stackexchange.com/privileges/trusted-user
Comment: @mattdm - Yeah, which is what confused the heck out of me... At half the needed rep, I can approve edits, but not make them? Seems pretty odd.
Answer: Correct, this is by-design.
At 10k we ensure at least 2 people look at the tag wiki edit (the editor and suggester)
At 20k we allow you to edit whatever you want

The idea is that we want more people looking at the wikis cause they are so prominent on the site.
Besides, we need to be able to give you something at 20k :)
Comment: Ah, I get it, that makes some sense. It's still a bit weird, but I can see the concept. Thanks.
Comment: I also discovered there's a limit on the approvals... One of our lads was busy today with good edits and I suddenly could no longer approve them having reached a cap for one user. So, now it makes a lot more sense.

Tag Wiki and Access to Moderator Tools


What is the point of normalizing rocks to chondrite or normalizing to anything else for that matter?

Question: To be exact, I'm talking about the Y-Axis. Normalizing does not make sense to me. How does this not skew data?
Answer: It does skew (at least the visual representation of) the data. However, it skews it in a way that is consistent: if you compare the shape of the line or an individual normalized value across two normalized samples, you're still able to visually distinguish which sample is more enriched and by how much. Trace elements are much more variable across rocks than are major elements, so this is a powerful tool to visualize those trends and differences.
Normalizing to chondrite is essentially asking: how does this rock's composition compare to bulk Earth? Is it evolved (i.e., is it enriched in incompatible elements)? If so, how much?
Same idea for normalizing to depleted mantle, except now you're examining whether a magma is likely to have been derived from a 'typical' source (the upper/depleted mantle is the easiest/most common area that mantle-derived magmas are generated) or if you're dealing with a deeper or enriched source (lower undepleted mantle/metasomatized part of the mantle).
Basically, it provides two major things: the ability to compare between samples, but also to obtain information about your samples' compositions relative to important compositional benchmarks.


What's the most useful way to think about a song that progresses from C to D and back again?

Question: I am thinking of a song that goes back and forth between a C major chord and a D major chord. It resolves to C. Does it make sense to still think of it as movement between tonic and supertonic, or is there a more useful way to think about this chord 'progression'?
Comment: To clarify: one bar on C, next on D, next on C etc?
Comment: It depends on your purpose. To what end would you use the label?
Comment: Aaron: My purpose is just to enhance my ability to think about music. I want to be able to discuss what I see and hear with myself and others intelligently and to the end that I can apply what I know to new situations, or allow my knowledge to suggest new situations to me.
Comment: Tim: The first several bars alternate back and forth between C and D, then there's a bar that has two beats of C and two beats of D. It stays on D for 3 bars, then goes to C, back to D for 3 bars then repeats itself.
Answer: If the song resolves to C, it suggests it is in the key of C major.
Then there are several possibilities. One is that the song bases on C lydian scale (c d e f# g a b). In this case D is simply a diatonic chord built on the second step, and it emphasizes the characteristic tone of raised fourth of the scale, that is f#.
If the song however doesn't base on lydian scale (e.g. uses note F over chord C, as a passing tone), then D is out of key, so it is a short modulation or modal interchange (D is borrowed from the lydian mode).
Answer: If this is a straightforward C chord = C major scale, D chord = D major scale I suppose we COULD think of it as a repeated series of modulations, though I wouldn't see this as being particularly useful.
It could be all in C Lydian, as @user1079505 suggested. What does the melody do?
ADDITION:  You seen to have confirmed this hypothesis in your comment.   So C Lydian it is!
It's quite common to do this sort of thing the other way round - based in C major, alternating to ♭VII (B♭).    There's not much to say about that either, except that it's an adjacent chord.  Here's a classic example (albeit in F, and with a pedal tonic bass note).
Comment: It's a song someone else wrote. The melody initially outlines the chords with some additional tones that mark it as being in C lydian. The bridge runs between g and c of the same scale, resolving on an 'a' over the D chord before repeating the entire song. I don't know any songs that move from C to Bb. Do you have an example in mind?
Comment: See addition to my answer.
Comment: Thanks for sharing the lead sheet. It helped to see that.


Ghidra what's the meaning of _0_4_

Question: What does _0_4_ mean in ghidra?
Comment: Did you look at the disassembly that related to this line?
Comment: iirc ghidra uses the split notations to indicate bitmasks i might be mistaken since you accepted pavels answer and it has been upvoted also dont have ghidra at hand so cant confirm
Answer: It is being used when there's a mismatch between type sizes in the decompiled code and Ghidra cannot show you that the whole variable is being modified.
Your PUCHAR - since it is a pointer and this is (probably) 64-bit is 8 bytes. But analyzing the disassembly Ghidra sees that only 4 bytes are being set to 0 in this line (for example a 32 bit register is used).
One of the fix you can apply is by correcting the type of local_res8 (CTRL+L) but it might be the case that the type is ok, and in fact only lower 32-bits are being set..

Ghidra what's the meaning of _0_4_


Configurable Products Show Simple Products Price

Question: How i can replace Configurable Products price with Simple Products Price without any additional price ?.
Answer: I will recommend to try this free extension.
https://github.com/organicinternet/magento-configurable-simple.
This will change the main price with simple price.
Hope this will help you!
Comment: This extension working perfectly in product view page but in category page not working how i can fix it plz.
Comment: It will not work on category page caz in category page you did not select any option! So the price will be **0**
Comment: But in my case i've select option in category page so i want to fix it plz.
Comment: Is this still recommended since the extension hasn't been updated since 2012?
Answer: If it is only a configures simple why not showing the simple with its correct price?
Sound like a pure display issue
Comment: My products has two different type like (item and box) so the item products has a specific price and the box products has a specific price so in configurable products if select item type i want to show orginal price of the item products.
Comment: In this case you could use the simple product price as price if the configured one an  then use the normal price logic to add some amount to the boxed/bundled variant.


How can I simply and reliably track my computer usage?

Question: I'm not after time tracking for the purpose of invoicing. I'm not even interested in which apps I use. I just want to know how much time I spend each day at my computer. One big pitfall I see is that many apps will suspend tracking when the user is watching a longer video or reading a long article. Are there any apps that work around this successfully, maybe by using the FaceTime camera as an additional source of data?
Answer: I've used RescueTime for years and it's been an informative little app.
They present your time consumption on a nice dashboard and you can categorize it and rate the productivity of your activities from "Very distractive" to "Very productive", set goals, etc.

If you wish they can send you a weekly digest email.
From what I've read on their forums –I don't watch movies on my computer– YMMV with movies; VLC seems to have problems being captured after the defined idle time, which is 5 minutes and other similar activities may have the same problem. Hangouts appeared as problematic while searching for "movies" on their site to answer this.
This is what they say regarding idle time:

When RescueTime detects that your computer is idle (no keyboard or mouse activity), it begins a 5 minute timer. At the end of five full minutes of inactivity, RescueTime will close the most recent record and subtract 5 minutes of time from that record.

If you are willing to pay, they offer a premium subscription that allows you to edit your idle time:

If you are a Premium user and have offline time enabled, you will get a pop up after becoming active again that will allow you to enter what you were doing when away from the computer, unless this time exceeds 4 hours. If your time away is greater than 4 hours, you can enter time manually on the Offline Time Entry page

It works on OS X and Windows.
Comment: @RusI it assigns categories to known apps and sites, you can modify them and add your own if you want. It will do what you ask. Not sure about tags.
Comment: Opposite to the OP, I would like to capture what sites I visited and what apps I ran and then assign various tags and categories to the said sites and apps. Cam this program do that?
Answer: I'm using ActivityWatch for about half a month and it really like it. So I recommend you try it :)

ActivityWatch is an open-source automated time tracker that's
cross-platform, extensible, and privacy-first.
We started building it years ago because we wanted highly detailed
automated time tracking without having to run a proprietary app (that
might not work on all platforms) or worse, sending it off to some
company server.
Features:

Tracking – Tracks active application and window title out of the box, more with watchers.
Categories – Get a better overview of your usage by breaking it down into categories.
Browser extensions – Track the active tab using the extensions for Chrome and Firefox.
Editor plugins – Track how you spend time writing code with editor watchers.
Privacy – Data is stored locally and doesn't leave your device, we put local and privacy first.
Cross-platform – Runs on Windows, macOS, Linux, and Android.

Originaly posted by Erik Bjäreholt on Quora
By the way, it also monitors your computer usage when you're idle and computer isn't sleeping or turned off ;)

Another option is to use the built-in Screen Time app, which is however only available in macOS Catalina or later...


Is Programming Witchcraft or Actual Magic?

Question: I may sound stupid, but few people say that programming is witchcraft (maybe Joking) as a Christian I Must take it seriously, because I am planning to become Software Architect in the future. Honestly I do not think it is like Witchcraft, since it has nothing to do with evil spiritual world. How can compiler translate Code into machine code... Please take seriously and answer ASAP. Thank you !
Comment: As a programmer, I sacrifice a virgin every month to improve my efficiency. Dunno if the blood pentacle I draw is considered witchcraft though.
Comment: @Nathaniel I wouldn't do that if I were you, I heard virgin sacrifices have a negative impact on space complexity.
Comment: @ThePirate42 but what about time complexity? I heard it can improve it up to an exponential factor
Comment: @nirshahar Really? I guess I could try some virgin-puppy hybrid approach then. I'll do some benchmarks and I'll let you know.
Comment: Planning is replacing happenstance with misconception.
Answer: In my opinion, programming is magic: you get into a small dark room and smash keyboards and poof you got infinite money.
Just kidding! programming isn't magic at all, nor witchcraft. If you will learn computer science or electronics, you will know how computers actually work. There is a lot of complex physics going on behind the scenes, that allows computers to actually compute. Programmers just know what kinds of things the computer can compute, and they know how to specify it in the computer so it will do what they want: this is called programming.
Higher level programs will all get compiled into something called "machine code", which basically is just all operations a computer knows how to calculate. Of course, this "compilation" process is also some program people wrote, that is also running in "machine code". In fact, the very first compiler just had to be written in machine code, because there was nothing to compile it to machine code otherwise. Then, all other programs and compilers will build upon previous ones, until we reach what we have today.


What is the legality of copying a game?

Question: What is the legality of making a new game that is essentially the same as another, without using trademark names? For example if I make an obviously knockoff iOS game that is essentially something like Angry Birds? Can one patent games?
Comment: My guess is it's about copyrights, but I think software patents also exist.
Answer: NOTE: Specific to the EU
Based on this:

Copyright will protect only the computer program in the form written by a programmer i.e. its source code. Neither the functionality of a computer program, nor the programming language or the format of data files used in a computer program in order to exploit certain of its functions constitute a form of expression of that program, and thus, those are not protected by copyright.

As such, you couldn't sell the direct source code, but you could make a derivative game with the same concept and execution, even in the same programming language, and sell it.
It's worth noting that creative works in the form of art are copyright-able, so you couldn't copy assets and if the assets were similar enough to the original game they might have a case against you. If in your Flappy Birds clone you made the bird a space ship and the pipes into asteroids then you'd likely have no problem.
Answer: Under US copyright law, claims have been made that the "look and feel" of a computer program is protected by copyright, particularly in Broderbund Software Inc. v. Unison World, Inc. That case established a broad protection for user interface elements of a program's design. More recent cases have narrowed this protection, and the extent of "look and feel" protection in US law is not currently clear. Non-US law may well be different, and the law on this point may change with future court cases.
As mentioned in another answer, specific artwork used in a computer game is protected by copyright, so any game using art based on the source (without permission) might be an infringement.
If you are planning to create or market such a "close" game in the US, you would be well advised to seek advice from a lawyer with experience in software copyrights, which is a sub-specialty of copyright law.

What is the legality of copying a game?


Sequence rule for $n^{th}$ term

Question: I have the following sequence and I need to find a rule for thr $n^{th}$ term:
$$\lbrace a_n\rbrace=\lbrace 0,1,1,2,2,3,3,4,4...\rbrace$$
The rule that I thought about is:
$$a_n=\left\lfloor\frac{n}2\right\rfloor, \ n \geq1$$
Is this valid?
Comment: This is of course assuming that the intended pattern is that apart from the term for zero, you have each number appears exactly twice.  Technically there is not enough information given to distinguish this from the sequence $\{0,1,1,2,2,3,3,4,4,4,5,5,5,6,6,6,7,7,7,7,8,8,8,8,\dots\}$ where the number of times each number repeats increases as you get further in the sequence, or some other arbitrarily chosen sequence with the same nine initial terms.
Comment: If you prefer to start your index at $0$, then try $a_n=\left\lceil\frac{n}{2}\right\rceil, \ n \geq 0$. This is [OEIS A110654](http://oeis.org/A110654).
Comment: $\dfrac{2n-1+(-1)^n}{4}$ works too.
Comment: Yes, it looks valid.
Comment: If the pattern will continue forever, yes, the formula is correct.
Answer: In order to make an answer I will write this.
There is a project called OEIS whose purpose is precisely to help people finding closed formulas or at least recognize their sequence in a dictionary of already existing sequences.
So when you have a sequence like yours, you go there, enter your numbers and you will be given possible matches.
As you can notice your formula appears first  $a(n)=\lfloor\frac n2\rfloor$ along with its cousin $\lceil\frac n2\rceil$ since it just depends of the starting indice.
But you will notice also that a lot more sequences are matching, why is that ?
This is because 9 terms are insufficient to decide, it could also be the examples below (I picked a few interesting ones). I also indicated where the sequences were branching :

$\lfloor n^\frac34\rfloor=0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6,\blacksquare\ 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, ...$
decimal expansion of $\frac{10}{891}=0,0112233445566778\blacksquare900112233...$
starting from water icing temperature, converting Farenheit to Celsius $\frac59(t-32)=0, 1, 1, 2, 2, 3, 3, 4, 4, 5, \blacksquare\ 6, 6, 7, 7, 8, 8, 9, 9, 10, 11, ...$
The minimum number of distinct distances determined by $n$ points in the Euclidean plane (no formula) $0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, \blacksquare\ 5, 6$
Comment: Thank you very much for the additional information! Very clear!

Sequence rule for $n^{th}$ term


Which definition of 'vest' applies in 'vested interest'?

Question: Which definition at http://www.oxfordlearnersdictionaries.com/definition/english/vest_2 applies to http://www.merriam-webster.com/dictionary/vested%20interest? I want to dredge below this term, and ask not about the Merriam Webster dictionary that I already apprehend.
Answer: The phrase vested interest has a different meaning in common usage than the individual words. Definition of vested interest noun from the Oxford Advanced Learner's Dictionary: "a personal reason for wanting something to happen, especially because you get some advantage from it". For example, "She has a vested interest in the proposed ban on plastic bags because she owns a business that sells canvas shopping bags."
The meaning probably evolved from the legal definition "A right or title, as to present or future possession of an estate, that can be conveyed to another." If you held a vested interest in a property, you would have a personal interest in increasing or maintaining the value of the property, so that your title to it is valuable.
Comment: Sounds a lot like being *invested* in something, no? I think the common meaning of *vested* is the same, not different from, the use of *vested* in *vested interest*. When you *vest* in a company you become involved with it, part of it. You have a vested interest in it.
Comment: The meanings are similar, but different unless you are talking specifically about the legal definition. There is a reason that dictionaries like OALD list "vested interest" as a phrase distinct from vest or invest, and that you will only find "vested right" defined in legal dictionaries. As a phrase, "vested interest" has come to mean more than the sum of its parts.


Duplicate video files in WhatsApp Sent items

Question: Is there any scenario where WhatsApp copies video twice in sent items (with different sizes) that was sent to the single recipient? I had a scenario where I am sure I have sent the video to single user, during the sent operation I got Retry options for few times ( due to disk was full and/or for network) so I remember I have retried 3-4 times to deliver that message, but now I can see two copies of the same video with different sizes. Is this scenario possible to occur or have I sent to another user by mistake. Cant check because later I have changed by phone losing all messages history.
Answer: It might be possible that the file failed in the middle of uploading for some reason and the uploaded part remained as an incomplete file in your sent items. Then when you sent the file again, instead of resuming the upload, a complete file was resent seperately. I'm not a 100% sure but it is possible.


Web hosting on another continent?

Question: My client from the US wants to have a website for Australian users. I am wondering if the web host really needs to be in Australia for this site. Does it really make any difference compared to having it hosted in the US?
Comment: Using a CDN for static content is usually a reasonable compromise.
Comment: Probably there are legal implications in Australia with a website not being hosted in the country?
Answer: Sort of. Two things to consider (although both are related):

Because the host will be on the other side of the planet, it will be relatively slow to respond versus hosting based locally. Since page speed directly correlates to positive conversion rates and a positive user experience hosting the site in the US may have a negative effect on their user experience and conversion rates.
Page speed is a ranking factor for Google. Sites that are slow will have their rankings affected. Keep in mind that fast sites do not receive a bonus and only the slowest sites are supposedly affected. But since their hosting will slow their site down if it is hosted in the U.S. this should be considered.
Answer: It won't make much difference in case you hosting has geographically distributed servers.
Still, you can take benefit of CDN to have goo page load time.
Take a note, "Only less than 20% of overall response time is spent downloading actual HTML document; rest over 80% of time is consumed downloading components associated on the page."
Answer: I am using linode vpn on dallas data center. but all of my visitor from turkey. I set up linux - redis - debian server for wordpress.Google is fetching my site on 20-25 ms.
for users, you must use cdn. than you should optimize your database via cache.

Web hosting on another continent?


Effective web driver management in Selenium2 + Grid2 + NUnit tests in C# for multiple browsers

Question: I've been struggling with this for a while.  We plan to move to a continuous integration server soon (probably TFS or Jenkins).  I'm having a hard time figuring out how to efficiently manage the webdriver to run all tests in selected number of browsers. Locally I use Resharper to run my tests.
What I want is an effective way to run tests for all browsers, and sometimes locally one browser. I want efficient webdriver management for grid2.  What is the ideal life of a WebDriver? A test fixture class? Or entire testing session? When should I call Exit() or  Quit()?
Before I just commented/uncommented out the browser I wanted in a Static Factory method, having one instance per testing session, which makes it impossible to run all the tests on all browsers and compare side by side results and parallelize the running of tests (which theoretically TeamCity can do).
I have tried adding a [TestFixture(Browser.XXXX)] enums to a top level WebDriverTest superclass and then setting the web driver from a factory method in the test fixture setup.  The problem is, adding many of these disables the possibility of parameterizing the the [TestFixture] attribute in subclasses. And I had some unexpected behavior (IEWebDriver completely not working) when I had multiple of these attributes.
The OOP suggestion is a test configuration. I'm not sure how to programatically configure the unit test settings in NUnit.  Can this be done in C# (ideal) or does it need to be something attached to the Test Runner (not ideal, if i have multiple test runners).
Any ideas to help me better run a Selenium Testing suite in IE would be great.
PS: I also tried Gallio/MBUnit.  The tests ran in parallel but not stable.  And I can't find a test runner as nice as Resharper.
Answer: One stable and fairly inexpensive option is to use a service like Sauce Labs https://saucelabs.com which allows you to run your tests on a grid that they maintain and has a bunch of browser versions and OS versions that you can target with your testing.  There are some other perks like there is a video of each test that ran that you can go and watch later, or stream as it is happening.  In this case with C# and Nunit you would do something similar to what you have already done with a parameterized test fixture and in the test setup you would set the browser - in the case of sauce labs you would use a remote driver with the correct DesiredCapabilities set.  There are pretty good examples on the sauce labs site.
If you don't want to use something like Sauce Labs, you're still on the right track.  You should be able to have a base class with a parameterized test fixture.  You should also be able to paremeterize the child class's test fixtures, but with different parameters, not overriding the same ones.
I'm unclear exactly what is causing the issue with the IEWebdriver not working.
In terms of keeping the webdriver instance open, I like to exit after every test case.  The reason is that the session will be the same and there may be tests where you want a clean session (not sharing from multiple tests).  You can do this pretty simply in your setup and cleanup methods, which can also be set in the base class.  Nunit will run the child class's setup/cleanup method first, then the base class's so you will still be able to have your own setup/cleanup for individual classes in addition to what you specify in the base class.
Comment: Trying to figure out questions like this is why I checked out Saucelabs, it's so much easier letting them handle the various Browsers, Versions and OSes.  They have free plans so you can play before pay.


Contact angle variation

Question: Is the contact angle dependent on gravity? I read it is independent of gravity but this seems counter-intuitive. I feel a liquid kept in 0 gravity won't stay in the container itself, so how can it be independent of gravity?
Answer: There are at least several models to calculate, predict the contact angle and some involve gravity, others do not. One practical method, the Wilhelmy Plate Method , also described here,  establishes a static equilibrium between the hydrostatic force in a column against the surface tension force
$$sin(\theta)=1-\frac{\rho g h^2}{2 \lambda}$$
where $h$ is the depressed column height, $\theta$ the contact angle, $\rho$ the fluid density and $g$ the local gravity.
So the answer is yes, a model does exist relating gravity to contact angle, however restricted to a specific arrangement of static equilibrium forces involving weight of the fluid.
Note that the Wilhemy formulation does not involve any property of the solid or gas in contact with the fluid. The other methods that predict contact angle without gravity involve energy relationships between the fluid, solid and gas interface. They are just different models, different balancing of equilibrium forces.

Contact angle variation


Regarding details usage of mvc toolkit & mvc contrib

Question: people use all utility , controls mvc toolkit & mvc contrib provide but my question is there any specific web site which guide me in details how to use mvc toolkit & mvc contrib related controls and classes. i can download those project from codeplex but without knowing how to use those then how can i implement those things in my project. so my request that please guide with all tutorial and docs for mvc toolkit & mvc contrib for using in project. i need details guidance for implementation in my project. thanks
Answer: I am the coordinator of the Mvc Controls tookit. You may find the list of all Mvc Controls toolkit tutorials here. Moreover, the codeplex web site contains a detailed documentation of all its featuree. See here.
Unluckly all asp.net mvc stuffs require a greater learning effort than the corresponding webforms stuffs because they give an higher control on the architecture of your application.


ASP.NET Web Forms - Manually Invoking a __doPostBack Call

Question: I have a web forms page with a button that involkes a __doPostBack callback to the page.  I would like to invoke this manually - by "manually" I mean from outside the webpage, for example by using wget.  Is there a way or an example of the best way to do this, please?
Answer: No, it's not impossible to do this, although I'm not sure if it can be done with wget, becuse you have to set page variables using javascript, which wget won't support.  You would most likely want to use something like perl or some other scripting language to post a postback with the correct variables set.
This is a non-trivial task, but it should be straight forward.  open your web page, and look at the source.  Then find the __doPostBack code and you should see how it works.  Use something like Fiddler to view your postback variables.  Then duplicate this on your "outside" code.
Answer: Rather looks like you can't do this, closing the Q
Answer: you can use something like WatIn http://watin.sourceforge.net/. Its not direcly intended for stuff like this, but can be used to programmatic click on buttons on a webpage.


In Quebec, what kind of financial assistance might be available to an unemployed single mother with kids?

Question: My husband will be separating from me in a couple of months. I am unemployed and have two kids both under the age of 6. Is there a single mother's compensation? Especially in my situation where I am unemployed.
Answer: 1) Child support from your ex. Google "Federal Child Support Guidelines", and ask questions on www.ottawadivorce.com/forum
2) See here for information on tax benefits for parents http://www.cra-arc.gc.ca/bnfts/
3) Low-income parents often qualify for subsidized (free or low-cost) daycare spots - though there can be a long wait-list for these.
4) See the Related Questions on this forum e.g. here Benefits available to single-mom with low income, in Canada?


Pruning a young honey locust tree

Question: I have planted a honey locust tree about three years ago. Ordered online.  I believe it is the kind that is thornless.  It is growing nicely as far as branching out but has not grown in height. My husband said I must have bought a shrub.  I know it is a tree.  Is it OK to trim the lower branches and will this help force some growth in height?
Answer: Stormy's answer is great.  I would wait to cut the lower branches until the tree has some shape.
One thing you can do to help the tree grow is water.  I know it seems obvious, but new trees take years to establish good root structure (see stormy's answer).  If it's a bare root tree five gallons of water a couple times a week would be great.  Otherwise five gallons per diameter inch of the trunk would be fine (a couple times a week).  Obviously if you live in a place like Missouri or somewhere with 30-60 inches of rain a year this may not be as important.
See stormy's answer.  What zone is the tree planted in - USDA plant hardiness zone map should be easily searchable.  If your local retailer sold you this plant I'm assuming it is a good choice for where you are.
Again, I agree with stormy.  Don't cut the lower branches as long as the tree is not hurting other aspects of your landscape aesthetically or otherwise.
Transplanted trees do go into shock when they are put in their new homes.  It takes a while for them to establish viable root systems to get the water and nutrients they need to thrive.  Again, see stormy's answer, but in general larger transplanted trees take longer to establish themselves than smaller younger trees.
Definitely follow up with photos stormy has requested.  It's very helpful to have more information.
Comment: What a sweetie, user22106, I am giggling and so very happy you agree with me.  Excellent additions to my answer!!  My name is in every paragraph?  Major huggs.
Comment: Im new here your answer seemed right on.  I'm an arborist as far as work but aways learning.  Thanks.
Answer: Gleditsia triacanthos inermis moraine  The inermis means 'without thorns'.  How long ago did you plant this tree?  Please send a picture of your tree in its environment.
Do not trim those lower branches. Yet. Would you say this little tree is multi trunked?  Do you remember the variety by chance?
Your tree is doing work you are unable to see below the ground. This root growth is done first by the plant before putting much effort in the top growth. This is the tree's foundation to counterbalance the canopy. Leaves are necessary to make the fuel to do the work growing roots, caliper of trunk. Those little branches with a few leaves out of the end and growing out of that trunk 'feed' the girth of the trunk while young as well as providing carbohydrates via photosynthesis to make a solid root system.
When your tree gets a great root system started it will take off vertically. Honey Locust is not a shrub or large shrub.  If you have Gleditsia it is a tree. Patience might be your only problem, grins.
I am fairly sure you purchased a bare root 'stick'?  Or did you get a tree in a pot?  To send in the mail, the lightest possible condition for plants is bare root.  Works well but takes longer to show any growth upwards.
Addressing your thoughts on pruning the lower branches. A branch on a tree will always stay at that height forever.  In fact, when taking the caliper of the branch thickening into consideration, that branch will even be lower in the future. The center of that branch will always exist at that height for the tree/shrub. Height and width happen at the apical tips of branches only.
The only trees I will stake until a decent root system is grown are bare root trees (and mature trees that blew over).  Staking is like the cast on a broken arm to a tree.  When you take that cast off that limb is very fragile, weak, atrophied.  If you planted a stick, staking would not be necessary nor a good thing.
Trees/shrubs grow stronger root systems and trunks when they are allowed to move in the wind.  All factors remaining the same, trees that aren't staked grow faster, their root systems more vigorous and stabilizing, the trunk girth or caliper is amazingly larger in non staked trees.
If you have a stick that is staked the staking is slowing down progress of healthier growth.  I hope this is understandable and meaningful. Please send more information.
Need to see this tree, how it was planted (tell me everything you can remember in as much detail possible), the name of this plant other than the common name, the scientific name is best.  If I am wrong about Gleditsia...then this is another tree with a similar common name.  If you get ERMIS or with thorns you will want to pull it up and start over.  Those thorns are a good 1 1/2 inches, so stout I swear you could use them for nailing wood.   Get one in your foot?  It will go through to the other side of your foot.
Gleditsia is a superb tree for a lawn, patio. (only the inermis plant). It allows enough light through its canopy for a healthy lawn.  The leaves are tiny, don't worry about raking (I use my gas powered blower to blow them around and off the lawn, patio).  Honey Locust is one of the hardiest trees that is also a valuable ornamental tree.  It is considered a small to medium sized tree, depending on the variety I would expect no more than 20 to 30 feet in height and half that for canopy.
This is one of the plants I know well and that scientific name just pops up and rolls right off the tongue. Let's make sure this is the tree ID for sure.  Where do you live?  What zone? Pictures, invoice, company's name where you purchased?
This is a picture of this tree getting ready to be made into bare root maybe B&B for half.  Look similar in size?

Pruning a young honey locust tree


What's the difference between WTFPL, CC0, and public domain?

Question: What's the difference between WTFPL, CC0, and public domain? Are they essentially the same thing?
Comment: When you find this question interesting, you might also be interested in the proposal for a new [Open Source Stackexchange](http://area51.stackexchange.com/proposals/82234/open-source?referrer=LYVOhcyWjB2btmuqLjy44w2).
Answer:
What is the difference between CC0 and the Public Domain Mark ("PDM")?
CC0 and PDM differ in important respects and have distinct purposes.
CC0 is intended for use only by authors or holders of copyright and
related or neighboring rights (including sui generis database rights),
in connection with works that are still subject to those rights in one
or more jurisdictions. PDM, on the other hand, can be used by anyone,
and is intended for use with works that are already free of known
copyright restrictions throughout the world. The tools also differ in
terms of their effect when applied to a work. CC0 is legally operative
in the sense that when it is applied, it changes the copyright status
of the work, effectively relinquishing all copyright and related or
neighboring rights worldwide. PDM is not legally operative in any
respect – it is intended to function as a label, marking a work that
is already free of known copyright restrictions.

http://creativecommons.org/about/cc0
Unlike Public Domain, the WTFPL is actually a license, and confers rights to the user of the software as such, whereas Public Domain doesn't confer any rights, but is merely an acknowledgement that no rights are asserted.  That's why a license is always preferable to Public Domain; a license explicitly gives permission.
Comment: CC0 is a waiver of rights, but also [functions as a license](http://wiki.creativecommons.org/CC0_FAQ#How_does_it_work.3F) as a legal fallback: "`If the waiver isn't effective for any reason, then CC0 acts as a license from the affirmer granting the public an unconditional, irrevocable, non exclusive, royalty free license to use the work for any purpose.`" There's very little legal precedent for the termination of copyright (outside of normal expiration) so the CC Foundation has its bases covered in the event that waiving copyright is not possible in some jurisdictions.
Comment: It's worth noting that in some parts of the world, your code _can't_ be used unless _explicit_ permission to use it is granted. Merely being in the public domain isn't sufficient in many places.
Comment: Being in the Public Domain means that *there is no copyright*. You don't need a copyright license to use something which isn't copyrighted.
Comment: @TimPost To be totally clear: are you saying that, in some jurisdictions, code whose copyright has expired normally cannot be used legally without permission? I'm not saying that's incorrect, but it seems to fly in the face of the entire point of copyright expiration (but then, law is often full of surprises).
Comment: @apsillers: He's saying that you're not granted explicit permission to use the code, and that in some places, that explicit permission is needed.
Answer: The public domain is a bit hard to define formally, as it varies per jurisdiction and there are even jurisdictions that don't recognize a creator's right to dedicate her works to the public domain. This is exactly the problem CC0 is designed to solve:

CC0 helps solve this problem by giving creators a way to waive all their copyright and related rights in their works to the fullest extent allowed by law. CC0 is a universal instrument that is not adapted to the laws of any particular legal jurisdiction, similar to many open source software licenses. And while no tool, not even CC0, can guarantee a complete relinquishment of all copyright and database rights in every jurisdiction, we believe it provides the best and most complete alternative for contributing a work to the public domain given the many complex and diverse copyright and database systems around the world.

CC0 is a license that is equivalent to dedicating your works to the public domain, but it also takes care of the various legal issues and ambiguities of the public domain by simply being a license. The same, more or less, holds true for WFTPL, it's an extremely permissive license you can apply to your works and not worry about the nuances of the public domain.


How can the angle be found in this triangle?

Question:
AD, DE, EC and BC are equal in length, and the bottom two angles are the same. How can the exact value of angle BAC be found?
Answer: We construct new points $F$ and $G$ such that the configuration $ABCDE$ is congruent to the configuration $BGAFD$.
I will spoilerbox the rest of the proof as these new points give away most of the question.
More hints:

 Note that $ACBG$ is a parallelogram and $FE$ is parallel and equal to $BC$. This creates the equilateral triangle $\triangle DEF$.

Rest of the question:

 We can start chasing down angles. We have $\angle BCA=\angle FEA=60^\circ+\angle DEA=60^\circ+\angle BAC$ and $2\angle BCA=180^\circ-\angle BAC$. Solving, we have $\angle BAC=20^\circ$.

Picture (for a hint you might want to take a glance at this):

Comment: I've taken the liberty to include a picture. The "congruent configuration" is achieved by mirroring horizontally and turning 180°.
Comment: OK but how did you figure out what lines have to be added and where? I know many problems like this one, where drawing some additional lines at certain places makes the solution simple. But the hardest part for me is usually to figure out where those lines should be drawn in the first place.
Comment: @BarbaraKwarc The main motivation is to create equilateral triangles. Here, you notice that EC can be moved to AD to the newly created  line DF to form an equilateral triangle.


What is a word for a possible error?

Question: Let's say you're cross-referencing two tables of information and you find a value that is not the same in both tables, but appears like it should be. How would you express the quality of this find? It's only an error if you assume that the values should be the same, but based on your limited context it may turn out that they are supposed to be different. It's a possible error or inconsistency. How would you express that?
Comment: Some data are labelled as 'anomalies' which are later proved to be either errors in documentation or real results that are inconsistent to expectations or even true readings that disprove the hypothesis.
Comment: Sorry, shoe; that has vastly less to do with English however general than with data processing.

As you said, "It's only an error if you assume that the values should be the same, but based on your limited context it may turn out that they are supposed to be different" and that simply means you need to describe the context more clearly. Most obviously, please specify exactly what you mean by "appears like it should be" in this case?

Until then what would be wrong with "suspect, please?
Answer: How about a discrepancy?
"I found a discrepancy in the data."  You are not implying error, just calling to attention that it needs review.
Sorry, I can't comment (not enough rep) so had to submit this as an answer.
Answer: I believe "I think there might be a issue with this field" would be correct, sorry, for not commenting, but I don't have enough rep.
Comment: Your suggestions are all synonyms for error. Unfortunately alone, they do not imply that the error/inconsistency is possible but not certain.
Answer: I tried looking in online dictionaries and synonym finders, and couldn't find a single word meaning "possible error." A possible error or possible inconsistency are still good ways to describe it; it's only one word extra!
If you really wanted to describe the value's quality in one word, you could say either:

the value's quality was questionable.
the value's quality was dubious

Or you could state that there may have been an error, which describes it in one word as an "error," but adds a word like "may" to imply ambiguity. In a sentence, that could read as:

These values differed between the two tables; we suspect this may have been an error.
Answer: The term "suspect value" is used in statistics for items which fall outside the spread of most of the other data (usually differing from the mean by more than the Standard Deviation). I couldn't find a definition online but I found a number of statistics sites which used the term such as this one and this one. If your tables contain experimental data then "suspect value" would be a good choice.
Comment: 'Suspect value' would seem to have the same number of words as 'possible error'. More than one. And I know which I'd choose.
Comment: @EdwinAshworth The OP didn't specify a single word answer, I thought he was just looking for alternatives, particularly ones which were accepted in the field
Comment: "What is a word for a possible error?" seems pretty clear to me.

What is a word for a possible error?


Handwriting Music

Question: I am a composer who started on computer software to write, but am now switching to handwriting music. I have read that one writes everything out in pencil first, then goes over it in pen, but how far does the pencil go? Do you write all lines, all key signatures, all time signatures, and all bar lines in pencil first in addition to notes and rests, or do you do the former list of items in pen first? I'm just worried that if you wrote everything out in pencil, absolutely everything, upon erasing, you would destroy the paper and remove some of the staff lines and things such as that.
Comment: Not an answer, but Clinton Roemer's book The Art of Music Copying is a very interesting read about how things used to be done "back in the day". It's about the copyists' role, but it also implies things about composers. https://www.amazon.com/Art-Music-Copying-Clinton-Roemer/dp/B000KTREQ4
Answer: Composers of the past few centuries have settled on a compromise: they tended to use staff paper with five-line staves already written in, like so:

They then wrote in everything else with pencil: key signatures, time signatures, accidentals, pitches, etc. This way, any erasing they did preserved the staff lines. Although, in my experience with manuscript study, they didn't erase anything, they just scratched stuff out like a banshee.
And more practically, composers rarely felt the need to write the key signature on every single musical staff; once they write it once, they just assumed it was in play until they changed it. Notational requirements like that can wait for the proper engraving process.
Comment: I think the composers of yore used pen instead of pencil, which explains the constant scratching out.
Comment: Perhaps [samples of handwritten sheet music from the past](https://medium.com/@bmsbmusic/mozarts-vs-beethoven-s-handwritten-sheet-music-687a68070456) might give the readers some insight :)
Comment: I think OP realized it's possible to buy or print paper with the staves already on it.  The concern was that vigorous erasing might lighten the printed staves.
Answer: This is a bit of an addition to Richard's answer:
I do compose semi-regularly, and when I do that, I often handwrite the music first. So you may find my procedure useful.
I write into music notebooks (= notebooks with pre-printed staves, a bit like what Richard shows). These should be easy to buy, as well as individual sheets of paper, if you don't like notebooks that much.
I'd just make sure that:

There are not only the staves themselves, but thin guidelines all around, both horizontal (that make it easy to make all ledger lines on the same level) and vertical (dtto for barlines). It makes the writing much easier.
It has a decent paper size. (I use A4, many of the staff papers are even larger).
If it's a notebook, it has a "normal" binding, not a "ring" one. (The hand can hurt quite a bit from writing from over the rings.)

When equipped with such a paper, I just take a pen and write, and when it's written, I go to the computer and typeset it in Lilypond. When I make a mistake, I just cross it out, or make an arrow to a notehead with label "this is a D" or whatever like that, and continue — so no pencil is actually needed. (I also use a lot of "shorthands", like arrows that "copy & paste" bars into different places. Nobody will ever read that — the main product is the Lilyponded score.)
Here's a little sample from my notebook:

If you look closely, you will notice that there are very thin grey lines all around the place. Those are the "guidelines" I keep talking about. You can also see some things scratched out and a note "ještě 3×" = "3 times more", which would be of course unacceptable in a normal score.
Comment: What are "guidelines"?
Comment: @chrylis — I added a little picture to the post, you will see them there. They help you to keep all the ledger lines at the same level.
Comment: There are also several tools online that will produce a PDF of custom staff paper for you with your selection of page size, size and number of staves, grouping, etc.
Comment: @chrylis: Are there any that would be able to print the vertical and horizontal guidelines too? I couldn't find such a tool, and the guidelines are just invaluable.
Comment: @chrylis - I would guess they are very faint lines (light light gray).
Comment: Interesting; I haven't seen that sort of faint grid before.
Answer: You can prepare the sheet with the staffs, names of instruments ore voices, clefs, key signs (and even the measure lines), then you make a copy of the empty original sheet (grand staff for piano or full score for band or orchestra). I did so when I wrote for brass bands or a quartet by hand. I never started with a pen, there were too many corrections. Only the final version was a new copy with pen. Some scores remained in pencil writing.
Comment: Great suggestion -- to make yourself a template.
Comment: There are actually sites offering templates for free as [here](https://www.blanksheetmusic.net/), so you just have to choose and print. (No light grey guidelines however.)
Comment: yes, and in finale you have all kind of templates and scores. The time I'm speaking about was 40 years ago  ;)
Answer: I'd suggest using manuscript paper marked with pre-printed musical staves. Or you can buy a five-nibbed pen for drawing your own staves. If you're reasonably confident about the bar lengths then you can prepare the page by drawing in the vertical barlines in black pen. That way you're less likely to run out of space at the right-hand end of the stave.
However, I should say the creation of the score as you compose and the subsequent preparation of publishable score and parts afterwards are two different processes.
I'd suggest choosing processes that let you maximise the time you spend composing.
I've created scores and parts by hand in the past, and I wouldn't willingly go back. Now for instance, if I want to add extra bars or an entirely new part to a score, I can do it and have beautiful printed parts in minutes. Making the same change for handwritten score and parts would require multiple pages of the score and all the parts to be rewritten - hours and hours of work. It's still creative work, but graphically creative rather than compositionally creative.
In addition, if you're creating a score for transposing instruments, the manual preparation of parts from score can be a lengthy, error-prone process, particularly if you're dealing with unfamiliar instruments.
But having said that, a well prepared hand-written score is a thing of wonder.
Answer: If you're the sort of person who works it all out in your head before you write it down, then you'll have no need for any pencil.  But look, in this day and age you can choose pen or pencil based on what's comfortable for you.  You can always use a copy machine to turn pencil into something indelible that will look like pen.
If you use pencil, sharpen it with a knife and give the lead the shape of a calligraphy pen.  This will make it easier to get the fat stuff with one stroke.  (You can sharpen a handful of pencils and then you won't have to stop to sharpen as often.)

Handwriting Music


What's in the center of a Galaxy?

Question: Ok, so it's supposed that there is a black hole in the center of any galaxy, that makes my head explode because:

There is light in the center of the galaxy, but it is supposed that black holes, also attract light.
For a black hole to exist there should be a star explosion, so what size does the star needed to be to create such a galaxy.
Why does the black hole doesn't eat us, I mean what objects are pulling us away from the extreme gravity of the black hole.

I'm not god, I didn't study Astronomy, I'm just a kid fascinated by the Universe. (This question should be dumb for anyone who studied Astronomy)
But if you think my question is dumb, (which isn't) or if you have any recommendation for further asking, let me know!
Comment: Welcome to [astronomy.se] @Antonio!
Comment: [Related](http://astronomy.stackexchange.com/questions/8593/what-is-supposedly-in-the-center-of-the-milky-way), though specific to the Milky Way.
Answer: At the center of our galaxy is a powerful radio source named Sagittarius A*, which is believed to be a super massive black hole (SMBH). This blackhole would contain far more mass than your run-of-the-mill supernova remnant. Our galaxy is believed to contain a SMBH containing the mass of likely a bit above 4 million times the mass (Gillessen) (2) (Ghez) of our Sun. For reference, I don't think we've ever discovered a star more massive than 600 times that of our Sun.
It's also important to understand that while many people look at blackholes as mystical or all-consuming, they actually have to follow the same rules as everyone else in the stellar neighborhood. The stars that make up our galaxy don't fall into the black hole for the same reason our planet doesn't fall into the Sun. Our star orbits black hole, our star system's velocity in equilibrium with the attractive force of the galaxy's center of gravity. This should hopefully resolve point 3.
For point 1, we should make clear that the 'black' part of the black hole is only true once you cross the event horizon. This is the case because at this point the escape velocity to escape the gravity of the black hole because greater than the speed of light. The light that isn't within the event horizon and is moving away from it is free to escape. So we can see light around it.  But why is there so much light? Well, as it happens there are a lot of rather young and large stars in this area. It is not completely understand why this is the case. Lots of stars, lots of light! There are other factors that can contribute to this too, such as there simply being lots of stars between us and the center, not just in the center itself. The accretion disk of a black hole can also be exceptionally bright. Hopefully that clears up part 1.
Now for part 2. As far as I know, we don't really have any way of determining exactly where our SMBH came from originally. Black holes aren't necessarily formed just from a supernova event, there are a handful of other ways they can be created in nature. What is apparent, however, is that SMBHs contain far too much mass to be from a single star. It has probably consumed plenty of other black holes to grow to what it is now.
One interesting and notable difference between the comparison of a star system and a galaxy is the distribution of mass. While our Sun is believed to contain 99.8% of the mass of our solar system, the SMBH at the center of the Milky Way is not nearly as massive as the total mass of the Milky Way. The ratio can vary a lot, and there are some galaxies which are believed to host no SMBH at all.

Gillessen, Stefan et al. (23 February 2009). "Monitoring stellar orbits around the Massive Black Hole in the Galactic Center". The Astrophysical Journal 692 (2): 1075–1109.
Ghez, A. M. et al. (December 2008). "Measuring Distance and Properties of the Milky Way's Central Supermassive Black Hole with Stellar Orbits". Astrophysical Journal 689 (2): 1044–1062.
Comment: Wouldn't surprise me much if Sagittarius A* didn't occasionally wander outside the center of mass of the galaxy. Given the size of Milky Way, and propagation speed of forces, things will be a bit sloppy.
Comment: @RobJeffries Edited that portion out. You're correct, I mispoke (miswrote?).   However, the last I had read on the subject opinions were a bit mixed as to whether a SMBH was *necessary* for the formation of large galaxies, or whether a SMBH was the *result* of the formation of a large galaxy.
Answer: If you understand the facts, your head won't explode!

You are right, light cannot escape from even a black hole, so why is there so much light in the center? Well, simply because there is a lot of light in the center of the galaxy, because there is a high concentration of stars. These stars are very far away from us, so the light from each together create a "halo" effect in the center, which makes it bright.
The type of black hole you are thinking of is a stellar black hole, caused by a supernova which eventually leads to a neutron star collapsing. Not all supernovae; become black holes, look up the Chandrasekhar Limit if you want more information. So it is believed that galaxies contain supermassive black holes at the center and the mass of the supermassive black hole is equivalent to the entire galaxy!
This black hole won't eat us. You have the typical misconception of black holes. Black holes don't have super sucking power; in fact, they do not "suck" at all. It is only if you get close to the event horizon of a black hole that you cannot escape it's gravitational pull. If the Sun became a black hole we wouldn't get "sucked" into it because it would have the same mass as itself before, and we would orbit it normally. Gravity and inertia is what keeps us in orbit and the stars in our galaxy in orbit, so as long as we stay in orbit, we will be okay. By the way, this supermassive black hole at the center of our galaxy is about 30,000 light years away, so even if we somehow get out of our normal orbit and head towards the center, we won't get "sucked" in for a very long time.

There are no dumb questions, just dumb answers.
Comment: I wouldn't consider a SMBH to be equivalent to an entire galaxy (at least not to the galaxy they're in). The mass of the milky way has been measured to be around 0.8-1.5x10^12. A pretty big difference from Sgr A*'s 4.1x10^6. The smallest ratio I know of is M60-UCD1, which hosts a SMBH of about 10% of the galaxy's total mass.
Comment: Worth pointing out that we can't "see" the Galactic centre. For that you need a radio or infrared telescope. Your answer to part 3 is not helpful and does not address the central misconception. We are much closer to the Sun, but we don't fall into that either.
Comment: Adding on to what @RobJeffries said: the reason we can't see the center is the large amounts of gas and dust blocking our view.
Comment: @RobJeffries  you are correct, I have updated my response to part 3 of the question and welcome any further comments.
Comment: @HDE226868 dust scatters, but how does gas help block the light at visual wavelengths? Or does "see" refer to a wider range of wavelengths?
Answer: I was about to put this in a comment, but it did not let me because it is too long. So, I will just put it here.
There is a certain radius from the center of the black hole, where light inside this radius cannot come out, i.e., event horizon.
The light that we see is from materials those are spiralling inwards into the black hole, and they are outside the event horizon. These materials experience frictions, therefore they are heated up, and lose their energy into radiation.
Black hole can be formed by various mechanisms, according to theories, with or without star explosions (a.k.a. supernovae, SNe). For star-forming black hole, the size, which is typically referred to the zero-age main sequence (a.k.a. ZAMS) mass, is still under debate. But for sure, the star has to be "massive" $> 8$ solar masses in ZAMS. Note that these massive stars might form neutron stars or black holes after the SNe; also the stars might not leave any compact object if the explosions are pair-instability SNe.
For a galaxy's black hole, how it is formed is still unknow. One theory is from the accumulation of stuff after SNe, like you said. But, we don't know exactly at this moment, therefore to answer about the "size," I don't think it can be answered.
A black hole is just another massive object possessing huge gravitational potential, like our Sun. Therefore, there are orbits those are stable and are not attracted into the center of the potential.
Comment: Sgr A* is fairly quiet, with no accretion disk to speak of, so there's not much light coming from its immediate vicinity. But I'm sure you know that and were just talking about the EM radiation from active black holes.
Answer: In the middle of the Milky Way is a supermassive black hole and a strong radio source in Sagittarius A*.
It is 26 thousand light years away from us.
Latest estimates estimate the black hole to be 4.31±0.38 million solar masses.
It's Schwarzschild radius is about 12Gm(0.08AU).

What's in the center of a Galaxy?


What do the passport stamps for Guernsey and Jersey look like?

Question: I am curious as to what the passport entry stamp for the Bailiwick of Guernsey and Bailiwick of Jersey look like. I would assume that I would receive a stamp if I enter from France since I am leaving Schengen and entering CTA. I've tried searching but surprisingly can't find anything.
Comment: [This Home Office document](https://www.gov.uk/government/publications/common-travel-area) mentions the stamps, but the photos have been redacted. Very frustrating, and quite silly. What's the point in redacting stamps you put in people's passports?
Comment: It's extraordinarily rare for anyone to post pictures of any particular passport stamp online, compared to the total number of travellers to that port of entry. So you can find lots of Heathrow stamps, the occasional Paris, Manchester, Birmingham or Edinburgh stamp, but other stamps are very hard to find, or impossible. It's even possible that no one has considered them noteworthy enough to take a picture of and post online.
Comment: Are you travelling there or making plans? If yes, it would be nice if you could share whether you could get such a stamp!
Comment: I added your link to my answer, thanks for thinking to look it up! It could have been a good source were the images not redacted.
Answer: Below is the entry stamp of Alderney (Bailiwick of Guernsey) - a UK stamp but with crowns rather than stars to designate officer ranks.
Passports of EU/EFTA states, Australia, Canada, Japan, New Zealand, Singapore, South Korea and the US are not stamped; however, the officer had no problem giving me the stamp (which is on a blank sheet).
Comment: @JakeDot We know nothing of OP's citizenship. Residence means nothing, only the passport used (except when an Article 10/20 card is used alongside the passport). FWIW, I'm an EU citizen but the officer had no problem giving me the stamp (on a blank sheet), though I had to wait for the others to pass (almost all French ID card holders so it was quick)
Comment: @JakeDot No, EU/Schengen, Australian, Canadian, Japanese, New Zealand, Singaporean, South Korean and US passports aren't stamped. Besides, specific categories of EU/Schengen citizens can still enter on an ID card (people below 19 in a school group, plus all categories that can enter the UK on one
Comment: do you have an answer to this part of the original question?

"I would assume that I would receive a stamp if I enter from France since I am leaving Schengen and entering CTA."

I'm not sure if it is possible for CTA or Schengen residents / EU citizens to get a stamp in their passport when they normally would be exempt.
Comment: Thanks for taking the time to scan/upload a picture!
Comment: @Crazydre do you know if this has changed after Brexit, do they stamp EU passports now? I'll go to Alderney from France next month. Passports are now required, ID cards no longer sufficient.
Answer: You will not necessarily receive a stamp. I have travelled from Schengen to CTA (both UK and Ireland, and also from the UK on to Isle of Man, Jersey and Guernsey) multiple times and have never received a stamp.
It may depend on your citizenship.
I think you can ask on arrival if they can stamp your passport. I heard from some travellers that they like to collect the stamps and usually are able to get their passports stamped on request.

I just found a better answer to your question:

In addition, Guernsey, Jersey and the Isle of Man apply UK entry regulations and issue UK entry stamps in passports. Consequently, the UK is henceforth taken to include these territories.

So, the stamps would presumably look like UK stamps, with text referring to the respective location.
An Example can be seen below in the answer of Crazydre - it shows that the stars in normal UK stamps are replaced by crowns.
Source: Answer to "uk - What do non-EU/Schengen citizens need [...] when travelling [...] CTA?"

As MJeffryes mentions in a comment above:

This Home Office document mentions the stamps, but the photos have been redacted.
Comment: If you are an EU/EEA citizen (which looks probable since your profile says you're in Austria), then you won't get any stamps from Ireland or the UK. It's different for people who are not.
Comment: @MichaelSeifert: It definitely won't change for Ireland; what happens for the UK nobody knows at this point.
Comment: Uploaded an image
Comment: @HenningMakholm:  Do we know whether that will change when/if Brexit happens?


detect DHCP server on a wired network

Question: On Windows 7, how can I check if there is a DHCP server ruling the LAN on which my computer is running ? How to detect its IP address ?
Comment: Technically, you'd implement half a DHCP client: Send `DHCPDISCOVER`, listen for `DHCPOFFER`.
Answer: Quite simply:
You can tell that there is a DHCP server on your network by testing your NIC configuration and seeing if it is set for DHCP, and if it is, if you've pulled an IP address.
You can kill that bird, and the other(what is the address of the server?) with one stone, simply by going to a command line and using "ipconfig /all". Look for an entry that says "DHCP Server. . . . . .:" and it will tell you the address of the DHCP server.
Now, if you're trying to determine if your DHCP server is actually a server or a router, you'd need to discuss that with an admin.
Comment: You can probably tell if the DHCP server is a router if the default route IP is the same IP as the DHCP server.
Answer: If your client computer is configured to get its address using DHCP, then ipconfig /all command will show you which server supplied its address.
If, however, your client is using a static IP address, this information will not be shown.  You can use the DHCPLOC TechNet / resource kit tool is a more informative solution, detecting DHCP servers - even ones that you aren't expecting.  It will show you the whole offer process.  It does not lend itself well to being a scriptable tool, since it is designed to be run interactively, but it will deliver the information.

detect DHCP server on a wired network


OAuth Server with Android Client

Question: I would like to implement OAuth authentication for my mobile Android users. At the Android part I can solve the problem with opening a HttpClient.
The HttpClient would connect to my site, where the OAuth server would run, presenting the providers to login to. The problem is that I don't know what OAuth server to use. I'm looking at open source alternatives, so nothing like janrain, etc.
Can you suggest any OAuth servers that would be useful in my configuration I'm describing. There are so many alternatives available (mostly in java, php, django, etc), but are just some projects maintained by a few individuals. That could also work, if the packages are maintained properly.
And I don't need so many oauth providers. I need the following ones: Yahoo, Twitter, Facebook, Google, and that's pretty much it.
Thank you
Answer:
And I don't need so many oauth providers. I need the following ones: Yahoo, Twitter, Facebook, Google, and that's pretty much it.

In this case why do you need an Auth server at all?
What authorization schema do you plan to use?

OAuth Server with Android Client


why is the denominator of the correlation coefficient the SD of X multiplied by SD of Y?

Question: I don't quite understand what is going on in the correlation coefficient formula. In the numerator we have the covariance, and in the denominator we have the standard deviation of variable x multiplied by the standard deviation of variable y.
So ultimately it is a ratio of covariance to the product of the two standard deviations.
What is dividing by the product of the two standard deviations doing to help us determine the corrrelation ?
I have tried to draw it out to help me visually understand it as I find this helps, but am stuck as to what I should be looking for.
Answer: Covariance and correlation coefficient measure essentially the same effect: How 'linked'[1,2] are two variables, i.e. if $X$ increases, how much will $Y$ increase on average?
The problem with covariance is that its value depends on the scales of the two variables:  The value of the covariance doesn't tell you much if you don't also know over what range $X$ and $Y$ vary.  Therefore, you don't know whether $X$ is more 'linked' with $Y$ or with $Z$ if you only know that, say, $cov(X,Y)=1000$ and $cov(X,Z)=0.1$.  Maybe $Y$ is income in dollars (with big spreads), and $Z$ is percentage of time spent brushing teeth (very small spreads) -- then $X$ (amount spent on toothbrushes) may be more linked to $Z$, although the covariance value is quite lower [3].
To account for that, the correlation coefficient norms the covariance: We divide the covariance by the spreads (measured as standard deviations) of $X$ and $Y$.  If you do the math (or run some simulations), you'll see that the correlation coefficient ranges from -1 (complete negative dependence) over 0 (no [linear] dependence) to 1 (complete positive dependence).  Thus, it's possible to compare the degrees of 'linkage' between different pairs of variables.  And after you've used them for a while, you get a feeling for how much 'linkage' exists for a certain correlation coefficient.

[1] I'd normally use 'correlated' instead of 'linked', but that might be confused with the correlation coefficient in this answer.
[2] To be more precise: 'linearly linked'. There are lots of examples where there is a clear relationship between $X$ and $Y$, but their correlation (and thus covariance) is zero, e.g. if the scatter plot of the two variables looks like a circle or a cross.
[3] And the covariance values will change if you change the units of the variables, e.g. if you express $Y$ in milliseconds or $Z$ in fraction of average income.
Comment: great I think I'm making more sense of it. Having looked at it further it kind of looks like a pair of Z-scores …?? (X- xbar)/SDx and (Y-ybar)/SDy……or is this not a good way to look at it ?
Comment: @B.Miller Yes, if you mean the similarity of normalizations: a z score normalizes the distance from mean (to the standard deviation); correlation coefficients similarly normalize the covariance (to the product of the two standard deviations).  But don't try to see the correlation coefficient as a product of the Z scores of the two variables -- the Z scores are for each variable individually; the covariance and correlation coefficient explicitly describe the interaction between the variables.