I have been doing some reading of  which is considered to be an indication of animal's ability to learn...  Before this I considered insects to be machine like - devoid of any sort of 'thinking' just doing things that evolution 'made' them to do to survive...  However I have found that  and even  could be conditionally trained...   Which made me wonder What would be the least complex species that respond to classical conditioning?  I have also read this question about  and I don't think that this 'cuts it'... this is nothing more than chemical response... however classical conditioning is different and in my opinion certainly does indicate ability to learn...
What is the simplest organism that was observed to learn: change its behavior permanently in response to some event/stimuli in a way that this change persists even if the event does not happen again?
Tangent lines to ellipse from external point Can I store my pixels somewhere so I don't lose them when I die? I die all the time. My pixel balance hovers around zero as a result. I'm trying to save up for armor but my nonstop deaths are making that difficult.  Is there anywhere I can store my pixels so that when I die, I won't lose a bunch of them? Let $q \in \mathbb C$, $|q|=1$ and $q^n \neq 1, \forall n \in \mathbb N$. Show that $\{q^n:  n \in \mathbb N\}$ is dense in $S^1$.  My attempt: As $(q^n)$ is limited, there is subsequence $(q^{n_j})$ convergent. So given $\epsilon &gt; 0, \exists j_0 \in \mathbb N, \quad |q^{n_j} - q^{n_k}| &lt; \epsilon, \quad \forall j,k \geq j_0$. Supose that $n_j &gt; n_k$, then  $|q^{n_j} - q^{n_k}| = |q^{n_k}||q^{n_j - n_k} - 1| = |q^{n_j - n_k} - 1| &lt; \epsilon, \quad \forall j, k \geq j_0$. So, there is a subsequence of $(q^n)$ that converges to $1$.  Using this fact, how can I ensure that for all $w \in S^1$ there is a subsequence of $(q^n)$ that converges to  $w$? Helpful flags not getting updated after getting 'close question' privilege "Have been having classes" or "have had classes for three months"? Which sentence is correct:  "I have been having classes for three months."  or  "I have had classes for three months." Homotopy functions I'm new here. Can anyone give me a hint in this problem? Please.  Let $X$ be a topological space. If $f,g$ are continuous function of $f,g\colon X\to S^n$  which $f(x)\neq -g(x)$ for all $x$ in $X$, show $f$ and $g$ are homotopics. I try to show a homotopy using $$q(x) = \frac{f(x)+g(x)}{\|f(x)+g(x)\|}$$ it's well defined, but i'm stuck. Why is the complex number $z=a+bi$ equivalent to the matrix form $\left(\begin{smallmatrix}a &-b\\b&a\end{smallmatrix}\right)$ Possible Duplicate:          On Wikipedia, it says that:     Matrix representation of complex numbers   Complex numbers $z=a+ib$ can also be represented by $2\times2$ matrices that have the following form: $$\pmatrix{a&amp;-b\\b&amp;a}$$   I don't understand why they can be represented by these matrices or where these matrices come from. Short-lived sci-fi series with a former astronaut turned superhero (or maybe a police officer?) using his spacesuit for his "powers" Plot Details/Summary I only watched an episode or two of this one, so I can't recall a whole lot about it.  The protagonist is a former astronaut of some sort, who makes it his mission to clean up the crime in his city.  He might have been a police officer in his &quot;new life&quot; or he might have decided to become a sort of quasi-superhero.  In either case, I distinctly recall his space suit being the gimmick that makes him an effective crime fighter in the show.  I seem to recall the protagonist being a young, dark-haired man, and I think he had a friendship or an alliance with a young woman (maybe a fellow cop, or someone from the space program?).  I don't think there were alien beings in the show.   The criminal threats were all quite terrestrial, IIRC. Timeframe and other Publication Details This was a syndicated tv show I saw on American television, probably around the late 90s to early 2000's.  I believe the show was filmed in Canada, though I'm not certain.  I don't think it lasted very long - it was pretty dreadful.  I can say for certain the show is not Space Cop or Gerry Anderson's Space Precinct. Is it possible to run Android apps on Ubuntu? And I don't mean inside an emulator, but natively, as you would with any other application installed using the Ubuntu Software Center. Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$ Let $f\in C^2(\mathbb{R},\mathbb{R})$.   Assume there exist  $(a,b) \in \mathbb{R}^2$ such that  $\forall x \in \mathbb{R}, (f(x))^{2} \leqslant a$ and $(f'(x))^{2} + (f''(x))^{2} \leqslant b$.   Prove that: $$(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$$ for all $x \in \mathbb{R}$.   I tried to use taylor lagrange with the integral form of the remainder but I did not succeed.  Ì really don't know how to tackle  the problem.   Any suggestion, Hint (or Answer) will be very helpful,  Thank you in advance, I have the following code in my theme's archive.php:  &lt;?php the_archive_title( '&lt;h1 class="page-title"&gt;', '&lt;/h1&gt;' ); ?&gt;   This gives me titles like "Category: Russia", "Tag: America", "Author: John".  I would like to remove the "Category:", "Tag:" and "Author:" part and just display the category, tag and author names.  Does anyone know how to accomplish this?  Thank you. Let $R$ be a commutative ring with identity and $I$ and $J$ be ideals in $R$.     Show that $R/I\otimes_R R/J\cong R/(I+J)$ as $R$-modules.   This is what I tried.  Define a map $f:R/I\times R/J\to R/(I+J)$ as $f(\bar r, \bar s)=rs+(I+J)$. This is a well-defined bilinear map.  By the universal property of tensor products, we get an $R$-linear map $F:R/I\otimes_R R/J\to R/(I+J)$ which sends $\bar r\otimes \bar s$ to $rs+(I+J)$.  This map is surjective.  So all we need to show is that the kernel of $F$ is $0$.  But I am unable to do this. On a series involving harmonic numbers Finding $$\sum^{\infty}_{n=1}\bigg[\bigg(\frac{(-1)^{n+1}}{n+1}\bigg)\bigg(\sum^{n}_{r=1}\frac{1}{r}\bigg)\bigg]$$   Try: Let $\displaystyle H_{n} =\sum^{n}_{r=1}\frac{1}{r},$ then series $\displaystyle \sum^{\infty}_{n=1}\frac{(-1)^{n+1}}{n+1}\cdot H_{n}=\frac{H_{1}}{2}-\frac{H_{2}}{3}+\frac{H_{3}}{4}\cdots\cdots$  could some help me to solve it, thanks i have a simple sort of a database file which consists only of entries in the following format     variable=value   i want to create a simple vim syntax highlighting for it and set it for specific file extension  for instance, variable part could be light blue, and value part light red  i googled it and came across things such as $vimruntime\syntax\, syntax set=, syntax match, and hi keywords, but couldn't set it up myself eventually  so i want a very simple vim code snippet that would realize it by matching the left and right hand sides and coloring them separately How can we prove that any bijection on any set is  a composition of 2 involutions ?  Since involutions are bijections mapping elements of a set to elements of the same set, I find it weird that this applies to any bijection.  Thanks for your help ! Identifying which part of a large document is being compiled How to highlight paragraph (linebreak preserving) as well as itemize, tabular etc.? I want to highlight changes which are introduced by myself in the pdf document. So far the soul package is very neat but it does throw errors when I want to highlight not only paragraphs but also some itemize environments, and I don't want to highlight the items separately. Also the \cite{...} command is not supported by \hl. I recently posted a slightly different question:   BTW: What I liked most over other approaches like pdfcomments etc. is that the \hl command from soul has a very exact and clear output, no icons, no clicking etc. involved. Together with todonotes it's very good and almost all I need. I watched a video on  and read a few  which say that human beings see 3D because we have two eyes. But does that mean when I close one of my eyes, I should see 2D? It doesn't happen so. Why am i still able to be understand depth? Would a person with one eye not be able to perceive depths? I want to resize the Unity launcher. Is that possible? How to loop over the lines of a file?