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How to minimize residual sum of squares of an exponential fit? I have the following data and would like to fit a negative exponential growth model to it:  Days &lt;- c( 1,5,12,16,22,27,36,43) Emissions &lt;- c( 936.76, 1458.68, 1787.23, 1840.04, 1928.97, 1963.63, 1965.37, 1985.71) plot(Days, Emissions) fit &lt;- nls(Emissions ~ a* (1-exp(-b*Days)), start = list(a = 2000, b = 0.55)) curve((y = 1882 * (1 - exp(-0.5108*x))), from = 0, to =45, add = T, col = "green", lwd = 4)   The code is working and a fitting line is plotted. However, the fit is visually not ideal, and the residual sum of squares seems to be quite huge (147073).   How can we improve our fit? Does the data allow a better fit at all?  We could not find a solution to this challenge on the net. Any direct help or linkage to other websites/posts is greatly appreciated. Quick way to remove solidify thickness I have made the mesh and added solidify modifier and applied. But later i thought to increase the thickness. So now i want to remove thickness so that i can added the solidify modifier again. I want to know is there any quick remove thicknes. When i select the edge then ctrl+ the selection goes downward not to single face. So i want to know a quick way to decrease thickness. Any suggestion or help. Ignore folders/files when Directory.GetFiles() is denied access I am trying to display a list of all files found in the selected directory (and optionally any subdirectories). The problem I am having is that when the GetFiles() method comes across a folder that it cannot access, it throws an exception and the process stops.  How do I ignore this exception (and ignore the protected folder/file) and continue adding accessible files to the list?  try {     if (cbSubFolders.Checked == false)     {         string[] files = Directory.GetFiles(folderBrowserDialog1.SelectedPath);         foreach (string fileName in files)             ProcessFile(fileName);     }     else     {         string[] files = Directory.GetFiles(folderBrowserDialog1.SelectedPath, "*.*", SearchOption.AllDirectories);         foreach (string fileName in files)             ProcessFile(fileName);     }     lblNumberOfFilesDisplay.Enabled = true; } catch (UnauthorizedAccessException) { } finally {} Can you cast a spell learned from the Magic Initiate feat using spell slots? Can you cast a spell learned from the Magic Initiate feat using spell slots? Say I play a wizard who learns cure wounds by taking the Magic Initiate feat. Could I cast that spell using the Wizard's spell slots? Space war, humans recreated, grown from plants with an alien female supervisor This was a small hardback book I read in the UK in the late eighties. No memory of the cover.  Some kind of space war and a long lived alien female escapes the conflict in her starship, her side had lost.  An evil enemy that she needs to trap so she gets (I think) human  DNA from space dust and sets up on a habitable planet. The story then gets like episodic and looks at the world every couple of generations while she hides out there.  Plants bud on the world and people pop out from big seedpods, the population listens out for babies crying and rescue them.  There are legends of the 'Earth mother’ who secretly guides them to become high tech.   In reality she is creating attractive food bait for the bad aliens.  I think an early human and her are attracted to each other and she (maybe) gives him long life or (maybe) uses reincarnation to keep seeing him.  Edit:- the name 'Rimstalker' has just now popped up in my brain! Multi armed bandit for general reward distribution Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$. I define a map $$\phi:D_{2n} \rightarrow \mathbb{Z}_2 \times D_n$$ by $R \mapsto (0,r^{\frac{n+1}{2}})$ and $M \mapsto(1,m)$. Then I am stuck at showing the map is bijective. By the way, do we need to show that $(0,r^{\frac{n+1}{2}})(1,m)(0,r^{\frac{n+1}{2}})^{-1}=(1,m)$ ? If we can prove this, then what can we conclude? I am looking for a clean and fast method to force GNOME in Ubuntu 14.04 to switch between active apps only on the current workspace when pressing the shortcut alt + tab. Windows 10 K&N Edition Anniversary update - Media player update not working I own a Windows 10 K or N Edition which doesn't include the media player package. My problem is: I want to have preview thumbnails in the explorer for my MP3s and videos.  I had the issue before when I updated to Win10 but there  saved me. Since the Anniversary update they are gone again.   Now I can install the old update but I still don't get the media player nor the preview images.  I tried most of the things Microsoft offers me but they are either not installable or don't work.  Any ideas what might be the correct update package?  Thx!  Ron I am currently in a clan with three members. When we tried to initiate a clan war it said we had insufficient clan requirements. Does anyone know what the full requirements are? Is there a minimum clan member requirement? "Failed to create user" due to regular expression error I'm running Ubuntu 12.10 desktop 32 bit. Currently I have only a user, type administrator. I'd like to create another administrator user but I keep getting the following error:  Failed to create user GDBus.Error:org.freedesktop.Accounts.Error.Failed: running '/usr/sbin/adduser' failed: /usr/sbin/adduser returned an error (1): adduser: Please enter a username matching the regular expression configured via the NAME_REGEX[_SYSTEM] configuration variable.  Use the `--force-badname' option to relax this check or reconfigure NAME_REGEX.  Any suggestion is appreciated. The square roots of different primes are linearly independent over the field of rationals I need to find a way of proving that the square roots of a finite set    of different primes are linearly independent over the field of    rationals.    I've tried to solve the problem using elementary algebra  and also using the theory of field extensions, without success. To  prove linear independence of two primes is easy but then my problems  arise. I would be very thankful for an answer to this question. Creating polyline-based "heatmap" from GPS tracks? This winter I am planning to track my downhill skiing/snowboarding using a GPS.  Most of my riding will occur at the same resort.  I would like to be able to create a sort of "heatmap" that shows the amount of runs that I have made in a given area.  As I add more and more GPS traces to my database, my goal would be to see a sort of linear heatmap of the most traveled areas.  Given the nature of downhill skiing, you would expect the uphill chairlift lines will be the "hottest" because it will be the only places visited over-and-over again.  Given that 1) my track will not be the same every time and 2) the area covered by following one "run" may be a few hundred feet wide, what might be the best way to analyze this "linear" data to create a sort of heatmap?  My thoughts were to buffer the lines, then intersect the polys to get a sort of Venn Diagram thing going.  My preference is to use open-source technologies.  I've got QGIS and PostGIS loaded and available.  UPDATE: In regards to @blah238's response, I was thinking of something that might be able to "collect" the number of passes ("runs") through an area, and then symbolize by the count.  Conceptually, this would be similar to ArcGIS "" (but for lines, not points) or  (but for multiple line in roughly the same area).  A more visual example of a similar concept might be a traffic-flow map, where highly-congested areas would equate to "highly-traveled" ski runs/areas:    I've read the following questions that may give some ideas, but they don't really address what I am trying to accomplish: Distribution of range of Uniform $(0,1)$ distribution Let $X_1,...,X_n$ be iid as $U \sim [0,1]$ with pdf $f(x) = 1(0 &lt;x&lt; 1)$. Determine the range distribution.   I have managed to determine the distribution of the minimum and the maximum, however I cannot/do not know how to determine the distribution of range.   Minimum:  $f_N = n(1-x)^{n-1}$ and maximum $f_M= nx^{n-1}$   I am aware that the calculation of range distribution is based on convolution: $f_R=\int f_{N,M}(x,x-r)dx$, However I cannot get the correct result, which according to my lecture slides is : $f_R= n(n-1)r^{n-2}(1-r)$  Could someone break this down for me ? My math background is not great C# getting its own class name How to open a web page from my application? I want to make my WPF application open the default browser and go to a certain web page.  How do I do that? UK visit visa: What documents prove genuine relationship with the visitor? How do you convert a number to a string showing dollars and cents?  eg: 123.45    =&gt; '$123.45' 123.456   =&gt; '$123.46' 123       =&gt; '$123.00' .13       =&gt; '$0.13' .1        =&gt; '$0.10' 0         =&gt; '$0.00' Convergence of sequence given by $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$ Be $(x_n)_n\ge 1 $  such that $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$ for every $n\ge 1$. Prove that the sequence $y_n=(2^n/x_n)_n \ge 1$ is convergent and find it s limit.  Being positive and decreasing, $y_n$ is clearly convergent. But finding it's limit really put me intro trouble. Any help?  Thank you! How can anything ever fall into a black hole as seen from an outside observer? The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a far-away-observer.  If this is the case how can anything ever fall into a black hole.  In my thought experiment I am in a spaceship with a powerful telescope that can detect light at a wide range of wavelengths.  I have it focused on the black hole and watch as a large rock approaches the event horizon.  Am I correct in saying that from my far-away-position the rock would freeze outside the event horizon and would never pass it? If this is the case how can a black hole ever consume any material, let alone grow to millions of solar masses.  If I was able to train the telescope onto the black hole for millions of years would I still see the rock at the edge of the event horizon?  I am getting ready for the response of the object would slowly fade.  Why would it slowly fade and if it would how long would this fading take?  If it is going to red shift at some point would the red shifting not slow down to a standstill? This question has been bugging me for years!  OK - just an edit based on responses so far.  Again, please keep thinking from an observers point of view.  If observers see objects slowly fade and slowly disappear as they approach the event horizon would that mean that over time the event horizon would be "lumpy" with objects invisible, but not passed through?  We should be able to detect the "lumpiness" should we not through?