Is there a way to exclude the row_number column from the final result?
How to exclude a column from SELECT query?
Incremental (delta) backup of a encrypted data I have several files that I need to keep encrypted on my home hard disk.  I currently use a TrueCrypt file container, currently around 100MB in size. I need to backup this file daily, and I'm looking for an incremental backup solution.  I read that on encrypted volumes even a small change in a file would change the whole volume and prevent the use of an efficient incremental backup solution. Any ideas how to backup in this case in an efficient way which would allow incremental solution?  I currently use TrueCrypt as my backup solution and CrashPlan as my backup utility, but I'm willing to experiment with alternatives. Proof for maximal ideals in $\mathbb{Z}[x]$ I have been trying to prove the following theorem:      Every maximal ideal in $\mathbb{Z}[x]$ has the form $(p, f(x))$ where $p$ is prime integer and $f$ is primitive integer polynomial that is irreducible modulo $p$.    Idea: I tried to establish a homomorphism $\phi: \mathbb{Z}[x] \rightarrow \mathbb{F}$. Since $\mathbb{F}$ is a field it has characteristic $p$ and so integer prime p are mapped to 0 in $\mathbb{F}$. Hence $p\in \ker \phi$. Next we consider $\phi': \mathbb{Z}[x] \rightarrow \mathbb{Z_p}[x]$ and pick an arbitrary maximal ideal $M\in \mathbb{Z}[x]$. So, $\phi'(M)$ is maximal as long as $p \in M$ by correspondence. But now I am stuck at this stage and do not know how to proceed. I guess we might have to use primitivity given in problem but dont know how. Convert a Pair of Integers to a Integer, Optimally? Scenario 1: A grimlock hits Alice with a Spiked Bone Club, dealing 5 bludgeoning damage, plus 2 piercing damage. Alice's HP was 12.   Using the optional Massive Damage rules on page 273 of the DMG, does this count as more than half the HP from a single source, or less than half, but twice?  Scenario 2: Assume the same grimlock hits Bob with the same attack, this time rolling 6 bludgeoning damage, plus 3 piercing damage. Bob's Max HP is 8, and he had 1 HP remaining before he was hit.  Using the Instant Death rules on page 197 of the PHB, does the character die, or are the two damage types tracked separately? Does the character have to make a death saving throw for the second part of the damage? Calculating well densities in selected counties using ArcPy? How to convert image of map into vector format? I was showing a GM friend of mine a build I was making that uses the Two-Handed Fighter Archetype and we are both unsure of how it interacts with the damage bonus you get from two-handed weapons (which is 1-1/2 times your STR.) It reads:     Overhand Chop (Ex): At 3rd level, when a two-handed fighter makes a single attack (with the attack action or a charge) with a two-handed weapon, he adds double his Strength bonus on damage rolls. This ability replaces armor training 1.   So, does Overhand Chop turn the 1-1/2 times multiplier from two-handed weapons into a 2 times multiplier, or do the two add up? Or, do they interact in some other way?   This assumes a Medium sized character with 20 STR and a greatsword with 3 levels. In statistical learning, implicitly or explicitly, one always assumes that the training set $\mathcal{D} = \{ \bf {X}, \bf{y} \}$ is composed of $N$ input/response tuples $({\bf{X}}_i,y_i)$ that are independently drawn from the same joint distribution $\mathbb{P}({\bf{X}},y)$ with  $$ p({\bf{X}},y) = p( y \vert {\bf{X}}) p({\bf{X}}) $$  and $p( y \vert {\bf{X}})$ the relationship we are trying to capture through a particular learning algorithm. Mathematically, this i.i.d. assumption writes:  \begin{gather} ({\bf{X}}_i,y_i) \sim \mathbb{P}({\bf{X}},y), \forall i=1,...,N \\ ({\bf{X}}_i,y_i) \text{ independent of } ({\bf{X}}_j,y_j), \forall i \ne j \in \{1,...,N\} \end{gather}  I think we can all agree that this assumption is rarely satisfied in practice, see this related  and the wise comments of @Glen_b and @Luca.  My question is therefore:      Where exactly does the i.i.d. assumption becomes critical in practice?    [Context]   I'm asking this because I can think of many situations where such a stringent assumption is not needed to train a certain model (e.g. linear regression methods), or at least one can work around the i.i.d. assumption and obtain robust results. Actually the results will usually stay the same, it is rather the inferences that one can draw that will change (e.g. heteroskedasticity and autocorrelation consistent HAC estimators in linear regression: the idea is to re-use the good old OLS regression weights but to adapt the finite-sample behaviour of the OLS estimator to account for the violation of the Gauss-Markov assumptions).   My guess is therefore that the i.i.d. assumption is required not to be able to train a particular learning algorithm, but rather to guarantee that techniques such as cross-validation can indeed be used to infer a reliable measure of the model's capability of generalising well, which is the only thing we are interested in at the end of the day in statistical learning because it shows that we can indeed learn from the data. Intuitively, I can indeed understand that using cross-validation on dependent data could be optimistically biased (as illustrated/explained in ).   For me i.i.d. has thus nothing to do with training a particular model but everything to do with that model's generalisability. This seems to agree with a paper I found by Huan Xu et al, see "Robustness and Generalizability for Markovian Samples" .   Would you agree with that?  [Example]   If this can help the discussion, consider the problem of using the LASSO algorithm to perform a smart selection amongst $P$ features given $N$ training samples $({\bf{X}}_i,y_i)$ with $\forall i=1,...,N$ $$ {\bf{X}}_i=[X_{i1},...,X_{iP}] $$ We can further assume that:   The inputs ${\bf{X}}_i$ are dependent hence leading to a violation of the i.i.d. assumption (e.g. for each feature $j=1,..,P$ we observe a $N$ point time series, hence introducing temporal auto-correlation) The conditional responses $y_i \vert {\bf{X}}_i$ are independent. We have $P \gg N$.    In what way(s) does the violation of the i.i.d. assumption can pose problem in that case assuming we plan to determine the LASSO penalisation coefficient $\lambda$ using a cross-validation approach (on the full data set) + use a nested cross-validation to get a feel for the generalisation error of this learning strategy (we can leave the discussion concerning the inherent pros/cons of the LASSO aside, except if it is useful). "Eat" is to "feed" as "drink" is to what? I can say "I feed someone". Am I forced to say "I give someone a drink", or is there a single word for this (as in "I [verb] someone")?  Unfortunately my thesaurus can't really help me. How do I do a case-insensitive string comparison? Cycles: How do I exclude the Environment Texture from reflections? In a Cycles scene I have an equirectangular image serving as an Environment Texture background (set in the World settings).  I have a glossy object being partially lit by the Environment Texture, as well as getting reflections from it.  Is there a way I can exclude the Environment Texture from affecting the glossy object completely? I want the image as background wallpaper only. The glossy object should be affected by other objects and lights within the scene: everything except the Environment Texture. What are Vertex and Pixel shaders? ASP.NET MVC controller actions that return JSON or partial html I am trying to create controller actions which will return either JSON or partial html depending upon a parameter. What is the best way to get the result returned to an MVC page asynchronously? Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. Prove that $G $ is an abelian group. Is there an easy way of getting the charset and collation of the DB tables in WordPress without resorting to SQL queries? Unexpected voltage with switch turned off $f(x)=x/1$ is not injective? When adding NOT NULL columns with a DEFAULT value - does PostgreSQL optimize this operation?  In case the table has n rows, a not-optimized alter-table-add-column would yield n writes of the default value - which could be very painful, obviously. With the optimization the DB would instantaneously create the new column, store just one copy of the default value which would be returned when no non-default value is found for that column in a suitable index data structure.  For example  such an . How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? Good review audit has "possible spam" warning? I was looking through someone's edit history and I was looking at :    Why does it give this notice, while at the same time saying that it's a high-quality post?