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Colors in Photoshop CS6/CC look different than in browser? Spotlight with Halo applied is creating rings around light Here's a portion of a render I'm working on, which is backlit from behind by a spotlight with a "Halo" effect applied:    If you look carefully in the background, you'll notice the halo effect is creating "rings" of shadow as it fades.  How can I remove these rings and make the halo effect fade out smoothly?  I've played around with all the settings I can find without any success.  Here's my current settings for the spotlight: Core Data NSPredicate with to-Many Relationship Generate the smallest $\sigma$-algebra containing a given family of sets My teacher gave me an example of performing the subject:     Example      Let $\Omega = \Bbb R$ and $\mathcal R = \{(-\infty,-1),(1,+\infty)\}$.   Then $\sigma(\mathcal R) = \{\emptyset, \Bbb R, (-\infty,-1),  (1,+\infty), [-1, \infty), (-\infty,1],  (-\infty,-1)\cup(1,+\infty),[-1,1]\}$.   There was a different example, where she also generated the smallest  $\sigma$-algebra for the family of sets $\mathcal A = \{A,B\} \subset 2^\Omega$ in the same way: $\sigma(\mathcal R) =  \{\emptyset, \Omega, A, B, A^C,B^C,A\cup B, (A\cup B)^C\}$.   I certainly understand why $\emptyset$, $\Omega $ and a family of sets itself are there, and I certainly know that $\sigma$-algebra is closed under the operations of complement and union. What I don't understand about the other elements of generated $\sigma$-algebras: why we are taking exactly them? Does this work in a general case? I looking for help with proving the following inequality. Any relevant logarithmic identities would be great. Tried differentiating and taking limits and I'm lost as to how to approach this.   $$\frac 1{x+1}&lt;\ln\left(\frac{x+1}x\right)&lt;0.5\left(\frac 1x+\frac 1{x+1}\right)$$ WinBUGS: Multiple definitions of a node So this question is about the BUGS modeling language. So you either know it or have no clue. I'm a newbie to this so it's been driving me mad. I want to define a simple two-state hidden Markov model (HMM) where the emission of each state follows a Normal distribution. I have an array data of Nxl dimension where each row is a subject and column is a continuous variable Time associated with the subject. So in WinBUGS, I would define the model as:   for(i in 1:N) { # for each subject     # Sample the initial observation     Time[i, 1] ~ dnorm(mu[State[1]], tau[State[1]])      for(j in 2:l[i]) { # for each observation         # Sample the observed variables         Time[i, j] ~ dnorm(mu[State[j]], tau[State[j]])         # Sample the hidden states         State[j] ~ dcat(P[State[j-1], ])     } }  # P is the transition matrix of the hidden Markov chain P[1, 1:2] ~ ddirch(Pinit) P[2, 1:2] ~ ddirch(Pinit)  # Set the initial states State[1] ~ dcat(Pinit)  # Sample the initial params mu[1] ~ dnorm(200, 1.0E-6) mu[2] ~ dnorm(400, 1.0E-6)  # The precision params tau[1] ~ dgamma(0.001, 0.001) tau[2] ~ dgamma(0.001, 0.001)   Initial values have also been provided via R2WinBUGS. The model is syntactically correct. But when I run, I got this error: "multiple definitions of node State[2]"  Can you please tell me why and how to solve this? I've searched around on the error but each has their own specific case and there's not a generic solution or explanation as to why this arises. Why do objects appear smaller when farther away? If $A$ is a non-square matrix with orthonormal columns, what is $A^+$? If a matrix has orthonormal columns, they must be linearly independent, so $A^+ = (A^T A)^{−1} A^T$ . Also, the fact that its columns are orthonormal gives $A^T A = I$. Therefore,  $$A^+ = (A^T A)^{−1} A^T = (I)^{-1}A^T = A^T$$  Thus, $A^+ = A^T$. Am I correct? Thank you. Dual-boot boot menu does not show up after installing Ubuntu 15.10 alongside Windows 10 Static posts page with home.php How can I extract text from images?  I am not talking about scanned files, but garden variety images, such as when you take a high-def picture of a blackboard at class, and it is nicely handwritten; or when you photograph a page from a recipe book and want the recipe in text format.  Any free and open software for that?  I tried tesseract, and the results were awful. How do I install an individual package on a Linux system? Is the product of symmetric positive semidefinite matrices positive definite? I see on Wikipedia that the product of two commuting symmetric positive definite matrices is also positive definite. Does the same result hold for the product of two positive semidefinite matrices?  My proof of the positive definite case falls apart for the semidefinite case because of the possibility of division by zero... How to treat English questions which have code in a foreign language? Convert a number to its expression in words (e.g. 55 -> fifty-five) Is there a way to convert a number to a string (Apex code, formula field ..)  For example: 5200 > cinq milles deux cents How to filter uninteresting questions Using a keyboard shortcut to paste text Copy-paste from question to snippet When I'm editing a stack snippet, I often want to copy code from the original question into the snippet. But while the snippet editor is on display, there's no way to access the question, other than opening another tab/window. What I often do instead is copy all the code in the question to the clipboard, open the snippet editor, then paste it all in and revise it to what I want. But when the original code is poorly designed, that ends up being more work than just copying the bits and pieces that I want.  There could be a "View Question" button that pops up the question over the snippet editor and allows copying. Or maybe the Snippet Editor could be draggable and resizable, so you can reveal the question and copy from it; but this would require that it not be purely modal. I followed @Micha's instruction and successfully used the modules in GRASS. I use r.watershed to get the basin raster and the drainage line：  and I use r.water.outlet to get the watershed of one outlet：  I got the whole basin area of the green outlet point, but all I want is the little part of the original basin area, like this：part B is what I want  This schematic photo shows the idea of what I want：  Can I achieve this goal using r.water.outlet or other modules in GRASS？ Or all I can do is using the intersect tool in Geoprocessing tools in QGIS？  I want to find the watershed area, but using QGIS. I have following files to work with：  stream network shapefile(polyline) point shapefile clipped from the polyline shapefile a whole island(the stream is inside the island) DEM(I got 2 types:.lan &amp; .tiff)  I want to find the total watershed area located upstream of every point in the network, here's the schematic diagram：  the green, red, and yellow line enclose the watershed of each point(here I only take 3 points as the example), and I want to calculate their area. I already got the DEM file, and I must cut the region that contains the stream off, should I polygonize it first？ Can I directly use this form(.lan or .tiff) to work with GRASS？ Are there any tools for merging CSS? I have a couple CSS files with overlapping CSS selectors that I'd like to programmatically merge (as in not just appending one file to the end of the other). Is there any tool to do this online? or a Firefox extension perhaps?