Can a discrete set of the plane of uniform density intersect all large triangles?

Question: Let S be a discrete subset of the Euclidean plane such that the number of points in a large disc is approximately equal to the area of the disc. Does the complement of S necessarily contain triangles of arbitrarily large area?
(Added in July 2021:) I have recently learned that this is Danzer's problem. A Danzer set
(https://en.wikipedia.org/wiki/Danzer_set) is a counterexample. It is apparently not so well-known although the beginning of Gowers answer suggests that he has heard of it.
Comment: Can I ask how much you care about this, and how much research you've put in? This problem is really addictive, and I don't want to put too much thought into a problem that might have already been solved by some Hungarian twenty years ago.
Comment: Can you make precise the senses of these approximations?  Do you mean disks of increasing size with any fixed center?  Do you mean triangles of large area?
Comment: Fix a point $P$ of the plane. The density of $S$ is then asymptotically uniform if the limit $\sharp\{\box{number of points of }S\mathbox{ in a closed disc centered at P with radius R}\}/R^2$ is $\pi$ (or any non-zero constant, it does not matter) for $R\rightarrow \infty$.

Yes, I mean triangles of large areas.
Comment: See Roland's answer below, which includes a reference to previous work. I'm tagging this "open-problem"!
Answer: Edit: The answer below is somewhat obsolete, due to the recent paper of Noga Alon, where he establishes the first non-trivial lower bounds for strong epsilon-nets.
Old answer: This answer uses some terminology from discrete geometry. The definitions, and more background material can be found in, for example, "Discrete geometry" by Jiří Matoušek chapters 9 and 10. Less thorough introduction can be consulted without going to the library.
If one drops the requirement that set has to have asymptotic density, and merely asks for the set to have a constant density on some large (but fixed) ball, and restricts the triangles to live inside that ball, the problem does not become much easier. In that case problem asks for a construction of an 1/r-net of size O(r) for the family of all triangles with respect to the Lebesgue measure on [0,1]^2 (or equivalently for a  construction of 1/r-net for a grid {1,..,N}x{1,...,N} for large N). The upper bound of r*log r on the size of the net follows from finiteness of Vapnik Chervonenkis dimension. For general range spaces with finite VC dimension the logarithmic factor is necessary. However, there is by now several results that remove or reduce the logarithmic factor in "geometrically interesting range spaces" (as a sample, here is a result for axis-parallel boxes). Unfortunately, as far as I know these developments do not include the space of triangles in the plane (I might be wrong; you should check with one of the experts).
Showing non-existence of small 1/r-nets for this problem is certainly open, and likely to be hard. The only currently known lower bound on 1/r-nets for any geometric problem whatsoever is in my paper with Matoušek and Nivasch, and is for the family of all the convex sets. However, there instead of a grid {1,...,N}x{1,...,N} that is featured in this problem, the construction is a kind of highly stretched grid.
Comment: If you can build an 1/r-net of size f(r) for the grid {1,...,N}x{1,...,N} for an arbitrarily large N for fixed r, then you can build an 1/r-net of size f(r) for the Lebesgue measure on [0,1]x[0,1]. That is because you can rescale the grid, and use compactness (the configuration space of positions of f(r) points in [0,1]^2 is compact). The point is that the number of point inside C in a sufficiently fine grid is almost proportional to the Lebesgue measure of C.
Comment: Could you clarify the relevance of the grid? I read through enough of you references to understand the statement that we are trying to build a "1/r-net of size O(r) for the family of all triangles with respect to the Lebesgue measure on [0,1]^2", but I don't understand why this is the same as building a "1/r-net for a grid {1,..,N}x{1,...,N} for large N".
Answer: This question is infuriating. I think I've made some progress, and would like to hear other's thoughts. Therefore, I am making this post a community wiki:

First of all, any triangle of area A contains a rectangle of area A/2. Proof: let the triangle be ABC, with AC the longest side. Let P and Q be the midpoints of AB and BC, and let R and S be the feet of perpendiculars from P and Q to AC. Then PQSR is a rectangle of the required area. Conversely, a rectangle of area A contains a triangle of area A/2. So we may instead ask whether there are large rectangles in the complement.
This is convenient because specifying a triangle involves 6 parameters, while specifying a rectangle has only 5. So this cuts our search space down a dimension. I find the most conveninent parameters for a rectangle to be the length of the longer side, L, the area, A, the angle of the longer side, $\theta$, and one of the vertices $(x,y)$. I'll call the type of the rectangle $(L, A, \theta)$, forgetting the translation parameters.

I now have a conjectural solution, although I have no idea how to prove that it works. I call this the sunflower configuration, because it was inspired by pattern of florets at the center of a sunflower.
Let $\tau$ be the Golden ratio. Consider the sequence of points $(\sqrt{k} \cos(2 \pi \tau k), \sqrt{k} \sin(2 \pi \tau k))$. A circle of radius $R$ around $0$ contains $R^2$ points, and has area $\pi R^2$, so the density is right.
Why do I think this is reasonable? There is a gorgeous property of the Golden ratio: if you look at the sequence $k \tau, (k+1) \tau, (k+2) \tau, ..., \ell \tau$ in $\mathbb R/\mathbb Z$, then the largest gap between any two consecutive angles is $\dfrac\tau{\ell-k}$. So multiples of $2 \pi \tau$ are very well distributed around the unit circle. I learned this from Volume 2 of the Art of Computer Programming; I'll try to find a reference later if no one else does.
I don't have a strategy yet for proving that the sunflower pattern doesn't contain large triangles (or rectangles). But, where ever I try to place one, heuristics indicate that this equidistribution of angles destroys me.

My first strategy, aiming to prove a "no", was to overlay several lattices which were all rotations of each other. Let's fix $A$ once and for all, our goal is to exclude a rectangle of size $A$. I first set out to see when a lattice could contain a rectangle of type $(L, A, \theta)$.
Translate the rectangle so that one of the short sides touches $(0,0)$. Then the rectangle contains a circular wedge of radius $L$ and angle approximately $A/L^2$ with no lattice points. In other words, there is no $(p,q)$ with $\sqrt{p^2+q^2} \le L$ and $|\theta - \tan^{-1}(p/q)| \le c\cdot A/L^2$, where $c$ is a constant I have not computed.
There are now a bunch of nuisances, having to do with the presence of that $tan^{-1}$ and the fact that people who do Diophatine approximation usually ask for $q$ to be small, not $\sqrt{p^2+q^2}$. Passing over all of the details, the set of $\theta$'s for which such a rectangle exists should look something like the union of all intervals in the $L$-th Farey sequence whose length is greater than $A/L^2$. Heuristics give me that the size of this is $c/A$ for $c$ a (different) constant that I haven't computed.
So, one lattice can't save me. The above suggests that, for every $L$, there will be a positive length set of $\theta$'s for which rectangles of type $(L, A, \theta)$ exist. Of course, we already knew that a single lattice couldn't work.
What about two lattices, rotated by some phi? I think I still lose. As $L$ grows, the set of theta's which work stays of size $1/A$, but becomes more and more spread out. Eventually, I would expect that it would contain two points that differ by phi. This part is very nonrigorous, though. In particular, I'm not sure whether we might be able to save things for some very special phi.
That's about how far I've gotten. I tried some other ideas, but didn't get anywhere. I'm not even sure which answer I think is right.
Answer: I've just spotted this question. It's a well-known open problem in discrete geometry. Unfortunately, I can't remember what it is called.
There is a paper that proves that no union of finitely many lattices can work. I'll try to remember what it is. I remember that it used a result of Mahler.
Added later: I think it was Mahler's selection theorem. Maybe that's enough of a clue for someone to reconstruct the proof (which I seem to remember wasn't hugely hard).
Comment: I would be glad to learn of any places mentioning this problem.
Answer: Concerning the nice construction David Speyer: I have the impression that it does not work.
Reason: There are large regions where the configuration looks very much like a lattice with fairly large density (no close points). Such a region contains thus large triangles (one can of course replace triangles by convex set or by rectangles, this does not change the problem). I did a fairly coarse and rapid computation which seems to show that there
are indeed regions contained in arbitrarily large discs where the points of the set are at most at distance \epsilon (for arbitrary small positive \epsilon) from the points of a dense lattice. This computation (if correct) implies easily the existence of arbitrarily large triangles in the complement.
Concerning the history of the problem: I am not aware that it has been considered in the present form. I have written a paper "Universal Convex Coverings" which is appearing
in the Bulletin of the LMS (a copy is on the arXiv) where I construct a set with R^2 log(R) points of (Euclideean) norm at most R which intersects all triangles (or equivalently, convex sets) of large enough area. (The paper contains in fact a construction for arbitrary dimensions). I am thus curious
if one can get rid of the logarithm. In fact, I believe that the logarithm can be improved to some smaller slowly increasing function but I would be very surprised by the existence of such a set with uniform density.
Comment: I don't understand, Roland. Why do you say "There are large regions where the configuration looks very much like a lattice with fairly large density" about David's proposed example?
Comment: I would also like more detail. On which region, and for what lattice, is this true?
Answer: This seems somewhat related to Heilbronn's triangle problem, which is about determining the worst-case behavior of the minimum area triangle determined by a set of n points in a unit disk. In this one, instead of the smallest triangle determined by a set of points, we want the largest empty triangle; I think an equivalent version of the question is to ask whether or not, for all sets of n points in the unit disk, the largest empty triangle has area O(1/n).
However unlike Heilbronn's problem the triangle we want isn't required to have three of the n given points as its vertices; for instance, if n points were placed close together within the disk there would be no large triangle having three of them as vertices but there would exist other large empty triangles. I did at least find one paper that's sort of related to this: On a Triangle with the Maximum Area in a Planar Point Set, Hosono et al. 2005, show that there exist sets of n points for which the ratio of areas of the largest empty triangle with three of the points as vertices and the convex hull of all the vertices is O(1/n).
By the way, it's easy to define sets of points such that there is no large empty triangle containing the origin: place a ring of 2^k points at radius 2^k, for k = 1, 2, 3, 4, ... The density of points within any nonconstant-area disk will then be upper and lower bounded by a constant times the area of the disk, and by adding other points one can make the upper and lower bound constants as close as one wishes to each other. So somehow, if the large triangles always exist, they must sometimes be far from the origin.
Answer: I believe that quite a lot of research has been put into related questions, with much of the attention given to the unit square (and even more, the unit cube in higher dimensions).  Some key references are:
[1] H.Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods (SIAM, 1992)
[2] J.Beck and W.Chen, Irregularities of distribution (CUP, 1987)
[3] B.Chazelle, The Discrepancy Method: Randomness and Complexity (CUP, 2000).
All I can do is quote you various results from these.  (Some of this is covered in Wikipedia-discrepancy.)  The results are typically expressed in terms of "discrepancy": for N points in the unit square, the discrepancy DN can be defined as supJ |A(J,N) - N λ(J)|where J is all subintervals of rectangles aligned with the axes, A(J,N) is the counting function (that is, the number of points inside J), and λ(J) is the Lebesgue measure.  This definition has an extra factor of N compared to [1], but I think this is useful when you scale the unit square to area N: a rectangle of area λ then "should" contain λ points; and the discrepancy is the difference between that and the number it actually contains.
There are results for the best possible behaviour of DN as a function of N.  For the axis-oriented rectangles, it is Ω(log N), and this can be achieved by the Halton-Hammersley sequence.  When J is changed to rectangles with any rotation, discrepancy is Ω(N1/4), and O(N1/4 √log N) can be achieved by jittered sampling.  When J is all convex subsets of the unit square, you've moved to "isotropic discrepancy" JN -- harder to study, but DN ≤ JN ≤ 8√(N DN).  Also, JN is Ω(N1/4).All of this is related to discrepancy of shapes that can contain some points, and the question is whether they contain the "correct" number.  If you start with a shape j1 with n1 points, and add an empty region (while staying in the set J), you can show that the empty region must have area O(2DN), but I can't see a guarantee that an empty shape obeys the Ω limit.
I'm not sure how close this is to an answer.  I certainly agree that it's a nice area, and I recommend those references -- they can all be read, if not fully understood, by someone with limited mathematical education, like me.
Comment: Thanks for this information which seems to be an analogue of epsilon-nets. I have the impression that these problems are slightly different due to the fact that one considers compact sets. There is
however an intriguing "log" appearing in a conjecture which I encountered also in my examples. I need probably some time for thinking (which I lack unfortunately at the moment) for understanding this better.
Answer: Here are a few details for proving that the construction of David Speyer does not work:
Consider an arbitrarily large "window", say $$W=\lbrace(x,y)|A-100\leq x\leq A+100,B-100\leq x \leq B+100]\rbrace$$ (one has to replace 100 by arbitrarily large numbers later) centered at some point $(A,B)$ of the plane. If $(A,B)$ is far from the origin, the intersection of $W$ with the set $S$ of all points of the form $(\sqrt{k}\cos(2k\pi),\sqrt{k}\sin(2k\pi)), k\in\mathbb N$, looks (generically, but one can neglect the non-generic case since it fits into the generic picture also) "almost" like a translate $\Lambda$ of a lattice with a fundamental domain of area $\pi$. This translate $\Lambda$ of a lattice depends of course on the precise location of $(A,B)$ but the "convergency" of $W\cap S$ to such a $\Lambda$ depends only on the norm of (A,B) and on the size of W. More precisely, convergency means that for any strictly positive epsilon there exists a real number $R=R(epsilon,100)$ depending only on epsilon and the size (here 100) of the window with the property that if $(A,B)$ has norm at least $R$, then there exists a translate $\Lambda$ (depending on $(A,B)$) of an Euclidean lattice with fundamental domain $\pi$ and a map from $S\cap W$  (the points of $S$ in the window $W$) into $\Lambda$ which moves points at most by $\epsilon$. For $\epsilon$ small enough (depending on nothing) there are arbitrarily large triangles not intersecting an $\epsilon-$neighbourhood of such a set $\Lambda$. For $\epsilon$ small enough, the diameter of such triangles of area $\alpha$ can be bounded above by some real number depending only on the area \alpha of the triangle but not on the translate $\Lambda$ of an Euclidean lattice with fundamental domain $\pi$. Given a real number $\alpha$, we can thus choose the window $W$ large enough such that it contains triangles of area $\alpha$ which avoid an $\epsilon-$neighbourhood of $\Lambda$. Such a triangle avoids thus $S$.
I hope that these explanations are sufficiently explicit.
All this is essentially only elementary lattice theory and
nothing is difficult to prove.
Answer: This answer concerns the search for grids in the sunflower model. My confidence is shaken but not broken.
I think I have figured out what Roland is saying. Consider a square of area A, at distance R from the origin, with R very large. It will be convenient to identify our plane with the complex plane. So our points are of the form e^{(1/2) log k + 2 pi i tau k}.
Let L(z) = R log z. On our little square, L is approximately area preserving and approximately linear, with error O(1/R). So our square will contain large lattice point free triangles if and only if L of our square does.
Well, L of the sunflower pattern is the points of the form (1/2) R log k + 2 pi i tau R k. We only care about k between (R-\sqrt{A})^2 and (R + \sqrt{A})^2 (roughly), which is to say k of the form R^2 +s for |s| < 2 \sqrt{A} R. For such k,
(1/2) R log k + 2 pi i tau R k =
R log R + (1/2) s/R + 2 pi i tau R^3 + 2 pi i tau s R =
c + (1/2) s/R + 2 pi i tau s R,
where c does not depend on s. Of course, log is multivalued, so the right answer is actually
c + s (1/2R + 2 pi i tau R) + t (2 pi i R).
In short, the sunflower pattern, restricted to our square, looks like the intersection of a similar square with a translate of the grid generated by (1/2R + 2 pi i tau R) and (2 pi i R). I notice this has fundamental domain 2 pi, so I am guessing this is the grid that Roland is discussing.
So, why am I not convinced this is a problem? The shape of the grid is changing with R. Basically, we are intersecting our square (of area A) with a grid whose fundamental regions are getting very thin and tall. It is not clear to me how we can find large triangles INSIDE the square of area A.
In fact, that would be a great question for some one to answer. Take a square of area 100. Intersect it with the grid spanned by (1/R, tau R) and (0, R). Let f(R) be the largest triangle inside the square, missing this lattice. As R goes to infty, does f(R) approach 1, or stay nearer to 100? (I have removed factors of 2 and pi that I expect to be nonessential.)
Of course, I may have misinterpreted Roland. Roland, which grid is close to the sunflower model?
Answer: I don't know that I'm quite as hooked on this problem as David S., but it really is addictive. My hunch is also that the answer should be "no," and I really really want this to be solvable by simple (if clever) combinatorial-geometry arguments. Here's some arguments of that nature which I don't think can be themselves made to go through, but which do rule out some approaches. I'm making the post community wiki, so people can add to it or correct the stupid mistakes which I've almost certainly made.
So we'll use the rectangle formulation. Suppose that S is a set of points that does intersect every sufficiently large triangle. Then if we project S onto any line, the image has to be dense. This is doable; I think that David's tau-construction has this property. But you can't build such a set up out of lattices in an easy way.
But we can do slightly better than that, although it's harder to state. You also need the projections of S  intersect a strip parallel to a line L onto L to be very nicely distributed. In particular, the maximum distance between two consecutive points has to be O(1/x) for a strip of width x, which is best possible up to a constant. (To see this, notice that there are O(Lx) points in the strip, and they have to cover an interval of length L.).
By the way, this subsumes the appeals to "embedding large almost-lattices." I'd (harrison) be interested to see a set that has this stronger projection property but provably contains large rectangles. ETA: Upon further reflection, if the implied constant is uniform for all lines L, then this property's necessary and sufficient, since the projection property bounds the size of a rectangle in the complement of S that's parallel to L.
It is important to note that this rules out most straightforward random constructions. If we place N points at random on a line segment of length 1, we anticipate a gap of length log N/N somewhere. We need to do better, achieving gaps of size O(1/N). Proof: Divide the segment into N buckets. For any k consecutive buckets, the chance that they are all missed is (1-k/n)^n ~ e^{-k}. So, if k is log N + O(1), the chance that a particular k buckets are missed will be of order 1/N. Since there are on the order of N blocks of k consecutive buckets, the expected number of such blocks which are missed will be positive. So there is a positive probability of missing a segment of length log N/N.
Answer: David, considering the logarithm is a nice idea. A small error: the fundamental domain has area pi: There is a factor of 2 in the denominator of the real part.
You are of course right: The area of all triangles (not intersecting sunflower points) contained in squares (or windows) of fixed area A is bounded. One has however to consider the limit when A goes to infinity. Then your argument is no longer valid and you get indeed arbitrarily large triangles not intersecting the sunflower points in sufficiently large squares sufficiently far away from the origin.
Your interpretation is correct: (Up to the logarithm,) this is indeed the grid (I prefer to speak of a translate of an Euclidean lattice).
Conclusion: A solution to the problem (if it exists) should have no arbitrarily large regions where it looks very much like a Euclidean lattice (which is the case for the sunflower point set).
Another nice idea which unfortunately fails to work is to take the set S of all vertices (or barycenters or ???) of all triangles involved in a Penrose tiling (giving those beautiful quasiperiodic pictures with almost symmetries  of order five). Indeed, such tilings contain arbitrarily long straight lines. This implies the existence of triangles with arbitrarily large area which do not intersect S.
Answer: I think I can rule out some really long rectangles, in David's sunflower model.
In particular, if one corner of the rectangle is with <code>\sqrt{R}</code> of the origin, then the rectangle has side length at most <code>R</code>. I'm not sure this is at all useful, however; polymath style, someone can point that out for me!
The argument is just the following. Let's write Θ<code>(x,y,r)</code> for the angular width of the widest empty wedge with base at <code>(x,y)</code> and radius <code>r</code>. The important property of the sunflower model is that the widest wedge at the origin with radius <code>r</code> has width at most <code>c/r^2</code>, for some constant <code>c</code>, i.e. Θ<code>(0,0,r)</code> ≤ <code>c/r^2</code>. Now let's move to an arbitrary point <code>(x,y)=(r</code>0<code>cos</code>θ<code>, r</code>0<code>sin</code>θ<code>)</code>. The angle to a point <code>P</code> differs from the angle from the origin to <code>P</code> by at most <code>r</code>0<code>/2R</code>, where <code>R</code> is the distance from the origin to <code>P</code>. Thus
Θ<code>(r</code>0<code>cos</code>θ<code>, r</code>0<code>sin</code>θ<code>, R')</code> ≤ Θ<code>(0,0,R'-r</code>0<code>) + r</code>0<code>/(R'-r</code>0<code>)</code>.
As long as <code>R'</code>≥<code>r</code>0<code>^2</code>, this is small enough that we don't need to worry. As it's the quantity <code>R</code>Θ<code>(x,y,R)</code> that we need to bound, unfortunately I think this is the best you can do without using anything stronger about the distribution of points.
Comment: Actually, this didn't use the sunflower model at all -- as long as you can't have arbitrarily large rectangles at the origin, this estimate works. That makes it sound less interesting, I guess.
Answer: I mentioned a necessary and sufficient condition that a set must satisfy to intersect all large triangles. Here I'll describe a set that satisfies a (very) weak version of that condition -- namely, the projections of strips around the x-axis satisfy the appropriate property. Actually I'll describe the construction on [0, 1) x [0, \infty); we can translate to get the whole x-axis. I'm not optimistic that this can be turned into something which solves the problem, but I'll describe it anyway since it's hopefully illustrative.
The key thing is that binary fractions m/2^k are dense in the reals, and the ones between 0 and 1 have a simple ordering which allows us to satisfy the density condition. The construction is as follows: Place a point at (0, 0), and for every positive integer m with binary expansion 1a_2...a_k, place a point at (0.a_k...a_2 1, m). So for instance there are points at (1/2, 1), and at (3/8, 6). Then a square of side length n has at most n^2 points within it, for obvious reasons. The projection property of strips R x [0, y) onto the x-axis is easily checked as well. (Question: Does this satisfy the projection property for strips parallel to the x-axis? I think it might, essentially because this is related to 2-adic-ness.)
Obviously we can do something similar for any prime p replacing 2. I'd be interested to see, though, if someone can provide an appropriate construction of this type for the "infinite prime" -- does it have similarly nice properties?


Is the skill to learn new math by reading textbook alone (no lectures) required when one becomes a PhD student?

Question: I've taken a few math classes in college. I'm wondering as one graduates college and applies to become a PhD student in math, is he/she going to be required to learn math related materials alone without lectures, only by reading books (ie. by following the examples in the book and doing exercises with solutions provided)?
Comment: With no solutions provided actually. It may take a while; some you won't see; but for the most part, read an appropriate-level text, and most exercises should be accessible.
Comment: Typically, there is more coursework, a foreign language, Ph.D. qualifying exam and a thesis with original work. For example, see [MIT](http://math.mit.edu/academics/grad/), but this is pretty standard across Universities. Of course, when researching, you are going to have do lots of things alone because you have to do original work, which means knowing what was done in the past. Also, the exam will require a lot of work and learning. Regards.
Comment: Absolutely they will!
Comment: When you get to the point where you are learning things from research papers in journals, you don't have any other choice.
Comment: Should this be on Academia SE?
Answer: Most certainly! Being able to independently learn mathematics (or anything else) is a vital ability any academically oriented (or any other person) needs to acquire. It is certainly required for a PhD and I would also say for a Masters.
It is my opinion that developing the ability to learn independently is something that needs to be done by the student as early as the first year of series studies (for most people this would be the first year of the Bachelor). A way to do it would be to supplement the dictated textbooks in any given course by books you find on your own in the library or online and reading these books alongside the course.
Comment: @user133466: If a student sees an intricate theorem statement or a particularly abstract definition for the first time in class, he/she is far more likely to benefit from any helpful explanations the instructor might provide if time has already been spent trying to understand how the pieces fit together. That said, even a cursory reading before lecture is probably beneficial in terms of mental organization.
Comment: in college, instructors always recommended students reading the section that's going to be taught before going to the lecture to increase the effectiveness of the lecture. But I often find myself spending more time reading the textbook on materials that the professor might not have covered. I'm not sure I see how reading prior going to the lecture is beneficial to a student... can you help to elaborate on that a little? Thanks
Answer: Very much so! Indeed! Although one may be misled by the required courses with homework and exams. Through various mechanisms, a tradition has arisen in which students are "required" (coerced, by fear of rejection) to do things which they should have desired to do. As is usual in human situations, "requiring" a thing generates a certain hostility, which, in this situation is counter-productive, and so on... Despite the (widespread, systematic) inaccuracies in the pedagogical design of graduate programs, people do suffer through these. :)  On the face of it, being able to independently assimilate things from sources is irrelevant... ?!?!? ... since the game appears to be compliance and obedience, going to class, doing homework, reviewing for exams. (For the first year or two of grad school.)
(Yes, obviously intellectually nonsensical, but this certification of nonsense does not say what one should do...)
... however... and somewhat unfortunately... the seemingly required willingness to play along with things that make only fractional sense becomes immediately irrelevant as soon as one has passed the standard hurdles. I note that it is very true that there appears to be a general proclivity to learn too little rather than too much (I would be interested to hear comments on this...), so a responsible mentor might worry that novices misinterpret advice about attending to research rather than "classes".
In that context, in my own life experience, and in observation of others, ... one must (I hesitate to do "MUST", but here it might be warranted) be able to cope with sources. Books. PDFs. Old papers. Essays by people who've thought about things.
If you can register for a class where the person in the front of the room seems to understand these issues, to address them, and be able to render sense of them, you are fortunate.
Answer: Getting a Ph.D. in math is (in part) getting an education in how to do research in math. Doing research in math doesn't mean that you necessarily have to do it sitting alone with books. Many researchers work together in groups and support each other.
However, doing research means that you have to move beyond what lectures cover. You will have to "come up with" new math. From what I understand, in many places when you start a Ph.D. program, then you start by taking classes. You will then at some point find an advisor and then gradually move from taking classes to independent studies with your advisor and/or other professors. Doing work with a professor will in the beginning (for most people) just be the professor that teaches you material. But more and more you will have to work independently. A good advisor (IMO) will know how much he/she needs to help. And he/she will be good at asking you questions and giving your problems that are enough beyond what you know and still isn't impossible for you to answer.
So at the end, you will hopefully be at a point where you can work more or less on your own.
Does that mean that you just sit and learn form books all day? No, it doesn't mean just that. You will also be studying research articles and you will try to move beyond what has been written down.
So, yes, you definitely will have to be able to teach yourself material without much help from anyone. It, however, doesn't mean that research is just a one man show. Researchers collaborate and help teach each other material.
Answer: You need to be able to learn independently. You need to be able to develop and asses arguments and solutions without an outside source to correct your work. You will become an outside source to others. This is not an irrelevant skill that you are being forced to do as a mere initiation. This is in fact, the skill you are attempting to master. As an expert, you will without doubt encounter situations for which you have no pre-packaged solution. Often, in order to resolve a problem of this sort, you will need to study new material in order to develop and refine your understanding. This is not a skill that is entirely new. As an undergraduate, and in many ways as a graduate student, your teachers are providing guidance only. They tell you where to look and what is important. They also tell you why things are important but it is only through your own studies and through situations that you encounter that you may finally see the wisdom of the guidance you have received. You dissertation is intended to demonstrate your ability to think independently.
Answer: Yes.  However, it's not something to be too afraid of; it's just one of the skills that you should expect/aim to acquire in the course of graduate school.
Different countries and universities have different cultures in this respect (unsurprisingly).  Most (all?) grad programs in the US start with a year or two of taught courses, through which you will gradually transition to more independent study.  For instance, when you are ready to start learning about an area that's too specialised to warrant a lecture course, you may well be able to take a "private study" course with a faculty member, so they will help guide your reading, recommending what books/papers to read, and discussing them with you as you read them.  Or you may be able to set up a reading group with fellow-students (and/or faculty members), where you read through some book or series of papers together — so then you read mostly on your own, but can discuss and compare notes with colleagues on a regular basis.
Some people are naturally good at learning direct from textbooks; but for the rest of us, things like these are how we learn, bit by bit, how to do it.  I was a comparative latecomer to the skill, and I'm still (as, currently, a post-doc) most at home learning more socially (lectures, discussions with collaborators, etc); but it's an essential skill to have to at least to some extent, and if it's something that scares you a little, then it's worth putting some effort into overcoming that fear.


Locating a Comet, how is it done?

Question: How are the comet-hunters able to precisely locate/know about the required comets ? How can they distinguish between comets from such a far distance ? How are they able to estimate the exact time period of these comets like Hale-Bopp's and Halley's comets have orbital time periods  2520-2533 yrs and 75.3 yrs respectively ? Do they have to follow the comet  throughout its whole orbital path to deduce that or are there any other procedures ?
I've heard of using computer generated programs that help in here. Please notify me some of these.
Answer: You look at the sky every night and see something that wasn't there last time you looked. If it moves the next night then it's a comet, if it doesn't move it's probably a supernovae
With three position measurements on different nights and a certain amount of algebra you can work out it's orbit then you have it's period and when/where it will reappear.
Now it's a little easier with telescopes and cameras that can image the entire sky in a night or two - and software that can spot changes. But a lot of comets (and supernovae) are still found by amateurs.
Although comets do change their orbit slightly with each trip into the inner solar system as they are effected by the gravity of each planet they pass. Also as they get close to the sun some of the surface ice boils off ,which gives the comet tail, but this can also provide a thrust which changes their path slightly.
Answer: I can't really answer your question because calculating a comet's orbit isn't something I can describe in a few lines (actually it's not something I can describe at all, but as always Google is your friend!).
As Martin says, finding your comet is easy in principle. You photograph the same bit of sky on (at least) three occasions a few days apart, then you look for anything that has moved i.e. that is in different positions in the three pictures. This sounds easy, but there is a lot of sky and only a few comets so it's incredibly painstaking work. Professionals have automated systems for comparing images and looking for moving objects, but amateurs just have to get on with it.
Anyhow, once you've found your moving object you can use the position in the sky and the change in position to calculate the orbit. Martin casually describes this as "a bit of algebra" but actually it's rather a lot of algebra. I found this book online if you really want the gory details.
I imagine most amateur astronomers would just feed their measurements into some software rather than do all the sums themselves. I confess I know little about this area but a quick Google found several calculators e.g. this one.
Incidentally, in a previous question you asked about how to tell a hyperbolic from a parabolic (and elliptical?) orbit. There's no easy way to tell except by calculating the orbit to see what shape it is.

Locating a Comet, how is it done?


Publishing an InfoPath form wiped out Personal Views in the Form Library

Question: I published an InfoPath 2007 form into a Form Library on MOSS 2010 and I lost all the data in the form column fields.  I was able to restore the data by doing a check-out/Check-in on the documents, but now realized it has screwed up the personal view that were created in that library.  The views no longer contain the filers or column that referred to the columns of the form data.  Any clue why this happened or how we can restore the personal views other then recreating them?
Comment: Is it possible that this is addressed in a service pack, cumulative update, or hotfix?
Comment: I experienced the same issue. I struggled for weeks trying to figure out how to update a 2007 InfoPath form in SharePoint 2010 without having to reopen each form and recreate each view. I found Dave's solution of re-promoting each field and specifying the existing column in the selected library to be simple and effective. Thanks, Dave. This saved me hours of work and allowed me to make changes to the form I wouldn't have been able to make without this solution.
Answer: You are probably facing the issue described in KB article 2554288 Columns published from InfoPath fields are recreated when the same InfoPath form template is re-published to more than one document libraries in a SharePoint site. The issue is that InfoPath isn't very flexible when it comes to matching up columns in SharePoint with what it's expecting in the form. It has probably duplicated all of the columns in the list.
The only way I know to resolve this is from backup or painstakingly cleaning up the mess.
Answer: The KB article Alex linked above offers one (theoretically) good solution: Publish the form as a Site Content Type and then associate that with the library.
After running into this today when publishing an updated form into a Test environment, I decided to try another solution when publishing into Production (you only live once), which worked well:
When in the publishing wizard and selecting fields to promote, go through the full list and Modify each field which already exists in the destination library: change the Site Column Group from "(None: Create new column...)" to "(This document library)" and then select the existing column.
I'm guessing that the safest practice for any forms deployed this way is to go through the Promotion list every time you change the environment/site/library you're publishing to and switch everything to "...Create new column..." (if not already set) and then change to "(This ... library)" to force the internal column GUID to be set correctly.
Answer: I had the same issues and the problem is related to how you publish your form. When I republished the form, the list view lost all lookup fields in the form and I had to add them again. Also any list view webpart containing these coloums needed to be updated. Also I needed to reopen all forms and save them again in order to have the lookup field information available in the SharePoint list.
To solve this problem i publish the form as a content type instead. I found this blog which describes step by step how to do this.
http://www.marclenferna.com/blog/archive/2009/01/18/how-to.-publish-your-infopath-form-to-sharepoint--a.aspx
Basically you upload the form as a content type to an new list which is only to contain the contenttype and then you create a new form library where you add the new content type.


How can I tell what has changed in a Comprehensive Rules update?

Question: As an example, the Comp Rules were updated February 1, 2012.  I know that a reference to "Fateful Hour" was added to 207.2c since I know to search for fateful hour, but how do I know what else changed?  Does Wizards of the Coast release an official list of changes when they make a revision?
Answer: They put an article in their website written by the current Rules Manager (the main authority in Wizards for Magic rules).
This is the one that corresponds to the February 1, 2012 rules update.
If you search for more articles by the same author, you'll find the articles for older rules updates. Searching for articles of previous Rules Managers is trickier.
Answer: I don't believe they release a full changelog every time they make a change to the rules, because most of the time, they're minor patches, like adding/removing creature types, or adding a few new block mechanics.
However, when big changes happen, such as Sixth Edition or M10, they usually discuss those changes in detail, in form of an article, such as this.
I do believe though that a full diff of rules changes would be pretty awesome for the rules lawyers among us. A website doing this could be fully automated, just checking the rules in txt format once a day or so.
EDIT: Googling a bit revealed this gem, which seems to be exactly what I had in mind: A privately maintained, exact changelog between rules versions
Answer: Wizards releases what they call Update Bulletins. Within this update bulletin, is a section called Comprehensive Rulebook Changes. You can search for the latter, and eliminate most other update bulletins not referring to the rules changes.
Search for comprehensive rulebook changes
Even if Wizards didn't release this list of changes, you could use something like the Internet wayback machine, and a text difference tool (meld, fd, etc.) to find the changes yourself.


How to measure distances to stars by means of spectroscopic parallaxes?

Question: How to measure distances to stars by means of spectroscopic parallaxes on practice?
What is the accuracy of measuring distances using this method compared with distances based on HIPPARCOS trigonometric parallaxes? My sample of objects consists of A-B type stars.
Answer: Actually the method described on Wikipedia is not the method that is meant by Spectroscopic Parallax. To determine the spectroscopic parallax, you'll need a spectrum of the star and measure the widths of the spectral lines. Compact stars have higher surface gravity, which means that their spectral lines are broader. This means that the radius of the star can be calculated from line widening. Using the observed effective temperature $T_{eff}$ and the radius R, you can get the Luminosity from Stefan's Law, which gives an absolute magnitude and together with the apparent magnitude, a distance modulus and therefore a distance.
This gives an accuracy of 10% in luminosity and 5% in distance for main sequence stars and 25-30% in distance for giant stars. (see de Grijs, 2011)
Wilson and Bappu (1957) proposed to use the width (W_0) of the emission core of the CaIII absorption line at 3933 Angstrom. Using data from Hipparcos the relation between the absolute magnitude in V and the width of the absorption line was calibrated to:
$M_V = 33.2-18.0 \log(W_0)$
by Pace er al. (2003).
So to use this method you would need to be able to measure the width of the CaIII absorption line, but other calibrations using the MgIIk line also exist.
As these distance measurements are calibrated using Hipparcos, they will never be able to be more accurate until better calibration data is available (i.e. with Gaia).
The much more simpler method as described on Wikipedia might also be used but that is even less accurate. NB. The relation between the colour (colour index B-V) and the spectral class is not linear. Many Hertzsprung-Russel diagrams show both colour and spectral type on the X axis but this is not really correct. A K0Ia supergiant has a different colour index than a K0V star on the main sequence.
On page 50 in de Grijs, 2011, this relation is shown in Fig 2.11. It should also be somewhere on Wikimedia (to which it is attributed) but I cannot find it.
EDIT: Here it is: http://en.wikipedia.org/wiki/File:H-R_diagram.svg
Answer: If you really want to use the method outlined in Wikipedia than you might use the Hipparcos catalogue to determine the mean absolute magnitude for each spectral type.
I tried this and I got the following values for A and B type main sequence stars:
<code>Spec        N    M_V           <d_err>  max(d_err)
B0V       [23]  -1.8 ± 2.3     130 %    1014 %
B1V       [95]  -2.1 ± 1.8      81 %     833 %
B2V      [223]  -1.6 ± 1.5      69 %    1562 %
B3V      [279]  -1.3 ± 1.4      59 %     739 %
B4V       [91]  -1.1 ± 1.1      44 %     232 %
B5V      [251]  -0.8 ± 1.2      44 %     465 %
B6V      [145]  -0.6 ± 1.3      53 %     881 %
B7V      [122]  -0.5 ± 1.4      70 %    1405 %
B8V      [522]  -0.2 ± 1.3      58 %    1988 %
B9V      [887]   0.4 ± 1.2      57 %    4613 %
A0V     [1206]   0.8 ± 1.2      54 %    2990 %
A1V      [735]   0.9 ± 1.1      50 %    2509 %
A2V      [491]   1.0 ± 1.0      42 %    1076 %
A3V      [451]   1.1 ± 1.1      51 %    3526 %
A4V      [178]   1.3 ± 1.1      49 %    1106 %
A5V      [214]   1.3 ± 1.1      45 %     762 %
A6V       [99]   1.4 ± 1.1      54 %    1924 %
A7V      [188]   1.6 ± 1.2      65 %    5371 %
A8V      [114]   1.7 ± 1.0      42 %     392 %
A9V      [329]   2.0 ± 1.2      57 %    2788 %
</code>
where Spec is the spectral type, N is the number of stars in the Hipparcos catalogue with that spectral type (nb. many stars do not have a spectral type, or a spectral type with the star type (e.g. main sequence or supergiant) missing), the average and standard deviation of the absolute magnitude (M_V), the average error in distance in percentages() and the maximum error in distance (max(d_err)).
NB. I did not take extinction into account!
So you can use these values to calculate the distance to a main sequence A or B type star.
$D = 10^{(m-M_V)/5+1}$
But as you can see the errors are quite large.
For A/B type supergiants, even the average error is more than 100%. The lowest average errors I found (25%) are for F type sub giant stars (type IV).


Keyword query string in SharePoint Search

Question: I need to create custom search web part with 3 filters. First filter will have all list names in a dropdown box. Second filter will have particular list column values(only 2 values like active and inactive) in a drop down box. Third filter will have some numeric values that is list column id in text box. Now on clicking search button i need to send query string to search result page with all these values..is this possible? Also i need to know wheather my search page can have multiple display groups for these drop down and any possiblity to add text box filter to existing search options.
Answer: I think you should go for CAML query or out-of-box filters instead of search to find items in specific lists.
If you want to use search anyhow, You can create a scope for each list and create managed property for each column to search for. Then, you can see below how to form keyword query with the properties and scopes :
http://extreme-sharepoint.com/2011/10/28/sharepoint-keywordquery/
Answer: Perhaps not an exact answer but an excellent blog post which will point you in the right direction:  http://consultingblogs.emc.com/mattlally/archive/2011/12/29/sharepoint-2010-custom-advanced-search-for-power-users.aspx. At least this should help when it comes to building up the search query.
As for your last questions they will have to remain unanswered by me.
How would the text box be used? To filter the result set? Or, in essence, changing the query string? That should be possible of course.
/Björn
Comment: I referred that link. It was useful link but in his case he had tried for same content type. Rather i want to search all content types in my site..


95 geo metro 1.0L pushing coolant out of overflow

Question: I have a 95 geo metro. Car runs good and has normal power. When car is idling it runs fine with no overheating or coolant being pushed out of the overflow. I was told to replace the water pump, thermostat, and radiator cap. I have replaced them and the problem still occurs. I do have a 50/50 mix coolant and no leaks at all. recently I have performed a compression test and found my middle cyl in 25 PSI low witch could be a blown head gasket allowing exhaust to be pushed into the radiator. I ordered a product called steel seal and followed their directions with no success. I called them back and they have sent me a second bottle to run with the spark plug out of the engine. i have ran the second bottle in my coolant and have not rechecked my compression to see if its still low. I did find my belt slipping and replaced it with no luck. the temp gauge on the dash does not show overheating but I can tell the engine does get hot only if I am driving it. if its idling it runs great with no issues. Just wondering what else could be my issue. coolant is flowing but I think I may have to replace my head gasket witch on this car does not seem to be a huge issue. A couple more things that I will be trying is making sure my radiator fins aren't bent over and restricting anything and make sure my cooling fan is spinning the right way. other then that HELP!!!!! HAHA.
Answer: This is almost surely a blown head gasket. A compression test might not even show it, especially if the leak only happens under the pressure of combustion (which is much higher than just the compression from the cylinder moving). You could get a block check kit (which works by pulling fumes from the radiator opening through pH test fluid to determine if there are combustion gasses in the coolant), but I would pretty much just assume this is a head gasket failure.
Fortunately, HG replacement is usually pretty easy on small 4-cylinder inline engines. The hardest part of doing it on my Civic was getting off the exhaust manifold. I've never worked with a Metro but I'd expect it's similar.
Answer: Thanks for the responce. I did run the steel seal with the 1 spark plugged removed for 1 hour. not only did it bring the compression back to that cyl but im not getting exhaust gasses in my coolant anymore. I recommend steel seal for any blow headgasket issues. not only do they stand behind their product IT WORKS!!!. also found the person i bought the car from put the cooling fan on a toggle switch and hooked it up backwards so it was pushing air forward witch was causing it to boil and push out the overflow. i wired it back so it pulled the air through the radiator tword the engine and it does not boil anymore. WOOOOHOOOOO. I hope this thread helps others out. GOOD LUCK!!!
Comment: Are you the OP?
Answer: I recommend always to overhaul the engine when something like this takes place and not just add sealant.
Doing so will give you another 200k miles.
The process of overhauling is not as difficult and you may think.  you will need a table grinder with a wire brush if you wan to just clean of any valves and not replace them.
Pull the engine if possible and take to car wash and spray clean.  If you have good cylinders just replace the rings and pistons. Replace the crank shaft bushings and all bearings.
You can get a overhaul kit at car parts dot com.


What is the best way to filter or otherwise manipulate the results returned by a stored procedure?

Question: Often I find myself wanting to filter or order the results returned by execing a stored procedure - for example to order the output of sp_who2 by login or CPU Time, or filter it by host name. What is the best way to achieve this?
Answer: One possible solution is to put the result set into a temp table and select from it. Here is an example for sp_who2: SQL Server: Filter output of sp_who2
Answer: I love the SMSToolpack. its a free download and lets you sort the resulting grid of any sql query you run.
On top of that, you can search the data just like searching for a text string in excel.
it helps format you SQL text and makes it look pretty so you can be proud of your SQL code and much more...
The best thing i think is it lets you color code windows to specific servers so its simple to know when you are running code on dev vs prod


Reject inference

Question: What are the most effective techniques for reject inference in the context of retail credit scoring.  Parcelling is something I use frequently... Any other approaches out there?
Comment: Nice question; well done!
Answer: Have you looked at the bivariate probit model at all?

Bivariate probit model with sample
selection assumes that the
distribution of the accepted applicant
population is different from that of
the rejected applicant population.
That is, it is assumed that
$P(default|X, rejected) \neq P(default|X, accepted)$
for some vector of
explanatory variables X of the model
predicting the default of companies.

I addition to that paper, there's an article that highlights different approaches available here: Theoretical approaches of reject inference.
It gives overviews of:

Several different parceling methods
Fuzzy reclassification
Iterative reclassification
Three-groups approach

among others.

Reject inference


Can you upgrade your habitats a second time, in dragonvale?

Question: I hate how the plant habitat only holds 500 coins. Especially when the plant dragon has one of the fastest income rates!
Answer: No. Two upgrades is all you're getting.
And pairing the high-income dragons with the lowest-capacity habitats (not counting the hybrid and epic dragons) was likely an intentional move on the part of Backflip Studios -- you can theoretically get the most money from a plant habitat, but only if you tap it once every thirty to fifty seconds.
You see the same trade-off of attention time over income in the treat farms as well -- speaking purely cash-to-food the very first treat has a better return than any of the others, but you'll need to give each farm attention every 30 seconds.
You might want to look here for a list of which dragon types and hybrids have the best earning rates, and how to breed them, but generally the bigger the habitat's capacity the slower the native dragon type earns it. (again excluding epic dragons which are really hard to get)
EDIT: A recent update allows you to upgrade "large habitats" to "giant habitats" at the low low price of 25 gems.
Giant habitats can hold more dragons and money than large ones, but even a Giant Metal habitat can still hold much less cash than the smallest epic dragon habitat. (200K versus 500K on the olympus one).
Answer: Nope; the "large" variety of each habitat type is the best there is. If you want habitats that hold more cash you'll have to level up and earn elemental habitats that hold more cash.
Answer: No, one upgrade is all you are going to get. Sorry.
I know some of them are really small like the plant habitat which only contains 500 drahon cash max. Maybe they will upgrade the game so I can. I suggest only have one plant habitat and one plant dragon, plant elements make money quickly so breed it with ice, ground or metal which have large habitats but make cash slower. You'll get the plants speed and the habitat's money.
Answer: At first it starts out as a regular plant habitat, but when you get to level 7 ( I think ) you can get a large one. Then at level 22 you can get a giant one, but it will cost 25 gems.
Answer: Yes you can called a judge habitat idk but the first one you get is the plant one near Lviv 30 and that concludes yes you can upgrade it a third time can


How to route MIDI CC #7 to instrument instead of track

Question: In Logic Pro 9, by default, the MIDI CC#7 is assigned to the volume of an instrument track.
I need to skip this assignment so the MIDI CC#7 goes directly to the virtual instrument.
How can this be done?
Answer: Use the Environment. Drop in a Fader that listens to incoming MIDI CCs and transforms them into Fader messages. Then figure out which settings will get you to your virtual instrument. You may also need a transformer to filter MIDI CC7 from hitting your sequencer input.


Lenovo Tablet A1 disable screen lock

Question: I have a Lenovo Tablet A1 and don't know how to configure the screen settings as I would like them. I want that after a certain timeout the screen dims, and/or goes black, but doesn't actually lock.
That is, right now if I choose a screen timeout the thing locks and I have to press the top power button and drag an icon across the screen -- extremely inconvenient.
I have disabled Screen Lock, but it doesn't change this aspect. I also installed No Lock, but it doesn't work on this device. So far my only half-success is to disable the screen timeout, but then it runs at maximum brightness the entire time.
I have checked many questions, and done searches, for disabling screen lock. Apparently none of these work on the Lenovo Tablet.
Answer: No Lock works for me on my Lenovo A1!

Lenovo Tablet A1 disable screen lock


How do I counter double-terran in 2v2 with zerg?

Question: The question is in the title. I play as zerg most of the time and I have almost no idea what to do against the terran marine-marauder-medic combo in 2v2. The normal 1v1 strategy (banelings, basically) doesn't seem to work against these masses.
Comment: What race is your teammate?
Comment: Go for the cheese! Send in early Zerglings or you can do Ultralisks or mutalisk harrass. Keep them confined and expand :)
Comment: if they have twice the number of marines, you will have twice the number of banelings!  so it should all work out.
Answer: What you can do is get Infestors.  Several of them would be ideal.  When the MMM mass bunch up, drop  fungal growth on them.  Then burrow your infestors so they don't take damage and spam infested marines as quickly as possible (they're cheap energy so several infestors can create a mass of them quickly).  Also, burrowed infestors can still spawn Infested Terrans.  This is also assuming you have other units with your infestors. Roaches get kited pretty easily with Mauraders but if you use fungal growth that won't happen.
If they're a heavier Maruader build with few marines then Mutalisks will be the best counter.  But don't relay heavily on them after you take out the first wave of Marauders because a smart opponent will switch to heavy marines and vikings if he sees you've gone mutas.
Comment: Wow, didn't know you could Spawn infested marines while burrowed.  Nice.
Answer: Marines in SC2 seem to be almost impossible to beat when there are enough of them, especially with marauder support, so your best chance is to destroy his supply and his reinforcements with drops, mutalisks or nydus worms while slowly killing his troops with suprise banelings (don't forget they can burrow, quite deadly if they jump out in the middle of a ball of marines) and hit-and-run tactics. Infestors work quite well, too, but if he has enough medics it will just slow him.
An MMM Ball moves relatively slowly so harassing his workers with some mutas and killing the marines that move from his base to his main unit ball should work quite well to prevent him to get enough reinforcements to fill his losses. In the worst case he has to keep half his army in his base to prevent your harass, which gives you an significant advantage at the front.
I do not recommend a frontal assault, even if you have a big ball of units yourself. It will cost a lot and then all of you just have to fill your losses and repeat from step 1. It's cheaper to hit-and-run, even if you have to sacrifice an expansion, just make sure you always have more expansions than your enemy.
Comment: The problem with this is that even if you harass the Terrans, they will just go for your base. And you're not going to win against Terran in a base-killing race, especially since Zerg tend to have fewer buildings to kill.
Answer: Obviously this depends on what your team mate is doing, you guys should be working together with scouting and communicating what the enemy is sending at you. If it's marine/marauder banelings and speedlings should definitely work if executed properly. Also infestors can turn the tide of a battle quickly. Beyond that, try to directly target the medivacs with some anti-air so that the healing support can be eliminated.
Answer: Usually the scouting in 2s is so bad you can get away with a baneling bust. If they have a solid wall (no reactors, techlabs or supply depots as vital parts of the wall) you will have to resort to hydras. The MMM ball is a whole lot more effective than your hydras but you have the macro advantage. Make sure you have one more exp than the terrans and that you spread creep everywhere. You will need that creep as the terran ball will move faster than your hydras off creep. If your macro is any good you should have a higher food count than the terran. Also mix in some infestors and fungal growth as many marines as possible.
You can't assault a tank position with hydras though. So if there are tanks you will have to resort to doom dropping to destroy their production.
It's not going to be easy, and it will feel like the terran army is a lot better. Just remember that you will have better production and more expansions.
Comment: Just out of curiosity, if the Terran makes a solid wall with no supply depots, how is he getting his units in and out of his base? Constantly lifting the barracks up and down, or sitting and waiting until Medivacs? Either way, if they've trapped themselves in their base you might as well take advantage of your map control and win the game.
Comment: In the higher levels, this is common. They build a solid wall with 2 raxes or a rax and a factory. When they the game is beyond the wall-busting stage, they can lift one and open it up.
Answer: If the other team is coordinating their bioballs, then you will need to coordinate your baneling/speedling attack.  if you mass up a bunch of blings then attack by yourself, while your buddy does the same thing a minutel later, you'll be in trouble.  if you hit at the same time, the m + m will have less chance to kill all the blings before the detonate.
Answer: You didn't mention what race your teammate plays, but my Zerg friend likes to build Infestors to prevent the endless Terran kiting. If I manage to build fast enough, I'll have psionic storm by the enemy's mid-game push which absolutely rips apart MMM since Fungal Growth prevents them from moving. It also makes it much easier to ambush them with banelings.
Answer: I play Terran at Diamond level 2v2 and I would suggest you scout properly. This way you can prevent them from getting very fast expansions. If you see them expand very fast just rush with Zerglings or/and Roaches.
If the Terran takes a fast expand, just expand more (3rd base). The key is to just "defend" until your macro kicks in. Then attack at different locations. As MMM is very slow you can usually pull back before the main force arrives.
This way Terran have to find the right timing. But if your scouting is good enough you will be more than prepared when they move out.
Also burrow 1-2 Banelings at good positions. They are forced to scan this way.
Comment: MMM is very slow?! Define slow.
Comment: Zerg units are generally faster than Terran units. Especially Speedlings and Mutas, even Roaches with speed upgrade are a faster than MMM without Stim. I suggest you make about 10-16 Speedlings if Terran expands too fast, otherwise go with 8-10 Mutas. A good tactic is to harass the main with Mutas and when he pulls his MMM ball back just attack the natural with Speedlings. As soon as you see his MMM pull back. This works agains most Terran up to Diamond, as many do not know how to split their army properly.
Answer: Easiest is Broodlords if you can get them.
Comment: usually bioballs can push before broodlords are really an option.


what is physical meaning of this partial derivative?

Question: what is physical meaning of this partial derivative:
$$\frac {\partial p_x}{\partial x}$$
i know how do i solve it when the case is just derivative but partial derivative is a bit Hectic!.
Comment: This question is lacking some context. A partial derivative is nothing but a normal derivative with the other variables taken as constants. What the physical meaning is depends on the function $p_x$.
Comment: If $p_x$ is momentum then the derivative is the spatial gradient along the `x`-axis.
Answer: A partial derivative basically tells you how a function changes if I change just one of many variables it may depend on, while keeping all other variables constant.
On the other hand, a total derivative tells you the "TOTAL" information about the function. It describes how a function changes if all (or some) variables are changed together.
When a function depends only on one variable then ALL = one variable. In this case, a partial derivative is the same as the total derivative.
Answer: If $p_x$ is taken to mean momentum in the $x$ direction, $\frac{\partial p_x}{\partial x}$ simply means that momentum in the $x$ direction changes as you move along $x$. So for an object with a given mass, $\frac{\partial p_x}{\partial x}$ describes how its $x$ velocity changes as the object moves along $x$. In everyday life, that would just be called an acceleration or deceleration, such as braking a car that is moving east, if you call east $x$.
Where partials get more complicated is that you can have several such things going on at once. More specifically, you can have other independent accelerations or decelerations going on in $y$ and $z$ (think roller coasters). Finally, for a partial derivative that is expressed in terms of momentum instead of velocity, you cannot always assume the mass is constant, so you also cannot always assume that the effects are equivalent to velocity expressions.
Answer: The partial derivative of a function $f(x_1,x_1,x_3,..)$ at a point $(k,x_2,x_3,...)$, e.g. with respect to $x_1$, is the slope of the tangent line to the curve obtained by the intersection of the plane $x_1=k$, with the plot of $f(x_1,x_2,...)$.
The partial derivative also gives the rate of change with respect to the quantity being changed. Your partial derivative would give the rate of change of the momentum in the $x$ direction with respect to change in $x$, it essentially is a measure of how the velocity along the $x$ axis, if mass is constant changes, as you move along $x$, i.e. the change in a quantity along the direction you are moving in.


Can I add two motion lights to an existing circuit?

Question: Can I use an exsisting line that feeds an outlet, and can I cut that line from the attic and use a junction box to feed power to new lights. I will be placing the ligts about 30 feet from each other.
Comment: You might have to provide a little more information. What else is on the circuit? Do you want to keep the current receptacle?
Answer: Lazy Way
Most likely the answer will be yes. Most circuits have at least a little bit of head room on them and if you plan on removing the current receptacle you will be reducing the potential load.
You could also put in some compact florescent bulbs to reduce your overall power usage on that circuit, but I would still recommend making sure you have enough head room on your breaker even if someone puts in more powerful bulbs.
There is a good chance you will never have a problem, but if you want to make sure everything is fine, read on.
Proper Way
You would need to start out by figuring what else is on the breaker. The simplest way to do this is to flip on all of the lights in the house, then turn off the breaker. Walk around to see what turned off and make a note of what all turned off. You will also need to check the outlets. You can buy an outlet tester, or you can just take anything that plugs in, like a radio or a lamp, and walk around to every outlet to see which ones are no longer on. Count the number of outlets that you see.
Basically what you are looking to do is add up the max current that you expect the circuit would ever need. So for lights, look to see what the max wattage bulb you can place in the socket. You can find out the current it pulls by using current = power / voltage. Then for outlets think about what all could be running at once on it, vacuum? tv? etc. Add all of those up, then just make sure you are still under the current rating for your breaker.
This question, Is there an average number of outlets that are wired off of one circuit breaker? , talks a little bit about how many outlets you can reasonably place on a single circuit.


Cutting phase: indicators for muscle loss

Question: I want to cut for a while and lower my fat percentage. As everybody I want to maximize fat loss and minimize muscle loss. Are there any warning indicators that my body is burning muscles instead of fat? What is the best way to avoid it? Should I eatless proteins than in bulking phase? Should I keep doing the same strength exercises with the same weight?
Comment: Could you narrow this question down to something more specific than "how do I cut?"
Comment: I just highlighted the main question
Comment: "How do I cut" is actually a whole lot less specific than this question, even tho easier to answer. I personally like the question in its current form and Im also interested in symptopms that could indicate im burning my muscles isntead of fat.
Answer: The body can use about 31.4 Cal / lb of fat / day. This key statistic tells you a lot about your maximum rate of fat loss, because fat loss only happens when the body is using calories from your fat stores.  There is thus a maximum rate of fat loss, and that rate is dependent on how much fat you have.
If you have 25 lbs of fat on your body, then you can metabolize about 31.4*25 = 785 fat Calories per day.
Meanwhile, a pound of human fat tissue is estimated to store about 3500 Cal. It might be a little higher or lower, but that is the number that is frequently thrown around.
If you estimate your weekly fat calories at 785*7 = 5495 Cal/week, and divide that by 3500 Cal/lb, then you get a maximum fat loss rate of about 1.57lb/week.
To avoid muscle loss, you should never run a deficit greater than what your body can make available from fat, or else you are guaranteed to lose muscle just to stay alive. Beyond that, you should train with weights and eat a high protein diet in order to prevent catabolism - the breakdown of muscle. Small and frequent meals to keep insulin levels constant is also believed to help. Another technique which is suspected to help but hasn't been proven is increasing your free testosterone, such as with a zinc supplement, or by abstaining from masturbation.
The obvious indicator that you're losing muscle is that your muscles get smaller and weaker. I don't know of any others.
Comment: Abstain from masturbation? There goes my cardio... ;-) Thanks Mason, this is very informative.
Comment: Don't knock it till you've tried it :)
Comment: @user41956 You might want to read the question [effect of masturbation on gym workout to gain muscle](http://fitness.stackexchange.com/q/9910/3941). (There is a similar one but I can't find it)
Comment: That's all BS. Debunk incoming when I get home. @informaficker
Comment: @masonk Looking forward to it :) [this](http://fitness.stackexchange.com/q/2640/3941) was the other question I was talking about, it actually was linked in the other one.
Comment: Done! Go vote me up :)
Answer: One point I should mention is that the 'bulking & cutting' method to building muscle is actually quite an inefficient one. Not that it doesn't work, it does and has done for decades but it is far easier for the body for you to eat sensibly but not intensely strict for 12 months a year than it is to pig out for 6-8 months and then cut for 3-4 months.
The 'bulking' phase of muscle building as you are aware, usually involves ingesting extreme excesses of calories. Now, unless everything you eat is basically steak, eggs, chicken for example and wholegrains & veg, then it is going to be hard to not put on excess fat. Your body can only synthesis muscle so quickly. No matter how many calories you eat or protein you eat, there will be a point when the body physically cannot build anymore muscle and when this point is reached, it will convert excess calories as fat.
By bulking, you are also then losing the amount of muscle you can gain in a year as you then have to spend several months 'cutting' which is essentially dieting. Real strict eating restricting calories is going to hinder muscle building. It may help you burn a lot of fat, but it isn't beneficial to continue building muscle. You may still be ingesting more calories than you are burning but after a significant period of bulking, high insulin release, fat cell hyperplasia (the expansion of fat cells due to extreme eating) then it will be really hard to build muscle, whilst you cut enough calories and consume enough nutrients to encourage muscle growth. It's not impossible, not at all, but it makes it more difficult.
You're honestly really better just addressing your diet all year round and having treat food every now and then and a couple cheat meals a week and just maintaining an excessive calorie intake but not going 100% bulking and then 100% cutting. Two extremes are difficult for the body to adjust to and means you have to waste time burning fat when you could be building muscle. Unless you're a bodybuilder and looking to compete, then bulking and cutting isn't really the best way to get in shape. There is a host of scientific reasons you should avoid this method but I won't bore you with them.
But if you have bulked, then a very high protein diet is the best way forward (higher than you would usually consume). Protein contains the least calories per gram in 4 compared to 7 & 9 in carbs and fat respectively. Protein is also a food that is difficult to break down and digest in the body and has been shown to enhance the body's metabolism due to the effort it takes to break down etc. although that is a very simplistic look at the whole process. It's best to work out your lean body mass in pounds (use a bio-impedance scale for a good measure) and consume between 1-1.5g of protein per pound of lean muscle mass. Keep wholegrain carbohydrates to the size of a clenched fist and then pack up on veg. to get your vitamins etc. Obviously not forgetting water! Cut down your sugar intake a lot too and increase your fat intake through butter, whole milk, natural Greek yoghurt etc. consuming naturally occurring fats stimulates the release of Glucagon, a hormone that stimulates the body to BURN fat and things like milk and yoghurt are usually high in protein too! While it is true that Insulin is important to increase muscle growth, insulin is also the primary hormone that stimulates fat storing and seeing as insulin isn't the most important part of building muscle, I'd focusing on reducing the secretion of it.
One other tip is regular HIIT. Cardio is another inefficient way to burn fat etc. but mainly it trains slow oxidative muscle fibres which are the less bulky fibres such as on distance runners like Mo Farrah. By doing high intensity exercises like sprints etc. you are stimulating the Fast Oxidative/Fast Glycolytic fibres which are the bulkier muscle fibres associated with sprinters and bodybuilders! By doing sprints etc. you are building bulkier muscles and burning the same number of calories in a shorter space of time!
You can build muscle by bulking and cutting, but it is a lot easier for the body to just continuously build muscle year round! I've not gone into the hormone responses to exercise/bulking/cutting but if you want any info or any studies to back up what I said then feel free to ask! Sorry that turned into a bit of an essay!
Comment: Nice answer, I can agree on almost all points. You do show a one-sided view of bulking, though, almost ignoring the idea of a more moderate bulk. Or at least the second paragraph reads like that, with 'extreme excesses' and such. Just wanted to point out, GOMAD and 4 Big Macs a day is not the only possible way of bulking. Also, your answer doesn't really answer the whole question (what are the signs of muscle loss when cutting?).
Answer: Stumbled upon this late, but, there's actually an indirect way of guesstimating that muscle is being catabolized.  I'm probably going to show my age in this question, but, back in the "old" bodybuilding days, we would use Ketostix to check the urine for the presence of Ketones.  Ketosis indicates a high level of ketones in the body.  Ketones appear in the urine when there is an insufficient supply of carbohydrates available for energy.  Fat is then used to provide the energy slack.  However, if fat stores are low, as would be the case for someone in a "cutting" phase, the next choice for energy would be lean protein (eg. muscle).  It's a fine line to walk to make sure you have enough carbohydrate to maintain energy, while at the same time, trying to reduce calories to reveal muscle.
Comment: One problem with this is that both protein and fat produce ketones when metabolized. So all it really tells you is that you're actually losing weight. AFAIK, it can't help you know which you're burning.


Do you read scripts?

Question: No matter what your role is (boom, recordist, dialogue editor, sound editor, rerecording mixer etc) on a film (short, long or otherwise) do you read the script before starting?
Answer: As a sound editor/designer for film and broadcast, I make sure I do everything I can to get a script in my hands, no matter how early in the process it is.  Before meeting about the film, I make sure to have read the script more than twice, and make notations all over it - ideas about the sound and how we can treat and add to the scenes through sound.  Additionally, if I'm working with a vet director, I will often view a few of his/her films prior to our first meeting, if not only to be able to bring up some specifics about the soundtrack in comparison to the script we're discussing.
I had a director decide to work with me because of all the sound editors he spoke with, only one actually read through and was ready to share ideas about the film (me).  The others were initially only concerned with budget and time, and brought no creative ideas to the table at that point.
That film turned out to have made the final 10 cut for an Oscar nomination (but unfortunately did not make the final cut).  That film put me on a stage at Skywalker working with Gary Rizzo and Richard Hymns.  That film put me in the Stag Theater watching our film next to Gary Rydstrom and behind Gwen Whittle.
I'm not bragging.  I'm saying that I went the extra mile and it paid off in ways I would have never dreamed of.
If we don't make a big deal about getting a script and meeting with the director prior to working together, then I think we're often overlooked as a creative part of the process.  We all have worked with people who don't want/need the creative input, or simply regard sound as a supporting creative role.  Make a big deal of yourself and the work you do.  Doesn't matter if you play a role in production or post-production.  Make a big deal.
Answer: If I get a copy of the script, I read it, always! Not to read it would be inpolite, and it is the best way to prepare you for the work ahead.
If I am only working as supervising sound editor / sound designer / re-recording mixer, and the film is already in editing, I am not always presented with a copy of the script, but with a rough cut of the film instead. In this case I am not asking for the script, but normally I am contacted before they shoot the film, and so I get to read the script.
Answer: Sometimes, when you're operating the boom mic and there's only one used in a dialogue, It's highly recommended that you read it so you know how u'll need to move it. So you find out when actor 1 line's over so that you can turn it and capture the actor 2's line.
At least in Brazil, where the independent production's budget is always low, you MUST be aware of that kind of stuff. We usually have only one mic here. About me, I had my 3 meals today, don't worry. LOL :)
Answer: Yes, I always read the script...at least once.  On the day of the shoot I like to have it handy, though usually you get given "Sides"...the pages out of the script scheduled to be shot that day, which I refer to prior to shooting a scene.  I sort of memorize lines roughly and try to be there for every rehearsal the actors and director may have.  It helps you prepare your boom movements, which mics to use, decide on the ambient sounds you may wish to capture and stuff like that.
It also tells you (as a boom swinger) just how long some scenes are going to be and you can prepare yourself for them!  :)
Answer: Speaking from a purely post production point of view I always prefer to read a script beforehand. I think it helps in a variety of ways, some aesthetic and some practical. It enables me to source difficult or specific sounds before production has started for example.
I also find it helps get a feel for a film/series, especially in animation where the editing is often more an assembly and probably wont be straying too far from the script.
If nothing else it can help start a dialogue between you and the Director/Producer which we all know is best to start as early as possible to ensure you're all on the same page from the off.
Answer: Absa-frickin-lutely.
Answer: I find the script essential and sometimes where available the story board (especially if i'm working on an animation project)
At present on the project i'm working on, without the script I'd be a bit lost as i'm editing the dialogue as well as designing and until I have been working on the film for a couple more weeks it helps immerse myself with the characters. It also helps me communicate more with the director in terms of specific sound design placements as we can talk the same language in terms of reference points and we're on the same page..
Before starting I was lucky to obtain the script and read it thoroughly before starting, kinda gives you a head start.
Answer: Yes, I do if there is one available when recording or boom swinging. In narrative style film making this is always a must. I also generally ask for sides for each day as well, especially on a shoot where the director/writer/producer keep changing up the dialogue.
Answer: I only recently started reading scripts -- thanks to my wild notion of writing my own movies simply so I can do sound for them -- and I wish it was mentioned earlier.  Scripts are invaluable.
On an unrelated note, I just started building mind-maps of things I can record at my work and at my house, so I plan on going through scripts and doing this per-scene, as well.
Answer: For me it depends on what the state of the film is. Often when directors or producers get in touch with me for sound editing, they'll already be editing or even picture locked. In this situation, I don't ask for the script - the film has already been shaped in editorial and is not the same film that the script envisioned.
If a project is brought to me in its pre-production stages, I will read the script carefully in order to understand what will be required from the sound department. If I'm handling production sound, there will inevitably be things that I find I'll need to prepare for - fight scenes, "live" performances that I'll insist to the director should be performed to playback, etc.
If I'm still only doing post sound work, it's useful to read the script in pre-production to decide out what major elements of the soundtrack will be need to be recorded in post and what has to be captured during production. Recently, I was working on a short film that was funded by Toyota Japan and featured the Toyota Mark-X, a car that physically does not exist in Los Angeles (where I'm based). I stressed to the director how important it would be that the production sound crew record great production tracks and wild sound FX for the car, and things worked out pretty well in the end.
Comment: "they'll already be editing or even picture locked"

you realise part of your job is to then educate them why that is not the best scenario? "If I had been onboard before you shot I could have...." etc etc

Do you read scripts?


Turtle-watching in Costa Rica and Panama in April

Question: Where can I watch the turtles lay their eggs in Costa Rica and Panama in the second half of April? I am mainly interested in places that are accessible by car (4x4 is fine).
Answer: There are at least 2 tours that I could find that could fit your criteria:
Undiscovered Carribean
and
LeatherBack Volunteer Vacation
I am sure that you could probably get to those beaches on your own if you choose to but I think these would be better.  There is actually a whole slew of tours just like those at SeeTurtles.org
EDIT
More on Turtle Watching in Costa Rica
And Even more on Turtle Watching including a map
And with the best map I could find
Answer: We ended up watching the leatherback turtles on the Gandoca beach. This was organized through an agency in Puero Viejo de Talamanca (I can't remember the name of the agency). I can certainly recommend this option, and after reading more about turtle watching I think it is actually get by far the highest probability of success in April.


Ubuntu 12.10 won't upgrade nVidia Drivers

Question:
Possible Duplicate:
There's an issue with an Alpha/Beta Release of Ubuntu, what should I do?

I've been running 12.10 for about a week now with pretty minimal issues so far; the main problem I'm experiencing is that the nvidia drivers I have are refusing to upgrade. I'm currently using the experimental drivers, so I'm not sure if that has anything to do with it. Either way, I was hoping to see if anyone could make any sense of this output:
From apt-get upgrade:
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following packages have been kept back:
  linux-headers-generic linux-image-generic ubuntu-desktop
The following packages will be upgraded:
  nvidia-settings-updates
1 upgraded, 0 newly installed, 0 to remove and 3 not upgraded.
308 not fully installed or removed.
Need to get 0 B/1,820 kB of archives.
After this operation, 1,675 kB of additional disk space will be used.
Do you want to continue [Y/n]? y
(Reading database ... 207320 files and directories currently installed.)
Preparing to replace nvidia-settings-updates 304.43-0ubuntu1 (using .../nvidia-settings-updates_304.51-0ubuntu1_amd64.deb) ...
Unpacking replacement nvidia-settings-updates ...
dpkg: error processing /var/cache/apt/archives/nvidia-settings-updates_304.51-0ubuntu1_amd64.deb (--unpack):
 trying to overwrite '/usr/share/man/man1/nvidia-settings.1.gz', which is also in package nvidia-settings-experimental-304 304.48-0ubuntu1
No apport report written because MaxReports is reached already
                                                              dpkg-deb: error: subprocess paste was killed by signal (Broken pipe)
Processing triggers for man-db ...
Errors were encountered while processing:
 /var/cache/apt/archives/nvidia-settings-updates_304.51-0ubuntu1_amd64.deb
E: Sub-process /usr/bin/dpkg returned an error code (1)

What would be the solution to this? I already tried an apt-get clean along with a apt-get -f upgrade after, and that didn't solve the problem.
Answer: nvidia-settings-updates and nvidia-settings-experimental are two version of the same software, you shouldn't use them both at a time, or you'd get an error as above. Uninstalling one of them should be fine.


Video game sound design

Question: Anyone recommend a specific sound design program or certificate or anything like that, that will help me prepare for video game sound design?
Answer: if you want to explore the technical aspect of game audio and make sure this is for you, grab a copy of Fmod or Wwise, get to know the concepts and start thinking. Of course, passion for games is a must, but game sound is as much about sound as it is about hacking. You can expect to work with other content people but also programmers and they have their own ways... mindset is not only important but gets a bit more specific on these projects... I agree with Ryan, it's entirely possible to be self-taught, but education can give you flying start and hook you up re work experience and such...
Comment: You can download wWise for free from the Audiokinetic (http://www.audiokinetic.com/en/products/wwise/introduction) website (free if you use it for non-commercial products). It's a good way to start to learn the software without having to pay anything...
Answer: I don't know of any certificate that would really help in being prepared for Game Sound Design. What does matter is a complete knowledge on the topic of audio in general, and a passion for non linear sound design.
You need to be educated and experienced in microphone techniques and recording, in hardware and software routing and processing, in acoustics and computer science as well.
I would be skeptical of any educational program that was based around sound design as a topic, before the world of sound and production were addressed correctly first, unless it was a graduate level program. At the beginning, you should find something that teaches every aspect of sound production, and focus your practice and skills towards Game Sound along the way.
A good deal of indy level game sound will go along way. There is nothing to replace actually doing and practicing the craft. Get on a mod team, and put your heart and soul into the process. Make your sound design unique and original, and practice implementation as often as possible.
Good audio schools are very expensive, and do not guarantee you a job in the industry. However, the amount of information that you need to be a solid audio producer often goes beyond what you could possibly teach yourself.
Have you taken a shot at any production yet?
Answer: The IASIG has been working on something. But it's not going to be "out" for a while.
Answer: They've got some good classes at Berklee with Jeanine Cowan teaching. Besides game sound, you should have a strong background in audio in general, music theory, psychoacoustics, etc. I agree with others that playing games and listening is crucial to your preparation, but also listening to your real world and understanding what makes your own acoustic universe function. Then learning the technical aspects will give you tools to do it yourself. I'm giving a free intro webinar Aug. 24 that will include a lot of this, not specifically for games but for all audiovisual. Check it out SoundDesignForPros.com.
Answer: Get on a game mod, or swap out the sounds of an existing game (I still use Doom editors for this, even though Doom's 16 years old.)  It really helps to hear your sounds in a game environment, to see if they all mesh well together.  I'm not sure about WWise, but FMOD has in-game emulation, but I feel it doesn't do it justice until you can experience it as a player.

Video game sound design


Back Gears Clicking

Question: I've got a ten gear cassette in the rear and the top gear is fine.  But, if I'm in my next four or five gears before the top gear I get a clicking noise of the type you get when you shift and it doesn't quite make it to the next gear.  The noise is worse if I'm in my lower gear up front.  Also, shifting down in the rear is a little wonky.  It is a Fuji Cross Comp.
Comment: Has the bike been adjusted recently?  You may simply need to have it "tuned up".  And, especially in the first few hundred miles, the cables stretch a bit, and you need to use the "barrel adjuster" to compensate -- something you should learn how to do.
Answer: If the chain is running smoothly in the top gear (the smallest sprocket) but it runs poorly in the larger sprockets then it is most likely that the cable tension is too loose.  The cable tension pulls the chain onto the larger sprockets.  Insufficient tension means it won't change cleanly on to them (which I think is what is meant by changing 'down' a gear) and even when the gear has changed the derailleur won't be aligned properly and the chain will be noisy.
The reason the smallest sprocket works OK is because the position of the derailleur is limited by one of the adjustment screws at that extreme.
The most likely cause has been given by Daniel R Hicks' comment above "in the first few hundred miles, the cables stretch a bit".
You can tighten the cable by turning the cable adjuster anticlockwise.  Use small changes as these 10-speed systems are very sensitive.
If you can't find the sweet spot with the adjuster then it is also possible that the derailleur has got knocked and is no longer aligned properly.
Answer: You are just cross chaining. Bicycle drive trains are designed so that if you are in your small chainring, you should be in one of the larger sprockets, and vice-versa. The chain is meant to be relatively parallel to the center line of your frame. When you deviate too much from this, the chain will rub on the derailleur. Cross-chaining is advised against because it increases wear, and you likely have a similar ratio with a different combination. It's not so bad to do it once in a while though.
Your front shifter may have a trim setting, which is kind-of a half-click between the main gears. This is a setting so that you can move the derailleur a little so that the chain won't rub when you are cross-chaining.

Back Gears Clicking


What mapping software can print large battlemaps for RPGs?

Question: Years ago, I used Dundjinni to create battlemaps for the RPG game that I ran. However, each individual map was restricted in size such that it corresponded to the size of a piece of normal 8.5" x 11" paper, and this meant I had to create a bunch of different maps, eyeballing them so that they'd be able to be printed separately and then joined up, which was frustrating and also required taping the map pieces together if I wanted to lay out a full dungeon level, or even just a large room. The software gave me very nice looking maps but simply couldn't create maps of the size I wanted.
I've got access to a large plotter at work which allows me to print out full-sized battlemaps (a little over 3' wide, however long I want). So far I've used a workaround where I convert maps to images, join all the images together in something like Paint, then print that image out to the plotter, but even this requires a lot of trial and error to get the scale right so that 1 square = 1 inch. I'd rather just find some mapping software that would handle all this for me.
Something like Dungeongrapher is a nice mapping utility and useful for creating dungeon maps like you'd find in a module, but is a little too basic and colorless for the types of battlemaps I want. I want full color with nice art so that when I set it on the table and plop the minis down, it really comes alive.
Is there any mapping software out there that supports creating full-color, detailed battle maps of large size such that they can be printed on a plotter?
Answer: The ProFantasy Suite supports custom grid dimensions, and is generally full-featured with good-looking assets. The downside is that it's quite expensive – $40 for the dungeon designer alone.