Average list of list of parameter values
GroupBy a list of associations with their keys
What is the relation between computational security and provable security? I read the book "Introduction modern cryptography". It gives the notion of computational security of private-key encryption at first which comes from perfect security and statistical security.     Let $(E,D)$ be an encryption scheme that uses $n$-bits keys to encrypt $l(n)$-length messages. $(E,D)$ is computationally secure if    $$E_{U_{n}}(x_{0}) \approx E_{U_{n}}(x_1)$$   And then it introduces the secure game (e.g. CPA, CCA)? I think it is a part of provable security.  "Unconditional security" (or "information-theoretic security" or "perfectly secrecy") and "computational security" are two opposite classes of security. But I do not think "computational security" and "provable security" are two independent classes of security. I know that computational security emphasizes the power of attacker is bounded (polynomial-time algorithm). And the provable emphasizes the mathematical assumptions or cryptography primitives. But it also related to the computational power. Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$. How do I copyright my website? My website has been in development for a long time and cost a lot of money.  How do I go about securing an enforceable copyright on my website design and what is the proper way to post a copyright notice on the site so others know the work is copyrighted? Geometric intuition behind gradient, divergence and curl Do the SO admins have any plans to release the underlying code for SO at all? I appreciate that the code may be part of their competitive advantage, but it strikes me that the underlying system would work for any topic, not just programming.  I am not advocating this, just curious really, but figured it might be under consideration as most of the value in SO is in the questions and answers, which have been released under a relatively open CC license. Is is possible to skip the confirmation step while adding a repository? When I add a repository by running  sudo add-apt-repository ppa:ubuntu-x-swat/x-updates   It outputs this dialog:  Updated versions of X.org drivers, libraries, etc. for Ubuntu.  This PPA is for stable upstream releases of X.org components.  If you're looking for something even more bleeding-edge, please see the xorg-edgers PPA.  While Ubuntu does not "officially/formally" support these packages, if you discover problems when installing these debs please feel free to report bugs to launchpad.  However, please make sure to clearly state that you are running packages from this PPA so we know the fixes need to come here.  If you are upgrading from one release to another with this PPA activated, please install the ppa-purge package and use it to downgrade everything in here beforehand. sudo ppa-purge ppa:ubuntu-x-swat/x-updates will do it.  [Directions for packaging drivers can be seen at https://wiki.ubuntu.com/X/DriverBuilding]  More info: https://launchpad.net/~ubuntu-x-swat/+archive/x-updates Press [ENTER] to continue or ctrl-c to cancel adding it   I want to skip the confirmation step  Press [ENTER] to continue or ctrl-c to cancel adding it   How can I automatically confirm the addition of a PPA? Should my flair be including sites with less than 200 reputation? Spaces in variable assignments in shell scripts Unwanted behaviour from dict.fromkeys I'm taking a course on waves and oscillations using Crawford from the Berkeley series (out of print excluding international copies), and would like to know if anyone has any suggestions for a better book. We cover:    coupled oscillators, forced oscillators,  Fourier analysis,  traveling waves,    and some other topics. Any help with the topic would be appreciated. I'm not entirely clear on how Counterspell works, when trying to counter higher-level spells: the CS description only talks about disrupting a creature you can see, within 60 feet, casting a spell.   However, when trying to counter a higher level spell:   Do I know what spell is being cast?  Do I at least know (somehow intuit, based on VSM components) the level of the spell? Or can I tell the spell/level of the spell by sensing a disturbance in The Weave? (I.e., if the spell is being cast using Subtle Spell, can I still tell what's going on?)   The point of the question is to determine how fruitful CS can be in combat--if I know what the other guy/gal is casting (or at least the level), I can decide whether I want to spend my L8 slot to counter his/her L8 slot. But if I have no idea, and I end up using a L8 slot to counter a L3 spell... seems a bit painful.  Hope this made sense! identifying which item is clicked in a multi level list using jquery How to stream a video with VLC in a LAN Can I disable pinch to show all open tabs in Safari? When we drop a ball, it bounces back to the spot where we dropped it, due to the reaction forces exerted on it by the ground. However, if a person falls down (say, if we push them), why don't they come back to their initial position where they started their fall?  According to Newton's 3rd law of motion, to every action there is always an equal but opposite reaction. If we take the example of ball then it comes back with the same force as it falls down. But in the case of a human body, this law seems not to be applicable. Why? 50 hertz sine wave in oscilloscope when I touch it I bought a new PicoScope USB oscilloscope and noticed that when I touch the tip of the probe with my hand I see a 50&nbsp;Hz signal of 2 volts on the screen. What is causing this? (Or rather, how is the mains 50 Hz sine wave getting through me to the scope?) I want to prove that $\lim_{(x,y)\to (0,0)} \frac{\sin(x+y)}{x+y} = 1$  Is it sufficient to say that if $u = x+y$ then as $(x,y) \rightarrow (0,0)$ then $u \rightarrow 0$ and then evaluate $\lim_{u\to 0} \frac{\sin u}{u}$ which is 1 by L'Hôpital's rule?  I feel that this is somehow "cheating" and I would really like to prove it in a more rigorous way, i.e., by using an $\epsilon$ - $\delta$ argument.  I have tried for a long time to use the one variable version and prove that if $0 \lt \sqrt{x^2 + y^2} \lt \delta$ then somehow $0 \lt |x+y| \lt \delta$ and it would follow from the one variable case that $| \frac{\sin(x+y)}{x+y} - 1| \lt \epsilon$. However, because $|x+y| = 0$ when $y = -x$ I am not getting anywhere with this.  Any input on this would be helpful :) How to add numbering to reference list but still use authoryear in natbib Is there an easy way to add numbers to the reference list generated by \usepackage[authoryear]{natbib} with whatever style file (using plainnat for ease)? Specifically, I use \cite and \citenum from natbib in order to have some references show up in the text as author-year and others just appear as numbers. Switching authoryear out for numbers in the natbib options generates a reference list with numbered references, but also causes the references in the text to all appear as numbers, which I don't want.  \documentclass[12pt]{article} % use larger type; default would be 10pt \usepackage[authoryear]{natbib} \begin{document}  \cite{A} said this, but other research \citenum{B,C} says otherwise.  \bibliographystyle{plainnat} \bibliography{MalariaBib,MST} \end{document} Consider the blow-up of the plane in one point. Let $E$ the exceptional divisor. We know that $(E,E)=-1$. What is the geometrical reason for which the auto-intersection of $E$ is $-1$? In general, what does it mean, geometrically, that a divisor has a negative self-intersection or that the "right" number of divisors gives rise to a negative intersection?  Thanks. Improve file-info visibility in Finder's preview pane I find the file information in the preview pane in column view is far more useful than the thumbnail.  I wish I did not have to continually resize the Finder window or scroll the preview pane to see the info I'm looking for.  As you can see below, the useful info is hidden in default  size  of Finder's new window under the preview options like rotate etc.        Is there a way to do any of these to achieve the said goal (listed in order of decreasing likelihood!):   reduce the size of the preview "thumbnail" covered by black here,  reduce the amount of whitespace(grey here) around the preview "thumbnail" (only significant for landscape thumbnails), remove the preview "thumbnail" altogether,  reorder the content of the preview column(bring file info up and send thumbnail down)?    includes the options:   resizing the Finder in every new window (which is labor intensive). Using View menu> Show Preview Options to turn off Quick Actions (which must be done for each file-type, and only reveals a small amount of file info).