Most bike lights seem to be the bar / seatpost mounted variety. Is it worth also having a headlamp for riding?  I go cycle touring, ride in the city and do mountain bike xc trail riding.  I've got a budget enough to buy something decent.
I am just curious, I use handlebar mounted lights, and since I have multiple bikes to switch, it's a lot of trouble changing the light from one to another. So, I am thinking of switching to helmet mounted lights.  Give me your point of view. Why or why not? Which is better suitable for which riding type?
Am I correct to say the difference between a signed and unsigned integer is:  Unsigned can hold a larger positive value and no negative value. Unsigned uses the leading bit as a part of the value, while the signed version uses the left-most-bit to identify if the number is positive or negative. Signed integers can hold both positive and negative numbers.  Any other differences? At college we use ArcGIS Desktop 10, but that does not function on my Mac so I have QGIS there instead.  I want to do my exercises with QGIS, but in ArcGIS Desktop we use .lyr files with ArcMap and .lyrx files with ArcGIS Pro, and they are not supported by QGIS.  Does anyone know, how I can connect the *.lyr files to my *.shp files to use them on my Mac with QGIS? Why "hide" Luke from his father somewhere Anakin knows? In Episode II Anakin goes to the Lars homestead and meets his extended family. How would sending Luke there be "hidden" to Vader in any way? At least Leia had a random planet and family. Prevent VLC from starting a new instance every time a media file is opened Why do backslashes appear twice? System.FinalException: Record is read-only: Trigger.updateCompetitors: line 24 I am writing a trigger to get all the Opportunity competitors into a field on Opportunity, however, getting an error while testing it.  Error: updateCompetitors: execution of AfterUpdate caused by: System.FinalException: Record is read-only: Trigger.updateCompetitors: line 24  Can you please check the below code and suggest me what's wrong with this?  trigger updateCompetitors on Opportunity(after insert, after update){    List&lt;Opportunity&gt; OppIds = new List&lt;Opportunity&gt;();     for (Opportunity opp: trigger.new){         OppIds.add(opp);     }  List&lt;OpportunityCompetitor&gt; oppComps = new List&lt;OpportunityCompetitor&gt;();  oppComps= [select id, CompetitorName, Strengths, Weaknesses from OpportunityCompetitor where OpportunityId in: Trigger.newMap.keySet()];  List&lt;Opportunity&gt; OppstoUpdate = new List&lt;Opportunity&gt;();   for (Opportunity opp: OppIds){     String allcomps = null;      if( oppComps.size()&gt;0 ) {       for (integer i = 0; i &lt; oppComps.size(); i++){          allcomps = allcomps + oppComps[i].CompetitorName+',';       }     }    opp.OpportunityCompetitors__c = allcomps;    OppstoUpdate.add(opp);  }    update OppstoUpdate; } Proof that every finite dimensional normed vector space is complete Can you read my proof and tell me if it's correct? Thanks.  Let $V$ be a vector space over a complete topological field say $\mathbb R$ (or $\mathbb C$) with $\dim(V) = n$, base $e_i$ and norm $\|\cdot\|$. Let $v_k$ be a Cauchy sequence w.r.t. $\|\cdot\|$. Since any two norms on a finite dimensional space are equivalent, $\|\cdot\|$ is equivalent to the $l^1$-norm $\|\cdot\|_1$ which means that for some constant $C$, $\varepsilon &gt; 0$, $k,j$ large enough, $$ \varepsilon &gt; \|v_j - v_k\| \geq C \|v_j - v_k\|_1 e_i= C \sum_{i=1}^n |v_{ji} - v_{ki}| \geq |v_{ji} - v_{ki}|$$ for each $1 \leq i \leq n$. Hence $v_{ki}$ is a Cauchy sequence in $\mathbb R$ (or $\mathbb C$) for each $i$. $\mathbb R$ (or $\mathbb C$) is complete hence $v_i = \lim_{k \to \infty} v_{ki} $ is in $\mathbb R$ (or $\Bbb C$) for each $i$. Let $v = (v_1, \dots , v_n) = \sum_i v_i e_i$. Then $v$ is in $V$ and $\|v_k - v\| \to 0$:  Let $\varepsilon &gt; 0$. Then $$ \|v_k - v\| \leq C \|v_k - v\|_1 = C \sum_{i=1}^n |v_{ki} - v_i| \leq C^{'}n \varepsilon$$  for $k$ large enough. Let $A$ be a non-empty set and $n$ be the number of elements in $A$, i.e. $n:=|A|$.  I know that the number of elements of the power set of $A$ is $2^n$, i.e.  $|\mathcal{P}(A)|=2^n$.  I came across the fact that exactly half of the elements of $\mathcal{P}(A)$ contain an odd number of elements, and half of them an even number of elements.  Can someone prove this? Or hint at a proof? split file lines based on first field Modify footer used by elsarticle.cls What is happening here, when I use squared loss in logistic regression setting? I am trying to use squared loss to do binary classification on a toy data set. I am using mtcars data set, use mile per gallon and weight to predict transmission type. The plot below shows the two types of transmission type data in different colors, and decision boundary generated by different loss function. The squared loss is $\sum_i (y_i-p_i)^2$ where $y_i$ is the ground truth label (0 or 1) and $p_i$ is the predicted probability $p_i=\text{Logit}^{-1}(\beta^Tx_i)$. In other words, I am replace logistic loss with squared loss in classification setting, other parts are the same. For a toy example with mtcars data, in many cases, I got a model &quot;similar&quot; to logistic regression (see following figure, with random seed 0).  But in somethings (if we do set.seed(1)), squared loss seems not working well.  What is happening here? The optimization does not converge? Logistic loss is easier to optimize comparing to squared loss? Any help would be appreciated.  Code d=mtcars[,c(&quot;am&quot;,&quot;mpg&quot;,&quot;wt&quot;)] plot(d$mpg,d$wt,col=factor(d$am)) lg_fit=glm(am~.,d, family = binomial()) abline(-lg_fit$coefficients[1]/lg_fit$coefficients[3],        -lg_fit$coefficients[2]/lg_fit$coefficients[3]) grid()  # sq loss lossSqOnBinary&lt;-function(x,y,w){   p=plogis(x %*% w)   return(sum((y-p)^2)) }  # this random seed is important for reproducing the problem set.seed(0)  x0=runif(3) x=as.matrix(cbind(1,d[,2:3])) y=d$am opt=optim(x0, lossSqOnBinary, method=&quot;BFGS&quot;, x=x,y=y)  abline(-opt$par[1]/opt$par[3],        -opt$par[2]/opt$par[3], lty=2) legend(25,5,c(&quot;logisitc loss&quot;,&quot;squared loss&quot;), lty=c(1,2)) Biblatex - capital names in references, regular in cites I am trying to achieve a biblatex style that would do the following:  in the case of \parencite{} I would get ...like that (Smith 2010).   in the case of \textcite{} I would get Smith (2010) says that...  but in References I would get SMITH, J. Bookname.  How can I achieve this?  I use \usepackage[style=authoryear, firstinits=true]{biblatex}  I tried \renewcommand*{\mkbibnamelast}[1]{\MakeUppercase{#1}} but that makes the name uppercase even in the text, which is undesirable especially with \textcite{} $\sum a_{n}$ is convergent, $\sum a_{n}^2$ is divergent. Prove $\sum a_{n}$ is conditionally convergent. Suppose that the series $\sum_{n=1}^{\infty}a_{n}$ converges while $\sum_{n=1}^{\infty}a_{n}^2$ diverges. Prove that $\sum_{n=1}^{\infty}a_{n}$ converges conditionally. How to parse a query string into a NameValueCollection in .NET I would like to parse a string such as p1=6&amp;p2=7&amp;p3=8 into a NameValueCollection.  What is the most elegant way of doing this when you don't have access to the Page.Request object? What screenshot tools are available? I have noticed that many people use images in their Ask Ubuntu answers. What software are people using? There is this famous example about the order difference between gravitational force and EM force. All the gravitational force of Earth is just countered by the electromagnetic force between the electrons on the surface of my feet and the ground.  But also wave-function of electrons(fermions) do not overlap each other due to Pauli exclusion principle.  So which one is the true reason of me not flopping inside the earth forever? Is it only one of them(my guess is Pauli exclusion) or is it both? Continuous Fibonacci number F(n) How would one format an Excel sheet so numeric fields are set to numeric field types when importing to ArcGIS 10.2? I was wondering how to list all the hardware info in my computer?   Both terminal and GUI solutions please. Is there a single utility to monitor most hardware's working status? Just like some software in Windows?   Thanks and regards! Android Phone SD Card Problem My Samsung Galaxy Admire phone is saying that an SD card isn't found when the SD card is inside the phone: it shows "Please insert SD Card".  What could be wrong?