Is the concept of "spacetime" just a way for us to make peace with what we observe, or does it provide insight into what's "actually" going on?

Question: Is the concept of "spacetime" just a way for us to make peace with what we observe, or does it provide insight into what's actually going on?
Comment: Could you expand a bit on what you mean by "make peace" or "what's actually going on" in a physics context, thanks
Comment: I'm voting to close this question as off-topic because it's philosophy not physics. Sorry :-(
Comment: Yogi, you could ask yourself the same question about "momentum". Or even about "velocity". Or about shadows on the cave wall as Plato did (to choose the earliest example known to my incomplete education).
Answer: Your question has an answer which applies to physics in its entirety.
Whenever we try to explain something in Physics; we come up with a model/hypothesis to explain a particular phenomenon. Then the model/hypothesis is extensively tested for inconsistencies and when people are satisfied that the model/hypothesis is correct, these become Laws.
Now, we never know what is "actually" happening. But present laws are the best ways to explain these phenomenon. If and when a better alternative comes along, we replace the existing law with the new one.
So although it might seem a bit creepy, we never know what is actually going on. But we always make peace with the best possible explanation.
So, the proper question to pose from a physics point of view is not "What is actually happening?" but "What is the best explanation for this phenomenon?"
Answer:
Is the concept of "spacetime" just a way for us to make peace with what we observe, or does it provide insight into what's actually going on?

I consider myself a relativist. I think relativity is one of the best-tested theories we've got, and a very important theory too. As such I think spacetime provides insight into what's actually going on.
But there's a problem. When you read the original material by Einstein Minkowski and others, you come to appreciate that there's a gulf between relativity "as it was written" and relativity "as it is taught". Spacetime offers a prime example of this. It's actually a mathematical space. You draw worldlines in it to represent motion through space over time, and use a version of Pythagoras's theorem for spacetime intervals. It  works. Only then you bump into people who've been taught some weird ersatz cargo-cult version of relativity, people who talk about motion through spacetime, people who confuse space with spacetime. You try to show them some material where Einstein talks about space as distinct from spacetime, and you try to explain that Minkowski died too young to qualify what he said in Space and Time:
"Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence".
But it's very difficult to get them to read about the original material and compare it to what they've been taught and with the hard scientific evidence. They come out with things like "your pencil falls down because spacetime is curved" even though Einstein never said that, and it's just not true. This wrong concept of spacetime doesn't  provide insight into what's going on. It might be a way for some to make peace with what we observe, but that stands four-square in the way of scientific progress. And in this Einstein's GR centenary year, some of us are damned if we're going to sit on our hands and do nothing about it.


Convex subsets of sumsets

Question: There's a famous old problem in additive number theory which asks whether, for any $\epsilon > 0$, if $B$ is a 2-basis for the set $A =$ {$1^2,2^2,...,n^2$}, i.e.: a set for which $B+B \supseteq A$, then $|B| = \Omega(n^{1-\epsilon})$ ? Erdos and Newman showed many years ago that the answer is yes if $\epsilon > 1/3$, but not much beyond that is known, I think. So what is it about the set of squares that makes them hard to "cover by sums" ? When thinking about this, I wondered if convexity might be an important property. A finite set $A =$ {$a_1 < a_2 < \cdots < a_n$} is said to be (strictly) convex if the consecutive differences $a_{i+1}-a_i$ are (strictly) increasing. My question, in its simplest form, is as follows: Let $B$ be a set of $n$ integers and let $A$ be a strictly convex subset of $B+B$. Must $|A| = o(n^2)$ ?
Comment: @Terry: Thanks for the link. Actually we (grad student + me) were already aware of that paper, and several like it which have appeared since. We had a look again and while there are certainly indications that the methods there are relevant to my formulation (for example, Lemma 2.1 in http://arxiv.org/pdf/1108.4382v1.pdf), it's still not clear to us how to deduce an answer. So I was just wondering if you had something very specific in mind with your comment, or if it was just a general suggestion ?
Comment: As I said, the results do not directly apply - they assume convexity on the summand sets, rather than the sumsets - but the proof techniques may possibly be adapted to your setting.  (One could of course move B on to the other side, and use the fact that if $A \subset B+B$, then $A-B$ has high overlap with $B$ counting multiplicity, though probably the existing results in the literature won't be able to say something nontrivial about this situation.) One might also contact some of the authors of these recent papers to see if they have any suggestions.
Comment: I would suspect some variant of the arguments of Elekes, Nathanson, and Ruzsa http://www.ams.org/mathscinet-getitem?mr=1772612 would answer your question affirmatively (although the results in that paper do not quite directly apply to your setting).
Answer: The conjecture has been resolved in the negative by I. Ruzsa and myself https://arxiv.org/abs/1708.04901

Convex subsets of sumsets


27.5 x 2.00 tyre, is different width a problem

Question: like i said i have a 27.5 inch by either 2.2 or 2.0 (rather 2.0 but i'm not 100% sure) width and there aren't many tires with size 2.0 in shops at my place. Probably will go with a different width and i want to Ask is that fine. For ex. 2.2 inches. Will that fit fine? I want to go tubeless too. Which tyre will be good for dry terrain and asphalt under 40€?
Comment: Hi and welcome to Bicycles . We recommend that new members [take the tour](http://bicycles.stackexchange.com/tour) to get to know how to make best use of the site. If you do a search for [tyre width](http://bicycles.stackexchange.com/search?q=tyre+width) using the search box on the top right of the page you will find a number of similar questions. We can't give you shopping recommendations because they are so specific to you, right now, where you are.
Answer: We don't recommend specific products here but you should have no issue as long as you don't try to make a huge jump in size and so as long as your frame has enough clearance. Changing between 2.00 and 2.20 should be fine going either direction (assuming tire clearance is not an issue).
The switch to tubeless is another task but also not too difficult but will involve setting the existing rim up for it with tape and sealant.


Checkout in one step

Question: I need to have a checkout page that allows the user to insert his data in one step.
So all the sections (billing, shipping, shipping method, payment method, review order, place order button) are in the same page displayed at the same time.
How can I do this?
Comment: You could install any one of the one page checkout extensions on connect, then watch conversion plummet and bounce skyrocket. A clean, well designed checkout that doesn't bamboozle customers can be achieved with CSS alone. Be sure to A|B test, because of the hundreds of stores I know that tried OPC, the sales dropped on all.
Answer: Go to http://www.magentocommerce.com/magento-connect and type 'checkout' in the Search box.
You'll find there are dozens of extensions. Some are free.
But whichever one your choose, be aware that there's still a lot of filling out to do, albeit it on just the one page.
This often involves the use of clumsy drop-downs. And if PayPal is involved some checkout pages take you away from your site and you may lose your customer in the final step: payment!
The best plugin I know that makes the UX of any checkout page really smooth is Braintree's latest "drop-in" UI, known as "v.zero" and we do a Magento extension for it.
Comment: Sorry. This got deleted in a cleanup of spam regarding the IWD checkout extensions. Also, please don't recommend that one in the future. it's bad and phones home. See my answer on this question. http://magento.stackexchange.com/q/8460/146
Comment: Thanks for the explanation @Marius. I've removed the recommendation.

Checkout in one step


Distribution of hitting time of Brownian motion

Question: Let $\tau = \inf\{t: B_t = 1\}$ where $B_t$ is the standard brownian motion. How does one find the distribution of $B_t$ without strong markov property ?
Comment: I assume you want the distribution of $\tau$ rather than the distribution of $B_t$?
Comment: Can you use the reflection principle ? (despite of the fact that it's a consequence of the strong Markov property). If yes, then $\mathbb P\{\tau\leq T\}=2\mathbb P\{B_T>1\}$
Comment: Yes. I can use reflection principle for random walks. Is there any proof without using that ?
Answer: Note that finding the distribution of $\tau$ is equivalent to evaluating its Laplace transform $\mathbb{E}[e^{-\mu \tau}]$ for all $\mu \ge 0$.
Let $M_t := e^{\lambda B_t - \frac 12 \lambda^2 t}$ for some $\lambda > 0$ to be chosen later.  Note that $M$ is a martingale, and by the optional stopping theorem so is $M_{t \wedge \tau}$.  Since $B_{t \wedge \tau} \le 1$ for all $t$, we have $M_{t \wedge \tau} = e^{\lambda B_{t \wedge \tau} - \frac 12 \lambda^2 (t \wedge \tau)} \le e^{\lambda}.$  Since $M$ is bounded, sending $t \rightarrow \infty$ and appealing to the dominated convergence theorem implies $\mathbb{E}[M_{\tau}] = M_0$, i.e.  \begin{align*}
1 &= M_0 \\
&= \mathbb{E}[M_\tau] \\
&= \mathbb{E}[e^{\lambda B_\tau - \frac 12 \lambda^2 \tau} ] \\
&= e^{\lambda} \mathbb{E}[e^{-\frac 12 \lambda^2 \tau}].
\end{align*}
Rewriting, we've shown $\mathbb{E}[e^{-\frac 12 \lambda^2 \tau}] = e^{-\lambda}$.  Letting $\lambda := \sqrt{2\mu}$, we therefore have $\mathbb{E}[e^{-\mu \tau}] = e^{-\sqrt{2\mu}}$, and hence we have identified the distribution of $\tau$ through its Laplace transform.
Comment: I am not aware of Laplace transform. I will look it up. But can we start with the characteristic function of $M_t$ and get a similar thing?
Comment: I think it would be tricky to get a factor of $i$ to appear with $\tau$ in $M_t$, but certainly if you are able to that would work.  The Laplace transform of $X$ is basically the same as the moment generating function $\mathbb{E}[e^{tX}]$, it's just only defined for $t \le 0$.


One-point compactification of a linear space

Question: Is it possible to take the one-point compactification of a linear space and get again a linear space? Like if $X$ is a normed space add $*$ to it and define $|x-*| = 1$?
Answer: This can't be achieved if you want the normed space structure to be compatible with the topology in the sense that the norm is continuous. Since otherwise, the norm function, now having compact domain, must achieve a maximum, which is impossible due to homogeneity.
In case what you are after is just 'compactifying' vector spaces (with no underlying topology), then you'll have to be more precise about what compact should mean. In any case, you can't take a vector space (in the presence of enough scalars), add a point to it, and extend the vector space structure to a vector space. The reason is that for every scalar $\alpha\ne 0 $ in the ground field, $x\mapsto \alpha x$ is injective. So if you add one new element, you must add at least $|\mathbb F|-1 $ other elements, where $\mathbb F $ is the ground field.
Comment: Does your argument with homogeneity still apply if the underlying field only contains finitely many scalars?
Answer: If $|x - *| = 1$ for all $x \in X$, then
$$
|x| \le |x - *| + |*| = 2
$$
for all $x$. If there exists $y \in X$ with $|y| > 0$, then there exists an integer $n$ with $n|y| = |ny| > 2$. Therefore, all $x \in X$ must satisfy $|x| = 0$.
Answer: Suppose $\hat{\Bbb R}$ is a copmpatification of $\Bbb R$ and the normal norm on $\Bbb R$ can be extended to $\hat{\Bbb R}$. Then $\Bbb R$ is a topological subgroup of the topological group $\hat{\Bbb R}$. This means that $\Bbb R$ is precompact. Precompactness of $\Bbb R$ means any sequence in $\Bbb R$ must have a Cauchy subsequence. $\{n^2\}$ has not a Cauchy subsequence. A contradiction.
See also: this post and Alex Ravsky's comments in this thread.
If anything is wrong let me know. I'll fix or delete this post.


Problem with a gridview, paging and "object reference not set" error

Question: I'm stuck with the following problem. I'm trying to implement a basic GridView paged result set, which connects to an Oracle database. By itself, the GridView, and the paged results, work fine. The problem comes when I try to put it in page layout class that we have at work.
We have ClassA, which inherits from Page, and is a corporate standard. Then I have ClassB, which inherits from ClassA and which includes application-specific code. The page that the GridView is on inherits from ClassB. This all seems to work fine in other pages, and I don't think it's the source of the problem, but I thought I'd mention it.
What happens is that the first time the page with the GridView loads, everything looks normal. The query runs and the first 10 records are displayed, with the numbers for paging below. When I click on "2" or any of the other pages, I get the "yellow screen of death" with the following message: "Object reference not set to an instance of an object". The object being referred to in that error line is "Me", the Page object (ASP.pagename_aspx in the debugger). I don't believe that the exact line it fails on is that important, because I've switched the order of a few statements around and it just fails on the earliest one.
I've traced through with the debugger and it looks normal, only that on Page 1 it works fine, and Page 2 it fails.
I have implemented the PageIndexChanging event (again, it works by itself if I remove inheritance from ClassB. Also, if I try inheriting directly from ClassA (bypassing ClassB entirely), I still get the problem.
Any ideas? Thanks.
Comment: Do you get that error when PageA inherits from system.web.ui.page?
Answer: I ran into a similar situation where the base (ClassA in your example) had variables that were set up to handle all the paging and sorting bits, and the GridView was wired up to events that used those variables. Not setting the proper base class variables in my page caused the exact same sort of error.
Comment: I was trying to keep it as simple as possible, so the GridView configuration is all directly in the page, at design time (except for the results of the SQL command).
Answer: When I've had similar problems in the past, it has usually been a databinding problem (not calling DataBind() at the right time so when it tries to look at the next page the DataSource is null).
Comment: I believe that DataBind() is being used properly as the paging works fine in isolation (minus the ClassA/ClassB code). I also stepped through with the Debugger and the error occurs well before the GridView is being used.
Answer: I agree with @DotNetDaddy in that you need to make sure you set the datasource on post-back, as this is almost certainly the reason for the "fun" yellow screen of death.  The below is a very simple example that shows sorting and paging for a GridView in .NET 2.0+
The below is the exact markup required for this gridview to work correctly w/ my vb code
<asp:GridView ID="gridSuppliers" EnableViewState="false" runat="server" OnPageIndexChanging="gridSuppliers_PageIndexChanging" AutoGenerateColumns="false" AllowPaging="true" AllowSorting="true" CssClass="datatable" CellPadding="0" CellSpacing="0" BorderWidth="0" GridLines="None">...</asp:GridView>

Next is the code-behind file w/ the required sorting/paging implementation for a collection based databind
Partial Public Class _Default
    Inherits System.Web.UI.Page
    Implements ISupplierView

    Private presenter As SupplierPresenter

    Protected Overrides Sub OnInit(ByVal e As System.EventArgs)
        MyBase.OnInit(e)
        presenter = New SupplierPresenter(Me)
    End Sub

    Protected Sub Page_Load(ByVal sender As Object, ByVal e As System.EventArgs) Handles Me.Load
        presenter.OnViewLoad()
    End Sub

    Protected Sub gridSuppliers_PageIndexChanging(ByVal sender As Object, ByVal e As System.Web.UI.WebControls.GridViewPageEventArgs) Handles gridSuppliers.PageIndexChanging
        gridSuppliers.PageIndex = e.NewPageIndex
        presenter.PopulateSupplierList()
    End Sub

    Private Sub gridSuppliers_Sorting(ByVal sender As Object, ByVal e As GridViewSortEventArgs) Handles gridSuppliers.Sorting
        If DirectCast(ViewState("PreviousSortExpression"), String) = e.SortExpression Then
            If DirectCast(ViewState("PreviousSortDirection"), String) = "Ascending" Then
                e.SortDirection = System.Web.UI.WebControls.SortDirection.Descending
                ViewState("PreviousSortDirection") = "Descending"
            Else
                e.SortDirection = System.Web.UI.WebControls.SortDirection.Ascending
                ViewState("PreviousSortDirection") = "Ascending"
            End If
        Else
            e.SortDirection = System.Web.UI.WebControls.SortDirection.Ascending
            ViewState("PreviousSortDirection") = "Ascending"
        End If
        ViewState("PreviousSortExpression") = e.SortExpression

        Dim gv As GridView = DirectCast(sender, GridView)
        If e.SortExpression.Length > 0 Then
            For Each field As DataControlField In gv.Columns
                If field.SortExpression = e.SortExpression Then
                    ViewState("PreviousHeaderIndex") = gv.Columns.IndexOf(field)
                    Exit For
                End If
            Next
        End If
        presenter.PopulateSupplierList()
    End Sub

#Region "ISupplierView Properties"
    Private ReadOnly Property PageIsPostBack() As Boolean Implements ISupplierView.PageIsPostBack
        Get
            Return Page.IsPostBack
        End Get
    End Property

    Private ReadOnly Property SortExpression() As String Implements ISupplierView.SortExpression
        Get
            If ViewState("PreviousSortExpression") Is Nothing Then
                ViewState("PreviousSortExpression") = "CompanyName"
            End If
            Return DirectCast(ViewState("PreviousSortExpression"), String)
        End Get
    End Property

    Public ReadOnly Property SortDirection() As String Implements Library.ISupplierView.SortDirection
        Get
            If ViewState("PreviousSortDirection") Is Nothing Then
                ViewState("PreviousSortDirection") = "Ascending"
            End If
            Return DirectCast(ViewState("PreviousSortDirection"), String)
        End Get
    End Property

    Public Property Suppliers() As System.Collections.Generic.List(Of Library.Supplier) Implements Library.ISupplierView.Suppliers
        Get
            Return DirectCast(gridSuppliers.DataSource(), List(Of Supplier))
        End Get
        Set(ByVal value As System.Collections.Generic.List(Of Library.Supplier))
            gridSuppliers.DataSource = value
            gridSuppliers.DataBind()
        End Set
    End Property
#End Region

End Class

And finally, the presenter class used in the code-behind
Public Class SupplierPresenter
    Private mView As ISupplierView
    Private mSupplierService As ISupplierService

    Public Sub New(ByVal View As ISupplierView)
        Me.New(View, New SupplierService())
    End Sub

    Public Sub New(ByVal View As ISupplierView, ByVal SupplierService As ISupplierService)
        mView = View
        mSupplierService = SupplierService
    End Sub

    Public Sub OnViewLoad()
        If mView.PageIsPostBack = False Then
            PopulateSupplierList()
        End If
    End Sub

    Public Sub PopulateSupplierList()
        Try
            Dim SupplierList As List(Of Supplier) = mSupplierService.GetSuppliers()
            SupplierList.Sort(New GenericComparer(Of Supplier)(mView.SortExpression, mView.SortDirection))
            mView.Suppliers = SupplierList
        Catch ex As Exception
            Throw ex
        End Try
    End Sub
End Class

**the class required to sort a generic collection that is referenced in the presenter
Imports System.Reflection
Imports System.Web.UI.WebControls

Public Class GenericComparer(Of T)
    Implements IComparer(Of T)

    Private mDirection As String
    Private mExpression As String

    Public Sub New(ByVal Expression As String, ByVal Direction As String)
        mExpression = Expression
        mDirection = Direction
    End Sub

    Public Function Compare(ByVal x As T, ByVal y As T) As Integer Implements System.Collections.Generic.IComparer(Of T).Compare
        Dim propertyInfo As PropertyInfo = GetType(T).GetProperty(mExpression)
        Dim obj1 As IComparable = DirectCast(propertyInfo.GetValue(x, Nothing), IComparable)
        Dim obj2 As IComparable = DirectCast(propertyInfo.GetValue(y, Nothing), IComparable)
        If mDirection = "Ascending" Then
            Return obj1.CompareTo(obj2)
        Else
            Return obj2.CompareTo(obj1)
        End If
    End Function
End Class

Answer: I lost my original unregistered login which I used to post this question.
Anyway, Harper Shelby's answer turned out to be correct. There was an unset variable in that base class (a custom object that is our corporate standard) that caused the problem (and no helpful error message).
If an admin, or someone with the right powers sees this, you could mark Harper's answer as the one, and close this. Thanks to everyone for their help.


How are the human enemies generated in Final Fantasy Tactics?

Question: What determines what abilities human enemy units have in Final Fantasy Tactics?
Comment: Err, this depends. I believe the abilities for campaign battles (essentially, not random battles) are fixed as I've replayed a few campaign battles multiple times and the abilities always appear to be the same. The abilities of enemies in random battles appear to be random within a certain subset, with that subset apparently widening as you progress in the game. I have no sources, though - this is just personal experience.
Answer: As far as I know, they are generated randomly based on your highest character's level, as well as the chapter you are in. See this answer for levels. So if an enemy wizard shows up in a random battle, he can have abilities that would be reasonable for someone your level to have (without grinding). There are certain abilities that are blacklisted of course, such as something like Ultima.
I'm not sure if there is an official algorithm but, in practice, something like a wizard would not be generated with something like Bolt 4, if the ability would easily overpower your top level character. As long as you are on equal footing on equipment, which can become a problem if you out-level your equipment without stealing from human enemies.
As far as the types of human enemies, it appears that there are a few lists out there that can help you pinpoint a specific job to target. So the types appear to be generated randomly from a few types that are available based on location. See here and here


Scanning LAN game servers using winsock

Question: I'm trying to figure out how to use winsockets to be able to turn my game into a LAN-playable game. I've read some winsockets documentation but I can't figure out how a client can get all the games that were created on LAN.
Does it have to try to 'connect' to each IP on LAN, like trying to connect to 192.168.0.1, then 192.168.0.2, etc? Is there a better way?
Comment: Check out http://en.wikipedia.org/wiki/Broadcast_address
Answer: You would use broadcasting to advertise your servers on the LAN. Clients can then listen for these broadcasts to 'find' servers.
See here for more info:
http://tangentsoft.net/wskfaq/intermediate.html#broadcast
Answer: Typically these game servers use the local UDP broadcast, which is something that all clients receive and can process so long as they are listening to it.
Here is some sample client and server code I found that may be of interest to you: http://visual-c.itags.org/visual-c-c++/29424/
Answer: I think there are two possible ways to do this.

Make a "lobby" that clients and servers connect to so they can find each other through it.
Servers broadcast UDP packets. Clients listen and update a list of servers.

If you need a quick and easy way, the 2nd option would be great but remeber most of UDP packets will be wasted as they are used only once for each client.
The 1st option is more general and extensile solution to this problem. However, it might need more time to design and implement.
Answer: First off, I suggest that you get wireshark for any networking development. It will show you what packet goes through the wire. It will allow you to see how other games do it since there are many ways of doing this.
Using the UDP broadcast is one way of doing it. Simply change the target ip's last byte to 255 and you should be ok.
Comment: Blindly changing the last byte will not always work.  It depends on the actual subnet mask being used on the network.  The correct way to generate a broadcast address is to take the local computer's IP, `AND' it with the subnet mask, then 'OR' it with the inverse of the subnet mask.  Alternatively, just use the global broadcast address 255.255.255.255, but not all firewalls/routers will allow that to pass through.

Scanning LAN game servers using winsock


How can I automatically add author and copyright info to newly created ipython notebooks?

Question: I'd like to pre-pend a simple author and copyright clause the beginning of newly created ipython notebooks.  Is this possible? If so how can it be done?
Answer: We want to support this in metadata at notebook top level, but nobody has taken time to write a proposal for metadata structure, how to edit it, and how to show it.
This would be usefull for view on nbviewer, but also for conversion to LaTeX, and other format. It might just be slightly more complicated that at first thought, as you probably want the Authors to be more that just first name/last name (like a full embeded vcard for example).
If you want to work on that you are welcomed, otherwise in the meantime I suggest adding a simple markdown cell at top with those info.
This should be easy to do on a buch on notebook at once as they are easy parsable json.
Comment: It's been a couple years. Is this answer still correct?


$SU(2)$ Symmetry of Hubbard Model

Question: I am confused with the $SU(2)$ spin rotation symmetry of the fermion Hubbard Hamiltonian. If the Hubbard model has $SU(2)$ rotational symmetry, it means that the Hubbard Hamiltonian commutes with the global spin operator in all direction:
\begin{equation}
[\vec S, H] = 0  ~~,~~ \vec S =  \frac{1}{2}\sum_{i}
\begin{pmatrix}
c^{\dagger}_{i \uparrow} & c^{\dagger}_{i \downarrow}
\end{pmatrix}
\vec{\sigma}
\begin{pmatrix}
c_{i \uparrow} \\
 c_{i \downarrow}
\end{pmatrix}
\end{equation}
Where $\vec \sigma$ is the Pauli matrices in vector form. My confusion is that whether $[\vec S, H] = 0$ implies $[S_{x}, H] = [S_{y}, H] = [S_{z}, H] = 0 $. I have proved that they are equal to zero but I thought that my calculation was wrong. The reason why I think my calculation is wrong since if both $S_{x}, S_{y} , S_{z}$ commutes with $H$, it means that they simultaneously share the same eigenstates and $[S_x, S_y] = 0$. However, we know that from elementary QM course:
\begin{equation}
[S_{i}, S_{j}] = i \epsilon_{ijk} S_{k} ~~,~~ ijk = xyz
\end{equation}
In my opinion, $[S_{x}, H] = [S_{y}, H] = [S_{z}, H] = 0 $ is not true because they cannot satisfy $SU(2)$ commutation relation if all commutes with $H$. May I know is it true that $[\vec S, H] = 0$ implies $[S_{x}, H] = [S_{y}, H] = [S_{z}, H] = 0 $?
Comment: In general, it is not true that if $[A,B]=[B, C]=0$, that $[A,C]=0$! For example, take $B=I$ the identity matrix. Everything commutes with the identity but not necessarily with each other.
Comment: Thank you for your comment . Yes, you are right. I originally thought that there was transitivity in the commutator. I  realise that they share the simultaneous eigenstates if all commutators equal zero( e.g. $[H,S_{x,y, z}] = 0 $ and $[S_{i} , S_{j}] = 0 $. However, due to SU(2) group property, they cannot form the simultaneous eignestates since  $[S_{i} , S_{j}] \neq 0 $.
Answer: From what I understand of the standard notation, the statement that $$[\vec{S}, H] = 0$$ is exactly the same as saying $$[S_j, H] =0$$ for all $j$. Then, to give a proof that a vector operator commutes with some operator simply amounts to proving each component commutes with the given operator.

$SU(2)$ Symmetry of Hubbard Model


visual studio debug vs release mode

Question: Hi I'm using Visual studio 2010 and I can't figure out one thing.  I can debug and set breakpoints in release mode as well as debug mode.  so then what's the difference between the two?
Comment: possible duplicate of [Debug VS Release in .net](http://stackoverflow.com/questions/90871/debug-vs-release-in-net)
Answer: The difference is optimizations that the compiler applies in Release mode. You can place breakpoints if you have PDB files and by default they are generated even in Release mode.
Comment: So you can build projects and test them with Release mode in Visual Studio with no fear to skip a breakpoint or don't get debug info?
Answer: here is a more detailed answer on Scott Hanselmans Blog
But the root of the issue is that the code is compiled with more optimizations, you can still debug due to the creation of the pdb files.
Answer: Newly allocated memory contains arbitrary values - whatever happened to be last sitting there. In release builds this is untouched. Debug builds in VS initialise newly allocated memory to 0xcdcdcdcd to flag is as "uninitialised".
Why would a release build fill memory with junk to make debugging easier? Release modes are just that - minimal extra overhead for actual releases.
Answer: Here is a link to a Microsoft page titled How to: Set Debug and Release Configurations
It discusses the difference between Debug and Release.  At the top of the page you can select different versions of Visual Studio.

visual studio debug vs release mode


If I use a factory contract to create a new contract, does it show that the factory contract created it in the blockchain?

Question: I am not sure if it would show my address or the factory contract's address (or both).
Comment: What or who is "it" in "it show"? And what do you mean "created in the blockchain"? Where else would it be created???
Comment: Plus, I doubt that anything would show you the key (given that one of the basic ideas about private keys is that they should remain secret).
Comment: I mean public key
Answer: The transaction which creates the sub-contract will of course originate from your account. The transaction is sent to the factory contract with data to call a function inside the factory contract.
Once the transaction is executed (by a miner) the function execution issues an internal transaction to create the new contract. Here's an example of a contract creating a contract: https://etherscan.io/tx/0x1cb928b1b237252a975719c4a7a26d90fc7bdee7569882b918510aff64fc8686 .
I'm not sure what you mean with your question about the key. No private keys are of course exposed, only public addresses.
Comment: They're closely related but not the same thing: https://ethereum.stackexchange.com/questions/33171/ethereum-address-vs-public-key
Comment: I meant public key (I thought that was the same thing as an address? maybe I am confused)
Answer: Contracts have no keys, but you will want the address.
There is no automatic way to see what happened other than interpreting the factory code, as all nodes do.
That's a little cruel for front-ends so emit an event in the factory.
MyContract c = new MyContract();
emit LogNewContract(msg.sender, address(c));

That's how you make it easily observable.
Hope it helps.
Answer: Blockchain contains enough information to find out whether particular contract was deployed by externally owned address or another smart contract.  In the latter case one may also find out what externally owned address initiated the transaction.  So the answer is: if you've created new smart contract by calling already deployed factory smart contract, then anyone may find out both: your address and factory contract address, having only blockchain data and the address of the contract you've deployed.
While this information is contained in blockchain, it cannot be extracted using Web3 API.  You will need to use blockchain explorer, such Etherscan.io, or something like Google BigQuery.
Comment: If I am running a full node, is there an API I can hit in the node to get this data for a given transaction?
Comment: Do you mean that you already know what transaction the smart contract was deployed within?  Because it is not easy to find out this.


Can Impeachment votes be filibustered?

Question: If a few members of the House of Representatives who opposed impeachment were to attempt to filibuster the impeachment, could they or are there any internal house rules that would prevent this?
Comment: No, Filibusters are a product of Senate rules and only exist in the Senate.
Comment: @divibisan is there a limit on how long part of the house can hold off a vote by starting a debate? There is not much time until the end of Trump's term so a few day delay could make a big difference in their ability to impeach Trump.
Comment: I'm not sure, but a general question about delays in the House would be interesting. It wouldn't affect Trump's impeachment, though, since, as other questions have addressed, he can be impeached after leaving office, and the limiting factor for when he could be removed is the fact that the Senate is on recess until the 19th
Comment: The senate will not convene until well after the inauguration, thus any possible impeachment trial cannot start while Trump is in office. So this question is fairly abstract.
Answer: There is no filibuster in the House of Representatives; it is only part of the Senate rules. Furthermore, a majority of the House can vote to end the debate anytime and proceed onto the impeachment vote.
From this CRS report, page 12:

A question of the privileges of the House is considered under the hour rule. Often, the House votes to dispose of such resolutions by referring them to committee or by tabling them. The House could also order the previous question to end debate on the resolution and then vote directly on it. However, the House has never impeached an officer without a committee investigation.
(emphasis mine)

The CRS report (page 12) also offers more details on the process where the resolution containing the article of impeachment was offered directly on the floor (as opposed to the regular House procedure where there would be committee hearings).

A House impeachment resolution would move to the floor and could get a vote quickly, because there would be no hearings to present evidence. The Judiciary Committee has not yet been constituted for the 117th Congress, so an impeachment resolution would go directly to the floor under what's known as a "privileged resolution." A simple majority of members in the House is required for impeachment, so it seems likely to pass.

Can Impeachment votes be filibustered?


How do I fit two equal-length arcs in the opposite corners of a right triangle?

Question: I am trying to make two arcs of the same length such that they will both fit in a right triangle like so:

I am given the first radius (r1) and a constant k that is the difference between the leg opposite angle one and the second radius (r2)
I know that the angle of the arcs have to add up to Pi/2. I also know that this becomes impossible at some small value of k - for instance, if k was zero there is no way the two arcs could be of equal length.
If I knew the angle, I could find the second radius, or vice-versa, using trigonometric functions.
In the case where both the angles were Pi/4, I know that k would be r*(sqrt(2) - 1).

In case anyone wants to know why I'm doing this, I'm trying to show a circle that is broken open at a point and the broken ends curve out until they are parallel and a certain distance apart. That distance will be 2*k. I want to make sure that the curved-outward parts are the same length as they would be if they were still completing the circle.
Answer: just hint
The same length means that
$$r_1\theta =r_2 (\frac {\pi}{2}-\theta) $$
or
$$\theta=\frac {\pi r_2}{2 (r_1+r_2)} $$
in the triangle,
$$\sin (\theta)=\frac {k+r_2}{r_1+r_2} $$
if we put $k=xr_2$ then
$$x=\frac {2\theta}{\pi}\sin (\theta)-1$$


Why is healthcare a federal issue and not a state issue

Question: Why is healthcare in the US viewed by many as a federal issue, instead of a state issue?
It seems to me, it would make more sense to implement healthcare reform on a state level, like they did in Massachusetts.
Comment: As I understood it's widely viewed as a state issue by Republicans, and widely viewed as a human right issue by Democrats.
Comment: I don't agree that the premise of this question is correct. Both state and federal governments currently, historically and going forward have a large role in different aspects of health care policy.
Answer: There are a couple of reasons.
Lots of things are seen as federal issues by some people and healthcare just happens to be one of them
The sort of federalism where there is a small federal government focused on a small set of responsibilities, with state governments that can focus on nearly anything else that they want, is not popular with everyone in the United States at the moment. There are many reasons for that, but they all tend to stem from a belief that government should be doing something it isn't presently, and that the federal government is uniquely powerful, so it should use its unique power to do whatever it is that should be done.
Healthcare is really expensive, so it's hard for states to pay for it
You cite Massachusetts as a state that implemented healthcare reform, and it is a good example. However, the current appetite for reform that some people have involves something vastly more complicated than a mandate to purchase health insurance; the current idea in vogue is a single payer healthcare system.
Single payer healthcare provided at the sort of standard Americans are used to receiving is really, really expensive. So much so that Vermont and California have both abandoned proposals to implement a statewide form of it over fiscal concerns. This doesn't stop people from wanting it, so the natural entity to try it is the Federal government, which has several unique advantages that states don't have:

The Federal government has a very large tax base compared to any one state
The Federal government can borrow money at really low rates compared to state governments
The Federal government can (indirectly) control the supply of money to make paying for all of this easier (this would be a bad thing but there's a new intellectual fad centered around this idea).

None of these things mean that single payer healthcare is more likely to succeed at being implemented, or be a success when implemented, but the federal government can hypothetically get any such scheme over all of the hurdles that states have already run into. Whether that would be desirable or not is an exercise I leave for the reader.
Comment: @agc So called "Modern Monetary Theory". I would have to take time to find a good citation for it; the wikipedia page is currently full of issues re: original research. Also, the question is specifically about why the Federal government is attractive compared to others. The motivating factor isn't economies of scale, which requires no government power of any kind at all, but that the federal government can print money, which state governments cannot do.
Comment: @FrankHopkins and to answer your first question, yes, state taxes are typically lower than federal taxes. More importantly, they are both much lower than European taxes. Your average American can not comprehend the idea of a 40% tax bracket applying to someone who makes the average wage, but this is totally common in most of Europe.
Comment: what is different in the health care system "being wanted" in the states to health care systems in place in Europe that makes it so much harder to finance on a state level - with several states having about the same GDP as European countries? Or is state taxation simply so much lower than federal taxation?
Comment: @FrankHopkins The bill "without a concrete funding plan" was estimated to cost $400 billon. Total California state spending this year is approximately $200 billion. There is no popular movement that is going to find double the current state spending in a state that already has significant problems in managing its debt and high taxes.
Comment: Re *"fad"*: which fad?  A cite URL would be useful.   Also, a link to [economies of scale](https://en.wikipedia.org/wiki/Economies_of_scale), or some similar concept, might fit the answer's main idea.
Comment: Also, how do you come to the conclusion that California has abandoned this due to it being not fundable? The Wikipedia article for instance does not support such a conclusion at all. It only refers to one bill that was rejected because a concrete funding plan was missing, but a) there were other bills before that only got vetoed by the governor and b) there is still a movement to get such a bill through accoding to that article:
https://en.wikipedia.org/wiki/Single-payer_healthcare#California
So respective references might be needed to improve this answer.
Comment: @Joe Alright, you might want to include those numbers along with resources. I'd consider that an improvement, but as always, your call.
Answer: Because the federal government spends a substantial portion of the healthcare dollars.  It's noteworthy that the United States government (federal and state combined) spends more money on healthcare than the United Kingdom's government.  There are basically four federal programs:

Veterans' Affairs.  For military veterans.  Funded entirely by the federal government.
Medicare.  For people 65 and older.  Funded entirely by the federal government.  Possibly with copays.
Employer.  For federal employees.  The insurance is funded entirely by the federal government but can include copays and deductibles.  The federal government employs one sixth of all US workers.
Medicaid.  For those with low incomes.  At least 50% funded by the federal government, with the remainder financed by state governments.  Can include copays and deductibles.

When Massachusetts passed its healthcare reform, it had to get waivers from the federal government.  Medicaid had requirements for who was eligible and for what that weren't met by Romneycare.  It was able to get these waivers because the legislators were Democrats and the governor (Mitt Romney) was a Republican.  So there was a bipartisan request to the federal government.
To make a serious reform at the state level, the state would have to get federal approval for waivers.  Since the current set of proposed reforms is only supported by Democrats, they are unlikely to get federal approval for the necessary waivers to take over VA hospitals, Medicare, the insurance of the federal employer, and Medicaid.  There are actually some proposals by Republicans that might help, but Democrats are ideologically opposed to things like block granting Medicaid or privatizing the VA and Medicare.
Another problem is taxes.  If Vermont, California, or New York passed single payer healthcare, then they'd have to fund it with state taxes (because states can't deficit spend).  Because rich people can move more easily than poorer people, those taxes would mostly have to be raised on the middle class or employers of the middle class.  And of course if they raise taxes on employers, it is possible that the employers might leave.
Another way of saying this is that state governments have found it impossible to fund single payer.  So supporters hope that the federal government will be able to do so.  This seems unlikely.  While the federal government can borrow money, it's already at its limits for a non-recession economy.  The only time that the US had a higher debt to GDP ratio was after World War II and the Great Depression.  Wikipedia
I also remain unconvinced that increasing tax rates on the rich will increase tax revenues in the long term.  The rich have far more options for collecting their income than the middle class do.  So they are likely to do so even in the face of high taxes.  Either by hiding their income in lower taxed income types (e.g. capital gains) or by hiding their income in lower tax jurisdictions (e.g. Caribbean island countries).
It's also noteworthy that even with static scoring (assuming no income hiding), the two main proposals, a wealth tax and a 70% income tax rate on incomes over $1 million, only produce $345 billion in revenue a year combined.  That's well under half the current budget deficit much less the costs of single-payer.  And as I said, I suspect that in reality the loss in taxes from increased evasion would  entirely offset any gains.  While other countries do have higher revenues per person, they do this not from higher taxes on the rich (the US has the highest percentage of its tax revenue paid by the rich among OECD countries), but through higher taxes on the middle class.
Politicians in the US have been talking about single payer health care for decades.  I witnessed it first hand in 1992.  Polls will even show it as popular until the costs are included.  But people who have employer-based health insurance don't want to give it up.  Most employers don't want to replace buying insurance with a tax.  Most employees don't want to replace insurance that their employer buys with a tax that they pay.  And most doctors and nurses don't want to take the pay cuts from single payer.
All those problems apply to states as much as the federal government.  Or more than.  It's much easier to migrate from a state than a country.  And the long term fixes (e.g. free education for doctors and nurses) are, well, long term and not much help in the near term.
Comment: While the first half of this shows a good argument for it being a federal issue vs the states, the latter part is more of an opinion against tax increases and single-payer in general.
Answer: One additional argument I have heard from single-payer supporters is that doing it on a state level will only encourage people to move to the state and potentially not work and drag down the healthcare system. And so, to avoid this, it must be done federally.


How do I make a high-level dish?

Question: What makes a dish grant a low, mid, or high level buff? I can only seem to make low-level cold/heat resistance dishes by cooking five of the same ingredient. I'd like to sneak around Hebra in my Sheika armor.
Comment: related: https://gaming.stackexchange.com/q/302414/183611
Answer: There are apps that can help you with recipes for your game, that can be downloaded on the Google Play/App Store.
For effective recipes, the best thing you can introduce is Dragon Horn Shards into your recipe. E.g., a Lizalfos Horn, and 3 Warm Darner will create a high level Cold Resistance elixir, that lasts for 8 minutes. However, if you also incorporate a Dragon Horn into the recipe, it will last for 30 minutes.
Additionally, you can also equip a fire weapon which will help keep you warm.
Answer: There are a few less than clear things about cooking in the game. It comes down to potency, effect, healing, and duration. Potency and effect are tied together, while duration and healing is not.
The Hebra area is cold, frequently dipping into a high level cold effect. To create foods or elixirs that can provide this protection, you need 6 points (values needed change between effects). Different foods and elixir ingredients have different potency levels.
If you were to use your spicy peppers, even using all 5 you would only reach a potency amount of 5 giving you a low level warming effect for 12:30, which fails to reach the 6 needed for a stronger effect. If you were to replace one of those peppers with a Sunshroom you would now have that stronger warming effect, but it still lasts 12:30 because they both provide the same duration boost.
I only found out about this type of information a few weeks ago thanks to this video on youtube. It was an excellent starting point as it covered the potency levels required for effects. I found it incomplete as it did not cover elixirs and other things so I have been expanding my own, as well as verifying that information and understanding it better.
Answer: A good recipe that I often use is three Sunshrooms. You can cook up some Spicy Mushroom Skewer with a level two cold resistance and 7:30 duration.
Satori Mountain (Mogg Latan Shrine) has a huge amounts of shrooms, as I've read on reddit.
If you want longer duration (30 minutes!), you'll need a shard of Faroshs Horn.
Get a Golden Bow (Gerudo Town South-east wall, chest hidden in a pile of garbage: use magnesis), a boatload of arrows and a Fireblade (north west of Death Mountain, in the camp under the Great Eldin Skeleton). Then go to the Shoda Sah Shrine below the Riola Spring in Faron Region. North of the Riola Spring there's a ledge you can hide under from potential rain. Put down a bundle of wood and light it with your Flameblade. Wait for morning and jump and glide as soon as Farosh shows up and the updrafts start. Instantly draw your bow and aim for the horn. You should be able to get about 3 horns per minute this way.
Now cook up some Spicy Mushroom Skewer with a level two cold resistance and 30 minutes duration.
I hope this is helpful and elaborate enough :D

How do I make a high-level dish?


Weight machine reading variations while doing squats

Question: While doing squats standing on a weight machine, I initially thought that while I go down, my mg force will be greater than the normal reaction the ground will provide, hence my center of mass is going down. Now the weight machine can only measure the Normal force on it, which should be lesser than my real weight, but when i actually tried it out, i found out it shows I weigh more while going down and less while going up. What's going on?
Comment: Clarification - when you say "weight machine," are you referring to a scale that measures weight, or an exercise machine of some sort?
Comment: @PLK I meant that weighing scale we stand on. P
Answer: Try doing your squats very slowly to see if you get the same result.
I suspect you might be observing the effects of phase lag due to the frequency response of your weight scale. Phase shift, ideally defined for linear systems is a behavior of the system that causes the system output to respond with a delay that depends on frequency. The scale has a specific frequency response and you may just be driving it faster than it can respond.
Answer: On the downward part of the squat, your legs are, in essence, letting your upper body fall toward the ground in a controlled manner.  Your legs must then stop that controlled fall before it hits the ground.
On the upward part of the squat, your legs propel your upper body upwards, and gravity then slows its ascent.
A good comparison would be an elevator ride.  Imagine that you enter an elevator at the top floor of a building and ride it down to the ground floor while standing on a scale.  Once the doors close, the elevator cable lets the car fall a bit before bringing it to its usual downward speed.  There is a short-duration acceleration (downward) that makes you feel a bit light.  If you watch the scale as the car starts moving, you will actually see your "weight" decrease.
As the car approaches the ground floor, the cable must slow the car's descent.  There is a short-duration acceleration (upward) that makes you feel a bit heavy.  If you watch the scale as the car starts comes to a stop, you will actually see your "weight" increase.
While doing squats, you are most likely seeing the scale's reading at the end of your body's journey upward or downward, giving you the counter-intuitive measurements you have observed.


The de Rham complex of the octonionic projective spaces

Question: The complex projective space $\mathbb{CP}^n$ is a complex manifold, and hence its de Rham complex carries a representation of the complex numbers in the form of its complex structure. The quaternionic projective space $\mathbb{HP}^n$ is a quaternionic Kähler manifold, and so its de Rham complex carries a local representation of the quaternions. Continuing the analogy, do the octonionic line $\mathbb{OP}^1$ and the octonionic projective plane $\mathbb{OP}^2$ carry some representation of the octonions, or at least have some extra structure reflecting their octonionic construction?
Answer: A description of the octonionic projective plane in terms of the octonionic algebra is described by John Baez in his notes on Octonionic projective geometry:
The Jordan algebra of 3×3 Hermitian octonionic matrices, with multiplication rule $x\circ y=(xy+yx)/2$, generates the octonionic projective plane $\mathbb{OP}^2$ if we restrict the matrices $p$ to unit trace and idempotent ($p^2=p$). Lines through the origin containing $(x,y)$ with $x\neq 0$ equal $\{(\alpha(y^{-1}x),\alpha):\alpha\in\mathbb{O}\}$.
The differential forms of the de Rham complex are constructed in terms of "octonionic Pauli matrices" by Piccinni in On the cohomology of some exceptional symmetric spaces (section 4).
Comment: Thanks for the reference. Can I ask how does the octoionic Kahler 8-form related to the 4-th power of the ordinary Kahler form of the manifold?
Comment: the octonionic 8-form is a coefficient in the characteristic polynomial of a skew-symmetric matrix of 2-forms, see definition 3.1 in Piccinni's paper; I don't see a simpler algebraic relation between the two.


How to interpret Jensen Alpha statistical significance?

Question: When you regress portfolio excess returns against relative benchmark excess return you get a model in which the beta (slope) could be interpreted as the one you get from the CAPM, that is systemic risk. According to Jensen the alpha (intercept) represents the stock picking ability of the fund manager. Evaluating the alpha let you make decision about the fund manager grade of activity: if alpha is 0 you can say the investment policy is passive, if alpha is negative, you can say the fund manager ability to select asset was not good. The more positive alpha is the better is the fund manager ability in security selection. How do you interpret the significance level of the alpha? What can you say about the fund manager ability in stock picking looking at significance level?
I would say that if the beta is significative, the R squared is high and the F statistic is significative the model fitting is good for the portfolio returns. But if the alpha is not significative?
Answer: This comes down to hypothesis testing the intercept of a simple linear regression: $y=\alpha+\beta x$.
If you test $H_0: \alpha=0$ versus $H_a: \alpha \ne 0$, you can say if the $\alpha$ is significantly different from 0. However, it matters if that is a positive or negative difference, so you would pay attention to whether or not the calculated $\alpha$ value is positive or negative.
If the p-value is significant, and the calculated $\alpha>0$, the manager is outperforming passive investment. If the p-value is significant, and the calculated $\alpha<0$, the manager is underperforming passive investment.
If all you want to know is if the manager is outperforming passive investment, you can do a one-sided test of $H_0: \alpha=0$ versus $H_a: \alpha >0$.
EDIT
You don't want to do the usual F-test in this case, as that will test the slope, not the intercept. That is, the "F-test" output of a typical software, say R, will not give you information about the intercept.


Can a wire go bad

Question: I recently touched a wire on fuse box and now I have no power. Fuses are all good breaker good. Can the wire be dead? Is that a thing?
Comment: Welcome to Stack Exchange. Could you post a picture of your electric panel and the wire you "touched"?
Comment: When you say you touched the wire did you short it? Arc and sparks?  In that case I would be rechecking the fuse as it probably opened.
Answer: Wires don't go bad, but wire connections can become loose. They can also develop a burnish or tarnish on the surface which can result in a poor electrical connection, lading to an increase in electeical resistance, which in turn can create a hot spot and melt nearby wire insulation, maybe even start a fire.
Comment: Wires do go bad! Insulation fails over time. The conductors get corrosion and break. These are typically unique situations though where the wire is old and/or moisture is getting into the wire.  Is this a house? Location? What stopped working? What is on the circuit?

Can a wire go bad


Deep Neural Network using mixture of image and non image data

Question: I have rectangular bounding boxes for an object in an image, and 3-point vector of relative distances (x,y,z) of the object w.r.t camera, and 3-point vector indicating the pose of the object. I want to take the cropped patch (from bounding boxes) and resize them to 224 X 224 and pass it through to some standard networks like resnet (training from scratch) to estimate pose. Now, I think results can be improved if I use the distances and the aspect ratio (from bounding box coordinates) as input too. How do I go about doing that?
Answer: You could create a network which merges the output layer of a convolution network like ResNet (minus the top layer, if you are using pre-trained weights), and an input layer that feeds your additional inputs (the distances and aspect ratios).
You can experiment with the type of merge operation, concatenation should be a good starting point. There is a basic example of the operation, using Keras, here.


Remove "title bar" at top of chrome

Question: I feel one of the biggest improvements with Chrome on Windows is moving the tabs all the way to the top to the screen (so the mouse can just go all the way up, then click). I went with the kubuntu because they do not include the normal (pointless) Linux menu bar at the top of the screen. It took me an hour to get chrome on here and now I see there is a Giant pointless title bar across the top. It is a good 5% of the total screen area and it is just the title and close buttons. Is there anyway to have the chrome tabs all the way at the top of the screen like was intended by Google?
Answer: Go to Chrome Menu ⇒ Settings ⇒ Appearance section, unmark Use system title bar and borders.
Comment: That didn't work with unity when at maximum size of the window.
Comment: Works for me on Manjaro with KDE Plasma. Thanks!
Comment: Works for me too in the plasma desktop.
Comment: It worked for me, on Linux Mint Mate.
Comment: How to do this from console ???
Comment: Also works for Kubuntu 20.04!
Comment: It works in Ubuntu Bionic Beaver 18.04!
Comment: Also works for Ubuntu DDE 20.04
Comment: Worked. Kubuntu 22.04. Thanks
Answer: In the latest build of Chromium, version 94 now, the Menu ⇒ Settings ⇒ Appearance ⇒ Use system title bar and borders option is no longer available there.
What you need to do to access this option is Right Click in any empty space in the Tab Bar and select or deselect the Use system title bar and borders option from the drop down menu, as shown in the screenshots below below.
Use system title bar and borders option - Selected:

Use system title bar and borders option - Deselected:
Answer: Open system settings (the systemsettings app), and go to WorkSpace Appearance → Window Decorations → Configure Decoration. Switch to the Window-Specific Overrides tab. There you have to add a new override, press Add button, you will see a new window with checkboxes. Press Detect Windows Properties button (your mouse cursor will turn into aim like icon), and click at the Google Chrome window. You will be prompted of whether to use window class, or just title, choose the window class checkbox. Finally, check Hide window title bar checkbox, press ok.
Note that you can move windows by holding Alt key and clicking them.
Comment: In the System Settings of Kubuntu 16.04 LTS (KDE 5) the item "WorkSpace Appearance" is renamed to "Application Style".
Answer: For those who also would like to get rid of window buttons (minimize, maximize, close).
Right-click the titlebar of Google Chrome, go to More Actions ⇒ Configure Special Application Settings... ⇒ Appearance & Fixes tab, mark No titlebar and frame, in the following menu select Force and then Yes on the right, click OK to save new settings.
If you need to access the window manager's menu in KDE (like right-clicking the titlebar), you can always use Alt+F3 shortcut.

Remove "title bar" at top of chrome


Yellow flickering exclamation mark appears on onion icon in toolbar when opening a new web page

Question: Can anyone tell me what it means? I suppose it's some kind of warning, but it doesn't say what for. I get it every time I open a new web page; then, choosing 'Preferences'-->'Restore Defaults' from the menu that opens when the icon is clicked on, it goes away, but it comes back every time I open a new web page. Can I make it disappear permanently? Thank you for your answer.
Answer: The flickering exclamation mark shows you that a new release of Tor Browser is available. It is a recommendation to download the new version. So the best way to get rid of it is to go to https://torproject.org/ and to download the new Tor Browser Bundle.


Relativistic kinematics of particle decay

Question: Suppose a particle decays to three other particles. The masses of all particles are assumed to be known and we work in the rest frame of the parent particle.
So there are 12 parameters for this because of the 4-momenta of the three daughter particles.
Now the constraint of momentum conservation imposes 4 constraints and reduces the number of parameters to 8. Further, the energy-momentum relation for each particle imposes three more constraints and reduces the number of parameters to 5.
Are there any other constraints that reduce the number of parameters to 2?
Answer: Well, yes and no. There is a set of Euler angles that describes the orientation of the product system in space, and the remaining two parameters are all that is needed to find the final $\left|\vec{p}\right|$s.
It's clearest to me when I am writing Monte Carlo generators. You do the physics in some conveniently defined coordinate system and then throw the dice to randomly assign a orientation for the system. Like this.

Choose one of the daughter particles, call the direction of it's three momentum the $\hat{z}$ axis.
You can still describe all possible relationships between the three products, so there is no loss of generality.
Insist that the three momentum of the second daughter lies in the $\hat{x}$-$\hat{z}$ plane.
Again, there is no loss of generality.
At this point you can use, say, $\theta_{1,2}$ and $\theta_{1,3}$ (the angles between the particles) to parameterize the physics. (That choice is not unique, of course, pick something that makes your math come out neatly.)
Choose $\phi \in \{0,2\pi\}$, $\cos(\theta) \in \{-1,1\}$, and $\psi \in \{0,2\pi\}$ (all uniformly) to describe the orientation of the whole system in space.
Comment: When you fix one direction, 1 parameter reduces. Next when you specify the plane as the xz plane, 4 more parameters reduce. This is because a plane is characterized by the normal and the angle(orientation). This normal has 3 components so the total comes to 4. Something seems to be wrong.
Comment: I can see how you got there, but that's not the right way to think of it. We really are just chosing a set of Euler angles to describe the orientation of the system. Putting particle 1 on the positive z-axis fixes $\phi$ and $\theta$, and all that remains is a single rotation to fix $\psi$.


How do I stop a deleted purchased apps from continously charging me?

Question: I bought this Starmaker app at the App Store for Iphone which cost me $1.79. I thought that I would be charged just one time. But every week, I have been getting email notifications that I am continously being charged $1.79 for each week. I deleted the app from my Iphone but they are still charging my credit card. How do I stop this?
Comment: Tell your credit card company, they will stop it.
Also contact Apple about this issue, they can refund it if you really paid more than once.
Comment: You are being charged by Apple?
Comment: The notification that I get is from Itunes Store so I suppose that is from Apple.
Answer: It's likely you made an in-app purchase of some sort of subscription. To check and deactivate the subscription, manage you Apple ID account in iTunes by clicking View My Apple ID in the Store menu.

Enter your password and on the resulting page you should see subscriptions listed under Settings with the number of subscriptions.

Click on the Manage link to the right. There you should be able to cancel any recurrent subscription plans.
Answer: You should go to Apple Support and contact the iTunes team. They are the only ones who can fix this.


Pantone 376 C to Web Safe Color

Question: I recently started at a new company and the company paid a contractor for a logo. The logo is in Pantone 376 C and unfortunately contains a gradient with Pantone 382 C. I am working on web content, and I am struggling with a web safe color. The equivalent RGB of 132,189,0 looks much deeper on display. I know all displays are different my MacBook Pro and two monitors all make this color look different. With this being said, the Pantone 376 C looks fine while I'm designing in Indesign, however when I export to a PDF or a PNG and open that file it looks horrid on the screen. Any suggestions to make better web materials with the color I am given. Any RGB's I should use instead? I have to create 4 PPT slides that will be projected onto a large wall for a corporate function and I'm concerned.
Comment: Hi. Welcome to GDSE. "Web safe" colours are obsolete - a hangover from the days of computers with 8bit graphics cards (in the mid 1990s), when computer displays could only manage 256 colours.  An RGB image, with an sRGB colour profile is the best standard for the web today.
Answer: Web Safe color palette is limited to 216 colors and it is a thing of the past (see here why). I don't think you meant that.
Pantone colors are the names of proprietary ink formulas. Those inks will look different depending on the type of the paper they are printed on. They will also look different under different light conditions. Your software tries to emulate those colors (convert subtractive colors to additive colors, inks to projected light). Different software emulates those colors differently.
This is because monitors do not use inks. Therefore you will need to specify colors for monitors using a color model that is supported by monitors. RGB, for example. But, as you mentioned yourself, all monitors are different, each will display colors differently. On some, the difference will be slight, on others will be significant. You can not do anything about that.
I suggest to spend some time and come up with RGB values for your brand colors and set them in stone (put them in the brand book guide). You can do that by matching the colors on printed materials with colors on your monitor. Use various printed materials, use different lighting conditions (day light, artificial light) and manually adjusts the RGB result on different devices.
Then keep all values in the brand book and use Pantone or CMYK for print and RGB for screens.
P.S. I would not rely on the help of the contractor who used Pantone colors as gradients.
Answer: Find the web safe table here:
goffgrafix.com/websafecolors.php .
You can find a similar color.
There is a page to compare the colors here:
goffgrafix.com/pantone-rgb-300.php
Answer: The "safest" thing you can do is:

Convert all images to sRGB, then strip the colour profile.
Use #84bd00 in your CSS.

This will cause your images and CSS colours to match in the vast majority of browsers, including ancient ones like Netscape. The most likely reason your PDFs were messed up is because they were still in CMYK, and browser CMYK support is notoriously awful.
But if you're on a wide gamut monitor (such as most current gen Macs), you may notice that the colour still doesn't quite match Indesign. This is because 376 C is outside the sRGB gamut. Wide gamut support on the web is still very spotty and only a very small number of visitors have screens that can even show the colours you want, so I'd suggest sticking to the sRGB approximation for the time being.

Pantone 376 C to Web Safe Color


What is the difference between LSTMBlockCell and BasicLSTMCell in Tensorflow contrib.rnn

Question: I know that LSTMBlockCell is efficient to initialize at the begining of training. The official API guides of Tensorflow said that LSTMBlockCell add a forgot_bias. Can I just replace the BasicLSTMCell with LSTMBlockCell in my RNN models? And there are too many stuffs in tf.contrib.rnn, I feel that those APIs are really inconsistent.
Answer: The main difference between LSTMBlockCell and BasicLSTMCell is that BasicLSTMCell is implemented in terms of primitive TensorFlow ops, so it's useful code to copy and edit if you want to play with your LSTM architecture. LSTMBlockCell, on the other hand, uses a fused kernel which allows for much better performance.
Comment: I trained a model used both LSTMBlockCell and BasicLSTMCell , but BasicLSTMCell works much better with a higher test accuracy


What is the reason why Microsoft decided not to provide updates when bypassing TPM requirements?

Question: I understand TPM is quite an important tool for security, but a lot of the updates not being offered should not be related to TPM. Not offering updates to people who bypass TPM on Windows 11 and also providing information on how to bypass TPM seems strange to me. Looked around for an answer, but there doesn't seem anything official.
Comment: Microsoft provides updates to Windows 11 installations that are bypassing the TPM requirement. What Microsoft does is they say that pontentially in future it may happen that such systems not passing all requirements may get no updates after a certain point.
Answer: Does Microsoft say they won't provide updates? The KB Doc about installing on unsupported systems says:

Devices [..] will no longer be guaranteed to receive updates

They want to use capabilities of modern TPMs in future updates. That's why there are those restrictions and why it is not recommended to install on unsupported systems. In case you have a PC without a compatible TPM, those new features won't work on your PC and therefore you won't receive those updates. But they aren't actively kicking out computers from their update mechanisms, as far as I know.
Comment: I wonder what MS will do with all the PC's that does not meet Windows 11's hardware requirements after 2025 when they end Windows 10. I mean, there would be millions computers. A lot of people probably will not buy a new PC to use Windows 11.


is Doubanjiang (sezhuan hot bean paste) an acceptable substitute in recipes calling for gochujang (Korean hot sauce)?

Question: These days I keep on seeing repeated shout-outs to gochujang, which is not available where I live. However, I do have a container of Doubanjang just sitting there in my fridge, taking up space. Would it be a reasonable substitute in recipes calling for gochujang?
Comment: without a chemistry conflict, substitution acceptability is in the mouth of the beholder.
Comment: Well, J, I moved to Abbotsford BC a couple of years ago. Forgot to update my profile.
Comment: @Doug Pan Asia Market on Fraser?
Comment: Thanks J, I didn't think of that and will give it a try.
Answer: Both are mildly spicy, but the similarities end there. Gochujang is tangy and slightly sweet, whereas doubanjiang is more salty, savory and fermented-tasting. Even the textures don't match up: gochujang is smooth, while doubanjiang is chunky and ragged. I wouldn't substitute either one for the other.
Incidentally, if your doubanjiang is just sitting there because you got it for some elaborate Sichuan recipe involving like eight other seasonings... doubanjiang is more flexible than that, and will work well as an addition or even just on its own. Try frying up some ground pork with a bit of doubanjiang and some scallions, served over rice.
Comment: It was ma-po tofu. I will give your suggestion a try.
Answer: As @Sneftel has said, the flavor profile of doubanjang is too distinctive to serve as a replacement for gochujang in any real context.
That said, the flavor of gochujang is relatively easy to compartmentalize, and thus reasonably replaceable. The uses of gochujang in Korean crusine stems pretty much directly from its constituent ingredients:

Ingredient
Purpose
Replacement

Gochugaru
color and hotness
can be replaced by gochugaru, or any type of red pepper flakes with a neutral aroma profile

Malt or sugar
sweetness
can be replaced by sugar, honey, or other sweeteners

Rice flour or other starch
thickening
a bit of potato starch or flour (typically not very important)

The meju and additional fermentation does impart some savoriness and fermented flavor, but Korean recipes will typically call for doenjang or even ssamjang (which is in essence doenjang and gochujang combined) if those flavors are significantly desired.
So, depending on the dish or even personal preference, a combination of ingredients that can impart the all or some of the above aspects will generally work quite well (although red pepper flakes are de facto mandatory) - for example, people who prefer a cleaner "broth" in their tteokbokki may use only gochugaru and sugar in place of gochujang.


Best graduate level text for econometric time series?

Question: I am a masters student studying economics.  The program that I am attending is extremely quantitative with a heavy focus on econometrics.  I am looking for a text on time series analysis.  I really want something applied but rigorous enough to be considered for an introductory PhD course.  I want a text that will be useful in the long run...a reference that I will continue to use later in my career as either an economic consultant or PhD student. Thanks for the help.
Comment: In case you're unfamiliar with it, consider economics.stackexchange.com.
Answer: I recommend two texts.

James D. Hamilton, Time Series Analysis, a classic textbook that covers all the theory you need, including fashionable state-space models. It doesn't have any source codes, but I wouldn't call it just theoretic. It has examples. This text is always cited, and it's good to have it handy.
Shumway, Stoffer, Time Series Analysis and Its Applications: With R Examples - this was our test in statistics PhD level time-series. It has good amount of theory. It's not shallow by any means, but it's focused on applications, comes with R package astsa available in CRAN! You get all the example data and source codes, and powerful functions. The guy who taught us was Bayesian, so this book is very Bayesian friendly without going nuts. It covers all the modern stuff in linear modeling. This is my favorite book on the subject.

Note, Stoffer et al. has a sequel for nonlinear analysis. I haven't read this book yet, can't comment on its merits.
There's one more text: Greene, Econometric Analysis, 7th Edition. It's a standard text in econometrics. It has quite a bit of theory for time series too. One advantage of this text is that all examples are from economics, and that time series chapters can be seen in the context of the body of knowledge of econometrics together with cross-sectional and panel analysis. It can be beneficial in some cases to look at time series this way. It also has many examples, but they're not code examples. If you're specifically interested in time-series, I would not pick this text.
Comment: Thank you for the input.  We have and are using Greene, which is an excellent overall text.  I was looking for an econometrics textbook  which focused specifically on time series analysis.  I will take a look at those other 2 you suggested.  Best Regards
Comment: If you're in PhD then consider taking ts course in stat dept.That's what I did. It gives you a different perspective


How to use a private network in geth?

Question: I am following this answer:
How do I set up a private ethereum network?
but my result of miner.start() will return null
Is it because my geth version is 1.6.6-stable?
Also welcome any beginner's guide to develop dApp.
Comment: After I type miner.start(), I found my Mist wallet mining in main network.
Answer: This is how I run my private network using geth on Ubuntu:
Create a simple genesis.json file, e.g.
{
  "config": {
    "chainId": 1907,
    "homesteadBlock": 0,
    "eip155Block": 0,
    "eip158Block": 0
  },
  "difficulty": "40",
  "gasLimit": "2100000",
  "alloc": {}
}

Create a first node and make sure it works:
$ mkdir node1
$ geth --datadir node1 account new
$ geth --datadir node1 account new
$ geth --datadir node1 init genesis.json
$ geth --datadir node1 --networkid 98765 console
> miner.start(1)

Once you have done some mining on this node, stop the miner with miner.stop() (This isn't absolutely necessary but it is just convenient so you don't see too many info messages appearing in the console while trying to copy/paste the enode address, coming up next).
Make sure you know the enode address of the first node, you will need this to connect your second node:
> admin.nodeInfo
{  enode: "enode://08993401988acce4cd85ef46a8af10d1cacad39652c98a9df4d5785248d1910e51d7f3d330f0a96053001264700c7e94c4ac39d30ed5a5f79758774208adaa1f@[::]:30303",
...

Let's do the same steps now to set up second node:
$ mkdir node2
$ geth --datadir node2 account new
$ geth --datadir node2 account new
$ geth --datadir node2 init genesis.json
$ geth --datadir node2 --networkid 98765 --port 30304 --bootnodes "enode://firstname.lastname@example.com:30303" console

Notice that we had to change [::] to the IP address of the host.
Once you start this node, wait for a little while and then you will eventually see the blocks that you mined on your first node being synced over.
I have written up more of my experiences getting started with geth, private network and smart contract here in case you want more details: https://alanbuxton.wordpress.com/2017/07/19/first-steps-with-ethereum-private-networks-and-smart-contracts-on-ubuntu-16-04/
Comment: These instructions were very helpful for a basic miner but my second node is not connecting to the first, and vice-versa.  `admin.peers` returns an empty set.  I'll have to start a new thread to see if I can figure that out.
Answer: I too have a private testnet working pretty OK till now. I am yet to start dApp development though - in fact, I require a good enough dApp tutorial. As far as your miner.start() returning null is concerned, that is pretty much alright. Ideally yes, it should return true, but if it doesn't, please check if the system is mining using the command eth.mining. If it is returning true, it means the blocks are getting mined.
Also keep in mind that if eth.mining is true for a very long time, say an hour or two, but eth.blockNumber still returns 0, it is because mining requires at least a minimum of 4GB RAM. So if you're on a virtual machine, make sure you give it enough RAM.
Comment: null is the correct return code for miner.start()

How to use a private network in geth?


Any ways to guesstimate IQ?

Question: Is there any way to roughly approximate someone's IQ simply based off of observing their behavior, mannerisms, speech, social interactions, etc? In other words, are their certain patterns of behavior that people exhibit as a function of their intelligence, allowing for the approximation of their IQ by observing them display these patterns (and if so, what are some examples throughout the IQ spectrum)?
Comment: Related to: [Can a shorter IQ test be devised that provides a more approximate measure of IQ?](https://psychology.stackexchange.com/q/16925/7001) and also [How to estimate IQ for public figures?](https://psychology.stackexchange.com/q/835/7001)
Answer: There's a body of research that shows that thin slices allow for reasonable discernment of intelligence and personality. Just two recent articles show the following:

Negative affect, extraversion, conscientiousness, and intelligence were judged moderately well after 5-s exposures.

Inferences of intelligence from thin slices of behavior strongly predicted intelligence test scores. A particularly strong single predictor was how persons read short sentences.

Note that this is alongside a large body of research done to show how thin slices of intelligence corresponds to real IQ. Both studies have further citations supporting this; they were just the first two I found off of Google.
References
Dana R. Carney, C. Randall Colvin ¤, Judith A. Hall. (2007). A thin slice perspective on the accuracy of Wrst impressions. Journal of research in personality. http://faculty.haas.berkeley.edu/dana_carney/slices.in.press.page.numbers.oct.2007.pdf
Borkenau, P., Mauer, N., Riemann, R., Spinath, F. M., & Angleitner, A. (2004). Thin slices of behavior as cues of personality and intelligence. Journal of personality and social psychology, 86(4), 599. doi: 10.1037/0022-35126.96.36.1999 https://psycnet.apa.org/record/2004-12052-006
Answer: After seeing the answer that cites the Borkenau study, I wondered how the reading of short sentences factors in, so I pulled up the full article [PDF]
It didn't entirely have the concrete details I was hoping for (I imagined something about intonation, body language, or the size of "chunks" read at once). The following seems to mean that people are reported to be more intelligent when they appear to quickly read and understand text, perhaps without any sign of hesitation or struggling, and that this does correlate strongly with measured intelligence.
Pg. 11: "Inferences of intelligence from Task 13 (reading 14 newspaper headlines and subtitles aloud) were more strongly related to the LPS–PC in both participant subsamples, and to the APM score in one subsample, than were inferences of intelligence from any of the 14 other tasks."
Pg. 14: "Performance on intelligence tests is most strongly related to inferences from observing targets who read short phrases aloud, as in the headlines task. This suggests that the way people read standard text provides particularly diagnostic cues of their psychometric intelligence. This resembles findings by Borkenau and Liebler (1993), who found that inferences of intelligence based on observations of how strangers read a standard text allow for quite accurate judgments of their intelligence. This finding is interesting from a theoretical as well as from an applied perspective. Concerning theory, the finding is consistent with the assumption that intelligent persons perform simple tasks more efficiently (Deary, 2000). According to this view, measured intelligence should not only be related to how persons solve complex problems but also to how efficiently they perform on everyday tasks like understanding and reading a short text. In this context, the strength of the correlation of judgments of intelligence from the headlines task with the performance measures of intelligence becomes important. The finding that the LPS is related to the headline task nearly as strongly as it is related to another test of intelligence shows that the headline task is a quite precise measure of intelligence."
Comment: I can't comment yet, but I thought this might be substantial enough to stand alone as it brings in information that isn't readily available in the content or links of the other answer, and serves mainly to answer the question directly. I figured I was dancing on the line here so it's understandable if I can't do this. I first wanted to PM the other author, but I couldn't find a way.
Comment: This seems like a comment to the other answer to me. Perhaps you can suggest that author to improve their answer, or you can write your own, but this answer is not an "answer" by itself.

Any ways to guesstimate IQ?


What is a battery backup up cache?

Question: I've read an article about Innodb performance optimization an in that post the author was repeatedly mentioning someting named a "battery back up cache". It is not clear for me what he was talking about and google did not help either. My guess is that this is some kind of backup storage in case there is a power outage. Am I right?
Comment: typically found on server RAID cards which support write caching. If the power fails and there is unwritten data, the battery will keep it alive in the cache so it can be written to disk when the server recovers
Answer: RAID arrays use a battery backed cache, so they can process data faster than they can write it. Without the battery, they couldn't do caching without risk of data loss during a power failure.
That's the only instance I can think of where you'd need a cache that is specifically battery backed. If it was backing volatile memory, it wouldn't matter.
I suppose I should note that this is a feature of a professional-grade hardware RAID setup, and not a software or consumer-grade "on board" RAID. The batteries are substantial, around the size of an altoids tin. They tend to go bad every 4-5 years, which kills your caching, and deals a performance hit to your backing store.
Comment: +1 - the original article actually specifies a 'battery backed up RAID cache' so this is almost certainly it
Comment: Yeah, a hardware RAID array is a perfect application for this technique. Overall it is a very general concept that can be used in many applications.
Answer: Magnetic storage is slow, so better put a cache in front of it.  It's easy to see how that accelerates reads, but can it accelerate writes too?

a writethrought cache doesn't, because although it keeps a copy of the written data in the cache (for subsequent reads), it doesn't acknowledge the operation as successful until it's on real storage ("hits iron oxide").
a writeback cache does, because it signals the host that the opration is finished as soon as it is on cache.  It will write to permanent (magnetic) storage somewhat later, in the background.

At first, writeback caches sound better, but they introduces a vulnerability window: if there's a power loss, any data acknowledged but not yet written would be lost.  The filesystems or databases can't prevent this, because any journalling, scheduler barriers, operation ordering, etc. depend on the write acknowledge to mean that data is already safely written.
The solution is to add a small battery to the cache, to allow it to survive a power loss.  As soon as power is restored, any pending writes will be completed (even before the host is booted up).
Now there are also two other alternatives:

replace the RAM cache with non-volatile storage.  SSD's can be much bigger for the same cost, but they're not as fast as RAM.  Still, in many cases they're faster than the data link, so they can be fast enough.
add a small non-volatile memory to the cache.  In the event of power loss, a very small battery (or a supercapacitor) allows it just enough extra time to save the pending cache entries to flash.  No need to keep RAM alive for an indeterminate amount of hours.
Answer: Caching is used to speed up operations.  A typical usage pattern for a user is to access the same record a couple of times.  Read it, review it, get some details on it, etc.  If the underlying system keeps whatever record in memory, even briefly, the next time the user tries to interact with the record, the access is thousands of times faster than loading it from disk again.
the problem comes when engineers get the bright idea that, to improve system performance, they will put things the user has added to the record in memory for a while.  The data is not written to disk until he cache is flushed, which could be a few seconds or maybe ten seconds, but because the cache is small and lots of changes won't fit, the possibility remains that some changes will be written to disk, while others will remain in write cache briefly.  If the power goes out while this is in limbo, the results can be devastating to the integrity of a file or database system.
So some systems implement a logical protection scheme in software, by dating changes or logging cached changes or all kind of slightly whacky things.  But if you have a battery backed write cache, well you can dispense with those things and safely know, that the write cache will always be written through.

What is a battery backup up cache?


Forces acting on a helicopter

Question: I was wondering about the force that a helicopter produces to descend to the ground being always upwards. How does that happen? I understand that it must be upwards but can't imagine it, how do the engines do it?
Answer: The engines power the rotor, which in turn produces lift.
Lift is produced due to the fact that the rotor blades have an aerofoil profile, similar to the profile of an aircraft wing.
In order to descend, the lift force of the rotor is simply set to be smaller than the weight pulling the helicopter down.
Answer: The lift in a helicopter is caused due to the air pressure difference above and below the blades. This pressure difference is the consequence of relative motion between the air and blades of the helicopter. The magnitude of lift force increase and decrease with increase and decrease in relative velocity between blades and air.
So to lift a helicopter upwards, the speed of blades is set in such a way that the lift would be grater than the weight. And while landing it, the speed is set such that the lift is less than the weight.

Forces acting on a helicopter


Use accelerometer values to control FPS on PC?

Question: If I was running a FPS like counter-strike on my PC would it be possible to have the phone (connected to the PC via WiFi/Bluetooth) act as the mouse and control the character's looking direction? For example, the player stands up in front of his computer and points his phone up + down, and 360 degrees around him, and the character in the game follows the direction with its gun?
Answer: Everything is possible.... Everything.
Assume you can write a socket class that would connect to your PC app.
I'm new to android so I don't know what it's got in it's native java
- That would handle sending info to the desk... I don't think it would have to be significant amounts of data, but it would be a stream.
With that in place, I'd create a way to capture the movements of the PDA and push them to the DESK.
Okay now you've got the data from the PDA in the desk app's sphere..
--it's best to do as much processing on the desk as you can.. More power.. --
Record the values as you do things like turn around, and point the device up/down.. all the movements you can think of.
Finally, take the recorded values and see if you can "mimic" the actual moves in the game.
So; can it be done.  Sure.. easily?  That depends on your def of the word easy.


Why is the authentication server needed in the Kerberos protocol

Question: Consider the diagram in https://en.wikipedia.org/wiki/Kerberos_(protocol)#/media/File:Kerberos_protocol.svg depicting the Kerberos protocol.
I'm wondering how the authentication server (AS) is useful.. Couldn't we drop the messages A, B, C, D and simply use the client key K_c (green) instead of K_C-TSG (red) to encrypt message F? I.e., the client would directly request the service from the TGS and authentication and authorization is directly handled in one message, instead of 3.
Answer: Theoretically, the AS and the TGS can be set up together (even on the same physical machine), and I think that in small systems you may spare some messages. This can also be seen in the image along the dashed line.
Also see the Needham–Schroeder protocol [1] that uses a two-way handshake with the AS (Kerberos is based on this protocol and improves it).
However, the TGS meets the essential requirements that Kerberos provides:

Scalability - The system must support a large number of servers and
clients. Only one server is a bottleneck.
Separation of duties - the AS shares a key with the clients (which is usually derived from the client's password), the TGS holds a key with the servers. The AS verifies the identity of the client and the TGS "links" it with the server.
Hierarchical structure - typical organizations have hierarchical structure. Kerberos allows you to have a single AS and multiple TGSs, which fits a typical organizational structure.

[1] https://en.wikipedia.org/wiki/Needham%E2%80%93Schroeder_protocol


How do economists gather retail price data, such as for tracking inflation?

Question: How do economists track the prices of things like milk, produce, furniture and other retail products? Do they have people with clipboards going out to stores and gathering data? Scrape web sites? Convince retailers to report prices voluntarily?  How precise is the process?
Answer: For the CPI, there is actually federal employees whose job it is to visit various stores to collect the prices of specific items (boy's size-14 collared shirt made of 97 percent cotton).  Planet Money did a great podcast on this, actually following one of these people for a day.
Answer: All of the above. There are scientific methods for surveying. Generally the "people with clipboards" is the most reliable, but is also the most expensive, so some might be getting the data directly from the retailers with some sampling for verification. The "margin of error" percentage is directly related to the method chosen.
Comment: I wonder how prevalent such practices are in the private sector (including both companies researching competitor prices and independent research companies selling data to retailers).
Comment: @cespinoza It happens all of the time. Analyst firms gather the data, and even local store management will check up on competitors. Wal-Mart used to be well known for giving General Managers the authority to adjust prices to beat competitors, and even source local produce at lower prices. Not sure if that's still true.
Comment: WalMart seems to be losing that price war according to their most recent filings (August 2011)...
Answer: Assume you're asking about things like the Consumer Price Index?  Different countries have different approaches.  If they're honest, then the statistical sampling is conducted independently and consistently, with a clear publication schedule, and - as littleadv answered - by the men with clipboards.
It is that publication schedule which leads to a little flurry of speculation as investors try to guess what unemployment, growth or inflation figures may be immediately prior to release.
For many countries, such inflation measurement is entirely political, and so the statistical sampling is anything but honest or consistent.  Argentina's official inflation rate, for example, is 9.7% but analysts regard the real inflation rate as closer to 25%.  Places like Venezuela, Zimbabwe, Iran and even Egypt (prior to their revolution, who knows now) all manipulate statistics to portray their countries' economies in a better light.
However, even in the US where the Bureau of Labour Statistics (BLS) has been nominally independent for over a century, the choice of what to include in the Consumer Basket (the official basket of items chosen to reflect cost-of-living, and measured by the men with clipboards) is not always honest.  For 30 years the US basket has excluded house prices, because they were too volatile.  Enter house-price credit disaster...
Comment: I wasn't specifically thinking about CPI, though obviously that's relevant.  I was wondering about the general methodology b/c I often hear on the evening news about how, say, tomato prices soaring after a cold winter, or how wheat-containing product prices rising due to climate issues, which raises the question "how do you track such prices, when prices vary quite a bit in time/location".
Comment: @cespinoza It's a combination of factors. Projections on tomato or milk prices will be based on information from wholesalers, government, trade associations or other organizations and survey data. Usually there's an analyst somewhere who does nothing but study trends in wheat or tomato production. I knew someone who did this with hay for most of the east coast -- he knew everything there was to know about hay, including local price fluctuations. When local markets were getting $2.00/bale, he would ship it somewhere and sell for $15/bale!
Comment: Yes, peculiar world, and you can always check out the future prices of a range of commodities at places like CME, NYMEX, etc.


Can I reap (or do something other than "fight") with the Gauntlet of Command?

Question: Consider the situation: I have a single creature and my opponent does not have any. I want to use the Gauntlet of Command on my creature: "Ready and fight with a friendly creature". But there is nothing to fight with. So can I ready my creature and reap (or do some other action) with it?
Answer: Yes, you can reap with a creature after readying it with Gauntlet of Command if there are no enemy creatures available to fight with.
Keyforge has a general rule to "Resolve As Much As You Can". So in this case, activating Gauntlet of Command tries to:

Ready the chosen creature (If the creature is already ready, this fails to happen but the ability still continues resolving),
then forces the chosen creature to fight (If there are no targets available, the fight fails and the creature remains in a Ready state).

You may then do whatever you can normally do with a Ready creature.
Comment: You're right, but maybe important to note that if the creature is not from your chosen house, you can't use it. For example: if you chose Brobnar you could use the Gauntlet on a Logos creature to ready it and fight with it when there is a target, but if there is no target, the Logos creature is ready, but can't reap or use its action.
Comment: I considered mentioning it, but decided to just go for the blanket statement in the last paragraph. That should also cover not just reaping, but also any special creature actions available or board-wide effects etc...