The meaning of the $\alpha$ helix and $\beta$ sheets in proteins
Is there a difference between "Alpha Helix" and "Alpha subunit"?
Prove that any continuous map on $\mathbb{R}$ which is the identity on $\mathbb{Q}$ is the identity map, hence Aut$(\mathbb{R}/\mathbb{Q})= 1.$  proof: Suppose $\sigma$ is continuous on $\mathbb{R}$ which is an identity on $\mathbb{Q}$. let $a \in R $. Then since $\sigma$ is continuous, then by definition there is $\delta_1 &gt; 0$ such that $|a - b| &lt; \delta_1$.  And assume $|\sigma(a) -\sigma(b)| &lt; \epsilon/2$ .  Let $\delta $= min{$\epsilon/2, \delta_1$}.  And now let $b \in \mathbb{Q}$ such that $|a - b| &lt; \epsilon$. Then  $|\sigma(a) - a| = |\sigma(a)  - b + b - a| \leq |\sigma(a) - \sigma(b) | + |b - a| &lt; \epsilon/2 + |b-a|$.  Can someone please help me? I am not sure . Can I say $|b - a| &lt; \epsilon/2 $? How do I detect orientation on app launch for splash screen animation on iPad! Algebraic dual of $\mathbb{R}^{\mathbb{N}}$ As in the title, my question is: What is the algebraic dual space of $\mathbb{R}^{\mathbb{N}}$ - the space of all $\mathbb{R}$-valued sequences. I think that it should be the direct sum $\bigoplus_{\mathbb{N}} \mathbb{R}$, via the natural duality, but I cannot proof it. How do I download a YouTube video? A saying for something that's good but also has a downside I'm trying to transition from a list of pros to a list of cons, and would like to have some sort of transition quote. Something in the form of,  "But, alas, (((something something quote quote)))"  Everything that has a beginning has an end, something along the lines of that. Can the Artificer Artillerist's tiny-sized Eldritch Cannon that is not held in hand still ride or be carried elsewhere on the body? If I run a randomForest model, I can then make predictions based on the model.  Is there a way to get a prediction interval of each of the predictions such that I know how "sure" the model is of its answer.  If this is possible is it simply based on the variability of the dependent variable for the whole model or will it have wider and narrower intervals depending on the particular decision tree that was followed for a particular prediction? What *is* an Artificial Neural Network? As we delve into  literature, we get to identify other methods with neuromorphic topologies ("Neural-Network"-like architectures). And I'm not talking about the . Examples are given below.  Then, it makes me wonder: what is the definition of an artificial Neural Network? Its topology appears to cover everything.    Examples:  One of the first identifications we make is between PCA and a linear Autoencoder with tied-weights in the encoder and decoder and thresholded activations in the bottleneck layer.  Also, a common identification is done between linear models (logistic regression in special) and a Neural Network with no hidden layer and a single output layer. This identification opens several doors.  . ? ANN. Gaussian Process? ANN (with single hidden layer with infinite hidden units).  And so, just as easily, we can incorporate arbitrary regularized versions with specialized loss functions of these algorithms into a Neural Network framework.  But the more we dig, the more similarities appear. I just stumbled into , which makes the identification of a specific ANN architecture with decision trees, allowing these to be learned by ANN methods (such as Gradient Descent backpropagation). From this we can construct Random Forests and Gradient Boosted Decision Trees from solely Neural Network topologies.  If everything can be expressed as an Artificial Neural Network, what defines an Artificial Neural Network? Can anyone make me understand in simple language why the second condition for being an Euclidean domain is superfluous ?  Why $v(a)  \leq v(ab)$ is not needed?  How we can deduce from the first one? What is the meaning of “runneth” in ? When you have a card like  which reads "Exile Target Creature with power 3 or less", as I understand it, it becomes untargetable if the opponent's creature power increases thanks to a pump spell like .  But what if the Disregard is already on the stack and targeting; and they respond with Brute Strength? I'm pretty sure (and my opponent with Brute Strength was certain) that it won't exile the creature, but I don't know which rule states this, and there's no gatherer ruling on the spell. Let $m,n$ be positive integers bigger than $1$. Show that $\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$.    I have no idea on how to start. Anyone hints are much helpful. Display error message if same record exist with combination of some fields? Static posts page with home.php Upper bound for $\sqrt[n]{n!}$ Linear functional on a Banach space is discontinuous then its nullspace is dense. My DOM looks like this:  &lt;div id="d1"&gt;    &lt;div class="c1"&gt;             &lt;a href="#"&gt;&lt;img src="img1_on.gif"&gt;&lt;/a&gt;             &lt;a href="#"&gt;&lt;img src="img2_on.gif"&gt;&lt;/a&gt;    &lt;/div&gt; &lt;/div&gt;   When someone clicks on an image, I want the image src to change to &lt;img src="imgx_off.gif"&gt; where x represents the image number 1 or 2.  Is this possible or do I have to use CSS to change the images? What's the max height of blocks for a redstone contraption to still work even I'm in the surface below?  Like if I build a pillar to the max height of blocks and build a redstone contraption there, is it still going to work even I'm on the surface below? Why is it differential equations exist on an interval instead of a domain? I understand a domain is the set of input elements a function is defined for (and can have breaks in it e.g. union of 2 sets) and a interval is a continuous range of real numbers. Why do we speak of the solution to a differential equation over an interval instead of an domain? If the solution to an ODE is just a function, and we normally speak of functions as having a domain, then why wouldn't we use domain? How did humans and vulcans communicate in Star Trek: First Contact?