Heston Model and antithetic variables

Question: I was implementing some variance reduction techniques for the heston model and came up with a question when implementing the antithetic variable technique. Namely, I was not sure if I had to implement it into the stochastic process (discretized process with the Euler scheme for the underlying and the volatility process) for the underlying and also for the volatility or would it be enough just to implement it in the stock price process?
Answer: Antithetic Sampling is used to reduce variance in simulation by sampling from two 'opposite' set of distributions. Since in Heston models you require sampling from normal for both the price and volatility, it would be better to use antithetic sampling for both.
Answer: Not sure I understand well your question, but in a stochastic volatility model you have to implement your discretised process for both underlying and volatility since the underlying's move are conditional on the volatility process value.
Note that more efficient discretisation schemes as Euler exist for the CIR process followed by variance in Heston's model :)
Comment: My question was more related to the antithetic variable. I did the discretization for both the stock and volatility, but I was unsure if I want to use antithetic variables to reduce the variance of the processes, if I needed to implement it in both processes too or is it enough if I just use it in the stock price process.

Heston Model and antithetic variables


Can't set cookie inside construct in codeigniter

Question: I trying to set a cookie if null but I can't get it to work:
public function __construct()
{
    parent::__construct();
    if ($this->input->cookie('ff', TRUE) == FALSE)
    {
        $this->input->set_cookie('ff', 'on', 86500);
        dump($this->input->cookie('ff', TRUE));
    }
}

What am I doing wrong?
Edit:
dump() it's just a custom debug function.
Comment: What does `dump()` do? Cookies need to be set before anything else is sent to the browser as they are in the response headers. http://php.net/manual/en/function.setcookie.php
Comment: dump is a custom debug function. Then how can I properly set in codeigniter a cookie if empty?
Comment: You can use a number of ways to debug without affecting the ability to set headers. You can use Firebug with FirePHP, email yourself the output with `mail()` or write to a log file or use PHPs output buffering. Additionally in this case you could just put your call to `dump()` after you have set the cookie.
Comment: the `dump()` function isn't the problem, I've tried all sorts of things... the cookie just won't set. It should give no problems when setting a cookie in construct, right?
Answer: A couple of reasons your set_cookie call might fail:
1) You've output something to the browser already when set_cookie is called, in which case you might get an error/notice along the lines of "Headers already sent".  To fix that, just ensure that the set_cookie call occurs before sending anything to the browser.
2) If you're doing local development and testing, "localhost" is not considered a valid domain, so no cookies will be saved for it.  A workaround would be to add an entry in your hosts file, for example:
localhost.dev    127.0.0.1

And then test with that domain, instead of "localhost".


What are the file types in the file metadata ("exportLinks") in Google drive API?

Question: I am developing a wrapper which called google drive api and retrieve exportLinks for the Google document in drive. I am trying to write a function to automatically identify the available links and assign to readable html href. So far, some of the type of files are :

application/pdf
application/rtf
application/vnd.oasis.opendocument.text
application/vnd.openxmlformats-officedocument.wordprocessingml.document
text/html
text/plain

I don't know how much there are and I want to know where I can find all type of files that Google Drive Api allow us to download.
Thanks!
Answer: As shown in the docs all possible mime types are allowed.
<code>Accepted Media MIME types: */*
</code>
Comment: See also http://stackoverflow.com/questions/11894772/google-drive-mime-types-listing


Nonlinear Grönwall inequality

Question: Let $T>0$, $\alpha,\beta>0$ and consider a non-negative continuous function $x$ on $[0,T]$ such that for all $t \in [0,T]$ one has
$$x(t) \leq \alpha+\beta\left(\int_0^t x(s)\,\mathrm ds \right)^{1/2}.$$
Does anyone knows what kind of Grönwall inequality I can get from this ? It would be fantastic if I can get something like $x(t) \leq Ct$.
Comment: It looks to me like it invites very much to try pulling the fundamental theorem of calculus, but I would not bet my freedom on it.
Answer: The inequality implies
$$
x(t) \le \alpha + \epsilon \int_0^tx(s) ds + \frac{\beta}{4 \epsilon}
$$
for any $\epsilon > 0$. By the usual Gronwall inequality, this implies
$$
x(t) \le \left(\alpha + \frac{\beta}{4 \epsilon} \right) e^{\epsilon t}
$$
for any $t > 0,\epsilon > 0$. Now set $\epsilon = t^{-1}$ to obtain
$$
x(t) \le \left(\alpha + \frac{\beta}{4} t \right)e
$$
You may be able to get better constants by choose $\epsilon = \delta t^{-1}$ with the right $\delta > 0$.
Answer: By an appropriate change of variables we may assume without loss of generality that $\alpha=\beta=1$. I will also asume that $x(t)\ge0$. Let $u(t)=\int_0^t x(s)\,ds$. Then
$$
u'(t)\le1+\sqrt u\implies\frac{u'}{1+\sqrt u}\le1.
$$
Integrating and using $u(0)=0$ we get
$$
2\sqrt{u}-2\log(1+\sqrt u)\le t.
$$
Let $f(u)$ be the function on the right hand side of the above inequality. It is a concave function, and satisfies the following inequalities:
$$
f(u)\ge\begin{cases}
2(1-\log2)u & \text{if }0\le u\le1,\\
1-2\log2+\sqrt u &\text{if }u>1.
\end{cases}
$$
From here we deduce that $u(t)\le C_1\,t$ where $0\le u\le1$ and $u(t)\le C_2\,t^2$ where $u>1$. This means that for $x$ we have bounds of the form
$$
x(t)\le\begin{cases}
1+A\,\sqrt t & \text{if $t$ small,}\\
B\,t &\text{if $t$ large,}
\end{cases}
$$
for some constants $A$ and $B$.
Comment: Can you please explain how to obtain $C_2$?

Nonlinear Grönwall inequality


In laymans terms, what does 'static' mean in Java?

Question: I have been told several definitions for it, looked on Wikipedia, but as a beginner to Java I'm still not sure what it means. Anybody fluent in Java?
Comment: Which static? There are a lot of statics (e.g. a non-exhaustive list http://mindprod.com/jgloss/static.html).
Answer: static means that the variable or method marked as such is available at the class level. In other words, you don't need to create an instance of the class to access it.
public class Foo {
    public static void doStuff(){
        // does stuff
    }
}

So, instead of creating an instance of Foo and then calling doStuff like this:
Foo f = new Foo();
f.doStuff();

You just call the method directly against the class, like so:
Foo.doStuff();

Comment: It should also be mentioned that a static field is shared by all instances of the class, thus all see the same value of it.
Comment: @Peter: it's not so much "shared by all instances" as that there's just one of it because it belongs to the class. Something `public static` is just free-for-all for everybody, not strictly just shared between instances.
Comment: static methods are conceptually similar to so-called free functions in languages like Python and C++.  Is just that the function name is scoped to be inside the class name.
Comment: This was a great answer! I am just a little confused on what the benefits of using static are.
Answer: In very laymen terms the class is a mold and the object is the copy made with that mold. Static belong to the mold and can be accessed directly without making any copies, hence the example above
Answer: The static keyword can be used in several different ways in Java and in almost all cases it is a modifier which means the thing it is modifying is usable without an enclosing object instance.
Java is an object oriented language and by default most code that you write requires an instance of the object to be used.
public class SomeObject {
    public int someField;
    public void someMethod() { };
    public Class SomeInnerClass { };
}

In order to use someField, someMethod, or SomeInnerClass I have to first create an instance of SomeObject.
public class SomeOtherObject {
    public void doSomeStuff() {
        SomeObject anInstance = new SomeObject();
        anInstance.someField = 7;
        anInstance.someMethod();
        //Non-static inner classes are usually not created outside of the
        //class instance so you don't normally see this syntax
        SomeInnerClass blah = anInstance.new SomeInnerClass();
    }
}

If I declare those things static then they do not require an enclosing instance.
public class SomeObjectWithStaticStuff {
    public static int someField;
    public static void someMethod() { };
    public static Class SomeInnerClass { };
}

public class SomeOtherObject {
    public void doSomeStuff() {
        SomeObjectWithStaticStuff.someField = 7;
        SomeObjectWithStaticStuff.someMethod();
        SomeObjectWithStaticStuff.SomeInnerClass blah = new SomeObjectWithStaticStuff.SomeInnerClass();
        //Or you can also do this if your imports are correct
        SomeInnerClass blah2 = new SomeInnerClass();
    }
}

Declaring something static has several implications.
First, there can only ever one value of a static field throughout your entire application.
public class SomeOtherObject {
    public void doSomeStuff() {
        //Two objects, two different values
        SomeObject instanceOne = new SomeObject();
        SomeObject instanceTwo = new SomeObject();
        instanceOne.someField = 7;
        instanceTwo.someField = 10;
        //Static object, only ever one value
        SomeObjectWithStaticStuff.someField = 7;
        SomeObjectWithStaticStuff.someField = 10; //Redefines the above set
    }
}

The second issue is that static methods and inner classes cannot access fields in the enclosing object (since there isn't one).
public class SomeObjectWithStaticStuff {
    private int nonStaticField;
    private void nonStaticMethod() { };

    public static void someStaticMethod() {
        nonStaticField = 7; //Not allowed
        this.nonStaticField = 7; //Not allowed, can never use *this* in static
        nonStaticMethod(); //Not allowed
        super.someSuperMethod(); //Not allowed, can never use *super* in static
    }

    public static class SomeStaticInnerClass {

        public void doStuff() {
            someStaticField = 7; //Not allowed
            nonStaticMethod(); //Not allowed
            someStaticMethod(); //This is ok
        }

    }
}

The static keyword can also be applied to inner interfaces, annotations, and enums.
public class SomeObject {
    public static interface SomeInterface { };
    public static @interface SomeAnnotation { };
    public static enum SomeEnum { };
}

In all of these cases the keyword is redundant and has no effect.  Interfaces, annotations, and enums are static by default because they never have a relationship to an inner class.
This just describes what they keyword does.  It does not describe whether the use of the keyword is a bad idea or not.  That can be covered in more detail in other questions such as Is using a lot of static methods a bad thing?
There are also a few less common uses of the keyword static.  There are static imports which allow you to use static types (including interfaces, annotations, and enums not redundantly marked static) unqualified.
//SomeStaticThing.java
public class SomeStaticThing {
    public static int StaticCounterOne = 0;
}

//SomeOtherStaticThing.java
public class SomeOtherStaticThing {
    public static int StaticCounterTwo = 0;
}

//SomeOtherClass.java
import static some.package.SomeStaticThing.*;
import some.package.SomeOtherStaticThing.*;

public class SomeOtherClass {
    public void doStuff() {
        StaticCounterOne++; //Ok
        StaticCounterTwo++; //Not ok
        SomeOtherStaticThing.StaticCounterTwo++; //Ok
    }
}

Lastly, there are static initializers which are blocks of code that are run when the class is first loaded (which is usually just before a class is instantiated for the first time in an application) and (like static methods) cannot access non-static fields or methods.
public class SomeObject {

    private static int x;

    static {
        x = 7;
    }
}

Comment: You really deserve more up-votes. The answer is on-point from start to finish.
Answer: Another great example of when static attributes and operations are used when you want to apply the Singleton design pattern. In a nutshell, the Singleton design pattern ensures that one and only one object of a particular class is ever constructeed during the lifetime of your system. to ensure that only one object is ever constructed, typical implemenations of the Singleton pattern keep an internal static reference to the single allowed object instance, and access to that instance is controlled using a static operation
Answer: In addition to what @inkedmn has pointed out, a static member is at the class level. Therefore, the said member is loaded into memory by the JVM once for that class (when the class is loaded). That is, there aren't n instances of a static member loaded for n instances of the class to which it belongs.
Answer: Above points are correct and I want to add some more important points about Static keyword.
Internally what happening when you are using static keyword is  it will store in permanent memory(that is in heap memory),we know that there are two types of memory they are stack memory(temporary memory) and heap memory(permanent memory),so if you are not using static key word then will store in temporary memory that is in stack memory(or you can call it as volatile memory).
so you will get a doubt that what is the use of this right???
example: static int a=10;(1 program)
just now I told if you use static keyword for variables or for method it will store in permanent memory right.
so I declared same variable with keyword static  in other program with different value.
example: static int a=20;(2 program)
the variable 'a' is stored in heap memory by program 1.the same static variable 'a' is found in program 2 at that time it won`t create once again 'a' variable in heap memory instead of that it just replace value of a from 10 to 20.
In general it will create once again variable 'a' in stack memory(temporary memory) if you won`t declare 'a' as static variable.
overall i can say that,if we use static keyword
  1.we can save memory
  2.we can avoid duplicates
  3.No need of creating object in-order to access static variable with the help of class   name you can access it.
Comment: They're not big words, but what you are claiming is completely false in Java, and irrelevant to the question anyway.
Comment: -1, The question was looking for something in beginner terms.  This talk of permanent, temporary and volatile is not really going to be understood by a beginner, and is factually incorrect anyway.
Comment: they are not a big words boss..they can understand that k.they have to know actual difference that why i have mentioned them.


Issues with Blazor and latest preview

Question: Blazor project having an issue with the render tree. I am using a project of Github I have updated the blazor reference to the latest.
But now I am getting the following error within Google Chrome.

Microsoft.AspNetCore.Components.RenderTree.RenderTreeDiffBuilder.InitializeNewComponentFrame
  (Microsoft.AspNetCore.Components.RenderTree.RenderTreeDiffBuilder+DiffContext&
  diffContext, System.Int32 frameIndex) <0x3564ae0 + 0x00082> in
  :0  d.printErr @
  blazor.webassembly.js:1

I updated to Preview 9 cause the fact the Microsoft.AspNetCore.Components.RenderTree. Component seems to be removed on the version that is in the latest visual studio 2019 is this a known bug I don't see many articles about it.
Answer: Sorry for anyone else the issue can be resolved using the following.
https://github.com/aspnet/Blazor/issues/46
Welcome to Blazor.

Issues with Blazor and latest preview


Is this Dieffenbachia (dumb cane) sick?

Question: I believe this plant to be Dieffenbachia (dumb cane). My mother got it about 40 years ago. The lower leaves have suddenly turned yellow (see pictures).  Is this plant sick? Does the soil lack proper nutrients? The plant is in a 10-inch pot - might be the original. It's in a house that is very hot and though it's near a large sunny window, it mostly gets light filtered through blinds. It gets water about 3 times a week. It's in the same location it's been for the past 40 years. I very much want to keep the plant alive and healthy.
Answer: If it's only a few leaves at the bottom that are dying off, and there is still new growth at the top, don't worry about it; that's how these plants grow.
Notice the rings around the trunk.
Every one of those rings used to be a leaf that yellowed and fell off.
Answer: Just cut off the yellow leaves with a pair of scissors. Put the yellow leaves and kitchen scraps in a compost pile in your front or back yard. The co.post will turn black after more than 6 months and will make excellent fertilizer for your lawn, flowers, or other plants, should choose to spread the fluffy black compost outside over a large area.

Is this Dieffenbachia (dumb cane) sick?


how to change content type from Document set to Item

Question: While creating content type I've selected Item as a parent but after created I can see its showing Document Set as a parent content type. Now can anyone please suggest if possible I can change the parent content type from Document Set to Item.
Answer: You might not have selected Parent Content Type Source properly, Do select Parent content Source and then select Item from the list.


Estimate the moment of inertia of nucleus

Question: How do I estimate the moment of inertia of the rotating nucleus, $^{232}_{90}Th$, using the first order estimate assuming the nucleus does not change shape at high rotational angular momentum? Can you provide me the formula? I can't seem to find it anywhere.
Comment: What would you need to know to learn the angular momentum of a uniformly charged billiards ball? Can you find an approach that works with kind of information you can look up about a nucleus?
Answer: You may wish to look at http://arxiv.org/abs/nucl-th/0104037 (Nucl.Phys. A694 (2001) 295-311) - they give figures for Th-224. For low deformation, the moment of enertia is about 5000 m fm^2, where m is the nucleon mass and fm is, I guess, Fermi (femtometer). I would think the moment of inertia of Th-232 should not be much different.


Best bijection between $\mathbb{N}^\mathbb{N}$ and $[0,1] \subset \mathbb{R}$.

Question: Cantor's diagonal argument proves as a special case that the set of functions from $\mathbb{N}$ to $\{0,1\}$ has the same cardinality as the interval $[0,1].$ There is an 'obvious' mapping from functions to real numbers that almost provides a bijection, except very few pairs of functions happen to map to the same reals. This can then be dealt with by using the Cantor-Bernstein-Schröder Theorem to prove the existence of a bijection.
For an application in number theory I would like to apply similar bijections between $\mathbb{N}^\mathbb{N}$ and $[0,1].$ The construction which is 'obvious' is to use dove-tailing, as follows. Let $M$ be a matrix with rows and columns indexed by $\mathbb{N}$ so that if $f$ is a function, then the binary representation of $f(n)$ is contained in the $n$'th row of $M.$ Now let $f$ correspond to the real number which has as its binary digits the entries (0,0),(0,1),(1,1),(0,2),(1,1),(2,0),(0,3) etc. of $M.$ Clearly each function produces a unique real number between $0$ and $1.$ Again it may be necessary to apply the Cantor-Bernstein-Schröder Theorem to eliminate double occurrences of real numbers. In my particular application I do not worry about this, since all my functions map only a finite number of natural numbers to zero.
But my question is whether other bijections are also known, other than this 'obvious' one.
Comment: There are 2 more examples of encoding described in this post. https://math.stackexchange.com/q/2146599/399263
Answer: Assuming you're talking about $\Bbb{N}$ starting at $1$ rather than $0$, the bijection I like best is $$(n_1, n_2, n_3, ...) \mapsto \frac{1}{2^{n_1}} + \frac{1}{2^{n_1 + n_2}} + \frac{1}{2^{n_1 + n_2 + n_3}} + ...$$ The first number of the sequence tells me how many digits after the binary point to count to see the first $1$ in the binary expansion of $x$, and every number after that counts the number of binary digits to the next $1$. Although $0$ is not in the image of this map as a result, it is a true bijection of $\Bbb{N}^{\Bbb{N}}$ with $(0, 1]$--nothing gets double counted because this function can never output an infinite tail of zeroes.
Comment: Yes, that is very nice.
Answer: The function provided in the answer by Rivers McForge can be slightly modified to include $0$:
\begin{equation}
f(n_1,n_2,n_3,...) = \begin{cases}
0, & n_i = 1\\
g(n_1 -1, n_2, n_3,...),&n_1 >1, ~ n_{i>1}=1\\
g(n_1, n_2, n_3, ...), & \text{otherwise}
\end{cases}
\end{equation}
where
\begin{equation}
g(n_1,n_2,n_3,...) = \frac1{2^{n_1}}+\frac1{2^{n_1+n_2}}+\frac1{2^{n_1+n_2+n_3}}+...
\end{equation}
This works by "making some space" when $n_i = 1$ for $i>1$ by shifting the function in $n_1$ in the sense of Hilbert's paradox of the Grand Hotel, which leaves an "empty space" at $n_i=1$ for all $i \in \mathbb N$. This "empty space" is then used to assign the value $0$ for $f(1,1,1,...)$, which makes $f(n_1,n_2,n_3,...)$ the bijection between $\mathbb N^{\mathbb N}$ and $[0,1]$, as requested in the question.
In general, a bijection $h: S \to S \cup \{a\}$, where $S$ is an infinite set, can be constructed by defining a sequence $(s_n)$ in $S$ with no repeating members to define the function $h(x)$ in the following way:
\begin{equation}
h(x) = \begin{cases}
a, & x= s_1 \\
s_{n-1}, & x=s_n, ~n>1 \\
x, & x \notin (s_n)
\end{cases}
\end{equation}
In the above example $S=(0, 1]$, $a=0$ and $s_n = 2^{-(n-1)}$ in order to have $f(n_1,n_2,n_3,...) = h(g(n_1,n_2,n_3,...))$.


How to calculate the stagnation temperature at the tip of the nose of a reentry module?

Question: A re-entry module flies with Mach 10 at an ambient temperature of –27°C with. CP = 840 J/kg-K, gas constant R = 140 J/kg-K. What is the stagnation temperature at the tip of the nose of the re-entry module?
Comment: Homework problem?
Comment: @uhoh I don't believe that answer is relevant at all to this question. Before you edited it this was a simple gas thermodynamics 101 homework problem. Note that heating does not enter into it, and the 're-entry module' part is irrelevant, it could be any M 10 flow./
Comment: @OrganicMarble rolled-back. I had thought that homework problems were off-topic. I'm surprised to hear that heating does not enter into a question about temperature at the tip of a nosecone during reentry, so I'll wait for the answer to find out!
Comment: Check the mach number form of the equation here. https://en.wikipedia.org/wiki/Stagnation_temperature
Comment: Thank you, everyone, for your comments. The "Re-entry module" part is indeed irrelevant and I've realized that after going through the question properly. I basically got panicked as I don't have much idea about the reentry module.I have solved the question using the relation between Stagnation Temperature and Mach number.
Comment: @alamtania since you've solved your problem, consider posting an answer.  Answering your own question is fine on stack exchange!
Answer:
Here's how I solved the question. Please ignore the (c) at the end of the solution.
Comment: Good work on this.  The caveat to this, of course, is that in a real-life application, the ideal gas assumptions used to derive these equations will break down at Mach numbers and temperatures that high.  The resulting temperature of a real gas with those thermodynamic properties at 300-ish K would be lower than this.


riemann surface and discontinuous group action

Question: If G is a group that acts properly discontinuously on a Riemann surface X , than we can give to the quotient X/G  a structure of Riemann surface such that the projection p:X→X/G  is holomorphic. How can I prove that?
Comment: could you tell me the book or source of the problem?
Comment: $G$ should act holomorphically right? and $p$ will be a covering map I guess.
Comment: Yes! The theorem says: "Let $G$ be a group acting properly discontinuously on a Riemann surface $X$. Then the quotient space $X/G$ is a Riemann surface and the canonical projection map $\pi:X\rightarrow X/G$ is holomorphic branched covering map of degree $|G|$. The fixed points of $G$ are the branch points of $\pi$." I can't understand how to prove this...
Answer: A (slightly terse) proof of a very similar result occurs as Proposition 13 in these notes.  The key point is that every fixed point of $G$ admits a local holomorphic coordinate in which the map is simply multiplication by a root of unity.  This is true because every holomorphic map $f$ in one variable is conformally equivalent near a fixed point $z_0$ to the linear map $z \mapsto f'(z_0)(z-z_0)$.
Note that the result does not hold for holomorphic maps in dimension greater than one -- not even for finite order linear maps of $\mathbb{C}^2$!  For instance consider the map $(z,w) \mapsto (-z,-w)$.  The ring of invariant functions is $\mathbb{C}[z^2,zw,w^2] \cong \mathbb{C}[a,b,c]/(b^2-ac)$, so the origin (the only fixed point of the map) is a singular point of the quotient.
I want to attribute the observation that the differing behavior in (complex) dimension one and dimension greater than one can be understood in terms of classical invariant theory to my colleague Robert Varley.  Last semester we team taught a course on modular curves and he introduced this perspective.
Finally, note also that if the action is not only properly discontinuous but free then in all dimensions the quotient is a complex manifold, and this is a much easier result.
Answer: I found two completely different proofs. The shorter is here: http://tinyurl.com/cg4plxx at page 9. I think, the main problem for me is to understand why the fixed points of $G$ are the branch points of $\pi$.


What User Space tools support Btrfs functionality (e.g. clone instead of copy)

Question: I've recently been starting to work with Btrfs on Ubuntu, and have it setup as my root filesystem, as well as home filesystem. I have it configured the way apt-btrfs-tools expects, and that is working well.
Of course, there are command line tools for Btrfs to do everything.
But, what I'm wondering is, is there support in any other tools for Btrfs-specific functionality. For example:

Clones (file 'copies' that initially don't take aditional space, but utilize the CoW feature of Btrfs to use space only as the two files are modified) - if I try to copy a file in Dolphin, Nautilus, or other GUI file management tools, will it try to do a reflink, or do they always just do full data copies?
GUI snapshot manager? Is there a gui tool to manage snapshots (list, create, delete), revert to a previous snapshot, revert individual files/directories from a previous snapshot.
Volume/file info - In Btrfs, traditional tools like 'du' and 'dh' do not do a great job of showing how much free space is available, or how much space a file or directory actually really use, because they are not aware of extents being shared between files (either clones, or with the same file in other snapshots). Are there any GUI file manager tools that will show info from Btrfs showing actual space used/free?
Answer: There is timeshift-launcher and snapper-GUI to help you boot into snapshots after a crash. some more tips can be found in the Howto of https://linuxreviews.org/Btrfs


Convergence of a sequence on the unit sphere of Bahach or Hilbert space

Question: Let $X$ be a Banach or Hilbert space and $A$ be a bounded linear operator on $X$, and fix an element $x \in X$. Then I want to know that are there any good ways or theories to deal with the convergence of the following sequence $\{ y_n\}$:
\begin{align}
y_n = \frac{A^nx}{||A^nx||}.
\end{align}
I'm sorry for an ambiguous question.
I welcome any kind of comments.
Comment: If your space $X$ is reflexive (satisfied by Hilbert spaces for example), then the unit ball is compact in the weak topology. In this topology you will thus always find possible limits.
Comment: Such a weak limit might be zero, which might come unexpected.
Answer: It does not always converge. As a counter example suppose a finite dimensional space $X = \mathbb{R}^2$, and
\begin{equation}
A = \begin{bmatrix} 1 & 1 \\ 0 & -1 \end{bmatrix},\quad x = \begin{bmatrix}1\\1\end{bmatrix}
\end{equation}
Of course $A$ is bounded. Then
\begin{equation}
y_n =
\begin{cases}
\displaystyle{\frac{1}{\sqrt{5}}}\begin{bmatrix}2\\-1 \end{bmatrix}, & n=2m+1, \\
\displaystyle{\frac{1}{\sqrt{2}}}\begin{bmatrix}1\\1 \end{bmatrix}, & n=2m.
\end{cases}
\end{equation}
In finite dimensional spaces, this is indeed the power iteration that converges to the eigenvector corresponding to the largest eigenvalue (in magnitude) of matrix $A$, and the convergence rate is determined by the ratio of first two largest eigenvalues in magnitude, $|\lambda_1 / \lambda_2|$.
I assume more than boundedness is needed for convergence of $y_n$. Perhaps if $A$ is compact, you may show similar argument for rate of convergence based on the singular values.
Comment: You are right @LutzL, I'll edit the answer.
Comment: I think it is clear that the sequence need not converge, for example even in one dimension you have the linear map $\Bbb R\to \Bbb R$, $x\mapsto -x$ for which the sequence will always alternate between two limit points. I think the interesting question is: When does it have limit points? In finite dimensions it is clear that the sequence always admits limit points, as the unit sphere is compact.


Integration by substitution as the chain rule for integration

Question: I know about the chain rule for differentiation. I am studying integration currently. I have done some reading on the internet. I read that integration by substitution is the chain rule for integration. What does this mean exactly? Does it mean that it is used for integrating composite functions like the chain rule for differentiation is used for differentiating composite functions or does it mean that there is some mathematical connection between integration by substitution and the chain rule for differentiation and if there is what is the connection? I am confused. Please help.
Comment: The fundamental theorem of calculus basically asserts that integration and differentiation are "inverse" operations (for some notion of "inverse" that I am leaving intentionally non-specific---the FTC makes this rigorous).  Morally, integration by parts is what you get if you run the product rule backwards, and the change of variables formula (i.e. integration by substitution) is what you get if you run the chain rule backwards.
Answer: The chain rule says that, under sufficient differentiability conditions,
$$
\frac{d}{dx}F(g(x)) = F'(g(x)) g'(x).
$$
Suppose we want to integrate $\int f(g(x)) g'(x) \ dx$ and we know an antiderivative $F(x)$ for $f(x)$.  Writing $u=g(x)$ so that $du = g'(x) \ dx$ we can do
$$
\int f(g(x)) g'(x) \ dx = \int F'(g(x)) g'(x) \ dx = \int F'(u) du = F(u)+C=F(g(x)) + C
$$
which is typically what you call integration by substitution.  The chain rule was used at the second equal sign.
Comment: What happens for $\int f(g(x)) \ dx$, that is with no $g'(x)$ ??
Comment: @user45664 there is no general technique for that.


What's the difference between Objective-C and Cocoa?

Question: I'm just learning Objective-C/Cocoa programming for the Mac.  All of the tutorials, books, blogs, podcasts, etc. I've been using really cover the two together.  Is there an easy way to tell which pieces are vanilla Objective-C and which come from Cocoa?
Answer: Objective-C is the language... it defines all the things like the keywords for defining objects, the syntax for messaging object, things like that.
Cocoa is a development framework (it's actually an umbrella framework which combines three other frameworks, Foundation, AppKit and CoreData).
These frameworks (Cocoa) define all the objects that are nice to use and interact with the operating system, as well as a number of functions. For example, Cocoa defines things like NSString and NSObject. Cocoa can currently be used with other language bindings, such as python or ruby, and used to be used with Java as well. So, if you were using Cocoa with Java, you would still get an NSString object, but you would call and use it from within a Java application.
Without linking to one of the Cocoa frameworks, Objective-C comes with only a very basic Object class as a pre-defined root class.
Comment: Thanks! I was especially curious about things like Foundation, NSString and NSObject
Answer: Objective-C is the language itself.
Cocoa, formerly NextStep, is the API and runtime that sits on top of Obj-C. Anything starting with NS (for NextStep) is part of Cocoa, not part of the language.
Answer: Sure, it is quite easy - Objective-C is the language, Cocoa is the API/library you are using to build you Mac App.
Answer: Look in /usr/include/objc/ — in there is pure Objective-C. Everything else is Cocoa. You might notice you almost never directly use anything in there.
However, in practice it makes little difference. Cocoa is the de facto Objective-C standard library. The only platform where Objective-C is used without Cocoa is Portable Object Compiler, and I'm guessing maybe three people still use that.
Comment: I think it's only two people now... that one guy with the green coffee mug has recently switched to C# exclusively...
Comment: Longish related discussion, quite interesting: [Why is Objective-C not widely used beyond Cocoa environments?](http://programmers.stackexchange.com/questions/101832/why-is-objective-c-not-widely-used-beyond-cocoa-environments)


Why do rootkits only attack 32 bit systems?

Question: Title says it all...
Answer: Because coders target 32-bit systems as they are the most commonly used desktop architecture. A 64-bit variant could be (and probably already has been) made. It's like the age old question of why there are more viruses for Windows based systems. You'd be foolish to not code for the most popular systems out there if you had malicious intent.
Comment: What does marketing and virii have in common?  They usually like to target the largest demographic. :)
Comment: haha, you're exactly right :)
Answer: The apocryphal quote comes to mind, supposedly said by Willie Sutton (he never actually said it, but ignoring that), when asked why he robbed banks: "Because that's where the money is".


Logging camera access on OS X Yosemite and up

Question: I'd like to have camera access by applications be logged in system logs, so that I can later search for camera access in the console app. Any idea if there is some debug feature in OS X to enable logging ?
Answer: I'm not certain how you would do it natively, but by pure coincidence I discovered this today, from Obdev, the makers of Little Snitch.

Micro Snitch
Ever wondered if an application records audio through your Mac's built-in microphone without your knowledge? Or if the camera captures video for no good reason?
With Micro Snitch there's no doubt anymore. This ultra-light menu bar application operates inconspicuously in the background. It monitors and reports any microphone and camera activity to help you figure out if someone's spying on you.
Logging
Never miss any microphone or camera activity, even in your absence. Every status change is logged to a file, so you can review it later to find suspicious activities.

€3.99 direct, or also on Mac App Store showing at $3.99 US or £2.99 UK
No affiliation, & I haven't tried it myself; I'm just a satisfied user of Little Snitch.


pypi erro when try to install gcsfs in google composer(airflow)

Question: I use google composer-1.0.0-airflow-1.9.0. I used dask in one of my DAG and wanted to setup composer to use dask. One of the required package for this DAG is gcsfs. When I tried to install it via Web UI I got the below error:
Composer Backend timed out. Currently running tasks are [stage: CP_COMPOSER_AGENT_RUNNING description: "Composer Agent Running. Latest Agent Stage: stage: DEPLOYMENTS_UPDATED\n ." response_timestamp { seconds: 1540331648 nanos: 860000000 } ].
Updated:
The error is coming from this line of code when dask tries to read file from gcp bucket:dd.read_csv(bucket)
log:
     [2018-10-24 22:25:12,729] {base_task_runner.py:98} INFO - Subtask:   File "/usr/local/lib/python2.7/site-packages/dask/bytes/core.py", line 350, in get_fs_token_paths
     [2018-10-24 22:25:12,733] {base_task_runner.py:98} INFO - Subtask:     fs, fs_token = get_fs(protocol, options)
     [2018-10-24 22:25:12,735] {base_task_runner.py:98} INFO - Subtask:   File "/usr/local/lib/python2.7/site-packages/dask/bytes/core.py", line 473, in get_fs
     [2018-10-24 22:25:12,740] {base_task_runner.py:98} INFO - Subtask:     "Need to install `gcsfs` library for Google Cloud Storage support\n"
     [2018-10-24 22:25:12,741] {base_task_runner.py:98} INFO - Subtask:   File "/usr/local/lib/python2.7/site-packages/dask/utils.py", line 94, in import_required
     [2018-10-24 22:25:12,748] {base_task_runner.py:98} INFO - Subtask:     raise RuntimeError(error_msg)
     [2018-10-24 22:25:12,751] {base_task_runner.py:98} INFO - Subtask: RuntimeError: Need to install `gcsfs` library for Google Cloud Storage support
     [2018-10-24 22:25:12,756] {base_task_runner.py:98} INFO - Subtask:     conda install gcsfs -c conda-forge
     [2018-10-24 22:25:12,758] {base_task_runner.py:98} INFO - Subtask:     or
     [2018-10-24 22:25:12,762] {base_task_runner.py:98} INFO - Subtask:     pip install gcsfs

When tried to install gcsfs in google composer UI using pypi got below error:
 {
   insertId:  "17ks763f726w1i"
   logName:  "projects/xxxxxxxxx/logs/airflow-worker"
   receiveTimestamp:  "2018-10-25T15:42:24.935880717Z"
   resource: {…}
   severity:  "ERROR"
    textPayload:  "Traceback (most recent call last):
    File "/usr/local/bin/gcsfuse", line 7, in <module>
    from gcsfs.cli.gcsfuse import main
    File "/usr/local/lib/python2.7/site-
     packages/gcsfs/cli/gcsfuse.py", line 3, in <module>
       fuse import FUSE
     ImportError: No module named fuse
    "
   timestamp:  "2018-10-25T15:41:53Z"
    }

Comment: check out these forums:
[1]: https://groups.google.com/forum/#!topic/cloud-composer-discuss/Jcrh8d2X3uU
[2]: https://groups.google.com/forum/#!topic/cloud-composer-discuss/A1xU5eTL4fg
Comment: @xiaoxia Lin: so is it a bug of google composer??!
Comment: Yeah, none of that is helpful (and doesn't mention fuse either). You want the logs of the install task - e.g., is it running conda or pip?
Comment: updated with google composer log when installing gcsfs
Comment: has this issue resolved?
Comment: @Sugimiyanto suma  no
Answer: Unfortunately, your error mssage doesn't mean much to me.
gcsfs is pure python code, so it is very unlikely that anything is going wrong with installing it - as is done very commonly with pip or conda. The dependency libraries are a bunch of google ones, some of which may require compilation (I don't know), so I would suggest trying to find out from logs which one is stalling and taking it up with them. On the other hand, this kind of thing can often be a network/intermittent problem, so waiting may also fix things.
For the future, I recommend basing installations around conda, which never needs to compile anything and is generally better at dependency tracking.
Comment: do you know gcsfs dependancies?I found here some: https://gcsfs.readthedocs.io/en/latest/fuse.html#requirements
Comment: Not those, you are not using FUSE, right? See instead https://github.com/dask/gcsfs/blob/master/requirements.txt
Comment: I dont import FUSE in my DAG. is it required by gcsfs?
Comment: No it isn't - the requirements link you posted are optional extras in the case you wish to use gcsfs with FUSE.
Comment: installed those listed in the link, didnt help though... I also installed conda, but the DAG error is still showing up the same
Comment: You will need to find the logs. Also, you should *use* conda, not just install it.
Comment: From log found that FUSE is required so installed fusepy but now getting this new error : should install gcsfuse too??

 textPayload:  "Usage: gcsfuse [OPTIONS] BUCKET MOUNT_POINT
Comment: FUSE (and fusepy) is not required unless you explicitly want to use it. You are apparently calling it to get that message - why? You need to give more detail about what you're doing...
Comment: updated the question. basically wanted to use dask to read a huge csv files in gcp bucket
Comment: how can I install gcsfs using conda on google composer?
Comment: I have no idea how google composer works. These steps work for general linux environment: `  > wget http://repo.continuum.io/miniconda/Miniconda3-latest-Linux-x86_64.sh -O miniconda.sh
  > bash miniconda.sh -b -p $HOME/miniconda
  > export PATH="$HOME/miniconda/bin:$PATH"
  > conda config --set always_yes yes --set changeps1 no
  > conda create -n test -c conda-forge dask gcsfs
  > source activate test
Answer: This has to do with the fact that Composer and Airflow have silent dependencies and they are not syncd. So if gcsfs installation has conflicts with Airflow dependency, we get this error. More details here. The only workarounds ( other than updating to the Nov 28 release of composer) are:
Source: Thanks to Jake Biesinger (firstname.lastname@example.com)

use a separate Kubernetes Pod for running various jobs, but it's a
  large change and requires infra we're not very familiar with (GKE).
  This particular issue can also be solved by installing dbt in a
  PythonVirtualEnvOperator, then having the python_callable re-use the
  virtualenv's bin dir, something like:
``` def _run_cmd_in_virtual_env(cmd):
  subprocess.check_call(os.path.join(os.path.split(sys.argv[0])[0], cmd)
task =
  PythonVirtualEnvOperator(python_callable=_run_cmd_in_virtual_env,
  op_args=('dbt',))  # this will call the temporarily-installed dbt
  binary, something like <code>/tmp/virtualenv-asdasd/bin/dbt</code>.

```
Answer: I haven't tried this, but this might help you out.
In general, installing arbitrary system packages (like fuse or whatever which becomes the dependencies of what you are trying to install) is not supported by Google Composer. As discussed here: https://groups.google.com/forum/?utm_medium=email&utm_source=footer#!searchin/cloud-composer-discuss/sugimiyanto%7Csort:date/cloud-composer-discuss/jpxAGCPFkZo/mCx_P1LPCQAJ
However, you may be able to do this by uploading the package folder that you have installed it in your local (i.e. fuse), into your Google Cloud Storage bucket for example: gs://<your_bukcet_name>/libs, so that it becomes shared libraries.
Then, you can set LD_LIBRARY_PATH environment variable in Google Composer to /home/airflow/gcs/libs, to make GCC look for shared libraries in that directory.
Then, try to reinstall the gcsfs using pypi Google Composer.


Dell Power Edge r610 and iDRAC Express

Question: ON a Dell Power Edge R610 with integrated iDRAC Express, has anyone has real world problems accessing the iDRAC in the event of a system hang or crash of the operating system?  I need to know because i am considering using some systems with iDRAC Express for production but dont want to risk it if they cant be accessed remotely to be power cycled in the event the system hangs.
Answer: I generally prefer the idrac enterprise as it has a dedicated ethernet port for management and remote media, but the express is fully accessible if configured properly even though it shares a nic. Just make sure if you are teaming the nics with your OS and switch, that the drac express is setup properly to account for that. I forget the exact setting, but Dell's documentation outlines it.
Comment: I also prefer iDrac Enterprise because iDrac Express does *not* have remote KVM

Dell Power Edge r610 and iDRAC Express


java games with maximum portability

Question: i want to program a simple java game, what should i consider to make it maximal portable? i'm pretty new to java, which grafik and rendering libraries should i use to make it easyly portable to mobile java (for mobile phones)?
i can't develop it directly for mobile java, because i also need a pc version.
or should i jast develop strait forward for pc and do a completele new mobile version later?
Answer: I'd say do the PC version first (portable across Mac, Linux, Windows if that is a priority for you), and develop a (or even several) completely new version for mobile handsets.
There may be some code (and art work) that you can re-use, but not too much, as a (good) game will have to be very different for a mobile phone than for a PC, not just screen sizes and input methods, but the major changes in game play that those differences probably result in to make it still fun to play.
The code that you can reuse will likely need to be adapted for J2ME or Android, but better to worry about that later than trying to be overly cross-platform from the beginning (which would place limitations on functionality on the PC version, and eat up a lot of time, without being sure if it ever pays off).
Again, if anything, worry about portability within the several desktop environments, and within several handsets, but not too much about portability between the two.
Of course, if your game has a server-side component, it would be ideal to have only one version of the server code that can talk to clients on all platforms.
Answer: I think it's feasible to create a game that is portable across a wide range of platforms.  While a desktop version of a J2ME game may look primitive, it does enable your users to preview the game before installing it.  Check out my project JGame, which enables writing a game that works without changes on J2ME, Android, and PC.  I believe the Slick project also has a working Android version.

java games with maximum portability


$\pi$ from the unit circle, $\sqrt 2$ from the unit square but what about $e$?

Question: If one wants to introduce $\pi$ to a not mathematically savvy person, the unit circle would be a good choice. The unit square would be the way to go for $\sqrt 2$. But what about $e$? I've reviewed the alternative characterizations on wikipedia and they all involve limiting processes in one form or another. So I was wondering: Is there a visual, easy-to-grasp way to present $e$? (Even if the presentation wouldn't be mathematically equivalent to the usual ones.)
Comment: At heart I think this is the same question as http://math.stackexchange.com/questions/159707/is-there-any-geometric-way-to-characterize-e which has been asked here a few times over.
Comment: The most "geometric" is that the area under the curve $(x,1/x)$ with $x\in[1,e)$ is $1$. That doesn't seem nearly as intuitive, however - it is not a length or area.  $e$ comes up a lot as a limit - for example, the derangement problem, or when dealing with compound interest.
Comment: @FrankMcGovern, in comparison to the circle and square it's somewhat mathematical. I was looking for something more tangible.
Comment: I think this question is rescuable as an independent question; the other question specifically asks for _geometric_ ways of constructing $e$, whereas this question asks for intuitive ways of describing $e$ to a layperson, which certainly don't need to be geometric.
Comment: You could demonstrate that $e^x$ is invariant under derivation? Is that too mathematical?
Comment: @ErickWong: you're right. I had a strong feeling that it must have been asked here before yet couldn't find anything. Thanks for the link.
Comment: $e$ appears naturally in [hyperbolic geometry](http://en.wikipedia.org/wiki/Hyperbolic_geometry).
Comment: $\sinh 1 + \cosh 1$.
Answer: The number $e$ is the number such that the area enclosed by the region bounded by $x=1$ on the left-hand side, the $X$ axis from below, $y=1/x$ from above and $x=e$ on the right-hand side is $1$. Hence, $e$ can be defined as the length (you need to add $1$, since you measure the length from $1$) you need to move along $X$ axis such that the area of the above enclosed figure is $1$.
Comment: You don't need integrals to understand area.
Comment: @Inceptio. If you don't understand area, it's liquely you won't understand $pi$ and $\sqrt{2}$ either.
Comment: *I am a kid, I don't understand areas or integral*. Now?
Comment: Agreed..Was being sarcastic(+1)
Comment: @arbautjc: How will you bring in $\pi$ to a kid? With a pictorial representation. He/she understands the concept of $\pi$, and anyway, $e$ has not fallen from heaven, it can be understood even by a small kid if there existed a very *elementary proof* for this.
Comment: @Inceptio The number $\pi$ is defined as the circumference of a circle with unit diameter. Similarly, $e$ is defined as the length you need to move along $X$ axis such that the area of the above enclosed figure is $1$.
Comment: @Viv: I get it. I do.
Comment: What did you use to graph this?
Comment: @ZettaSuro The graph was made in GeoGebra on ubuntu.
Answer: A different take on the 'classical' limit that I think is my favorite way of thinking about $e$ recreationally (and a remarkably useful approximation for many games): "I take a six-sided die and roll it six times.  What are the odds I never roll '1' in those six rolls?  Okay, now I take a twenty-sided die and roll it twenty times.  What are the odds I never roll '1' in those 20 rolls?"  The latter value, of course, is $\left(\dfrac{19}{20}\right)^{20} = \left(1-\dfrac{1}{20}\right)^{20}\approx e^{-1}\approx .37$; in fact, it's within a 3% relative approximation.
This is a nice way of showing the limiting process in action 'in reality', especially for any gamers, and the way that the result (power-law) scales with number of rolls is an excellent back-of-the-envelope estimate for figuring probabilities on the fly; I can know that if I roll that d20 ten times, I've got roughly a $\sqrt{.36}\approx 60\%$ chance of not hitting a 20, or equivalently a $40\%$ chance of getting one.  (Or, to pick a different example, I can know that with 3 Plains left in my Magic sealed deck's 30-card library, my odds of drawing one in the next ten turns are only about 2/3rds.)
Comment: Similarly, if a lazy coat room attendant for a large event hands back coats randomly, what is the approximate probability that nobody gets their own coat back?  (The `hat' variant is more commonly told but seems a bit contrived.)
Comment: Thank you for the great answer. Even though I wouldn't try to use this way to explain $e$ to a person who doesn't understand limiting process (the odds are that he doesn't understand probability either, since it's more advanced in my opinion). Yet I highly enjoyed the answer myself. Do you have a nice example of a word problem converging to $e$ instead of $e^{-1}$?
Answer: It's the only number where this happens:
Comment: What just happened?
Answer: The notion of period, which is introduced by Kontsevich and Zagier, would partially give a negative answer to your question. According to this article, it is now known whether $e$ is a period or not, though it is conjecturedly not a peroid. In particular, $e$ seems not to arise as an area or a length of a geometric figure defined by an algebraic equation.
This may imply that any description involving $e$ would eventually require some extent of advanced calculus.
We may circumvent this problem by arguing that the concept of $e$ arises rather naturally by considering some real-world problems. For example, we can think of compound interest:
Given an annual interest $100r$% with compounding period $1/n$ year, the relative value at the end of a year is
$$ \left( 1 + \frac{r}{n} \right)^{n}, $$
which converges to $e^{r}$ as $n \to \infty$ (that is, the period of interest goes to zero).
Here is another, though odd, characterization of $e$:
Suppose that a drunk man starts at $x = 0$ at time $t = 0$, and then at each second he walks to the right with a step size randomly and evenly between $0$ and $1$. That is, if $X_i$ are i.i.d. random variables having a uniform distribution on $[0, 1]$, then the position of the drunk man at time $t = n$ is $x = X_1 + \cdots + X_n$. Let $T$ be the time when his position first exceeds the point $x = 1$. Then the mean of $T$ is exactly $e$.
Answer:
$$e\approx 2.71828182846$$

Consider the equation:
$$f(n)=(1+\frac{1}{n})^n$$
As $n$ gets larger and larger, notice what the result approaches.
$$f(1)=2$$
$$f(2)=2.25$$
$$f(3)\approx2.3703703$$
$$...$$
$$f(100)\approx2.7048138$$
$$...$$
Comment: Have you read the question?
Comment: What's visual and easy-to-grasp in this answer?
Comment: @MartinBrandenburg Why yes, I did read the question I answered.
Answer: This one is not visual or graphical, but may be easiest to understand for a non-mathematician.
Suppose you have $\$1000$ and you want to put it in a bank account. You have picked a bank that, besides giving you an absurd interest over your money, gives you a choice between several interest schemes:

An annual interest of $100\%$.
An interest of $50\%$, but then twice a year.
A quarterly interest of $25\%$.
A monthly interest of $8.33\%$.
...
A daily interest of $0.27397\ldots\%$
...

As you may have picked up, the interest is $1/k$, where $k$ is the number of times a year you get that interest. Of course, the interest is computed over the current amount of money in your bank account, including previous interest.
So which scheme would you choose? And how much money would you have after $1$ year?


Communicating via RS232 cable in Win 8

Question: I have been trying to communicate to a device via an RS232 cable and Win8 does not recognize the device. It recognizes it when I use a USB cable instead but I would like it to work both ways. Is this possible or does Windows 8 not support serial communication?
Comment: Can you give us more detail on the code you're using to operate with RS232?
Comment: I believe plug and play has never worked with RS232.
Answer: When you say 'recognize the device' it sounds like you're expecting the RS232 connected device to act like a plug-n-play device?
Plug-N-Play requires some auto-negotiation and in some cases auto-configuration. While legacy RS-232 communication can support the P-n-P negotiations, it's quite the exception to find a device that implements this interface and is P-n-P compatible as RS-232 is getting long in the tooth and short on available bandwidth.
Unless there's a specific driver loaded for that device on your system, and your RS-232 cable is wired appropriately (DTR/CTS), there's no native operating system mechanism to detect that a serial RS-232 connected device is attached via the port.
The device manufacturer could write a driver that would detect the device on a RS-232 port and auto-negotiate the port settings appropriately.
Look at it this way, what you're expecting is for the OS to know about every device made by every manufacturer in every configuration since the dawn of the PC era. Only the manufacturer, or intrepid engineers with open source information about the device can make it 'plug-n-play' for a given operating system.

Communicating via RS232 cable in Win 8


Can I open Peazip files on windows operating system?

Question: Can I open peazip files with winrar or winzip on Windows operating system? If they can not be open is there a way to create rar and zip files that can be open on Linux and Windows operating systems?
Comment: PeaZip is available both for Linux and Windows. If you compress using the .PEA file format, then you need PeaZip. If you compress using a more common format such as .ZIP then you can open it with most compression/archiving tools. .ZIP is common on Windows, gzip (.tar.gz) is popular in Linux. 7z and XZ are great formats.
Answer: Yes you can open .zip, .rar, .tar, etc. files in Ubuntu just fine. And create said files that will open in Windows.
Answer: Peazip is both available for Windows and Linux so any files that you create with Peazip in Ubuntu can be used in Windows.
As an alternative you can also create files in .zip and .rar formats with many popular compression tools in Ubuntu that can be opened in similar tools for Windows.
Answer: Yes, you can integrate Peazip files with Windows by doing the following:

To send input objects to a indicated function, just right-click on any group of objects then use the Peazip entries in "SendTo" menu.
Drag the object or group of objects on Peazip icon. It will automatically choose the objects you provided.
Drag objects on your open Peazip so you can have full access to the process.
Double-click on your Pezip file types to open it.

You can re-arrange the application's system integration in the configuration tools in Options> System integration that requires administrative rights if really needed. Or by simply selecting Custom installation/configuration in the installer to open more options.
For more information, you can visit Peazip's site


How can we restrict some account from making a transaction on chain?

Question: I am using the proxy account. Can I restrict the main account to make transactions on the chain, so the transaction can be done only from the proxy account?
Answer: Not really, but you could lose the private key by "mistake", or what is similar, create an anonymous proxy where the calling account becomes a proxy of a newly generated account that exists only on-chain and has no known private key, therefore no transactions can be signed directly by it.
Comment: Agree, you should probably use Anonymous Proxy for this, just be careful not to restrict the proxy type (it should be `Any`) or else you will not be able to transfer the tokens.
Comment: Yup, after creating the anonymous account and add some more account as controllers, you can safely remove the creator from the anonymous proxy account.


Building Asp.net Page code behind correctly

Question: I need some guidelines about building the code behind of my pages correctly. I mean, I'm building in asp.net for a year now, and mostly using the Page_Load event. (and ofcourse "event handling" the events triggered by the user's actions). I know about the page life cycle and the order of events that happens when a page is requested etc.. . Is it normal that, generally, in a data-driven page, for example, I'm not using any of the "pre_render", "page_unload", "pre_init" etc.. event handlers? or am I missing something here? any guidelines would help me a lot, including links or whatever you think that would instruct me well. thanks.
Answer: You are not missing anything.
Most asp.net code does not use these events, and you should only be using the handlers if you need to.
For example - if you really need to change the output of the page after all control event handlers (for example button clicks) have fired, use the pre_render event. In my experience this is a rare thing to need.
Many of the event are there just in case you need them.
Comment: @Hagai - My bad. I meant `pre_render`, not `pre_init`.
Answer: Page_Load actually is the most used event handler in page life cycle. What i've used relatively often is Page_Init when i added controls dynamically to the page(ViewState issue).
Look here for further informations:
http://www.csharper.net/blog/page_lifecycle_methods_in_asp_net_2_0.aspx


Remove App Catalog from site collection on premises

Question: I have a problem with App Catalog in an on-premises farm, somebody created it previously and it's not working correctly (I am a farm admin, and I'm unable to access it). I want to remove it, and create it again, but there's no option in Central Administration to do that. Nor there is a powershell command, the only one Remove-PnPSiteCollectionAppCatalog is for SP Online. Any ideas?
Comment: Have you tried making yourself a Site Collection Administrator of the App Catalog via central admin? Being farm admin doesn't mean you have access to the sites, you have to give yourself access.
Answer: You can delete sites, including the App Catalog, from Central Admin -> Application Management -> Delete Site Collection or use Remove-SPSite.
As a farm admin, I would make sure you set the User Policy on your Web Application to provide yourself with Full Control which will allow you full control on all sites in that Web Application without having to promote yourself to SCA on a per-site basis.


Power Serves To Create Power

Question: What does the quote, "Power serves to create power. Powerlessness serves to reinforce powerlessness" mean? Does it mean that those with power remain powerful, and those without power aren't able to rise above powerlessness? Can you please elaborate?
Comment: What is the source of this quotation?  Who was the author, what was the audience, and when was it written?
Comment: @JagmeetSingh Context matters.  Where did the quote come from?
Comment: @Jasper I was given the quote and asked to elaborate on it. I have already submitted the paper :)
Comment: I can't tell you what the author meant (hence the comment rather than an answer) but it sounds like it's talking about how these things serve the people in power. It serves them by creating more power, and it serves them by reinforcing powerlessness in the powerless. So yeah, what you said, basically. Bit of an oversimplification and generalisation, but most quotes are.
Comment: I found the source of the quote: It's from [Power and Powerlessness](http://www.amazon.com/s?search-alias=stripbooks&field-isbn=0252009851) by John Gaventa.  If you search the phrase you can find a few textbooks that quote it from there.
Comment: I'd look at it from a perspective that a regime or a proposed political system that does everything for the country really well but is not efficient at keeping power is useless, as it will be replaced by some other regime/system. I.e., in a democratic society it is often harmful to execute policies that are long-term beneficial but hurt influential voter groups in short term, since that would only cause you to be removed from power and the policies would be reverted - not achieving the long term gain, but after already paying part of the short term cost.
Answer: It's obviously impossible to know what was meant by whoever said it as you didn't provide any context.
But the general idea, in a politics and game-theoretical sense, is that when someone has power (to do things), they can - and frequently do - use that power to effect changes and outcomes which serve to enhance their power.
Examples from real life would include:

"Incumbent advantage" in politics.
The person already holding a political position, by virtue of holding it, has the power to do things that help them get re-elected (or elected to higher position) - they can pass popular/populist laws; they can make speaches; they can get financial contributions from people who hope to get (or already got) contracts or fevorable decisions from the government.
Financial security.
If you have financial means, it's easier to grow your wealth (e.g. you can have investment profits in general. Or, if you have enough money for a margin account, you can short stocks. Or you can wait until specific market segment cycles down and invest in that buying low).
If you have wealth, it's easier to obtain loans with low interest rate - because you're less of a credit risk. Which is of course how lending should work, but it still benefits those who need the lending the least, most.

Vice versa, if you don't have power, you have no way to sway things to help you gain power - or to stop people who have power from swaying things so you lose even more, in zero-sum situations.

Evolution in general
Let's say you have 2 organisms, with one more fit than another. Let's say the first one is stronger. If they are, they can take the food away from the weaker one (in many cases, it's a zero sum game as there's not enough food for everyone to get enough). They get more food which makes them even MORE fit (being well fed) and the weaker one even LESS fit (being undernourished). There are game theoretical models and equasions describing the phenomena, but details would be more on topic on Biology.SE

As an aside, please note that this sometimes gets incorrectly universally misinterpreted as always being true, even though very frequently, the "zero-sum" requirement isn't met. For example "the rich are getting richer and poor are getting poorer" is a nice soundbite, up until you realize that in most Western countries, the quality of life of the poor is significantly improved compared to both the recent; and even more so the not-so-recent past; due to the fact that quality of life isn't usually a zero-sum game in Western economy.
Comment: As my pet peeve, the complaint about "digital divide" as applies to having (or not having) broadband Internet is moronic to the extreme. 20 years ago, even the rich didn't have broadband. 40 years ago, nobody had Internet. Somehow, that didn't stop me - or any other computer programmers my era/age - from learning our craft.

Power Serves To Create Power


Do you "stand/get on" or "stand/get up on" a higher object?

Question: I feel a bit embarrassed to ask this question after all the years of learning English, but do you "stand/get on" or "stand/get up on" a higher object (for example, a bench)? I mean when you change your position.
Comment: Both are correct. The addition of the particle changes the meanimg.
Answer: Typically, you:

(just) sit (or stand) on a bench/ a chair/ a couch / a bed

climb onto (or over) a table/ a gate / a wall or similar obstacle

climb through a window

climb a ladder/ a mountain

climb up a tree/ a rope

mount, get (up) onto, a horse / donkey etc

Scale is often used (transitively) instead of climb, especially when challenging climbs are involved.
You can ** get onto** or step onto/over any object that requires you to mount something, a stile for example.
You get into a vehicle / clamber or climb (up) into a truck.
And many more.
(Don't get into a pickle over prepositions)
Comment: If you change your position so that you are no longer standing on the floor and instead standing on a bench, are any of my proposals correct or is there no way around 'onto' (to be frank, I just forgot that preposition)? And can I use 'onto' with 'stand'? Can it describe that kind of motion or does it only refer to a stationary state (other meanings aside)?


Ionic charge factors

Question: New to chemistry so forgive the fundamental question. What exactly determines the element's charge? Oxygen has 2- and hydrogen has 1+. Oxygen wants to receive 2 electrons to complete a shell when hydrogen wants to donate 1 electron. For example why wouldn't hydrogen want to gain 1 to complete its shell? What exactly is the methodology to  this of any given element (non transitional obviously). I understand that the groups of the periodic can be used and memorized but whats the actual scientific theory as to why a given element donates rather than accepts and vise versa.
Comment: There's no such thing as "element's charge" and saying that hydrogen wants to get rid of electrons is nonsense.
Comment: @Mithoron then when we say oxygen is 2- what is that referring to? Its ionic form? Can u better explain?
Comment: You can say for example that Na2O consists of sodium cations and oxygen anions, but it's simplification.
Answer: Since you are new to chemistry, I assume the concept you are searching for is electronegativity.
Each element has an electronegativity, which in short is its tendency to attract electrons. Hence, since oxygen has electronegativity 3.4 and carbon has electronegativity 2.6, the $\ce{CO2}$ molecule can be seen as one $\ce{C^{4+}}$ and two $\ce{O^{2-}}$.
Of course this is a gross oversimplification and not actually how the $\ce{CO2}$ molecule works, so don't get attached to this view as you learn more chemistry.
To go forward, I suggest you check the different kinds of chemical bonds.

Ionic charge factors


steering does not respond appropriately

Question: I started my car this morning and backed up out of my parking spot.  When I left the parking lot I lost steering (the response from the wheel is extremely stiff and behaves as if there is no power steering.) There are no leaks indicating loss of power steering fluid and the reservoir is full, so I am at a loss for ideas.  What do you think could cause this?
Comment: While this could be universal, it would help if you would add some information as to what make, model, and year this relates to. Some cars are more prone to certain behaviours, and it could be easier to pinpoint.
Answer: Check the power steering belt. If the belt is slipping, it would probably squeal horribly, but it might not if it's really loose. It could also have broken, in which case there would be no sound. If the belt isn't turning the power steering pump, then you won't have any power steering.
Answer: Depending on the age of the car you may be experiencing "steering rack morning sickness". If it gets better as the car warms up you most likely have a steering rack that is on its' way out. This is a common first symptom of rack failure. Generally it occurs after the car has sat for an extended period like overnight. It will get gradually take longer and longer for the power steering to come back. At some point the power assist will fail. Since steering is a pretty important function you should have it checked by your mechanic to verify that nothing is near immenant failure.
Answer: If everything in the power steering system checks out, it could be a binding U joint: http://my.cardone.com/techdocs/PT%2027-0007.pdf
Comment: Quoting links with very little summary information is frowned upon here as the link can go 'stale' - please summarise what that document says, and declare any affiliation you may have with the site you're linking...

steering does not respond appropriately


Should I eliminate all ID columns and similar columns from training data?

Question: This is a basic question so bear my ignorance. I feel like they contribute collectively in no way to the target. This is for performance and accuracy.
The target is polar (0,1).
Comment: Your intuition is correct, remove the ID column if it is clearly not correlated in any way with the label
Comment: But how do we determine that relationship? Let's say the id cols are just integers from 1 to n but they add a huge boost the the score on a LB because the test set also has the same ids and your model feature Importance tell that's this is col matters a lot..(3x times the second imp feature let's say)
Answer: It depends.
If your data samples are IID (independent and identically distributed) then you can remove the sample ID, given that all samples come from or refer to the same source/object and they don't somehow identify the sample class.
But, if your data is sequential, such as time series, it would be a big mistake to neglect the ID, as it identifies the time order between the samples. The time dependencies are a great source of information for problems such as time series forecasting, regression and classification. If you treat sequential data (time series) as IID (by removing the ID), you will have inferior performance, because you neglect one source of information, i.e. temporal dependencies. You should not include the ID as input to your model, but you should respect the order of the samples, which is shown by the ID.
Comment: Making sure it isn't a time-series is a good catch (as it wasn;t mentioned in the question). One could even do further pre-processing on the ID column to generate new columns such as a binary `is_weekend`, taking either 0 or 1.


garage door opener replacement

Question: i am looking to replace my current garage door opener. the images below show that the opener track was installed on an angled bracket along with the torsion spring. is it safe to remove the track screws on the angle bracket without having an issue with the spring losing its tension and causing injury?
Comment: When I replaced my Craftsman with a Chamberlain, the new unit's bolt holes matched up perfectly with the old unit's holes.   I didn't have to muck with any of the other stuff.
Answer: yeah it's safe if you are careful. The attachment points you can disconnect safely are circled in blue.

The torsion spring is attached to the bracket separately. Don't touch any of the other bolts on the bracket while the spring still has tension.

garage door opener replacement


How important is the exact name of an undergraduate degree?

Question: How important does one think the exact name of a degree is? Suppose a student had a BASc in Software Engineering (Bachelor of Applied Science, somewhat common in Canada) or a student with a BSE degree (Bachelor of Software Engineering, as awarded by, say Waterloo), would you perceive the students differently? Do you know of instances where this may have affected a student in a job search or in grad school admissions?
Comment: No and no, respectively.
Comment: In general, we try to be cautious about creating new tags - see [When should I create new tags?](https://academia.stackexchange.com/help/privileges/create-tags). Having a large number of overly specific tags makes it harder to group questions, and makes it harder for new users to find appropriate tags for their question.
Answer: The students would be perceived the same. When applying for a graduate program, you submit your transcripts. The classes you took, your letters of recommendation, and your grades would be more important than the name of your degree.


What does this snort rule mean?

Question: alert tcp $EXTERNAL_NET any -> $HOME_NET any (msg:"MALWARE-BACKDOOR access remote pc runtime detection - init connection"; flow:to_server,established; content:"|99 F3 00 00 00 00 00 00 FF FF FF FF|"; depth:12; flowbits:set,AccessRemotePC_detection; flowbits:noalert; classtype:trojan-activity; sid:12142; rev:3;)
Comment: There are many parts here. Please indicate which parts you already understand so that we don't have to explain what `tcp` means, for instance.
Answer: It will 'alert' on any TCP connection from an external network to an internal network (DMZ) as long as the content of the packet matches '99 F3 00 00 00 00 00 00 FF FF FF FF' (which matches the BackoffPOS 1.56 process injection module).
While there is more to the rule; depth, setting the flowbits to a pre-defined class (AccessRemotePC_detection; used for easier reporting) as well as 'classtype', in simplest terms that is your rule breakdown.

What does this snort rule mean?


Run-time AOP vs Compile-time AOP

Question: What's the advantage and disadvantage of these two type of AOP framework? I'm using Unity as my aop framework, but I guess the compile-time aop framework such as postsharp may have better performance than run-time aop framework? It looks like run-time aop framework use reflection to implement the injection.
Answer: I am not a .NET guy, but I know the AOP world in the Java ecosystem, especially AspectJ and Spring AOP. Basically there are 4 types of aspect weaving:

Source code weaving: Aspect code is injected as source code statements into your application source code. This is some kind of preprocessor approach. No AOP framework in the Java world uses this approach nowadays, but there used to be some in the early days of AOP.

The advantage would be complete independence of any runtime libaries or special AOP compilers during runtime, if done right.
The disadvantage would be bloated source code and a preprocessing / code generation step before compilation. You would always need the generated source code for debugging.

Compile-time weaving: Aspect code is woven into your application by a special compiler.

The advantage is no runtime overhead for aspect weaving. The only thing you need is a small runtime library on your classpath.
The disadvantage is that you cannot defer the decision if you want to weave aspects into your application at all to runtime. But this is only a problem when dealing with debugging or tracing aspects not needed all the time. Another disadvantage is that this approach only works for code under your control, i.e. you need to have the source code. It does not work for 3rd party libs.

Binary weaving: Aspect code is woven into existing class files after compilation rather than during compilation.

The advantage is that it also works for 3rd party code you do not have the source code for. This approach can also be mixed with compile-time weaving. You also avoid the overhead of load-time weaving (see below).
The disadvantages are similar to compile-time weaving: You cannot unapply an aspect once it is woven into the code, merely deactivate its execution by pointcuts such as if(). But this can be quite efficient.

Load-time weaving (LTW): A weaving agent/library is loaded early when your VM/container is started. It gets a configuration file with rules describing which aspects should be woven into which classes.

The advantage is that you can dynamically decide if/what to weave. If done via byte-code transformation and not via dynamic proxies or reflection (see below), the resulting bytecode is equally efficient as the one created via compile-time or binary weaving. Another advantage is that like binary weaving it works for your own code as well as 3rd party code, as long as the weaving agent can "see" it, i.e. it happens in a child classloader.
The disadvantage is the one-time weaving overhead during application start-up because weaving is done while classloading occurs.

Proxy-based LTW: This special LTW form is used by Spring AOP while AspectJ does the previous 3 forms listed above. It works by creating dynamic proxies (i.e. subclasses or interface implementations) for aspect targets.

I cannot think of any special advantage other than maybe your framework of choice (such as Spring) happens to support it.
Disadvantages are limitation to public, non-static methods and runtime overhead due to the proxy-based approach. It also does not capture internal method calls, i.e. when a proxied class calls one of its own methods because those calls are not captured by the proxy. Special types of pointcuts such as constructor interception, member variable read/write access and many more are not supported, making this more of an "AOP lite" approach. But it can be sufficient for your purposes.

Generally, good aspect compilers such as AspectJ create very efficient bytecode and do not heavily rely on reflection during runtime. If your aspect framework of choice does rely on reflection, probably it is not very fast. But maybe it is fast enough, depending on how heavily you use aspects.
Probably I have written too much already, but I could write even more. This is why I am stopping now. Besides, this kind of question is not well-suited to StackOverflow because it can lead to philosophical discussions and opinion-based debates. I hope I managed to be fairly objective/impartial even so.
Comment: that was awesome explanation. cant we say aspectJ doesnt use reflection ? also you said AspectJ does these three : compile-time, binary, load-time can we choose which one to use or it happens internally ?
Comment: Amir, you can learn more about AspectJ by reading the [documentation](http://www.eclipse.org/aspectj/docs.php). I suggest to try and use it instead of asking yourself theoretical questions about it. As for the second question, you as a developer decide which type of weaving you want to use. AspectJ does not do anything without you configuring your build environment correspondingly.
Comment: @kriegaex Does aspectj compiler has any disadvantage over java compiler? Let's say we use compile time weaving and we face an issue due to the aspectj compiler. In the case where we can't get the aspectj compiler fixed, we'll have to make a lot of changes to get things working again. In short, compile time weaving seems like the best choice but aspectj compiler seems like a deal breaker. What is your opinion on that?
Comment: My opinion is: Some people find a solution for every problem. Others find a problem in every solution. Besides, the AspectJ compiler is a regularly refreshed fork of the Eclipse Java compiler and very well maintained. It is much easier to get the maintainer's attention than with the Oracle JVM. My recommendation is: See chances too, not just risks. I cannot see any "deal breaker" here.
Comment: Really appreciate your answer!
Comment: Can you please tell if it Is possible to use both CTW and LTW for different annotations on a single method? That is, configure LTW for some annotations while CTW for others. I recently faced an issue while attempting this and had to configure LTW for all annotations. Any help would be highly appreciated.
Comment: Please do not hijack a 5+ years old question with a follow-up, but create a new question and select the correct tags, then I will be notified automatically. You can link to this question from the new one. But when you do ask the new question, please provide an [MCVE](https://stackoverflow.com/help/mcve) and not just two sentences. I cannot debug prose. "I tried X, it is not working" does not qualify as a good question.

Run-time AOP vs Compile-time AOP


Create a new Home page layout and assign a dashboard to it

Question: I have created a dashboard folder with two charts and I have given access to the folder to three user. Now what i want is that I want to create a new home page layout and assign that dashboard to that home page layout. I am not exactly sure how to achieve this. Can anyone tell me how to do this. I am very new in Salesforce and any help would be appreciated
Comment: this should get you started https://developer.salesforce.com/events/webinars/Lightning-App-Builder and remember you can always check for salesforce documentation at https://help.salesforce.com/ prior to posting questions
Answer: Follow the steps for your requirement.

Click on the Home tab and go to Dashboard section.

Click on "Customize Page" link on the right side.
Choose your Dashboard in the "Customize Home Page" screen.

Finally, you can assign the homepage to the respective profiles.


One query at a time on a SharePoint list

Question: I have a small application that uses a SharePoint list as the data source. This application has to be used by many users at the same time. There may occur a situation when more than one user woult want to edit the same list item of the SharePoint list. And that's not the way the application is intended to work.
I need to modify the way the application accesses the list so that there will be one query at a time and the conflict would not occur. How can i do it?
Answer: assuming all the users of the list will only access it through your application, could you synchronize access to the lie using a "lock" file that your application creates, similar to the way MS Access uses a .ldb file to manage concurrent access. The lock file would contain the name of the application instance/connection/computer that was currently accessing the list, and the application would check to see if a lock file existed before accessing the list.
Answer: Without more specifics I have to say this strikes me as 'code smell' and you may be better off looking at your applications design/architecture.
A more helpful suggestion is to use version control and 'requires checkout' on your list as the locking mechanism.
Answer: If you are operating against a list, check the modification date and/or the version umber before you save, if it's different than the date or version in the client's copy then notify the user.
If your list is is a form or document librry your endeavor is much easier, check the file out when the user opens it.  I would set a timeout just in case somebody's app crashes or they close the lid on their laptop before you have a chance to clean up.
SPListItem.File.CheckOut()

Or, you could check to see if the files is checked out before you check it in
SPListItem.File.CheckedOutBy
SPListItem.File.CheckedOutExpires


Scattered Pixel Effect in Photoshop?

Question: I'm trying to learn how to create a scattered pixel effect in Photoshop. I know how to create pixelated graphics. But i'd like to know how to create an effect where the pixels are scattered. Similar to this photo.
Comment: Do you want the result to be a bitmap, vector paths, or would either be ok? There's quite a few ways to automate something like this.
Comment: vector or psd is fine no bitmaps
Answer: I was able to achieve something similar, try the following:
Click the screenshots for full resolution
Create a new document with relatively small dimensions.

Select the Pen tool, change the size to 1px

Edit the Brush settings (Window → Brush) for Spacing
I set Spacing at 750%

Edit the Brush settings for Scattering
I set Scatter at 1000% and Count Jitter at 100%.

Edit the Color Dynamics for the Brush settings
This is a "play around with the settings and see what works" step. I changed the saturation and brightness to 92% and 61% respectively.

With the color you want the pixels to be selected, scribble around the document.
The result will be randomly scattered pixels.

Enlarge the image using Nearest Neighbor enlargement to preserve the hard edges.
Answer: I would build a segment by hand and then apply it as a pattern.
You could also build the segment in Illustrator and create a pattern brush with it.

Scattered Pixel Effect in Photoshop?


Is it a fallacy to say "A = B therefore more A = more B?"

Question: For example, 70% nominal tax rate leads to more growth, therefore, 100% nominal tax rate must lead to the most growth.
Comment: Maybe [Faulty generalization](https://en.wikipedia.org/wiki/Faulty_generalization) : "a conclusion about all or many instances of a phenomenon that has been reached on the basis of just one or just a few instances of that phenomenon. It is an example of jumping to conclusions." In your case, we may be in presence of an unstated economic law correlating tax rate with economic growth.but if we do not state the law we cannot be sure that the correlation is perfectly linear.
Answer: If the '=' sign is the sign of identity, so that in this case 'A' and 'B' are the very same thing, as in 'The Morning Star' = 'The Evening Star' = 'the plate Venus', then everything true of A is necessarily true of B. If we see more of the Morning Star then we will see more of the Evening Star and of the planet Venus.
To take another example, since there's nothing like variety, if water = H2O then the more water the more H20. Nothing fallacious here that I can see - no error of reasoning.
This answers the question in your heading. Your text box reads differently. It certainly does not follow that if A and B are not identical and that only a causal or correlational link holds between them, increasing A will increase B. More A may produce or correlate with less B. If average rainfall produces a certain amount of corn, no-one would expect more rain - a 6 months' solid deluge, say - to produce more corn. Expect the whole crop to perish. This is, I think, an illustration of Mauro indicates as a failure of linear correlation.
Answer: I don't see a formal fallacy in your example. You just don't agree with the hidden premise that higher nominal tax rates imply more growth.
Consider the syllogism:

Nominal tax rates higher than 70% lead to more growth than a 70% nominal tax rate.
A 100% nominal tax rate is a nominal tax rate higher than 70%.
Therefore, a 100% nominal tax rate will lead to more
growth than a 70% nominal tax rate.

There may be an informal fallacy in presuming higher nominal tax rates imply more growth. Mauro ALLEGRANZA probably guessed correctly with the fallacy of faulty generalization. It would ultimately depend on the justification provided, which is missing from the question.

Now to address the question in the title. The equality sign usually means the identity function in logic. So when you say "A=B" that means A and B are literally the same thing. There is a whole different syntax for saying A and B share some quality/belong to the same set (P(A)∧P(B)) or that A implies B (A→B). I believe you meant A→B.
Additionally I am not aware of a way to represent non-binary inequalities in formal logic (greater than, less than). This is because formal (predicate) logic doesn't navigate ordered sets. This is the reason arithmetic, in particular the axiom of induction in Peano arithmetic, doesn't translate to formal logic.
This means we can't directly translate "more A = more B" into formal logic. We can get around that by making a new set of "tax rates higher than 70%" and presuming a 100% tax rate belongs to this set, as I did above.
If you were to try and say "more A → more B", "more A" is not identical to A and "more B" is not identical to B so the previous premise A→B does not apply. You may as well say C→D. And so the argument devolves into the self-reliant fallacy (begging the question):

A→B
C→D
∴C→D


Who should claim Flexible Spending Account in a household

Question: Suppose my wife and I both can claim FSA but the max is 5k. And suppose we both have two dependents on our w-4. The big difference is lets say I get paid 100k and she gets 50k. Who is the better candidate to claim the FSA?
Comment: what do you mean "claim"? Are you filing jointly? In what state? That's a question to your tax advisor, not a "suppose" question on a forum.
Comment: The question is valid, the syntax is confusing.
Answer: Your wife.
You are very close to the social security wage base limit, $110,100 in 2012. FSA is withheld pre-FICA, so in future years when you are over the limit, you may still hit the maximum withholdings. Your wife, at $50K will save both your marginal rate (25%) as well as the normal 6.2% for social security withholding.
Edit - to add a clear example - At $50K, if your wife takes out $5K for FSA, the $5K avoids FICA withholding. Same for you at $10K, but, suppose your income were $115K, if you withheld $5K for FICA, you still hit the $110K limit and pay the full maximum for social security. Until you are over the limit, the point is moot.
Comment: Dilip - thanks, that issue is a real oddity that's overlooked. i.e. for most, FSA is a savings of marginal rate + 6.2%
Answer: If you are filing jointly, it doesn't make a difference. In your example it will be 5K out of 150K.
It could make a difference in state taxes, because some will allow to file separately on your state taxes, while filing jointly on the federal forms.
Ignoring taxes it could make sense to link it person paying for the insurance policy. Many insurance companies will give you a credit card to pay for co-pays, and prescriptions. If you go out of network the credit card can even be used to pay the part that is not covered by the insurance. I would think having them linked together will make the transactions smoother.
Comment: That's not necessarily correct. In community law states, earned income is divided equally, so filing jointly or separately doesn't matter. The question as asked cannot be properly answered, and information you're giving may be misleading and incorrect.
Comment: +1 - there's logistical (as opposed to 'logical') value in having the FSA with the same person who holds the primary insurance. That's actually how we do it here.


Missing Operating System

Question: So I recently made a post about my Mac not recognizing USB's or Boot. here's the link : MacBook Wont Boot or Recognize USB. Anyway this is an update. So my 2009 MacBook is still not working. It doesnt show the question mark folder, rather it goes to a command like screen with text saying "missing operating system". I know now my Mac CAN recognize USB's since it recognized a USB that had Refit on it. But it just doesnt recognize my bootable USB's with a OS on it. Also when I press opt(or alt if you want to call it that) it shows a HD called "Windows" but I never installed Windows or used bootcamp ever! I still cant use cmd + r for OS Utilities or cmd + opt + r since it doesnt have internet recovery ( 2009 Macs dont support internet recovery ). If anyone could please help I would thank you a lot! I need this MacBook for future projects!
It's a MacBook 2009
Comment: Can you get to the recovery console (hold the command key + R) on a boot up? If so, what's the time on the system (open a terminal and type in `date`). Also, can you confirm that the USB you are using will boot another Mac?
Comment: like I said. I cant enter recover mode or internet recover mode
Comment: Can you confirm that the USB you are using boots off of another Mac correctly (i.e. you get to the OS X install menu)?
Comment: well atm I dont have another Mac, but I assume it would since my MacBook recognized it before I deleted the HD
Answer: An option would be to purchase the Mac OS X Snow Leopard for $20 USD. Once you have installed Snow Leopard and upgraded to 10.6.8, then you can download and install El Capitan.
BTW, the icon labeled Windows indicates the Mac Startup Manager is detected the installation of a legacy BIOS booting operating on your Mac. This does not mean the operating system was Windows.
According to everyman.com a 2009 MacBook was shipped with OS X 10.5.6, OS X 10.5.7 or OS X 10.6.1 preinstalled. You did not provide enough information to determine which 2009 MacBook model your have. Apple does not provide enough information to determine which version of Snow Leopard you would be buying. One can assume this would be OS X 10.6.x, but what x is I do not know. You would have to ask to Apple. I assume you are buying a DVD and that your DVD drive works. The idea was to install Snow Leopard from the DVD, then download and install the Mac OS X 10.6.8 Update Combo v1.1. Next, you can download and install El Capitan from the Apps Store. This would avoid using a USB port.
To get the Mac to recognize the DVD, you would need to hold down the option key at startup until the Startup Manager appears. Select the DVD icon to boot from the Snow Leopard DVD.
Comment: Would it be able to recognize the disc? Also that would make since that it would be a LEgacy BIOS, since when I opened Refit, I chose an option to boot a Legacy OS
Comment: @Galaxy Enliv: I updated my answer.

Missing Operating System