Can. MacBook Pro run in closed-display mode without physically. closing the lid?
Can I turn off macOS Catalina's internal display without close the lid while using an external monitor?
I've heard you can start with pikachu in pokemon go instead of the 3 standard starters. How would one do this? Is this even possible? Should flagging a question for closure prevent close-voting? What is the value of lim$_{n\to \infty} a_n$ if $\lim_{n \to \infty}\left|a_n+ 3\left(\frac{n-2}{n}\right)^n \right|^{\frac{1}{n}}=\frac{3}{5}$? Let $\{a_n\}$ be a sequence of real numbers such that $$\lim_{n \to \infty}\left|a_n+ 3\left(\frac{n-2}{n}\right)^n \right|^{\frac{1}{n}}=\frac{3}{5}.$$  What is the value of $\lim_{n\to \infty} a_n$? I have recently been reading a lot on this site (@Aniko, @Dikran Marsupial, @Erik) and elsewhere about the problem of overfitting occuring with cross validation - (Smialowski et al 2010 Bioinformatics, Hastie, Elements of statistical learning).  The suggestion is that any supervised feature selection (using correlation with class labels) performed outside of the model performance estimation using cross validation (or other model estimating method such as bootstrapping) may result in overfitting.   This seems unintuitive to me - surely if you select a feature set and then evaluate your model using only the selected features using cross validation, then you are getting an unbiased estimate of generalized model performance on those features (this assumes the sample under study are representive of the populatation)?  With this procedure one cannot of course claim an optimal feature set but can one report the performance of the selected feature set on unseen data as valid?  I accept that selecting features based on the entire data set may resuts in some data leakage between test and train sets. But if the feature set is static after initial selection, and no other tuning is being done, surely it is valid to report the cross-validated performance metrics?   In my case I have 56 features and 259 cases and so #cases > #features. The features are derived from sensor data.  Apologies if my question seems derivative but this seems an important point to clarify.  Edit: On implementing feature selection within cross validation on the data set detailed above (thanks to the answers below), I can confirm that selecting features prior to cross-validation in this data set introduced a significant bias. This bias/overfitting was greatest when doing so for a 3-class formulation, compared to as 2-class formulation.  I think the fact that I used stepwise regression for feature selection increased this overfitting; for comparison purposes, on a different but related data set I compared a sequential forward feature selection routine performed prior to cross-validation against results I had previously obtained with feature selection within CV. The results between both methods did not differ dramatically. This may mean that stepwise regression is more prone to overfitting than sequential FS or may be a quirk of this data set. Implementing INotifyPropertyChanged - does a better way exist? Understanding slice notation I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it. The meaning of Bit-wise NOT in Python Expected Number of coin flips for 2 consecutive heads for first time. I was working on problems on expectation and found this one as a question from a well-known exam  Assume that you are flipping a fair coin, i.e. probability of heads or tails is equal. Then the expected number of coin flips required to obtain two consecutive heads for the first time is.  (A)4  (B)3  (C)6  (D)10  (E)5  I worked up like Let N be the number of tosses required untill 2 consecutive heads are obtained for the first time.  Let the probability of obtaining heads be p and tails be q and for a coin p=q=1-p=1-q.  For N=2, the probability will be $p^2$  For N=3, the probability will be $p^2.q$  For N=4, the probability will be $q^2.p^2$  For N=5, the probability will be $q^3.p^2$  and so on...  Now, $E[N]=2(p^2)+3(p^2.q)+4(q^2.p^2)+5(q^3.p^2)+......$  and this comes out to be $\frac{3}{2}$ but it matches with none of the options.  Please tell me where I am wrong and what should I do to reach the correct solution? $C^2 $embedded in holder space? I have a question on Holder space.Is the space $C^2(\mathbb{R}^n)$ embedded in $C^{1,\alpha}(\mathbb{R}^n)$? I think in the bounded domain case, this should be true. But what if in the case where the domain is not bounded? Thanks for any hint! Does the proof of Bolzano-Weierstrass theorem require axiom of choice? OS is openSUSE 12.1, PostgreSQL - 9.1, PostGIS - 2.0. Postgre/PostGIS are installed from Application:Geo repository.  After recent updates when I try to connect to my database I get the following error:      ERROR:  could not load library "/usr/lib/postgresql91/lib64/postgis-2.0.so":  /usr/lib/postgresql91/lib64/postgis-2.0.so: undefined symbol: pj_get_spheroid_defn   I searched the web for this error (, ) and seems that it may have something to do with ld.so.config (or ldconfig command). But I can't figure out what I have to do in my case. Uniform distribution on the surface of unit sphere A more specific question about a tricky redirect case How to retrieve all keys (or values) from a std::map and put them into a vector? This is one of the possible ways I come out:  struct RetrieveKey {     template &lt;typename T&gt;     typename T::first_type operator()(T keyValuePair) const     {         return keyValuePair.first;     } };  map&lt;int, int&gt; m; vector&lt;int&gt; keys;  // Retrieve all keys transform(m.begin(), m.end(), back_inserter(keys), RetrieveKey());  // Dump all keys copy(keys.begin(), keys.end(), ostream_iterator&lt;int&gt;(cout, "\n"));   Of course, we can also retrieve all values from the map by defining another functor RetrieveValues.  Is there any other way to achieve this easily? (I'm always wondering why std::map does not include a member function for us to do so.) Finding $\int \frac {dx}{\sqrt {x^2 + 16}}$ Bold italic vectors I am trying to display vectors as bold and italic. The command \mathbf sets the letters non-italic. I also googled a bit and stumbled upon \mathbf{\em y} or \mathbfit{y}, which all didn't work.  I hope someone can help me on this. I am trying to test the impact of a sale initiative on store revenue. I have created 10 matched pairs of stores and then randomly distributed one store in each pair into a test or control group.  I then ran the sale for 21 days within the test group (keeping control constant) and measured relative lift in revenue compared to baseline.  My questions  1.) Should I be using a paired t-test based on the previous store matching  2.) Should I be measuring across each day of the test such as:          Control Test 1/1/2017    4   3 1/2/2017    3   4 1/3/2017    1   3 1/4/2017    2   3 1/5/2017    2   4 1/6/2017    1   7   Or measuring across my paired markets such as:                 Test Control Market Pair 1   10  5 Market Pair 2   8   3 Market Pair 3   5   1 Writing test code for wrapper class What's the difference between using a 50mm f/1.8G and a 50mm f/1.8D with a Nikon D80? Recently, Nikon announced their , as revamp of the old 50mm f/1.8D. :     The main difference between this new   "nifty fifty" and the almost   decade-old ƒ1.8D is that it has an   autofocus motor inside. This means you   can use it with any current or recent   Nikon SLR. The older lens lacks this   motor and is instead driven by one in   the camera, which cheaper bodies don't   have.   I currently use a Nikon D80 (and I don't plan on changing that any time soon), and I've been considering getting such a lens. Is there any difference between the D and the G lenses when used on a D80? I believe that the D one works just as well, since D80's have internal autofocus motors - is that right?  Besides the autofocus motor aspect, is there any other big difference between them? Since the D is priced at around $120 and the G at $220, should I just get the D? I'm trying to understand the /etc/rsyslog.conf file, but I'm missing something. For example, this is a part of the file:  auth,authpriv.*         /var/log/auth.log *.*;auth,authpriv.none      -/var/log/syslog cron.*              /var/log/cron.log daemon.*            -/var/log/daemon.log kern.*              -/var/log/kern.log lpr.*               -/var/log/lpr.log mail.*              -/var/log/mail.log user.*              -/var/log/user.log   According to  page:     The facility is one of the following keywords: auth, authpriv, cron,   daemon, kern, lpr, mail, mark, news, security (same as auth), syslog,   user, uucp and local0 through local7.      The priority is one of the following keywords, in ascending order:   debug,info, notice, warning, warn (same as warning), err, error (same   as err) crit, alert, emerg, panic (same as emerg). The keywords error,   warn and panic are deprecated and should not be used anymore. The   priority defines the severity of the message.      An asterisk ("*") stands for all facilities or all priorities,   depending on where it is used (before or after the period). The   keyword none stands for no priority of the given facility.      You can specify multiple facilities with the same priority pattern in   one statement using the comma (",") operator. You may specify as much   facilities as you want. Remember that only the facility part from such   a statement is taken, a priority part would be skipped.      Multiple selectors may be specified for a single action using the   semicolon (";") separator. Remember that each selector in the   selector field is capable to overwrite the preceding ones. Using this   behavior you can exclude some priorities from the pattern.   So, this is pretty understandable but what about the file path on the right. It can be just a path, or path with | or - before it (or maybe even something else). What is the difference between the three?