I am assuming a sphere which can reflect, refract and diffuse a light ray. So when a light ray hits the surface of the sphere from outside, a part of it gets reflected, a part of it gets diffused and a part of it enters the sphere being refracted. Now the ray which entered the sphere will again hit another portion of the surface of the sphere. Will it be reflected again? Or it will be refracted only?
Let's say you have the ability to shine some light into a perfectly round sphere and the sphere's interior surface was perfectly smooth and reflective and there was no way for the light to escape.  If you could observe the inside of the sphere, what would you observe? A glow? And would temperature affect the outcome?  Seems silly, it's just something I've always thought about but never spent enough time (until now) to actually find an answer.
How to decide whether missing values are MAR, MCAR, or MNAR I have a large proteomics dataset. In the rows I have the proteins , and in the rows I have the samples.The dataset contains a lot of missing values.  I would like to know I can find out whether missing values are MAR, MCAR, or MNAR, and how I can decide the best imputation technique. Kind regards. Can't delete folder in Windows 7 PCIe Bus error severity=Corrected I have a new HP Pavilion Gaming Notebook and a new installation of Ubuntu 16.04. When I press Ctrl + Alt + F1 I go start seeing the errors shown in the following image and it doesn't allow me to interact with the console:    I also see these errors for a while everytime I boot. I need to do Ctrl + Alt + F1 to access a non graphical terminal to install some Nvidia drivers. What's going on?  What's causing the problem seems to be: 00:1c.5 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #6 [8086:a115] (rev f1)  jpiabrantes@joao:~$ lspci -nn 00:00.0 Host bridge [0600]: Intel Corporation Sky Lake Host Bridge/DRAM Registers [8086:1910] (rev 07) 00:01.0 PCI bridge [0604]: Intel Corporation Sky Lake PCIe Controller (x16) [8086:1901] (rev 07) 00:02.0 VGA compatible controller [0300]: Intel Corporation Skylake Integrated Graphics [8086:191b] (rev 06) 00:04.0 Signal processing controller [1180]: Intel Corporation Skylake Processor Thermal Subsystem [8086:1903] (rev 07) 00:14.0 USB controller [0c03]: Intel Corporation Sunrise Point-H USB 3.0 xHCI Controller [8086:a12f] (rev 31) 00:14.2 Signal processing controller [1180]: Intel Corporation Sunrise Point-H Thermal subsystem [8086:a131] (rev 31) 00:16.0 Communication controller [0780]: Intel Corporation Sunrise Point-H CSME HECI #1 [8086:a13a] (rev 31) 00:17.0 SATA controller [0106]: Intel Corporation Sunrise Point-H SATA Controller [AHCI mode] [8086:a103] (rev 31) 00:1c.0 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #5 [8086:a114] (rev f1) 00:1c.5 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #6 [8086:a115] (rev f1) 00:1c.6 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #7 [8086:a116] (rev f1) 00:1f.0 ISA bridge [0601]: Intel Corporation Sunrise Point-H LPC Controller [8086:a14e] (rev 31) 00:1f.2 Memory controller [0580]: Intel Corporation Sunrise Point-H PMC [8086:a121] (rev 31) 00:1f.3 Audio device [0403]: Intel Corporation Sunrise Point-H HD Audio [8086:a170] (rev 31) 00:1f.4 SMBus [0c05]: Intel Corporation Sunrise Point-H SMBus [8086:a123] (rev 31) 01:00.0 3D controller [0302]: NVIDIA Corporation GM107M [GeForce GTX 950M] [10de:139a] (rev a2) 07:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS522A PCI Express Card Reader [10ec:522a] (rev 01) 08:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter [10ec:b723] 09:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8101/2/6E PCI Express Fast/Gigabit Ethernet controller [10ec:8136] (rev 0a) I run Windows XP and the wallpaper I used to have got lost. I have backups of the system itself, so if I knew where to look, I could find a copy of the old wallpaper.  I have some idea of the original filename (searching now), and I recall it saves it as a bitmap, but an exact location would be helpful.  It was a photo/JPEG that used to be on the filesystem, and I don't have backups, so the Firefox, and Internet Explorer wallpaper locations are unlikely. I checked %SYSTEMROOT%\system32 as well - so I'm assuming it's somewhere else. Relative log file matching with linux? Is it possible to downgrade an OEM Windows 8 install to Windows 7? I recently purchased an ASUS K55A. Like all Windows 8 machines, it come with a UEFI feature called Secure Boot. This basically makes sure that the laptop won't load anything other than the Windows 8 OEM version that came with it.  However the Asus UEFI allows for me to disable Secure Boot, and therefore I should be able to revert to Windows 7, Linux, etc. (drivers may or may not be supported). When I insert my Linux Mint boot disc and try to boot from it, though, nothing happens. There isn't even a boot priority list in the UEFI settings (I can provide screenshots later). It just says "Windows 8 Bootloader" and also on the other tab it says "WINDOWS 8 BOOT OVERRIDE".  Has anybody purchased a Windows 8 machine and successfully installed Windows 7 or Linux on it? I've setup a plane with a particle emitter system. When I render the footage and the particles are glowing. Where do I find the settings for that? Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$ Can this integral be solved with contour integral or by some application of residue theorem? $$\int_0^\infty \frac{\log (1+x)}{1+x^2}dx = \frac{\pi}{4}\log 2 + \text{Catalan constant}$$  It has two poles at $\pm i$ and  branch point of $-1$ while the integral is to be evaluated from $0\to \infty$. How to get $\text{Catalan Constant}$? Please give some hints. I have an iPhone 6 128 GB which is not jailbroken. The current version of iOS on the phone is 8.1.3 and yesterday I wanted to update to iOS 8.2.  The download went through without any problem but while installing, it gave the error:     Unable to Install Update   An error occurred installing iOS 8.2   Tried installing after switching Off and ON and also tried Hard Reset (Holding Home button and On/off switch).  Same error displays every time.  Also the Touch ID has stopped working and I find that the Settings - Touch ID &amp; Passcode - iPhone Unlock is OFF.  When I try to switch it ON, the system displays the error     Failed   Unable to complete Touch ID setup. Please go back and try again.   Is anyone facing this problem?  I live in India. How do I clear Bash's cache of paths to executables? When I execute a program without specifying the full path to the executable, and Bash must search the directories in $PATH to find the binary, it seems that Bash remembers the path in some sort of cache. For example, I installed a build of Subversion from source to /usr/local, then typed svnsync help at the Bash prompt. Bash located the binary /usr/local/bin/svnsync for "svnsync" and executed it. Then when I deleted the installation of Subversion in /usr/local and re-ran svnsync help, Bash responds:  bash: /usr/local/bin/svnsync: No such file or directory   But, when I start a new instance of Bash, it finds and executes /usr/bin/svnsync.  How do I clear the cache of paths to executables? I'm trying to match SHA1's in generic text with a regular expression.  Ideally I want to avoid matching words.   It's safe to say that full SHA1's have a distinctive pattern (they're long and a consistent length) - so I can match these reliably - but what about abbreviated SHA1's?  Can I rely on the presence of numbers?  Looking at the SHA1's in my commit log - numbers always appear in the first 3 characters. But is this too short? How many characters of SHA1 do I need to consider before I can assume a number would have appeared?    This does not have to be 100% accurate - I just need to match an abbreviated SHA1 99% of the time. Finding the limit of $\left(\frac{n}{n+1}\right)^n$ Duplicate questions without answers Single word for people who are like "a frog in the well" Is there a single word describing someone who is like a frog in a well? The frog believes the well is the entire world. How can I describe people who think that their own small environment is the entire world? How do I backup my Stackexchange favorites for offline use? How do we know the brain flips images projected on the retina back around? For about 2 days I'm trying to configure Ubuntu so that I can send an email, but when I type in:  echo "Subject: sendmail test" | sendmail -v my@email.com   I'll get:  postdrop: warning: unable to look up public/pickup: No such file or directory Mail Delivery Status Report will be mailed to &lt;andreigbr&gt;.   Even if I change my@email with mine, the inbox will be empty. Can somebody help me, please? I watched about 5 tutorial about how to send an email fom the command line but still doesn't work. Keyboard key stuck or not being recognized; how to fix This is an attempt to write a canonical QA for this issue, as per the Meta post:   I expect it to be periodically edited with the goal of becoming a comprehensive information resource.  I have a MacBook Pro that has a key(Shift, Return,   Command, P, etc.) that doesn’t respond when pressed or is stuck in the down position.    It's possible that my favorite beverage was spilled (or some other liquid damage).  It's also possible that I have no idea what happened.  It was working yesterday and suddenly today it's no longer working.  Is there any way to bypass or remap the key?  Can I  have the system ignore it completely?  (This question can also apply to external USB keyboards or the Bluetooth keyboards) How would you know if your (high dimensional) data exhibits enough clustering so that results from kmeans or other clustering algorithm is actually meaningful?  For k-means algorithm in particular, how much of a reduction in within-cluster variance should there be for the actual clustering results to be meaningful (and not spurious)?  Should clustering be apparent when a dimensionally-reduced form of the data is plotted, and are the results from kmeans (or other methods) meaningless if the clustering cannot be visualized? Is there a way to switch the mesh selection mode by a shortcut?