Is there any critical feature present in Nikon 85mm f/1.8G over 50mm 1.8G?
Why are 50mm Lenses Cheaper?
Fighting a black hole: Could a strong spherical shell inside an event horizon resist falling in to the singularity? As a thought experiment imagine an incredibly strong spherical shell with a diameter a bit smaller than the event horizon of a particular large black hole.  The shell is split into two hemispheres, and the two hemispheres are released from either side of the black hole such that they will meet and join inside the event horizon, forming a stationary uniform shell around the singularity. Of course, we consider that the shell is flawless, and exactly centred around a stationary singularity - clearly this is an unstable equilibrium but we imagine it is possible.  Is is possible that the structural forces provided by such a shell could be strong enough to resist the extreme gravity conditions inside the event horizon, and hence avoid being sucked into the singularity?      (For the purposes of this question we can consider taking the shell to extreme levels of strength, e.g. consider that the shell is made from a theoretical maximally densely packed neutronium-like material that is strongly resistant to any further compression due to the Pauli exclusion principle). Today i was at a arena. A player from the red team put a Grimer there, which causes my game to crash every time I select the arena (Samsung Galaxy S4 mini). All other pokemons i saw so far did not make any problems  I searched a bit, and found out that this is a known bug, e.G.:   Now my question, is there a way to battle in the arena or even select it without crashing my app? Some option like "hide model in arena",changing some smartphone-settings or another trick? Or do i have to wait till a bugifx from niantec comes or somebody else which has a handy which dont crashes with grimer clears the arena, before selecting the arena?  Because somebody could place him there i guess this is only a bug for specific smartphones, but this could be used to exclude a lot of players from arenafighting by only placing grimers in arenas to let the game crash for them, are there some official notes about this from niantec or how to avoid the crash? Control a property with no socket (color ramp swatch, etc) from a Group Node input? I'm running Bash scripting, but sometimes I get confused which of these commands I use belong to who. Sometimes man xxx works, sometimes doesn't, so I use --help or info, mostly one of these works to show description of the command. Can anyone tell me how I would know what command belongs to what? Bash builtin, GNU utility, etc. Auto mount a disk drive in ubuntu 14.04 LTS (Bookmark directory not found) I'm using ubuntu 14.04 LTS. When I start my pc and click on any bookmark from the file manager it shows this error:   Unable to find the requested file. Please check the spelling and try again. Unhandled error message: Error when getting information for file '/media/angel/DOC/edu': No such file or directory   But when I open DOC drive and again clink on the same bookmark it works properly. Can anybody tell me why is this happening and how to solve this issue?   Edit: Output of lsblk is following: (ubuntu is installed in sda5)  NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 119.2G  0 disk  ├─sda1   8:1    0  91.3G  0 part  ├─sda2   8:2    0     1K  0 part  ├─sda5   8:5    0  24.1G  0 part / └─sda6   8:6    0   3.8G  0 part [SWAP] sdb      8:16   0 465.8G  0 disk  ├─sdb1   8:17   0  93.2G  0 part  ├─sdb2   8:18   0     1K  0 part  ├─sdb5   8:21   0  93.2G  0 part  ├─sdb6   8:22   0  89.3G  0 part  ├─sdb7   8:23   0  93.2G  0 part  ├─sdb8   8:24   0  93.2G  0 part  └─sdb9   8:25   0   3.8G  0 part  sr0     11:0    1  1024M  0 rom     After opening the disk drive the output of lsblk is bellow:   NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 119.2G  0 disk  ├─sda1   8:1    0  91.3G  0 part  ├─sda2   8:2    0     1K  0 part  ├─sda5   8:5    0  24.1G  0 part / └─sda6   8:6    0   3.8G  0 part [SWAP] sdb      8:16   0 465.8G  0 disk  ├─sdb1   8:17   0  93.2G  0 part  ├─sdb2   8:18   0     1K  0 part  ├─sdb5   8:21   0  93.2G  0 part  ├─sdb6   8:22   0  89.3G  0 part /media/angel/DOC ├─sdb7   8:23   0  93.2G  0 part  ├─sdb8   8:24   0  93.2G  0 part  └─sdb9   8:25   0   3.8G  0 part  sr0     11:0    1  1024M  0 rom   The output of sudo blkid gives the following information about sdb6:  /dev/sdb6: LABEL="DOC" UUID="04280A22280A12FA" TYPE="ntfs" Kinematic Viscosity Find the sum : $\frac{1}{\cos0^\circ\cos1^\circ}+\frac{1}{\cos1^\circ \cos2^\circ} +\frac{1}{\cos2^\circ \cos3^\circ}+......+$ Find the sum of the following :   (i) $$\frac{1}{\cos0^\circ \cos1^\circ}+\frac{1}{\cos1^\circ\cos2^\circ} +\frac{1}{\cos2^\circ \cos3^\circ}+......+\frac{1}{\cos88^\circ \cos89^\circ}$$  I tried :  $$\frac{1}{\cos1^\circ}\left[\frac{\cos(1^\circ-0^\circ)}{\cos0^\circ\cos1^\circ} + \frac{\cos(2^\circ-1^\circ)}{\cos1^\circ\cos2^\circ}+...\right]$$  = $$\frac{1}{\cos1^\circ}\left[\frac{\cos1^\circ\cos0^\circ}{\cos0^\circ\cos1^\circ} - \frac{\sin1^\circ \sin0^\circ}{\sin0^\circ\cos1^\circ} + \frac{\cos2^\circ \cos1^\circ}{\cos1^\circ\cos2^\circ} -\frac{\sin2^\circ \sin1^\circ}{\cos1^\circ\cos2^\circ}...\right]$$  For this, as well, I am not getting any pattern to solve further. Please suggest, thanks. ROC vs Precision-recall curves on imbalanced dataset I just finished reading  discussion. They argue that PR AUC is better than ROC AUC on imbalanced dataset.   For example, we have 10 samples in test dataset. 9 samples are positive and 1 is negative. We have a terrible model which predicts everything positive. Thus, we will have a metric that TP = 9, FP = 1, TN = 0, FN = 0.  Then, Precision = 0.9, Recall = 1.0. The precision and recall are both very high, but we have a poor classifier.  On the other hand, TPR = TP/(TP+FN) = 1.0, FPR = FP/(FP+TN) = 1.0. Because the FPR is very high, we can identify that this is not a good classifier.  Clearly, ROC is better than PR on imbalanced datasets. Can somebody explain why PR is better? How can author deal with late reviews? Another problem I personally struggle with in peer-review publication process is the situation when review takes really, really, really long. The precise definition of "long" is probably very area-specific: for example a paper in Maths will probably took longer to review than one in Physics. Many well-established journals and major publishers, sadly, prefer not to specify the "rules of the game" precisely, particularly how long the review process should normally take. Fortunately, I quite often serve as a referee with the very same journals and know the amount of time I am given to write a review. Unfortunately, when I am an author, I do not observe these deadlines to be always met. For example, a notable U.S. publisher would ask a reviewer to send a review in 2 months; but in practice a first review of my paper once took as long as 8 months.  As a rule of thumb, I usually start writing to editors with questions about "the status of my paper" in X+1 months time, when X is a deadline time for a reviewer to submit a review. This strategy is not particularly successful &mdash; what I usually get is a recommendation to be more patient. Since there is no "official" deadline time announced, there is no formal ground for complaints here.  Of course, such delays lead to a whole bunch of funny situations, particularly if a preprint is put online (e.g., on arXiv) and the results are presented in some conferences. Follow-ups with no official paper to cite, grant applications in which you can not justify by a solid publication, good research but bad bibliometrics or CV, to name just a few.   Could you recommend an efficient way to deal with this problem? Preserving signatures of decorated functions Suppose I have written a decorator that does something very generic. For example, it might convert all arguments to a specific type, perform logging, implement memoization, etc.  Here is an example:  def args_as_ints(f):     def g(*args, **kwargs):         args = [int(x) for x in args]         kwargs = dict((k, int(v)) for k, v in kwargs.items())         return f(*args, **kwargs)     return g  @args_as_ints def funny_function(x, y, z=3):     """Computes x*y + 2*z"""     return x*y + 2*z  &gt;&gt;&gt; funny_function("3", 4.0, z="5") 22   Everything well so far. There is one problem, however. The decorated function does not retain the documentation of the original function:  &gt;&gt;&gt; help(funny_function) Help on function g in module __main__:  g(*args, **kwargs)   Fortunately, there is a workaround:  def args_as_ints(f):     def g(*args, **kwargs):         args = [int(x) for x in args]         kwargs = dict((k, int(v)) for k, v in kwargs.items())         return f(*args, **kwargs)     g.__name__ = f.__name__     g.__doc__ = f.__doc__     return g  @args_as_ints def funny_function(x, y, z=3):     """Computes x*y + 2*z"""     return x*y + 2*z   This time, the function name and documentation are correct:  &gt;&gt;&gt; help(funny_function) Help on function funny_function in module __main__:  funny_function(*args, **kwargs)     Computes x*y + 2*z   But there is still a problem: the function signature is wrong. The information "*args, **kwargs" is next to useless.  What to do? I can think of two simple but flawed workarounds:  1 -- Include the correct signature in the docstring:  def funny_function(x, y, z=3):     """funny_function(x, y, z=3) -- computes x*y + 2*z"""     return x*y + 2*z   This is bad because of the duplication. The signature will still not be shown properly in automatically generated documentation. It's easy to update the function and forget about changing the docstring, or to make a typo. [And yes, I'm aware of the fact that the docstring already duplicates the function body. Please ignore this; funny_function is just a random example.]  2 -- Not use a decorator, or use a special-purpose decorator for every specific signature:  def funny_functions_decorator(f):     def g(x, y, z=3):         return f(int(x), int(y), z=int(z))     g.__name__ = f.__name__     g.__doc__ = f.__doc__     return g   This works fine for a set of functions that have identical signature, but it's useless in general. As I said in the beginning, I want to be able to use decorators entirely generically.  I'm looking for a solution that is fully general, and automatic.  So the question is: is there a way to edit the decorated function signature after it has been created?  Otherwise, can I write a decorator that extracts the function signature and uses that information instead of "*kwargs, **kwargs" when constructing the decorated function? How do I extract that information? How should I construct the decorated function -- with exec?  Any other approaches? Guarding against cryptanalytic breakthroughs: combining multiple hash functions cron Vs. sleep - which is the better one in terms of efficient cpu/memory utilization? Though I never quite understood what those numbers were and they were quite ugly, they were the only reason I ever visited the reviews page.   Can we have similar functionality back on the top bar please? I am supposed to integrate $f(z)=$$\frac{5}{z}$ from -3 t0 3 but I am having trouble understanding how to do this. I've done the integration the "hard" way by using parametrizations but now I need to use the fact that $f(z)$ is analytic everywhere except at $z=0$ and a different method to perform the integration but I am stumped. What is the meaning of "algebraically indistinguishable" I heard the term couple of times (in Field theory class and book), for example: The different roots of $p(x)=x^3-2$ are "algebraically indistinguishable".  I understand the meaning intuitively, but what does it really mean ? sudo apt upgrade error 18.04 (Broken Packages) Gaming the system for Populist badges SEO for importing the page header with JavaScript rather than PHP My website has the same header/sidebar/footer on every page, so I have been importing them using PHP. To do this I forced all html files to be processed through the apache servers PHP handler via htaccess. I have come to understand that is not necessarily the best thing to do and so found out how to do everything I need using simple JavaScript. I also store a variable in the initial page that then gets used in the imported html.  Questions: By switching from:  &lt;?php include "_header.html";?&gt;   to  &lt;script type="text/javascript" src="_header.js"&gt;&lt;/script&gt;   I am noticing that the "view source" shows the header.js link, whereas the PHP method will show the source as if the html had been there all along. Will search engines recognize the html in the JavaScript just as they would when loaded with PHP?  I understand it is bad practice to alter the page contents -after- it is downloaded, but this doesn't fall into that category does it? That would detail things like after a wait function, or after user interaction, correct?  Are there any other foreseeable downfalls to switching to JavaScript and turning off the forced PHP processing? Point vs Pixel: What is the difference? What is the difference between points and pixels? Expectation of a function of a random variable from CDF Is it possible to calculate the expectation of a function of a random variable with only the the r.v.'s CDF? Say I have a function $g(x)$ that has the property $\int_{-\infty}^{\infty}g(x)dx \leq \infty $ and the only information I have about the random variable is the CDF.  For example, I have a scenario where there are three timers that can be modeled as exponential random variables $X_1,X_2,X_3$ with rate parameters $\lambda_1,\lambda_2,\lambda_3$ respectively. For each moment in time I earn a reward according to some reward function $g(x)$. That is, my reward for waiting until time $t$ can be written as $\int_0^tg(x)dx$. However, $g(x)$ experiences diminishing returns so the the marginal reward received from waiting one second at $t=0$ is greater than one second at say $t=27$. This 'game' ends when one of two things happens. Either both timers $X_1$ or $X_2$ must ring or timers $X_1$ or $X_3$ must ring. I'm trying to find the expected reward of playing this game.  Currently I can calculate the the CDF of the random variable modeling the time until the game ends, but I dont know how to use this information to when what I really need is reward associated with this time.  So far I have the additional random variables: $$ W_{12}=\max(X_1,X_2) \quad W_{13}=\max(X_1,X_3) \quad Z=\min(W_{12},W_{13})$$ Also let $F_i(x), i\in \{1,2,3\}$ denote the CDF of $X_i$ The CDF of $Z$, can be written as: $$F_Z(t) = F_1(t)F_2(t) + F_1(t)F_3(t) - F_1(t)F_2(t)F_3(t)$$  I know when a random variable takes on non-negative values, you can use a shortcut to calculate the expectation using the CDF. That is, $E[X] = \int_0^\infty F(X\geq x)dx$. Is there something similar I could use for a function of a random variable, or is it necessary to compute the pdf of $Z$ first to compute $\int_0^\infty g(t)f_z(t)dx$