Can't install VLC package from the PPA "The following signatures couldn't be verified because the public key is not available"
How do I resolve unmet dependencies after adding a PPA?
PHP - Get rid of notation What ways could you create a data extension that contains all the subscribers (SubscriberKeys) that are currently “in” a Journey (Journey Builder)?  The Journey I would like to do this for is a complex activity with multiple decision branches resulting in multiple possible journey durations. For example; if the customer didn’t open Email1 after 2 days, then send Email2; else Exit Journey. If the customer didn’t open Email2 after 2 days, then send Email3; else Exit Journey. Wait 2 more days, then End Journey. The minimum journey duration for the above example is 2 days, while the maximum is 6 days.  Note that I don’t want a list of subscribers that “entered” a Journey, but a list of the ones that are “currently in” a Journey and have not yet exited. Answer must account for non-standard Journey exits including Unsubscribes/Contact Deletes, etc. Assume $R=(\mathcal{U}_n)_n$ is a sequence of distinct ultrafilters on some set $X$. Since every Hausdorff space has an infinite discrete subspace, there is a subsequence $R=(\mathcal{V}_n)_n$ of $R=(\mathcal{U}_n)_n$ such that $\{\mathcal{V}_n|n \in \mathbb{N} \}$ is a discrete subspace of $\beta X$. In particular, there is a sequence $(A_n)_n$ of sets with $A_n \in \mathcal{V}_m$ if and only if $m =n$. If we let $B_n=A_n - (A_0 \cup...\cup A_{n−1})$, then the sequence $(B_n)_n$ is pairwise disjoint and $B_n \in \mathcal{V}_m$  iff $m=n$. If we let $B =\cup_n B_{2n}$, then $B \in \mathcal{V}_m$ if and only if $m$ is even. In other words, if $B =\{ \mathcal{V} \in βX|B \in \mathcal{V}\}$, then $B$ is a clopen set with $\mathcal{V}_m \in B$ iff $m$ is even. Therefore, we conclude that the sequence $(\mathcal{V}_m)_m$ cannot converge to any point, so the sequence $(\mathcal{U}_n)_n$ cannot converge to any point either.     I would like to know that:      (1) Why "$B_n \in \mathcal{V}_m$  iff $m=n$"? And " $B =\cup_n B_{2n}$, then $B \in \mathcal{V}_m$ if and only if $m$ is even "?      (2)$B$ is a clopen set with $\mathcal{V}_m \in B$ iff $m$ is even all the LaTeX-tutorials tell me how LaTeX is an extention simplifying the building of TeX documents. Understandably, no one uses plain TeX anymore, right?  But I seem to learn better when I grasp the link between TeX and LaTeX. Does someone have a link to example files in plain TeX? I'd like to know which commands, macros etc. are LaTeX-specific. Photoelectric effect intensity I understand the PE effect quite well but I'm failing to understand one thing. Intensity is the amount of energy per second incident to a given area.   So can you can increase the intensity by either increasing the electrical energy or making the area smaller? By increasing the electrical energy, what exactly is happening?  I assume that by increasing intensity you are increasing the number of photons incident to an area of the metal thus increasing the rate of photoelectric emission. But why doesn't increasing intensity via more electrical power lead to greater energy of the electrons, if by increasing intensity you are increasing the energy of the incident waves?  I understand the results but I'm trying to understand why the intensity works the way it is thanks Can't boot XP after Ubuntu Installation, how to fix? I installed Ubuntu and after the installation, i can't boot to XP. When i choose XP from the Grub menu, I got black screen for like 30 sec, and then it returns to the Grub menu.  Thanks! .toArray(new MyClass[0]) or .toArray(new MyClass[myList.size()])? Assuming I have an ArrayList  ArrayList&lt;MyClass&gt; myList;   And I want to call toArray, is there a performance reason to use  MyClass[] arr = myList.toArray(new MyClass[myList.size()]);   over  MyClass[] arr = myList.toArray(new MyClass[0]);   ?  I prefer the second style, since it's less verbose, and I assumed that the compiler will make sure the empty array doesn't really get created, but I've been wondering if that's true.  Of course, in 99% of the cases it doesn't make a difference one way or the other, but I'd like to keep a consistent style between my normal code and my optimized inner loops... Definition of autocorrelation time (for effective sample size) I've found two definitions in the literature for the autocorrelation time of a weakly stationary time series:  $$ \tau_a = 1+2\sum_{k=1}^\infty \rho_k \quad \text{versus} \quad \tau_b = 1+2\sum_{k=1}^\infty \left|\rho_k\right| $$  where $\rho_k = \frac{\text{Cov}[X_t,X_{t+h}]}{\text{Var}[X_t]}$ is the autocorrelation at lag $k$.    One application of the autocorrelation time is to find the "effective sample size": if you have $n$ observations of a time series, and you know its autocorrelation time $\tau$, then you can pretend that you have  $$ n_\text{eff} = \frac{n}{\tau} $$  independent samples instead of $n$ correlated ones for the purposes of finding the mean.  Estimating $\tau$ from data is non-trivial, but there are a few ways of doing it (see ).  The definition without absolute values, $\tau_a$, seems more common in the literature; but it admits the possibility of $\tau_a&lt;1$.  Using R and the "coda" package:  require(coda) ts.uncorr &lt;- arima.sim(model=list(),n=10000)         # white noise  ts.corr &lt;- arima.sim(model=list(ar=-0.5),n=10000)    # AR(1) effectiveSize(ts.uncorr)                             # Sanity check     # result should be close to 10000 effectiveSize(ts.corr)     # result is in the neighborhood of 30000... ???   The "effectiveSize" function in "coda" uses a definition of the autocorrelation time equivalent to $\tau_a$, above.  There are some other R packages out there that compute effective sample size or autocorrelation time, and all the ones I've tried give results consistent with this:  that an AR(1) process with a negative AR coefficient has more effective samples than the correlated time series.  This seems strange.    Obviously, this can never happen in the $\tau_b$ definition of autocorrelation time.  What is the correct definition of autocorrelation time?  Is there something wrong with my understanding of effective sample sizes?  The $n_\text{eff} &gt; n$ result shown above seems like it must be wrong... what's going on? I have a long running BASH script that I am running under CYGWIN on Windows.  I would like to limit the script to run for 30 seconds, and automatically terminate if it exceeds this limit. Ideally, I'd like to be able to do this to any command.  For example:  sh-3.2$ limittime -t 30 'myscript.sh'   or   sh-3.2$ limittime -t 30 'grep func *.c'   Under cygwin the ulimit command doesn't seem to work.   I am open to any ideas. How can I send the stdout of one process to multiple processes using (preferably unnamed) pipes in Unix (or Windows)? I'd like to redirect the stdout of process proc1 to two processes proc2 and proc3:           proc2 -&gt; stdout        /  proc1        \           proc3 -&gt; stdout   I tried   proc1 | (proc2 &amp; proc3)   but it doesn't seem to work, i.e.   echo 123 | (tr 1 a &amp; tr 1 b)   writes   b23   to stdout instead of    a23  b23 I wanted to create a WP plugin. So I requested and my request was approved by WordPress.org But I don't want to develop that plugin anymore. How can I delete the repository forever or request its deletion. What makes you lose the Field Upgrade Score? When playing in a squad, you can get "Field Upgrades". However, sometimes when I die, it tells me that I have lost the "Field Upgrade Score".   Where can I see this score and what are the events that make me lose it? What is the correct JSON content type? I've been messing around with  for some time, just pushing it out as text and it hasn't hurt anybody (that I know of), but I'd like to start doing things properly.  I have seen so many purported "standards" for the JSON content type:  application/json application/x-javascript text/javascript text/x-javascript text/x-json   But which one is correct, or best? I gather that there are security and browser support issues varying between them.  I know there's a similar question, , but I'd like a slightly more targeted answer. Negation in English What's better here - a single column or multicolumn primary key? Let's assume you have a table groups and a table item. Each item belongs to exactly one group. It is an inherent part of that group. An item cannot exist outside of a group and it cannot be moved to another group.  When trying to decide on a primary key for the item table, what should I use?  Should I make up an artificial global serial key like this:  CREATE TABLE items (     item serial PRIMARY KEY,     group integer NOT NULL REFERENCES groups(group), );   ... or should I rather use a composite key and per-group item serial like this:  CREATE TABLE items (     group integer NOT NULL REFERENCES groups(group),     item integer NOT NULL,      PRIMARY KEY(group, item) );   The reason why I'm leaning more towards the second solution is that the post URL will always show the group and item, so it makes sense to have both of them as the composite primary key. In case of the first solution, the URL contains superfluous information because the group ID can already be deduced from the item ID alone. The URL structure is given, however, and cannot be changed.  The disadvantage of the second solution is that you have to manage a per-group serial (i.e. each item integer should start from 0 for each group).  What's better in terms of best practices, normalization and performance? Or is it simply a matter of taste? How can adding an infinite number of rationals yield an irrational number? For example how come $\zeta(2)=\sum_{n=1}^{\infty}n^{-2}=\frac{\pi^2}{6}$. It seems counter intuitive that you can add numbers in $\mathbb{Q}$ and get an irrational number. What Thunderbolt to USB 3.0 cables/adapters exist for OS X and Mac hardware? I have the Late 2013 Macbook Pro, which has two USB 3.0 ports and two Thunderbolt 2 ports. I currently use both USB 3.0 ports and one TB2 port. I want to connect a third USB 3.0 device to the machine, but I don't want to use a USB splitter on one USB port as I'm concerned the devices would draw too much power from the bus. I have no current use for the second TB2 port and I would love to be able to use it for this purpose.   Browsing extensively online, I've found numerous docks, such as , that connect via a Thunderbolt cable. This would work, but it's an expensive, 'bulkier' solution (and not the one I'm looking for).   I'm aware that a USB 3.0 device wouldn't be able to take advantage of Thunderbolt's I/O speeds, but it's certainly compatible, which is all I'd need. After all, Apple even sells a . I also know that Thunderbolt is not only used for digital video purposes (along with the TB > Firewire option, there exists ).   There are almost no Thunderbolt to USB 3.0 cables/adapters on the market. I'd think this hardware would be more prevalent given the prominence of USB devices out there. What adapters are available for OS X? Weight Painting Won't Get Rid of Weird Protrusions What does the "private" modifier do? Considering "private" is the default access modifier for class Members, why is the keyword even needed? I have a UK Refugee passport. Do I need a visa to go to France?   I want to go for two days with my husband, but I'm not quite sure if I can go without a visa.