EXCEL VBA: regEx.Pattern colorize font color between first | and second |
What special characters must be escaped in regular expressions?
Which loss function is correct for logistic regression? I read about two versions of the loss function for logistic regression, which of them is correct and why?  From  (in Chinese), with $\beta = (w, b)\text{ and }\beta^Tx=w^Tx +b$: $$l(\beta) = \sum\limits_{i=1}^{m}\Big(-y_i\beta^Tx_i+\ln(1+e^{\beta^Tx_i})\Big)  \tag 1$$  From my college course, with $z_i = y_if(x_i)=y_i(w^Tx_i + b)$: $$L(z_i)=\log(1+e^{-z_i}) \tag 2$$    I know that the first one is an accumulation of all samples and the second one is for a single sample, but I am more curious about the difference in the form of two loss functions. Somehow I have a feeling that they are equivalent. Image of Jacobson Radical is the Jacobson Radical I'm stuck on the following problem:      Let $R$ be a commutative ring with $1$, and suppose $R$ is semilocal with maximal ideals $\mathfrak m_1, ... , \mathfrak m_s$.  Let $\mathfrak a$ be an ideal of $R$. The problem is to show that under the usual surjection $\pi:R \rightarrow R/\mathfrak a$, the Jacobson radical of $R$ is sent to the Jacobson radical of $R/\mathfrak a$.   My attempt: suppose that $\mathfrak m_1, ... , \mathfrak m_t$ contain $\mathfrak a$, but $\mathfrak m_{t+1}, ... , \mathfrak m_s$ do not.  Then $Jac(R/\mathfrak a) = (\mathfrak m_1/ \mathfrak a) \cap \cdots \cap (\mathfrak m_t/ \mathfrak a)$.  Obviously $\pi Jac(R) \subseteq Jac(R/ \mathfrak a)$, and the converse inclusion is equivalent to the following claim: if $x \in \mathfrak m_1 \cap \cdots \cap \mathfrak m_t$, then there exists a $y \in \mathfrak m_1 \cap \cdots \cap \mathfrak m_s$ such that $x - y \in \mathfrak a$.    This should be some application of the Chinese remainder theorem, but I'm not seeing it.  All I have to go on is that there exist $m_i \in \mathfrak m_i$ ($t+1 \leq i \leq s$) with $m_i \not\in I$.  I also haven't found out a way to use the fact that $\mathfrak m_1 ,... , \mathfrak m_s$ are all the maximal ideals of $R$.  I was also thinking about looking at some explicit maps.  If we let $\Gamma$ be the composition $$\frac{(R/\mathfrak a)}{Jac(R/ \mathfrak a)} \xrightarrow{\cong} \frac{(R/\mathfrak a)}{(\mathfrak m_1/\mathfrak a)} \oplus \cdots \oplus \frac{(R/\mathfrak a)}{(\mathfrak m_t/\mathfrak a)} \xrightarrow{\cong} R/\mathfrak m_1 \oplus \cdots \oplus R/\mathfrak m_t$$ then we have a commutative diagram $$\begin{matrix} R/Jac(R) &amp;  \rightarrow &amp; \frac{(R/\mathfrak a)}{Jac(R/\mathfrak a)} \\ \downarrow &amp; &amp; \downarrow \Gamma \\ R/\mathfrak m_1 \oplus \cdots R/\mathfrak m_s &amp; \rightarrow &amp; R/\mathfrak m_1 \oplus \cdots \oplus R/\mathfrak m_t \end{matrix}$$ where the vertical arrows are isomorphisms, and the horizontal arrows are surjections. What is the difference between DPI (dots per inch) and PPI (pixels per inch)? There are lots of other questions on Graphic Design which partly cover this, e.g. .  However, I have become frustrated at the number of questions and answers which confuse the two terms. I think understanding the difference is important.  So here's a place to answer this question well and clear up the confusion! I have an iPhone 5 running iOS 9.1 and a Macbook Pro running Yosemite.  Both devices are set up to sync photos to and from iCloud.  When I take a photo on the iPhone (for further processing on the Macbook), it takes an inordinate amount of time until the photo shows up in the Macbook's photos library - sometimes up to 10-20 minutes. Sometimes it seems to work faster if I quit the Photos app on both devices, and start it again.  I often end up sending myself photos through E-Mail because it's quicker. That seems ridiculous!  Is there a way to force a sync on the iPhone, or to speed up the process some other way? What algorithm(s) are used by MoleculeModify's GenerateConformers? I was practicing with modeling a leaf using a image reference. Everything went fine and I finished modeling my leaf, but I wanted to make it more realistic (I'll add textures later), I saw lots of people using the Subdivision Surface modifier but it doesn't work for me.  My model:   My model when I add the Subdivision Surface modifier English idiom for 'bad consequences stemming from too much ambition' I'm looking for an idiom that is equivalent to the Portuguese:  Quem tudo quer, tudo perde. Who wants everything, loses everything.  It basically points out that being too ambitious will have bad consequences: not only does one not get what one's striving for, but one also ends up losing what one already had (and probably took for granted). This idiom should be usable in everyday speech. I installed Ubuntu (twice actually) onto the same drive. I wanted to 'try again' since one of them didn't install correctly and the other installed differently, but it worked.   I was getting frustrated with the GRUB menu because it was really sloppy (There were two Windows options - one with the Windows bootloader to go into Ubuntu, and two different versions of Ubuntu from the first install for some reason and memtest, etc.).  In my attempts at getting rid Ubuntu to do a fresh installation, I went ahead and deleted the partitions that weren't swap or main via Windows 7. As I said, I am a noob.  Now, even though I though I completely got rid of Ubuntu, including the GRUB menu, when I boot my PC I am brought directly to GRUB Rescue. And from what I've found from other forums, GRUB rescue isn't even completely functional for me (it doesn't recognize any commands that it should support besides ls. It also returns unknown filesystem for any partition I try to view or boot.)  Is there any way that I can boot straight into Windows? I fear I may have gone about deleting those partitions in the wrong way. If so, what are my options? I've been working with ArcGis for a while now and was wondering if there was a way to change positions of parameters inside the toolbox for the user. The only time I have seen this done in arc toolbox is with the Raster clip tool with the Rectangle parameter where the 4 parameters are aligned in a circle in the toolbox.     I don't know if what I want is possible since I haven't seen anyone else do it. What happens if no one survives the Hunger Games? It is possible that the remaining last two tributes might get killed at the same time, for example, by a land mine explosion, and in that case the games will end with no victor standing.  Is there a reference in the original books as to what happens if nobody emerges victor in the Hunger Games? That car is way better than any car any of us have/has ever driven.      None of us know/knows which direction Ron's house is (in).    I have two questions here.   In both the cases, are we to use the singular verb, or the plural? In the end of the second sentence, is using the preposition where it's been used, necessary? Would it be okay if it had no prepositions in it? I have multiple Amazon EC2 accounts and want to quickly be able to switch variables, such as $EC2_HOME, using a script.  I have have a shell script set up like this:  #!/bin/sh export EC2_HOME=/home/me/.ec2 echo $EC2_HOME   When I run the script I know that EC2_HOME is set, but I thought that using export would make the variable stick around after the script completed. It does not, as running echo $EC_HOME does not show anything.  I know this must be very rudimentary Linux scripting knowledge, but I don't know it. I tried looking for related questions without luck - so my apologies if this is a duplicate. Say I have two Chrome windows open like this:   It seems that the most recently used window always appears on top. In other words, the &quot;Apply Digital Signatures&quot; was the window I had open last. If I were to switch to the window showing the new tab, then the order in which the windows are displayed in the task bar suddenly changes. Is there a way to keep them from shuffling around? I'd like to be able to order them however I want, like tabs in a web browser. (I'd also like to put them across different workspaces.) How do I upgrade from 12.10 to 13.04? SCP through multiple hosts describes how to SSH into a machine that can only be accessed through one or more hosts (that can also be SSH'd into).  Is there an equivalent way of using scp? That is, copy a file to my local machine from the far machine (assuming I have password or key access to all machines along the way)? The Wifi is working fine but no internet connection in Windows 8 When does HashSet 'add' method calls equals? In Revenge of the Sith, we learn that Anakin's final seduction to the Dark Side occurs because of his obsession with power and especially his obsession with the power to cheat death to save Padme.       PALPATINE: Only through me can you achieve a power greater than any Jedi. Learn to know the dark side of the Force, Anakin, and you will be able to save your wife from certain death.   (Note, save your wife from certain death, not resurrect)  This obsession is motivated by Anakin's repeated visions of Padme's death during childbirth.   Also, we have     PALPATINE: To cheat death is a power only one has achieved, but if we work together, I know we can discover the secret.   Yet when Padme confronts Anakin on Mustafar, and then Luke and Leia are born, they are full term or close to it.   So how did Anakin think this would help?   Did he expect to figure out this power with Sidious in a matter of days or weeks? There is a common story that airline ticket prices rise significantly if you buy them less than two weeks before departure.  And that any time before that will yield standard prices.  Is that advice valid for flying during holiday seasons?  As an example: if I want to fly coast to coast USA on December 7th, must I buy my ticket ASAP, or would I get a similar price buying on November 21st? Using Either a Comma or a Semicolon My teacher was explaining how sometimes a comma isn't enough to make a sentence correct, and that sometimes you have to use a semicolon. I am having trouble figuring out when you should use which.   Can someone please explain?