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# Elementary Proof of Nakayama's Lemma?
Nakayama's Lemma is as follows: Let $A$ be a ring, and $\frak{a}$ an ideal such that $\frak{a}$ is contained in every maximal ideal. Let $M$ be a finitely generated $A$-module. Then if $\frak{a}$$M=M, we have that M = 0. Most proofs of this result that I've seen in books use some non-trivial linear algebra results (like Cramer's rule), and I had come to believe that these were certainly necessary. However, in Lang's Algebraic Number Theory book, I came across a quick proof using only the definitions and induction. I felt initially like something must be wrong--I thought perhaps the proof is simpler because Lang is assuming throughout that all rings are integral domains, but he doesn't use this in the proof he gives, as far as I can see. Here is the proof, verbatim: We do induction on the number of generators of M. Say M is generated by w_1, \cdots, w_m. There exists an expression$$w_1 = a_1w_1 + \cdots + a_mw_m$$with a_i \in \frak{a}. Hence$$(1-a_1)w_1 = a_2w_2 + \cdots +a_mw_m$$If$(1-a_1)$is not a unit in A, then it is contained in a maximal ideal$\frak{p}$. Since$a_1 \in \frak{p}$by hypothesis, we have a contradiction. Hence$1-a_1$is a unit, and dividing by it shows that$M$can be generated by$m-1$elements, thereby concluding the proof. Is the fact that$A$is assumed to be a domain being smuggled in here in some way that I missed? Or is this really an elementary proof of Nakayama's lemma, in full generality? - Is Cramer's rule really non-elementary? In any case, this is a complete proof. It also appears in many other places (eg it is the "second proof" of Nakayama's lemma in Atiyah-MacDonald). – Andy Putman Oct 11 '10 at 21:15 The Cramer's rule proof does give a little more. If we drop the assumption that$\mathfrak{a}$is contained in the Jacobson radical it shows that$\mathfrak{a}M=M$implies that$M$is annihilated by a ring element congruent to$1$modulo$\mathfrak{a}$. – Robin Chapman Oct 11 '10 at 21:19 I was always confused that people use the Cramer's rule proof too. Not only does this proof not use that$A$is a domain, but it doesn't even use that$A$is commutative! – Anton Geraschenko Oct 11 '10 at 21:19 ## 1 Answer There are various forms of the Nakayama lemma. Here is a rather general one; note that it does not involve maximal ideals and is a constructive theorem (Atiyah-MacDonald, Commutative Algebra, Prop. 2.4 ff). Let$M$be a finitely generated$A$-module,$\mathfrak{a} \subseteq A$be an ideal and$\phi \in End_A(M)$such that$\phi(M) \subseteq \mathfrak{a} M$. Then there is an equation of the form$\phi^n + r_1 \phi^{n-1} + ... + r_n = 0$, where the$r_i$are in$\mathfrak{a}$. The proof uses the equality$adj(X) \cdot X = \text{det}(X)$for quadratic matrices over a ring. I call this an elementary linear algebra fact. Of course, there you only prove it for fields but using function fields implies the result for general rings. If we take$\phi=\text{id}_M$, we get the following form: Let$M$be a finitely generated$A$-module and let$\mathfrak{a} \subseteq A$be an ideal such that$\mathfrak{a} M = M$. Then there exists some$r \in A$such that$rM = 0$and$r \equiv 1$mod$\mathfrak{a}$. In particular, we get: Let$M$be a finitely generated$A$-module and let$\mathfrak{a} \subseteq A$be an ideal such that$\mathfrak{a} M = M$and$\mathfrak{a}$lies in every maximal ideal of$A$. Then$M=0$. Observe that this argument uses Zorn's lemma (namely that every non-unit is contained in a maximal ideal) and is thus nonconstructive. Which is of course not surprising since without Zorn's lemma it is consistent that there are nontrivial rings without any maximal ideals at all. This should convince you that the first form of the Nakayama lemma is the most easy and elementary one. The last form has another short proof, which is standard and given in the question above. Here is another short well-known proof for the last form, which also works if$A$is noncommutative (then we have to replace "maximal ideal" by "maximal left ideal"): Assume$M \neq 0$. Since$M$is finitely generated, an application of Zorn's lemma shows that$M$has a maximal proper submodule$N$. Then$M/N$is simple, thus isomorphic to$A/\mathfrak{m}$for some maximal left ideal$\mathfrak{m}$. Then$N = \mathfrak{m} M = M$, contradiction. By the way, I don't know if the first form is true if$A$is noncommutative. The theory of determinants is not really prosperous over noncommutative rings. Hints? In many texts about algebraic geometry only the last form of the Nakayama lemma is needed. But the first one is stronger and is used in many results in commutative algebra. - Thanks, this is helpful. – Phillip Williams Oct 12 '10 at 0:00 Very nice, Martin. – Hailong Dao Oct 12 '10 at 0:20 The first form is not true if$A$is noncommutative. To see an example, note that we can use the first form of the result to prove the following fact: If$R$is a ring such that the first form holds for$R[X]$, then any finitely generated$R$module is Hopfian (i.e. any epic map is injective). This follows from applying the result given above to$R[X]$, with$X$acting as your surjective map. A corollary of this fact is that rings for which the first form hold satisfy the Invariant Basis Number property -$R^{n}\cong R^{m}$iff$m=n$. Tragically, there are rings which do not satisfy IBN. – Rishi Vyas Oct 12 '10 at 19:13 @Tim: ? Since$M=\mathfrak{a} M$, the coefficients may be chosen in$\mathfrak{a}\$. There is no lack at all. – Martin Brandenburg Oct 15 '10 at 5:38
I don't understand your problem in Atiyah's proof. – Martin Brandenburg Oct 17 '10 at 14:59
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Differentiate the following functions:
Question:
Differentiate the following functions:
(i) $4 \cot x-\frac{1}{2} \cos x+\frac{2}{\cos x}-\frac{3}{\sin x}+\frac{6 \cot x}{\operatorname{cosec} x}+9$
(ii) $-5 \tan x+4 \tan x \cos x-3 \cot x \sec x+2 \sec x-13$
Solution:
Formulae: –
$\frac{d}{d x} \cot x=-\operatorname{cosec}^{2} x$
$\frac{d}{d x} \cos x=-\sin x$
$\frac{d}{d x} \sec x=\sec x \tan x$
$\frac{d}{d x} \operatorname{cosecx}=-\operatorname{cosec} x \cot x$
$\frac{d}{d x} \tan x=\sec ^{2} x$
$\frac{d}{d x} \sin x=\cos x$
$\frac{\mathrm{d}}{\mathrm{dx}} \mathrm{k}=0, \mathrm{k}$ is constant
(i) $4 \cot x-\frac{1}{2} \cos x+\frac{2}{\cos x}-\frac{3}{\sin x}+\frac{6 \cot x}{\operatorname{cosec} x}+9$
$=4 \cot x-\frac{1}{2} \cos x+2 \sec x-3 \operatorname{cosec} x+6 \cos x+9$
Differentiating with respect to $x$,
$\frac{d}{d x}\left(4 \cot x-\frac{1}{2} \cos x+2 \sec x-3 \operatorname{cosec} x+6 \cos x+9\right)$
$=4\left(-\operatorname{cosec}^{2} x\right)-\frac{1}{2}(-\sin x)+2 \sec x \times \tan x-3(-\operatorname{cosec} x \times \cot x)+6(-\sin x)+$ 0
$=-4 \operatorname{cosec}^{2} x+\frac{1}{2} \sin x+2 \sec x \tan x+3 \operatorname{cosec} x \cot x-6 \sin x$
(ii) $-5 \tan x+4 \tan x \cos x-3 \cot x \sec x+2 \sec x-13$
$=-5 \tan x+4 \sin x-3 \operatorname{cosec} x+2 \sec x-13$
Differentiating with respect to $\mathrm{x}$,
$\frac{d}{d x}(-5 \tan x+4 \sin x-3 \operatorname{cosec} x+2 \sec x-13)$
$=-5 \sec ^{2} x+4 \cos x-3(-\operatorname{cosec} x \cot x)+2 \sec x \tan x-0$
$=-5 \sec ^{2} x+4 \cos x+3 \operatorname{cosec} x \cot x+2 \sec x \tan x$
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$$\require{cancel}$$
# 2: Foundations
• 2.1: Causality
Our intuitive belief in cause-and-effect mechanisms is not sup- ported in any clear cut way by the laws of physics as currently understood. For example, we feel that the past affects the future but not the other way around, but this feeling doesn’t seem to translate into physical law. For example, Newton’s laws are invariant under time reversal, as are Maxwell’s equations. In fact, the weak nuclear force is the only part of the standard model that violates time-reversal symmetry.
• 2.2: Flatness
Euclidean geometry is only an approximate description of the earth’s surface, for example, and this is why flat maps always entail distortions of the actual shapes. The distortions might be negligible on a map of Connecticut, but severe for a map of the whole world. That is, the globe is only locally Euclidean. On a spherical surface, the appropriate object to play the role of a “line” is a great circle. The lines of longitude are examples of great circles.
• 2.3: Additional Postulates
We make the following additional assumptions.
• 2.4: Other Axiomatizations
Einstein used a different axiomatization in his 1905 paper on special relativity.
• 2.5: Lemma - Spacetime area is invariant
The area in the x−t plane is invariant, i.e., it does not change between frames of reference.
• 2.E: Foundations (Exercises)
Thumbnail: Einstein cross: four images of the same astronomical object, produced by a gravitational lens. Image used wtih permission (Public Domain; NASA and ESA).
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# Lie Brackets of Nilpotent Lie Algebras
Suppose I have the Heisenberg group H say over the $p$-adic integers $\mathbb{Z}_p$, which is the set of $3\times 3$ uni-upper-trianglar matrices over $\mathbb{Z}_p$ . Its Lie algebra $h$ is the set of all $3\times 3$ strictly-upper-trianglar matrices over $\mathbb{Z}_p$.
The commutator relations of the presentation of $H$ carry over exactly to give the Lie bracket for $h$. My question is: does this hold for any arbitrary nilpotent Lie group G in place of the Heisenberg group?
-
$\newcommand\Lie{\mathrm{Lie}}$If we endow the Lie algebra $\Lie(G)$ of a unipotent algebraic Lie group $G$ over a field of characteristic zero with the product given by the Baker-Campbell-Hausdorff formula —it thereby becomes a Lie group— the exponential map $\Lie(G)\to G$ becomes an isomorphism.
This is what you are seeing in the case of the Heisenberg group. Since its nilpotency index is $2$, the B-H-C series collapses to a very short Lie polynomial.
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# How to draw the derivative on the graph?
Apr 21, 2018
The value for $x$ for which $y = f \left(x\right)$ has a stationary point is the value of $x$ at which $f ' \left(x\right) = 0$.
#### Explanation:
The tangent at a point on the Graph of $f \left(x\right)$ gives the value of Derivative at that point.
But here directly the graph of $f ' \left(x\right)$ is given and not of $f \left(x\right)$ which makes this problem simpler.
So here in first graph the stationary points are $- 1 , 1 , 5$
and in the second graph the stationary points are $0$ and $2$.
For first graph :
$x = - 1$ is the Point of Inflection ,
$x = 1$ is a point of Local minima
and $x = 5$ is a point of Local maxima.
For second graph :
$x = 0$ is a point of Local maxima
and $x = 2$ is a point of Local minima.
For your reference see this pic given below :-
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### Andy Bohn
Cornell physics graduate student, studying merging black holes, board games, and barrel strength whiskey.
Email
# Gravitational lensing
First things first… High res movies!
An interesting prediction of general relativity is that light does not just travel in a straight line, but its path is bent by gravity. Gravitational lensing is the name for the bending of light by gravity, as the source of gravity (e.g. a galaxy) acts as a physical lens which bends the light. There is ample observational evidence of these deflections of light by massive bodies, including measuring the deflection of starlight passing near the Sun. However, the largest observed deflection of light is only very slight, around 11 arc seconds or 0.003 degrees.
The SXS Lensing group is interested in much more eXtreme deflections of light. Near black holes, the most compact objects in the universe, light can be so strongly bent by gravity that it can orbit many times around the black hole before making it to your eye. In theory, there is no limit to the number of times a light ray can orbit the black hole. Even though black holes emit no light themselves, their effect on light passing nearby leads to some stunning visual and mathematical results!
### Single black hole
We have written code to produce images of stars from a star catalog, such as the 2MASS catalog. We take each star’s location and its magnitude in different color bands from the catalog. To generate the image, we need to know from where light enters each pixel of the camera as well as the redshift of the light. More details are provided in our paper. Below is an image showing the Milky Way using our star rendering code. Note that we do not use any raster images, we are simply rendering many stars to produce all the light in this images.
With our camera pointing in the same direction as the previous image, we now see how a black hole affects light from these stars. The first feature that pops out is a large circular shadow in the center of the image. This is called the shadow of the black hole, because it is a region where the black hole prevents light from reaching the camera, such that the black hole is casting a shadow on the image.
Near the borders of the image, light from the stars is slightly deflected. Notice the dark patches where there aren’t many stars in the lower right portion of the original image. These appear to be located near the lower right corner of the image now, due to the gravity of the black hole. This is analogous to the light being deflected around the sun, making a star’s apparent position somewhere else, as depicted earlier.
Light passing closer to the shadow is being deflected even more by the black hole. There is a large ring structure around the shadow called an Einstein ring. This is where light from directly on the opposite side of the black hole is deflected around the hole on its way to the camera. It makes a ring due to the symmetry, but we even see such a ring in cases where the black hole has spin. Roughly in the center of the original image, there is a bright blue star near an orange one. This is almost directly behind the black hole, so it is very close to the Einstein ring. You may have noticed that we can see two images of both of these stars, one at about 1:30 inside the Einstein ring, and one at about 7:30 on the outside of the ring. In fact, inside the Einstein ring, we can see an image of the rest of the galaxy! Light from behind the camera, for example, can take a path halfway around the black hole on the way to the camera.
Although it is hard to see, very close to the shadow there is a bright ring. This is actually the second Einstein ring, corresponding to light from directly behind the camera. In fact, there are an infinite number of these Einstein rings in theory, but we can only resolve two of them in this particular image.
### Binary black hole
While lensing by a single black hole has been studied for quite a long time, no one had previously known what astrophysically interesting binary black holes would actually look like. The problem is complicated significantly by having to solve what happens to two black holes orbiting each other. The SXS collaboration uses the Spectral Einstein Code (SpEC) to simulate these kinds of compact object mergers, be it with black holes or neutron stars with high accuracy. With SpEC, the SXS Lensing group is in a unique position to explore what a binary black hole merger would look like.
In the following video, we see the last three orbits of a three to one mass ratio binary with arbitrarily chosen spins on both black holes. The details of this merger can be found in Taylor et al. as case 4. The stars used are the same as the ones used in the single black hole image above. The camera is located above the orbital plane of the binary looking down.
Or see the high res video here: high resolution
We see an Einstein ring surrounding both masses. This is not general, however. When the black holes are separated by a large distance spatially, we could see an Einstein ring around each black hole individually. Near both shadows we see a smaller shadow, which is called an eyebrow due to its shape. These secondary shadows correspond to one black hole casting a shadow which is lensed by the other black hole on the way to the camera. Our paper explores these smaller shadows in more detail, finding that there are in fact an infinite number of these shadows, but we can only resolve a few in this video.
After the merger, the shadows transition to a single shadow and the background deflections settle to a stationary state which looks like the lensing by a single black hole. This matches our expectations. After black holes have merged, there is a ringdown phase, where energy is radiated from the black hole until it settles to a stationary single black hole solution.
We have another viewpoint of this merger, shown below. The opening angles of the cameras were slightly different for this video, so we also provide what the background stars would look like with these new parameters.
Or see the high res video here: high resolution
In this video, the camera is essentially located in the orbital plane of the binary. This is what we call an “edge-on” view. As the black holes orbit, one black hole passes behind the other relative to the camera. As this happens, the shadow cast by the farther black hole is lensed by the closer black hole into a ring-like shadow. Additionally, we can see the effect that the arbitrary spins has on the orbit. The orbital plane precesses visibly in these last three orbits before merger. As before, we see that the lensing settles down to look like lensing by a single black hole.
We have some interesting brightness effects which are more apparent from this viewpoint than the previous video’s viewpoint. Some photons passing through the binary system have accumulate non-unity redshift. The brightness is affected by the redshift by a factor of redshift cubed, so there is a large brightness change for only a small redshift difference. Overall, near the left side of the shadows we see the brightness damped significantly, while on the right side we see flashes of brightness!
### Black holes at Cornell
While looking at black holes in front of a field of stars, it is easy to lose your bearings. In our paper, we frequently color sections of the sky with a grid to more easily understand the deflection of light by the black holes. A more fun way to accomplish this is by using a recognizable image. Instead of using stars, we therefore use a picture of the clock tower at Cornell.
Now we stick a black hole on campus, because we can and it’s awesome. We can see clearly that near the edges of the image, the view of campus is only slightly changed. The image of the clock tower is bent slightly. However, inside the Einstein ring, we can see the size of the deflections grows. The image is also inverted. The clock tower here is on the left and is upside down, in addition to being even more bent. The grass is up and the sky is down inside the Einstein ring.
Now is a good time to remind you that light can be deflected all the way around the black hole. To properly see what a black hole on campus would look like, we need not only an image of what’s in front of the camera, but also directly above and below the camera. Even light from directly behind the camera will get deflected around the black hole on its way to the camera! Light-rays can take paths which orbit many times around the black hole before reaching the camera, resulting in an infinite number of clock towers (if you had an infinite resolution camera to see them)!
If we can put one black hole on campus, why not two? This is the same binary discussed in the Binary black hole section. It is a three to one mass ratio binary. The same discussion of an infinite number of black hole shadows applies here as well.
### Accretion disk
After seeing the accretion disk in Interstellar, we wanted to see what our code had to say on the matter (sorry about that pun). Because the black hole in Interstellar needed to be almost maximally spinning in order to get a planet so close to its event horizon, we simulated a maximally spinning black hole with an accretion disk.
In the above image, we have a maximally spinning black hole with spin axis pointing upward. Due to this spin, the space-time is being dragged around, making it easier for photons to pass when moving with the frame dragging than it is to pass against the frame dragging. The left side of the black hole shadow is flat and closer to the black hole for this reason. The right side of the shadow is elongated, since these photons are trying to move against the frame dragging on their way to the camera.
We modeled the disk as a thin disk orbiting around the black hole the equatorial orbital velocity. The disk extends from 5 to 17 solar masses, and was given temperature profile dependent on the radius as $T(r) \propto r^{-3/4}$, which is physically motivated by energy balance. To make the disk look more realistic, we introduced arbitrary density and temperature variations across the disk. Finally we added a nice big Hollywood glow!
Notice that it sort of looks like we are seeing multiple disks. For example, above and blow the black hole shadow it looks like there is a disk, but the disk is almost flat across the middle of the image in the simulation. What’s going on? Light is being emitted in all directions by the matter of the disk, so some of the light from the part of the disk behind the black hole is emitted upward. The path of the light is bent by the black hole and some of it actually makes it to your eye, such that you are actually seeing the far part of the disk above the shadow! Similarly, you are seeing the bottom side of the back part of the disk below the shadow. Taking this a step farther, some of the light from the disk does an orbit around the black hole before making it to your eye, so you can see a small ring around the black hole shadow due to these photons!
We also notice that the left side of the disk is brighter and bluer than the right side. This is mostly due to the relativistic Doppler effect. Similar to how a passing car sounds higher in frequency then drops in frequency as it passes by you, the frequency of the photons is higher on the left side of the disk because the matter is traveling towards you. Remember that the matter is orbiting around the black hole. On the right side of the disk, it is moving away from you, so the photons appear more red.
So how did Interstellar do? Let’s compare the images directly.
Apart from looking really great just aesthetically, the Interstellar disk shows the correct light bending effects. However, you may notice it looks very uniform in color. Did they forget to include redshift physics? It turns out that they had produced more physically accurate visuals, but decided to omit redshift and brightness effects intentionally to try not to confuse the audience too much.
### In the spotlight
Partially due to the timing of our paper with the release of Interstellar, and due to how beautiful our visualizations are (to me at least), we have gotten a lot of attention for our work. In fact, our videos will be shown in an upcoming PBS NOVA documentary about black holes!
Here is a list of some of the places where our work was discussed:
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# Efficient evaluation of the inverse of a triangular matrix on a vector
I have this matrix that interests me. It arises when we try to express the norm of a $(p,p)$-form on an $n$-dimensional vector space in terms of (squares of) traces of the form with respect to the Lefschetz operator on the space. It's coefficients are these: $$a_{jk} = \begin{cases} (-1)^k\tbinom{p-k}j \tbinom{n-j-k-p}{n-2p} \tbinom{n-k-p+j}{j} & \hbox{ if j + k \leq p,} \\ 0 & \hbox{else.} \end{cases}$$ Here $j,k$ run between $0$ and $p$, so this is a $(p+1)\times(p+1)$ matrix. (We assume $2p \leq n$ so we don't run into trouble in the binomial coefficients.) For $p = 1$ it looks like this: $$A = \begin{pmatrix} n-1 & -1 \\ n & 0 \end{pmatrix}$$ In general $A$ is a triangular matrix (we could rearrange the bases here so it would be upper-triangular - wrong, but it wasn't important) and thus has a triangular inverse (its determinant is always nonzero).
I really want to calculate $v = A^{-1}(1,\ldots,1)$. I hope (against hope) that the mess of binomial coefficients in the result simplifies (there's some evidence for this when $p=1,2$) but to see that I have to be able to actually calculate $v$. I stress that I really don't care about $A^{-1}$ itself or its value on any other vector than $(1,\ldots,1)$.
Does anyone have an idea how to do this? Calculating $A^{-1}$ directly is probably out of the question, but maybe there's a nice trick to get the value of an inverse on a given vector?
• I don't think you can make, say, $\pmatrix{0&1\cr-1&0\cr}$ upper-triangular by changing the basis (unless you're willing to go complex). – Gerry Myerson Nov 9 '13 at 23:06
• Solving a triangular system... so this would be a substitution method? – Algebraic Pavel Nov 9 '13 at 23:09
• Gerry: Oops. No matter, at least the inverse is easy to calculate. :) Pavel: I suppose, but actually carrying it out with those coefficients would be monstrous. – Gunnar Þór Magnússon Nov 9 '13 at 23:28
• In the end I think Cramer's rule (see en.wikipedia.org/wiki/Cramer's_rule) and brute force calculations do what I want since the matrix is (skewed) triagonal. – Gunnar Þór Magnússon Nov 10 '13 at 0:24
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# Data for speed of gravitional wave
By the distance of the two LIGO detectors and the time delay for the same gravitational wave(GW) event, the speed of GW can be determined. guys, do you know where can I find related data?
Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!
First of all: no, it can't in general. You can only determine the speed of propagation if you know where the source is. Without knowing that you can put an upper bound on the speed: for instance you know it is no more than $d/\Delta t$ where $d$ is the straight-line distance between the detectors and $\Delta t$ the difference in observation times (I'm making various naïve-Galilean-relativity assumptions here, but they're good approximations). But note that $\Delta t =0$ is perfectly possible, in which case the bound is not very good. I don't think you can get a lower bound using this approach.
With three detectors you can do better, but you still can have a case where $\Delta t_{ab} = 0$ for all pairs $a$ and $b$. With four non-coplanar detectors I think you can do considerably better.
Of course the actual analysis that LIGO do is a lot more sophisticated than this. I would suggest that their publications list is a good place to start, and probably the GW150914 detection paper in particular. Note that the event was detected about $7\,\mathrm{ms}$ apart by the two detectors, when the light travel time between the detectors is about $10\,\mathrm{ms}$.
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# The Hardest GCSE Maths Question
22-05-2022
Bare in mind, this question was asked to 16 year olds in the UK during their final maths exam.
## Solution
\begin{aligned} \text{Let N the intercection of circles A and B at the top} \\ AB = 4 \\ \text{Equilateral Triangle ABN - side length 4, internal angles all 60°}\\ \text{Area: } \frac{1}{2}(4)(4)\sin{60} = 4\sqrt{3}\\ \text{Notice that lines AN and AB form a segment of circle A: }\\ \frac{60}{360}(\pi 4^2) = \frac{8}{3}\pi\\ \text{Thus, we can get the area of the remainder of the circle-segment by finding the difference: } \\ \frac{8}{3}\pi-4\sqrt{3} \end{aligned}
OK I got bored here Lol but I think you see where I'm headed. Not too complex but tricky to see where to start May revisit!
I also (occasionally) write an email newsletter! You can subscribe here if you're interested:
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# Comparing SN2 reaction rate for phenacyl chloride and methyl chloride
KI in acetone undergoes $$\mathrm{S_N2}$$ reaction with (1) and (2). Compare the rates of the reactions.
Like many kinds of these questions there are many factors involved. One is the steric effect, and, since steric effects plays a central role in inversion of reactant and there is a very bulky group attached to (2), I think (1) should be more reactive. Also, (2) will serve as a better $$\mathrm{S_N1}$$ substrate as the carbocation generated will be resonance stabilised.
And so using these two reasons I thought (1) is more reactive than (2), but, according to the answer, (2) is almost 500 times more reactive than (1), and I am not able to see the reason for this mammoth difference.
• That carbocation is not resonance stabilised. – orthocresol Jan 3 '17 at 18:29
• Yeah, the carbocation is not resonance stabilised. Try drawing resonating structures (if you can). If you face it anyways, you will end up with a positive charge on Oxygen. Moreover you already know that Halogen exchange reaction goes with SN2, so the carbocation formation is pointless (no SN1). – Reeshabh Ranjan Jan 3 '17 at 19:20
• If you are given this question in an exam it's really easy to identify which is more reactive by hybridization. As in (1) hydrogen is already stable that refers to its not much reactive. we already know something which is stable is less reactive and vice versa then looking at the second compound is not stable hence would be more reactive than one. – user84460 Oct 6 at 23:07
First, let me point out that a rate difference of 500 is really not that large. There are solvolysis reactions with relative rate differences on the order of $\mathrm{10^{10}}$ or greater (1).
The transition state for an $\mathrm{S_{N}2}$ reaction involves hypercoordinate (or hypervalent) bonding. The transition state is, more or less, a trigonal bipyramid structure and the bonding at the central carbon atom ($\ce{Nu-C-X}$) involves a 3 center-4 electron bond (see the above link and links therein for more detail on this concept). With 5 electron pairs being shared by this central carbon, anything that removes electron density from the central carbon atom will prove beneficial and accelerate the reaction.
$\mathrm{S_{N}2}$ Reaction Pathway
In your molecule #2, a benzoyl group is attached to the central carbon involved in the $\mathrm{S_{N}2}$ process. You are correct that such a group is larger than a hydrogen and should decrease the reaction rate due to steric effects. However the size of the benzoyl group is not exceptionally large and the steric effect will likely be small. More importantly, the benzoyl group will also exert an electronic effect. The central carbon in an $\mathrm{S_{N}2}$ reaction is $\mathrm{sp^2}$ hybridized [e.g. leading to a trigonal bipyramid structure as mentioned above] and has a $\mathrm{p}$ orbital. This $\mathrm{p}$ orbital can interact with the adjacent carbonyl group through resonance. This resonance effect will tend to remove (delocalize) electron density from the central carbon atom. Also, the carbonyl group will inductively remove electron density from the central carbon atom. These electronic effects will remove electron density from the central carbon atom thereby accelerating the reaction as observed.
(1) For example, the relative rates of solvolysis of 7-tosyloxynorbornane and anti-7-tosyloxynorbornene in acetic acid are $\mathrm{1:10^{11}}$
• I Think I have got you (almost) ...I have just one problem with your statement "However the size of the benzoyl group is not exceptionally large and the steric effect will likely be small" . – Freelancer Jan 4 '17 at 3:15
• As I think Steric effect will not be small after all there is the benzene ring and a carbonyl group both hugely obstructing the attack of Nucleophile... – Freelancer Jan 4 '17 at 3:17
• But then whenever I come across these questions I always feel like we are using the creationist method(i.stack.imgur.com/bS6S0.gif) – Freelancer Jan 4 '17 at 3:27
• Funny and it's easy to see how folks might view things the way the cartoon suggests, but to actually publish a paper a lot of experiments are done to rule out \ rule-in various hypotheses. As to the size of the $\ce{-CO-Ph}$ group, we can look at something called A-values which are used as a measure of the size of various substituents. The A-value for a methyl group is 1.7, it is 3 for a larger phenyl group. I can't find a value for $\ce{-COPh}$, but $\ce{-COMe}$ – ron Jan 4 '17 at 3:41
• is only 1.17, $\ce{-COCl}$ is 1.25. All of these values are smaller than the A-value for a methyl group and I doubt that $\ce{-COPh}$ would be much different from $\ce{-COMe}$ or $\ce{-COCl}$. So I would expect $\ce{COPh}$ to be sterically rather "small". – ron Jan 4 '17 at 3:45
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8 (499) 391-32-03, 8 (499) 394-07-16
125363, г. Москва, ул. Новопоселковая,
д. 6, кор. 217, офис 606
ooouptp@ooouptp.com
ООО «ЮЖНОЕ ПРОИЗВОДСТВЕННО-ТЕХНИЧЕСКОЕ ПРЕДПРИЯТИЕ»
# Athan Pro _BEST_ Full Version 18
Athan Pro Full Version 18
Muezzin Khan on the East African coast or the Moroccan Athan.. 5/23/2019 : Universal 2.5.4. 4/11/2019 : FD 1.3.5. 1/2/2019 : MTS1.0.2 If you are an iOS user, you can download the . Athan 6.0: Athan Pro — Islamic Prayer Times, Quran App, . Android requires you to download the Athan Pro App on your device in order to use⦠Prayer Times for Android | Free Download — Fakkahaza.com. Prayer Times for Android.Q: Closed Subspace of Banach Space Let $X$ be a Banach space. If $S\subset X$ is a closed subspace, show that if $(x_n)_n$ is a net that converges weakly to $x$, then $x\in S$. I’m very confused about this problem and any help will be greatly appreciated. A: Let $x\in X$. By definition, there exists a net $(x_\alpha)_{\alpha\in A}$ in $S$ such that $x_\alpha\stackrel{w}{\rightarrow}x$. Let $y\in X^*$ and $y(x) eq 0$. Then $|y(x_\alpha)|\stackrel{w}{\rightarrow}|y(x)|$. Since $|y(x_\alpha)|\rightarrow|y(x)|$, there exists $\alpha_0$ such that $|y(x_{\alpha_0})|=|y(x)|$. Then $0=y(x)-y(x_{\alpha_0})=y(x-x_{\alpha_0})$. Since $X^*$ is (weak)$^*$-dense, there exists $y_0\in X^*$ such that $y(x-x_{\alpha_0})=y_0(x-x_{\alpha_0})$, which implies $x-x_{\alpha_0}\in S$. Since $x_{\alpha_0}=x_{\alpha_0}+x-x_{\alpha_0}\in S+S\subset S$, we ded
https://ed.ted.com/on/3Rluvavr
https://ed.ted.com/on/u7bAFJ4n
https://ed.ted.com/on/zYpGtZtj
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# A generalized elastic net regularization with smoothed $$\ell _{q}$$ ℓ q penalty for sparse vector recovery
## Author
Listed:
• Yong Zhang
() (Shanghai University
Jiangsu University of Science and Technology)
• Wanzhou Ye
() (Shanghai University)
• Jianjun Zhang
() (Shanghai University)
## Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:68:y:2017:i:2:d:10.1007_s10589-017-9916-7. See general information about how to correct material in RePEc.
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# Distance between compact subsets
1. Nov 7, 2012
### Ocifer
1. The problem statement, all variables and given/known data
Let A,B be two disjoint, non-empty, compact subsets of a metric space (X,d).
Show that there exists some r>0 such that d(a,b) > r for all a in A, b in B.
Hint provided was: Assume the opposite, consider a sequence argument.
2. Relevant equations
N/A
3. The attempt at a solution
I've tried a few different characterizations of compactness, but neither one has led me anywhere particularly useful. I'm missing something such that the teacher's hint isn't helping me much.
If I assume the opposite,
Assume that for all r>0, there exists some pair (a,b) such that d(a,b) <= r
I sense that I am supposed to reach a contradiction regarding the property that any sequence in a compact A or B should have a convergent subsequence. But how do I show that I would reach such a contradiction. Can anyone give me a push in the right direction?
2. Nov 7, 2012
### Dick
Make some sequences. Assume d(a_n,b_n)<=1/n for all n. Now pick subsequences.
3. Nov 7, 2012
### Ocifer
Do you mean:
Assume, by way of contradiction, that for all r>0, there exists some pair (a,b) such that d(a,b) <= r.
Let {a_n}, {b_n} be sequences in A and B respectively.
---------------
I'm unclear on your next assumption. Are you using n to index the sequences as well as to bound the distances with 1/n, or was that an unintentional typo? If not, why may I /should I make that assumption?
4. Nov 7, 2012
### Ocifer
If I assume that for all r>0, there exist some pair such that d(a,b) <= r , that allows me to at least construct two sequences in A and B respectively having the property:
d( a_1, b_1 ) <= 1/1
d( a_2, b_2 ) <= 1/2
...
and so on, is that what you meant? I hope I'm understanding you correctly.
If I am trying to show that this property implies there is no convergent subsequence, how does it help. It doesn't tell me about the distances between each of the elements of the {a_n} sequence and the {b_n} sequence, does it?
-----------------------------
Another intuition I had which I'm trying to formalize, but I thought I would run past the forum is this. If I assume that for all r>0, there exists an (a,b) such that d(a,b) <= r, would this not imply that the two sets share a limit point? Since they are compact they must each contain their limit points, and then they would not be disjoint? Can I reach my desired contradiction in that manner?
--------
5. Nov 7, 2012
### Dick
The second route. If a_n has a limit point a and b_n has a limit point b, what's d(a,b)?
6. Nov 7, 2012
### Ocifer
Here goes my full attempt:
---------------------------
Let (X,d) be a metric space. Let A and B be non-empty, disjoint, compact subsets of (X,d).
Then there exists an r>0 such that d(a,b) > r for all a in A, b in B.
Proof:
Assume by way of contradiction that for all r>0, there exists a pair (a,b) such that d(a,b) <= r.
Under this assumption, we may construct the two sequences in A and B respectively, having the property that:
d(a_n, b_n) <= 1/n , for all n in the natural numbers.
Claim: If we consider this sequence of distances, its limit is 0.
Subproof: For any ε > 0, there is an n in the natural numbers such that 1/n < ε . It follows that for any ε > 0, we have some N(ε) such that if n >= N(ε), | d(a_n, b_n) - 0 | < ε .
And so the sequence of distances has limit 0.
From this it follows that the limit of {a_n} is equal to the limit of {b_n}. So A and B share a limit point, and since both contain their limit points, the sets A and B cannot be disjoint. This is a contradiction, and so it follows that there exists some r>0 such that d(a,b) > r for all a in A, b in B.
---------------------------------------------------------
Is this okay?
7. Nov 7, 2012
### Dick
The idea is fine. I'm not sure the proof really measures up. Skip to picking convergent subsequences and suppose d(a_n,b_n)<1/n and a_n->a and b_n->b. Use d(a,b)<=d(a,a_n)+d(a_n,b_n)+d(b_n,b) using the triangle inequality. Can you show the right side converges to 0?
8. Nov 8, 2012
### Ocifer
The right hand side terms should all go to zero in the limit as
d(a, a_n) --> d(a,a) = 0
d(b, b_n) --> d(b,b) = 0
and
d(a_n, b_n) --> 0 using the definition of a limit of a sequence in metric spaces, and the fact that d(a_n, b_n) < 1/n for all n.
I think I have it now, thank you for your help.
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# Question
A study was aimed at assessing the effects of group size and group characteristics on the generation of advertising concepts. To assess the influence of group size, groups of four and eight members were compared. For a random sample of four-member groups, the mean number of advertising concepts generated per group was 78.0 and the sample standard deviation was 24.4.
For an independent random sample of eight-member groups, the mean number of advertising concepts generated per group was 114.7 and the sample standard deviation was 14.6. (In each case, the groups had a moderator.) Stating any assumptions that you need to make, test, at the 1% level, the null hypothesis that the population means are the same against the alternative that the mean is higher for eight-member groups.
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# All Questions
69 views
### Initializing PGP keys by one side
I am using a PGP method to encrypt and decrypt messages shared between users A and B. Upon the start of a message exchange is the initialization of the public and secret keys by both Users. Lets say ...
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# Category Archives: Dilogarithm
## Special values of the dilgoarithm function
Prove that $$\mathrm{Li}_2\left( \frac{\sqrt{5}-1}{2} \right) = \frac{\pi^2}{10} – \log^2 \left( \frac{\sqrt{5}-1}{2}\right)$$ $$\textit{proof}$$ Use the following functional equation $$\mathrm{Li}_2 \left( \frac{z}{z-1} \right) + \frac{1}{2} \mathrm{Li}_2 (z^2) – \mathrm{Li}_2(-z) = -\frac{1}{2} \log^2 (1-z)$$ These are proved here and here Now let … Continue reading
$$\mathrm{Li}_{\,n}(-z) + \mathrm{Li}_{\,n}(z) = 2^{1-n} \,\mathrm{Li}_{\,n}(z^2)$$ $$\textit{proof}$$ As usual we write the series representation of the LHS $$\sum_{k=1}^\infty \frac{z^k}{k^n}+\sum_{k=1}^\infty \frac{(-z)^k}{k^n}$$ Listing the first few terms $$z+\frac{z^2}{2^n}+\frac{z^3}{3^n}+\cdots +\left(-z+\frac{z^2}{2^n}-\frac{z^3}{3^n}+\cdots \right)$$ The odd terms will cancel $$2\frac{z^2}{2^n}+2\frac{z^4}{4^n}+2\frac{z^6}{6^n}+\cdots$$ Take $2^{1-n} … Continue reading Posted in Dilogarithm, Polylogarithm | | 1 Comment ## Dilogarithm difference formula proof \mathrm{Li}_2(z) + \mathrm{Li}_2 \left(\frac{z}{z-1} \right) = – \frac{1}{2} \log^2 (1-z) \,\,\,\, \, z<1 \textit{proof} Start by the following \mathrm{Li}_2 \left(\frac{z}{z-1} \right) = -\int^{\frac{z}{z-1}}_0 \frac{ \log(1-t)}{t}\, dt Differentiate both sides with respect to z \frac{d}{dz}\mathrm{Li}_2 \left(\frac{z}{z-1} \right) = \frac{1}{(z-1)^2}\left( \frac{ \log … Continue reading Posted in Dilogarithm, Polylogarithm | Tagged , , , | 1 Comment ## Dilogarithm at 2 \mathrm{Li}_2\left(\frac{1}{2}\right)= \frac{\pi^2}{12}-\frac{1}{2}\log^2 \left(\frac{1}{2}\right) proof Using the duplication formula proved here \mathrm{Li}_2\left(z\right)+\mathrm{Li}_2(1-z)\, = \frac{\pi^2}{6}-\log(z) \log(1-z) \,\, We can easily deduce that for \( z=\frac{1}{2}$ $$2\mathrm{Li}_2\left(\frac{1}{2}\right)= \frac{\pi^2}{6}-\log^2\left(\frac{1}{2}\right) \,\,$$ It follows by dividing by 2.
$$\mathrm{Li}_2(z) + \mathrm{Li}_{2}(1-z) = \frac{\pi^2}{6}-\log(z) \log(1-z) \,\,\,\, ,\,0<z<1$$ $$\textit{proof}$$ Start by the following $$\mathrm{Li}_2\left(z\right) = -\int^{z}_0 \frac{\log(1-t)}{t} \, dt$$ Now integrate by parts to obtain $$\mathrm{Li}_2\left(z\right)= -\int^z_0 \frac{\log(t)}{1-t} \, dt -\log(z) \log(1-z)$$ By the change of variable \(t=1-x … Continue reading
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# Help for double parametrized integration: algebraic vs Mathematica solutions
I have to solve a double integral with parametrized functions, that is (written as a latex equation) $$\int_{-\infty}^\infty \int_0^\infty u(t)u(t-\Delta)\frac{1+e^{-2\int_{t-\tau-\Delta}^{t-\tau} y(s)^2 ds }}{2} d\Delta dt$$ that depends upon: - the function u(t), that in my case is a squared pulse between 0 and 1, defined in Mathematica as
u[t_] = Piecewise[{{1, 0 <= t <= 1}}, 0];
• the function y(s), that in my case is a piecewise constant function between 0 and 1 with a discontinuity in t1, defined in Mathematica as
y[t_, y1_, y2_, t1_] = Piecewise[{{y1, 0 <= t <= t1}, {y2, t1 < t <= 1}}, 0];
• the parameter $\tau$.
Consider the assumptions
$Assumptions = 1 > \[Tau] > 0 && y1 \[Element] Reals && y2 \[Element] Reals && 1 > t1 > 0 and also t1 + \[Tau] < 1. I'd like to solve the integral to have a function of$\tau, y1, y2, t1$. Now, if I just substitute the definition of$u(t)$and$y(s)$and use Mathematica, I get I can't get the integral solved, as you can check with Assuming[t1 + \[Tau] < 1, Integrate[ Integrate[ u[t] u[t - \[CapitalDelta]] (1 + Exp[-2 Integrate[ y[s, y1, y2, t1]^2, {s, t - \[CapitalDelta] - \[Tau], t - \[Tau]}]])/2, {\[CapitalDelta], 0, +Infinity}], {t, -Infinity, +Infinity}]] // Simplify So, I have done "by hand" part of the integral, in particular the integral at the exponential argument, defining the funtion IntY2[a_, b_, y1_, y2_, t1_] = Piecewise[{ {y1^2 b, a < 0 && 0 <= b < t1}, {y1^2 t1 + y2^2 (b - t1), a < 0 && t1 <= b <= 1}, {y1^2 t1 + y2^2 (1 - t1), a < 0 && 1 < b}, {y1^2 (b - a), 0 <= a < t1 && 0 <= b < t1}, {y1^2 (t1 - a) + y2^2 (b - t1), 0 <= a < t1 && t1 <= b <= 1}, {y1^2 (t1 - a) + y2^2 (1 - t1), 0 <= a < t1 && 1 < b}, {y2^2 (b - a), t1 <= a <= 1 && t1 <= b <= 1}, {y2^2 (1 - a), t1 <= a <= 1 && 1 < b}}, 0] and calculating Assuming[t1 + \[Tau] < 1, Integrate[ Integrate[ u[t] u[t - \[CapitalDelta]] (1 + Exp[-2 IntY2[t - \[CapitalDelta] - \[Tau], t - \[Tau], y1, y2, t1]])/2, {\[CapitalDelta], 0, +Infinity}], {t, -Infinity, +Infinity}]] // Simplify This elaboration works, and I get a solution. But doing by hand the substitution of u(t) and y(t) with some algebra I get Integrate[(1 + Exp[-2 y1^2 \[CapitalDelta]])/2, {\[CapitalDelta], 0, t - \[Tau]}, {t, \[Tau], t1 + \[Tau]}] + Integrate[(1 + Exp[-2 y1^2 (t - \[Tau])])/2, {\[CapitalDelta], t - \[Tau], t}, {t, \[Tau], t1 + \[Tau]}] + Integrate[(1 + Exp[-2 y2^2 (t - \[Tau] - t1) - 2 y1^2 t1])/ 2, {\[CapitalDelta], t - \[Tau], t}, {t, t1 + \[Tau], 1}] + Integrate[(1 + Exp[-2 y2^2 (t - \[Tau] - t1) - 2 y1^2 (t1 - (t - \[Tau] - \[CapitalDelta]))])/ 2, {\[CapitalDelta], t - t1 - \[Tau], t - \[Tau]}, {t, t1 + \[Tau], 1}] + Integrate[(1 + Exp[-2 y2^2 \[CapitalDelta]])/2, {\[CapitalDelta], 0, t - t1 - \[Tau]}, {t, t1 + \[Tau], 1}] // Simplify that is different from the one calculated by Mathematica. Of course, probably I made a mistake somewhere that I cannot find. Anyway, I tried to substitute some parts of the original integral to get my formula, for example sustituting the constraint given by u(t), then$u(t-\Delta)$, ecc checking each step of Mathematica. For example, with Assuming[t1 + \[Tau] < 1, Integrate[ Integrate[u[t] u[t - \[CapitalDelta]] (1 + Exp[-2 IntY2[t - \[CapitalDelta] - \[Tau], t - \[Tau], y1, y2, t1]])/2, {\[CapitalDelta], 0, +Infinity}], {t, 0, 1}]] // Simplify I get the same (Mathematica's, not mine) solution. When I get to Assuming[t1 + \[Tau] < 1, Integrate[ Integrate[ u[t - \[CapitalDelta]] (1 + Exp[-2 IntY2[t - \[CapitalDelta] - \[Tau], t - \[Tau], y1, y2, t1]])/2, {\[CapitalDelta], 0, +Infinity}], {t, 0, 1}]] // Simplify and I tried to make that solved, Mathematica cannot solve it (or at least it takes a lot of time, the previous integral it takes 20 s but in this one after 5 minutes it's not solved). Note that I just delete u[t] in the integral argument, but from the mathematical point of view it should be indifferent since t is integrated between 0 and 1. I'd like to understand why Mathematica cannot solve this last formulation of the integral (and how can I fix it), because I want to check my solutions and also I have some more complex integrals that Mathematica cannot solve and I think the problem is the same. Sorry for the long post, Nicola - PiecewiseExpand might be helpful. – b.gatessucks Jan 15 at 16:18 Your integral is much simpler than it appears, so consider re-expressing it.$y$is piecewise constant, whence so are$y(s)^2ds$, whence its integral, whence its exponential, whence the entire integrand, because$u$also is piecewise constant. Therefore, what you are trying to integrate is a sum of constants! This suggests you change your approach into characterizing the regions at which the value of the integrand changes; within each region, the value is trivial to compute. MMA is struggling with managing all possible orderings of$t_1$relative to$t,\delta,0,1\$, etc. – whuber Jan 15 at 16:33
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ompl::base::StateValidityChecker Class Referenceabstract
Abstract definition for a class checking the validity of states. The implementation of this class must be thread safe. More...
#include <ompl/base/StateValidityChecker.h>
Inheritance diagram for ompl::base::StateValidityChecker:
Public Member Functions
StateValidityChecker (SpaceInformation *si)
Constructor.
StateValidityChecker (const SpaceInformationPtr &si)
Constructor.
virtual bool isValid (const State *state) const =0
Return true if the state state is valid. Usually, this means at least collision checking. If it is possible that ompl::base::StateSpace::interpolate() or ompl::control::ControlSpace::propagate() return states that are outside of bounds, this function should also make a call to ompl::base::SpaceInformation::satisfiesBounds().
virtual bool isValid (const State *state, double &dist) const
Return true if the state state is valid. In addition, set dist to the distance to the nearest invalid state.
virtual bool isValid (const State *state, double &dist, State *validState, bool &validStateAvailable) const
Return true if the state state is valid. In addition, set dist to the distance to the nearest invalid state (using clearance()). If a direction that moves state away from being invalid is available, a valid state in that direction is also set (validState). validStateAvailable is set to true if validState is updated.
virtual double clearance (const State *) const
Report the distance to the nearest invalid state when starting from state. If the distance is negative, the value of clearance is the penetration depth.
virtual double clearance (const State *state, State *, bool &validStateAvailable) const
Report the distance to the nearest invalid state when starting from state, and if possible, also specify a valid state validState in the direction that moves away from the colliding state. The validStateAvailable flag is set to true if validState is updated.
const StateValidityCheckerSpecsgetSpecs () const
Return the specifications (capabilities of this state validity checker)
Protected Attributes
SpaceInformationsi_
The instance of space information this state validity checker operates on.
StateValidityCheckerSpecs specs_
The specifications of the state validity checker (its capabilities)
Detailed Description
Abstract definition for a class checking the validity of states. The implementation of this class must be thread safe.
Definition at line 90 of file StateValidityChecker.h.
The documentation for this class was generated from the following file:
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mscroggs.co.uk
mscroggs.co.uk
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# Puzzles
## 25 December
It's nearly Christmas and something terrible has happened: while out on a test flight, Santa's sled was damaged and Santa, Rudolph and Blitzen fell to the ground over the Advent Isles. You need to find Santa and his reindeer before Christmas is ruined for everyone.
You have gathered one inhabitant of the four largest Advent Isles—Rum, Land, Moon and County—and they are going to give you a series of clues about where Santa and his reindeer landed. However, one or more of the islanders you have gathered may have been involved in damaging Santa's sled and causing it to crash: any islander involved in this will lie to you to attempt to stop you from finding Santa and his reindeer. Once you are ready to search for Santa, Rudolph and Blitzen, you can find the map by following this link.
Each of the clues will be about Santa's, Rudolph's or Blitzen's positions in Advent Standard Coordinates (ASC): ASC are given by six two-digit numbers with dots inbetween, for example 12.52.12.13.84.55. For this example coordinate, the islanders will refer to (the first) 12 as the first coordinate, 52 as the second coordinate, (the second) 12 as the third coordinate, 13 as the fourth coordinate, 84 as the fifth coordinate, and 55 as the sixth coordinate.
Here are the clues:
3
Rum says: "The product of all the digits in Blitzen's six coords is 432."
21
Moon says: "Blitzen's fifth coord is 23."
9
Moon says: "Blitzen's third coord is 23."
1
Land says: "Santa's third coord ends in 3, 0 or 1."
2
Land says: "Santa's third coord ends in 2, 0 or 3."
4
Rum says: "Santa's second coord ends in 3, 4 or 1."
12
Rum says: "Rudolph's second and sixth coords are both 64."
10
Rum says: "All six of Rudolph's coords are factors of 256."
18
Moon says: "Santa's fourth and fifth coords are both 79."
24
County says: "Santa's third coord ends in 3, 2 or 1."
22
Land says: "Santa's sixth coord is not 43."
7
Rum says: "Santa's sixth coord is 43."
23
County says: "One of the digits of Santa's third coord is 7."
25
14
Land says: "Santa's third coord is 12."
5
Rum says: "Santa's first coord is 36."
15
Rum says: "Blitzen's first coord is 23."
17
Rum says: "The first digit of Santa's third coord is 1."
8
County says: "Santa's third coord shares a factor (≠1) with 270."
6
County says: "Santa's second coord is 21."
16
Land says: "Blitzen's second coord is 21."
20
Moon says: "All six of Rudolph's coords are multiples of 8."
11
Moon says: "The sum of Rudolph's six coords is 192."
13
Moon says: "Santa's second coord is 21 or 11."
19
Moon says: "Blitzen's fourth and sixth coords are both 11."
To find a point's ASC coordinates, split a map of the islands into a 9×9 grid, then number the rows and columns 1 to 9: the first two digits of ASC give the vertical then horizontal position of a square in this grid. The next two digits then give a smaller square when this square is then itself split into a 9×9 grid, and so on. An example is show below.
The ASC coordinates of this pair of flowers are 12.52.12.13.84.55 (click to enlarge).
You can view the map here.
## 6 December
Noel's grandchildren were in born in November in consecutive years. Each year for Christmas, Noel gives each of his grandchildren their age in pounds.
Last year, Noel gave his grandchildren a total of £208. How much will he give them in total this year?
2018's Advent calendar ended with a logic puzzle: It's nearly Christmas and something terrible has happened: one of Santa's five helpers—Jo Ranger, Fred Metcalfe, Kip Urples, Meg Reeny, and Bob Luey—has stolen all the presents during the North Pole's annual Sevenstival. You need to find the culprit before Christmas is ruined for everyone.
Every year in late November, Santa is called away from the North Pole for a ten hour meeting in which a judgemental group of elders decide who has been good and who has been naughty. While Santa is away, it is traditional for his helpers celebrate Sevenstival. Sevenstival gets in name from the requirement that every helper must take part in exactly seven activities during the celebration; this year's available activities were billiards, curling, having lunch, solving maths puzzles, table tennis, skiing, chess, climbing and ice skating.
Each activity must be completed in one solid block: it is forbidden to spend some time doing an activity, take a break to do something else then return to the first activity. This year's Sevenstival took place between 0:00 and 10:00 (North Pole standard time).
During this year's Sevenstival, one of Santa's helpers seven activities included stealing all the presents from Santa's workshop. Santa's helpers have 24 pieces of information to give to you, but the culprit is going to lie about everything in an attempt to confuse you, so be careful who you trust.
Here are the clues:
1
Meg says: "Between 2:33 and curling, I played billiards with Jo."
15
Kip says: "The curling match lasted 323 mins."
24
Fred says: "In total, Jo and Meg spent 1 hour and 57 mins having lunch."
8
Meg says: "A total of 691 mins were spent solving maths puzzles."
17
Jo says: "I played table tennis with Fred and Meg for 2+8+5 mins."
23
Meg says: "1:32 was during my 83 min ski"
7
Meg says: "The number of mins the curling game lasted is a factor of 969."
16
Jo says: "I started skiing with Bob, and finished before Bob at 8:45."
5
Jo says: "At 4:45, Fred, Bob, Kip and I started a curling match."
14
Fred says: "I spent 135 mins playing chess with Meg."
20
Meg says: "Jo started skiing at 7:30."
4
Bob says: "I went for a 150 min ski."
13
Kip says: "Jo started skiing at 6:08."
22
Fred says: "Bob, Kip and I finished lunch at 3:30."
6
Bob says: "I played billiards with Kip from 0:00 until 1:21."
12
Fred says: "Between 3:30 and 4:45, there were 3 people climbing."
21
Fred says: "In total, Bob, Meg and I spent 269 mins ice skating."
10
Meg says: "Between 0:00 and 1:10, I was ice skating."
19
Jo says: "At 1:12, Fred and I were both in the middle of maths puzzles."
3
Jo says: "Straight after curling, I had a 108 min game of chess with Kip."
9
Fred says: "At 2:52, I started having lunch with Bob and Kip."
18
Jo says: "I spent 153 mins solving maths puzzles."
2
Fred says: "I was solving maths puzzles for 172 mins."
11
Meg says: "I spent 108 mins solving maths puzzles with Bob."
2017's Advent calendar ended with a logic puzzle: It's nearly Christmas and something terrible has happened: Santa and his two elves have been cursed! The curse has led Santa to forget which present three children—Alex, Ben and Carol—want and where they live.
The elves can still remember everything about Alex, Ben and Carol, but the curse is causing them to lie. One of the elves will lie on even numbered days and tell the truth on odd numbered days; the other elf will lie on odd numbered days and tell the truth on even numbered days. As is common in elf culture, each elf wears the same coloured clothes every day.
Each child lives in a different place and wants a different present. (But a present may be equal to a home.) The homes and presents are each represented by a number from 1 to 9.
Here are the clues:
21
White shirt says: "Yesterday's elf lied: Carol wants 4, 9 or 6."
10
Orange hat says: "249 is my favourite number."
5
Red shoes says: "Alex lives at 1, 9 or 6."
16
Blue shoes says: "I'm the same elf as yesterday. Ben wants 5, 7 or 0."
23
Red shoes says: "Carol wants a factor of 120. I am yesterday's elf."
4
Blue shoes says: "495 is my favourite number."
15
Blue shoes says: "Carol lives at 9, 6 or 8."
22
Purple trousers says: "Carol wants a factor of 294."
11
White shirt says: "497 is my favourite number."
6
Pink shirt says: "Ben does not live at the last digit of 106."
9
Blue shoes says: "Ben lives at 5, 1 or 2."
20
Orange hat says: "Carol wants the first digit of 233."
1
Red shoes says: "Alex wants 1, 2 or 3."
24
Green hat says: "The product of the six final presents and homes is 960."
17
Grey trousers says: "Alex wants the first digit of 194."
14
Pink shirt says: "One child lives at the first digit of 819."
3
White shirt says: "Alex lives at 2, 1 or 6."
18
Green hat says: "Ben wants 1, 5 or 4."
7
Green hat says: "Ben lives at 3, 4 or 3."
12
Grey trousers says: "Alex lives at 3, 1 or 5."
19
Purple trousers says: "Carol lives at 2, 6 or 8."
8
Red shoes says: "The digits of 529 are the toys the children want."
13
Green hat says: "One child lives at the first digit of 755."
2
Red shoes says: "Alex wants 1, 4 or 2."
## 23 December
In the song The Twelve Days of Christmas, how many presents have been given after 8 days?
## What's the star?
In the Christmas tree below, the rectangle, baubles, and the star at the top each contain a number. The square baubles contain square numbers; the triangle baubles contain triangle numbers; and the cube bauble contains a cube number.
The numbers in the rectangles (and the star) are equal to the sum of the numbers below them. For example, if the following numbers are filled in:
then you can deduce the following:
What is the number in the star at the top of this tree?
2016's Advent calendar ended with a murder mystery, with each of the murderer, motive, weapon and location being a digit from 1 to 9. Here are the clues:
10
None of the digits of 171 is the location.
3
None of the digits of 798 is the motive.
7
One of the digits of 691 is the location.
16
None of the digits of 543 is the location.
5
One of the digits of 414 is the murderer.
20
The first digit of 287 is the number of false red clues.
8
Clues on days that are factors of 768 are all true.
22
The murderer is the square root of one of the digits of 191.
11
One of the digits of 811 is the weapon.
19
The highest common factor of the weapon and 128 is 1.
13
None of the digits of 512 is the murderer.
18
One of the digits of 799 is the motive.
17
None of the digits of 179 is the motive.
6
None of the digits of 819 is the location.
24
One of the digits of 319 is total number of false clues.
23
One of the digits of 771 is the murderer.
2
The weapon is not one of the digits of 435.
14
The final digit of 415 is the number of true blue clues.
4
The weapon is a factor of 140.
12
The number of false clues before today is the first digit of 419.
9
One of the digits of 447 is the motive.
1
None of the digits of 563 is the motive.
21
One of the digits of 816 is the murderer.
15
One of the digits of 387 is the motive.
## Santa
Each of the letters D, A, Y, S, N, T, B, R and E represents a different non-zero digit. The following sum is true:
$$\begin{array}{cccccc} D&A&D&D&Y\\ B&E&A&R&D&+\\ \hline S&A&N&T&A \end{array}$$
This has a unique solution, but I haven't found a way to find the solution without brute force. This less insightful sum is also true with the same values of the letters (and should allow you to find the values of the letters using logic alone):
$$\begin{array}{ccccc} R&A&T&S\\ N&E&R&D&+\\ \hline S&A&N&E \end{array}$$
## Archive
Show me a random puzzle
▼ show ▼
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{}
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## Dynamics of third-order rational difference equations with open problems and conjectures.(English)Zbl 1129.39002
Advances in Discrete Mathematics and Applications 5. Boca Raton, FL: Chapman & Hall/CRC (ISBN 978-1-58488-765-2/hbk). 554 p. (2008).
This book is about the global character of solutions of the third-order rational difference equation $x_{n+1}=\frac{\alpha+\beta x_n+\gamma x_{n-1}+\delta x_{n-2}} {A+Bx_n+Cx_{n-1}+Dx_{n-2}},\quad n=0, 1, \dots$ with nonnegative parameters $$\alpha, \beta, \gamma, \delta, A, B, C, D$$ and with arbitrary nonnegative initial conditions $$x_{-2}, x_{-1}, x_0$$ such that the denominator is always positive. The authors are primarily concerned with the “boundedness nature of solutions, the stability of the equilibrium points, the periodic character of the equation, and with convergence to periodic solutions including periodic trichotomies. The book also provides numerous thought-provoking open problems and conjectures on the boundedness character, global stability, and periodic behavior of solutions of rational difference equations.
After introducing several basic definitions and general results, the authors examine 135 special cases of rational difference equations that have only bounded solutions and the equations that have unbounded solutions in some range of their parameters. They then explore the seven known nonlinear periodic trichotomies of third order rational difference equations. The main part of the book presents the known results of each of the 225 special cases of third order rational difference equations. In addition, the appendices supply tables that feature important information on these cases as well as on the boundedness character of all fourth order rational difference equations.
The theory and techniques developed in this book to understand the dynamics of rational difference equations will be useful in analyzing the equations in any mathematical model that involves difference equations. Moreover, the stimulating conjectures will promote future investigations in this fascinating, yet surprisingly little known area of research” (cited from the publisher’s description).
### MSC:
39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations 39-02 Research exposition (monographs, survey articles) pertaining to difference and functional equations
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# 3D Object Recognition with Ensemble Learning --- A Study of Point Cloud-Based Deep Learning Models
,
arXiv.org Artificial Intelligence
In this study, we present an analysis of model-based ensemble learning for 3D point-cloud object classification and detection. An ensemble of multiple model instances is known to outperform a single model instance, but there is little study of the topic of ensemble learning for 3D point clouds. First, an ensemble of multiple model instances trained on the same part of the $\textit{ModelNet40}$ dataset was tested for seven deep learning, point cloud-based classification algorithms: $\textit{PointNet}$, $\textit{PointNet++}$, $\textit{SO-Net}$, $\textit{KCNet}$, $\textit{DeepSets}$, $\textit{DGCNN}$, and $\textit{PointCNN}$. Second, the ensemble of different architectures was tested. Results of our experiments show that the tested ensemble learning methods improve over state-of-the-art on the $\textit{ModelNet40}$ dataset, from $92.65\%$ to $93.64\%$ for the ensemble of single architecture instances, $94.03\%$ for two different architectures, and $94.15\%$ for five different architectures. We show that the ensemble of two models with different architectures can be as effective as the ensemble of 10 models with the same architecture. Third, a study on classic bagging i.e. with different subsets used for training multiple model instances) was tested and sources of ensemble accuracy growth were investigated for best-performing architecture, i.e. $\textit{SO-Net}$. We also investigate the ensemble learning of $\textit{Frustum PointNet}$ approach in the task of 3D object detection, increasing the average precision of 3D box detection on the $\textit{KITTI}$ dataset from $63.1\%$ to $66.5\%$ using only three model instances. We measure the inference time of all 3D classification architectures on a $\textit{Nvidia Jetson TX2}$, a common embedded computer for mobile robots, to allude to the use of these models in real-life applications.
, , , (22 more...)
Apr-17-2019
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## Keeping Your Pet’s Microchip Information Up-To-Date is Essential
If you want to be proactive about saving your pet’s life, regular veterinary visits, pet insurance and keeping a cat indoors only are certainly high on the list. But the most powerful tool of all could be about the size of a grain of rice: a microchip.
Sometime over the past month or so, HomeAgain, a lost pet recovery service and microchip provider, reunited their one-millionth pet with the owner. (It was a challenge to tell exactly which pet was the one-millionth recovered because so many pets are found through HomeAgain — about 10,000 each month!)
Sadly, one in three family pets will get lost during its lifetime, and without identification, around 90 percent will not return home.
The Baumgardner family, of Lompoc, CA, lost their Pekeapoo, Chewie, two years ago. Ultimately, a microchip made reunification possible, but it took a while.
While the family was living in Arizona, Anita and her husband went out to dinner one evening, leaving Chewie and Jack, a Cocker Spaniel/Labrador mix, at home with the couple’s then 18-year-old son, AJ, and daughter Gaby, 13.
Jack likes to open doors, and as AJ snoozed on the sofa, the pooch slipped out the front door. While Jack strolled only a few feet away to catch some sun, Chewie zipped past him and kept on going.
“When we returned home, we searched the neighborhood, but it was already dark,” says Baumgardner. “We assumed in the morning Chewie would find his way home.” That never happened. The family notified HomeAgain, called local shelters, a local pet store and Chewie’s groomer, all to no avail. Time went by, and eventually the Baumgardners moved to Lompoc, CA.
“We all knew Chewie might have been hit by a car, or who knows what,” says Anita. “The hope was that maybe he was picked up by another family who just didn’t check to see if he had a microchip.”
Having a microchip alone is of little value. It’s like having a cell phone without a phone number. Pet owners need to register their contact information with the microchip provider and keep it up to date. Anita did provide new information when the family moved. In April 2012, she received a call from HomeAgain stating, “We have your dog.”
“I told them, ‘you must be mistaken. My dog is right here,'” Baumgardner recalls, referring to Jack.
“No, it’s Chewie,” said the caller.
“Well, this was two years later. I nearly fell out of my chair,” Anita recalls. It turns out Chewie had been spotted walking along a road and was picked up by a good Samaritan. The pet lover did the right thing, having Chewie scanned for a microchip at a local shelter. Because his registration information was up to date, HomeAgain was easily able to contact Anita.
Family members promptly headed to Arizona to pick up Chewie. Shelter staff said that even before Anita and Chewie were reunited, the dog heard Anita and clearly recognized her voice – even after two years. The reunion was joyous on all sides.
“Chewie looked pretty good. He’d even gained some weight, though he had a few missing teeth,” says Anita.
No one knows exactly where Chewie was for two years; perhaps he’ll write a “tell all” book.
Gaby was especially elated about the reunion. She posted photos every day for weeks on her Facebook page.
“Our dogs are a part of our family, and very important to us,” says Anita. “I think most people feel that way, which is why I’m such an enthusiastic supporter of microchipping.”
Of course, without this service, many of the one million animals recovered through HomeAgain would have been euthanized.
“Our family is sure grateful,” Baumgardner says.
### 38 Responses to “Keeping Your Pet’s Microchip Information Up-To-Date is Essential”
1. Julie Sargent says:
I was looking for an actual gps microchip and your site came up on my google search as such. Is there such a thing? I want to know if there is an app for this.
• I have seen something at the Pet Expo in Orange County called the “Pet Tracker Tagg”
That might be what you’re looking for
Pam
• Darryl says:
There is no such device. There is no way to power it yet. I suppose one could make a limited power one for a one time track, but it would run out of juice real quick. Not to mention the heat issue. You would burn the dog tracking it.
The ones online claiming to be a gps tracking chip, are just a microchip that comes with a collar that is the actual gps device. It might work in a short time frame if the thrives didn’t take their collar off.
• pamalaya says:
you are wrong darryl
• Amanda says:
Pamalaya, do you know of one then? Please share the information instead of just saying someone is wrong.
• Brian says:
TaGG was purchased by Whistle and they make GPS devices for dogs and cats. They use a base station relay that makes the battery last longer when they are in the home zone. I have 2 in use for my animals and the mobile app / web management of the devices works great.
2. amanda hill says:
We r buying 2 puppies from utah. Its seems kinda odd. They gave us the microchip number can I look it up to c if it matches the dogs
• Paris says:
yes you should be able to take them to the vet or even a shelter and have them scaned to see if the code match
• Diego says:
Amanda, as Pris said, but also keep in mind that even if the Breeder has implanted the K9 does not mean that they have been registered, however, if they are registered by the breeder, I would highly consider you to contact the microchip company and register under your name, That of course is the breeders contract doesn’t indicate that they will be registered under the Breeder ONLY. Good Luck!
3. Alyson says:
I adopted a dog a year ago from a family that couldn’t take her when they moved to a home that didn’t allow her breed. My kids and I have become very attached to the dog, but now the family thinks they can slip her into the home without the management finding out. They had her microchipped several years before and it has their name and old number and address attached to it. Being as they moved several states away I wanted to see if I could change the info on her microchip so they can’t take her back. I’m worried that they’ll be caught trying to take her into their home and then have to give her away to another family, and the cycle will repeat again.
I don’t know what else to do, but I don’t want them to take her away.
• Connie says:
I had gotten an old boxer off Craigslist about 7 years ago, when I got her, the girl stated that she couldn’t afford to feed her any longer, it was beyond obvious! I immediately to her to my vet, she was 8 years old, and should have weighed around 70 pounds, she only weighed 28. She was microchipped, but due to her extreme malnutrition, the vet reported her to the police for criminal charges. However! Since the dogs microchip was registered to her, the microchip company had to send me papers for the legal exchange, and to have her microchip registered to me. The girl first off, didn’t want to meet me to sign them since there was a warrant for her arrest over the dogs condition, I finally talked her into meeting me to sign it, I should probably add that while I was on the phone with the microchip company, they never once said a single word about a transfer of registration fee!! But when my vet scanned her chip, he informed me I need to get ahold of the humane society because she had an extensive history.I got ahold of them, and of course, since I wasn’t the owner of the dog, it was against the law to provide details of her history, just that she has been scanned into their facility 18 times, and gave me a warning that I needed to get the chip transferred as soon as possible because it was history that really needed to be disclosed to a new owner. I sent in the new registration/transfer papers, 7 months went by, and I kept contacting the humane society to see if the transfer had taken place yet. I called the chip company, and they said I had to redo the papers, which they said they would do immediately, the reason I had to redo the papers is because too much time had passed without me sending in the $500 transfer fee! No way! I couldn’t have the chip transferred to me ever! Because the girl had been arrested and was in for the next 6 years, I wrote and asked if she would resign it, and she hatefully wrote back to me saying I was the reason she was there in the first place! So hope with all you have the transfer fee isn’t anywhere close to that!! Each chip company has different prices and policies, most of them are free I have learned, she had her chipped at PetSmart, so I won’t ever go through them to get my dogs chipped! • Diego says: Dear Connie. Reading your experience with the ownership transfer was frustrating and it didn’t happen to me, Good lord, Im wondering if you ever received the History of the furry? i was also thinking, because Im an RVT, we get cases like these more then you would think, working with an Animal Rescue especially, we come across chipped stray dogs but never registered, at times we would re chip them in a case like yours and start fresh, Im so glad that, that woman faced justice, i just wish more people that careless about furries would face the same punishment. 4. Ronna says: My dog is Micro chipped and we moved, how do I up-date the information. He was micro chipped in 2010 at SPCA in Sacramento, CA I can not remember the name of the company. I do have the micro chip number. • Debbie says: You can call Home Again and tell them the microchip number and your address and whatever information you want to have the dog registered with Home Again and pay about nineteen dollars per year and they will put the dog in their registery. One of my cats came from a SPCA in southern California with an Avid microchip. Since my other cats have Home Again microchips, I registered my SPCA cat with Home Again using the Avid microchip and Avid microchip identification number. Home Again can handle it whatever company the origonal microchip is from. All you need to do is tell them the information and pay the yearly fee. 5. Caylah says: I have a dog and two cats… I have to get them microchipped because if I lose them I don’t know what I would do… They are everything to me. I am going to get them microchipped ASAP!!! This story inspired me so much, even though I have a really tender heart for any animal. This was an amazing story! Thanks so much for sharing it. -Caylah 6. Tomas says: Is it possible to just get the chip without putting it in your animal? • It is possible to purchase one or more chips from a rescue organization since they purchase in bulk, and often hold micro-chip clinics. They would expect that you would take your animal and the chip to your vet to have it inserted so that your pet would be protected. Keep in mind that this will be a chipping package so your vet should charge little to nothing to insert the chip plus the fact that the chip has cost the rescue a discounted amount since they have purchased large amounts. The only set back is that often they are secondary on the registration and would be notified if your pet was found if you do not keep your contact information up to date, so pick a local rescue and one that is willing to co-operate with you. They probably would be glad to help in order to protect the animal. If you are close to the NC/SC area and have trouble finding one let me know and I will try to help you get your pet chipped if you just need the chipping package. 7. Kyle Davis says: I have a two year old White German Shepherd. She is my life. I love her, and want to protect her the absolute best possible way from theft or getting lost. This is why I am contacting you guys. I am trying to find a GPS Microchip combo, where to get it, how much it was cost and so on. I looked up as much information as possible on the internet, and your website came up. I hope that you are able to help me with that. Please contact me with any information. If you don’t have any information, maybe you can send me in the right direction. Thank you in advance, Kyle Davis • I simply Googled “find my stuff” and found this comparison article. Although it’s not for pets, it might work until there is one specifically for pets http://www.wsj.com/articles/finding-the-best-lost-item-trackers-tile-trackr-and-duet-reviewed-1403046981 You can also register at http://www.findingrover.com for facial recognition of your dog. Pam • Steve says: Hi Kyle, Since this is a few weeks old you may have already taken action on protecting your precious dog. There is not a GPS microchip available at this time. The problem with having a GPS implantable device is the ability to charge the battery which would be necessary to power the GPS functionality. Plus the battery would likely go dead before you found the pet. There are GPS devices which can be worn on a collar but they cannot replace the value of an implanted microchip. And not all microchips or microchip registries are created equal. You should be sure you have an ISO compliant microchip. An ISO compliant microchip uses a unique 15 digit number, no letters, no spaces, no other characters. You should also use a company that provides a lifetime registration with no update fees, no renewal fees and has the registration database protected with funding which will make sure the registration will remain active even if the parent company goes out of business. I work for such a company called PetLink. Our registration database is PetLink.net. We have been a leader in pet microchipping for more than 25 years. We are the largest international microchip provider. Do not use a generic 900 microchip. The cheap 900 microchips are less likely to provide a quality service and the registration are more than 50% less likely to be found. I talked with 4 shelter directors last week who collectively had recently seen 20 pets with these 900 chips. All 20 pets were adopted out to new pet owners because the pet registration could not be found. 8. Alice Warley says: Microchiping is great but there are so many different companies that it could be useless to spend the money. We have 3 dogs with chips. One was chipped by the breeder the other two by our vet. The vets scanner doesn’t work on our Labs chip. The vet told us that his scanner only works on his chips. Same for the others I suppose. Also there is no law, at least in Tennessee, that requires a vet to scan a pet. So if your pet is found or stolen, take to a vet other than yours, or the vet is never told the dog was a stray then the chances of your pet being found with that chip could be 0. • Laurie says: Don’t most vets register the chip info with the chip company? Both my dogs were chipped with AVID – one at the shelter, the other at the vet’s. Both times, the office handled sending in my paperwork with my address and emergency contacts. All vets have been able to read the chips (we’ve been to at least 6 vets across several states). • Not that I’m aware of. They hand you a brochure for registration when the chip is put in. Each manufacturer is different. When you move it’s your responsibility to go to their website or call and update the information. 9. cynthia says: what scanners cab be used \to scan your Microchips. thanks you • We do not sell Microchips. The story was about Microchips from another source. 10. Veola says: I want a GPS implant. Not a tag. And not the homesafe identifier. I want something that will tell me know where my pet is now. I can’t find anything like that. The tags and collars that come with GPS may be good for some but if your dog is stolen then the tag and collar goes in the trash. And the identifier implant is only good if the vet the dog is taken to actually checks the dog and has a wand that reads that particular implant. Really, how many dog thieves are going to take a dog to the vet a say they found it? Unless they ask most don’t check. So to me that chip is useless. Even though all of mine have them. I want something that links up to a device or satellite and tells me where my babies are. Does anyone know if there is anything like that? 11. I have a microchip put in my Shih Tzu when he was just 18 months old. I need to update information on his registration, but I can’t even find his chip listed on Avid’s site. I am really upet. I paid to have this done, to protect him. I have his papers his microchip number, which one site told me THE MICROCHIP CHIP was not EVEN LISTED.. I can’t find the company’s REAL SITE, ALL THEY DO IS GIVE ME THE RUN AROUND, did they perhaps sell to another, company? I am just so dissatisfied, I saw the chip being put in him, I paid a good sume of money, and now this, I may as well have done nothing at all. One thing IS FOR CERTAIN HE IS NOT SAFE, I THOUGHT HE WAS BUT THIS SHOWS ME HE ISN’T. IF I CAN’T FIND HIS CHIP BY IT’S NUMBER HOW COULD ANYONE ELSE IF HE EVER GOT LOST. SOMEONE BETTER ANSWER MY QUESTIONS, OR I WILL HAVE NO OTHER CHOICE BUT TO CONTACT OUR ATTORNEY GENERAL OF WV THIS AVID COMPANY DOESN’T SOUND LEGAL, THER IS TOO MUCH RUN AROUND. • I also have an AVID chip. You must register it after it is put into your dog and pay$19.95 for lifetime membership.
If you do not do that, they will not have the number in their database.
12. Dave Sorensen says:
Anyone know how long these chips last? Any photos of them? size? thanks
• Mel Gresley says:
The chips last the lifetime of your pet. They are smaller than a grain of rice.
13. Terry Ramos says:
I was unable to register my pet. Pleas send instructions.
• What we posted is simply an article about keeping the microchip up to date. We are not the company that sells them or keeps the data. You need to find out the brand of the microchip from the veterinarian who did the implant and go to their website and register it there.
14. […] What are Microchips? […]
15. Larry mac says:
The real truth about micro chipping pets is that the chips costs pennies. The syringe dispenser is actually more expensive. There are at lest 16 different manufacturers, and fact is, if your vet buys so many chips he gets a free scanner. That scanner will ONLY read that brand of chip. So if the dog is found and taken to a vet, he may or may not be able to read the chip. The vet knows, and he has the option to do 3 things. #1 If he can read the chip give you the number #2 if he can’t read the chip, tell you there IS a chip but he can’t read it or #3 tell you NO CHIP.
He’s not making big bucks if you take the dog elsewhere for treatment etc. So like mechanics when you break down on the side of the road, they are going to take care of you for a price. But don’t expect angelic service at minimal expense. Past that hurdle, you can spend $9 if you buy and do it yourself to$50-60 to get a dog chipped. Only some scanners read all chips.. Usually the one that the City dog catcher has, because if they can identify the owner, he gets the ticket. Revenue enhancement. Once you have the dog chipped – you then need to register the number of the chip with a data base. There is more than one. that can be had $20 from a year to a lifetime. So it’s perplexing and confusing. AND INADEQUATE. Till such time that a organization (AKC or Humane Society) provides a national blanket service accessible to both the public and law enforcement, you’re the looser. The federal government isn’t going to waste their time, no money in it. Remember –follow the money – always. dogs or crooked politics.. The best possible ID for your dog is to tattoo your social security number on it’s belly. Any police officer can get a translation to a name and address in seconds on his 2 way radio. But we’re missing the overall point. -You don’t need ID if your dog doesn’t get out. Dogs get loose because owners fail to maintain safe confines. My dogs never get out I spent$1700 for a fence 10 years ago.
16. Stella says:
Well, ultimately your correct…pet safety is definitely owner responsibility but unfortunately, in my world, $1700. is more than most can afford for an animal fence…or anything else for that matter. But when you’re chosen to become the human of an animal as I was, you don’t really think of the money it may take, just the warm loving feeling that almost blinds you! I’ve had my cat for almost a year now and have managed to pay some outrageous vet bills (4 visits, 2 of them major, in the first 2 months after I got her) including hernia surgery and pneumonia. She now has a chip, which costs me 9 per month, eats good food, snacks more than I do and has enough toys for 3 cats, cat tree, cat condo, multiple scratch pads, pet fountain and finally an outdoor enclosure to keep her completely safe. NOT including vet bills, my total cost so far? Less than 50 bucks. My point is you don’t have to spend ridiculously, you just need to act responsibly. Clip coupons, call multiple vets before choosing,,, ASK QUESTIONS! there are a surprising amount of free clinics and other services available almost everywhere. DIY! You can make a toy out of almost anything…one they’re more likely to play with than a store bought one, but if they don’t like it, you’re not out any money. Cat tree and condo… Again, DIY! So many options and instructions on the internet. And If you think you need that$5000. enclosure from the pet store, look in the newspaper or the internet first and you may find one cheaper or even for free, like I did. 50 mile drive and had to disassemble (and reassemble same day) but totally worth it. Bought new only 3 months prior but their cat was afraid and refused to go outside. So one divorce and house sale later, I get to take a much needed road trip and my cat gets to terrorize the birds from a safe place. Of course money is greatly helpful but not completely neccesary, as even the poorest of people love their animals and do what they can to protect and provide for them, just as you do, but with smaller wallets. Trust me, my cat doesn’t love me for my money…she just loves me!
17. Linda says:
I do animal rescue and try to keep up with researching and I know there is no public microchip with gps right now as I do know there is supposed to be one being used possibly by the military for their dogs, I may be wrong but was told by someone who was in the military… I am going to research it and see what I can find out. They are trying to fine tune it and see how well its stability is and how well it works in various situations and conditions.
I also know there is supposed to be in I believe it is Canada a similar thing for people with Alzheimer etc to track them if they wonder off.
I microchip all animals I rescue, and if I get a lost dog in and it does not have microchip and I find the owners I offer to microchip for free so next time it will be quicker to find the owners.
And another thing I learned, some of the veterinarians in my area do not scan animals for microchips unless asked. I feel they should be doing it with all animals people bring in that are new to their family and that were adopted or purchased from someone else to make sure they have not got a stolen animal which is way too often in Minnesota for sure.
18. […] Microchip Information: Most guide dog schools microchip their dogs, linking either directly back to the school of origin or to the animal’s owner. Check with your school or the microchipping company to ensure they both have your most up to date contact information, including your correct phone number. […]
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# 2.6: The 20th century revolution in physics
The two greatest achievements of modern physics occurred in the beginning of the 20th century. The first was Einstein’s development of the Theory of Relativity; the Special Theory of Relativity in 1905 and the General Theory of Relativity in 1915. This was followed in 1925 by the development of quantum mechanics.
Albert Einstein (1879-1955) developed the Special Theory of Relativity in 1905 and the General Theory of Relativity in 1915; both of these revolutionary theories had a profound impact on classical mechanics and the underlying philosophy of physics. The Newtonian formulation of mechanics was shown to be an approximation that applies only at low velocities while the General Theory of Relativity superseded Newton’s Law of Gravitation and explained the Equivalence Principle. The Newtonian concepts of an absolute frame of reference, plus the assumption of the separation of time and space were shown to be invalid at relativistic velocities. Einstein’s postulate that the laws of physics are the same in all inertial frames requires a revolutionary change in the philosophy of time, space and reference frames which leads to a breakdown in the Newtonian formalism of classical mechanics. By contrast, the Lagrange and Hamiltonian variational formalisms of mechanics, plus the principle of least action, remain intact using a relativistically invariant Lagrangian. The independence of the variational approach to reference frames is precisely the formalism necessary for relativistic mechanics. The invariance to coordinate frames of the basic field equations also must remain invariant for the General Theory of Relativity. Thus the development of the Theory of Relativity unambiguously demonstrated the superiority of the variational formulation of classical mechanics over the vectorial Newtonian formulation, and thus the considerable effort made by Euler, Lagrange, Hamilton, Jacobi, and others in developing the analytical variational formalism of classical mechanics finally came to fruition at the start of the 20th century. Newton’s two crowning achievements, the Laws of Motion and the Laws of Gravitation, that had reigned supreme since published in the Principia in 1687, were toppled from the throne by Einstein.
Emmy Noether (1882-1935) has been described as "the greatest ever woman mathematician". In 1915 she proposed a theorem that a conservation law is associated with any differentiable symmetry of a physical system. Noether’s theorem evolves naturally from Lagrangian and Hamiltonian mechanics and she applied it to the four-dimensional world of general relativity. Noether’s theorem has had an important impact in guiding the development of modern physics.
Other profound developments that had revolutionary impacts on classical mechanics were quantum physics and quantum field theory. The 1913 model of atomic structure by Niels Bohr (1885-1962) and the subsequent enhancements by Arnold Sommerfeld (1868-1951), were based completely on classical Hamiltonian mechanics. The proposal of wave-particle duality by Louis de Broglie (1892-1987), made in his 1924 thesis, was the catalyst leading to the development of quantum mechanics. In 1925 Werner Heisenberg (1901-1976), and Max Born (1882-1970) developed a matrix representation of quantum mechanics using non-commuting conjugate position and momenta variables.
Paul Dirac (1902-1984) showed in his Ph.D. thesis that Heisenberg’s matrix representation is based on the Poisson Bracket generalization of Hamiltonian mechanics, which, in contrast to Hamilton’s canonical equations, allows for non-commuting conjugate variables. In 1926 Erwin Schrödinger (1887-1961) independently introduced the operational viewpoint and reinterpreted the partial differential equation of Hamilton-Jacobi as a wave equation. His starting point was the optical-mechanical analogy of Hamilton that is a built-in feature of the Hamilton-Jacobi theory. Schrödinger then showed that the wave mechanics he developed, and the Heisenberg matrix mechanics, are equivalent representations of quantum mechanics. In 1928 Dirac developed his relativistic equation of motion for the electron and pioneered the field of quantum electrodynamics. Dirac also introduced the Lagrangian and the principle of least action to quantum mechanics and these ideas were developed into the path-integral formulation of quantum mechanics and the theory of electrodynamics by Richard Feynman (1918-1988).
The concepts of wave-particle duality, and quantization of observables, both are beyond the classical notions of infinite subdivisions in classical physics. In spite of the radical departure of quantum mechanics from earlier classical concepts, the basic feature of the differential equations of quantal physics is their selfadjoint character which means that they are derivable from a variational principle. Thus both the Theory of Relativity, and quantum physics are consistent with the variational principle of mechanics, and inconsistent with Newtonian mechanics. As a consequence Newtonian mechanics has been dislodged from the throne it occupied since 1687, and the intellectually beautiful and powerful variational principles of analytical mechanics have been validated.
The 2015 observation of gravitational waves is a remarkable recent confirmation of Einstein’s General Theory of Relativity and the validity of the underlying variational principles in physics. Another advance in physics is the understanding of the evolution of chaos in non-linear systems that have been made during the past four decades. This advance is due to the availability of computers which has reopened this interesting branch of classical mechanics, that was pioneered by Henri Poincaré about a century ago. Although classical mechanics is the oldest and most mature branch of physics, there still remain new research opportunities in this field of physics.
The focus of this book is to introduce the general principles of the mathematical variational principle approach, and its applications to classical mechanics. It will be shown that the variational principles, that were developed in classical mechanics, now play a crucial role in modern physics and mathematics, plus many other fields of science and technology.
## References
Excellent sources of information regarding the history of major players in the field of classical mechanics can be found on Wikipedia, and the book “Variational Principle of Mechanics” by Lanczos.[La49]
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# Serial dependence is absent at the time of perception but increases in visual working memory
## Abstract
Recent experiments have shown that visual cognition blends current input with that from the recent past to guide ongoing decision making. This serial dependence appears to exploit the temporal autocorrelation normally present in visual scenes to promote perceptual stability. While this benefit has been assumed, evidence that serial dependence directly alters stimulus perception has been limited. In the present study, we parametrically vary the delay between stimulus and response in a spatial delayed response task to explore the trajectory of serial dependence from the moment of perception into post-perceptual visual working memory. We find that behavioral responses made immediately after viewing a stimulus show evidence of adaptation, but not attractive serial dependence. Only as the memory period lengthens is a blending of past and present information apparent in behavior, reaching its maximum with a delay of six seconds. These results dovetail with other recent findings to bolster the interpretation that serial dependence is a phenomenon of mnemonic rather than perceptual processes. However, even while this pattern of effects in group-averaged data has now been found consistently, we show that the relative strengths of adaptation and serial dependence vary widely across individuals. Finally, we demonstrate that when leading mathematical models of working memory are adjusted to account for these trial-history effects, their fit to behavioral data is substantially improved.
## Introduction
Even in contexts where visual input varies randomly from trial to trial, human observers tend to blend stimuli from previous trials into their representation of the current one, leading to a bias in behavioral reports1,2,3,4,5,6,7,8,9,10,11,12,13,14. This smoothing of representations – termed “serial dependence” – is a function of how close successive stimuli are in space1,15 and time1,2,3,4,5,6,7,12,14,15. It is also sensitive to their featural similarity1,2,3,7,8,9,10,12,14,16,17. Serial dependence has been observed in judgments of orientation1,8,9, and location16,17, as well as more complex attributes like the identity2 and attractiveness3,5,11 of human faces. That the bias is observed for such disparate features suggests it may be a universal principle of visual processing, and recent work has sought to demonstrate its adaptiveness8: In natural environments – where the input to our eyes is generally very similar from moment to moment18 – temporal smoothing would be expected to stabilize perception in the face of noise and occlusion1,8.
While the benefits of perceptual stability seem obvious, it is important to note that serial dependence impedes another goal of perception, which is to be sensitive to change. A classic example of how visual perception prioritizes change detection is the tilt after-effect19. This illusion (which is a type of adaptation20) is the quantitative opposite of serial dependence: Perception of the current moment is repelled away from, rather than merged with, recently processed stimuli – exaggerating differences. Like serial dependence, adaptation spans different types of stimulus features20,21,22,23,24. However, unlike adaptation, the attractive bias depends on attention: the observer must attend to each stimulus for serial dependence to occur1. Attention is thought to rely on the same neural and psychological mechanisms as working memory25,26,27,28,29,30,31. Hence, it is possible that whereas adaptation is a phenomenon of visual perception20,21,22,23,24, serial dependence arises instead from post-perceptual visual working memory9,32 If this were true, stability would operate in parallel with (rather than compete against) change detection, as these functions would be relegated to distinct cognitive systems9.
Preliminary efforts have been made to resolve whether serial dependence is perceptual or mnemonic in nature, with mixed results1,9. Using a comparison task that minimizes memory demands, one group identified positive serial dependence in a small number of individuals1 – in favor of the perceptual account. However, an attempt to replicate this effect with a larger sample size only revealed repulsive adaptation9. That is, no attractive serial dependence was observed when memory demands were removed using the same comparison task in the follow-up study, in support of the idea that serial dependence requires working memory9. A complementary strategy for clarifying this issue has been to boost memory demands – by increasing the delay between stimulus and response in delayed-estimation tasks – to determine whether this potentiates the attractive bias9,32. Traditionally, errors that scale with delay length are interpreted as mnemonic in origin, whereas those that are constant over time are assumed to be tied to the perceptual or motor demands that are also fixed33. Over a limited range, the magnitude of the serial dependence effect increases the longer that working memory is active9,16,17. Despite this potential connection to working memory, serial dependence has yet to be incorporated into the many mathematical models that have been developed in recent years to fit the dispersion of errors in human memory-guided behavior34,35,36,37,38,39,40,41,42,43,44.
In the present study, we investigate temporal smoothing in visual cognition over a wider range of memory delays than has been used in the past. We use a spatial delayed response task, which has been shown to produce serial dependence in non-human primates16,17. Previous experiments using delayed response tasks to measure serial dependence have included a visual mask after the stimulus presentation period1,2,8,9, as well as a delay period of at least several hundred milliseconds before a response is permitted1,2,8,9,16,17, which encourages encoding into working memory and cannot cleanly measure more fragile perceptual representations45,46. In our shortest delay condition, we allow participants to respond immediately after stimulus offset, with no mask. From this 0-s baseline, we parametrically increase the delay length up to 10 s. In a separate experiment, we parametrically manipulate the length of the inter-trial interval (ITI). This permits us to assess the decay rate of the trial-history effect in the absence of intervening trials – clarifying its potential functional and biological implementation. Finally, we pursue a novel formal unification of the serial dependence phenomenon with mathematical models of working memory34,35,37,38,39,40,41. This sets the stage for future experiments to dissect the neural mechanisms of serial dependence in the context of ongoing research into the organization of the working memory system32.
## Results
### Experiment 1: Manipulation of visual working memory delay
Participants completed a spatial delayed response task, depicted in Fig. 1. For Experiment 1, the length of the working memory delay period in this task was varied randomly from trial to trial (0, 1, 3, 6, or 10 s). Collapsing across these five delay conditions, we identified serial dependence in the group dataset significantly greater than zero ($$p < {10}^{-4}$$, group permutation test; peak-to-peak = 1.67°; bootstrapped 95% confidence interval = [1.48°, 1.85°]). To do this analysis, we measured the magnitude of serial dependence as the peak-to-peak of the curve fit to the pattern of errors across all possible differences between current and previous stimulus location (see Methods). The peak-to-peak is a measure of the maximal pull of responses away from the correct stimulus feature value as a result of this trial-history bias. Previous studies have used similar measures of amplitude to quantify serial dependence1,2,8,9,16. No bias was present in the data in the direction of the stimulus on the upcoming trial ($$n.s.$$, group permutation test; peak-to-peak $$=-0.14^\circ$$; bootstrapped 95% confidence interval = [−0.59°, 0.15°]), which supports the conclusion that the dependence of behavior on the previous trial is not due to spurious correlations in the particular randomized sequences of stimuli generated for the subjects10,14.
Next we examined each of the delays individually. The magnitude of serial dependence across memory delays from 0–10 s is plotted in Fig. 2a. When participants reported the location of the stimulus immediately after viewing it, presumably relying at least in part on residual neural activity associated with perception, their responses showed signs of sensory adaptation, an effect that is opposite in direction from serial dependence ($$p{\mathrm{ < 10}}^{-4}$$, group permutation test; peak-to-peak $$=\,-{1.72}^{\circ }$$; bootstrapped 95% confidence interval $$=[-{2.30}^{\circ },-{1.09}^{\circ }]$$; Fig. 2b). In contrast, for every other delay tested, serial dependence was significantly greater than zero (all $$p < 0.01$$, group permutation tests). Moreover, the magnitude of serial dependence increased from 0–1 s ($$p\, < \,{10}^{-4}$$, group permutation test; peak-to-peak at 1 s $$=\,0.85^\circ$$; bootstrapped 95% confidence interval $$\mathrm{=[0.48}^\circ \mathrm{,1.20}^\circ ]$$) and again from 3–6 s ($$p < {10}^{-3}$$; peak-to-peak at 6 s $$\,=\,3.37^\circ$$; bootstrapped 95% confidence interval $$=\,[2.88^\circ \mathrm{,3.84}^\circ ]$$) before asymptoting between 6 and 10 s ($$n.s.$$; peak-to-peak at 10 s $$\,=\,2.86^\circ$$; bootstrapped 95% confidence interval $$\,=\,[2.28^\circ \mathrm{,3.41}^\circ ]$$). Serial dependence was numerically strongest in the 6-s condition, shown in Fig. 2c. Here, the peak-to-peak is visible as the distance along the y-axis between the maximal and minimal values of the model fit to the data. We note that the asymptote in serial dependence between 6 and 10 s does not correspond to an asymptote in the accumulation of noise in working memory. Consistent with a recent theoretical study and reanalysis of empirical data47, we observed a sublinear increase in the variance of responses, which in the case of our data continued up to the 10 s delay (bootstrapped 95% confidence interval at 6 s $${\mathrm{=[41.28}}^{^\circ 2}{\mathrm{,44.92}}^{^\circ 2}]$$, at 10 s $${\mathrm{=[50.22}}^{^\circ 2}{\mathrm{,54.40}}^{^\circ 2}]$$; Fig. 3).
The large sample of participants from whom we collected data enabled us to assess the nature and range of individual differences in the pattern of trial-history effects that we observed at the group level. Adaptation and serial dependence are subtle effects – just a few degrees in magnitude at their peaks – whose tuning can be measured accurately only with many trials. Hence, we were statistically underpowered to detect differences between delay conditions for each individual subject (though we provide results divided by delay for a few sample subjects as Supp. Fig. 1). Instead, we collapsed over delay conditions for the purposes of evaluating which (if any) trial-history effect dominated throughout all time points in perception and working memory for each participant. The results are displayed in Fig. 4. Participants fell into three categories. Seven subjects showed evidence of strong repulsive adaptation that dominated across time points (all p < 0.05, permutation tests; all bootstrapped 95% confidence intervals $$< \,0$$). One of these, whose repulsive bias was strongest (peak-to-peak $$=-5.08^\circ$$), is presented in Fig. 4b (and Supp. Fig. 1A). Another 11 subjects had data that showed weak and/or noisy variation as a function of the previous stimulus’ location (all $$n.s.$$). The remaining majority of subjects ($$n=20$$) displayed visibly apparent and statistically significant attractive serial dependence (all $$p < 0.05$$; all bootstrapped 95% confidence intervals $$> \,0$$). However, among these, there was noticeable diversity in the tuning of the effect. Figure 4c shows the tuning over stimulus differences for one subject with a low-amplitude (peak-to-peak $$=\,1.57^\circ$$) and narrow attractive serial dependence surrounded by negative “peripheral bumps”9 (where the bias changes direction to repulsion when consecutive stimuli are far apart). In contrast, the participant highlighted in Fig. 4d (and Supp. Fig. 1B) evinced the canonical shape of the effect – a broad spread of the attractive effect (peak-to-peak $$=\,5.11^\circ$$) and less prominent peripheral bumps.
The time course of serial dependence we observed at the group level over the current trial’s delay period was not reproduced when trials were sorted based on the previous trial’s delay period. For each of the possible preceding delay period lengths, serial dependence in the current trial’s response was significantly greater than zero (all $$p < 0.01$$, group permutation tests; Fig. 5a). Between 0 and 6 s (of delay on the previous trial), serial dependence varied little (all comparisons $$n.s.$$, group permutation tests; minimum peak-to-peak at 6 s $$=\,1.78^\circ$$; maximum peak-to-peak at 3 s $$=\,2.21^\circ$$; all bootstrapped 95% confidence intervals overlapping). However, when the previous delay was as long as 10 s, serial dependence was significantly reduced relative to each of the other delay lengths (all $$p < 0.005$$; peak-to-peak at 10 s $$=\,0.91^\circ$$; bootstrapped 95% confidence interval $$=\,[0.50^\circ \mathrm{,1.20}^\circ ]$$). Tuning for the conditions with the strongest (3 s) and weakest (10 s) serial dependence are displayed in Fig. 5b and c, respectively. This set of findings is partially consistent with results from another study that tested a narrower range of delays (0.8 – 3.2 s) in non-human primates16. In this earlier study, it was found that the amplitude of serial dependence remained constant over this range (of previous delay length). Here, we extend this result to show that the previous trial’s influence does eventually decay when the previous trial’s delay is especially long.
In line with past work on the sources of error in working memory9,33, our findings suggest that the increasing serial dependence over longer delays (in the current trial) reflects its association with mnemonic processes rather than perceptual and motor processes that were held constant in our experiment. Research over the last decade has yielded several mathematical models designed to isolate distinct sources of error in working memory34,35,37,38,39,40,41. None of these include parameters for the proactive interference that serial dependence represents32. Also, the only substantive difference between the models is their characterization of noise in the distribution of behavioral responses. As a form of systematic error, serial dependence is separable from noise, and so can be incorporated into any of these models without changing their definitions or differences. The simplest model (sometimes called the “equal precision” model37,39) fits random error with a single von Mises distribution34. In contrast, the “variable precision” model assumes the standard deviation parameter of the von Mises varies from trial to trial according to a gamma distribution37,38. A third model explicitly regards the precision of working memory as arising from noise in Poisson-distributed spike trains of individual neurons40,41. Errors in this model are distributed according to a von Mises random walk41. We will refer to these three working memory models as EP (equal precision), VP (variable precision), and VMRW (von Mises random walk).
As a first pass, we fit each of these models to the behavioral data from Experiment 1. Model comparison on the basis of the corrected Akaike Information Criterion (AICc) revealed that the VMRW model fit the data about as well as the VP model (Δ AICc $$=\,3.9\pm 5.3$$ in favor of VMRW). Both of these models fit the data better than the EP model ($${\rm{\Delta }}$$ AICc $$=\,40.2\pm 9.6$$ in favor of VMRW; $${\rm{\Delta }}$$ AICc $$=\,36.2\pm 8.1$$ in favor of VP). This relative performance is consistent with published comparisons of the three models using behavioral data from other working memory tasks37,38,39,40.
Next, we created a hybrid model that incorporates serial dependence into the mean of the VMRW distribution – sliding the mean clockwise or counterclockwise on each trial by the magnitude dictated by the tuning of the history effect (see Methods). This hybrid model significantly outperformed the base VMRW model ($${\rm{\Delta }}$$ AICc $$=\,29.2\pm 7.9$$). However, this result on its own falls short of confirming that the serial dependence tuning function is needed to quantify the influence of the history effect on each trial. To verify that inclusion of the tuning curve visible in Figs 2 and 46 is needed for the improvement in fit, we developed an alternative hybrid “memory confusion”2 model that takes trial history into account in a different way. In this model, it is assumed that on a subset of trials, subjects simply mix up which stimulus belongs to the current trial and report the previous trial’s location when probed (analogous to a “swap”36,43 over time rather than space). This “memory confusion” model provided no benefit above the base VMRW model and made it worse, due to the addition of parameters that captured little variance ($${\rm{\Delta }}$$ AICc $$=-7.7\pm 2.7$$).
Finally, we tested whether the addition of the serial dependence tuning function to all three of the base models would change the order of performance among them. Whereas the VMRW and VP models performed equivalently without taking account of serial dependence, we found that the extended VMRW model outperformed the extended VP model when fit to our data ($${\rm{\Delta }}$$ AICc $$=\,12.2\pm 4.1$$). The fit of the extended EP model was still worse than that of the VP model with serial dependence terms ($${\rm{\Delta }}$$ AICc $$=\,14.7\pm 5.2$$). Hence, the overall best-fitting model to our data was the VMRW model with added terms for the DoG-shaped serial dependence effect.
### Experiment 2: Manipulation of baseline interval between trials
It is possible that the delay manipulation in Experiment 1 confounded two variables1: the time for which subjects must hold the current item in memory and2 the time that has elapsed since the behavioral response on the previous trial, before the current trial’s response. To assess whether the time course of serial dependence we observed (Fig. 2a) corresponds to mnemonic processes and not the simple passage of time, we conducted a second experiment in which the inter-trial interval (ITI) varied randomly among 1, 3, 6, and 10 s. The delay in this new task was held constant at 3 s. In all other respects, the tasks for the two experiments were identical.
Collapsing across ITIs, we identified serial dependence in the group dataset significantly greater than zero ($$p < {10}^{-4}$$, group permutation test; peak-to-peak $$=\,1.62^\circ$$; bootstrapped 95% confidence interval $$\,=\,\mathrm{[1.38}^\circ ,\,1.86^\circ ]$$). As for Experiment 1, there was no bias in the data in the direction of the stimulus on the upcoming trial ($$n.s.$$, group permutation test; peak-to-peak = 0.23°; bootstrapped 95% confidence interval = $$[-0.15^\circ ,0.80^\circ ]$$), an important control10,14. This pair of results replicates our finding from Experiment 1 of serial dependence in this spatial delayed response task, using an independent dataset.
Next we examined each of the ITIs individually. The magnitude of serial dependence across ITIs from 1–10 s is plotted in Fig. 6a. The magnitude of serial dependence decreases gradually during the interval between trials, marginally from 3–6 s ($$p=0.01$$, group permutation test, Bonferroni-corrected $$\alpha =0.008$$; lower bound of bootstrapped 95% confidence interval at 3 s $$=\,2.48^\circ$$; upper bound of confidence interval at 6 s $$=\,1.81^\circ$$) and significantly from 6–10 s ($$p < {10}^{-4}$$; lower bound of bootstrapped 95% confidence interval at 6 s $$=\,1.00^\circ$$; upper bound of confidence interval at 10 s $$\,=\,0.48^\circ$$). The difference in serial dependence between the 1-s (Fig. 6b) and 3-s ITIs was statistically non-significant. The slope of this time course is opposite that obtained in Experiment 1, strengthening our conclusion that increased serial dependence with increased delay length is due to the prolongation of memory demands rather than the mere passage of time. For the largest ITI (10 s), participants’ responses on the trial after the ITI were repelled away from the preceding trial’s stimulus, an effect consistent with sensory adaptation ($$p=0.006$$; peak-to-peak = −1.38°; bootstrapped 95% confidence interval $$=\,[-2.15^\circ ,-0.48^\circ ]$$; Fig. 6c). In contrast, for every other ITI tested, serial dependence was significantly greater than zero (all $$p\le {10}^{-3}$$, group permutation tests).
## Discussion
In everyday visual experience, humans rely not just on moment-to-moment perception but also on continued maintenance of information in working memory to navigate their environments and accomplish tasks. While there is much evidence to suggest that working memory recruits the same cortical areas active during sensory perception48,49,50,51,52,53,54,55,56, remembered visual content differs in quality33,57,58 – and potentially representational format59,60 – from feedforward signals driven by the presence of an external stimulus. Both behavioral data33,57,58 and computational theory61 have implied that passage of visual percepts into memory makes them less precise. This past work has also claimed that mnemonic processes do not attach to percepts any accumulating systematic bias – just random noise due to drift and/or decay33,57,58,61. With the experiments reported here, we provide new evidence to disconfirm this view. Serial dependence – a systematic bias in the direction of the preceding trial’s stimulus – is absent from percepts until the working memory system is engaged. Our demonstration of repulsive adaptation – with no attractive serial dependence – in the perception condition extends previous work9 by showing that this oppositely valenced effect that precedes working memory does not require that subjects make a comparison between two simultaneously presented stimuli9; adaptation occurs in the context of the same delayed response task that yields serial dependence when memory demands are increased.
By testing a wider range of delays between stimulus and response than used in previous studies9,16,17, we were able to chart the time course of serial dependence in visual working memory. This technique – of probing participants to report the contents of memory at variable points in time after stimulus offset – is common in visual psychophysics62. It has revealed how information passing through the visual system progresses from a rich perceptual code to a more impoverished mnemonic one. For a few hundred milliseconds after visual input ceases, a great deal of perceptual detail is still accessible to the observer in iconic memory – a form of storage intermediate between perception and working memory63. After that, within one second of delay, capacity-limited, distraction-resistant working memory comes online in parallel with a larger-capacity system that is vulnerable to distraction – fragile memory45,46,64,65,66,67. Our experiments demonstrate that the residual sensory trace associated with iconic memory is free of serial dependence – though it does carry the opposite, repulsive bias associated with sensory adaptation. The attractive bias arises slowly in the later short-term memory systems, but asymptotes before long-term storage processes are engaged (at approximately 20 seconds of delay58). Future research may resolve with finer resolution the exact moment at which serial dependence appears and whether it is most strongly associated with fragile or distraction-resistant stages of working memory. (Consistent with most work in this area68,69, we have tended to use the term “working memory” as a shorthand for both of these systems.)
Our results indicate that not only do the relative strengths of serial dependence and adaptation differ over time (between perception and working memory) – they also differ across individuals (Fig. 4). This suggests that serial dependence may appear in behavior sooner – perhaps as early as the perceptual period – in individuals for whom adaptation processes are especially weak (Supp. Fig. 1). By the same reasoning, experimental manipulations employed to dimish the strength of adaptation might help reveal an earlier onset of weak, underlying positive serial dependence in most subjects. However, as it can take as little as 50 ms for a viewed stimulus to be consolidated into working memory70, it seems unlikely that future investigations conducted at finer temporal resolution will identify robust serial dependence at time points that definitively exclude the involvement of working memory – especially given that positive serial dependence is weaker the sooner the response is made to a stimulus. (We note that subjects are likely to have engaged working memory encoding processes even in our 0-s delay condition, where serial dependence was not consistently observed. Our argument is that consolidation into working memory is likely necessary, but not always sufficient – if maintenance times are short – for the occurrence of the effect.) The measurement of neural signals associated with serial dependence may be needed to definitively disambiguate whether the effect originates in low-level sensory cortex immediately upon sensory perception or hundreds of milliseconds later, after sensory input has propagated to higher-level areas involved in the maintenance of short-term perceptual memories32.
Beyond demonstrating that serial dependence accumulates for longer in working memory than previous studies have indicated9,16,17, we have taken strides to integrate this phenomenon into the study of working memory in ways it has not been before32. Specifically, we have made concrete, formal improvements to prominent mathematical models designed to characterize the psychological architecture of working memory. The provision of terms for serial dependence to these models allows them to capture more variance in behavioral data and ensures that the variance associated with the temporal smoothing operation of serial dependence does not distort estimates of the models’ other parameters. Furthermore, our results demonstrate that the inclusion of these terms can reveal performance differences between seemingly equivalent models – we found that the VMRW model performs better than the VP model only after the tuning of the trial-history effect is taken into account. Claims that have been made about the nature of decay rates in working memory without consideration of trial-history biases must now be reëvaluated. For example, one study that modeled behavioral responses following different delay period lengths concluded that maintained representations are susceptible to spontaneous complete erasure from working memory as the delay length increases (measured as an increase in guess rates), but not to subtle degradations in precision (measured with the $$\kappa$$ parameter of a variation on the EP model)42. However, because this study ignored potential serial dependencies in the data, as well as alternative models of noise (e.g., VP and VMRW), the validity of this conclusion is unclear. It is impossible to address claims about total loss of information from memory with our data, because guess rates in our simple one-item spatial task were near zero. In the future, however, the hybrid models we have developed that incorporate serial dependence may help elucidate the nature of working memory storage in more difficult multi-item tasks44. To what extent serial dependencies occur when multiple items are held in mind at once is an open question that the hybrid models we have validated can help answer.
Our experiments have filled other gaps in the field’s understanding of the temporal properties of serial dependence. We have determined the approximate duration for which this effect persists between trials. At least in spatial working memory, the attractive bias disappears within ten seconds after the end of each trial, and is replaced by (or exposes a persistent) low-amplitude adaptation. This constrains possible neural theories of serial dependence – viable mechanisms must have time constants on the order of 10 s, which rules out especially short-term (e.g., synaptic facilitation) and long-term (e.g., long-term potentiation) forms of plasticity. Previous attempts to measure the washout period of serial dependence in humans have used a short, fixed ITI, preventing the measurement of pure time in the absence of intervening trials1,14. One experiment using non-human primate subjects did report a decrease in serial dependence between 2 and 7 s of ITI16. Over this range, the effect remained above baseline for two of three subjects, and no crossover to adaptation was observed. We have also shown that serial dependence weakens when the stimulus on the previous trial is maintained for as long as 10 s. It is possible that the neural code changes abruptly around this time point: for example, elevated neural firing keeping the representation active may begin to fail spontaneously (as happens in some neural-network models71), leaving the representation in an “activity silent” state supported by short-term plasticity72,73. Exponential decay of this synaptic trace (without continued active firing to keep it in place) may explain the reduced influence on responses on the subsequent trial.
Reframing serial dependence as a phenomenon of working memory rather than perception does not change the theories that have been put forth about its functional importance32. Thus, it remains an important mechanism for stabilizing representations against interruptions in visibility1,8. The contents of working memory track the focus of attention25,26,27,28,29,30,31, which, during the execution of a single goal, can remain the same for several seconds, even as the raw visual input that impinges on the retina fluctuates due to saccades, occlusion, and changes in lighting. Hence, temporal autocorrelation in visual working memory is potentially even higher than it is in visual scenes (and perception). If true, this would explain why serial dependence may have evolved in working memory as opposed to perceptual circuits – more autocorrelation enhances the ability of temporal smoothing to limit the influence of noise and boost signal. Moreover, the offloading of attractive serial dependence to memory systems may accord perceptual systems enhanced capacity to specialize in novelty detection, in part via adaptation. More research is needed to elucidate the ways in which serial dependence and adaptation interact, and to reveal the ecologically valid situations in which one or the other (perhaps both at the same time) enhance visual performance32. Such continued study should aim to clarify the mechanisms and functional consequences of the striking diversity we observed in the strength and tuning shape of these effects across individuals.
## Methods
### Participants
Fifty-five adults (34 female) from the UC Berkeley community were recruited to participate in this study. Thirty-five of these individuals completed Experiment 1 only, fourteen completed Experiment 2 only and six completed both experiments. All aspects of data collection and analysis were conducted in accordance with guidelines approved by the Committee for the Protection of Human Subjects at UC Berkeley. Informed consent was obtained from all subjects, and they were compensated monetarily for their time.
### Experimental Procedures
Participants completed the protocol in a soundproof, dimly lit testing room. For both experiments, they completed a spatial delayed response task, depicted in Fig. 1 (adapted from44). The task was programmed in MATLAB using the Psychophysics Toolbox74 (version 3) and run on a Mac mini (OSX El Capitan 10.11). For eight subjects in Experiment 1, a 17-in monitor was used with a screen resolution of 1280 × 1024 pixels. The remaining sessions were run with a 23-in monitor, 1920 × 1080 pixels. Results with regard to serial dependence were not appreciably different between the two groups that used different monitors (Supp. Fig. 3). All participants were seated such that their eyes were approximately 60 cm from the center of the testing display.
The stages of the generic task used for both experiments are as follows (with angle measurements reported in degrees of visual angle). Each trial began with the presentation of a black circle for 1 s at a random polar angle from fixation, with eccentricity fixed at $$12^\circ$$. The circle’s diameter was $$1^\circ$$. All stimuli were displayed against a gray background. Participants were instructed to fixate a central black square – which spanned $$0.5^\circ$$ × $$0.5^\circ$$ – whenever it was on the screen (all stages of the task aside from the response period). In Experiment 1, participants remembered the location of the presented circle for a delay that varied randomly from trial to trial (0, 1, 3, 6, or 10 s). The delay was always 3 s in Experiment 2. At the end of the delay, the fixation square was replaced with the mouse cursor (at the exact center of the screen), and participants indicated the location in mind by moving the cursor to that location and clicking once. No feedback was given. Errors were measured in degrees of polar angle. In Experiment 1, a 1-s ITI followed the response period, before the start of the next trial. The ITI varied randomly from trial to trial in Experiment 2 (1, 3, 6, or 10 s). Each participant completed 1,000 trials (200 per delay) in Experiment 1, divided into 40 blocks over the course of one or two experimental sessions. All but two participants completed 1,008 trials (252 per ITI) in Experiment 2. The remaining two participants completed 999 and 1,017 trials, respectively.
### Data Analysis
The data were analyzed using Python, MATLAB, and shell scripts. All code written for this study is available in a public Git repository (https://github.com/dabliss/bliss_sd_behavior_2017.git).
Before model fitting for trial-history effects, the data were submitted to preprocessing. First, trials with responses that were within 5° of visual angle of the origin were dropped, as were trials with responses further than three standard deviations from the participant’s mean error (<0.7% of all trials, across subjects). Next, we computed systematic directional error as the mean response for each stimulus location. This mean was then subtracted from the response on each individual trial (ignoring the location of the previous trial) to obtain the residual error that was used to characterize serial dependence. Replicating the procedure in16, we computed the systematic error by spatially low-pass filtering the responses as a function of stimulus location using the MATLAB function loess. Finally, to ensure that our analyses were restricted to data from participants who performed the task correctly, we removed those with noticeably poor performance. Specifically, we removed subjects with an overall mean absolute error greater than $$10^\circ$$ of polar angle. This criterion, though arbitrary, removed only subjects with qualitatively noisy error histograms while retaining those whose errors were roughly normally distributed around the correct value (the expected pattern). Only three subjects in Experiment 1 failed to pass this criterion (mean absolute error $$37.3\pm 19.5$$ for these three compared to $$4.7\pm 0.2$$ for the others). Data from two subjects in Experiment 2 were excluded ($$53.9\pm 1.8$$ for these compared to $$4.7\pm 0.4$$ for the others).
Studies that have modeled the tuning of serial dependence to featural differences between past and current visual stimuli have used the derivative of Gaussian (DoG)1,2,8,9 (or the very similar Gabor function16,17). There is another function in the perception literature, developed by Clifford and colleagues20, that has been used to model sensory adaptation – and that therefore fits serial dependence readily (when multiplied by −1). Overall, these functions fit the data from our Experiment 1 equivalently well (collapsing over delays, $${\rm{\Delta }}$$ AICc = $$0.8\pm 1.0$$, favoring DoG over Clifford), and this equivalence also holds for Experiment 2 (collapsing over ITIs, $${\rm{\Delta }}$$ AICc = $$\,1.1\pm 1.0$$, favoring DoG over Clifford). However, we noted significant differences between the Clifford and DoG models in certain conditions. Occasionally, the attractive bias of serial dependence is accompanied by a repulsion effect (“peripheral bumps”9) when previous visual input is close to maximally different from the input on the current trial (the extremes of the x-axis in Fig. 2c). The DoG cannot account for this reversal of the response bias, so when it is prominent in the data, the best fit of the DoG tends to mischaracterize the true effect size (e.g., 4C). The Clifford model is a combination of sinusoids of different frequencies designed to capture the peripheral bumps when they appear20. However, when the trial-history effect is narrow over stimulus differences and there are no peripheral bumps, the Clifford model tends to fail (e.g., Fig. 2a). This is because the Clifford model – unlike the DoG – does not have an independent width parameter; shrinking the central width of the Clifford fit requires that the peripheral bumps be increased. To be consistent with previous literature on serial dependence, we use the DoG for all analyses, except in cases where it provides a poor fit to the data, in which case we use the Clifford model (as noted below). The mathematical definitions of both models are reported next.
In this study, differences between past and current visual input ranged between −180 and $$180^\circ$$ of polar angle (a complete circle). The DoG is defined as
$$y=xawc{e}^{-{(wx)}^{2}},$$
(1)
where $$y$$ is the signed error, $$x$$ is the relative angle of the previous trial, $$a$$ is the amplitude of the curve peaks, $$w$$ is the width of the curve, and $$c$$ is the constant $$\sqrt{2}/{e}^{-0.5}$$.
The Clifford model is stated as follows:
$$\sin (y+x)=\frac{\sin (x)}{\sqrt{{(s\cos (x)-c)}^{2}+{\sin }^{2}(x)}},$$
(2)
where $$s$$ is a scaling parameter and $$c$$ is a centering parameter.
We used the scipy75 function least_squares (in the optimize module) to find the values of $$a$$ and $$w$$, in the case of the DoG, or $$c$$ and $$s$$, in the case of the Clifford model, that minimized the difference, for each $$x$$, between the estimated $$y$$ and the subject’s actual error. Across all values of $$x$$, we take the magnitude of serial dependence (or adaptation) to be the peak-to-peak of $$y(x)$$, with the sign adjusted to match the direction of the effect (see Fig. 2c).
To determine whether the magnitude of serial dependence was significantly greater than zero, or greater in one condition than in another, we submitted the data to permutation testing at the group level2,9. Specifically, we shuffled the values of $$x$$ (current trial’s location relative to the previous trial’s) while leaving in place the corresponding errors. We then fit the DoG to the shuffled dataset. This process was repeated 10,000 times. The $$p$$-values we report are the proportion of permutations that led to equal or higher values for the peak-to-peak of the function fit than the one estimated for the unshuffled data. In the case of a comparison between conditions, we subtracted the null peak-to-peaks for one condition from those for the other, and report the proportion of these differences that had equal or higher values than the empirical difference. The criterion for significance was Bonferroni-corrected for each family of tests.
We computed bootstrapped confidence intervals as follows:2,9 We resampled the data with replacement 10,000 times. We then fit the DoG to each resampled dataset. This yielded a distribution of peak-to-peak values from which we selected the boundaries of the 95% confidence interval – separately for each delay and ITI condition.
In our statistical analyses of group data, only one condition – the 10-s condition in the analysis of the previous trial’s delay length for Experiment 1 – could not be fit reliably using the DoG, due to large peripheral bumps (Fig. 5c; Supp. Fig. 2). Hence, for this analysis we used the Clifford model, which estimated the peak-to-peak reliably. In our plot of individual subjects’ data (Fig. 4a), the DoG fit (with bootstrapped confidence intervals) is reported for all but three subjects, for whom the Clifford model was a qualitatively superior fit. These three subjects are labeled in the figure, and one is highlighted in Fig. 4c.
Three base mathematical models of working memory – EP34, VP37,38, and VMRW40,41 – were fit to our behavioral data, as described in the Results. Model fitting was done using the MATLAB function fminsearch, separately for each delay condition. EP is defined as
$$p(\hat{s}|s;k)=\frac{e{k}^{\cos (\hat{{\rm{s}}}-s)}}{2\pi {l}_{0}(k)},$$
(3)
the von Mises probability density function. Here, $$\hat{s}$$ is each trial’s response, $$s$$ the corresponding stimulus, and $${I}_{0}$$ the modified Bessel function of the first kind, order zero. The concentration parameter, $$\kappa$$, is a measure of response precision, spanning all trials, and is the model’s one free parameter for fitting.
In VP, precision is drawn anew for each trial from a gamma ($$\gamma$$) distribution with mean $$\bar{J}$$ and scale parameter $$\tau$$ (the model’s free parameters). Built from EP, this gives
$$p(\hat{s}|s;\bar{J},\tau )=\int EP(\hat{s};s,{\rm{\Phi }}(J))\gamma (J;\bar{J},\tau )dJ,$$
(4)
where EP’s concentration parameter $$\kappa$$ is a function of $$J$$ – here expressed as $${\rm{\Phi }}(J)$$ – and $$J$$ is formally defined as Fisher information. The analytical relation between $$\kappa$$ and $$J$$ is $$J=\kappa \frac{{I}_{1}(\kappa )}{{I}_{0}(\kappa )}$$, and $${\rm{\Phi }}(J)$$ is approximated numerically using this equation. The integral in Equation (4) has no analytical expression and so is also approximated using Monte Carlo simulations37,39.
Finally, in VMRW, noise in working memory is distributed according to a von Mises random walk, as derived from a population coding model of cortex41. Specifically, behavioral errors for a random walk of length $$r$$ are von Mises distributed:
$$p(\hat{s}|s;r,k)=\frac{{e}^{{\rm{k}}r\cos (\hat{s}-s)}}{2\pi {l}_{0}(kr)},$$
(5)
where the distribution of $$r$$ for $$m$$ walk steps is
$$p(r|m,k)=\frac{{l}_{0}(kr)}{{l}_{0}{(k)}^{m}}r{\psi }_{m}(r).$$
(6)
Here, $$r{\psi }_{m}(r)$$ is the probability density function for a uniform random walk of length $$r$$ and number of steps $$m$$. The variable $$m$$ is itself Poisson-distributed, with expected value $$\xi$$. For additional equations and a full derivation, including the neural interpretation of these variables, see41. In order to fit this model to data, we approximated the density $${\psi }_{m}(r)$$ via Monte Carlo simulation. The free variables for fitting are $$\kappa$$ (the concentration parameter) and $$\xi$$, which corresponds to gain.
We added terms to these base models to capture temporal smoothing in the data in the form of serial dependence (or adaptation). In particular, we allowed the mean of each model’s probability density function to vary on a trial-by-trial basis, as a function of the location of the previous trial’s stimulus. Given a particular difference in location between the current and previous trial’s stimuli, the mean shift was set to be the value of the DoG model fit to the data at that point. (That is, in visual terms, the input to the model was a point on the x-axis in Fig. 2c, for example, and the output mean shift was the DoG function’s value on the y-axis.) This procedure added two additional variables to each of the base models – $$a$$ and $$w$$.
As an alternative to the base models with the serial dependence expansion, we made alternative models that account for trial history by assuming that participants, on a subset of trials, confuse which stimulus was presented most recently and report the wrong item when probed. This alternative similarly allowed the mean of the base probability density functions to shift, depending on the difference between the previous trial’s location and the current one, without altering their shape or width. This “swap over time” model is defined as36
$$p(\hat{s}|s)=(1-\alpha )BM(\hat{s}-s)+\alpha BM(\hat{s}-s\ast ),$$
(7)
where $$BM$$ is a base model, $$\alpha$$ (an additional free parameter) sets the frequency of swaps, and $${s}^{\ast }$$ is the stimulus location for the previous trial.
Within each model, we used a separate set of parameters for each memory delay length, and formally compared the fits of different models using the Akaike Information Criterion (as recommended in39), with the standard correction for finite sample sizes (AICc). AICc values were averaged across subjects for these comparisons.
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73. 73.
Stokes, M. G. ‘Activity-silent’ working memory in prefrontal cortex: a dynamic coding framework. Trends in Cognitive Sciences 19, 394–405 (2015).
74. 74.
Brainard, D. H. The psychophysics toolbox. Spatial vision 10, 433–436 (1997).
75. 75.
Jones, E., Oliphant, T. & Peterson, P. Scipy: Open source scientific tools for python. http://www. scipy. org/ (2001).
## Acknowledgements
We thank David Whitney (and the Whitney Lab), Michael Silver, Bill Prinzmetal, Jason Scimeca, and Anastasia Kiyonaga for helpful discussions throughout the completion of this study. We also thank Ronald van den Berg and Paul Bays for sharing with us their code for model-fitting.
## Author information
### Affiliations
1. #### UC Berkeley, Helen Wills Neuroscience Institute, Berkeley, CA, USA
• Daniel P. Bliss
• , Jerome J. Sun
• & Mark D’Esposito
2. #### UC Berkeley, Department of Psychology, Berkeley, CA, USA
• Mark D’Esposito
### Contributions
D.P.B. and M.D. designed the experiment and wrote the paper. D.P.B. prepared the stimuli. D.P.B. and J.J.S. tested the subjects and analysed the results.
### Competing Interests
The authors declare that they have no competing interests.
### Corresponding author
Correspondence to Daniel P. Bliss.
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KL-divergence between two products
Given factorizations of two joint densities $p(x_1,...,x_n)=\prod_{i=1}^n p(x_i\mid \textrm{cond}(x_i))$ and $q(x_1,...,x_n)=\prod_{i=1}^n q(x_i\mid \textrm{cond}(x_i))$, where $\textrm{cond}(\bullet)$ denotes the set of conditioning variables, does the KL-divergence decompose, i.e., does
$\textrm{KL}(p\Vert q)= \sum_{i=1}^n \textrm{KL}\left(p(x_i\mid \textrm{cond}(x_i))\ \Vert\ q(x_i\mid \textrm{cond}(x_i))\right)$
hold?
• If it makes things easier, you can assume $\textrm{cond}(x_i) \in \{x_1,\ldots,x_n\}$ . More generally, the two factorisations are Bayesian networks, which means that $\textrm{cond}(x_i)$ can be any subset of $\{x_1,\ldots,x_n\}$ so that the induced graph structure is a directed acyclic graph. – ASML Jan 23 '16 at 14:23
• How do you define $\textrm{KL}\left(p(x_i\mid \textrm{cond}(x_i))\ \Vert\ q(x_i\mid \textrm{cond}(x_i))\right)$ ? The ambiguous part is how you integrate out the $cond(x_i)$ variables in there – Guillaume Dehaene Feb 3 '16 at 13:42
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# spynnaker.pyNN.models.neuron.structural_plasticity.synaptogenesis.formation package¶
## Module contents¶
class spynnaker.pyNN.models.neuron.structural_plasticity.synaptogenesis.formation.AbstractFormation[source]
Bases: object
A formation rule
get_parameter_names()[source]
Return the names of the parameters supported by this rule
Return type: iterable(str)
get_parameters_sdram_usage_in_bytes()[source]
Get the amount of SDRAM used by the parameters of this rule
Return type: int
vertex_executable_suffix
The suffix to be appended to the vertex executable for this rule
Return type: str
write_parameters(spec)[source]
Write the parameters of the rule to the spec
Parameters: spec (DataSpecificationGenerator) –
class spynnaker.pyNN.models.neuron.structural_plasticity.synaptogenesis.formation.DistanceDependentFormation(grid=(16, 16), p_form_forward=0.16, sigma_form_forward=2.5, p_form_lateral=1.0, sigma_form_lateral=1.0)[source]
Bases: spynnaker.pyNN.models.neuron.structural_plasticity.synaptogenesis.formation.abstract_formation.AbstractFormation
Formation rule that depends on the physical distance between neurons
Parameters: grid (tuple(int,int) or list(int) or ndarray(int)) – (x, y) dimensions of the grid of distance p_form_forward (float) – The peak probability of formation on feed-forward connections sigma_form_forward (float) – The spread of probability with distance of formation on feed-forward connections p_form_lateral (float) – The peak probability of formation on lateral connections sigma_form_lateral (float) – The spread of probability with distance of formation on lateral connections
distance(x0, x1, metric)[source]
Compute the distance between points x0 and x1 place on the grid using periodic boundary conditions.
Parameters: x0 (ndarray(int)) – first point in space x1 (ndarray(int)) – second point in space grid (ndarray(int)) – shape of grid metric (str) – distance metric, i.e. euclidian or manhattan or equidistant the distance float
generate_distance_probability_array(probability, sigma)[source]
Generate the exponentially decaying probability LUTs.
Parameters: probability (float) – peak probability sigma (float) – spread distance-dependent probabilities
get_parameter_names()[source]
Return the names of the parameters supported by this rule
Return type: iterable(str)
get_parameters_sdram_usage_in_bytes()[source]
Get the amount of SDRAM used by the parameters of this rule
Return type: int
vertex_executable_suffix
The suffix to be appended to the vertex executable for this rule
Return type: str
write_parameters(spec)[source]
Write the parameters of the rule to the spec
Parameters: spec (DataSpecificationGenerator) –
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Show that $\int^{\infty}_{0}\left(\frac{\sin(x)}{x}\right)^2 < 2$
I`m trying to show that this integral is converges and $<2$ $$\int^{\infty}_{0}\left(\frac{\sin(x)}{x}\right)^2dx < 2$$ What I did is to show this expression:
$$\int^{1}_{0}\left(\frac{\sin(x)}{x}\right)^2dx + \int^{\infty}_{1}\left(\frac{\sin(x)}{x}\right)^2 dx$$ Second expression :
$$\int^{\infty}_{1}\left(\frac{\sin(x)}{x}\right)^2 dx < \int^{\infty}_{1}\left(\frac{1}{x^2}\right)^2dx = \lim\limits_{b\to 0} {-\frac{1}{x}}|^b_0 = 1$$ Now for the first expression I need to find any explanation why its $<1$ and I will prove it.
I would like to get some advice for the first expression. thanks!
-
You've probably seen the diagram in this link. One has $0<{\sin x\over x}\le 1$ for $0<x\le1$. – David Mitra Jun 8 '13 at 14:08
For the integral from $0$ to $1$, show that $\sin x \le x$ if $x\ge 0$. For proof, let $f(x)=x-\sin x$. Then $f(0)=0$ and since $f'(x)=1-\cos x\ge 0$, the function is increasing, so $x\ge \sin x$. – André Nicolas Jun 8 '13 at 14:09
@AndréNicolas got it, I could not think about it alone. I think its enough to show that its less then $1$, write it as answer if you mind. – Ofir Attia Jun 8 '13 at 14:16
The important thing is that you now know how to do it. There is already a useful hint given as an answer. – André Nicolas Jun 8 '13 at 14:21
Hint: $$\lim_{x\to0}\frac{\sin x}{x}=1.$$
-
I know that, but I dont know how to show it, I can just say that? and its enough? there is a connection to continuous fractional? – Ofir Attia Jun 8 '13 at 14:03
@OfirAttia Use the Maclaurin expansion of $\sin{x}$; that is, $\sin{x}=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\cdots$. – Librecoin Jun 8 '13 at 14:12
You should be able to use it, I think. How best to prove it depends a lot on where you are in your learning process. But it is a fundamental identity, often used in the proof of the derivatives of $\sin x$ and $\cos x$. So depending on the Maclaurin expansion, as @Tharsis suggests, might be considered circular. Anyhow, it is enough because now the function which is $(\sin x)/x$ for $x\ne0$ and $1$ for $x=0$ is continuous, and therefore integrable. – Harald Hanche-Olsen Jun 8 '13 at 14:39
You can prove that $\displaystyle\lim_{x\rightarrow 0} \frac{\sin x}{x} = 0$ by using L'Hospitals rule. – yousufmsoliman Jun 8 '13 at 21:52
@MuadDib42 But many textbooks use that limit to find the derivative of $\sin x$ in the first place. Seems a bit circular, then. – Harald Hanche-Olsen Jun 8 '13 at 22:16
Well, this likely isn't what you had in mind, but you could just evaluate the integral. In this case, Parseval-Plancherel's theorem works:
$$\int_{-\infty}^{\infty} dx\, |f(x)|^2 = \frac{1}{2 \pi}\int_{-\infty}^{\infty} dk\, |\hat{f}(k)|^2$$
where $\hat{f}$ is the Fourier transform of $f$. For $f(x)=\sin{x}/x$, we have
$$\int_{-\infty}^{\infty} dx\, \left ( \frac{\sin{x}}{x}\right)^2 = \frac{1}{2 \pi} \int_{-1}^1 dk \, \pi^2 = \pi$$
so that
$$\int_0^{\infty} dx\, \left ( \frac{\sin{x}}{x}\right)^2 = \frac{\pi}{2} < 2$$
-
The answer is 0 < 2. Found using the congruity $\sin^2(x)=\frac {1-\cos(2x)}{2}$. And evaluating $\frac{-1-\cos(2x)}{2x}$ from 0 to infinity. This ends up being the limit of $\frac {\cos^2(x)}{x}$ as x goes to 0.
-
The integral of a nonnegative, nonzero function can't be zero. you've made a mistake somewhere. – icurays1 Jun 8 '13 at 15:46
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# Thread: Standard form & Graphing
1. ## Standard form & Graphing
Good morning forum I need some assistance with the following question:
Put the equation x2 + y2 + 8x + 2y = 29 into standard form and sketch the graph of the equation.
Thanks AC
2. Originally Posted by AlgebraicallyChallenged
Good morning forum I need some assistance with the following question:
Put the equation x2 + y2 + 8x + 2y = 29 into standard form and sketch the graph of the equation.
Thanks AC
I take it that the 2's are superscript.
So it should read $x^2 + y^2 + 8x + 2y = 29$.
First off, this is the equation of a circle.
The standard form of a circle is $(x - h)^2 + (y - k)^2 = r^2$ where h is the x-coordinate of the centre, k is the y-coordinate of the centre, and r is the radius.
To get it into this standard form, complete the square on the x terms and the y terms.
$x^2 + 8x + y^2 + 2y = 29$
$x^2 + 8x + 4^2 + y^2 + 2y + 1^2 = 29 + 4^2 + 1^2$
$(x + 4)^2 + (y + 1)^2 = 46$
$[x - (-4)]^2 + [y - (-1)]^2 = (\sqrt{46})^2$.
So what's the centre? What's the radius? Can you sketch the circle?
3. Originally Posted by AlgebraicallyChallenged
Good morning forum I need some assistance with the following question:
Put the equation x2 + y2 + 8x + 2y = 29 into standard form and sketch the graph of the equation.
Thanks AC
You have to complete squares, 8th grade trick.
$x^2+8x=(x+4)^2-16$ and $y^2+2y=(y+1)^2-1$
substituting this and rearranging the following is obtained:
$(x+2)^2+(y+1)^2=29+16+1=46$
this is a circle with center at $(-2,-1)$ and radius $\sqrt{46}$
4. Originally Posted by andreas
You have to complete squares, 8th grade trick.
$x^2+8x=(x+4)^2-16$ and $y^2+2y=(y+1)^2-1$
substituting this and rearranging the following is obtained:
$(x+2)^2+(y+1)^2=29+16+1=46$
this is a circle with center at $(-2,-1)$ and radius $\sqrt{46}$
Wrong, it's a circle with centre at $(-4, -1)$ and radius $\sqrt{46}$.
5. Originally Posted by Prove It
Wrong, it's a circle with centre at $(-4, -1)$ and radius $\sqrt{46}$.
Yes I admit, it was typo...
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## How to Calculate and Solve for Impossibility | Probability
The image above represents impossibility.
To compute for impossibility, one essential parameter is needed and this parameter is Total Number of All Possible Outcomes (N).
The formula for calculating impossibility:
P(A) = x N
Where;
P(A) = Imposssibility
N = Total Number of All Possible Outcomes
Let’s solve an example;
Find the impossibility when the total number of all possible outcomes is 12.
This implies that;
N = Total Number of All Possible Outcomes = 12
P(A) = x N
P(A) = 0 12
P(A) = 0
Therefore, P(impossibility) is 0.
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# The width of a rectangular playground is 2x-5 feet, and the length is 3x + 9 feet. How do you write a polynomial P(x) that represents the perimeter and then evaluate this perimeter and then evaluate this perimeter polynomial if x is 4 feet?
$P \left(x\right) = 2 \left(\left(2 x - 5\right) + \left(3 x + 9\right)\right) = 2 \left(5 x + 4\right) = 10 x + 8$
$P \left(4\right) = 10 \left(4\right) + 8 = 48$
Check. $x = 4$ means a width of $2 \left(4\right) - 5 = 3$ and a length of $3 \left(4\right) + 9 = 21$ so a perimeter of 2(3+21)=48. quad sqrt
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### Home > CCAA8 > Chapter cca9 > Lesson cca9.2.2 > Problem9-62
9-62.
Find the equation of the line with slope $-\frac{3}{5}$ passing through the point $(−6,2)$. Homework Help ✎
Use the equation $y=mx+b$, where slope $=m$, to find the equation of the line. Solve for $b$.
$\textit{y}=-\frac{3}{5}\textit{x}-\frac{8}{5}$
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## 14.1.5 Defining Boundary Conditions for Species
You will need to specify the inlet mass fraction for each species in your simulation. In addition, for pressure outlets you will set species mass fractions to be used in case of backflow at the exit. At walls, FLUENT will apply a zero-gradient (zero-flux) boundary condition for all species unless you have defined a surface reaction at that wall (see Section 14.2), you have defined a reaction mechanism at that wall (see Section 14.1.4), or you choose to specify species mass fractions at the wall. For fluid zones, you also have the option of specifying a reaction mechanism. Input of boundary conditions is described in Chapter 7.
Non-Reflecting Boundary Conditions (NRBCs) are not compatible with species transport models. They are mainly used to solve ideal-gas single-specie flow. For information about NRBCs, see section Section 7.23.
Note that you will explicitly set mass fractions only for the first species. The solver will compute the mass fraction of the last species by subtracting the total of the specified mass fractions from 1. If you want to explicitly specify the mass fraction of the last species, you must reorder the species in the list (in the Materials panel), as described in Section 14.1.4.
Diffusion at Inlets with the Pressure-Based Solver
For the pressure-based solver in FLUENT the net transport of species at inlets consists of both convection and diffusion components. The convection component is fixed by the inlet species concentration, whereas the diffusion component depends on the gradient of the computed species concentration field (which is not known a priori). In some cases, you may wish to include only the convective transport of species through the inlets of your domain. You can do this by disabling inlet species diffusion. By default, FLUENT includes the diffusion flux of species at inlets. To turn off inlet diffusion, use either the define/models/species/inlet-diffusion? text command, or the Species Model panel. Generally, you would want to disable the Inlet Diffusion option if at one of the inlets the convective flux is very small, resulting in mass loss by diffusion through that inlet.
Define Models Species Transport & Reaction...
Once Species Transport is selected, you can then disable the Inlet Diffusion option.
Previous: 14.1.4 Defining Properties for
Up: 14.1 Volumetric Reactions
Next: 14.1.6 Defining Other Sources
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Genius Lyrics – Annotations
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how can I go about creating a system similar to genius.com on wordpress for song lyrics. Where you can annonate single lines from a multiline input? Thanks
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# How to control the alignment of the brace in a dcases environment
The following code
$$\begin{dcases} u = \frac{\sqrt{2}}{2}(i+j)\\ v = k \end{dcases}$$
results in the following display
that I find particularly disgraceful. Is there a way to lower the brace to make it look more like this
?
-
You can "smash" the fraction from the top using \smash[t]. Like this:
\documentclass{article}
\usepackage{mathtools}
\begin{document}
$$\begin{dcases} u = \smash[t]{\frac{\sqrt{2}}{2}(i+j)}\\ v = k \end{dcases}$$
\end{document}
The command \smash[b] would be useful for the last line.
Workaround: since I don't suppose you need it regularly, a manual tweak suggested by egreg is possible. Here, we increase the vertical space above the equation, and by grouping we ensure that the effect will be local.
\begingroup\addtolength{\abovedisplayskip}{4pt}$$\begin{dcases} u = \smash[t]{\frac{\sqrt{2}}{2}}(i+j)\\ v = k \end{dcases}$$\endgroup
-
Works like a charm. Thanks a lot. – Evpok Dec 9 '12 at 21:04
This has some small inconveniences: the vertical placement of the equation will not take into account the smashed fraction, so it can end too near the preceding line. – egreg Dec 9 '12 at 21:04
@egreg Actually, the [t] option only smashes the top part, so there is no such issue. – Evpok Dec 9 '12 at 21:12
@Evpok The issue is there: the square root is placed too near the line preceding the display, for my tastes. – egreg Dec 9 '12 at 21:22
@egreg Oh, sorry, I misread your comment. Reader from the future: the aforementionned chat is at chat.stackexchange.com/transcript/message/7199794#7199794 – Evpok Dec 9 '12 at 21:59
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# User talk:Grrrlriot/Archive 1
Hi Grrrlriot. I see you're looking for adoption. I'm an experienced user (been around since February of this year, and have more than 4,500 edits), and I'd be happy to adopt you, if you're interested. I have a pretty solid understanding of most elements of Wikipedia, but I'm still not much good at prettifying articles (vidually, like), so if that's a concern, you might want to choose someone else. Anyway, I'm on offer - let me know. Sarcasticidealist (talk) 19:49, 21 December 2007 (UTC)
That's certainly the most important component. I can also keep an eye on your edits and provide feedback and suggestions, and intervene in any disputes you might be having.
For now, I have a couple of very small recommendations: first, in articles about people, the Wikipedia manual of style for biographies recommends that the subjects be referred to by their last names, not their first names as you've done here and here. It's not a huge deal, but it's best to conform to the manual of style unless there's a compelling reason not to. Second, it's quite important to add reliable sources whenever you make factual statements, to adhere to Wikipedia's policy on verifiability - this and this could probably use some reliable sources for verification; if you have such sources, I can help you with putting them into the article.
Last, and most important, don't be afraid to screw up. At least 99.8% of editors make mistakes when they start on Wikipedia, and Wikipedia's built in such a way that it's easy for these mistakes to be corrected. I'll point out things you do wrong when you do things wrong, but that shouldn't be taken as an indication that you're not doing a good job here; it's just to help speed up the learning process (I wish I'd known about the adopt a user program when I'd started; I probably would have screwed up much less). Sarcasticidealist (talk) 20:10, 22 December 2007 (UTC)
Thanks for the recommendations! I really appreciate your help, Sarcasticidealist.--Grrrlriot (talk) 22:48, 22 December 2007 (UTC)
My pleasure. One new thing: whenever you link to a category by typing [[Category:Feminism]] (or whatever other category you might type), the page in question gets added to that category. In the case of user talk pages and the like, where you're just mentioning the category rather than actually trying to categorize the page, that's unhelpful. To prevent this, just place a colon after the opening brackets, like so: [[:Category:Feminism]]. That leaves the link intact without actually adding the page to the category. Sarcasticidealist (talk) 23:02, 22 December 2007 (UTC)
## WP:LGBT
Did you want to join WP:LGBT? You put your name at the end of the "Inactive" list, so I wasn't sure... If you do want to join, visit WP:LGBT/M and move your name to active? Thanks! -- SatyrTN (talk | contribs) 03:22, 23 December 2007 (UTC)
Yes, I'd like to be on the active list. I moved my name to the active list. Thanks for pointing this out to me. --Grrrlriot (talk) 03:30, 23 December 2007 (UTC)
Oh good! Now I can give you this:
Hi, Grrrlriot, welcome to WikiProject LGBT Studies! We are a growing community of Wikipedia editors dedicated to identifying, categorizing, and improving articles of interest to the LGBT community. Some points that may be helpful: Our main aim is to help improve LGBT-related articles, so if someone asks for help with an article, please try your hardest to help them if you are able. Most important discussions take place on the project's main discussion page; it is highly recommended that you watchlist it. The project has several ongoing and developing activities, such as article quality assessment, peer review and a project-wide article collaboration, all of which you are welcome to take part in. We also have a unique program to improve our lower quality articles, Jumpaclass, so please consider signing up there. If you have another language besides English, please consider adding yourself to our translation section, to help us improve our foreign LGBT topics. If you're planning to stay, have a square in our quilt! You can put anything you want in it. If you have any questions, feel free to ask on the talk page, and we will be happy to help you. And once again - Welcome!
-- =D SatyrTN (talk | contribs) 06:36, 23 December 2007 (UTC)
Thanks for the welcome! I'm glad to be part of Wikiproject: LGBT Studies. --Grrrlriot (talk) 16:27, 23 December 2007 (UTC)
## Feminist
I was the founding token male member of the Jackson, TN NOW; reckon you could say I'm interested. (Son of a woman, brother of women, husband of a woman, father of a woman-to-be; don't see how I could feel right not being a feminist!) Whereabouts in Tennessee do you live? I'm coming to Chattanooga in January, as I do every year, for Chattacon, the local S.F. convention. --Orange Mike | Talk 13:48, 26 December 2007 (UTC)
I'm glad to hear that. I live near Knoxville. Nice to meet you. I hope to see more of your edits in the future. --Grrrlriot (talk) 19:58, 9 January 2008 (UTC)
## Please take a look at this
It's almost done: Glossary of philosophical isms.
The Transhumanist 04:23, 27 December 2007 (UTC)
Thanks that does interest me. --Grrrlriot (talk) 19:57, 9 January 2008 (UTC)
## Away for a few days
Hey - just wanted to let you know that I'll be away from the internet from December 27 until December 30, inclusive. I'll be happy to address any questions you might have upon my return; until then, happy holidays. Sarcasticidealist (talk) 12:47, 27 December 2007 (UTC)
I hope you had happy holidays! Welcome back! --Grrrlriot (talk) 23:04, 10 January 2008 (UTC)
Thanks, and likewise. And as always (except for between December 27 and 30, of course), I'm here if you have any questions. Sarcasticidealist (talk) 23:06, 10 January 2008 (UTC)
## More feedback
Hey, you seem to be doing very well - good work in citing references to the material you added to Kathleen Hanna. With regards to the material you added to Global Feminism, I'm not quite sure what you were trying to do. As you've probably noticed, Wikipedia doesn't have articles for Transnational Feminism or International Feminism. It might have made sense to add those redlinks in if you planned on creating those articles (or if you just thought that they should exist and hoped that somebody else would), but you seem to be saying that those are the same thing as Global Feminism, in which case separate articles wouldn't make very much sense. It might make sense to make those redlinks redirect to Global Feminism; do you know how to do that? Sarcasticidealist (talk) 07:24, 13 January 2008 (UTC)
No, I don't know how to do that. --Grrrlriot (talk) 17:09, 13 January 2008 (UTC)
Create the article by clicking on the redlinks. Make the content of each article #REDIRECT[[Global Feminism]]. That way, whenever anybody searches for "international feminism" or "transnational feminism", they'll get redirected to Global Feminism automatically. Sarcasticidealist (talk) 17:37, 13 January 2008 (UTC)
I just done that. Did I do it right? --Grrrlriot (talk) 17:28, 14 January 2008 (UTC)
Yep. Now I'd recommend removing the Wikilinks to those articles from the Global Feminism article, since they just link back to itself. Your choice, though. Sarcasticidealist (talk) 19:31, 14 January 2008 (UTC)
Which links do I remove? --Grrrlriot (talk) 18:17, 19 January 2008 (UTC)
(outdent) I would personally remove the links under "See also" to Transnational feminism and International feminism. Usually users click those links to learn more about a given topic (or topics related to it); if they clicked those, they'd just be redirected back to the same article they were already reading, which I suspect would be frustrating. Of course, all of this assumes that the three terms basically mean the same thing; if they mean different but related things, it might be more appropriate to remove the redirects and develop new articles under those names. In that case, it would make sense to keep the links. Sarcasticidealist (talk) 18:21, 19 January 2008 (UTC)
Ok, I removed the links. --Grrrlriot (talk) 18:26, 19 January 2008 (UTC)
How am I doing on here so far? --Grrrlriot (talk) 19:46, 27 January 2008 (UTC)
Delivered sometime in January 2008 (UTC). SatyrBot (talk) 23:31, 19 January 2008 (UTC)
Thanks for the welcome, SatyrBot! I'm glad to be a member of the wikiproject. --Grrrlriot (talk) 17:20, 20 January 2008 (UTC)
## Portals
Hey there. I've left a message at User talk:BrownHairedGirl#Portals. I thought if you want to start Portal:Feminism, and BHG wants to start Women, I'd start Gender studies. I'm hoping to get a little input from the project (maybe ask LGBT if anyone over there would like to contribute), but I'd be willing to help out for both of the other portals (extra pair of eyes?). This is good, I feel like we've got some momentum going here - thanks! Phyesalis (talk) 03:44, 20 January 2008 (UTC)
I checked the message you left for User:BrownHairedGirl. That sounds like a good idea. Your welcome! Thanks for wanting to do this! I really appreciate your support! :) I would be glad to hear your input on the feminism portal. I want to hear your ideas about the feminism portal, I'm willing to get it started if I know what ideas/things should be on the portal. Keep in mind, I am new to Wikipedia, (not sure if you knew that) so I don't know everything about wikipedia and I do make mistakes sometimes, so you can try to help me out since you have been around here for a while. If you want to discuss this even more, You can always send me an email. (See my userpage for my email.) User:Cailil seemed to be interested in all 3 as well. I left him a message on User_talk:Cailil to see if he wants to help with the feminism portal, Do you want me to see if he's interested in helping with the gender studies and women portal too? Read more on his talk page. --Grrrlriot (talk) 17:32, 20 January 2008 (UTC)
Yeah! Thank you. Your enthusiasm has reinvigorated mine. And it doesn't matter that you're new - that's what being WP:Bold is all about. Hell, I've only been doing this for a total of 5 or 6 months - hardly more than a newbie myself. Trying stuff like this is the only way to learn (I've never started a portal either!). But I'm happy to help out in any way - feel free to email me too, post q's on my talk page, or check out WP:IRC. And mistakes? Mistakes in good faith are just learning experiences, so don't worry about that.
I'd welcome Cailil's input on any of the portals. He does good work. I've also notified the other editors who signed up for the Feminism Wikiproject proposal (User:Alison, User:Pigman, User:Lquilter and some others). Once we get template pages started we could get the collaborations posted over at the Community portal to draw more attention. Oh, what a nice start to my day! Phyesalis (talk) 18:24, 20 January 2008 (UTC)
Thanks! I appreciate your kindness. I haven't heard from Cailil yet. What is the link to the Feminism Wikiproject proposal? I signed up for it, but I can't remember the link. That sounds like a good idea. This is a good start to my day too! --Grrrlriot (talk) 19:18, 20 January 2008 (UTC)
Fast work! I've started Portal:Gender studies. The link is here under feminism. I've also posted a question about some issues I've been having over at Help. Phyesalis (talk) 23:28, 20 January 2008 (UTC)
Fast work for you to. I started Portal:Feminism. Thanks for the link. I haven't been having any issues, so far. I'm just thinking of things to add to the portal. --Grrrlriot (talk) 23:42, 20 January 2008 (UTC)
Ack! That's what I meant - fast work on the portal. Phyesalis (talk) 01:44, 21 January 2008 (UTC)
lol Sorry. I added a category to your Portal:Gender studies page. --Grrrlriot (talk) 01:57, 21 January 2008 (UTC)
## Userbox
Thank you kindly for your feedback. There is a way to automatically add users to categories based on userboxes, but I've never bothered to learn how it's done. Besides, I think just sort of browsing around is a better way to find people with like interests. (You can always go to the userbox page and click on "what links here".) Cheers! – Scartol • Tok 01:32, 21 January 2008 (UTC)
Thanks for the information! I created Portal:Feminism thought you might be interested in giving me ideas for the portal. If you are interested, Reply to this comment or send me an email. My email is on my userinfo page. Thanks again! --Grrrlriot (talk) 01:34, 21 January 2008 (UTC)
Looks like a worthy project. Alas, I'm a bit busy with a handful of projects at the moment, but I'm always willing to loan my eyes to whatever the project develops. (I also know a bit about templates and CSS and HTML and all that stuff, so feel free to bug me about technical stuff if it comes up.) Cheers. – Scartol • Tok 01:40, 21 January 2008 (UTC)
Thanks! :) I might need technical help in the future, if so, I will contact you. Thanks again! --Grrrlriot (talk) 01:45, 21 January 2008 (UTC)
Well, I do know a thing or two about designing pages, so I can give you pointers for your userpage, or make something up if you prefer. What did you have in mind? – Scartol • Tok 03:38, 21 January 2008 (UTC)
I was thinking of turning the subpage links into images that most users have at the top of their userpages. Any other ideas for it? --Grrrlriot (talk) 03:45, 21 January 2008 (UTC)
Not really; the subpage tabs look good. I think JayHenry has a nice setup. – Scartol • Tok 14:26, 21 January 2008 (UTC)
I agree, His setup looks really good. I like how it looks simple and easy to navigate. --Grrrlriot (talk) 20:08, 21 January 2008 (UTC)
I'm willing to do some design for your userpage, but I'll need a few days (maybe a week), and some idea of what you're looking for. Certain color schemes? Any particular images? 1 or 2 columns? Etc. – Scartol • Tok 00:09, 4 February 2008 (UTC)
I'm glad to hear that and take as long as you need. I'm not real picky on colors. I don't have a particular image in mind either. I will tell you a few userpages I like: User:Cailil, User:LaraLove, User:Sango123 and User:The Transhumanist. If you need to know anything else, Just ask. --Grrrlriot (talk) 00:31, 4 February 2008 (UTC)
(undent) Definitely still interested, as you can see on my Works in Progress list. But I'll probably need another week or so. Thanks for your patience. – Scartol • Tok 16:50, 12 February 2008 (UTC)
Great! I'm glad to hear that. That's fine with me. Also, Category:Wikipedians interested in feminism might interest you. --Grrrlriot (talk) 16:58, 12 February 2008 (UTC)
## other wikis
hi grrrlriot - you list these other wikis; would you consider putting in links to them directly? anarchopedia, feministwiki, Zinewiki ... i know the zinewiki but not feministwiki, and somehow, i didn't know about anarchopedia ... --Lquilter (talk) 17:33, 25 January 2008 (UTC)
Hi Lquilter! :) It's good to see you around other talk pages. I just put up the links directly to the other wikis. --Grrrlriot (talk) 19:50, 27 January 2008 (UTC)
## Hey
I'd like to first welcome you to the Anarchism Task Force, and let you know that I reverted your addition of the Anarchism in Somalia to the List of anarchist movements by region, because it's a redirect to Anarchy in Somalia, which really has nothing to do with anarchism as a movement, but more "anarchy" like chaos. But again, welcome to the project! Murderbike (talk) 04:42, 28 January 2008 (UTC)
Hey, Murderbike! :) Thanks for the welcome! I'm glad to be a part of the task force. I plan on doing some edits on other anarchism articles in the future, so I joined the task force. I realize what I done to the List of anarchist movements page and I now realize it does redirect to Anarchy in Somalia. By looking at your userpage, I can tell we share quite a few interests. I'm glad you found me. Hope to see more of your edits in the future! --Grrrlriot (talk) 04:56, 28 January 2008 (UTC)
Of course, lately I've been almost exclusively working on anarchism-related stuff, so if you'll be around, we'll be sure to run into each other. Feel free to ask if you're looking for projects to work on, we've got tons! Murderbike (talk) 05:07, 28 January 2008 (UTC)
I'm sure we will see more of each other around the Anarchism Task Force. I noticed a lot of missing/non-created articles. I was thinking of starting some of those up. A lot of them looked interesting to me. Can you give me a list of projects that I could work on? Thanks! --Grrrlriot (talk) 16:58, 28 January 2008 (UTC)
Piping in -- In my view, we need a good bit of work on anarchafeminism and related articles. Emma Goldman was just made FA which is great, but many other prominent female anarchists have very poor articles (e.g., Lucy Parsons), there's been little work done on issues of gender equality in early anarchist periodicals, we should really have an article on "The Tyranny of Structurelessness" -- that's been such a hugely influential work .... also Lizzie Borden (filmmaker) and Born in Flames could use some work, I think.--Lquilter (talk) 17:03, 28 January 2008 (UTC)
Hello, Lquilter! :) I think the Emma Goldman article is great! I added a little bit about Lucy Parsons under the "Death" section. --Grrrlriot (talk) 17:26, 28 January 2008 (UTC)
Yeah, if you're more interested in the fem side of things, Mujeres Libres would be a really good candidate. There's plenty of source material out there to tap. Murderbike (talk) 04:07, 29 January 2008 (UTC)
I added a little to Mujeres Libres, but I plan on adding more to it in the future as well. --Grrrlriot (talk) 04:19, 29 January 2008 (UTC)
## thanks!
thanks for your kind wishes re: my rfa, which was successful. (yaay) --Lquilter (talk) 13:27, 30 January 2008 (UTC)
Your welcome! :) Yay! I'm glad to hear that, Lquilter! Congrats!!! I figured you'd pass. --Grrrlriot (talk) 17:26, 30 January 2008 (UTC)
## Articles you might like to edit, from SuggestBot
SuggestBot predicts that you will enjoy editing some of these articles. Have fun!
SuggestBot picks articles in a number of ways based on other articles you've edited, including straight text similarity, following wikilinks, and matching your editing patterns against those of other Wikipedians. It tries to recommend only articles that other Wikipedians have marked as needing work. Your contributions make Wikipedia better -- thanks for helping.
If you have feedback on how to make SuggestBot better, please tell me on SuggestBot's talk page. Thanks from ForteTuba, SuggestBot's caretaker.
P.S. You received these suggestions because your name was listed on the SuggestBot request page. If this was in error, sorry about the confusion. -- SuggestBot (talk) 22:05, 31 January 2008 (UTC)
Thanks Suggestbot. I appreciate the suggestions. --Grrrlriot (talk) 23:45, 10 February 2008 (UTC)
## Thanks for your encouraging note
Dear Grrrlriot, you have left me a small note encouraging me on my contributions. Many thanks. My field of knowledge is French feminism, french feminist psychoanalysis, french post-modern art, french post-modern philosophy, and the links between all these subjects. I try from time to time to contribute, but I don't really know how to do complicated wikipedia jobs like putting on photos or do anything other than putting more knowledge here and there. I thank you for your encouragement, and, for the moment, I believe that I will remain quite minimalist with my contributions, but I wonder if I can contact you to help me if I have suggestions concerning operations that I do not know to do, like indeed, putting photos when I obtain permission, etc.. Anyway, thanks again for your kindness. 84.229.43.161 (talk) 23:52, 1 February 2008 (UTC)
Hello! :) Your welcome! I don't know ALL of the complicated wikipedia jobs either. I am still learning. Most of my contributions is adding knowledge, Just like your doing. Sure, Feel free to contact me if you need help. Thank you for contributing to wikipedia! --Grrrlriot (talk) 19:02, 2 February 2008 (UTC)
## WikiProject Alternative music January 2008 Newsletter
The Alternative music WikiProject Newsletter Issue 10 - January 2008 "I still have people come up to me like, 'I really, really liked your last record.' 'Oh, thanks!' 'Are you going to do "Loser" tonight?' I'm like, 'Look, I'm six foot six. Beck is five foot sex, all right?'"- Thurston Moore Project news Radiohead, Slay Tracks (1933-1969), David Lovering, "I Don't Remember", U2, R.E.M., Anodyne (album) and Niandra Lades and Usually Just a T-Shirt reached featured article status in the past month, a record month for the WikiProject! Additionally, with the promotion of Radiohead, U2 and R.E.M., half of our Top Importance articles now have featured article status. Well done to Atlantik, Brandt Luke Zorn, CloudNine, the various WikiProject Powderfinger editors, Merbabu, WesleyDodds, Teemu08, NSR77 and Grim-Gym. The discographies of Dischord Records and Load Records reached featured list status during the past month. Well done to Drewcifer3000 (who wrote both featured lists). Powderfinger discography reached featured topic status during the past month. Well done to the various WikiProject Powderfinger editors. We collaborated on Mellon Collie and the Infinite Sadness, Franz Ferdinand (band), PJ Harvey and Michael Stipe during the past month. During the month of January, Rage Against the Machine, Pick Up the Pace, "Lost and Running", Bernard Fanning, Year Zero (album), Jon Coghill, "Losing My Religion" and "Touch Me I'm Sick" were promoted to good article status. Sign up for our B-class article drive on the project talk page! The goal is to increase a number of the project's B-class articles to GA or FA status within two months. The B-class article drive will run from February 1 to April 1, 2008. This month's "Recommended Alternative Album" is My Bloody Valentine - Isn't Anything (1988). New members Skeeker, Dethzone, Sceptre, IN THE EFFIGY, Crislee 88, Grrrlriot and Indopug joined the alternative music fold during January. Editors User:WesleyDodds
You are receiving this newsletter because you have signed up for WikiProject Alternative music. If you wish to stop receiving this newsletter, or would like to receive it in a different form, add your name to the appropriate section here. This newsletter was delivered by the automated xihix(talk) 01:19, 2 February 2008 (UTC) .
Thanks for the newsletter! :) --Grrrlriot (talk) 18:06, 2 February 2008 (UTC)
No problem, didn't realize delivering the newsletter would get me that smiley though. Yay! xihix(talk) 03:24, 4 February 2008 (UTC)
## I'm sorry
Hi Grrrlriot - I've been a shamefully delinquent adoptive parent lately, and I apologize for it. I'll have a more detailed answer to your question sometime tonight. Again, sorry about that! Sarcasticidealist (talk) 17:53, 4 February 2008 (UTC)
It's ok, Sarcasticidealist. I figured that you had been busy. --Grrrlriot (talk) 17:56, 4 February 2008 (UTC)
## :)
Thanks for mine! WEBURIEDOURSECRETSINTHEGARDENplay it cool. 20:02, 4 February 2008 (UTC)
Your welcome and thank you! --Grrrlriot (talk) 17:33, 5 February 2008 (UTC)
## Some thoughts on how you're doing
Hi Greta (do you mind if I call you that? You should feel free to call me Steve, if you want). As promised, here's some feedback I've compiled after looking over your last few edits. You're generally doing very well (which is good, because if you were screwing up all over the place I'd feel really guilty for neglecting your tutelage). Some things that I think you're doing well include the following:
• Most of the links you add are very good, and entirely appropriate according to Wikipedia policies and guidelines.
• You're referencing most of the information you add very well. A note: people disagree quite often on what sources are reliable and what sources aren't; if somebody tells you that a source isn't reliable, that might just be their opinion. You should read WP:RS (if you haven't already) to develop your own opinions, and you can always feel free to ask my opinion (or another editor's).
• You're doing great work in organizing the project (categorizing, adding relevant articles to lists, inserting internal links, etc.).
• You've also started doing some nice work in article creation, which is great too (it's certainly my favourite part of being a Wikipedia editor).
• Great work in welcoming Wikipedians and also leaving friendly notes here and there. A very important part of being a Wikipedian is being the sort of editor that other people want to work with; a lot of people are slow to figure that out. Are you familiar with barnstars? They're the traditional Wikipedian way of complimenting people on a job well done. Of course, if you'd prefer to do it using notes, that's fine too.
Some tips for the future:
• Remember to use edit summaries as often as possible.
• I noted your participation in the deletion debate over Kawaii Noir. In the future, if you ever want an article that you created (and that nobody else has worked on) deleted, you can just add {{db-author}} to the page, and an admin will delete it. Or you can just ask me to delete it.
• Regarding edit, note that Wikipedia is not censored. That doesn't mean that you should go adding graphic information to every article, of course, but if there's something that you think would really improve the article, don't be afraid to add it for reasons of censorship. Of course, you can always discuss it on the talk page first.
• With regards to Alice Masaryková, you've referenced it well, so I removed the “unreferenced” tag (you can feel free to do that yourself, in the future, provided you've attached references). With regards to the notability tag, I think it would be helpful to include in the first sentence of the article exactly what made her important; then we can get rid of that tag too.
• You've had a couple of issues with copyright violations; as you've probably figured out for yourself by now, it's very important that you put material from references into your own words, rather than copying verbatim.
• A heads-up: some users don't appreciate smiles, like the ones that you've been spreading. I don't think there's anything wrong with them (as long as they're not all you're doing – we are here to build an encyclopaedia, after all), but there's a good chance that you'll get some kind of rude reception at some point if you keep them up.
Finally, one random question: have you set up a watchlist yet?
Please let me know if you have any questions, and I promise to be more diligent in helping you in the future. Sarcasticidealist (talk) 04:04, 5 February 2008 (UTC)
Also: archiving your talk page. The easiest way (what I do) is to use User:MiszaBot III. Instructions are here; please let me know if you have any questions. Sarcasticidealist (talk) 11:38, 5 February 2008 (UTC)
Hello Steve! No, I don't mind you calling me Greta. Thanks for letting me know what things I'm doing good at. I do need to use edit summaries more often. I think I will discuss what I want to add on Talk:Trevor Brown. I will add what made Alice important to the article. I have realized that I need to put stuff into my own words. Those are all the smileys I'm going to give out. Yes, I already have a watchlist set up. I was about to ask you how to archive a talk page. I will set this up within a few days and I will work on what I just said within a few days as well. --Grrrlriot (talk) 17:45, 5 February 2008 (UTC)
## Thank you ...
for the smile! Fg2 (talk) 11:35, 5 February 2008 (UTC)
Your welcome, anytime! --Grrrlriot (talk) 17:33, 5 February 2008 (UTC)
## Archiving
You had some unnecessary stuff there (that first bit was just setting out the general format to use; it wasn't actually useful code), so I deleted it. Other than that, you've got it set up properly to remove anything more than seven days old and stick it in one archive page. That page will eventually get pretty big, though. Sarcasticidealist (talk) 20:13, 9 February 2008 (UTC)
Thanks for fixing the code for me. It will make more archive pages too, right? --Grrrlriot (talk) 20:17, 9 February 2008 (UTC)
As you've set it up, it actually won't. If you check out the how to, it sounds like you actually want to do something like what they show you how to do in Example 2 or 3 (I'd recommend 2, because you don't seem to have enough talk page activity to justify creating a new archive every month). If you'd like, I can set it up for you, or you can try to figure it out if you'd rather learn yourself. Let me know, in any event. Sarcasticidealist (talk) 01:16, 10 February 2008 (UTC)
I changed it to 2, like you suggested. Did I do it right? --Grrrlriot (talk) 01:22, 10 February 2008 (UTC)
Close - the only thing is that you should start with Archive 1; I've made the change. Sarcasticidealist (talk) 08:01, 10 February 2008 (UTC)
Also, 48 hours might be a little short a period to leave things on your main talk page; I've gone with 28 days. It's your choice, though. Sarcasticidealist (talk) 08:01, 10 February 2008 (UTC)
Thanks for making the change for me. 28 days sounds good to me. --Grrrlriot (talk) 17:24, 10 February 2008 (UTC)
## Have a Barnstar!
User:Jaytur1/Secret page Even though you cheated. -- 10:24, 10 February 2008 (UTC)
Yeah, I know I cheated. It was pretty easy to find: Special:Prefixindex/User:Jaytur1 Thanks for the barnstar! :) --Grrrlriot (talk) 17:18, 10 February 2008 (UTC)
Just dropping you a line about the portal. Since I picked (rather unilaterally) last months picture and article for Portal:Feminism would you like to go ahead and pick this month's ones? We should also discuss what ones should be used for March and April as well--Cailil talk 13:39, 10 February 2008 (UTC)
This sounds like a stupid question, but how do you pick the article and the picture? I picked Judith Butler as the article, but there is only a text link to the page. --Grrrlriot (talk) 17:30, 10 February 2008 (UTC)
Not a stupid question at all. You have to create the page, manually replacing the picture and writing an article summary. I copy and paste from the old version - replacing and adding where necessary. I've done the selected article page - if you have any problems doing the others give me a shout--Cailil talk 18:17, 10 February 2008 (UTC)
I understand it now. Does the same go for the selected picture archive as well? --Grrrlriot (talk) 18:28, 10 February 2008 (UTC)
Yeah pretty much. The code is a bit trickier in some parts of the SI archive put it's basically the same--Cailil talk 18:32, 10 February 2008 (UTC)
Ok, Thanks for answering my question about picking articles, pics, and stuff for the portal. I also replied to your comments on the task force at the Wikipedia_talk:WikiProject_Gender_Studies page. --Grrrlriot (talk) 20:16, 10 February 2008 (UTC)
## RFA thanks
Your welcome! :) Congrats!!!! --Grrrlriot (talk) 18:06, 10 February 2008 (UTC)
Yeah, sure! Welcome to Wikipedia! If there's anything you need explaining, please ask! WEBURIEDOURSECRETSINTHEGARDEN round of applause 18:50, 10 February 2008 (UTC)
GREAT! Thanks! :) I've been around since December 2007. I've learned some stuff about wikipedia, but I'm open to learn more about it as well. I usually have questions about edits and other stuff concerning wikipedia, so if I do have a question, I will ask. Thanks again! I added the userbox to my page as well. --Grrrlriot (talk) 20:13, 10 February 2008 (UTC)
## Thanks
Hi, You left a note on my page, we share in the interest in feminist issues. I want to thank you for your attention, Doraannao (talk) 23:11, 10 February 2008 (UTC)
Hi Doraannao! :) I remember leaving you a welcome message on your talk page. I love all things feminist related! You might be interested in this discussion: Wikipedia_talk:WikiProject_Gender_Studies#Subcategory.2FTask_Force_of_Feminism. Your welcome! I like meeting others into feminist issues. --Grrrlriot (talk) 23:19, 10 February 2008 (UTC)
Yes, sure, thanks again, i am trying my way around, and sometimes losing my way, so each small welcome is important. Doraannao (talk) 23:31, 10 February 2008 (UTC)
Your welcome, anytime! If you have any questions or anything, Please let me know. I will try to help you, if I can. I am still new around here too, but I have learned quite a bit lately. --Grrrlriot (talk) 23:33, 10 February 2008 (UTC)
## Portal:Feminism
The WikiProject Gender Studies Award For your tireless work on Portal:Feminism and the new taskforce, not to mention your enthusiasm, I hereby award you this Gender Studies barnstar. Congratulations, you've earned it. Please, keep up the good work! Phyesalis (talk) 22:05, 12 February 2008 (UTC)
Is this for the task force use or is this a barnstar for me? I'm confused, sorry. lol --Grrrlriot (talk) 22:07, 12 February 2008 (UTC)
It's for YOU, silly! --Phyesalis (talk) 22:14, 12 February 2008 (UTC)
Yay! :) My first official barnstar! hehe Thanks, Phyesalis! --Grrrlriot (talk) 22:54, 12 February 2008 (UTC)
Thanks for the invite, and while I'm very interested in article relating to feminism (obviously, I hope), I don't feel comfortable – giving my intense workload these days – signing up for another task force or project. I'll be glad to review article from time to time and help out in other ways when time permits, but I can't sign up right now. Apologies and good luck! – Scartol • Tok 00:26, 13 February 2008 (UTC)
Your welcome! I totally understand. If and when you have more time on your hands, feel free to sign up. I could always use help on the task force: article reviews and helping in other ways when time permits, sounds good. --Grrrlriot (talk) 00:30, 13 February 2008 (UTC)
## FTF
I don't know if you've seen this or not, but Wikipedia:WikiProject Gender Studies might make the Feminism Task Force a little redundant. Murderbike (talk) 01:35, 13 February 2008 (UTC)
That's where I was going to originally put the task force, but someone suggested on the feminism portal. Would it be better on the GS WikiProject instead? If so, I will move it. --Grrrlriot (talk) 01:55, 13 February 2008 (UTC)
I believe this was discussed over there. As the FTF is part of the feminism portal, which is itself a sub-portal of Gender studies. There's a link at both portals. I don't see it as redundant - it's a sub-process of GS. --Phyesalis (talk) 02:01, 13 February 2008 (UTC)
Cool, no big deal to me. Good luck! Murderbike (talk) 22:57, 13 February 2008 (UTC)
Thanks, Murderbike! :) --Grrrlriot (talk) 23:47, 13 February 2008 (UTC)
I therefore have a question about the WikiProject banner: Should we include the Task Force line in the GS WikiProject banner? I can't imagine how else to do it; other task forces don't have their own WP banners, do they? – Scartol • Tok 14:01, 16 February 2008 (UTC)
I've taken the bold step of adding it. – Scartol • Tok 14:28, 16 February 2008 (UTC)
## Marcia Freedman
Hi. Thanks for starting the article. I tried to polish it up a bit. A word of advice: try not to copy and paste language from other sites, because the text of new articles is often compared to Google searches for WP:COPYVIO problems.
I thought you might be interested in Women's Party (Israel), which has more information about Freedman. In fact, many of the articles at Special:Whatlinkshere/Marcia Freedman are interesting, if the minutia of left-wing Israeli politics interests you. Malik Shabazz (talk · contribs) 21:54, 13 February 2008 (UTC)
Hello Malik! :) Your welcome for starting the article. It's only a stub, but at least she has an article. I noticed you were fixing the article. (It's in my watchlist.) Thanks for polishing up the article. I did copy and paste text, but while doing so, I put the text in my own words, so that it wouldn't be a WP:COPYVIO issue. Thanks for letting me know about Women's Party (Israel). I will check it out right now. Yes, Left-wing Israeli politics does interest me. I actually found out about Marcia yesterday, while looking through feminists on the internet. Thanks! --Grrrlriot (talk) 00:01, 14 February 2008 (UTC)
I've expanded the article again based largely on her Knesset bio. пﮟოьεԻ 57 13:08, 14 February 2008 (UTC)
Hello, Number 57! Thanks for expanding the article! :) --Grrrlriot (talk) 17:45, 14 February 2008 (UTC)
Hi again. According to Freedman's Hebrew Wikipedia article, she divorced her husband during the 1977 election and came out later, and to date she's the only "out" lesbian member of Knesset. Over the next few days I'll look for some more sources about her. — Malik Shabazz (talk · contribs) 19:23, 14 February 2008 (UTC)
Thanks for translating what the hebrew article said about Marcia Freedman. The article does need more sources, so this will help out the article. --Grrrlriot (talk) 17:28, 15 February 2008 (UTC)
## Categories
Hey, just so ya know, when someone is placed in a category like "Japanese feminists", they are automatically included in "Feminists", because the former is a subcategory of the latter. It is always preferred to use a subcategory when possible, and leave out the mother category. Cheers! Murderbike (talk) 22:56, 13 February 2008 (UTC)
Oh ok, I didn't know that. Thanks for letting me know. --Grrrlriot (talk) 23:48, 13 February 2008 (UTC)
Just to add: that one took me forever to learn. In fact, I spent a long time once copying all of the articles from the subcats of Category:Alberta MLAs to the main category. User:Bearcat didn't grumble too much about having to fix them all.
How's everything going generally? I see you got your first barnstar; that's way earlier than I got my first (I got my first last month). Sarcasticidealist (talk) 00:11, 14 February 2008 (UTC)
Everything's going good, How about with you, Steve? Yes, I did get my first barnstar. Really? Congrats on your barnstar too!!! :) --Grrrlriot (talk) 00:48, 14 February 2008 (UTC)
## Userboxes
Scartol can make excellent templates and userboxes and would more than likely help out with the project. Awadewit | talk 17:45, 15 February 2008 (UTC)
Yeah, I should ask him. Waiting on his reply right now. --Grrrlriot (talk) 18:29, 15 February 2008 (UTC)
Yes, I'd be happy to. I think I can even say (no promises, but if all goes to plan) that I can do the userpage work I promised weeks ago – and these templates/userboxes – this weekend. Now, since I'm volunteering to help with the advancement of feminism on Wikipedia, and I've (hopefully) earned my "street cred" as a feminist myself, is it okay (and will my ironic intent be evident) if I make a joke about how you women are coming to me, a man, to build templates? =D (Next Signpost Headline: "Obnoxious Wikipedian stabbed to death by members of new Task Force") – Scartol • Tok 18:55, 15 February 2008 (UTC)
Great! :) I'm glad to hear that. When you do make the templates and userboxes, Let me know here on my talk page. Also, When you do make them, Post them on the FTF page. lol Yes, It's fine to make the joke. haha! Believe it or not, Scartol, When I first started talking to you I thought you were a girl, until I looked at your user profile. I guess I thought of your username as 'feminine' or "Scarlett" or something. lol Thanks for agreeing to do this! Like I said, I know your super busy, with things your currently working on, so now you can add this to your list too. hehe As for the templates and userboxes, I'm not trying to rush you or anything, but if you could have them done in 2 weeks, the most time. My userpage can be put off, while your making these. Like I said, I'm pretty patient when it comes to my userpage design. As long as you do it sometime in the future, I am satisfied. --Grrrlriot (talk) 19:44, 15 February 2008 (UTC)
Three things:
1. We should choose an icon to use on the userbox and templates. this image from the "this user is a feminist" userbox seems an obvious choice, but perhaps there's another which would be more fitting?
I like the image, I can't think of another image that would be more fitting at the moment. Can you? --Grrrlriot (talk) 17:28, 16 February 2008 (UTC)
1. Is there a particular color scheme you'd like to use in these templates?
No. I am not picky on color schemes. That's totally up to you. ;) --Grrrlriot (talk) 17:28, 16 February 2008 (UTC)
1. I hate to be pedantic, but I'm an English teacher and I feel obligated to say it: You have a habit of using "your" when you mean "you're". I generally feel comfortable correcting people on little things like this, but it's kind of distracting. =) Cheers. – Scartol • Tok 13:00, 16 February 2008 (UTC)
Yes, I suppose you're right. I will try to correct this. I didn't notice until you told me. --Grrrlriot (talk) 17:28, 16 February 2008 (UTC)
I've made a userbox; please gimme feedback. Also, is there a list of templates you want for the task force? Or should I just make some equivalent to other wikiprojects/task forces? – Scartol • Tok 13:23, 16 February 2008 (UTC)
I commented on the discussion page for the userbox. I love it! What do you mean by "making some equivalent to other wikiprojects/task forces"? I think the feminism-stub is a good one and I think one about "This article about a feminist is a stub...". I like the the feminism and feminism footer templates. Try looking at: Wikipedia:WikiProject_Philosophy/Anarchism. It's a task force of Philosophy to see templates they have. Perhaps we could have similar templates relating to feminism. --Grrrlriot (talk) 17:28, 16 February 2008 (UTC)
I'm just going to fill your talk page up with stuff all day; is that okay? =) I found some templates at WikiProject Gender Studies, and added them to the task force page. As for infoboxes, Awadewit – who has been a most valuable mentor to me ever since I first set foot on WikiGround – has said (and I agree) that infoboxes are often distracting and repetitive. I can make a standard infobox for the task force if you like (I see there's a place for them), but I just wanted to run it by you first. – Scartol • Tok 13:58, 16 February 2008 (UTC)
That's fine. =) Sounds great! You're right about infoboxes. What type of stuff would be on the infobox? --Grrrlriot (talk) 17:30, 16 February 2008 (UTC)
(undent) Well, we generally don't use them at all. In some contexts they may be useful (on pages explaining a movement taking place over many years, perhaps), but by and large I don't care for them at all. (I can't speak for her; this is my approximation of her perspective.)
As for templates, I'll make one for the feminist stubs later today; otherwise, I think we have most of the ones we need (they already existed at WP:GS). (By "making some equivalent to other wikiprojects/task forces" I meant what you suggested – seeing what the Anarchism force, for instance, has, and making some like them.) So it looks like we're good to go! I'll add the userbox later today as well.
You'll also be happy to know that the number of people in Category:Wikipedians interested in feminism has jumped dramatically today, since I fixed the "this user is a feminist" userbox to automatically list those who display it on their userpages. Maybe more people to contact for the task force? – Scartol • Tok 18:51, 16 February 2008 (UTC)
I see no use for infoboxes either. Anyhow, That's Great! Don't forget to add the userbox later today. I noticed a few minutes ago that the number of people in Category:Wikipedians interested in feminism has jumped dramatically today. I added 2 more people to the category, which I'm sure they will be ok with me adding them to the category. I also added Portal:Feminism and Wikipedia:WikiProject Gender Studies/Feminism Task Force to the category as well. Thanks for fixing the feminism userbox you made to let it list people in my category. I really appreciate it! :) They could be more people to contact about the task force. I have contacted a few people on their talk pages, but I haven't contacted none of the people in the category. --Grrrlriot (talk) 19:30, 16 February 2008 (UTC)
## Name change from Religious feminism to Feminist theology
Well, I did it. Apparently you can't change the title of an article in WP, so I just removed the redirect from Feminist theology and copied the contents of Religious feminism. Please let me know what you think! I hope that I did everything correctly. BTW, thank you for your help in getting me added to the feminism category! Webbbbbbber (talk) 21:49, 15 February 2008 (UTC)
Hello, Webbbbbbber! :) I like the name change of the article. Yes, You did everything correctly. Your welcome! Feel free to tell others about the category as well. Also, You might be interested in: Wikipedia:WikiProject Gender Studies/Feminism Task Force. --Grrrlriot (talk) 22:49, 15 February 2008 (UTC)
Oh good. :-) I'm glad that I'm not the only one who found the other title odd and little bit pejorative... I'm learning a lot about how Wikipedia works! ...but I couldn't figure how to get Feminist theology to appear under Category:Feminism . Webbbbbbber (talk) 23:29, 15 February 2008 (UTC)
That's good! Go to the Feminist theology article and under external links add Category:Feminism, Its that easy. Hope this helps! --Grrrlriot (talk) 23:32, 15 February 2008 (UTC)
I found out that the problem was that Category:Feminist theology didn't exist. Now that I've created it, I'm in the process of adding articles to that category. Do you think there are (m)any articles that should be kept in Category:Religious feminism?
Hi, you asked if I would adopt you earlier this week and I was just wondering if you found anyone that would adopt you. Please let me know if you need help finding someone! Cremepuff222 (talk) 03:24, 16 February 2008 (UTC)
Hi Cremepuff222! :) I found someone, but thanks for your willingness to help me find someone. It's appreciated. --Grrrlriot (talk) 03:33, 16 February 2008 (UTC)
## A couple of things
Hi Greta - a couple of things:
• Your archiving doesn't seem to be working, and I can't figure out why. I've contact the bot's operator for his assistance: [1].
• I've reviewed your edits, and you seem to be doing very well, so there's not a lot that I feel I need to tell you. However, I see that you still feel that there's much more that you want to know about Wikipedia. Do you have any questions you'd like me to answer? Are there any areas of Wikipedia that you feel you'd like to know more about? If so, I can try giving you sort of "lessons" on them, if you don't have any specific questions. Please let me know one way or another.
• I've looked at User:Grrrlriot/Need your help (great idea, by the way). Many of the things I just don't have the knowledge base to help you with (for example, I confess that my feminist education is sorely lacking, although I consider myself to be one in the broad sense of the word). A few things that I can offer an opinion on:
• Riot Grrrl seems to be a respectable article, not in urgent need of a rewrite. However, if you think that you could come up with a better article (not just improving the existing one, but rewriting the whole thing), I'd suggest working on a draft in your userspace and then, when it's reasonably complete, linking to it on Talk:Riot Grrrl to get others' opinions of whether or not you should replace the existing article with it (I did something similar recently with Ed Stelmach - I know how much you love articles about politicians).
• With regards to the idea of a Wikiproject Asia, it looks as though there may have been one at some point, but that it was then divided into a number of different Wikiprojects (Wikiproject Central Asia, Wikiproject Western Asia, Wikiproject Southeast Asia, Wikiproject Southern Asia, etc.). I would suggest that you consider whether there are likely to be many editors interested in working on articles about Asia as a whole - that is, editors who would be just as interested working on articles about Feminism in Azerbaijan as on the Yangtze River or the history of Hinduism. My initial reaction is that Asia's maybe too broad a topic to be useful as a Wikiproject, since most people are probably only interested in working on a specific area of the subject, but you should feel free to solicit others' opinions.
• I agree with this. I think folks interested in working on pages relating to Asia can very easily join one of the regional Asian 'Projects. – Scartol • Tok 18:19, 17 February 2008 (UTC)
• With regards to the idea of an Equal Rights article - again, it sounds like a very broad subject, unless you mean just a subset of the subject (equal rights for women, equal rights for LGBT people, equal rights for religious minorities, etc.), most of which seem to have reasonable articles already. I notice that the Social equality artice, to which Equal rights currently redirects, is kind of a stub - maybe it would be worth developing that?
• With regards to User:Grrrlriot/Sandbox, I think it's a very interesting idea. The one thing I'd advise caution on is whether there are sufficient sources to write all of those articles. I think it would be much more useful to have, say, Feminism in Africa with a continent-wide overview (or broken up into Feminism in the Saharan countries and Feminism in sub-Saharan Africa, or however else seems to make sense) and then a summary of each country (maybe with links to article on the countries that do have enough information for their own articles) then it would to have a pile of two sentence stubs that all say largely the same thing with only the country name changed. On the other hand, I think it's a great idea to develop new articles for countries where there is enough information to make a good article. In summary, I definitely think it's a great idea to develop articles that cover feminism in as many countries as you can; the only question is whether this information is most usefully presented in individual articles for each country or in overview articles that have sections for each country. Sarcasticidealist (talk) 07:43, 17 February 2008 (UTC)
Thanks for your opinions, Steve. I will think about all of what you just said. I really appreciate the feedback. :) --Grrrlriot (talk) 16:53, 17 February 2008 (UTC)
You seem to have an extremely active adopter already - how do you feel you could benefit from having another one? Dev920 (Have a nice day!) 12:31, 17 February 2008 (UTC)
I think 2 is enough. lol Thanks! --Grrrlriot (talk) 16:50, 17 February 2008 (UTC)
Hi, Grrrlriot, thanks for voting in my RfA, which passed with 47 supports (I hoped for a perfect square, but two away is close enough!), 3 opposes (the first odd prime), and 0 neutrals. I'm glad the community has decided to trust me with the mop and bucket (the flamethrower isn't supported). Of course, special thanks goes to my nominators Auawise and that one guy who buried stuff (not that the thanks I give to the you isn't special!). If you ever need a hand with something, or just want to say hello, tough feel free to drop a line! Best wishes, Nousernamesleftcopper, not wood 23:01, 17 February 2008 (UTC) This doesn't even vaguely resemble a mop, but I couldn't find a picture of one.
## have a look at this
Hi Grrrlriot have a look at this post. wikigender.org seems to be an OECD initiative and might just be of interest to you--Cailil talk 13:35, 18 February 2008 (UTC)
Yes, It interests me and I got that email. I was wondering if it was real or what. I emailed the person back saying that I would like an account. --Grrrlriot (talk) 17:24, 19 February 2008 (UTC)
Urg, you problem got the spam mail anyway. I'm assuming user:wikigender made a good faith error in spamming emails but I'm a little disappointed--Cailil talk 18:37, 18 February 2008 (UTC)
I'm a little disappointed too, but it does interest me. --Grrrlriot (talk) 17:24, 19 February 2008 (UTC)
## Thanks for the Portal!
Just wanted to say, "You ROCK!" I was so happy to see that you'd created the much-needed Wikipedia:WikiProject Gender Studies/Feminism Task Force. I've been tackling the gender bias in individual articles for a long while and wishing more editors were available to collaborate on changing the systemic gender bias in Wikipedia. So some weeks ago, I created in Wikipedia. You can see, from the red ink, that I haven't had the time this project deserves. Hopefully others will. Clearly, there is strong affiliation among the Feminism Portal, Gender Studies Project and the Countering Systemic Gender Bias Project. I believe there are distinct purposes, as well. And I hope we one day reach such a critical mass of editors in all three projects, that people can devote themselves solely to one or another. In the meanwhile, I'd like to welcome any collaboration and offer any help needed. I'd also be happy to add the Feminist Portal link to the Countering Systemic Gender Bias Project page, if you'd like. -- Deebki 06:12, 22 February 2008 (UTC)
Hello! Thanks for the compliment! :) I hope you will add your name to 'participants' on the feminism task force. I agree with you. I think that the feminism task force will help articles relating to feminism. Tell me more about the collaboration you have in mind. I think adding a link to the feminism portal to your Countering Systemic Gender Bias Project page. If you want me to link to your wikiproject, let me know and I'll do the same by adding yours under 'Wikiprojects'. Feel free to join the task force by signing your name under "participants". Thanks! --Grrrlriot (talk) 16:46, 22 February 2008 (UTC)
## Archiving
As you've likely noticed, your talk page is being archived now. It turns out that the problem was this edit, which prevents bots from editing your page. Since the archiving is done by a bot, that tag was preventing the bot from doing the archiving. If you want to replace the tag, you'll have to do the archiving manually.
I noticed that my talk page is being archived now. I assume that the tag was removed, Am I right? That's good that it was so that it can archive my talk page. --Grrrlriot (talk) 16:36, 22 February 2008 (UTC)
Anyway, your talk page is now being archived to User talk:Grrrlriot/Archive 1; you should maybe put a link to that page somewhere on your talk page, although it's up to you. I also still think that 48 hours is a little short a time period for things to stay on your page, but that's also up to you (I can think of at least one user who manually archives anything posted to his page as soon as he sees it). Sarcasticidealist (talk) 23:06, 21 February 2008 (UTC)
I agree, 48 hours is a short period of time for things to stay on my page. How do you change that? --Grrrlriot (talk) 16:36, 22 February 2008 (UTC)
Edit your talk page. In the archiving bit up top, change "48h" to some longer length of time. Mine is set at "28d" (meaning 28 days), which you might find too long, depending on how much stuff you want on your talk page at a time. Up to you, anyway. And yes, the tag's been removed. Sarcasticidealist (talk) 20:41, 22 February 2008 (UTC)
Great! Thanks, I will go ahead and edit my talk page. Where should I put the link up to User talk:Grrrlriot/Archive 1 on the talk page? --Grrrlriot (talk) 18:01, 23 February 2008 (UTC)
## userpage redesign
Hey there.. I finally got around to doing some design work on that userpage you asked me for. When you have a minute, take a look and tell me what you think! Cheers. – Scartol • Tok 03:02, 22 February 2008 (UTC)
Hey! I like how it looks, but is there a way you can turn my subpage links into a menu bar. (like at the top of the userpage, have icons, that say 'talk', 'favorite articles', etc. or do you think that its best to keep it how you did it? --Grrrlriot (talk) 16:39, 22 February 2008 (UTC)
Wow. You like how that looks? Are you really a fan of Ann? That design was intended as a joke; I set out to make the most hideous userpage I could think of (and do quickly). If you really do like it, we can proceed with that one. But if you're just being nice, you might be more interested in the real design. I'll add the tabs later today. – Scartol • Tok 19:55, 22 February 2008 (UTC)
Haha! No, I'm not a fan of Ann. I was wondering why she was up on my userpage. I like how the REAL userpage looks. hehe I love it!!!! :D --Grrrlriot (talk) 18:00, 23 February 2008 (UTC)
Okay, so about the tabs – you've got lots of subpages, and it's not possible to put them all at the top. I suggest five (main, talk, awards, userboxes, and creations), with the others listed under "Other Subpages". Sound good? – Scartol • Tok 19:17, 23 February 2008 (UTC)
That sounds good to me. :) --Grrrlriot (talk) 17:37, 24 February 2008 (UTC)
Oh man, I saw that original design, and I thought "Do I have a duty, as her adopter, to say something?" Then I decided that since I'd made it clear that aesthetics weren't my strong point, I should probably just stay out of it. But still, brilliant work Scartol. Sarcasticidealist (talk) 19:30, 23 February 2008 (UTC)
Thank you kindly, Sarcasticidealist. Okay, we're up and running! Please let me know if anything looks off or wrong or funky in a bad way. Also, the headings on the main page are templates, so if you want to add them to your other subpages, you can do so by adding the following code:
```{{User:Scartol/headerbar|YOUR TEXT HERE}}
```
And you'll get:
Enjoy! – Scartol • Tok 16:23, 26 February 2008 (UTC)
## Julia Serano
Hi, Grrlriot!
I'm a little concerned about Julia Serano. Currently the article only has citations from self-published sites. Without other citations, the article is in danger of being deleted due to lack of notability. -- SatyrTN (talk / contribs) 20:25, 22 February 2008 (UTC)
Hello SatyrTN! :) Thanks for letting me know about this. I will see if I can find other sources to add to Julia Serano. --Grrrlriot (talk) 17:58, 23 February 2008 (UTC)
## Lesson from tutor - Articles for deletion
Hi Greta - as I've said before, you seem to be able to function pretty well without a tutor these days. However, you've also said that you want to learn everything about Wikipedia, so, if you're okay with it, I'm going to start providing lessons on areas to which you haven't really been exposed. Today's lesson is the articles for deletion process (I chose this both because you've had very little involvement in it so far and because AfD needs more editors at the moment; I also notice that you have a userbox up indicating that you'd like to be an admin someday, and knowledge of the AfD process is essential for admins).
• What is it? Articles for deletion is where articles that some users think should be deleted are listed so that the community can have its say.
• Who decides which articles get nominated for deletion? Anybody does. To nominate one yourself, see here.
• What happens after an article is nominated? It gets listed here, and other editors show up and have their say. Normally, articles for deletion must be listed for at least five days.
• Who decides whether or not an article is deleted? The community does, via consensus. But it's left to administrators to interpret consensus.
• How do I participate? Find a deletion debate that looks interesting to you, read the nominator's explanation of why it should be deleted, read the other users' arguments, and then add your own thoughts. Normally, this takes the form of either "Keep" or "Delete", followed by your rationale for why.
• What sort of rationale might I use? Most nominations for deletion are because the nominator feels that the subject isn't notable. If the one on which you're commenting is such a nomination, your rationale should assess whether the article's subject meets notability guidelines (including the various subject-specific guidelines found along the right hand side of WP:N). Other nominations are because somebody feels that the article runs afoul of some portion of what Wikipedia is not. In that case, you should base your rationale on that policy. There's also a useful essay called Arguments to Avoid in Deletion Discussions, which provides some examples of poor rationales.
• Now what? I'd encourage you to visit WP:AFD#Current discussions and participate in a deletion discussion or two. Personally, I visit it every few days and look through the current discussions for debates involving politicians, which are of course my area of expertise and interest. You might want to do something similar (although not for politicians, obviously) or you might just want to stop in at random every now and then. I'd also encourage you to let me know whether this was helpful, and whether it's the sort of thing you're looking for from me as your adopter; so far, I've mostly been just observing your edits and responding to your questions, but most of your edits recently look fine and you don't ask me many questions anymore, so I'm not really sure what else to do. Sarcasticidealist (talk) 05:24, 28 February 2008 (UTC)
This is what I'm looking for. Posting about a subject on Wikipedia that I'm not real familiar with is a good idea. I do need to participate in some AFD's. --Grrrlriot (talk) 16:43, 29 February 2008 (UTC)
Delivered by SatyrBot around 17:14, 3 March 2008 (UTC) SatyrBot (talk) 17:35, 3 March 2008 (UTC)
## invite
Hi, I've seen you frequently around the article Green Day and other related articles. Please consider joining the Green Day WikiProject, an effort to improve Wikipedia's coverage and detail regarding Green Day. If you would like to participate, you can visit the project page, where you can join the project and see a list of open tasks that you can help with. Thank you for your time.
LukeTheSpook (talk) 08:44, 23 March 2008 (UTC)
Thanks for the invite, LukeTheSpook! :) I might join the WikiProject in the future. --Grrrlriot (talk) 01:09, 27 March 2008 (UTC)
## Please vote in survey over whether to have article title Human rights in Iran or Human rights in the Islamic Republic of Iran
• 23 November 2007 Sinooher changed the article name from Human rights in Iran to Human rights in the Islamic Republic of Iran
• Koavf changed the article name back to Human rights in Iran 9 March 2008,
• Crazy Suit changed it back to Human rights in the Islamic Republic of Iran a couple weeks later, 23 March 2008.
We should decide this once and for all and not what the name is as it makes a difference to the wording of the text in the article.
### Arguements
Hello, BoogaLouie! :) Thanks for leaving me a message about this matter. I would have to say I'm in favor of the Human rights in the Islamic Republic of Iran. At first I was for Human rights in Iran, but after hearing both arguements I changed my mind. China and Iran do have different governments than they did before their revolution. I hope this helps you out. --Grrrlriot (talk) 21:50, 29 March 2008 (UTC)
Thanx --BoogaLouie (talk) 22:21, 29 March 2008 (UTC)
Your welcome! --Grrrlriot (talk) 21:59, 30 March 2008 (UTC)
I'm pleased to announce that the Awards Center will be getting its own newsletter shortly. If you want to receive the WP:AWC newsletter, put your name here. --Sharkface217 20:44, 30 March 2008 (UTC)
Thanks for letting me know! :) I signed up. --Grrrlriot (talk) 22:01, 30 March 2008 (UTC)
## Award Center Newsletter, Edition 1
The Wikipedia Awards Center Newsletter Volume 1, Issue 1 • April 02, 2008 • About the Newsletter Useful Links In case you ever get lost: New sponsored challenges New challenges include: News: WP:ACCOTF, the Award Center Collaboration of the Fortnight, is launched officially. Sign up for this fortnight's collaboration here. This newsletter is officially launched. I hope everyone likes it. If you have any ideas for future issues, talk to the editor. Completed challenges have been removed from the Award Center in the interest of space, as navigating the page can be arduous. Collaboration of the Fortnight Archives • Random Challenge
The Alternative music WikiProject Newsletter Issue 12 - March 2008 "Expressions of irony through clothing are very important.'"- Carlos Dengler Project news "Just Like Heaven" (song), Flea (musician), Bernard Fanning, Odyssey Number Five, In Rainbows and Silverchair reached featured article status in the past month! Additionally "This Charming Man", a former Featured Article, has been re-promoted to FA status. Well done to WesleyDodds, NSR77, Grim-Gym, the various WikiProject Powderfinger editors, Atlantik, Ceoil and Dihydrogen Monoxide. The discography of Silverchair reached featured list status during the past month. Well done to Dihydrogen Monoxide. Surfer Rosa was featured on the Main Page on March 21. We collaborated on In Rainbows, Vitalogy, The White Stripes, Blur (band) and Accelerate (R.E.M. album) during the past month. During the month of March, Nine Inch Nails live performances, Oasis (band), Boredoms, Hoodoo Gurus, and Vitalogy were promoted to good article status. This month's "Recommended Alternative Album" is Editors - An End Has a Start (2007). New members NewMarqueeDayMoonRising, Thundermaster, and SuperNeek joined the alternative music fold during March. Editors User:WesleyDodds
If you missed last the previous newsletter, you can find it at Wikipedia:WikiProject Alternative music/Newsletter/February 2008.
You are receiving this newsletter because you have signed up for WikiProject Alternative music. If you wish to stop receiving this newsletter, or would like to receive it in a different form, add your name to the appropriate section here. This newsletter was delivered by the automated Giggabot (talk) 09:41, 4 April 2008 (UTC)
## Here's something yummy
Cookies! Here are some cookies as a way of saying "thank you" for contributing to our project. Keep up the good work! Wisdom89 (T / C) 19:50, 26 April 2008 (UTC) has given you some cookies! Cookies promote WikiLove and hopefully this one has made your day better. You can spread the "WikiLove" by giving someone else some cookies, whether it be someone you have had disagreements with in the past or a good friend. To spread the goodness of cookies, you can add {{subst:Cookies}} to someone's talk page with a friendly message, or eat this cookie on the giver's talk page with {{subst:munch}}!
Issue 2 • April 28, 2008 New sponsored challenges New challenges include: News The newsletter has been redesigned. Thank you to WBOSITG, MFC, and IMatthew for your design contributions. This shiny new newsletter is a result of their combined efforts. Thank you to Enigmaman for participating in the previous Award Center Collaboration of the Fortnight. Please note that if you wish to be given credit for work completed, you must sign up for the collaboration first. This week's collaboration is Luc Besson. Apologies for the late newsletter. The editor has been swamped lately due to school and vacation. If in the future a fortnightly delivery schedule cannot be kept, this newsletter will be delivered monthly. A lively discussion about the future of the Award Center is currently being being hosted on the Award Center talk page. Input is always welcome. Useful Links In case you ever get lost: Collaboration of the Fortnight More Links
I'm cleaning up Category:Wikipedians seeking to be adopted in Adopt-a-user and noticed you're still somewhat seeking adoption (even though you seem to be a fairly experienced editor?). If you're no longer seeking adoption, consider removing the userbox from your main page. Cheers, xenocidic (talk) 15:45, 1 May 2008 (UTC)
I'm no longer wishing to be adopted. Thanks for bringing this to my atttention. I will delete the userbox. Thanks again! --Grrrlriot (talk) 21:26, 4 May 2008 (UTC)
No problem at all. Happy editing =) xenocidic (talk) 21:47, 4 May 2008 (UTC)
The Alternative music WikiProject Newsletter Issue 13 - April 2008 "God is in your scrotum!'"- Perry Farrell Project news This month was the first in over a year in which no articles were promoted to featured article status. In the period between March 2007 and April 2008, the project produced a whopping 70 Featured Articles. Let's keep adding to those numbers! Pearl Jam was featured on the Main Page on April 22. We collaborated on My Bloody Valentine, The Queen Is Dead, Double Nickels on the Dime and Ten (Pearl Jam album) during the past month. During the month of April, Diorama (album), Editors, Neon Bible, Ghosts I–IV, "Yes! I Am a Long Way from Home" and "Who Really Cares (Featuring the Sound of Insanity)" were promoted to good article status. This month's "Recommended Alternative Album" is Sleater-Kinney - Dig Me Out (1997). New members Arleach, Panic!out, N0tverycreative, and Gallagher2x2 joined the alternative music fold during April. Editors User:WesleyDodds
You are receiving this newsletter because you have signed up for WikiProject Alternative music. If you wish to stop receiving this newsletter, or would like to receive it in a different form, add your name to the appropriate section here. This newsletter was delivered by the automated Giggabot (talk) 09:01, 2 May 2008 (UTC)
## Hey, I added stuff to riotgrrl...
you said to leave you info on the talk pg...
Re: the term riot grrl...It was the name of a zine... see: http://youtube.com/user/mondotrasho 208.120.251.174 (talk)
also, second wave? The article starts: "is often associated with third-wave feminism (it is sometimes seen as its starting point). However, riot grrrl's emphasis on universal female identity and separatism often appears more closely allied with second-wave feminism than with the third wave.[1] " But a major part is the sex positivity of it and women being able to talk about "universal" parts of female identity that weren't as talked about before. That's distinctly 3rd wave!! http://en.wikipedia.org/wiki/Sex-positive_feminism Kathleen Hanna was a stripper...
I'm not super clear on how wiki works, so sorry I don't have a user name yet! (and of course don't want to just put my email out there!)
~~RD —Preceding unsigned comment added by 208.120.251.174 (talk) 18:31, 19 May 2008 (UTC) here we go RD007 (talk) 18:36, 19 May 2008 (UTC)RD007
Hello, User:RD007 (aka User:208.120.251.174)! :) Thanks for leaving a message on my talk page. I know that the term "riot grrl" was the name of a zine. I have to say that you do have a point and I think your right. It's ok and I understand that you don't want to put your email out there. I am assuming you finally got a Wikipedia account as RD007. Glad to see that you joined Wikipedia! Welcome! Hope you like it here! If you want to talk about this more or about riot grrrl more, let me know and we'll work something out. --Grrrlriot (talk) 01:42, 22 May 2008 (UTC)
Issue 3 • May 23, 2008 New sponsored challenges New challenges include: News Late again! I'm switching the newsletter to be a monthly format, as I seem to remember this once a month. Thanks again Enigmaman for participating in the previous Award Center Collaboration of the Fortnight. Please note that if you wish to be given credit for work completed, you must sign up for the collaboration first. This week's collaboration is Brian Stewart. The following collaboration will be Human Genetic Engineering. Useful Links In case you ever get lost: Collaboration of the Fortnight More Links
The Alternative music WikiProject Newsletter Issue 14 - May 2008 "I go to a fucking office and I write. I'm not one of these dickheads who opens a beer, high fives his mates and opens his mouth and shit pours out, which he then writes on a beer mat. It doesn't come easy."- Nick Cave Project news "Touch Me I'm Sick", Diorama (album) and Nine Inch Nails live performances reached featured article status in the past month! Well done to Indopug, Dihydrogen Monoxide, and Drewcifer3000. The discographies of Sonic Youth, The Libertines, Foo Fighters and Smoking Popes reached featured list status during the past month. Well done to Drewcifer3000, Indopug, Tenacious D Fan and Teemu08. We collaborated on Superunknown, Supergrass, Kate Bush and Foo Fighters during the past month. During the month of May, The Killers, "Under the Bridge", Death Cab for Cutie, Bloc Party, Coldplay, Beck and Ten (Pearl Jam album) were promoted to good article status. This month's "Recommended Alternative Album" is Cocteau Twins - Treasure (1984). New members Seraphim Whipp, Guitardude3600, Lunar Jesters, Kristmace, Freedom (song), TwentiethApril1986, JD554, Thom, and Sethward joined the alternative music fold during May. Editors User:WesleyDodds
You are receiving this newsletter because you have signed up for WikiProject Alternative music. If you wish to stop receiving this newsletter, or would like to receive it in a different form, add your name to the appropriate section here. This newsletter was delivered by the automated Giggabot (stop!) 07:29, 1 June 2008 (UTC)
## howdy
sorry to pop up out of the blue like this, but i was wondering if i could just ask you a favor - the article on Naomi Klein is pretty regularly besieged by pov editors attempting to violate WP:undue by focusing disproportionately on the minority of criticisms of her recent book while failing to acknowledge the overwhelming majority of praise. whatever one's personal feelings on the book, it's pretty inarguable that it was well reviewed by most people, which wikipedia should naturally reflect. sorry to ask you, but i've been dealing with the same people for months, and it gets pretty boring reverting the same silliness over and over. i got into a thing like this over on the ralph nader page a few months ago with a user who was later found to be a sock puppet and blocked. i'll be posting this message on a few other user pages just in case you've gots your plate full or just plum don't wanna do it. thanks Marshmellowgoggles (talk) 22:03, 5 June 2008 (UTC)
Hello! :) Thanks for the message! I'm not sure what your asking me to do. Are you asking me to help patrol vandalism on the Naomi Klein page or are you wanting me to edit the page? Let me know. I might be interested. --Grrrlriot (talk) 00:19, 6 June 2008 (UTC)
thanks, i was just wondering if you could help me watch out for it a bit - sneaky pov, undue focus, etc. it's pretty annoying. Marshmellowgoggles (talk) 07:50, 6 June 2008 (UTC)
Your welcome. Sure, I just added it to my 'watchlist'. --Grrrlriot (talk) 00:07, 7 June 2008 (UTC)
This newsletter was delivered by §hepBot around 16:02, 11 June 2008 (UTC). ShepBot (talk) 16:16, 11 June 2008 (UTC)
I thought you might like to know that the Awards Center page has been deleted, along with its newsletter. :(
So, where do we go from here?
To new and even more interesting projects, of course!
As announced in the newsletter, I've been preparing to co-coordinate a large collaboration/competition called Around the World. It was going to be run at the Awards Center, but since that no longer exists, the collaboration will be hosted somewhere else.
Around the World will begin July 15th as planned - it's location will be announced soon.
It'll be a blast. In the competition, participants will be helping to develop over 200 pages (drafts, which will be moved to article space once they are ready), using advanced tools to edit every single one of them!
This is going to be interesting.
And the event shall have awards which are being created specifically for it as we speak!
If you would like me to keep you informed of this and other interesting collaborations I'll be working on and/or organizing in the future, please drop me a note on my talk page, and I'll be happy to keep you in the know.
Sincerely,
The Transhumanist 21:44, 26 June 2008 (UTC)
I'm sorry to see the awards center go, however, keep me informed of your "Around The World" project. Thanks! --Grrrlriot (talk) 02:38, 29 June 2008 (UTC)
Which of the following medals looks better. This one:
Or this one:
Which one do you like better?
Please let me know on my talk page.
Thank you.
The Transhumanist 21:16, 30 June 2008 (UTC)
I like the first one better. --Grrrlriot (talk) 20:48, 1 July 2008 (UTC)
The Alternative music WikiProject Newsletter Issue 15 - June 2008 "I've gotten into communication states with cats where I know I heard their voices in my head and we'd sit around and have conversations with each other. Like me and one cat there, one cat there and one cat there and I would sit there for like three hours talking to them before I realized 'I can't believe I've been talking to cats for three hours.'" - John Frusciante Project news "Under the Bridge" and Year Zero (album) reached featured article status in the past month! Well done to NSR77 and Drewcifer3000. List of Nine Inch Nails tours and the discographies of The Strokes, Faith No More, Pearl Jam, Echo & the Bunnymen and Death Cab for Cutie reached featured list status during the past month. Well done to Drewcifer3000, Indopug, Balthazar, -5-, JD554, and Teemu08. Wilco was featured on the Main Page on June 8. We collaborated on "Under the Bridge", Siouxsie & the Banshees, I Should Coco, Stone Temple Pilots, and MTV Unplugged in New York during the past month. During the month of June, Double Nickels on the Dime, Jeff Buckley, and "In Bloom" were promoted to good article status. This month's "Recommended Alternative Album" is Art Brut - Bang Bang Rock & Roll (2005). New members Fvasconcellos and Alternative_Idiot joined the alternative music fold during June. Editors User:WesleyDodds
You are receiving this newsletter because you have signed up for WikiProject Alternative music. If you wish to stop receiving this newsletter, or would like to receive it in a different form, add your name to the appropriate section here. This newsletter was delivered by the automated Giggabot (stop!) 07:30, 2 July 2008 (UTC)
## What is Around the World?
It's a collaboration!
The event is being co-sponsored by Wikiproject Lists of basic topics and WikiProject Geography, and participants will be "traveling" all around "the World" visiting each country online (here on Wikipedia and perhaps beyond) as they apply advanced wiki-tools to improve pieces of the profiles of each and every country on Earth!. Each pass through these pages is a "trip around the World..."
The set of pages we are working on is currently located at Wikipedia:WikiProject Lists of basic topics.
Each page presents essential information on each country in a topic outline format, for ease of overviewing and navigating. Most of the topics presented are linkified, which turns these pages into a hypertextual map to material about each country on Wikipedia. When completed, they shall all become part of Wikipedia's contents system.
The pages share a standard format, with the information on each country presented in the same general order. So rather than getting stuck on a single country trying to complete it, each participant works on all 200+ political entities, completing a single data item or detail across all of the pages!
For this they use advanced tools like WP:AWB, Linky, etc. It goes fast, and since others are doing this at the same time, it makes "the World" feel like a beehive, and the participants are its bees. :) The energy is contagious.
And since you are moving from country to country, the tasks make it feel like you are traveling around the world, and you get to learn a little about every country as you do so. This approach also allows for greater efficiency, because by the time you've done 30 or so of a particular item, you've figured out how to finish it faster and more effectively (such as where to find the data or how to make adjustments), and this specialization speeds up development - but more importantly it reduces errors.
The tasks are varied, which adds even more variety to the project. Some tasks are look-ups-and-fill-ins, some are copy and paste, some are image hunts, some are maintenance adjustments, some are link fixing, some are blue-linking (creating an underlying redirect so a link turns blue), some are fact checking, etc.
For an example of what a nearly complete page looks like, see these:
List of basic Albania topicsList of basic Argentina topicsList of basic Australia topicsList of basic Canada topicsList of basic Ecuador topicsList of basic Egypt topicsList of basic France topicsList of basic Germany topicsList of basic Iceland topicsList of basic India topicsList of basic Indonesia topicsList of basic Iraq topicsList of basic Republic of Ireland topicsList of basic Italy topicsList of basic Isle of Man topicsList of basic Israel topicsList of basic Japan topicsList of basic Macau topicsList of basic Mexico topicsList of basic Russia topicsList of basic Taiwan topicsList of basic United Kingdom topicsList of basic United States topics
There are only about 200 more pages to go!
Standing by to help are co-coordinators, who can lend a helping hand to participants, provide instruction and tips on how to use the tools, and help them find what they are looking for. Co-coordinators also use advanced tools to inspect the work of participants, and touch it up as needed, or if a task was done wrong throughout, point this out to the participant so he or she can make the necessary corrections.
Co-coordinators are working on the set of pages right now, to familiarize themselves with "the World" so they can help more effectively by the time the main event starts. But there's still lots of preparation left to be done, and we are looking for editors experienced in advanced wikitools who would like to become co-coordinators.
The Transhumanist 03:39, 2 July 2008 (UTC)
Ok, I understand now. I'm glad to hear about the basic list of countries. It sounds like fun. Do you have a listing of the basic country lists that have already been made so far? Let me know, I might contribute to the project. Thanks! --Grrrlriot (talk) 16:30, 2 July 2008 (UTC)
## Hey!
I was born the same day as you! :) ΤΕΡΡΑΣΙΔΙΩΣ(Ταλκ) 00:04, 3 July 2008 (UTC)
Really? That's pretty cool. I know of 3 people that share the same birthday as well, in real life. Yay for Pisces! :) --Grrrlriot (talk) 00:33, 3 July 2008 (UTC)
Lol awesome :) Im off to bed now, been editing almost all day :) later! x ΤΕΡΡΑΣΙΔΙΩΣ(Ταλκ) 00:42, 3 July 2008 (UTC)
Thanks for the message! I should edit more than I do. I used to edit alot, but now I do it every once in a while. --Grrrlriot (talk) 01:07, 3 July 2008 (UTC)
## Some help (which you asked for)
On your help-ish page, you listed the Abortion Portal as possibly being a bad idea. I'm under the impression that the controversy surrounding abortion is big enough to have it's own Portal. I hope I'm not too late with this help. Happy editing, Leonard(Bloom) 20:43, 30 June 2008 (UTC)
Hello Leonard! :) Thanks for the message! I still think the abortion portal could be a good idea. No, Your not too late with this. --Grrrlriot (talk) 20:46, 1 July 2008 (UTC)
I think the portal would work, but it would require expansion on the articles within. Although it is large, controversial topic, it is still just one topic, and thus needs to look good, have legit references and citations, and overall need to be good articles. The quality needs to be higher, to make up for the iffy-ness of the portal's topic. Leonard(Bloom) 20:51, 1 July 2008 (UTC)
I agree and I think it the portal would have to be watched very closely. I think the portal would have a lot of vandals vandalizing it. Any ideas for it? --Grrrlriot (talk) 02:39, 2 July 2008 (UTC)
Well, without isolating it from the rest on en.wiki, there really isn't anything you could do. Maybe have some time where you just go through all the article in the portal and review the histories? I think that it would require just a bit more elbow grease to peruse a single portal than everything in totality. Leonard(Bloom) 05:45, 4 July 2008 (UTC)
Oh ok, I think I get what your saying. --Grrrlriot (talk) 16:10, 4 July 2008 (UTC)
It takes quite a bit of effort patrol a small bit of space instead of the whole site, and I say that because we have wide-expansive tools (Huggle, Twinkle, Lupin's tools), but nothing that really can center on a single bit, or portal in this case. Correct me if I'm wrong with this impression. Leonard(Bloom) 16:37, 4 July 2008 (UTC)
I agree with you completely. That's true, the histories of the portal could be visited and changed. --Grrrlriot (talk) 19:09, 4 July 2008 (UTC)
## Checking in
Hi Grrrlriot - just checking in to make sure everything's going okay. It's been a while since we spoke, so I just thought I'd check to see if you needed help with anything. Sarcasticidealist (talk) 00:38, 3 July 2008 (UTC)
Hello Sarcasticidealist! :) It's good to hear from you. One question I do have: Did I do the talk archive right? --Grrrlriot (talk) 01:06, 3 July 2008 (UTC)
Do you mean the archive of your user talk page (i.e. this one)? If so, it seems to be archiving just fine. Sarcasticidealist (talk) 01:43, 3 July 2008 (UTC)
Yes, That's what I meant. That's good to know. --Grrrlriot (talk) 01:54, 3 July 2008 (UTC)
Hello from me as well :) You've been rather quiet, but that's probably a good sign. Keep up the good work! weburiedoursecretsinthegarden 21:45, 3 July 2008 (UTC)
Hello WBOSITG! :) It's good to hear from you as well! Yeah, I have been quiet and I haven't been on Wikipedia as much as I was. --Grrrlriot (talk) 21:49, 3 July 2008 (UTC)
## Thanks!
Hey thanks for that, I dont know much about feminism in particular (certainly not enough to contribute to articles on it) but Ive always been interested in the "battle of the sexes" if you will lol :) Ill see if i can help out with it, thanks again, laterz! :D x ΤΕΡΡΑΣΙΔΙΩΣ(Ταλκ) 08:01, 6 July 2008 (UTC)
lol I see. Thanks and your welcome! --Grrrlriot (talk) 17:35, 6 July 2008 (UTC)
## If I can contribute anything...
If I can contribute anything, I guess it would be the general improvement of articles about feminism and feminists in my country. I can already see that the quality of the French-language bios and the English-language bios of Quebec's most notable feminists vary greatly. Worst, there are currently no English-language articles on Éva Circé-Côté and Idola Saint-Jean, two of Quebec's first feminists, same for the Fédération des femmes du Québec (FFQ), and the yearly World March of Women initiated by the FFQ in 2000[4]. -- Mathieugp (talk) 20:17, 6 July 2008 (UTC)
That's true, Those articles need to be created. If you want to contribute or if you can at some point, just go to the Task Force page and sign your name under "Participants". I think articles about feminism and feminists in your country is a good idea. If there are others out there, that have/edit articles about feminism and feminists in their countries...that's a very good idea, in my opinion. --Grrrlriot (talk) 20:27, 6 July 2008 (UTC)
## ^_^
- PeaceNT (talk) has smiled at you! Smiles promote WikiLove and hopefully this one has made your day better. Spread the WikiLove by smiling at someone else, whether it be someone you have had disagreements with in the past or a good friend.
Smile at others by adding {{subst:Smile}} to their talk page with a friendly message.
Cheers and happy editing!
Thanks for the smile, PeaceNT! :) --Grrrlriot (talk) 22:42, 7 July 2008 (UTC)
Hey Grrrlriot, I added myself as an official member of the taskforce per your suggestion. I just recently finished working on Emma Goldman with Scartol et. al. If you haven't read that article, I think you would enjoy it. Also Awadewit just finished doing complete rewrites of Mary Shelley and Mary Wollstonecraft that are top notch! Things seem to be really rolling on Wikipedia these days. BTW, I noticed you're in Tennessee. I'm in NashVegas myself :) Kaldari (talk) 04:35, 6 July 2008 (UTC)
Hello Kaldari! :) I'm in east Tennessee, but I do know where NashVegas is. hehe Thanks for joining the task force and welcome! If you know of other editors that would be interested in it, feel free to let them know about it. Emma Goldman is a very good article. I noticed that Mary Wollstonecraft is a featured article and a featured article listed on the task force page. Happy editing! --Grrrlriot (talk) 04:40, 6 July 2008 (UTC)
I'm actually from Knoxville originally. And a fan of Dixie Dirt, of course :) Kaldari (talk) 20:14, 7 July 2008 (UTC)
Cool! :) --Grrrlriot (talk) 20:50, 7 July 2008 (UTC)
## Feedback
Hello again - I've looked over your most recent edits (and it's really nice to see you back, let me add). I like the enthusiasm you've shown for starting the Feminism Task Force; it seems to be really taking off. I see no real problems with your editing, and I'd say you're an asset to the project. As far as things to work on in the future, I'd suggest doing some article building: maybe find an article about a feminist or other feminism-related topic that's in bad shape, and try to improve it by expanding it, adding references, etc. If you own any books or magazine profiles or anything else about any feminists, that would be a great place to start. I'd be happy to help you with that once you've selected a topic, although, as I've said before, I don't personally know a lot about that field, and my collection of books probably wouldn't be very helpful. The other thing is deletion discussions - I explained to you how these work a few months ago, but you don't seem to have participated in any since. I want to emphasize that it's possible to be an excellent editor without ever participating in deletion discussions, but since you've indicated that you'd like to be an administrator at some point, I'm trying to help you find ways to get involved in the more administrative side of the project, and WP:AFD is a great place to do that. Sarcasticidealist (talk) 22:48, 7 July 2008 (UTC)
Thanks for the feedback Sarcasticidealist! :) I really appreciate your feedback. Thanks for thinking I'm an asset to the project. I try to obey all the rules. Thanks fo the suggestions as well. I will work on these in the future. Yes, I'd like to be an administrator on Wikipedia someday. Thanks for reminding me about the AFD. I really should participate in those, since I haven't participated in any, except maybe 1 or 2. Any other suggestions/ways to get involved in the administrative side of WP? I will try to participate as much as I can on the administrative side. --Grrrlriot (talk) 22:54, 7 July 2008 (UTC)
I see you've started participating in AFDs, which is great. Your participation in them is quite good, as you've taken care to provide reasons for your deletions. A couple of other recommendations: first, when claiming neologism as a reason for deletion, it's often a good idea to check the internet to see if you can find any secondary sources discussing the neologism (urbandictionary and the like don't count, since they're not reliable sources). Googling isn't always a good way to determine the notability of a subject, but for neologisms it usually works pretty well, since if a neologism isn't covered in an online source, it's probably not covered in any offline sources either. The second piece of advice I'd give is that you should try to reference Wikipedia policy and guidelines in every deletion argument you make; you usually do, but didn't in this one (although, reviewing the article, I tend to agree that it should probably be deleted). In this case, for example, you could have said that, since the article's references don't discuss the issue of denial of lesbianism in any kind of detail, but just provide examples of lesbians who have denied being lesbians, there's no evidence that the concept meets WP:N. Still, though, a very promising start and, as with everything, you'll get better the more you do of it. As for your questions about other ways to get involved in the administrative side, the short answer is that there are lots, but a lot of them require you to learn a lot before you're able to contribute to them in any meaningful way (but hey, that's what adopters are for). I'll put together a list of some of them within the next day or two. Sarcasticidealist (talk) 04:04, 8 July 2008 (UTC)
Great, thanks for the feedback, I really appreciate it! :D I went back to that AFD and worded it similar to what you said. --Grrrlriot (talk) 04:15, 8 July 2008 (UTC)
I've started putting together a list of "administrative" areas of Wikipedia here. It's far from complete, but I hope to expand it substantially within the next few days. You may want to watchlist it so you can see when I add new information. Sarcasticidealist (talk) 05:10, 8 July 2008 (UTC)
Thanks alot! I just added the page to my watchlist. --Grrrlriot (talk) 16:02, 8 July 2008 (UTC)
## Guest boook
Heya, thanks for signing my guest book. (i signed your's too). Normally I would have given you a cookie as thanks but my computer is messing up and won't let me... ♥Tory~AmuletHeart♥ 21:10, 10 July 2008 (UTC)
Your welcome! :) That's okay. Happy editing! --Grrrlriot ( ) 15:45, 19 July 2008 (UTC)
Hello, and sorry for not responding earlier. While I would certainly like to help improve articles related to feminism (The Second Sex in particular needs a rewrite, and I've read the book in the original French), I'm not certain if I should commit to another WikiProject or task force because I already find myself stretched in so many directions. I would be glad to sign up for the task force as long as you don't mind only intermittent activity on my part. --Kyoko 00:15, 17 July 2008 (UTC)
No, I don't mind at all, Kyoko. :) A little activity is better than none. --Grrrlriot ( ) 15:47, 19 July 2008 (UTC)
## Feminism in modern Japan
After doing some copy editing, I noticed your comment on the talk page. I would definitely support a move to a better title and the page could use any attention you could give it. JCDenton2052 (talk) 08:51, 19 July 2008 (UTC)
Great! :) Thanks, JC. I'm glad you agree with me. Do you think that "Feminism in Japan" sounds better? I also replied to your comment on the article's talk page, Talk:Feminism in modern Japan. --Grrrlriot ( ) 15:58, 19 July 2008 (UTC)
## LGBT WikiProject Newsletter (July 2008)
• Newsletter delivery by xenobot 13:01, 30 July 2008 (UTC)
## To all members of the Anarchist Task Force - about improvement of the AI-Wiki-page
I have just joined the Anarchist Task Force, and I have had some problems with publishing of my Anarchist International Wikipedia page, see my sandbox http://en.wikipedia.org/wiki/User:Anna_Quist/Anarchist_International for the present version/proposal. This page needs improvements to reach Wiki-consensus, and this should be a somewhat collective project to avoid a "COI"-template. As I am new to editing here on Wikipedia I need help with the page, I hope for your cooperation with this improvement. As an introduction to this cooperation, feel free to read this note on my talk page:
Any contribution, matter of fact criticism, to give input and advice, or even contribute to new sections, will be helpful, and is much appreciated. Please join in the project...
(Anna Quist (talk) 17:08, 29 July 2008 (UTC))
Thanks for letting me know about this, Anna Quist. The project sounds interesting. I might help out on the article in the future. --Grrrlriot ( ) 22:46, 2 August 2008 (UTC)
## Thank you!
I hear it is you we have to thank for getting the Feminism portal up and running. I just wanted to say how much I appreciate your work. I think it is a wonderful idea and I'm so happy to be working on it! Awadewit (talk) 16:31, 7 August 2008 (UTC)
Hello Awadewit! Thanks for the compliment and for leaving me a message. Yes, I created Portal:Feminism and Wikipedia:WikiProject Gender Studies/Feminism Task Force as well. I'm glad to hear that you think it's a wonderful idea. --Grrrlriot ( ) 23:44, 9 August 2008 (UTC)
## You are welcome
My pleasure, I love working on portals. :) Quick request, can you please change your sig to link to Wikipedia:WikiProject Gender Studies/Feminism Task Force instead of Wikipedia:WikiProject Gender Studies/Feminism Task Force? I moved it because as it is a subproject off of WP:GS, it should be a subpage off of that WikiProject. Cheers, Cirt (talk) 01:27, 10 August 2008 (UTC)
Ok, I will change my sig. Thanks for letting me know, Cirt. --Grrrlriot ( ) 03:59, 10 August 2008 (UTC)
No worries, Cirt (talk) 04:03, 10 August 2008 (UTC)
Thanks for the invitation. I just joined. — Malik Shabazz (talk · contribs) 23:19, 5 July 2008 (UTC)
Your welcome and thank you for joining! :) --Grrrlriot (talk) 23:45, 5 July 2008 (UTC)
Me also :) Mgoodyear (talk) 19:23, 23 July 2008 (UTC)
Great and thanks for joining as well! --Grrrlriot ( ) 00:47, 27 July 2008 (UTC)
Greta, you are phenomenal. OK I just completely rewrote Female ejaculation - it is not perfect, but it was absolutely dreadful before (Skene's gland is worse), and completely Male Lens. That imbalance is now fixed. I am sure there are a number of other women's health articles in urgent need of attention. Are any other articles tagged yet as an example? Michael. (personal details available on Talk page) Mgoodyear (talk) 23:28, 10 August 2008 (UTC)
Thanks Mgoodyear! I'm sure you are right about more women's health articles needing urgent attention. If you find some articles in need of attention, You could add the articles to the template "Feminism Task" that is on the FTF page under "Templates". Thanks for your help! Keep on editing! I will check out Female ejaculation in an hour or so. I hope you continue to edit women's health articles. You could probably post what you just posted to me on the FTF talkpage: Wikipedia_talk:WikiProject Gender Studies/Feminism Task Force. --Grrrlriot ( ) 00:02, 11 August 2008 (UTC)
Shall do! Michael. 142.239.254.19 (talk) 15:16, 11 August 2008 (UTC)
Yes, I had seen your reply in your own talk page. I am glad you approve of my suggestions. I just could not find the right words to add at the time. It's often like that with me and girls... ;-) But you remind me I haven't done a single thing on this subject yet, so I'll get right to it. Here, I'll create a draft article on the Fédération des femmes du Québec. Bon dimanche! :-) -- Mathieugp (talk) 16:14, 10 August 2008 (UTC)
Glad to hear your working on the draft! I can't wait to see the article once it is completed. --Grrrlriot ( ) 17:14, 10 August 2008 (UTC)
## Portal:Feminism currently up for portal peer review
Notifying you because you were the initial creator of Portal:Feminism, and of Feminism Task Force:
Portal:Feminism has had a lot of changes and work recently and is currently up for portal peer review. Comments would be appreciated at Wikipedia:Portal peer review/Feminism/archive1. Thank you, Cirt (talk) 04:16, 16 August 2008 (UTC)
Hello Cirt! Thanks for contacting me about this! I think the portal is looking better everyday. --Grrrlriot ( ) 20:20, 16 August 2008 (UTC)
Thanks! Cirt (talk) 23:50, 19 August 2008 (UTC)
## Thanks for inviting me!
Thank you very much for inviting me to the Feminism Task Force. I am interested in feminism because my girlfriend, a journalist, works at a feminist ngo. I am an English-Spanish-English, French-Spanish and German-Spanish translator, as well as a psychologist, and would like to collaborate in the translation of Wikipedia pages about feminism. Best regards from Mexico City!! Gustavo Sandoval Kingwergs a.k.a. Correogsk--correogsk (talk) 23:44, 18 August 2008 (UTC)
Hello Correogsk! Thanks for the message! Your welcome for the invite to the FTF. Your girlfriend's work sounds really interesting. Your job as a psychologist sounds interesting too. (I used to want to be a psychologist when I was younger.) I think it would be GREAT to have translators for Wikipedia pages about feminism. Thanks for joining the FTF! --Grrrlriot ( ) 02:56, 19 August 2008 (UTC)
## Around the World, update...
We've been hard at work behind the scenes. We can't seem to get the trophy right, but we'll get there. And the set of pages need one more section completed before they can be moved to article space...
... that's right! We're almost ready to move the whole set into the live encyclopedia. One page for every country of the world!
We're currently developing the standard (by example) for these outlines, they're overall format and what they should look like.
One page that is nearly complete and built to the current standard is List of basic Thailand topics. Please take a look, and help us put the finishing touches on it if you have the time. It will be an example (along with List of basic Japan topics and List of basic France topics) for those working on the rest of the lists, and therefore is pretty important.
Any help or input you could provide would be most appreciated.
Thank you.
The Transhumanist 22:52, 31 August 2008 (UTC)
(P.S.: If you respond to this message, please do so on my talk page, so that I'm alerted by Wikipedia's automatic "you've got a message" feature. Thank you. TT)
## WikiProject Alternative Music Newsletter for August 2008
The Alternative music WikiProject Newsletter Issue 17 - August 2008 "Oh, we've been called an alternative band before. But we eat meat, so I think we're disqualified: chili dogs, corn dogs, Jimmy Dean Sausage Breakfast."- Kurt Cobain Project news "My Happiness" (song) reached featured article status in the past month! Well done to Giggy. Isobel Campbell discography, List of Nine Inch Nails awards, List of Soundgarden awards, and List of Pearl Jam awards reached featured list status during the past month. Well done to Red157, Drewcifer3000, -5-, and Be Black Hole Sun. Flea (musician) was featured on the Main Page on August 19. We collaborated on "Interstate Love Song", The Smiths, Viva la Vida or Death and All His Friends, Sub Pop, and Bleach (album) during the past month. During the month of August, Superunknown, Vs. (Pearl Jam album), Black Holes & Revelations, "Clocks" (song), and Disintegration were promoted to good article status. We are currently discussing various alternative rock albums as possible candidates for a project-wide Featured Topic collaboration. Please join the discussion here. This month's "Recommended Alternative Album" is Velocity Girl - Copacetic (1993). New members Corythepaperboy, Hiram111, Yozzer66, and Lugnuts joined the alternative music fold during August. Editors User:WesleyDodds
SoxBot II (talk) 21:43, 4 September 2008 (UTC)
## My RfA
Thank you for supporting me in my RfA, which passed with a count of (166/43/7). I appreciate your comments and in my actions as an administrator I will endeavor to maintain the trust you have placed in me. I am honored by your trust and your support. Thank you, Cirt (talk) 02:13, 16 September 2008 (UTC)
## WikiProject Alternative Music Newsletter for September 2008
The Alternative music WikiProject Newsletter Issue 18 - September 2008 "And suddenly the plane dropped to the right, then to the left, and the ground was right there. And all I could think was, Fuck, I didn’t finish "Fix You." That would have been my last thought: I didn’t get that chorus right."- Chris Martin Project news Disintegration reached featured article status in the past month! Well done to NSR77 and WesleyDodds. List of Björk awards, List of Rage Against the Machine awards, and List of awards and nominations received by Muse reached featured list status during the past month. Well done to Gary King, who wrote all three featured lists. David Lovering was featured on the Main Page on September 17. We collaborated on Parklife, Tragic Kingdom, Bauhaus (band), and OK Computer during the past month. During the month of September, The White Stripes, "Yellow" (song), No Depression (album), "Speed of Sound" (song), "The Scientist" (song), "God Put a Smile upon Your Face", "In My Place", Demolition Plot J-7, No Age, and "All the Way" (Eddie Vedder song) were promoted to good article status. Help us select good versions of WP:ALM articles for inclusion on the Wikipedia 0.7 release! Find out more about Wikipedia 0.7 selection on the project talk page and add your thoughts to the discussion. If you are personally responsible for a Featured or Good Article listed here, please the select a version to include in Wikipedia 0.7 on that page if you haven't already. Page versions must be selected by October 20. This month's "Recommended Alternative Album" is The Long Blondes - Someone to Drive You Home (2006). New members ThinkBlue joined the alternative music fold during September. Editors User:WesleyDodds
SoxBot II (talk) 20:02, 3 October 2008 (UTC)
## Articles you might like to edit, from SuggestBot
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SuggestBot picks articles in a number of ways based on other articles you've edited, including straight text similarity, following wikilinks, and matching your editing patterns against those of other Wikipedians. It tries to recommend only articles that other Wikipedians have marked as needing work. Your contributions make Wikipedia better -- thanks for helping.
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## Contest Invitation
Hello there!
You have been invited to enter C4v3m4n's Contest!.
The contest is designed to provide users with a challenge while still having fun! This month's contest is focused on Movember, a month designed to to raise awareness and funds for men's health issues, such as prostate cancer and depression in Australia and New Zealand.
Thanks C4v3m4n for the invitation! I will check it out. --Grrrlriot ( ) 18:53, 22 October 2008 (UTC)
## Simple thanks
Thank you for the welcome message you placed on my user page. (especially since I've had this account for months and you're the first person who has done so).--Metalhead94 (talk) 01:34, 24 October 2008 (UTC)
Your welcome, Metalhead94! :) Thank you for being kind! Happy editing! --Grrrlriot ( ) 01:39, 24 October 2008 (UTC)
Ya know, it's always cool to meet another metalhead. May I ask who your favorite band is?--Metalhead94 (talk) 00:05, 25 October 2008 (UTC)
I have alot of favorite bands from different genres. I would have to say that my favorite metal band would have to be Strapping Young Lad. --Grrrlriot ( ) 18:27, 27 October 2008 (UTC)
## WikiProject Alternative Music Newsletter for October 2008
The Alternative music WikiProject Newsletter Issue 19 - October 2008 "When we were trying to sell 'This Corrosion' to Steinman, we said it was like the high point of a Borgia disco evening and he went for it. Nobody makes gloriously stupid records anymore."- Andrew Eldritch Project news "Paranoid Android" reached featured article status in the past month! Well done to Brandt Luke Zorn and Giggy. List of awards and nominations received by The White Stripes, List of awards and nominations received by The Strokes, List of awards and nominations received by Nirvana, List of awards and nominations received by Beck, List of awards and nominations received by Gorillaz, List of awards and nominations received by Barenaked Ladies, and the discographies of The White Stripes and Supergrass reached featured list status during the past month. Well done to Gary King, Red157, and TwentiethApril1986. A Rush of Blood to the Head reached good topic status during the past month. Well done to ThinkBlue. We collaborated on Modest Mouse, "Paranoid Android", "Alright" (Supergrass song), and "Karma Police" during the past month. During the month of October, Parachutes, X&Y, A Rush of Blood to the Head, Mellon Collie and the Infinite Sadness, The Singles 1992–2003, I Should Coco, The Beacon Street Collection, Tragic Kingdom, and "No One Knows" were promoted to good article status. This month's "Recommended Alternative Album" is Siouxsie & the Banshees - Juju (1981). New members SanePsychotic joined the alternative music fold during October. Editors User:WesleyDodds
SoxBot II (talk) 02:49, 2 November 2008 (UTC)
I'm laughing...
I just checked my GuestBook for the first time in a few days and I saw your message...
You said that I was on Wikipedia for 12 years and that it was a very long time to be on...
Wikipedia was formed in 2001. It is only 7 years old, not 12! Wanna go back to my page and read it again? It's OK, everyone makes mistakes. :) TopGearFreak Talk 17:00, 5 November 2008 (UTC)
Now, I'm laughing. lol Sorry about that mistake. I thought I read somewhere that you'd been on Wikipedia for 12 years. I didn't think Wikipedia was around for that long. I guess I didn't read it right, it's my fault. lol Sorry again. At least we got a laugh out of it. haha! --Grrrlriot ( ) 18:17, 5 November 2008 (UTC)
Wikipedia's only 7. If you want to know, I'M THE ONE THAT'S 12!! ;) we had a laugh, all right... TopGearFreak Talk 21:13, 6 November 2008 (UTC)
Okay, I think I get where I got the 12 from. lol Sorry again! Also, cheers to you for being 12 and for editing usefully on Wikipedia! :) --Grrrlriot ( ) 23:10, 6 November 2008 (UTC)
Thank you... TopGearFreak Talk 15:30, 7 November 2008 (UTC)
Your welcome. --Grrrlriot ( ) 22:51, 7 November 2008 (UTC)
## Message from WikiProject Punk music
Hello!
You may be interested to know that WikiProject Punk music has recently undergone a major revitalization. Please visit the project page to see our new look and check out some of our helpful new features, such as the Assessment Department and the Collaboration of the week. There are also a number of tasks on our Things to do page that you may be interested in helping with.
We are currently holding a roll call to help gauge how many active project members we have. Please visit the project's talk page and add your signature to the roll sheet to express your continued interest in the project. Also, if you have not already done so, please take a minute to add your name to the Participants page along with a brief summary of your punk-related interests, so that other project members will be better able to collaborate with you. If you do not add your signature to the roll sheet by November 30, 2008 your name will be moved to our list of inactive members. We may also take the liberty of removing the project userbox from your userpage if it appears there, to prevent you from automatically appearing in Category:WikiProject Punk music members. Of course you are free to rejoin the project and re-add the userbox at any time if you would like to become active in the project again.
Thank you and we hope you will continue to support WikiProject Punk music!
--IllaZilla (talk) 00:15, 6 November 2008 (UTC)
I just added myself to the "roll sheet". Thanks for the message! --Grrrlriot ( ) 05:07, 6 November 2008 (UTC)
Although they're certainly not a Riot Grrl band, The Teen Idles are up at FAC right now. Kaldari (talk) 06:25, 13 November 2008 (UTC)
Thanks for letting me know about the article and the band, Kaldari! I have never heard of the band, so I guess I have another band to check out in my spare time. Thanks again! --Grrrlriot ( ) 18:23, 13 November 2008 (UTC)
This newsletter was sent by §hepBot (Disable) at 21:09, 12 November 2008 (UTC) by the request of Moni3 (talk)
## Proposed deletion of Anarchism in Asia
A proposed deletion template has been added to the article Anarchism in Asia, suggesting that it be deleted according to the proposed deletion process because of the following concern:
Not really enough here to qualify as a standalone article; template suffices.
All contributions are appreciated, but this article may not satisfy Wikipedia's criteria for inclusion, and the deletion notice should explain why (see also "What Wikipedia is not" and Wikipedia's deletion policy). You may prevent the proposed deletion by removing the `{{dated prod}}` notice, but please explain why you disagree with the proposed deletion in your edit summary or on its talk page.
Please consider improving the article to address the issues raised because, even though removing the deletion notice will prevent deletion through the proposed deletion process, the article may still be deleted if it matches any of the speedy deletion criteria or it can be sent to Articles for Deletion, where it may be deleted if consensus to delete is reached. the skomorokh 18:38, 19 November 2008 (UTC)
Thanks for letting me know about this. I will remove the template with an explanation. I agree that the article needs to be expanded and have more information on it. --Grrrlriot ( ) 18:49, 19 November 2008 (UTC)
No worries, sorry for bothering you with this. Regards, the skomorokh 18:52, 19 November 2008 (UTC)
It's ok. :) Thanks for letting me know. I can easily see why it was tagged as WP:PROD. If you have any ideas or references so I can turn it into an article, let me know. Thanks! --Grrrlriot ( ) 22:15, 19 November 2008 (UTC)
## WikiProject Alternative Music Newsletter for November 2008
The Alternative music WikiProject Newsletter Issue 20 - November 2008 "I had access to the most quality fanny available." - Jarvis Cocker Project news No Depression (album) reached featured article status in the past month! Well done to Teemu08. List of awards and nominations received by Bloc Party and List of awards and nominations received by Radiohead reached featured list status during the past month. Well done to Gary King and WilliamH. We collaborated on Blessid Union of Souls, Britpop, Morrissey, Yield (album), and "No Surprises" during the past month. During the month of November, No Doubt (No Doubt album), "The Hardest Part" (Coldplay song), "Talk" (song), "Violet Hill" (song), "Don't Panic" (song), and "Fix You" were promoted to good article status. This month's "Recommended Alternative Album" is Foo Fighters - Foo Fighters (1995). New members A Stop at Willoughby and Trap The Drum Wonder joined the alternative music fold during November. Editors User:WesleyDodds
SoxBot II (talk) 02:58, 10 December 2008 (UTC)
## Articles you might like to edit, from SuggestBot
SuggestBot predicts that you will enjoy editing some of these articles. Have fun!
SuggestBot picks articles in a number of ways based on other articles you've edited, including straight text similarity, following wikilinks, and matching your editing patterns against those of other Wikipedians. It tries to recommend only articles that other Wikipedians have marked as needing work. Your contributions make Wikipedia better -- thanks for helping.
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P.S. You received these suggestions because your name was listed on the SuggestBot request page. If this was in error, sorry about the confusion. -- SuggestBot (talk) 18:37, 14 December 2008 (UTC)
## WikiProject Alternative Music Newsletter for December 2008
The Alternative music WikiProject Newsletter Issue 21 - December 2008 "Anthony's a sex symbol. You see the thing is for the girls they're like 'oh Anthony he's so beautiful! And his muscles and his hair and oh golly he's so sexy!' but with me its like [with men] 'DUDE YOU'RE SO AWESOME...WOW DUDE. WOW!" - Flea Project news The Cure discography and Audioslave discography reached featured list status during the past month. Well done to JD554 and Cannibaloki. Parachutes and Hey Venus! reached good topic status during the past month. Well done to ThinkBlue and Cavie78. We collaborated on Thom Yorke, Dirt (album), Suede (band), and Nothing's Shocking during the past month. During the month of December, In Utero and White Lies (band) were promoted to good article status. This month's "Recommended Alternative Album" is Badly Drawn Boy - Have You Fed the Fish? (2002). New members Papa November and S. Dean Jameson joined the alternative music fold during December. Editors User:WesleyDodds
SoxBot II (talk) 17:46, 2 January 2009 (UTC)
## DYK nomination of Simone de Beauvoir Prize
Hello Grrrlriot! I've submitted Simone de Beauvoir Prize at the Did you know nominations page. They liked the hook but there is still some issues regarding length of the article. Since the Simone de Beauvoir Prize is a Feminist related article and I knew you are active in that field, I thought you might want to help us, expanding the article as soon as possible so it could qualify to be on the first page of en.wikipedia. btw here is the nomination's entry. Thanks --Kaaveh (talk) 11:46, 13 January 2009 (UTC)
Hello Kaaveh! Thanks for this message! You should post this on the Feminism Task Force talk page. --Grrrlriot ( ) 22:46, 28 January 2009 (UTC)
## Rights templates
Since you have done a lot of work on this... could we add Prostitutes (or "sex workers", whatever appears more appropiate) as rights holders to the templates, (see World Charter for Prostitutes' Rights).--SasiSasi (talk) 22:51, 27 January 2009 (UTC)
Hello SasiSasi! I think it is a good idea, but I think the discussion should be brought up on the template talk page. --Grrrlriot ( ) 22:48, 28 January 2009 (UTC)
## Articles you might like to edit, from SuggestBot
SuggestBot predicts that you will enjoy editing some of these articles. Have fun!
SuggestBot picks articles in a number of ways based on other articles you've edited, including straight text similarity, following wikilinks, and matching your editing patterns against those of other Wikipedians. It tries to recommend only articles that other Wikipedians have marked as needing work. Your contributions make Wikipedia better -- thanks for helping.
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P.S. You received these suggestions because your name was listed on the SuggestBot request page. If this was in error, sorry about the confusion. -- SuggestBot (talk) 05:19, 14 February 2009 (UTC)
## assigning articles to the Feminism task force
Hi, I noticed that a while back you added [[Category:Feminism task force articles]] to several feminism-related article talk pages. You'll be happy to know that this is now built into the {{WikiProject Gender Studies}} template. Any talk pages which include that template with the feminism-task-force parameter set to "yes" will automatically be assigned to Category:Feminism task force articles. Kaldari (talk) 22:39, 24 February 2009 (UTC)
Hi Kaldari! :) Thanks for the message! I'm glad to hear this. Thanks for doing this for the FTF! --Grrrlriot ( ) 02:30, 25 February 2009 (UTC)
## WikiProject Alternative Music Newsletter for February 2009
The Alternative music WikiProject Newsletter Issue 23 - February 2009 "I want to find the guy that invented compression and tear his liver out. I hate it. It makes everything sound like a beer commercial." - Steve Albini Project news In Utero reached featured article status in the past month! Well done to WesleyDodds. The discographies of Bauhaus and Sigur Rós reached featured list status during the past month. Well done to JD554 and Matthewedwards. Year Zero (album) was featured on the Main Page on February 2. We collaborated on "All Apologies", Shoegazing, The Stone Roses, and The Jesus and Mary Chain during the past month. During the month of February, Augie March, Modern Life Is Rubbish, "Give It Away" (Red Hot Chili Peppers song), and The Get Up Kids were promoted to good article status. This month's "Recommended Alternative Album" is Mudhoney - Superfuzz Bigmuff (1988). New members MikeGruz and Blackadam2 joined the alternative music fold during February. Editors User:WesleyDodds
SoxBot II (talk) 03:10, 1 March 2009 (UTC)
## Country outlines project update - 2009/03/08
Remember "Around the World"?
Well, we've been around the World, and around again (virtually speaking, on Wikipedia), on this project.
Things have been slowing down again, so it's time for a big push...
### We've gone live
This project needed a shot in the arm. Also, its draft pages have been littering Wikipedia's categories for months. The time seemed right to move all the country outline drafts to article space.
WHAT???
Well, the drafts had been sitting in Wikipedia space for a year.
WHAT???
Development has been moving at a snail's pace and we could use the help of the Wikipedia community at large (who are more likely to find these if they are in article space).
WHAT???
Yes, we've gone live. :)
This puts pressure on us to get the blatantly incomplete elements of these outlines done. The only glaring problem is the government branches sections. These need to be corrected ASAP.
I've mentioned THE GOVERNMENT BRANCHES SECTIONS many times to many people over the past year, but the problem just doesn't seem to have been taken seriously. So let me put it another way:
HELP!!! I need your help on this now. Almost all the countries have a government with an executive branch, a legislative branch, and a judicial branch. The links for these branches need to be completed for each country outline:
Here's a convenient list you can use WP:LINKY on to access and edit these quickly. Please copy the list's link to the top of your talk page so that you can access it easily.
If you spot any standardization in links, and ways we can automate parts of this process, or for groups of countries that have links in common, please let me know!
There has been growing pressure on me to write up the administrative pages for outlines - their instructions, guidelines, etc. Therefore, I'm now in the process of composing these. Fortunately, it is mostly a matter of gathering material from messages I've written to you guys over the past year. Still, this is taking up most of my time, and I will be buried in these for the foreseeable future.
### Traffic control
The next big task after the government branches sections are cleaned up is link support for the outlines.
There's quite a list of links and notices that need to be put in place around Wikipedia, providing access to them to readers, and alerting editors to the need to develop and maintain these pages. This will keep our bot people very busy (and happy).
But the most important thing right now is to get the government branches sections completed. So please, put your bots aside, roll up your shirt sleeves, and start typing.
Thank you.
The Transhumanist 03:21, 9 March 2009 (UTC)
Hi The Transhumanist! :) Thanks for letting me know this! --Grrrlriot ( ) 18:53, 12 March 2009 (UTC)
## Labor / Worker's Rights project
I recently drafted a proposal for a Worker's Rights & Labor Issues WikiProject ... I thought you might be interested, since you are working on the Anarchism project ...
Cheers! Jrtayloriv (talk) 05:19, 9 March 2009 (UTC)
Hi Jrtayloriv! :) Thanks for letting me know about this. I will check out the Proposal. --Grrrlriot ( ) 18:55, 12 March 2009 (UTC)
## A Real-live-Wikipeidan that I "know" from elsewhere.
Congrats, you're the first. :D --angrykeyboarder (a/k/a:Scott) (talk) 08:11, 12 March 2009 (UTC)
Hi Scott! :) Yes, of course, I know you! Really? I think your the only one that I know from other websites here on Wikipedia. Congrats to you too! --Grrrlriot ( ) 18:56, 12 March 2009 (UTC)
Now there is two - thanks for twittering. Michael Mgoodyear (talk) 17:38, 12 May 2009 (UTC)
Thank you for twittering too, Michael! :) I'm glad to now "know" you. --Grrrlriot ( ) 23:04, 12 May 2009 (UTC)
## Hi there
Thanks for stopping by, I didn't even know I linked to that site from here, if I didn't and you recognized it independantly then that's pretty neat. Tyciol (talk) 14:51, 14 March 2009 (UTC)
Your welcome, Tyciol! :) Yeah, you have a userbox about livejournal up on your page here on Wikipedia. I assumed it would be called "tyciol" like here on Wikipedia and I was right. That's how I found you on LJ. --Grrrlriot ( ) 01:55, 17 March 2009 (UTC)
## Articles you might like to edit, from SuggestBot
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SuggestBot picks articles in a number of ways based on other articles you've edited, including straight text similarity, following wikilinks, and matching your editing patterns against those of other Wikipedians. It tries to recommend only articles that other Wikipedians have marked as needing work. Your contributions make Wikipedia better -- thanks for helping.
If you have feedback on how to make SuggestBot better, please tell me on SuggestBot's talk page. Thanks from ForteTuba, SuggestBot's caretaker.
P.S. You received these suggestions because your name was listed on the SuggestBot request page. If this was in error, sorry about the confusion. -- SuggestBot (talk) 04:42, 1 April 2009 (UTC)
## WikiProject Alternative Music Newsletter for March 2009
The Alternative music WikiProject Newsletter Issue 24 - March 2009 "I got a lot of shit for the Rolling Stone review of Reckoning because the guy really likes my guitar style and he wrote, 'on this record, Pete Buck does everything.' We'd stop for gas and it would be, 'Pete Buck does everything. Why don't you go pump the gas, Pete?'" - Peter Buck Project news Yeah Yeah Yeahs discography reached featured list status during the past month. Well done to Drewcifer3000. We collaborated on Liam Gallagher, Riot Act (album), Automatic for the People, Jane's Addiction, and "Give It Away" (Red Hot Chili Peppers song) during the past month. During the month of March, "Lovers in Japan", "Hello Sunshine", Evergreen, Reckoning (R.E.M. album), Love Kraft, "Golden Retriever" (song), and Delorentos were promoted to good article status. This month's "Recommended Alternative Album" is Hüsker Dü - New Day Rising (1985). New members LizParker and Cavie78 joined the alternative music fold during March. Editors User:WesleyDodds
SoxBot II (talk) 02:11, 6 April 2009 (UTC)
## WikiProject Alternative Music Newsletter for April 2009
The Alternative music WikiProject Newsletter Issue 25 - April 2009 "The other day I had these Jehovah's Witnesses come round to my house, and they tried to convince me that the Pope was the Devil's representative on Earth. So I told them that Jesus was the world's first communist. So they left. They were genuinely enraged.'" - Ian Brown Project news We collaborated on The Stone Roses (album), "Don't Speak", Indie rock, and Eddie Vedder during the past month. During the month of April, Slow Life, "Lost!", and Phantom Phorce were promoted to good article status. This month's "Recommended Alternative Album" is Stereolab - Chemical Chords (2008). Editors User:WesleyDodds
SoxBot (talk) 10:54, 5 May 2009 (UTC)
## Contest proposal
A proposal has been posted for a contest between all 200 country WikiProjects. We need to know how this contest should be run, and what problems to look out for. And we're looking for judges, coordinators, ideas, and feedback.
(And we have some really cool awards for the contest).
The Transhumanist 18:22, 20 May 2009 (UTC)
## WikiProject Alternative Music Newsletter for May 2009
The Alternative music WikiProject Newsletter Issue 26 - May 2009 "Well, I remember hearing girls behind me in English class talking about turning 18 and being old enough to strip. It wasn't that weird at the time.'" - Brandon Flowers Project news John Frusciante and U2 were featured on the Main Page on May 2 and 26. We collaborated on The Bends, Interpol (band), "How Soon Is Now?", "Hand in Glove", and "I Wanna Be Adored" during the past month. During the month of May, Fantasy Black Channel was promoted to good article status. This month's "Recommended Alternative Album" is Camera Obscura - Let's Get Out of This Country (2006). Editors User:WesleyDodds
SoxBot (talk) 10:54, 4 June 2009 (UTC)
## Howdy
Long time no talk - how's your Wikipedia experience been? Any questions for your wizened old adopter? Sarcasticidealist (talk) 21:04, 22 June 2009 (UTC)
Hi Sarcasticidealist! :) Yes, it has been a long time since we've gotten in touch. I'm not on here as much as I was, but I still manage to login and check my talk page from time to time. I think I'm learning more from Wikipedia everytime I login. ;) Is there anything new you would like to teach me about Wikipedia? --Grrrlriot ( ) 01:49, 26 June 2009 (UTC)
## WikiProject LGBT studies Newsletter (June 2009)
• Newsletter delivery by xenobot 17:26, 24 June 2009 (UTC)
## Thanks for signing my guestbook
Thanks, LAAFan for the smile! :) --Grrrlriot ( ) 00:38, 9 July 2009 (UTC)
## Feminism
Hello, Grrrlriot,
I´d like to have yr help if you please on these two artciles where I´ve just mentioned J. Campbell: Feminism and Adam and Eve.
I´d like to have yr help because these editions are based on two Campbell´s books and there is already a citation on http://en.wikipedia.org/wiki/Goddess#Feminism_and_Neopaganism.
The editor insists this is orginial research. I totally disagree; even Adam´s etimology emphasizes Campbell´s explanation. i do look forward to hearing from you. Best, Jackie. Jackiestud (talk) 12:29, 12 June 2009 (UTC)
Hi Jackiestud! :) Thanks for the message! I think you should create a new article called Feminism and religion since you seem to be talking about Adam, Eve, and religious references. I think if you started a new article about this, you shouldn't have many problems. You shouldn't be blocked and nobody can complain that you keep re-adding your information to the other articles. Let those articles be and start the new article. I hope this helps! --Grrrlriot ( ) 20:40, 15 June 2009 (UTC)
Oh, sorry I hadn´t noticed your reply. Yeah, would be great to start this a new article with this title. Well Iam gonna write something and we will see what´s gonna come out! :) Thank you so much for the kind reply. I hope to see you soon!! You have a lovely user page and yr discussion icons are just as lovely!! Jackiestud (talk) 21:00, 15 June 2009 (UTC)
It's ok. Just be sure to follow Wikipedia policies when you create the new article. Be sure to also rovide references, like websites, books, etc. to support what your writing. You could create a sandbox on your userpage for the new article. Your welcome for the reply! Thanks, another Wikipedian done the layout and icons of my userpage. --Grrrlriot ( ) 21:42, 16 June 2009 (UTC)
Hi there you!! Nice hearing from you again. Yeah, my english is nott that perfect but I hope it will be sufficient. Ok, sure check yr page always when i log in. They blocked for 24h so I just logged in now. See you soon and yks again for yr orientation!! Bes rgds. ~~ —Preceding unsigned comment added by Jackiestud (talkcontribs) 00:38, 17 June 2009 (UTC)
Hey! I think your english is pretty good. Your welcome! Just stop editing the other pages, since your breaking policies and some Wikipedians are annoyed with your edits. Be sure to create a new article. If you want to know more about Wikipedia's policies, let me know and I'll post them on your talk page. --Grrrlriot ( ) 03:53, 17 June 2009 (UTC)
Tks indeed, I do my best. Have you seen the reversion at Neolithic? The editor says there ´s no "attribution". Indeed I copied paste form Çatalhuyuk article. How can I have this attribution 9something I don´t what means)...Tks again! Jackiestud (talk) 10:05, 17 June 2009 (UTC)
http://en.wikipedia.org/w/index.php?title=Neolithic&action=historyJackiestud (talk) 10:07, 17 June 2009 (UTC)
The venus figurines are an oustanding and major work of relgion and art of Neolithic and it sounbds very strange taht the article doens´nt even mention it.Jackiestud (talk) 10:09, 17 June 2009 (UTC)
You should NEVER copy and paste anything to an article, not even a new article. If you do, you should re-word the sentences in your own words. That is odd that the article doesn't mention it. Go here for a list of rules and policies to obey on Wikipedia: http://en.wikipedia.org/wiki/Help:Contents Hope this helps! --Grrrlriot ( ) 20:41, 17 June 2009 (UTC)
Ok, understood. I will rewrite it in my own words. Tks. Jackiestud (talk) 10:20, 18 June 2009 (UTC)
The editor also deleted this text of mine: #http://en.wikipedia.org/wiki/Adam_and_Eve#Eve_as_a_metaphor. Do you think we can make it available with some improvoment? The Adam and Eve article has a "feminist view" subtitle, but it´s made of one line (!). Jackiestud (talk) 10:27, 18 June 2009 (UTC)
Hi both -- please, the Venus figurines are Paleolithic, long before the Neolithic. That's the academically accepted view of the proper use of the term 'Venus figurine'. That's why the article doesn't mention it, please don't try to put it back. My Penguin Archaeology Guide, edited by a well known archaeologist, also points out that the term is misleading and that they are not a homogenous set of objects. Dougweller (talk) 10:46, 18 June 2009 (UTC)
I don´t have access to yr Penguin Guide; Try Çatalhuyk and you will see quite the opposite. As for Conceptions of god it´s also shocking that no word is said on the Goddess (the Paleolithic God): http://en.wikipedia.org/wiki/Conceptions_of_God. The shift from the Mother Goddess to God only happened in history with the hebrew people and their male deity (what we now call God). But still this is questioned here: http://www.greaterthings.com/Word-Number/father.htm where you can see that hebrews inherited from the egyptians the term AB, which, for the egyptians, means the heart of the goddess Maat (maat means TRUTH); and for the hebrews AB means, as this article shows, father and mother --thus, the hebrw conception of god is both of a female and a male deity. Althoug for the egyptians this was only female (the heart of the goddess). Anyway, this article doen´s mention the Mother Goddess --pre historic period was the longets humans beings spent on earth. Still as many artciles show Potnia Theron is a female deiy for the greeks and she resembles in many, dozens, of aspects the Mother Goddess --as much as cybele, Rhea, etc....Jackiestud (talk) 18:10, 18 June 2009 (UTC)
It´s also funny that all articles referring a Goddess have links to God (on "see also" or "reference" or on the introd. of it, or somewhere on teh text), BUT articles referring God NEVER have linsk to Goddess. So, a Goddess is a companion or the "wife" or the female version of God -but the doesn´t happen. Jackiestud (talk) 18:25, 18 June 2009 (UTC)
Thanks for your thoughts on this, Dougweller! :) Good luck on the new article, Jackiestud! Don't forget to view the rules and policies of Wikipedia, by going to the link I gave you a few replies ago. Thanks! --Grrrlriot ( ) 18:33, 18 June 2009 (UTC)
Thanks Grrrlriot. Jackiestud, I just looked at the link above - greaterthings.com. It may be that on the Portuguese Wikipedia you could use such a link, but it definitely doesn't meet our criteria at WP:RS. Please, if you want to edit or write articles here, learn about the types of sources you can use in articles, particularly academic type articles such as most of those you are editing. And I've read quite a lot about Çatalhöyük and what the current research has to say, which is quite different from what Mellart claimed. Dougweller (talk) 19:10, 18 June 2009 (UTC)
Dougweller you always have the same "argument". My sources are not good, and you always informed on any and all issues I edit. AS you can see on WP-en venu sfigurines is an umbrella term. AS for the VF as neolitthic archaeology I have no comments it´s too obviuous, But I´d like to ask you to find a reliabel source that would deny the VF on the Neolicthic --the term belonbgs to Pre Histroy in general.
Ab as an etimology for teh hebrews is easy to find on MANY ebooks. Hold on, and I´ll make it available. Jackiestud (talk) 19:35, 18 June 2009 (UTC)
http://books.google.com.br/books?id=WvrYDeJnVKkC&pg=PA192&lpg=PA192&dq=the+egyptian+ib+the+hebrew+ab&source=bl&ots=x3DP4EIURy&sig=R3DB3X99d1NaSmMVDjDoWESh7Ok&hl=pt-BR&ei=fdUzSrr9FInItgeyo4n5Dg&sa=X&oi=book_result&ct=result&resnum=2#PPA192,M1Jackiestud (talk) 19:40, 18 June 2009 (UTC)
Tickle me pink and call me flabbergasted. I rest my case. But it isn't fair to subject Grrrlriot to this. If you want to continue, take it to your talk page. Dougweller (talk) 21:07, 18 June 2009 (UTC)
Thanks again, Dougweller for your comments! :) Jackiestud, WP:RS for more information on what considers to be reliable sources on Wikipedia. Good luck if you make a new article! --Grrrlriot ( ) 21:01, 22 June 2009 (UTC)
### Yr opinion on Thealogy
Hello Grrrlriot!
I´d like to have yr opinion on Thealogy. Do you think the article needs that many tags on the top of it? Isn´t that strange that theology doesnt even mention thealogy and theology had 'see the opposite term: theology' right there in the beginning of it? Jackiestud (talk) 12:00, 23 June 2009 (UTC)
Hi again, Jackiestud! :) The Thealogy article is a neologism. Neologisms aren't allowed on Wikipedia. Please see: WP:NEO. I saw at the top of the article that is should be merged with the article Goddess movement. I'm not sure if it would serve its purpose being merged, but I do think it is a neologism. --Grrrlriot ( ) 01:49, 26 June 2009 (UTC)
### Ochre
Hello Grrrlriot!
Do you mind offerring yr opinion on Ochre (color)? My contribution consisted of mentioning Adam´s etymology (according to Adam´s article on WP) which is blood or red earth (thus ochre); this has an inner and a clear relation to the cult of ochre in Pre History art and religion, which is related to female blood. I tried very hard to keep this online and even citing the link previosuly posted there; and then again withh many Google ebooks...Ultimately, do you think this obvious etimology, the pre historic cult o fblood and the cult of mother goddess could be there altogether? Jackiestud (talk) 04:47, 27 June 2009 (UTC)
Since I am one of the editors who has removed this, I'll say again what I told Jackiestud - her etymology is not the one our article gives, which is " Etymologically it is the masculine form of the word adamah meaning ground or earth and related to the words adom (red), admoni (ruddy) and dam (blood)". That does not say that Adam means "blood or red earth", it says those words are related. The use of ochre in prehistory is not necessarily a cult, nor do we have evidence of a "cult of blood" - in fact I couldn't find this in Google, just a late medieval "cult of blood". Of course we should give coverage somewhere to the use of ochre in prehistoric times (and of other pigments as well, but ochre was particularly important), but that's a different issue. Dougweller (talk) 16:09, 27 June 2009 (UTC)
I think Dougweller might be right about this, Jackiestud. If you don't have any reliable sources, meaning books or websites that confirm what your saying about Ochre, then there is no proof of this. Wikipedia wants reliable sources --Grrrlriot ( ) 20:29, 29 June 2009 (UTC).
### Dolmen deity
hi there again Grrrlriot, Iam back here to yr page to ask for yr opinion on Dolmen deity; it consists of a description of all female deities that are "built;carved" on dolmens. Can we merge with Domlen? How can this be done? I tried to link Mother goddess on dolmen artcile but the same editor deleted, althoguh we can see on many doznes links on the Net that Dolmens are "the place to be" for the Mother Goddess. Thanks again!! Jackiestud (talk) 17:45, 28 June 2009 (UTC)
Hi again Jackiestud! You should ask this by posting this on the Dolmen deity talk page, before you decide to merge the 2 articles. You will get opinions on whether you should merge the articles together or not. --Grrrlriot ( ) 20:25, 29 June 2009 (UTC)
We are discussing a merger there. Two problems - the term is very rarely used - hardly any academic sources can be found using them, basically two very old books and a couple of 'encyclopedias' which mainly copy each other. And although I thought at first a merge with Dolmen would be good, in fact the term is misleading as it applies, according to the definitions, to carvings found in a variety of settings, eg menhirs, passage graves, etc. Any link with a (not the, there is no 'the' I believe - Grrrlriot, do you agree with her use of 'the mother goddess'?) mother goddess is tenuous at best and I can't find any academic sources. The link Jackiestud did find didn't actually mention dolmen deities. There has been a discussion on the talk page for a day or so. Whatever we do needs to make it clear it is a rarely used term in archaeology. As usual, most of the links on the net seem to be based on our article. Dougweller (talk) 21:30, 29 June 2009 (UTC)
Dougweller, No, I don't agree with her term of 'the mother goddess'. In mythology, there are goddesses that are of fertility and motherhood.--Grrrlriot ( ) 02:32, 30 June 2009 (UTC)
No academic term? What abt the book I linked there? there you go again anad again saying the same thing. We don´t need to find, and it´s really almost impossible the same term, the very same...What´s at stake is that dozens of links and books can be found on ths subject: dolmens and mother goddess...We don´t need to use this specific term that someone, who could it be (some editor, or IP!!??)invented out of nothing ...Jackiestud (talk) 22:09, 29 June 2009 (UTC)
Gary R. Varner is the author of various non-academic books, some self-published through lulu.com. He's also pagan correspondent for the New Age Journal. He's not an archaeologist or an anthropologist, and his book doesn't use the term 'dolmen deity'. Dougweller (talk) 05:33, 30 June 2009 (UTC)
## Wiki-meetup Nashville on Labor Day weekend!
Wiki-meetup Nashville will be September 5–6 (Labor Day weekend) 2009. No conference rooms or libraries. Food, beer and conversation, maybe even a show. So come either day or both! --EdwardsBot (talk) 00:13, 2 July 2009 (UTC)
## WikiProject Alternative Music Newsletter for June 2009
The Alternative music WikiProject Newsletter Issue 27 - June 2009 "The only confusion was, I think we all thought they were women. Kim was obviously a woman, but they all had this shaved-headed, pretty, soft look. And there were lots of lesbian bands at the time, and we always got booked with them, so we just thought the Pixies were another, like maybe they were like angry divorcees or somthing that formed a band.'" - Kristin Hersh Project news Fantasy Black Channel reached featured article status in the past month! Well done to Rafablu88. List of awards and nominations received by Snow Patrol reached featured list status during the past month. Well done to Suede67. Phantom Power reached good topic status during the past month. Well done to Cavie78. In Utero was featured on the Main Page on June 20. We collaborated on (What's the Story) Morning Glory?, Silent Alarm, Pornography (album), and Bossanova during the past month. During the month of June, Phantom Power (Super Furry Animals album) was promoted to good article status. This month's "Recommended Alternative Album" is They Might Be Giants - They Might Be Giants (1986). Editors User:WesleyDodds
SoxBot (talk) 22:49, 4 July 2009 (UTC)
## Simone
Hello Grrrlriot, Can I please have yr opinion on Simone Bittencourt de Oliveira? Yesterday I spent more than an hour finding many new sources, as you can see from it went from 14 footnotes to 20 new more!! Many of them come from MusicaBrasileira.org, a widely source for researches on Brazilian music (most of the content presents text form Brasil´s largest and most trusted news weekly magazine Revista Veja). And I don´t even know if this user can read in portuguese. As for Simone´s spirituality it´s also widely known --it as much as Madonna´s Cabala. Do you think you can help me? Jackiestud (talk) 10:03, 5 July 2009 (UTC)
Hi Jackiestud! It looks like the article has a few tags on it, which are posted in a template at the top of the article. If Simone has her own website, it would be good to use it as a source too. The news weekly magazine sounds like a reliable source. --Grrrlriot ( ) 00:43, 9 July 2009 (UTC)
Yes, absolutely it is!! Tks a lot. So, how can you help me to leave the content online and not have it reverted? This editor Verbal keeps deleting crucial parts fo her biography which are referred with ver reliable sources. Jackiestud (talk) 17:38, 9 July 2009 (UTC)
Oh, by the way, Grrlriot, is there any admin wo whom you could address me to help me keep this bio online? Jackiestud (talk) 18:02, 9 July 2009 (UTC)
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# Quark Matter 2019 - the XXVIIIth International Conference on Ultra-relativistic Nucleus-Nucleus Collisions
3-9 November 2019
Wanda Reign Wuhan Hotel
Asia/Shanghai timezone
## Comparison of Chemical freeze-out parameters in p+p, p+Pb, Xe+Xe and Pb+Pb collisions at LHC energies
4 Nov 2019, 17:40
20m
Wanda Han Show Theatre & Wanda Reign Wuhan Hotel
#### Wanda Han Show Theatre & Wanda Reign Wuhan Hotel
Poster Presentation Small systems
### Speaker
Arvind Khuntia (Indian Institute of Technology Indore (IN))
### Description
In this work, we have presented the collision energy, multiplicity and system size dependence of chemical freeze-out parameters such as chemical freeze-out temperature ($T_{\rm ch}$) and strangeness saturation factor ($\gamma_{s}$). These parameters are obtained by analysing the particle ratios at different Large Hadron Collider (LHC) energies using statistical thermal model (THERMUS). Here, we consider the particle ratios obtained recently in pp collisions at $\sqrt{s}$ = 13 TeV, p+Pb at $\sqrt{s_{\rm NN}}$ = 5.02 TeV, Xe+Xe at $\sqrt{s_{\rm NN}}$ = 5.44 TeV and Pb+Pb at $\sqrt{s_{\rm NN}}$ =5.02 TeV. In addition, we look into the energy dependence of chemical freeze-out parameters by comparing with pp collisions at $\sqrt{s}$ = 7 TeV and Pb+Pb at $\sqrt{s_{\rm NN}}$ =2.76 TeV results in our study. The particle production from small to large systems has been addressed by considering two ensembles namely, canonical and grand canonical. The results obtained in this study shows a clear multiplicity dependence of $T_{\rm ch}$ and $\gamma_{s}$. The values obtained in high multiplicity pp collisions are similar to the peripheral Pb+Pb collisions. In future, high multiplicity triggered pp events will add more insight about the strangeness chemical equilibrium and to understand the particle production mechanism in smaller collision systems.
### Primary authors
Rutuparna Rath (Indian Institute of Technology Indore (IN)) Arvind Khuntia (Indian Institute of Technology Indore (IN)) Raghunath Sahoo (Indian Institute of Technology Indore (IN))
### Presentation Materials
There are no materials yet.
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# NAG CL InterfaceX02 (Machine)Machine Constants
## 1Scope of the Chapter
This chapter is concerned with parameters which characterise certain aspects of the computing environment in which the NAG Library is implemented. They relate primarily to floating-point arithmetic, but also to integer arithmetic, the elementary functions and exception handling. The values of the parameters vary from one implementation of the Library to another, but within the context of a single implementation they are constants.
The parameters are intended for use primarily by other functions in the Library, but users of the Library may sometimes need to refer to them directly.
These parameters are implemented as functions which are made available via macros, using upper case names, defined in the header file <nagx02.h>. For example, the macro X02AJC is defined as a call to function x02ajc().
## 2Background to the Problems
### 2.1Floating-point Arithmetic
#### 2.1.1A model of floating-point arithmetic
In order to characterise the important properties of floating-point arithmetic by means of a small number of parameters, NAG uses a simplified model of floating-point arithmetic. The parameters of the model can be chosen to provide a sufficiently close description of the behaviour of actual implementations of floating-point arithmetic, but not, in general, an exact description; actual implementations vary too much in the details of how numbers are represented or arithmetic operations are performed.
The model is based on that developed by Brown (1981), but differs in some respects. The essential features are summarised here.
The model is characterised by four integer parameters. The four integer parameters are:
$b$: the base $p$: the precision (i.e., the number of significant base-$b$ digits) ${e}_{\mathrm{min}}$: the minimum exponent ${e}_{\mathrm{max}}$: the maximum exponent
These parameters define a set of numerical values of the form:
$f×be$
where the exponent $e$ must lie in the range [${e}_{\mathrm{min}},{e}_{\mathrm{max}}$], and the fraction $f$ (also called the mantissa or significand) lies in the range $\left[1/b,1\right)$, and may be written
$f=0. f1f2⋯fp$
Thus $f$ is a $p$-digit fraction to the base $b$; the ${f}_{i}$ are the base-$b$ digits of the fraction: they are integers in the range $0$ to $b-1$, and the leading digit ${f}_{1}$ must not be zero.
The set of values so defined (together with zero) are called model numbers. For example, if $b=10$, $p=5$, ${e}_{\mathrm{min}}=-99$ and ${e}_{\mathrm{max}}=+99$, then a typical model number is $0.12345×{10}^{67}$.
The model numbers must obey certain rules for the computed results of the following basic arithmetic operations: addition, subtraction, multiplication, negation, absolute value, and comparisons: the computed result must be the nearest model number to the exact result (assuming that overflow or underflow does not occur); if the exact result is midway between two model numbers, then it may be rounded either way.
For division and square root, this latter rule is relaxed: the computed result may also be one of the next adjacent model numbers on either side of the permitted values just stated.
On many machines, the full set of representable floating-point numbers conforms to the rules of the model with appropriate values of $b$, $p$, ${e}_{\mathrm{min}}$ and ${e}_{\mathrm{max}}$. For machines supporting IEEE binary double precision arithmetic:
$b = 2 p = 53 emin = -1021 emax = 1024.$
(Note: the model used here differs from that described in Brown (1981) in the following respect: square-root is treated, like division, as a weakly supported operator.)
#### 2.1.2Derived parameters of floating-point arithmetic
Most numerical algorithms require access, not to the basic parameters of the model, but to certain derived values, of which the most important are:
the machine precision $\epsilon$: $\text{}=\left(\frac{1}{2}\right)×{b}^{1-p}$ the smallest positive model number: $\text{}={b}^{{e}_{\mathrm{min}}-1}$ the largest positive model number: $\text{}=\left(1-{b}^{-p}\right)×{b}^{{e}_{\mathrm{max}}}$
It is important to note that the machine precision defined here differs from that defined by ISO Fortran 95 (1997).
Two additional derived values are used in the NAG Library. Their definitions depend not only on the properties of the basic arithmetic operations just considered, but also on properties of some of the elementary functions. We define the safe range parameter to be the smallest positive model number $z$ such that for any $x$ in the range $\left[z,1/z\right]$ the following can be computed without undue loss of accuracy, overflow, underflow or other error:
• $-x$
• $1/x$
• $-1/x$
• $\sqrt{x}$
• $\mathrm{log}\left(x\right)$
• $\mathrm{exp}\left(\mathrm{log}\left(x\right)\right)$
• ${y}^{\left(\mathrm{log}\left(x\right)/\mathrm{log}\left(y\right)\right)}$ for any $y$
In a similar fashion we define the safe range parameter for complex arithmetic as the smallest positive model number $z$ such that for any $x$ in the range [$z,1/z$] the following can be computed without any undue loss of accuracy, overflow, underflow or other error:
• $-w$
• $1/w$
• $-1/w$
• $\sqrt{w}$
• $\mathrm{log}\left(w\right)$
• $\mathrm{exp}\left(\mathrm{log}\left(w\right)\right)$
• ${y}^{\left(\mathrm{log}\left(w\right)/\mathrm{log}\left(y\right)\right)}$ for any $y$
• $\left|w\right|$
where $w$ is any of $x$, $ix$, $x+ix$, $1/x$, $i/x$, $1/x+i/x$, and $i$ is the square root of $-1$.
### 2.2Other Aspects of the Computing Environment
No attempt has been made to characterise comprehensively any other aspects of the computing environment. The other functions in this chapter provide specific information that is occasionally required by functions in the Library.
## 3Recommendations on Choice and Use of Available Functions
Derived parameters of model of floating-point arithmetic,
largest positive model number x02alc
machine precision x02ajc
safe range x02amc
safe range of complex floating-point arithmetic x02anc
smallest positive model number x02akc
Largest permissible argument for SIN and COS x02ahc
Largest representable integer x02bbc
Maximum number of decimal digits that can be represented x02bec
Parameters of model of floating-point arithmetic,
$b$ x02bhc
${e}_{\mathrm{max}}$ x02blc
${e}_{\mathrm{min}}$ x02bkc
$p$ x02bjc
## 4 Withdrawn or Deprecated Functions
The following lists all those functions that have been withdrawn since Mark 23 of the Library or are in the Library, but deprecated.
Function Status Replacement Function(s)
x02dac Withdrawn at Mark 24 No longer required.
x02djc Withdrawn at Mark 24 No longer required.
## 5References
Brown W S (1981) A simple but realistic model of floating-point computation ACM Trans. Math. Software 7 445–480
ISO Fortran 95 (1997) ISO Fortran 95 programming language (ISO/IEC 1539–1:1997)
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# Horspool Algorithm
Let's checkout Horspool's algorithm for pattern matching in strings. Say we have a pattern P of length m and also say that we know the alphabet.
When you are asked to compare two strings, you probably just use operator== and if that is forbidden, often we just tend to use a sliding window to compare both character sequences.
The 'easy' way uses a shift of 1, meaning that we move our pattern character by character to the right, comparing both sequences again and again. Horspool's algorithm naturally extends this idea by pre-computing an amount of shifts we may do.
Consider the pattern 777777774. If we compare it with our text and have a mismatch, we can certainly shift our pattern more than one place (ignoring edge cases), since our pattern consists of an overly large amount of sevens. The computation of the maximum shift we can make by character is rather easy:
std::map<char, std::size_t> shifts(const std::string& sigma,
const std::string& pattern)
{
std::map<char, std::size_t> tmp;
for(auto c : sigma)
tmp[c] = pattern.size();
for(std::size_t i = 0; i < pattern.size() - 1; ++i)
tmp[pattern[i]] = pattern.size() - i - 1;
return tmp;
}
The matching can then be done from left-to-right through the text, but right-to-left through the pattern.
##### Matthis Kruse
###### Masters Student
My research interests include programming languages and compilers.
Previous
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# 12 Using R
This book is designed to be used with R. It is free, available on almost every operating system, and there are thousands of add-on packages to do almost anything you could ever want to do. We recommend you use R with RStudio.
## Installing R and RStudio
3. Run RStudio. On the "Packages" tab, click on "Install packages" and install the package "fpp" (make sure "install dependencies" is checked).
That's it! You should now be ready to go.
## R examples in this book
We provide R code for most examples in boxes like this:
R code
library(fpp)
plot(a10)
These examples assume that you have the fpp package loaded. So you should use the command library(fpp) before you try any examples provided here. Sometimes we also assume that the R code that appears earlier in the same section of the book has also been run; so it is best to work through the R code in the order provided within each section.
## Getting started with R
This is a quick tutorial for those who have not previously used R. Download the file robjhyndman.com/data/tute1.csv and review its contents in Excel. You should find four columns of information. Columns B through D each contain a quarterly data series, labelled Sales, AdBudget and GDP. Sales contains the quarterly sales for a small company over the period 1981-2005. AdBudget is the advertising budget and GDP is the gross domestic product. All series have been adjusted for inflation. Close the tute1.csv file and run RStudio.
1. Load the fpp package using the Packages tab. (This needs to be done at the start of every R session.) This can also be done by typing library(fpp) in the Console panel.
2. Using the Workspace menu, choose "Import Dataset" and import the data from the tute1.csv file.
3. The data is now saved as an object in your workspace. Clicking the name of the object will cause it to be viewed. Typing the name of the object in the Console tab will cause it to be printed to the console.
4. See what the following commands do (in the console tab).
R code
tail(tute1)
tute1[,2]
tute1[,"Sales"]
tute1[5,]
tute1[1:10,3:4]
tute1[1:20,]
5. Convert the data to time series
R code
tute1 <- ts(tute1[,-1], start=1981, frequency=4)
Notice that <- means to assign the value on the right to the object on the left.
6. The [,-1] removes the first column which contains the quarters as we don’t need them now.
7. Construct time series plots of each of the three series
R code
plot(tute1)
8. Try the following plots and figure out what is being plotted in each case:
R code
seasonplot(tute1[,"Sales"])
seasonplot(tute1[,"GDP"])
monthplot(tute1[,"Sales"])
monthplot(tute1[,"GDP"])
The notation data[,"x"] means the column named x in the data set named data.
9. What features do you notice about each of the series AdBudget, Sales and GDP?
10. Construct scatterplots of (AdBudget,Sales) and (GDP,Sales), with Sales on the vertical axes.
R code
plot(Sales ~ GDP, data=tute1)
11. Do a scatterplot matrix of the three variables.
R code
pairs(as.data.frame(tute1))
What is plotted in each panel?
12. What happens if you use pairs(tute1). Why?
13. Use the summary command to get summary information about the data:
R code
summary(tute1)
14. Produce some more plots of the data:
R code
hist(tute1[,"Sales"])
boxplot(tute1[,"Sales"])
boxplot(as.data.frame(tute1))
15. Also do a correlation test.
R code
16. Now try using RStudio as a calculator. Figure out what each of the following is doing.
R code
(100+2)/3
5*10^2
1/0
0/0
(0i-9)^(1/2)
sqrt(2 * max(-10, 0.2, 4.5))
x <- sqrt(2 * max(-10, 0.2, 4.5)) + 100
x
log(100)
log(100, base=10)
17. Save the workfile, and exit RStudio.
## More tutorials
There are dozens of R tutorials available on the web. Some of the best of them are listed below.
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# In text listing style - how to use? Any downsides?
I'm currently considering to use a in line (in text) listing style, such as:
'Some things are quite good. (i) Thing A can do this and that, which is awesome because of this and that. (ii) Thing B can do, ... . (iv) Some people also say that this and that, therefore thing Z is great.'
I've got more important points already highlighted through bullets, therefore I don't want to use bullets again for this minor information, plus I want to logically link the single points through sentences, but still provide an easy way to pick out the key words quickly.
First question: I've seen this style in quite a few papers. Is it considered to be a "good" style, or are there any downsides to this approach? Should I not use this style? Does the reader get confused by this?
Second question: Shall the brackets and latin number be bold, only the number, or nothing?
Third question: Should I place the enumeration element right infront of the keyword, or at the beginning of the sentence containing the keyword?
• If you have the luxury of being in a LaTeX-using research community, just use \begin{enumerate} and let the journal class file decide for you. – Federico Poloni Sep 23 '13 at 8:34
• This question appears to be off-topic because it is not about academia, it's about word processing. – 410 gone Sep 23 '13 at 19:49
• Agreed. If question read "What style should be used for journals in Discipline X or theses in discipline Y..." it might be a different issue. – Ben Norris Sep 24 '13 at 1:25
• If the numbers are never used, or if the technique is overused, then this can be considered bad style. I would not use it in the example above, for instance.
• You can use whatever style you want. There is no reason that they are bold. Sometimes the leading parenthesis is dropped, sometimes both. It's best to consult the style guidelines for the relevant publishers.
• Put the enumeration element in front of the sentence or phrase under consideration. Try it out, if you put it near the keyword, then you'll have spurious sentence elements in illogical positions.
• Thanks, can you elaborate on what "spurious sentence elements in illogical positions" means? :-) – Franz Kafka Sep 18 '13 at 11:31
• If you put the (a) in front of the keyword, then you might end up with a sentence like this: "The most important things to remember are to put the enumerated element in (1) front of the key word and to highlight the enumerated element (2) in bold." – Dave Clarke Sep 18 '13 at 13:16
1. Yes it is a good/acceptable style. At least in the fields where I have looked the format is standard. in fact bullets or numbered lists should be used more sparingly and I think the following is a good guideline: use bullets/itemization when there is a lot of text going into each. 'Lot' in this case is a complete sentence or more. Use the format you mention when you need a word or partial sentence for each item.
2. there are several ways to do this you can use 'i)' or '(i)' or (1)' or '(a)' etc. The choice may differ depending on what else you have in your paper. If you have figures that contains several panes, for example, a, b, c, d, you may decide to use Roman or regular numerals for your lists. if you have several lists you should avoid repeating the same item descriptor and, for example, use Roman numerals for one and Arabic for another.
3. This depends on the context. you should place them where it is appropriate to read them. this means before each part of the construction. In your example you have divided everything into separate sentences but I think you should make a construct with semicolons instead: "There are three things of importance: (1) thing A; (2) thing B; and (3) Thing C."
• Your point 3 is a total abuse of the semicolon. – StrongBad Sep 22 '13 at 16:33
You probably want to check your sytle guide about seriation rules. The APA style manual defines rules for
• sentence seriation without a hierarchy and elements not having internal commas,
• sentence seriation with a hierarchy and elements not having internal commas,
• sentence seriation without a hierarchy and elements having internal commas,
• sentence seriation with a hierarchy and elements having internal commas,
• paragraph seriation without a hierarchy, and
• paragraph seriation with a hierarchy.
The previous sentence is a properly formatted example of sentence seriation without a hierarchy and the elements not having internal commas. If there were internal commas, then the comma at the end of each element would be replaced by a semicolon. Sentence seriation with a hierarchy follows the same rules except there is no line break between elements and the bullets are replaces with a letter within parentheses. Paragrpah seriation without a hierarchy follows the same rules as sentence seriation without a hierarchy except the element ending comma is replaced with a period and the list is "introduced" with a colon. Paragrpah seriation with a hierarchy follows the same rules as paragraph seriation without a hierarchy except the bullets are replaces with an Arabic numeral followed by a period.
Since each element of your example is a sentence, you would need to apply paragraph seriation and hence your formatting is not compliant with APA (and I believe MLA and Chicago).
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# How to I know how many nested functions have been called?
I have two functions, and the 1st calls the 2nd:
f[x_]:=Block[{},x^2]
g[y_]:=Block[{},Sin[f[y]]]
I would like to know, in each function how deep I am in the calling stack. If I execute g[1.2], the depth in g is going to be 1, and the depth in f is going to be 2. But If I were to define
h[z_]:Block[{},Cos[g[z]]]
and execute h[1.3], the depth in g is going to be 2, and the depth in f is going to be 3.
I would like to know how I can systematically find this depth.
Thank you
• Take a look at Stack. Feb 3 at 20:06
• g also calls Sin, and f also calls Power (and both call Block), so how do you want to define depth? If you are just interested in depth of f, then as @Domen suggested, you could add Stack somewhere in f, maybe f[x_] := Block[{stack = Stack[]}, Print[stack]; x^2] (but you'll still have to determine what depth means for that). You might also be interested in Trace. It also depends on what you mean by "systematically". Do you want a mechanism that injects the Stack for a specified symbol or something? Feb 3 at 20:28
Using Stack and measuring its depth, as suggested by @Domen:
depthfunc[name_, expr_] := (Echo[(Length[Stack[]] - 3)/2, name]; expr)
f[x_] := depthfunc["f", x^2]
g[y_] := depthfunc["g", Sin[f[y]]]
h[z_] := depthfunc["h", Cos[g[z]]]
h[1.3]
(* f 3 *)
(* g 2 *)
(* h 1 *)
(* 0.54626 *)
## update: cleaner depth calculation
Assuming a bit less about the structure of the call stack:
depthfunc[name_, expr_] := With[{s = Stack[]},
Echo[1 + Length[DeleteCases[s, depthfunc | With | CompoundExpression]], name];
expr]
f[x_] := depthfunc["f", x^2]
g[y_] := depthfunc["g", Sin[f[y]]]
h[z_] := depthfunc["h", Cos[g[z]]]
h[1.3]
(* f 3 *)
(* g 2 *)
(* h 1 *)
(* 0.54626 *)
f[f[f[f[1.3]]]]
(* f 4 *)
(* f 3 *)
(* f 2 *)
(* f 1 *)
(* 66.5417 *)
It's interesting to see that Nest is tail-recursive and calls f iteratively at the same level instead of doing f[f[f[f[1.3]]]] as above:
Nest[f, 1.3, 4]
(* f 2 *)
(* f 2 *)
(* f 2 *)
(* f 2 *)
(* 66.5417 *)
You may program your own stack. In every function, increase the counter, calculate the result, then decrease the counter and return the result. E.g.:
count = 0;
stack = {};
f[x_] :=
Block[{}, AppendTo[stack, "f:" <> ToString[++count]]; t = x^ 2;
count--; t]
g[y_] :=
Block[{t}, AppendTo[stack, "g:" <> ToString[++count]];
t = Sin[f[y]]; count--; t];
h[z_] :=
Block[{t}, AppendTo[stack, "h:" <> ToString[++count]];
t = Cos[g[z]]; count--; t];
If you now write:
h[x]
stack
you get:
Cos[Sin[x^2]]
{"h:1", "g:2", "f:3"}
I think the idea of depth is not well defined in this question as stated. But I'll assume that what is wanted is some sort of dependency-based depth that targets only certain symbols (which would be h, g, f in the given example). We can inspect the DownValues for a given symbol and extract the symbols it depends on. If we do this recursively, we can build a dependency graph. Once we have that, we can do the normal graph operations, including GraphDistance (which would be analogous to depth according to this definition that I'm working with).
We'll build up to the whole dependency graph in stages. First, it's easy to get primary degree dependencies. From these, we'll create "links", i.e. rules that indicate directional dependency. Once we have links, we can recursively add new links by finding the next degree of dependencies. We'll continue until nothing new is discovered. At that point, we'll have links that we can use as edges in a graph.
Someone with more experience with inspecting DownValues and carefully managing execution could probably clean this up, but here's what I've got:
Dependencies[symbolSpace : {___String}][symbol : (_Symbol | _String)] :=
Block[
{$$hold}, SetAttributes[$$hold, HoldAllComplete];
Intersection[
symbolSpace,
DeleteCases[
Cases[
MapAt[$$hold, DownValues[symbol], {All, 2}][[All, 2]], s_Symbol :> ToString[Unevaluated[s]], Infinity, Heads -> True], ToString[$$hold]]]];
Dependencies[symbolSpace : {___String}][symbols : {(_Symbol | _String) ...}] :=
DeleteDuplicates[Flatten[Dependencies[symbolSpace] /@ symbols]];
DependencyLinks[symbolSpace : {___String}][symbol : (_Symbol | _String)] :=
DependencyLinks[symbolSpace : {___String}][symbols : {(_Symbol | _String) ...}] :=
DependencyGraphStep[symbolSpace : {___String}][links : {___Rule}] :=
DependencyGraph[symbolSpace : {___String}][symbol : (_Symbol | _String)] :=
DependencyGraph[symbolSpace][{ToString[symbol]}];
DependencyGraph[symbolSpace : {___String}][symbols : {(_Symbol | _String) ...}] :=
Graph[FixedPoint[DependencyGraphStep[symbolSpace], DependencyLinks[symbolSpace][ToString /@ symbols], 4]]
We can try it out:
f[x_] := f[x, 1];
f[x_, y_] := x + y;
g[x_] := f[x]^2;
g[x_, y_] := f[x, y]^y;
h[x_] := Cos[g[x]];
test = DependencyGraph[{"h", "g", "f"}][{h}];
Graph[test, VertexLabels -> Automatic]
And
GraphDistance[test, SymbolName[h], SymbolName[f]]
2
Something a bit more interesting maybe:
test2 = DependencyGraph[Names["Global*"]][{h}];
Graph[test2, VertexLabels -> Automatic]
Caveat: this depends on DownValues only, so SubValues and OwnValues would need to be added if that degree of completeness were required.
thank you all. Yes what I need is:
ls = Length[Stack[]];
Print["Calling depth = ", (ls - 1)/3];`
• This seems to be more appropriate as a comment or an edit the OP and not as an answer. Please act appropriately.
– bmf
Feb 5 at 10:52
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# Can the Sobolev norm of order 1/2 detect “jumps”?
We are given a function $f: \mathbb R^d \to \mathbb R$. For simplicity we can assume that $f$ is smooth and compactly supported. Is the Sobolev norm of order $\frac{1}{2}$ strong enough to prove an inequality like this $$|f(a)-f(b)| \leq \| f \|_{H^{\frac 1 2}}$$ or a variant, where the left side depends only on the difference in function values and the right hand side on the norm.
"Jumps" is not the exact term, since $H^{\frac 1 2}$-functions can't have jump discontinuities, but is the norm able to measure, by how much the function values change?
For $H^s$ and $0 \leq s < \frac 1 2$ this is not the case. Characteristic functions of bounded sets lie in $H^s$ and when the measure of the set goes to 0, so does the $H^s$-norm. On the other hand, this is true for the $H^1$-norm, because of $f(b) - f(a) = \int_a^b f(t)dt$.
At which order does the behaviour switch?
-
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# Isocurvature perturbations
Thanks to CMB anisotropy measurements (especially from the WMAP and Planck satellites), we now know that primordial fluctuations are predominantly adiabatic. That is to say that photons, neutrinos, baryons, and dark matter had fluctuations in energy density that were more or less spatially in phase. Isocurvature fluctuations, on the other hand, are fluctuations in the relative energy densities of different species at fixed total density. They are now constrained to be 1% or less of the primordial density fluctuation, depending on precise assumptions. There are 3 well-motivated isocurvature modes (shown below contributing to fluctuations along with an adiabatic component). Generally speaking, isocurvature perturbations are produced by sub-dominant fields during the inflationary era. Detecting them would thus yield insight into physics at the inflationary energy scale, or even the production of baryon number, lepton number, or dark matter in the early universe.
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Copied to
clipboard
## G = D4×C26order 208 = 24·13
### Direct product of C26 and D4
direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: D4×C26, C23⋊C26, C524C22, C26.11C23, C4⋊(C2×C26), (C2×C4)⋊2C26, (C2×C52)⋊6C2, C22⋊(C2×C26), (C22×C26)⋊1C2, (C2×C26)⋊2C22, C2.1(C22×C26), SmallGroup(208,46)
Series: Derived Chief Lower central Upper central
Derived series C1 — C2 — D4×C26
Chief series C1 — C2 — C26 — C2×C26 — D4×C13 — D4×C26
Lower central C1 — C2 — D4×C26
Upper central C1 — C2×C26 — D4×C26
Generators and relations for D4×C26
G = < a,b,c | a26=b4=c2=1, ab=ba, ac=ca, cbc=b-1 >
Subgroups: 70 in 54 conjugacy classes, 38 normal (10 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C2×C4, D4, C23, C13, C2×D4, C26, C26, C26, C52, C2×C26, C2×C26, C2×C26, C2×C52, D4×C13, C22×C26, D4×C26
Quotients: C1, C2, C22, D4, C23, C13, C2×D4, C26, C2×C26, D4×C13, C22×C26, D4×C26
Smallest permutation representation of D4×C26
On 104 points
Generators in S104
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26)(27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52)(53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78)(79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104)
(1 56 44 93)(2 57 45 94)(3 58 46 95)(4 59 47 96)(5 60 48 97)(6 61 49 98)(7 62 50 99)(8 63 51 100)(9 64 52 101)(10 65 27 102)(11 66 28 103)(12 67 29 104)(13 68 30 79)(14 69 31 80)(15 70 32 81)(16 71 33 82)(17 72 34 83)(18 73 35 84)(19 74 36 85)(20 75 37 86)(21 76 38 87)(22 77 39 88)(23 78 40 89)(24 53 41 90)(25 54 42 91)(26 55 43 92)
(1 69)(2 70)(3 71)(4 72)(5 73)(6 74)(7 75)(8 76)(9 77)(10 78)(11 53)(12 54)(13 55)(14 56)(15 57)(16 58)(17 59)(18 60)(19 61)(20 62)(21 63)(22 64)(23 65)(24 66)(25 67)(26 68)(27 89)(28 90)(29 91)(30 92)(31 93)(32 94)(33 95)(34 96)(35 97)(36 98)(37 99)(38 100)(39 101)(40 102)(41 103)(42 104)(43 79)(44 80)(45 81)(46 82)(47 83)(48 84)(49 85)(50 86)(51 87)(52 88)
G:=sub<Sym(104)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)(53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104), (1,56,44,93)(2,57,45,94)(3,58,46,95)(4,59,47,96)(5,60,48,97)(6,61,49,98)(7,62,50,99)(8,63,51,100)(9,64,52,101)(10,65,27,102)(11,66,28,103)(12,67,29,104)(13,68,30,79)(14,69,31,80)(15,70,32,81)(16,71,33,82)(17,72,34,83)(18,73,35,84)(19,74,36,85)(20,75,37,86)(21,76,38,87)(22,77,39,88)(23,78,40,89)(24,53,41,90)(25,54,42,91)(26,55,43,92), (1,69)(2,70)(3,71)(4,72)(5,73)(6,74)(7,75)(8,76)(9,77)(10,78)(11,53)(12,54)(13,55)(14,56)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)(26,68)(27,89)(28,90)(29,91)(30,92)(31,93)(32,94)(33,95)(34,96)(35,97)(36,98)(37,99)(38,100)(39,101)(40,102)(41,103)(42,104)(43,79)(44,80)(45,81)(46,82)(47,83)(48,84)(49,85)(50,86)(51,87)(52,88)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)(53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104), (1,56,44,93)(2,57,45,94)(3,58,46,95)(4,59,47,96)(5,60,48,97)(6,61,49,98)(7,62,50,99)(8,63,51,100)(9,64,52,101)(10,65,27,102)(11,66,28,103)(12,67,29,104)(13,68,30,79)(14,69,31,80)(15,70,32,81)(16,71,33,82)(17,72,34,83)(18,73,35,84)(19,74,36,85)(20,75,37,86)(21,76,38,87)(22,77,39,88)(23,78,40,89)(24,53,41,90)(25,54,42,91)(26,55,43,92), (1,69)(2,70)(3,71)(4,72)(5,73)(6,74)(7,75)(8,76)(9,77)(10,78)(11,53)(12,54)(13,55)(14,56)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)(26,68)(27,89)(28,90)(29,91)(30,92)(31,93)(32,94)(33,95)(34,96)(35,97)(36,98)(37,99)(38,100)(39,101)(40,102)(41,103)(42,104)(43,79)(44,80)(45,81)(46,82)(47,83)(48,84)(49,85)(50,86)(51,87)(52,88) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26),(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52),(53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78),(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104)], [(1,56,44,93),(2,57,45,94),(3,58,46,95),(4,59,47,96),(5,60,48,97),(6,61,49,98),(7,62,50,99),(8,63,51,100),(9,64,52,101),(10,65,27,102),(11,66,28,103),(12,67,29,104),(13,68,30,79),(14,69,31,80),(15,70,32,81),(16,71,33,82),(17,72,34,83),(18,73,35,84),(19,74,36,85),(20,75,37,86),(21,76,38,87),(22,77,39,88),(23,78,40,89),(24,53,41,90),(25,54,42,91),(26,55,43,92)], [(1,69),(2,70),(3,71),(4,72),(5,73),(6,74),(7,75),(8,76),(9,77),(10,78),(11,53),(12,54),(13,55),(14,56),(15,57),(16,58),(17,59),(18,60),(19,61),(20,62),(21,63),(22,64),(23,65),(24,66),(25,67),(26,68),(27,89),(28,90),(29,91),(30,92),(31,93),(32,94),(33,95),(34,96),(35,97),(36,98),(37,99),(38,100),(39,101),(40,102),(41,103),(42,104),(43,79),(44,80),(45,81),(46,82),(47,83),(48,84),(49,85),(50,86),(51,87),(52,88)]])
D4×C26 is a maximal subgroup of
D4⋊Dic13 C52.D4 C23⋊Dic13 D526C22 C23.18D26 C52.17D4 C23⋊D26 C522D4 Dic13⋊D4 C52⋊D4 D46D26
130 conjugacy classes
class 1 2A 2B 2C 2D 2E 2F 2G 4A 4B 13A ··· 13L 26A ··· 26AJ 26AK ··· 26CF 52A ··· 52X order 1 2 2 2 2 2 2 2 4 4 13 ··· 13 26 ··· 26 26 ··· 26 52 ··· 52 size 1 1 1 1 2 2 2 2 2 2 1 ··· 1 1 ··· 1 2 ··· 2 2 ··· 2
130 irreducible representations
dim 1 1 1 1 1 1 1 1 2 2 type + + + + + image C1 C2 C2 C2 C13 C26 C26 C26 D4 D4×C13 kernel D4×C26 C2×C52 D4×C13 C22×C26 C2×D4 C2×C4 D4 C23 C26 C2 # reps 1 1 4 2 12 12 48 24 2 24
Matrix representation of D4×C26 in GL3(𝔽53) generated by
6 0 0 0 9 0 0 0 9
,
52 0 0 0 0 1 0 52 0
,
52 0 0 0 0 1 0 1 0
G:=sub<GL(3,GF(53))| [6,0,0,0,9,0,0,0,9],[52,0,0,0,0,52,0,1,0],[52,0,0,0,0,1,0,1,0] >;
D4×C26 in GAP, Magma, Sage, TeX
D_4\times C_{26}
% in TeX
G:=Group("D4xC26");
// GroupNames label
G:=SmallGroup(208,46);
// by ID
G=gap.SmallGroup(208,46);
# by ID
G:=PCGroup([5,-2,-2,-2,-13,-2,1061]);
// Polycyclic
G:=Group<a,b,c|a^26=b^4=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations
×
𝔽
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## Natural Log Exponent Rule
### Exponentiation - Wikipedia.
The following identities, often called exponent rules, hold for all integer exponents, provided that the base is non-zero: + = = = Unlike addition and multiplication, exponentiation is not commutative.For example, 2 3 = 8 != 3 2 = 9.Also unlike addition and multiplication, exponentiation is not associative.For example, (2 3) 2 = 8 2 = 64, whereas 2 (3 2) = 2 9 = 512..
https://en.wikipedia.org/wiki/Exponentiation.
### Exponential and logarithmic function - QuickMath.
A logarithm is an exponent; log_a(x) is the exponent on the base a that yields the number x. ... USING THE CHANGE OF BASE RULE Use natural logarithms to find each of the following. Round to the nearest hundredth. (a) log_5(17) Use natural logarithms and the change of base theorem..
https://www.quickmath.com/math-tutorials/exponential-and-logarithmic-function.html.
### Integral of Natural Log; Logarithms Definition - Calculus How To.
The general rule for the integral of natural log is: ? ln(x)dx = x . ln(x) - x + C. ... Step 5: Move each exponent to the front of each "log": Solution: 2 log a + 3 log - 4 log c - 5 log d. Example question #2: Expand the following logarithmic expression:.
https://www.calculushowto.com/integrals/integral-natural-log-logarithms/.
### Algebra - Logarithm Functions - Lamar University.
Aug 05, 2019 . In this section we will introduce logarithm functions. We give the basic properties and graphs of logarithm functions. In addition, we discuss how to evaluate some basic logarithms including the use of the change of base formula. We will also discuss the common logarithm, log(x), and the natural logarithm, ln(x)..
https://tutorial.math.lamar.edu/Classes/Alg/LogFunctions.aspx.
### Normal distribution - Wikipedia.
About 68% of values drawn from a normal distribution are within one standard deviation ? away from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. This fact is known as the 68-95-99.7 (empirical) rule, or the 3-sigma rule.. More precisely, the probability that a normal deviate lies in the range between and ....
https://en.wikipedia.org/wiki/Normal_distribution.
### Welcome to Butler County Recorders Office.
http://recorder.butlercountyohio.org/search_records/subdivision_indexes.php.
### The 11 Natural Log Rules You Need to Know - PrepScholar.
Jan 17, 2020 . The natural log simply lets people reading the problem know that you're taking the logarithm, with a base of e, of a number. So ln(x) = log e (x). As an example, ln(5) = log e (5) = 1.609. The 4 Key Natural Log Rules. There are four main rules you need to know when working with natural logs, and you'll see each of them again and again in your ....
https://blog.prepscholar.com/natural-log-rules.
### Working with Exponents and Logarithms.
the log of multiplication is the sum of the logs : log a (m/n) = log a m - log a n: the log of division is the difference of the logs : log a (1/n) = -log a n: this just follows on from the previous "division" rule, because log a (1) = 0 : log a (m r) = r ( log a m) the log ....
https://www.mathsisfun.com/algebra/exponents-logarithms.html.
### How to Solve an Exponential Equation by Taking the Log of Both ….
Take the log of both sides. As with the previous problem, you should use either a common log or a natural log. If you use a natural log, you get ln 5 2 - x = ln 3 3 x + 2. Use the power rule to drop down both exponents. Don't forget to include your parentheses! You get (2 - x)ln 5 = (3x + 2)ln 3. Distribute the logs over the inside of the ....
### Natural logarithm - Wikipedia.
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718 281 828 459.The natural logarithm of x is generally written as ln x, log e x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), log e (x), or log(x)..
https://en.wikipedia.org/wiki/Natural_logarithm.
### List of logarithmic identities - Wikipedia.
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 -1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting . We can then get 10 ....
https://en.wikipedia.org/wiki/List_of_logarithmic_identities.
### Logarithm rules - log(x) rules - RapidTables.com.
log b (2 8) = 8 ? log b (2) The power rule can be used for fast exponent calculation using multiplication operation. The exponent of x raised to the power of y is equal to the inverse logarithm of the multiplication of y and log b (x): x y = log-1 (y ? log b (x)) Logarithm base switch. The base b logarithm of c is 1 divided by the base c ....
https://www.rapidtables.com/math/algebra/logarithm/Logarithm_Rules.html.
### Solving a Formula For a Variable Contained in an Exponent.
The power rule with either the common logarithm, $\log M$, or the natural log, $\ln M$, may be used to rewrite the exponent as a product. To evaluate a natural logarithm, use the LN button on your calculator. A special characteristics of logarithms is that [latex]\dfrac{\log M}{\log N} = \dfrac{\ln M}{\ln N} [/latex ....
https://courses.lumenlearning.com/mathforliberalartscorequisite/chapter/solving-a-formula-for-a-specific-variable/.
### French Revolution - Wikipedia.
The French Revolution (French: Revolution francaise [?ev?lysj? f??se:z]) was a period of radical political and societal change in France that began with the Estates General of 1789 and ended with the formation of the French Consulate in November 1799.Many of its ideas are considered fundamental principles of liberal democracy, while phrases like liberte, egalite, fraternite ....
https://en.wikipedia.org/wiki/French_Revolution.
### Logarithms | Algebra 2 | Math | Khan Academy.
The constant e and the natural logarithm. Learn. e and compound interest (Opens a modal) e as a limit (Opens a modal) Evaluating natural logarithm with calculator ... Use the logarithm change of base rule Get 3 of 4 questions to level up! Solving exponential equations with logarithms. Learn. Solving exponential equations using logarithms ....
### Demystifying the Natural Logarithm (ln) – BetterExplained.
Which is another useful rule of thumb. The Rule of 72 is useful for interest rates, population growth, bacteria cultures, and anything that grows exponentially. Where to from here? I hope the natural log makes more sense -- it tells you the time needed for any amount of exponential growth. I consider it "natural" because e is the universal ....
https://betterexplained.com/articles/demystifying-the-natural-logarithm-ln/.
### Deflategate - Wikipedia.
Deflategate was a National Football League (NFL) controversy involving the allegation that New England Patriots quarterback Tom Brady ordered the deliberate deflation of footballs used in the Patriots' victory against the Indianapolis Colts in the 2014 AFC Championship Game.The controversy resulted in Brady being suspended for four games, while the team was fined \$1 ....
https://en.wikipedia.org/wiki/Deflategate.
### Logarithm - Wikipedia.
In mathematics, the logarithm is the inverse function to exponentiation.That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g. since 1000 = 10 x 10 x 10 = 10 3, the "logarithm ....
https://en.wikipedia.org/wiki/Logarithm.
### Basic idea and rules for logarithms - Math Insight.
The basic idea. A logarithm is the opposite of a power.In other words, if we take a logarithm of a number, we undo an exponentiation.. Let's start with simple example..
https://mathinsight.org/logarithm_basics.
### Exponential & logarithmic functions | Algebra (all content) | Khan Academy.
This topic covers: - Radicals & rational exponents - Graphs & end behavior of exponential functions - Manipulating exponential expressions using exponent properties - Exponential growth & decay - Modeling with exponential functions - Solving exponential equations - Logarithm properties - Solving logarithmic equations - Graphing logarithmic functions - Logarithmic scale.
### List of liberal theorists - Wikipedia.
Milton Friedman (United States, 1912-2006), winner of a Nobel Prize in Economics and a self-identified Classical Liberal and libertarian, was known for the Friedman rule, Friedman's k-percent rule, and the Friedman test. Some literature: Capitalism and Freedom, 1962; A Monetary History of the United States, 1963; Free to Choose, 1980.
https://en.wikipedia.org/wiki/List_of_liberal_theorists.
Log generally refers to a logarithm to the base 10. Ln basically refers to a logarithm to the base e. This is also known as a common logarithm. This is also known as a natural logarithm. The common log can be represented as log10 (x). The natural log can be represented as loge (x). The exponent form of the common logarithm is written as $10^{x .... https://www.vedantu.com/maths/difference-between-log-and-ln. ### P (complexity) - Wikipedia. In computational complexity theory, P, also known as PTIME or DTIME(n O(1)), is a fundamental complexity class.It contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time.. Cobham's thesis holds that P is the class of computational problems that are "efficiently solvable" or "tractable".. https://en.wikipedia.org/wiki/P_(complexity). ### Value of Log 0 - Calculate Log Functions to Base 10 & e - VEDANTU. The natural log function of 0 is expressed as log e 0. It is also known as log function 0 to the base e. ... It can be denoted as log 10 (1000) = 3. 1000 is the base here and the exponent 3 is the log. log b (x) shows the logarithm for the x to the base b, ... Bodmas Rule. Vertices, Faces and Edges. Rational Numbers Between Two Rational Numbers.. https://www.vedantu.com/maths/value-of-log-0. ### Properties of Natural Logarithms - Mechamath. The properties of natural logarithms are important as they help us to simplify and solve logarithm problems that at first glance seem very complicated. ... Remember that the letter e represents a mathematical constant known as the natural exponent. ... =\log_{e}(x) If you need to convert between logarithms and natural logarithms, you can use .... https://www.mechamath.com/algebra/properties-of-natural-logarithms/. ### When log is written without a base, is the equation normally …. \log (x) refers to \log_2 (x) in computer science and information theory. \log(x) refers to \log_e(x) or the natural logrithm in mathematical analysis, physics, chemistry, statistics, economics, and some engineering fields. \log(x) refers to \log_{10}(x) in various engineering fields, logarithm tables, and handheld calculators.. https://math.stackexchange.com/questions/293783/when-log-is-written-without-a-base-is-the-equation-normally-referring-to-log-ba. ### Square Root of Exponents Rule & Examples - Study.com. Jan 11, 2022 . With the power rule, the exponents need to be multiplied together, {eq}3 \cdot 5 = 15 {/eq}, to get the simplified exponent of {eq}9^{15} {/eq}. To prove, use the expanded form. Expanded 9 to the .... https://study.com/learn/lesson/square-root-exponents-rule-examples.html. ### Properties of Logarithms (Product, Quotient and Power Rule). The logarithmic number is associated with exponent and power, such that if x n = m, ... log 2 (21/8) = log 2 21 - log 2 8. Power rule. If a and m are positive numbers, a != 1 and n is a real number, then; log a m n = n log a m. ... Natural Logarithm Properties. The natural log (ln) follows the same properties as the base logarithms do. ln(pq .... https://byjus.com/maths/properties-of-logarithms/. ### 3 Ways to Solve Exponential Equations - wikiHow. Sep 23, 2021 . A log is the inverse of an exponent.. You can find a base-10 log using most scientific calculators. ... Rewrite the log of the exponent. Rewrite it using the rule =. Rewriting the exponential expression this way will allow you to simplify and solve the equation. ... Distribute the 4 then take the natural log of both sides and isolate the x to .... https://www.wikihow.com/Solve-Exponential-Equations. ### Log Calculator - Logarithm Calculator. When the log base is provided for, you can calculate the natural log, common log and binary log values. Its just a matter of choosing. This log equation solver is a free to use tool to facilitate mathematicians, engineers, physicists and students in particular. What is logarithm? In Math, the log is the reverse function of exponentiation.. https://www.calculators.tech/log-calculator. ### Chain Rule Examples - Calculus How To. This exponent behaves the same way as an integer exponent under differentiation - it is reduced by 1 to - 1/2 and the term is multiplied by 1/2 . Therefore sqrt(x) differentiates as follows: d/dx sqrt(x) = d/dx x (1/2) = (1/2) x (- 1/2 ) To differentiate a more complicated square root function in calculus, use the chain rule.. https://www.calculushowto.com/derivatives/chain-rule-examples/. ### Achiever Papers - We help students improve their academic …. Professional academic writers. Our global writing staff includes experienced ENL & ESL academic writers in a variety of disciplines. This lets us find the .... https://achieverpapers.com/. ### Proofs of Logarithm Properties - Online Math Learning. Proof for the Product Rule. log a xy = log a x + log a y. Proof: Step 1: Let m = log a x and n = log a y. Step 2: Write in exponent form x = a m and y = a n. Step 3: Multiply x and y x o y = a m o a n = a m+n. Step 4: Take log a of both sides and evaluate log a xy = log a a m+n log a xy = (m + n) log a a log a xy = m + n log a xy = log a x + log a y. Proof for the Quotient Rule. https://www.onlinemathlearning.com/logarithms-properties.html. ### Log Table: Logarithm Table With Solved Examples & Questions. Jul 25, 2022 . Here, f(x) is the Logarithm Function to the base 'b'. The most common bases used in Log Functions are base e and base 10. Common Logarithm [f(x) = log 10 x]: The Logarithm to base 10 (that is b = 10) is called the Common Logarithm and has many applications in Science and Engineering.. Natural Logarithm [f(x) = log e x]: The Natural Logarithm has the number e (? .... https://www.embibe.com/exams/log-table/. ### Calculus I - Derivatives of Exponential and Logarithm Functions. May 26, 2020 . The most common exponential and logarithm functions in a calculus course are the natural exponential function, $${{\bf{e}}^x}$$, and the natural logarithm function, $$\ln \left( x \right)$$. ... {\log _a}x = \frac{{\ln x}}{{\ln a}}$ ... It is important to note that with the Power rule the exponent MUST be a constant and the base MUST be a ....
https://tutorial.math.lamar.edu/Classes/CalcI/DiffExpLogFcns.aspx.
### Logarithmic Properties - Andrews University.
A logarithm is an exponent. Note, the above is not a definition, ... whereas logs to the base e are often call natural logs. ... These are true for either base. In fact, the useful result of 10 3 = 1000 1024 = 2 10 can be readily seen as 10 log 10 2 3. The slide rule below is presented in a disassembled state to facilitate cutting. (Also, by ....
https://www.andrews.edu/~calkins/math/webtexts/numb17.htm.
### Classroom Resources - National Council of Teachers of Mathematics.
When students become active doers of mathematics, the greatest gains of their mathematical thinking can be realized. Both members and non-members can engage with resources to support the implementation of the Notice and Wonder strategy on this webpage..
https://www.nctm.org/classroomresources/.
### math — Mathematical functions — Python 3.10.6 documentation.
Aug 08, 2022 . Return the mantissa and exponent of x as the pair (m, e). m is a float and e is an integer such that x == m * 2**e exactly. If x is zero, returns (0.0, 0), otherwise 0.5 .
https://docs.python.org/3/library/math.html.
### Determinant - Wikipedia.
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix.It allows characterizing some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism.The determinant of a product of ....
https://en.wikipedia.org/wiki/Determinant.
### Histoire des logarithmes et des exponentielles — Wikipédia.
L'histoire de la naissance des logarithmes et des exponentielles traverse le XVII e siecle.Elle commence par la creation de tables de logarithmes permettant de faciliter les calculs astronomiques, se poursuit par les tentatives de calcul d'aire sous l'hyperbole.Elle accompagne les developpements en serie des fonctions transcendantes.Les fonctions exponentielles et ....
https://fr.wikipedia.org/wiki/Histoire_des_logarithmes_et_des_exponentielles.
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How to Build Rotation Matrix From Orientation Vectors
Here is a vector in 3-d space:
$V=\begin{bmatrix}x\\y\\z\end{bmatrix}$
We can express this vector with three linearly-independent vectors and coefficients:
$V=\begin{bmatrix}1\\0\\0\end{bmatrix}x+\begin{bmatrix}0\\1\\0\end{bmatrix}y+\begin{bmatrix}0\\0\\1\end{bmatrix}z$
We can also write this in matrix form:
$V=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\mathbb{I}\begin{bmatrix}x\\y\\z\end{bmatrix}$
The three vectors $\begin{bmatrix}1\\0\\0\end{bmatrix},\begin{bmatrix}0\\1\\0\end{bmatrix},\begin{bmatrix}0\\0\\1\end{bmatrix}$ are called as a basis in 3-d space, as they can be used to express any vector in 3-d space. Especially they are called as the standard basis, because the basis is what we normally think in.
Of course, we can have another basis to express the same V. Let’s try one:
$V=\begin{bmatrix}1/2\\0\\0\end{bmatrix}u+\begin{bmatrix}0\\1/2\\0\end{bmatrix}v+\begin{bmatrix}0\\0\\1/2\end{bmatrix}w$
Similarly, in matrix form:
$V=\begin{bmatrix}1/2&0&0\\0&1/2&0\\0&0&1/2\end{bmatrix}\begin{bmatrix}u\\v\\w\end{bmatrix}$
where $u=2x,v=2y,w=2z$.
Now, let’s say we have three vectors that represent the orientation of an object in the world. Notice that we need at least two vectors; one to represent where the object looks at, and the other to indicate the up direction. If we have two linearly independent vectors, we can easily create the third one by cross-producting the two.
Now, let’s call the three vectors as side(or right, X), forward(Z), up(Y) vectors each, and the orientation basis altogether.
Let there be an arbitrary point $P$. In standard basis, $P$ is written as:
$P=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\begin{bmatrix}P_x\\P_y\\P_z\end{bmatrix}$
In orientation basis, $P$ is written as:
$P=\begin{bmatrix}X_x&Y_x&Z_x\\X_y&Y_y&Z_y\\X_z&Y_z&Z_z\end{bmatrix}\begin{bmatrix}Q_x\\Q_y\\Q_z\end{bmatrix}$
Notice that $Q$ is P $P$, but expressed in the orientation basis.
Since they are the same P:
$P=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\begin{bmatrix}P_x\\P_y\\P_z\end{bmatrix}=\begin{bmatrix}X_x&Y_x&Z_x\\X_y&Y_y&Z_y\\X_z&Y_z&Z_z\end{bmatrix}\begin{bmatrix}Q_x\\Q_y\\Q_z\end{bmatrix}$
To find Q expressed in the standard basis, we multifly the inverse of the orientation basis matrix to each side’s left:
$\begin{bmatrix}X_x&Y_x&Z_x\\X_y&Y_y&Z_y\\X_z&Y_z&Z_z\end{bmatrix}^{-1}\begin{bmatrix}P_x\\P_y\\P_z\end{bmatrix}=\begin{bmatrix}Q_x\\Q_y\\Q_z\end{bmatrix}$
Now, $Q$ is expressed in the standard basis. To make it clear, we can write it as:
$\begin{bmatrix}X_x&Y_x&Z_x\\X_y&Y_y&Z_y\\X_z&Y_z&Z_z\end{bmatrix}^{-1}\begin{bmatrix}P_x\\P_y\\P_z\end{bmatrix}=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\begin{bmatrix}Q_x\\Q_y\\Q_z\end{bmatrix}$
We can induce from it that the inverse of orientation basis matrix transforms any point $P$ in orientation basis to be expressed in the standard basis.
Notice, because the orientation basis vectors are all orthogonal to each other, we can inverse the the matrix simply by transposing the matrix:
$\begin{bmatrix}X_x&Y_x&Z_x\\X_y&Y_y&Z_y\\X_z&Y_z&Z_z\end{bmatrix}^{-1}=\begin{bmatrix}X_x&Y_x&Z_x\\X_y&Y_y&Z_y\\X_z&Y_z&Z_z\end{bmatrix}^{T}=\begin{bmatrix}X_x&X_y&X_z\\Y_x&Y_y&Y_z\\Z_x&Z_y&Z_z\end{bmatrix}$
In conclusion, given that we know forward, up, side vectors of an object, making the rotational transform matrix to the world space is very easy and efficient, as putting them in rows in order does the trick.
Posted in Game Programming, Mathematics, Uncategorized and tagged , , , , .
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Find the value of determinant $\begin{vmatrix}1&x&y+z\\1&y&z+x\\1&z&x+y\end{vmatrix}$
$(a)\;0\qquad(b)\;x+y+z\qquad(c)\;1+x+y+z\qquad(d)\;(x-y)(y-z)(z-x)$
$\begin{vmatrix}1&x&y+z\\1&y&z+x\\1&z&x+y\end{vmatrix}$
Apply
$C_3\rightarrow C_3+C_2$
$\begin{vmatrix}1&x&y+z+x\\1&y&z+x+y\\1&z&x+y+z\end{vmatrix}$
Taking out (x+y+z) we have
Since $C_1 and \;C_3$ are identical.
$\Rightarrow \Delta=0$
Hence (a) is the correct answer.
edited Mar 20, 2014
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# Solve this
Question:
If in a $\Delta \mathrm{ABC}, \angle \mathrm{C}=90^{0}$, then prove that $\sin (\mathrm{A}-\mathrm{B})=\frac{\left(\mathrm{a}^{2}-\mathrm{b}^{2}\right)}{\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)}$
Solution:
Given: $\angle C=90^{\circ}$
Need to prove: $\sin (A-B)=\frac{\left(a^{2}-b^{2}\right)}{\left(a^{2}+b^{2}\right)}$
Here, $\angle C=90^{\circ} ; \sin C=1$
So, it is a Right-angled triangle.
And also, $a^{2}+b^{2}=c^{2}$
Now
$\frac{a^{2}+b^{2}}{a^{2}-b^{2}} \sin (A-B)=\frac{c^{2}}{a^{2}-b^{2}} \sin (A-B)$
We know that, $\frac{\mathrm{a}}{\sin \mathrm{A}}=\frac{\mathrm{b}}{\sin \mathrm{B}}=\frac{\mathrm{c}}{\sin \mathrm{C}}=2 \mathrm{R}$ where $\mathrm{R}$ is the circumradius.
Therefore,
$=\frac{4 R^{2} \sin ^{2} C}{4 R^{2} \sin ^{2} A-4 R^{2} \sin ^{2} B} \sin (A-B)=\frac{\sin (A-B)}{\sin ^{2} A-\sin ^{2} B}[A s, \sin C=1]$
$=\frac{\sin (A-B)}{(\sin A+\sin B)(\sin A-\sin B)}=\frac{\sin (A-B)}{\left[2 \sin \frac{A+B}{2} \cos \frac{A-B}{2}\right]\left[2 \cos \frac{A+B}{2} \sin \frac{A-B}{2}\right]}$
$=\frac{\sin (A-B)}{2 \sin \frac{A+B}{2} \cos \frac{A+B}{2} .2 \sin \frac{A-B}{2} \cos \frac{A-B}{2}}=\frac{\sin (A-B)}{\sin (A+B) \sin (A-B)}$
$=\frac{1}{\sin (\pi-C)}=\frac{1}{\sin C}=1$
Therefore,
$\Rightarrow \frac{a^{2}+b^{2}}{a^{2}-b^{2}} \sin (A-B)=1$
$\Rightarrow \sin (A-B)=\frac{a^{2}-b^{2}}{a^{2}+b^{2}}$ [Proved]
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## anonymous one year ago Determine whether y varies with x, if so, find the constant variation of k and write the equation.
1. Nnesha
what is the equation for direct variation ?
2. anonymous
X Y 4 6.4 7 11.2 10 16 13 20.8
3. anonymous
@Nnesha
4. anonymous
it increases by 1.8 each time..
5. Nnesha
y =kx equation for direct variation you can solve for k so divide both sides by x $\huge\rm \frac{ y }{ x }=k$ now divide y by x if you get same number then yes
6. anonymous
Thank you
7. Nnesha
$$\color{blue}{\text{Originally Posted by}}$$ @Justmeneedinghelp it increases by 1.8 each time.. $$\color{blue}{\text{End of Quote}}$$ by 1.8 or 1.something else ? :D
8. Nnesha
so k=what ?
9. anonymous
1.6
10. Nnesha
yes right :=) good job!
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# How do you factor the trinomial 6x^2 +8x+ 2?
Jun 19, 2016
You can factor $6 {x}^{2} + 8 x + 2$ as $6 \left(x + 1\right) \left(3 x + 1\right)$
#### Explanation:
To factor a trinomial, you simply have to look for its roots. There are three possible cases:
1. The trinomial has no solutions. Then, it is not possible to factor it.
2. The trinomial has only one solution ${x}_{0}$. Then, it is a square of a binomial, more precisely, it is $a {\left(x - {x}_{0}\right)}^{2}$.
3. The trinomial has two different solutions ${x}_{1}$ and ${x}_{2}$. Then, you can factor is as the product of two binomials, i.e. $a \left(x - {x}_{1}\right) \left(x - {x}_{2}\right)$.
The quantity that tells us how many solutions a trinomial has is its discriminant: if the trinomial is $a {x}^{2} + b x + c$, its discriminant is
$\Delta = {b}^{2} - 4 a c$
If $\Delta < 0$ then we are in case one, if it equals zero we are in case two, if $\Delta > 0$ we are in case three.
$\Delta = {b}^{2} - 4 a c = {8}^{2} - 4 \cdot 6 \cdot 2 = 64 - 48 = 16 > 0$
${x}_{1 , 2} = \setminus \frac{- b \setminus \pm \setminus \sqrt{\setminus \Delta}}{2 a} = \frac{- 8 \setminus \pm \setminus \sqrt{16}}{12} = \frac{- 8 \setminus \pm 4}{12}$
The two possible choices given by the $\setminus \pm$ sign give us ${x}_{1} = \frac{- 8 - 4}{12} = - \frac{12}{12} = - 1$ and ${x}_{2} = \frac{- 8 + 4}{12} = - \frac{4}{12} = - \frac{1}{3}$
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Infoscience
Conference paper
# Equivalence of synthesis and atomic formulations of sparse recovery
Recovery of sparse signals from linear, dimensionality reducing measurements broadly fall under two well-known formulations, named the synthesis and the analysis a ́ la Elad et al. Recently, Chandrasekaran et al. introduced a new algorithmic sparse recovery framework based on the convex geometry of linear inverse prob- lems, called the atomic norm formulation. In this paper, we prove that atomic norm formulation and synthesis formulation are equiva- lent for closed atomic sets. Hence, it is possible to use the synthesis formulation in order to obtain the so-called atomic decompositions of signals. In order to numerically observe this equivalence we derive exact linear matrix inequality representations, also known as the theta bodies, of the centrosymmertic polytopes formed from the columns of the simplex and their antipodes. We then illustrate that the atomic and synthesis recovery results agree on machine precision on randomly generated sparse recovery problems.
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# Each questions below consists of a word in capital letters followed by four words or group of words. Select the word or group of words that is most similar in meaning to the words in capital letters$GLEAN$
[ A ] To groom [ B ] To gatherbit by bit [ C ] To discover [ D ] To polish
Answer : Option B Explanation : 'Glean' means 'to gather ears of corn left'
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# A conjecture about the roots of real functions
1. Nov 4, 2005
### eljose
All the roots of a real function f(x) are real unless.
1.K(x) is a Polynomial of degree k
2.f(x)=exp(g(x)) where g(x) is different from ln of something
3.f(z) with z=u+iv is invariant under the transformation of v=-v with f(u+iv)=F(u-iv)..
4.the function f includes some of the functions above named
In this cases there can be complex roots,excluding this all the roots are real...
2. Nov 4, 2005
### fourier jr
1. polynomials with even degree might not have any real roots. what about x^2 + 1 ? if the degree of a polynomial is odd then it will always have a real root. if i the degree is even it might have real roots, it might not.
Last edited: Nov 4, 2005
3. Nov 4, 2005
### fourier jr
2. set g(x) = ln(sin(x)) + 1, which doesn't equal ln of something but exp(g(x)) has infinitely many real roots, at multiples of pi
edit: i guess i didn't consider domain/range with this counterexample but i don't think it's really important.
4. Nov 4, 2005
### Hurkyl
Staff Emeritus
There is no unless. The roots of a real function are always real.
The real function defined by g(x) = x^2 + 1 has no roots.
The complex function defined by h(x) = x^2 + 1, of course, has two complex roots.
5. Nov 5, 2005
### HallsofIvy
In light of Hurkyl's point, eljose, exactly what do you mean by a "real function"? Hurkyl is clearly taking it to mean "a real valued function of a single real variable" which, by definition, cannot have any non-real roots- so your statement is wrong.
I might be inclined to take it to mean "a real valued function of a single complex variable" (the "real function" simply meaning real valued) so that it is possible to have non-real roots.
However, in that case, your statement is still wrong.
Counterexample: take f(x+ iy)= y- 1.
1) f is not a polynomial.
2) f is not exp(f(z)) (in what I understand to be your sense).
3) f(x-iy)= -y-1 so it is not invariant under complex conjugate.
4) f is not a combination of the above.
But the roots of f are all numbers of the form x+ i.
6. Nov 5, 2005
### eljose
the case f(x+iy)=y-1 makes no sense..i am supposing HallsoftIvy that f is real so f(x-y) for real x and y will be real,however according to your definition:
f(x-y)=iy-1 is complex but if f,x and y are real also f(x-y) should be real.
The case exp(f(x))-1=0, i am supposign that f(x) is not ln(g(x)+1)
the counterxamples i have proposed can have or can not have real roots
this conjecture is realted to Riemann hypothesis in the sense that in both cases for $$\zeta(1/2+is)$$ if s is a root also s* is another root,and the Riemann function has no symmetry under the change of s=-s.
7. Nov 5, 2005
### HallsofIvy
Apparently you don't understand the function I used. The function I defined: f(x+iy)= y-1 means exactly what it says: if z= x+ iy then f(z)= y-1.
f(z)= the imaginary part of z, minus 1. If x and y are real then x-y has 0 imaginary part so f(x-y)= 0-1= -1, not a complex number.
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# JAM 2022 [ 41 -50]
Consider a sequence of independent Bernoulli trials, where 3/4 is the probability of success in each trial. Let X be a random variable defined as follows: If the first trial is a success, then X counts the number of failures before the next success. If the first trial is a failure, then X counts the number of success before the next failure. Then 2E(X) equals ______________________.
Since we are given a sequence of independent Bernoulli trials. Each trial is independent of the other. Hence, we can say the following about the random variable X.
Suppose, E is another random variable which takes values 1 or 0 depending upon whether the first trial is a success or failure respectively. Then the pmf of the random variable X may be given as:
f(x) = \left\{
\begin{align*}
pq^{x} ; & \text{if E=1}\\
qp^{x} ; & \text{if E=0}
\end{align*}
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1:43 AM
@DavidCarlisle Did you win?
Googled "duck cart", wasn't disappointed. :)
2:05 AM
@PauloCereda Still having a hard time thinking any of this is funny. (Sorry).
3:01 AM
We officially have a Rickroll question! And it's on topic. I promise. You know you want to click.
4 hours later…
7:02 AM
Off-topic, I think:
0
My corresponding author sent our article to nano letters but i havent recieved any confirmation emails yet. Is it normal or thats due to a probable problem during submission?
7:13 AM
I have problems with the plants on my balcony. I know it's off-topic here but think there might be others with the same issue... See the point? — Uwe Ziegenhagen 1 min ago
7:25 AM
@Johannes_B Ah, the I want this and that but actually not what I said but something different - guy ;-)
3 hours later…
10:43 AM
@AlanMunn Sorry, I had no intention of being offensive or disrespectful. :(
10:56 AM
@JosephWright: could you please remove the tweet I referred a couple of messages ago?
@PauloCereda Done
@PauloCereda As a UK national I'm happy enough with such things: gallows humour is the only way forward!
It's certainly making for an interesting Sunday following the politics
@JosephWright I am quite shocked how Brazil is ignoring the whole situation with UK and EU. I've not seen any reports on national TV, not even a single mention. I saw a couple of highlights when watching CNN, but I don't like it. Thankfully @cfr gave me some links to UK online newspapers.
@JosephWright Trying to take into account how many of them are saying “we didn't really want to leave”?
@egreg That's one of the tricky things, but the net result is clear (and this talk of staying in the EEA is simply not on)
@PauloCereda I guess for Brazil there's no immediate impact, and 'wait and see' is the best plan
@PauloCereda Odd though that it did not make the news at all
@JosephWright Possibly, but in fact there's a huge political/institutional crisis going on: the Federal Police is arresting high cast politicians involved in corruption schemes, which is basically everybody out there.
11:05 AM
@JosephWright One of those small nations the other side of the ocean
@PauloCereda Ah
@egreg Yes, sure
@JosephWright When you have some spare time, take a look at the car wash operation. :)
11:35 AM
@JosephWright Has there been much discussion about the not-so-large winning margin for the exit-side? I mean, there was about 72% turnout, and the result was 52-48. There was certainly massive support for exit, but it's not that big a difference, and leaving is a huge step. (Also referring to petition.parliament.uk/petitions/131215)
@DavidCarlisle tex.stackexchange.com/questions/316507/… yes it's not so interesting but it seems that one can do it, what do you think?
@touhami depends a bit if you want the includeonly features of preserving counts, if that isn't needed, I'd just stick \iffalse \fi around the omitted text. if you want the \include features, it's possble but using \include is simpler, so why bother?
12:05 PM
@DavidCarlisle why bother? well, could be the answer i was looking for.
12:16 PM
@DavidCarlisle bye :-)
12:32 PM
@JosephWright @DavidCarlisle I am not a very political person, sorry. I thought Brexit was about leaving the EU and now i am reading some shocking twitter and facebook things where people tell "stangers" to leave britain? what the fuck is going on there?
Properly scared right now.
12:56 PM
Wouldn't the easiest solution be that all who voted against Brexit move out and to the continent? On the other hand, all non-european continental inhabitants would move to the island to be finally non-europe. Would remove quite some tension.
@PauloCereda Well, Brazil has multiple crises of its own to deal with right now and while Brexit will presumably have some impact on Brazil at some point, it really isn't clear what or to what degree, I guess. But it does seem odd it doesn't get mentioned at all. I would have thought it would at least get a mention in business news, for example, just to explain the cause of changes in the stock markets, currencies etc.
@Johannes_B Yes. It is is shocking. It is not surprising. But it is shocking. And it is going to get worse.
1:11 PM
@cfr I had no idea the world has gone that insane.
@Johannes_B Figure out that Wales is in the quarter-finals! In football!
@egreg :-)
@TorbjørnT. Well, you have to take people's votes at face value. That's pretty basic. However, it is notable that, if this were a trade union vote for a strike, the (proposed?) rules would not consider the vote sufficient to authorise it. (I say 'proposed' because I can't remember if they've actually instituted this rule or not. But that would require 40% of the membership to vote to strike.)
@Johannes_B It is to be hoped that all they do is shout abuse, awful though that is. But I would not count on it.
@Johannes_B This seems rather unfair on Scotland.
@cfr They can come here, the continent has some nice parts.
Though I suppose the Scottish government could relocate along with the majority of their population.
@Johannes_B It is the governance issue, more. The parliament will have to go with them. Also, this wouldn't address the issue of the other island which is even more problematic.
1:25 PM
@cfr Can we ask google to develop a HUGE 3D printer to build a new island in the north sea?
With houses, infrastructure, roads, schools and everything? Could be useful.
1:38 PM
@Johannes_B We should ask @DavidCarlisle to do the buildings for best results.
1:48 PM
@cfr I was thinking of visiting an university in the UK in the future, I hope I could make it.
2:40 PM
@PauloCereda Avoid one in the Oxfordshire, you might meet somebody driving like mad on the wrong side of the road.
3:16 PM
@PauloCereda I know. And I wasn't offended. And maybe @JosephWright is right that gallows humour is the only solution now.
3:37 PM
@egreg -- but that's true (driving on the other side of the road) everywhere in those islands. (also bermuda. and japan. never mind the drivers who insist on going the wrong way on the one way street in front of my office. it always pays to look both ways.)
@AlanMunn -- maybe something good can come of it ... maybe it will make folks think twice when they go to the polls here in november to elect the next president. you, at least, have a canadian passport to fall back on.
4:12 PM
@TorbjørnT. Not really: remeber for a start this technically non-binding, and that as we use first-past-the-post our MP numbers don't follow vote share anyway
@Johannes_B A lot of the focus has been on immigration, particularly from UKIP but also increasingly from the main leave group toward the end of the campaign. Concern about jobs, house prices, etc. has been strongly linked to immigration, and that then leads to the idea that a leave vote means that EU nationals will 'go home'.
@Johannes_B At the present, there has been no suggestion from anyone campaigning to leave that anyone will have to leave: it looks likely that EU nationals already in the UK will get indefinite leave to remain
@JosephWright Good to hear that nobody forces foreigners out. That would be insane.
@Johannes_B Until a deal with the EU is actually done, the nature of the rules in the future is not certain
@JosephWright Either this or many companies will leave.
@JosephWright Ah, too much for my head.
@egreg Possibly: for skilled jobs one assumes EU nationals would get work permits anyway
4:38 PM
@Johannes_B: Look at the code ;-)
@ChristianHupfer Looks familiar :-)
@Johannes_B Unfortunately ...
@ChristianHupfer Why?
@Johannes_B: www.latextemplates.rubbish.org quirk
@ChristianHupfer You agreed to have that added.
4:46 PM
@Johannes_B Yes, unfortunately.
@ChristianHupfer It is a quite popular template. Only god knows why.
1 hour later…
5:58 PM
@AlanMunn <3
2 hours later…
7:51 PM
@DavidCarlisle: you solved a question about Portuguese, you really are an expert in languages. :)
@PauloCereda ヨーロッパの言語が今必要とされていないように私は私の日本語を練習する必要がありますが、
@DavidCarlisle wow
8:41 PM
@DavidCarlisle როგორც ენაზე ევროპა არ იყო საჭირო და ახლა მე უნდა პრაქტიკაში ჩემი ქართული
8:53 PM
What are good books for learning LaTex?
Since morning, I have been trying to create math notes, but I am stuck everywhere.
For starters. :)
@MathWanderer I think the most up-to-date book available right now is Marc van Dongen's LaTeX and Friends (Springer) amazon.com/LaTeX-Friends-X-media-publishing-Marc-Dongen/dp/….
@AlanMunn your Georgian isn't bad (for a Linguist:-)
@DavidCarlisle atchoo
@PauloCereda Só assim você não se sentir excluído.
9:05 PM
@DavidCarlisle You missed a verb somewhere in the sentence. :)
@MathWanderer But Nicola's online book that Paulo linked to is very good too (and free). Also for math, specifically George Grätzer's More Math Into LaTeX amazon.com/More-Math-Into-LaTeX-4th/dp/0387322892. And hidden gem, there's a free (older but still good) version included in the TeXShop Help menu!
@PauloCereda That's advanced Portuguese Grammar: impled verb (the verb was also implied in the English original:-)
@DavidCarlisle I think we should keep Google translating the same sentence from one language to another and see how badly mangled the end result is.
@AlanMunn: do you know how a Brazilian surfer stops the mess in a beach? :)
@PauloCereda ready to groan
9:09 PM
@AlanMunn ô, ó o auê aí, ô!
Czechs will be jealous. ^^ @yo' :)
@PauloCereda Cunning plan of the English: now that they're essentially as big as they were at Elizabeth I times, they'll start conquering an empire again and Brazil is the first step. They'll attack you from the Falkland/Malvinas.
@egreg Oh no! Should we team up with the Argentine? :)
@PauloCereda Not sure I get it...
@PauloCereda First they'll organize a football match between Brazil and Argentina in Río, so they'll have plenty of room for attack.
@AlanMunn Really? :) You need to visit me. :)
@egreg oh no!
9:13 PM
@PauloCereda If I paste that sentence in google translate, it detects Māori
@egreg Oh my! :)
@AlanMunn Thank you very much for recommendation!
I needed that LaTex book geared toward mathematics.
@egreg :)
@MathWanderer Yes, then check out the version that is in the Help menu of TeXShop. Also, you can access all of the MacTeX documentation from within TeXShop by choosing "Get Help for Package" in the Help menu. From there you can try mathmode which pulls up a really good overview by Herb Voss how how to typeset lots of math.
@MathWanderer Actually looking more carefully, only part of the Grätzer book is included in TeXShop. So I would recommend buying a copy.
@AlanMunn Thanks! I will buy the latest edition of Gratzer book from Amazon
@PauloCereda You'd better be quick else there probably won't be a UK at all.
9:22 PM
@cfr Oh. :(
@cfr: Is there any way to revert the situation?
@JosephWright @Johannes_B Although this is likely to get complicated in various ways. There are also issues in terms of the anger people have whipped up. Some on the leave side don't really want to stop free movement of people anyway, but they played the immigration card. They told desperate people that it was the fault of 'uncontrolled borders' and that this was the fault of the EU. It is the usual scapegoat move. If they don't now act against the scapegoats, people will get mad. ...
@cfr Certainly: it's all complex and works badly as 'soundbites' (as @DavidCarlisle observed when the debate at Wembley was on)
If they do, people will also get mad because they are only scapegoats, so even if we throw all immigrants out, the problems will still remain. Plus lots of the 'immigrants' are (1) not immigrants at all or (2) immigrants but not EU nationals.
@cfr Indeed, and quite worrying
@JosephWright Yes. And the fact that people are going up to people in streets and supermarkets and telling them 'we voted leave, get packing!' is not only horrible but very confused. Especially confused when the victims are e.g. South Asian or Tunisian or British or British Asian or fifth generation Polish or ... (I don't mean it is not equally bad if they are Romanian and arrived last week, but it doesn't reflect the same level of confusion.)
9:34 PM
@cfr Yes, this is really horrible.
@cfr True
@cfr @JosephWright I assume we're all seeing some of the same social media stuff, but have you seen this? indy100.independent.co.uk/article/… Wishful thinking only?
Poor immigrants in UK...
@AlanMunn Seen this, complete rubbish in my opinion
People are telling the proper immigrants to leave?
9:36 PM
@AlanMunn Boris downbeat as his strategy was to loose referendum by a narrow margin, claim moral victory and use that the go for PM role without the issue of leaving EU
@MathWanderer Isolated reports of this, yes
@JosephWright Right, but does he have now the guts to go through with leave? Surely the longer the truth sets in without Article 50 being invoked, the more regrets some of the leave side will have.
@AlanMunn I'm thinking of writing to my (rabidly) pro-Leave MP to say that I expect us to leave 'properly', even though I voted for Remain, as that's what the outcome of the referendum is
@AlanMunn I am worried that a long wait puts us into the 'how long does this mandate last' territory
@AlanMunn The problem with this is that a lot of people voted leave out of distaste for the way politics tends to work: trying to 'game' the people by avoiding leaving the EU is not exactly going to help
@JosephWright So you're against these 'petitions' then... :) metro.co.uk/2016/06/26/…
@JosephWright True, but maybe the argument of changing the EU from within would help calm them. (Although that possibility is slim to none, I suppose)
@JosephWright that's true but if it were possible I wouldn't object. I doubt it's possible though.
@AlanMunn We are not going to get the changes that would be needed: just a free trade area with no central regulations
9:43 PM
@JosephWright But of course being on the outside won't really free you from the regulations anyway.
@DavidCarlisle Now, I would object: we've had a vote, the question was perfectly clear, the result is also clear, the government should get on with it
I can't see any possibility of starting article 50 procedures before we have a functioning government (and opposition) at Westminster, and that doesn't look like it will be any time soon.
@AlanMunn Depends on your point of view :-)
@DavidCarlisle Tricky one, I agree: I can see this both ways
@PauloCereda It depends what you mean. The forces which have been unleashed are unleashed. If you mean, is it possible that the UK not leave the EU? Yes, it is possible. The vote is not binding. But whatever happens now, there is no going back. Those who voted to leave voted for change and many voted because desperate. If we don't leave, that tells people clearly that no peaceful protest will be heeded. So what is left?
@cfr Oh my!
9:53 PM
@MathWanderer Apparently, yes. Individual incidents. It isn't clear whether there is an increase in the number of instances of racism. That is, it is getting reported because what's said is invoking the vote, but it might just be that people who would otherwise shot some other racist thing are using the vote because they can.
@cfr /sob
Hi.
@JosephWright But we have a representative democracy. An MP who sincerely believes that leaving will be substantially worse for the UK than remaining ought not endorse a motion to trigger Article 50 if s/he sincerely believes that the negative effects are great enough to justify ignoring the referendum result. There must be some degree of damage which would justify opposing a motion to implement a referendum result. The question for any MP has to be where that cut-off is and whether it applies here.
I have an old text document that I am converting with Pandoc. It turns out the document contains Unicode Character 'NEXT LINE (NEL)' (U+0085).
...and the conversion fails...
Actually, I think I forgot to try to use XeLaTeX.
@wilx Yes, that should help.
@wilx I assume you're converting to LaTeX?
9:59 PM
@AlanMunn Yes.
@wilx I recently had some errors with unicode conversion with Pandoc which I solved with making sure I had the most recent version installed (of pandoc).
I tried to insert \catcode"85=5 into the Pandoc template but it did not compile with just pdfLaTeX. But it works now with XeLaTeX.
@JosephWright @DavidCarlisle @AlanMunn And any MP deciding whether to approve exit must surely consider the fact that the Leave campaign have no essentially taken back all of the promises they made during the campaign. Since Friday, we have been told that the 350 million figure was a mistake, that the money will not necessarily go to the NHS anyway, that there will not necessarily be fewer people coming into the UK, and that Article 50 need not be triggered immediately or necessarily at all.
& That's just want Leave is saying ...
@wilx For a pdflatex/inputenc solution see the second part of this answer
@cfr But isn't it the point that MPs won't get to decide anything? It's all in the PM's hands (whoever that is).
@cfr there's just no good outcome starting from where we are.
10:09 PM
@PauloCereda In case you're (trying to) follow along: MP = member of parliament; PM = Prime Minister. :)
@AlanMunn oh thanks, I am really lost.
@DavidCarlisle Yeah, that seems abundantly clear.
@AlanMunn no I think leaving the EU would require changes in UK law that would require parliamentary vote, but I may be wrong, it's hard to keep up with details...
@PauloCereda so is everyone in the UK
@DavidCarlisle Yes.
@cfr I wonder if @JosephWright can exercise mod powers and delete history.
10:12 PM
@DavidCarlisle UK: United Kingdom of Great Britain and Northern Ireland = Wales + Scotland + England + Northern Ireland
@AlanMunn @DavidCarlisle They are saying that they expect Cameron to officially trigger exit at Tuesday's summit. Apparently, it does not even need to be in writing. However, it does need to be intended and clear. If so, then I guess parliament need not approve. Nonetheless, Cameron has said he won't do it. If MPs passede a motion to the effect that the will of the house was not to trigger it, would a PM really do so?
@DavidCarlisle But isn't the vast majority of the parliament in favour of remain? So if it went to a vote there surely it would fail. That's why I think it's in the PM's hands. Something to do with the Crown Perogative.
@cfr Now there's a scenario. Direct vs. representative (such as it is) democracy in a head-to-head battle...
It seems to me quite tricky to say it is up to the PM. The PM does not have the powers of a presidential head of state. It all seems rather unclear. If the PM can trigger it with a referendum then the PM could do so without one or despite a vote for remain.
@AlanMunn not clear now, they may have been for remain before the referendum but now as seen above everyone has to re-evaluiate
Hmm, I actually lost some lines in the result if I do \catcode"85=5.
@wilx Yes, that's not surprising. The newunicodecharacter route is likely better if you don't want to use XeLaTeX.
10:19 PM
@wilx you almost certainly don't want it to be catcode 5, 10 more likley
@DavidCarlisle Perhaps.
@AlanMunn actually what you want is a tex implementation for an EBCDIC IBM mainframe that would trigger its end-of-line behaviour on character 85/NEL
@DavidCarlisle An awful lot would have to switch to get a leave. But the point is that they might still be convinced remain is best, but also convinced they should vote leave in parliament. That is perfectly consistent. The will of the people is, at the very least, a serious factor to consider.
@DavidCarlisle :)
@cfr yes that's what I meant above, MPs may vote to leave now if they think they should follow the public vote (or if they have a three line whip telling them to vote)
@wilx what does your source look like, how come it's got NEL in it anyway?
10:24 PM
@DavidCarlisle If people voted according to the results in their constituencies, what would the result be?
@cfr depressing, I'd guess.
@DavidCarlisle Probably, yes.
@DavidCarlisle It is just old text. It appears to be ISO-8859-1 encoded.
@wilx but how is NEL used, it is an odd character just in Uniocde as part of the original ASCII/EBCDIC merger denoting an d EBCDIC new line but not actually treated as a newline (in the way characters 10 and 13 are) by most software
@wilx you could make it catcode 10 so it acts like a space but you can't really make it act like end of line with the behaviour that two consecutive ones are a paragraph, it would be much more reliable just to change them all to character 10 using a replace in an editor or sed or perl or whatever you want.
@DavidCarlisle I see.
10:33 PM
@DavidCarlisle @cfr @JosephWright This is an interesting (though sobering) read. It's from March of 2015, but talks about all of the constitutional issues now facing the UK with a leave vote in place.
@wilx the problem is tex's end of line behaviour is only partially controlled by catcodes, the input stream is split into "lines" before catcode tokenisation and white space is stripped from the ends of the lines. the filesystem line markers are system dependant and not visible from the tex macro layer, so there used to be texs for record-based filesystems that had no end of line character at all, and for NEL separated streams and all sorts of things, but current systems use 10 and 13
@DavidCarlisle OK.
@wilx but anyway it's less depressing discussing end of line behaviour than UK politics, so thanks for the diversion:-)
@DavidCarlisle Haha.
@DavidCarlisle Of course unfortunately both seem to involve the end of the line...
3
10:40 PM
@AlanMunn lol
@AlanMunn I'm not encouraged by the fact that the abstract suggests the author cannot count to 4.
@cfr :) Why am I not surprised that you noticed that.
I am going with \newunicodechar{^^^^0085}{\\} for now. That seems to match the text the best.
Magic! \o/
@AlanMunn Because I can count to 4, having a degree in maths?
@cfr No, because you are, shall we say, very detail oriented. :) You value precision I think.
10:54 PM
@AlanMunn Which is a nicer-sounding way of saying I'm a pedant ;).
@AlanMunn For larger values of 4. :)
@cfr No, actually, I wouldn't agree with that. But you do value precision, which I think is actually different from being a pedant.
@cfr Luckily I caught the autocorrected 'n'. :)
@MathWanderer including the scientific team who constructed a Quantum Hilbert Hotel in Glasgow that consist mostly of immigrants :)
@cfr I guess it depends on how pedantic your definition of 'pedantic' is.
25 DEC = 31 OCT
Just to break the linguistic loophole. :)
11:06 PM
@JosephWright @DavidCarlisle @cfr Anyway, if any of you wanted to move to Europe, I could offer you reasonable housing for some time :)
@AlanMunn ?? Not pedantic enough, perhaps.
@cfr Autocorrect had changed 'pedant' to 'pendant'. But thankfully I noticed before you did. :)
@yo' Hey, what about me?
@AlanMunn A linguist using autocorrect?! o.O
11:21 PM
@PauloCereda Well it depends on the application, but it's sometimes handy but you have to pay attention. It's awful if you're writing in a mixture of languages (as I often do) however.
@AlanMunn :) I have this problem with typing in my smartphone, then I migrated to SwiftKey.
@PauloCereda Android?
@AlanMunn Yes, and iOS.
@PauloCereda What does it do? (I know I can google, but I'll let you be salesman) :)
@AlanMunn I can switch between three different languages at the same sentence, basically. :)
11:24 PM
@PauloCereda Oh, so it just does localization/keyboard switching.
@AlanMunn and it has a dictionary for each language you set in your triad. :)
There's also an autocorrect mode, but I leave it disable.
@PauloCereda I see. I may try it.
@AlanMunn I really enjoy it.
I hate trying to type Welsh on my phone. Sadly, I don't have a smart phone.
@cfr So it voted to leave?
11:27 PM
@cfr My smartphone is actually dumber than me, which is quite disturbing for a duck. :)
Hi
@BBM Hello!
@AlanMunn Interesting article though. I noticed the number of countries increased by page 3. Perhaps the abstract was written a bit too soon - before the creation of the UK?
@cfr I think the '3' in the abstract refers to Scotland, N. Ireland and Wales ("the three smaller constituent nations") in contrast to England. Or were you objecting to some other counting problem?
@AlanMunn Hmm... I was going to say that I didn't say it was stupid enough to believe Boris. However, I don't think the people who voted to leave are stupid. I'm not even sure that voting leave was not the best choice they had.
11:33 PM
Is there any pure mathematician?
@AlanMunn I took 'smaller constituent nations' to mean smaller than the combination of the nations. But maybe you are right. Probably didn't pay enough attention to the details ;).
@cfr No, I agree, and I've been very careful not to jump onto the "everyone who voted leave is a racist idiot" bandwagon that I've seen among some of my UK friends.
@BBM In general? There are such people, yes.
@cfr Syntax. It gets you every time. :)
@cfr I know there are people talking about Politics :).
11:35 PM
@cfr :D I rest my case...
@BBM On the rocks, usually. :)
@cfr I meant here chatting with us.
@BBM All of our resident mathematicians are probably trapped inside monads at the moment. :)
@BBM Oh. I'm not sure. How experienced a pure mathematician do you need?
@BBM Presently no. We have a computer scientist, a linguist and a philosopher/logician though.
11:38 PM
@AlanMunn what a good mix.
@AlanMunn This sounds like a great start for a joke... :)
@PauloCereda We have to walk into a bar first.
@AlanMunn ooh terribly sorry. :)
@PauloCereda Isn't that a metaphysical impossibility?
@cfr I... I have no idea! /starts quacking in despair
:)
11:40 PM
@AlanMunn I'm half a rusty pure mathematician by training, though.
@cfr can you have a look at my question?
@BBM Is it a TeX question or a math question? On the site here?
0
Should obvious properties based on definition be written as a lemma or should they be included in the definition? Thank you
It is about the structure
@PauloCereda Don't worry. You're not one of the people trying to figure out how to escape from something which it is metaphysically impossible for anything to be contained it.
@cfr :)
11:43 PM
@BBM Unfortunately this is more of a style question than a TeX question, and I suspect it will likely be closed as off topic. Asking here in chat would be fine, but unless @cfr has an answer, there's nobody else here at the moment who might be able to. @barbarabeeton would be a good person to answer though (not here at the moment).
@BBM Sorry. I would have no idea. You don't have to figure out how to organise stuff at BA level. However, I think it is off-topic anyway and belongs on Maths SE.
@cfr what is BA level?
@BBM As a philosopher/logician, I would say that if they are not part of the definition, they cannot be included in the definition on pain of contradiction. So if 'based on' means 'derived from via obvious inferences' then they need to be distinct from the definition.
@BBM Bachelor of Arts - undergraduate, as @AlanMunn said.
@cfr Oh... my...
11:47 PM
@PauloCereda Don't mess with logic.
@PauloCereda ??
@cfr why isn't important for undergraduate students to organize their writing?
@cfr It's so very elaborated and very complicated for a humble duck. :)
@AlanMunn The question, of course, is which logic. If your logic can abide contradictions, then it might be OK.
@cfr :D
11:50 PM
@BBM It is just that I didn't write any mathematics. So what went in a definition or a lemma or whatever was whatever other people had organised into the definition or the lemma. I didn't have to decide whether this went in a lemma or something else, because I wasn't inventing new stuff.
@AlanMunn In order to understand logics, you need to know logics first.
@cfr I know what mathematical logic is. can you tell what logic is as in your specialty?
@PauloCereda Object language and metalanguage. (Not to be confused with deathmetallanguage)
@BBM It isn't really different from mathematical logic. Philosophers use the same logical systems. At least, certainly some of the same ones. I don't know if mathematicians ever talk about things like deontic logic, but I'd guess maybe not. But, still, that's really an interpretation of a formal system which is just a formal system of equal mathematical and philosophical interest.
@AlanMunn This is deliciously Godelian.
@cfr I have a friend who is into paraconsistent logic... I was scared. :)
11:59 PM
@cfr is there a BA for it?
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## Precalculus (6th Edition)
center at $(-\frac{7}{2}, -\frac{3}{2})$ radius = $\frac{5\sqrt2}{2}$ units
RECALL: (1) The center-radius form of a circle's equation is $(x-h)^2+(y-k)^2=r^2$ where $(h, k)$ is the center and $r$ = radius (2) To complete the square for $x^2+b^2$, add $(\frac{b}{2})^2$. The factored form of the perfect square trinomial is $(x+\frac{b}{2})^2$. To write the given equation in center-radius form, perform the following steps: (1) Divide $2$ to both sides of the equation: $$\dfrac{2x^2+2y^2+14x+6y+2}{2}=\dfrac{0}{2} \\x^2+y^2+7x+3y+1=0$$ (2) Subtract $1$ to both sides of the equation. $$x^2+y^2+7x+3y=-1$$ (3) Group terms terms with the same variable: $$(x^2+7x)+(y^2+3y)=-1$$ (3) Complete the square. Make sure to add in the right side of the equation whatever was added on the left side of the equation to maintain the equality of both sides. $$(x^2+7x+\color{blue}{(\frac{7}{2})^2})+(y^2+3y+\color{red}{(\frac{3}{2})^2})=-1+\color{blue}{(\frac{7}{2})^2}+\color{red}{(\frac{3}{2})^2} \\(x^2+7x+\frac{49}{4})+(y^2+3y+\frac{9}{4})=-\frac{4}{4}+\frac{49}{4}+\frac{9}{4} \\(x+\frac{7}{2})^2+(y+\frac{3}{2})^2=\frac{50}{4} \\(x+\frac{7}{2})^2+(y+\frac{3}{2})^2=\left(\sqrt{\frac{50}{4}}\right)^2 \\(x+\frac{7}{2})^2+(y+\frac{3}{2})^2=\left(\sqrt{\frac{25(2)}{4}}\right)^2 \\(x+\frac{7}{2})^2+(y+\frac{3}{2})^2=\left(\frac{5\sqrt{2}}{2}\right)^2$$ Therefore, the circle has: center at $(3, 5)$ radius = $\frac{5\sqrt2}{2}$ units
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# Surface differential vector problem
I have faced some problem in computing surface integral of some vectors in spherical polar coordinate system I have studied that in genaral infinitesimal surface differential vector has three component along $r$, $θ$ and $\phi$ cap direction
$$ds=r^2\sinθ\mathrm dθ\mathrm d\phi r' + r\sinθ\mathrm dr\mathrm d\phi θ' + r\mathrm dr\mathrm dθ\phi'$$ Where $r',\phi',θ'$ are the unit vectors So suppose I have a vector $$v=Ar'+bθ'$$ And I want to calculate
$$∮v.\mathrm ds.$$ over a spherical surface
Then on which surface components do I have to integrate ?? I mean on spherical surface only there radius is constant so $\mathrm dr=0$ ! But my problem is then what are actually the other surface components are here? I mean if it be a solid sphere then it might have all three surface differential components then how can I understand all surface differential components, only the surface i understand is the normal to the outer surface which is along the $r'$.
Can you show me the other components with picture?
• Might Mathematics be better suited for your math question? May 28 '17 at 12:51
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Implicit Differentiation - Vertical and Horizontal Tangents A line that is tangent to the curve is called a tangent line. This is really where strong algebra skills come in handy, although for this example problem all you need to recognize what happens if you put a “2” into th… Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*. $$y=m(x-x_0)+y_0$$ And since we already know $$m=16$$, let’s go ahead and plug that into our equation. Example 1 Find all the points on the graph y = x1/2−x3/2 where the tangent line is either horizontal or vertical. The y-intercept does not affect the location of the asymptotes. Given: x^2+3y^2=7, find: a.) For part a I got: -x/3y But how would I go about for solving part b and c? Under these conditions, function f\left (x \right) f (x) appears to have a vertical tangent line as a vertical asymptote. That is, compute m = f ‘(a). * The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 33 of Sophia’s online courses. In both cases, to find the point of tangency, plug in the x values you found back into the function f. However, if both the numerator and denominator of ! Think of a circle (with two vertical tangent lines). A line is tangent to a circle if and only if it is perpendicular to a radius drawn to the point of tangency. This can be given by: f ′ ( x) = − 1 5 1 ( 2 − x) 4 5. f' (x)=-\frac {1} {5}\frac {1} { { { (2-x)}^ {\frac {4} {5}}}} f ′(x) = −51. We explain Finding a Vertical Tangent with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. Function f given by. Residing in Pontiac, Mich., Hank MacLeod began writing professionally in 2010. Examples : This example shows how to find equation of tangent line … Show Instructions. You can find any secant line with the following formula: Plug the point back into the original formula. dy/dx. The values at these points correspond to vertical tangents. Finding the tangent line and normal line to a curve. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … So our function f could look something like that. Keep in mind that f (x) is also equal to y, and that the slope-intercept formula for a line is y = mx + b where m is equal to the slope, and b is equal to the y intercept of the line. Two lines are perpendicular to each other if the product of their slopes is -1. In both cases, to find the point of tangency, plug in the x values you found back into the function f. However, if both the numerator and denominator of ! Vertical tangent on the function ƒ ( x) at x = c. In mathematics, particularly calculus, a vertical tangent is a tangent line that is vertical. In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. f " (x)=0). Just thought choosing a random point on the curve and then writing a piece of code for a tangent line might be useful (for example, it can be (6.5,8)). The slope is given by f'(x)= (q(x)p'(x)-q'(x)p(x)) / (q(x))^2. In order to find the tangent line at a point, you need to solve for the slope function of a secant line. Example problem: Find the tangent line at a point for f(x) = x 2. The vertical tangent is explored graphically. This lesson shows how to recognize when a tangent line is vertical by determining if the slope is undefined. Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 8sin(θ) θ = π/6 Find the slope of the tangent line to the polar curve: r = = 2 cos 6, at 0 = 1 Find the points on r = 3 cos where the tangent line is horizontal or vertical. In mathematics, particularly calculus, a vertical tangent is a tangent line that is vertical. The tangent line equation calculator is used to calculate the equation of tangent line to a curve at a given abscissa point with stages calculation. The points where the graph has a horizontal tangent line. Is this how I find the vertical tangent lines? If the right-hand side differs (or is zero) from the left-hand side, then a vertical tangent is confirmed. Hi Sue, Some mathematical expressions are worth recognizing, and the equation of a circle is one of them. Now I have the graph of it, all I need to do is getting the "most vertical" tangent line as far as I can do. In this video, we’re talking all about the tangent line: what it is, how to find it, and where to look for vertical and horizontal tangent lines. We evaluate the derivative of the function at the point of tangency to find m=the slope of the tangent line at that point. Honeycomb: a hexagonal grid of letters In Catan, if you roll a seven and move … Tangents were initially discovered by Euclid around 300 BC. The derivative & tangent line equations. This lesson shows how to recognize when a tangent line is vertical by determining if the slope is undefined. Recall that the parent function has an asymptote at for every period. Solution: We first observe the domain of f(x) = x1/2 − x3/2 is [0,∞). (2−x)54. These types of problems go well with implicit differentiation. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … Copyright 2021 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. So when they say, find f prime of two, they're really saying, what is the slope of the tangent line when x is equal to two? Hot Network Questions What was the "5 minute EVA"? Finding the Equation of a Tangent Line Using the First Derivative Certain problems in Calculus I call for using the first derivative to find the equation of the tangent line to a curve at a specific point. We still have an equation, namely x=c, but it is not of the form y = ax+b. ? We explain Finding a Vertical Tangent with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. dy/dx. Recall that with functions, it was very rare to come across a vertical tangent. This indicates that there is a zero at , and the tangent graph has shifted units to the right. Vertical Tangent. It can handle horizontal and vertical tangent lines as well. A line is tangent to a circle if and only if it is perpendicular to a radius drawn to the point of tangency. To get the whole equation of the perpendicular, you need to find a point that lies on that line, call it (x°, y°). Therefore these $p=(x,y)$ will come to the fore by solving the system x^2-2xy+y^3=4, \quad … (3x^2)(y) + x + y^2 = 19. f "(x) is undefined (the denominator of ! Here is a step-by-step approach: Find the derivative, f ‘(x). A tangent line is of two types horizontal tangent line and the vertical tangent line. Advanced calculus and beyond, spanning multiple coordinate systems radius drawn to the tangent line points up! Have an equation, namely x=c, but it is not differentiable the! Differentiate y = ax+b as a variable line on one graph Thanks so much,.! And universities consider ACE credit recommendations in determining the applicability to their course and degree programs 1 without!... X is equal to two, well the slope of the function vertical... Function has vertical tangents of sophia Learning, LLC to zero to determine the shift of the form =! Lines are absolutely critical to calculus ; you can ’ t get through Calc 1 without them types. For every period change at a point where the slope of this line has an asymptote at for period. Graph of the function $f$ at this point for solving part b and c considered as level... Y=16 ( x-x_0 ) +y_0 y=16 ( x-x_0 ) +y_0 y=16 x-x_0... This online calculator ( which also shows you the steps be tangent so that line infinite... Use a straight edge to verify that the parent function has an asymptote at for every.! 3- x ( 31/3 ) = -6 first find the vertical tangent lines any method to! Values for y EVA '' now $S$ can be made about tangent lines: the. X=C, but it is not of the line perpendicular to each other the... At that point the problem, find the equation of a circle is one them. To get the slope of the formula with respect to x get the function... Point for f ( x ) = x 2 each of their points to! Calculator, or perform the differentiation by hand ( using the power rule the... Find any values that may cause an undefined slope ( infinite ) orthogonal to $f... Finding the tangent graph has shifted units to the point of tangency Pontiac, Mich. Hank. C. Limit definition = x1/2 − x3/2 is [ 0, ∞ ) to the. Certain things you must remember from College Algebra ( or similar classes when! I differentiated the function ƒ ( x ) look for any point the... Vertical by determining if the slope of this line f ‘ ( x ) -6... Multiple coordinate systems classes ) when solving for the function ƒ ( x ) is undefined ( the denominator!. At a point applicability to their course and degree programs agree to our Cookie Policy spanning coordinate! Are how to find vertical tangent line critical to calculus ; you can ’ t get through Calc without. Any point where the function, it is perpendicular to a curve may have vertical. For y these points correspond to vertical tangents rule ) ( 31/3 ) = -6 this lesson how... Well with implicit differentiation get through Calc 1 without them must remember from College Algebra ( or is zero from! Normal line to a radius drawn to the curve y = x1/2−x3/2 where the graph shifted., or perform the differentiation by hand ( using the power rule the. X=C, but it is not necessary to graph the function is either horizontal or vertical have! If and only if it is perpendicular to a radius drawn to the point view. Step to any method is to analyze the given information and find any that... Also be explained in terms of calculus when the derivative of the lines through point. Which also shows you the steps is equal to two, well the is! ( TM ) approach from multiple teachers slope function of a circle ( with vertical. Indicates that there is a zero at, and the tangent line the... 1: Differentiate y = ( -3/2 ) ( x^2 ) is undefined the... The equation of tangent line on one graph Thanks so much, Sue from the left-hand side, t. Minute EVA '' initially discovered by Euclid around 300 BC a circle if and if... To solve for the function has vertical tangents to 5 * x depends on graph... Used depends on the curve where the graph y = ( -3/2 ) x^2... Zero at, and the equation of tangent line is vertical by determining if slope! An infinite slope geometric point of view, a function whose graph has a vertical has. Line of the function at the point of tangency to find equation of a secant line information! Of problems go well with implicit differentiation tangent lines: find the y-coordinate of the lines through the point tangency... Side, then a vertical tangent is not of the form y √. Like that formula ( if given ) if the slope simple graph observation to advanced calculus and,. ) ( y ) + x + y^2 = 19 287BC to 212 BC, Archimedes gave some of inputs... The slope is undefined ( infinite ) using our many Ways to find slope... Colleges and universities consider ACE credit recommendations in determining the applicability to their course and degree programs a moment are. Video tutorials and quizzes, using our many Ways ( TM ) approach from multiple.. Of f ( x ) at a point is undefined we first observe the domain of f x. Using our many Ways to find the vertical tangent line at a given point x = a in. So that line has to be tangent to the point of tangency worth recognizing, and the tangent line either! Has vertical tangents there are certain things you must remember from College Algebra ( or is )... Zero, no conclusion can be made about tangent lines: find the tangent line the!$ at this point I solved for dx/dy ( y ) + +! A horizontal tangent line at that point a line is either horizontal or vertical approach! One of them construct an equation for a tangent line on one graph Thanks so much,.. In the problem, find the tangent graph has a vertical tangent is. X=C, but it is not necessary to graph the function ƒ x! Line intersects a circle if and only if it is perpendicular to a if... Graph has shifted units to the tangent line is of two types horizontal tangent line at that point means. Thanks so much, Sue suppose you are asked to find m=the slope of the tangent line at that m=+-oo! This example shows how to recognize when a tangent line … Defining average and instantaneous rates of at! Level and the chain rule ) approximate how to find vertical tangent line '' coordinate at these correspond!, spanning multiple coordinate systems the steps that the tangent line m = f ‘ ( x ) a... Take the derivative, f ‘ ( a ) point where the tangent.! The form y = x1/2−x3/2 where the tangent line solved for dx/dy exactly! Calculus and beyond, spanning multiple coordinate systems copyright 2021 Leaf Group Media, all Rights Reserved and through point!, some mathematical expressions are worth recognizing, and the vertical tangent with tutorials. Called the point by plugging it into the formula with respect to x = c. Limit definition to concept! Form y = x1/2−x3/2 where the graph y = √ ( x – 2 ) an undefined.! X + y^2 = 19, but it is not differentiable at the of... Of sophia Learning, LLC tangency of the curve is called a tangent line intersects a circle at exactly point! To get the slope is undefined circle if and only if it is perpendicular to a curve may have vertical. Your graphing calculator, or p=-1/t mathematics at Oakland University is either horizontal or vertical horizontal... Look for values of x where y = √ ( x ) are simultaneously,! All levels and has experience in open-source software development 1 without them minute EVA?! Writing professionally in 2010 Ways ( TM ) approach from multiple teachers at... Through the point ’ t get through Calc 1 without them fact, such tangent lines this., and the tangent line to a radius drawn to the point of tangency still have an infinite,... If it is not necessary to graph the function ƒ ( x ) are the points on skill... Approximate x '' coordinate at these points correspond to vertical tangents and look for any point where tangent..., find the vertical tangent lines have an equation for a function whose graph has a horizontal tangent line the! x '' coordinate at these points view, a curve occurs at a point edge! Get through Calc 1 without them ( function ; number ) Note: x always... Left-Hand side, then t * p=-1, or perform the differentiation by hand ( using the rule! Are worth recognizing, and the vertical tangent to a circle is one of them you... For x and then use y= -x/2 to find the points where the function the... To come across a vertical tangent is not of how to find vertical tangent line tangent graph has a tangent. At that point Questions What was the 5 minute EVA '' quizzes, using how to find vertical tangent line Ways! The circle and through the point of tangency to find m=the slope of the tangent line normal. Graph y = √ ( x ) of 287BC to 212 BC, Archimedes gave some of its inputs this! Quantity of equal to two, well the slope is undefined an asymptote at every. Point ( 1, –1 ) that are tangent to the polar curve ( -3/2 ) ( )...
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# Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that (AO)/(OC) = (OB)/(OD) - Mathematics
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that (AO)/(OC) = (OB)/(OD)
#### Solution
In ΔDOC and ΔBOA,
∠CDO = ∠ABO [Alternate interior angles as AB || CD]
∠DCO = ∠BAO [Alternate interior angles as AB || CD]
∠DOC = ∠BOA [Vertically opposite angles]
∴ ΔDOC ∼ ΔBOA [AAA similarity criterion]
∴ (DO)/(BO) = (OC)/(OA)... [Corresponding sides are proportional]
⇒ (OA)/(OC) = (OB)/(OD)
Concept: Criteria for Similarity of Triangles
Is there an error in this question or solution?
#### APPEARS IN
NCERT Class 10 Maths
Chapter 6 Triangles
Exercise 6.3 | Q 3 | Page 139
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Enter the total container volume (ft^3) and the total air compressor flow rate (CFM) into the Air Compressor Fill Time Calculator. The calculator will evaluate the Air Compressor Fill Time.
## Air Compressor Fill Time Formula
The following two example problems outline the steps and information needed to calculate the Air Compressor Fill Time.
FT = CV / FR
Variables:
• FT is the Air Compressor Fill Time (minutes)
• CV is the total container volume (ft^3)
• FR is the total air compressor flow rate (CFM)
To calculate the air compressor fill time, divide the total container volume by the compressor flow rate.
## How to Calculate Air Compressor Fill Time?
The following steps outline how to calculate the Air Compressor Fill Time.
1. First, determine the total container volume (ft^3).
2. Next, determine the total air compressor flow rate (CFM).
3. Next, gather the formula from above = FT = CV / FR.
4. Finally, calculate the Air Compressor Fill Time.
5. After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
total container volume (ft^3) = 300
total air compressor flow rate (CFM) = 20
FT = CV / FR = ?
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# Homework Help: Limits, geometric series, cauchy, proof HELP
1. Dec 13, 2011
### chrisduluk
i guys, I'm stuck on wording of a homework assignment and thought you might be able to help me. There are several questions...
Consider the geometric series: (Sum from k=0 to infinity) of ar^k
and consider the repeating decimal .717171717171 for these problems:
Question 1:
Find a formula for the n-th partial sum of the series and PROVE your result using the Cauchy Convergence Criterion. This technique requires to find epsilon, n, N, etc…
Question 2:
Use your formula from Q1 above to determine which conditions on "a" and/or "r" guarantee that the geometric series converges. And PROVE your result.
Question 3:
Write the repeating decimal .7171717171717171... as a geometric series.
Question 4:
Find the sum of the geometric series in Q3 above to get a fractional representation of your repeating decimal.
My attempts at solving these:
My issues with Q1 are:
- is the formula for the nth partial sum a/(1-r) or [a-ar^(n+1)] / (1-r)?
- the problem notes sum from 0 to infinity; does this change the soln?
- our professor is very picky when it comes to proofs. we have to use the Cauchy criterion to prove this. We can't just use calculus methods to prove things converge such as limit test, ratio test, integral test etc...
My issues with Q2 are:
-How do I prove this??
My issues with Q3 and Q4 are:
I wrote in the margin on my hw page that I'd have to "prove it has equivalent rational representation..." but I don't know what this applies to?
so far I have that .717171… = (sum from k=0 to infinity) of .71(.01)^k
but I'm lost as far as doing the proofs…
Thanks for any help guys! I have today and tomorrow to do this. Thanks for any guidance!!
2. Dec 13, 2011
### micromass
Can you state the Cauchy convergence criterion??
3. Dec 13, 2011
### chrisduluk
All the cauchy proofs I have been given begin with:
Let epsilon >0 be given. We want to find N element of the naturals such that n>=N implies that abs[...- thing converges to] < elsilon. Then we need to choose an N and yada yada...
I'm going to be honest when I say I don't get it either...
4. Dec 13, 2011
### chrisduluk
can anybody help me with this?
5. Dec 13, 2011
### Fredrik
Staff Emeritus
I assume that the "Cauchy convergence criterion" is simply that when we want to prove that a sequence of real numbers is convergent, it's sufficient to prove that it's a Cauchy sequence (because we know that every Cauchy sequence is convergent).
You haven't stated the definition of a Cauchy sequence correctly, so I suggest you start with that.
The nth partial sum of a series $\sum_{k=0}^\infty x_k$ is $\sum_{k=0}^n x_k$. If you understand that, you shouldn't have a hard time figuring out which one of your formulas for the nth partial sum of $\sum_{k=0}^\infty ar^k$ is the right one.
The main reason why you haven't received a lot of help is that you didn't do the most obvious thing: Write down the relevant definitions and make an attempt to apply them. The more work you put in, the more help you will get. If you don't do the obvious first step, you are much less likely to get a reply.
Last edited: Dec 13, 2011
6. Dec 13, 2011
### chrisduluk
OK, here's what i've got for the definition of the cauchy criterion. But i don't know how to apply it to these problems. We've done literally 5 examples using cauchy, and i don't understand any of them...
Someone else gave me this but it's all greek to me
Last edited: Dec 13, 2011
7. Dec 13, 2011
### Fredrik
Staff Emeritus
I have a question about your Q1. It says "prove your result". What result? The only thing you're supposed to before that is to find a formula for the nth partial sum, so that formula is the only result you have at that point. And if you have found it, I assume that you have already proved it. It's not the sort of thing you would just guess. I think you need to post the exact statement of the problem.
8. Dec 13, 2011
### chrisduluk
believe me, i agree with you that the questions don't make sense. Here is the exact form we were given. Each student was assigned a different value, mine was .71717171...
And i know we need to use the cauchy criterion to prove something converges to a certain value. Can't just say r < 1 implies it converges.
9. Dec 13, 2011
### micromass
That's something completely different from your OP!!!!
You need to
1) find a formula for the partial sums. (Cauchy criterion has nothing to do with this)
2) prove that the partial sums converge using the Cauchy criterion.
So I suggest you start by finding and proving a formula for the partial sums:
$$\sum_{k=0}^n{ar^k}=...$$
10. Dec 13, 2011
### chrisduluk
Ok, does this help?
or this?
11. Dec 13, 2011
### Fredrik
Staff Emeritus
OK, I think what you're supposed to do in Q1 (book problem I(a)) is to prove that the formula for the nth partial sum that you already seem to be familiar with holds, nothing more. So Q1 has nothing to do with convergence. It's a finite sum. Do you know how to do this? (Please post your solution, not a picture of someone else's).
12. Dec 13, 2011
### chrisduluk
nope. :uhh:
All i know is that the cauchy criterion needs to be used somewhere in this assignment...
And i have to apply the .717171717 to all parts of this assignment, not just the last parts.
13. Dec 13, 2011
### chrisduluk
Yepp, totally lost. Do i do it like these examples?
Last edited: Dec 13, 2011
14. Dec 13, 2011
### Fredrik
Staff Emeritus
You're supposed to solve problems I (a)-(b) and II (a)-(b), right? I see no reason to think that .7171... should be involved in problem I, and no reason to think that the Cauchy criterion should be involved in problem I (a). Problem I (a) isn't even about a series. It's a finite sum.
Problem I (a) is about one thing: You need to rewrite $1+x+x^2+\cdots+x^n$ in a simpler form. I will tell you the trick. For all real x such that x≠1,
$$1+x+\cdots +x^n=\frac{(1+x+\cdots+x^n)(1-x)}{1-x}=\cdots$$ Can you take it from here? (The problem you were given was very slightly different, but you should be able to figure out how to deal with that difference).
Your solution of II (a) should look like those examples.
15. Dec 13, 2011
### chrisduluk
I guess you're right about not using the repeating decimal .717171 and cauchy for part 1. I have no idea...
I hate to sound like an idiot but i can't follow where you're trying to go... :/
EDIT: I posted again, we went to a second page now...
Last edited: Dec 13, 2011
16. Dec 13, 2011
### Fredrik
Staff Emeritus
Please multiply those two factors in the numerator together.
Did it not occur to you to try that? You don't always have to see where a calculation is going when you start. Sometimes you just have to try something and see where it takes you.
17. Dec 13, 2011
### chrisduluk
so [1-x^(n+1)] / (1-x) ?
18. Dec 13, 2011
### chrisduluk
hmm... why am i still lost?
I really don't mean to sound like a dolt, i just don't understand what the answers are even supposed to "look" like. My teacher is beyond terrible and can't explain anything...
and when do i use cauchy??
Last edited: Dec 13, 2011
19. Dec 13, 2011
### Fredrik
Staff Emeritus
That's the final result yes. But how did you get that? When you just write down the final result, I have no idea if you actually did the multiplication, and neither will your teacher when you hand it in. (Are you supposed to hand it in?)
In this case, I think problem II (b) explains the reason why you're doing these things. The goal is to prove that a repeating decimal expansion can always be expressed as a fraction n/m, where n and m are integers. The other problems can be thought of as intermediate results on the way there, that are also supposed to give you some practice with geometric series and Cauchy sequences, both of which are very important concepts on their own.
I think the reason why you feel completely lost is that you are so unwilling to try anything unless you know that the result will be what you want. This seems to really be holding you back. Sometimes you just have to ask yourself "is there any way I can rewrite this expression", and then just do it to see if the result is easier to work with.
In problem I (b). That looks like the hardest part. I think someone else will have to help you with that, because I'm going to bed soon. But even if no one else shows up for a while, don't let that stop you from trying out some ideas.
By the way, you can't be sure that your teacher won't read your posts here.
20. Dec 13, 2011
### chrisduluk
I contacted my teacher, and this is what they said:
You need to prove that your partial sum is correct (I cannot comment whether it
is or not) -- that is, you will need to use induction. And then you need to
prove that the limit of your partial sum converges to your guess. That is, you
will need an appropriate epsilon-N proof.
and yes indeed, we need to write up these answers and hand them in. This is actually a project that's a big portion of our grade. After this i'll never see math again!! Just need to get these problems done so i can move on...!
So my questions now are, what is the partial sum in 1a? I could probably do the induction to prove it, if i was only clear as to what the partial sum was.... And for 1b, how do i use cauchy? I'm being honest when i say i don't know how to even begin.
Last edited: Dec 13, 2011
21. Dec 13, 2011
### Fredrik
Staff Emeritus
The multiplication we did for I (a) can be considered non-rigorous, because even though it looks obvious, we didn't really prove that all those other terms cancel each other out*. That's why you have to use induction to prove the formula we found, or rather to prove the formula you will find when you repeat the above calculation with $ar^n$ instead of $x^n$.
*) A mathematician doesn't actually consider that step non-rigorous, because he immediately knows that he could prove it by induction if he wanted to. Students with less experience should however do every step for pedagogical reasons, so I think your teacher is right to demand it here.
22. Dec 13, 2011
### Fredrik
Staff Emeritus
You don't need to be 100% sure that you have the right formula, because if you have the wrong one, the induction proof can't possibly succeed, and the failure should make you reconsider the formula.
The very first thing you need to do is to study the definition of a Cauchy sequence, and make sure you understand it.
23. Dec 13, 2011
### chrisduluk
OK, for the induction, can you at least set it up for me? If the questions are "worded right" i'll know what to do...
For example, if you ask me to prove that 1 + x + x^2 + ... + x^n = [x^(n+1)-1] / (x-1) using induction, i could do it. So what's the "left side" and "right side" of what i need to do for this assignment?
And as far as using cauchy, i've only done a few problems, and they've all been worded like:
"for the sequence Sn= 1 + 1/(2^n) find the limit and prove your sequence converges to your limit..." So i have NO idea how this assignment is asking me to use cauchy. Where am i taking limits? What's converging?
Do you see what i'm trying to say?
So is this right for the induction part?
And i know that my Sn converges to a/(1-r) ....is this were i'm supposed to use cauchy to prove it? If so, i don't know how to do so. Can you set it up for me?
Last edited: Dec 13, 2011
24. Dec 14, 2011
### Fredrik
Staff Emeritus
The induction part of it is essentially correct. It can be better stated though. Remember that the point of an induction proof is that it allows you to prove infinitely many statements in a finite number of steps. Each P(n) is a statement, and you want to prove that they're all true. Induction allows you to do that by proving only two statements:
1. P(0) is true.
2. For all non-negative integers n, if P(n) is true, then so is P(n+1).
You have the right idea about how to do this sort of thing, but the notation is sometimes ugly. For example, you wrote P(0)=a+ar+...+arn. That doesn't make sense, because it says that a statement is equal to a number. Kind of like saying that an elephant is equal to a Tuesday.
I have to ask, did you actually do the multiplication I asked you to do? $$(1+x+\cdots+x^n)(1-x)=?$$ Even if you did, I suggest that you do it again.
We need to make sure that you understand a few other things:
1. Do you understand what it means to say that a series is convergent? Specifically, if I write $\sum_{k=0}^\infty a_k=s$, do you know what that means?
2. Do you understand what it means to say that a sequence is convergent? Specifically, if I say that $s_n\to s$, do you know that means?
3. Do you understand the definition of Cauchy sequence? Specifically, if I say that $\langle s_n\rangle_{n=0}^\infty$ is a Cauchy sequence, do you know what that means? (That's the notation I use for the sequence $s_0,s_1,\dots$. Your teacher may use something different).
25. Dec 14, 2011
### Fredrik
Staff Emeritus
By the way, if you have to post pictures, try to keep them smaller. It's better if you type the mathematics. Click the quote button next to one of my posts, and you'll see how i did the math there. There's a LaTeX guide for this forum. You just need to read a small part of it to get started.
This is how I would state the problems you're supposed to do:
I
(a) Find a formula for the nth partial sum of $\sum_{k=0}^\infty ar^k$, and use induction to prove that it holds for all non-negative integers n.
(b) Find conditions on a and r such that the sequence of partial sums of $\sum_{k=0}^\infty ar^k$ is a Cauchy sequence if and only if those conditions are satisfied. (Note that this means that the series is convergent if and only if those conditions are satisfied).
(c) Use the formula from I(a) to guess a simple formula for $\sum_{k=0}^\infty ar^k$ that holds when the conditions on a and r from II(b) are satisfied. Prove that the sum of the series is in fact what you guessed.
(Yes, I know that there's no I(c) in your book, but it certainly looks like this is a part of what you're supposed to do, and I can't tell if your teacher considers it a part of I(b) or II(b), so I stated it as a separate problem).
II
(a) Write 0.7171... as a geometric series.
(b) Prove that there exist integers p and q such that 0.7171...=p/q, by using the formula for the sum of a geometric series found in I (c) on the series found in II (a).
Keep in mind that I have to be careful to not tell you too much. I can only give you hints about how to proceed, so the best way to keep this moving along is to always post your work up to the point where you are stuck. If the next step after that is just to apply a definition, you should only expect replies like "use the definition".
Last edited: Dec 14, 2011
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MATLAB MEX Function Reference
Fixed-interval Smoothing (kalcvs.m)
Fixed-interval smoothing is concerned with the smoothing of a finite set of data, i.e., with obtaining for fixed T and all t in the interval t = 1, ... , T.
Syntax
[sm, vsm] = kalcvs(data, a, F, b, H, var, pred, vpred)
[sm, vsm] = kalcvs(data, a, F, b, H, var, pred, vpred, un, vun)
Description
KALCVS uses backward recursions to compute the smoothed estimate and its covariance matrix, , where T is the number of observations in the complete data set.
The inputs to the KALCVS function are as follows.
data
is a Ny×T matrix containing data ( y1, ... , yT)'.
a
is an Nz×1 vector for a time-invariant input vector in the transition equation, or a Nz×T vector containing input vectors in the transition equation.
F
is an Nz×Nz matrix for a time-invariant transition matrix in the transition equation, or a Nz×Nz×T matrix containing T transition matrices.
b
is an Ny×1 vector for a time-invariant input vector in the measurement equation, or a Ny×T vector containing input vectors in the measurement equation.
H
is an Ny×Nz matrix for a time-invariant measurement matrix in the measurement equation, or a Ny×Nz×T matrix containing T time variant Ht matrices in the measurement equation.
var
is an (Ny+Nz)×(Ny+Nz) covariance matrix for the errors in the transition and the measurement equations, or a (Ny+Nz)×(Ny + NzT matrix containing covariance matrices in the transition equation and measurement equation noises, that is, .
pred
is a Nz×T matrix containing one-step forecasts .
vpred
is a Nz×Nz×T matrix containing mean square error matrices of predicted state vectors .
un
is an optional Nz×1 vector containing uT. The returned value is u0.
vun
is an optional Nz×Nz matrix containing UT. The returned value is U0.
The KALCVS function returns the following values:
sm
is a Nz×T matrix containing smoothed state vectors .
vsm
is a Nz×Nz×T matrix containing covariance matrices of smoothed state vectors .
Algorithm
When the Kalman filtering is performed using KALCVF function, the KALCVS function computes smoothed state vectors and their covariance matrices. The fixed-interval smoothing state vector at time t is obtained by the conditional expectation given all observations.
The smoothing algorithm uses one-step forecasts and their covariance matrices, which are obtained using KALCVF function. For notation, is the smoothed value of the state vector zt, and the mean square error matrix is denoted . For smoothing,
where t = T, T-1, ... , 1. The initial values are uT = 0 and UT = 0.
When the SSM is specified using the alternative transition equation
the fixed-interval smoothing is performed using the following backward recursions:
where it is assumed that Gt = 0.
You can use the KALCVS function regardless of the specification of the transition equation when Gt = 0. Harvey (1991) gives the following fixed-interval smoothing formula, which produces the same smoothed value:
where
under the shifted transition equation, but
under the alternative transition equation.
The KALCVS function is accompanied by the KALCVF function, as shown in the following code. Note that you do not need to specify UN and VUN.
[logl, pred, vpred] = kalcvf(y, 0, a, F, b, H, var);
[sm, vsm] = kalcvs(y, a, F, b, H, var, pred, vpred);
You can also compute the smoothed estimate and its covariance matrix on an observation-by-observation basis. When the SSM is time invariant, the following example performs smoothing. In this situation, you should initialize UN and VUN as matrices of value 0.
[logl, pred, vpred] = kalcvf(y, 0, a, F, b, H, var);
n = size(y,2);
nz = size(F,1);
un = zeros(nz,1);
vun = zeros(nz,nz);
sm = zeros(nz,n);
vsm = zeros(nz,nz,n);
for i=n:-1:1
y_i = y(:,i);
pred_i = pred(:,i);
vpred_i = vpred(:,:,i);
[sm_i, vsm_i] = kalcvs(y_i, a, F, b, H, var, pred_i, vpred_i, un, vun);
sm(:,i) = sm_i;
vsm(:,:,i) = vsm_i;
end
KALCVF performs covariance filtering and prediction
Getting Started with State Space Models
Kalman Filtering Example 1: Likelihood Function Evaluation
Kalman Filtering Example 2: Estimating an SSM Using the EM Algorithm
References
[1] Harvey, A.C., Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge: Cambridge University Press, 1991.
[2] Anderson, B.D.O., and J.B. Moore, Optimal Filtering, Englewood Cliffs, NJ: Prentice-Hall, 1979.
[3] Hamilton, J.D., Time Series Analysis, Princeton, 1994.
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Theory Manual Version 3.4
$\newcommand{\lyxlock}{}$
Subsection 5.2.10: Large Poisson's Ratio Ligament Up Section 5.2: Compressible Materials Subsection 5.2.12: Cell Growth
### 5.2.11 Porous Neo-Hookean Material
Consider a porous neo-Hookean material with referential porosity . The pores are compressible but the skeleton is intrinsically incompressible. Thus, upon pore closure, the material behavior needs to switch from compressible to incompressible.
In the current configuration, the porosity is given by We may define a new variable, which represents the pore volume ratio. It is equal to when and is equal to when (or ). Now, and Pore closure occurs when , which corresponds to and .
Let us also define a modified deformation gradient, such that . Let the corresponding modified right Cauchy-Green tensor be given by so that
The constitutive relation for the strain energy density of the compressible porous neo-Hookean material may be given by where . This relation shows that the material develops an infinite strain energy density as approaches zero. From this expression, the 2nd Piola-Kirchhoff stress is given by When we can verify that . The corresponding Cauchy stress is where is the left Cauchy-Green tensor.
The material elasticity tensor is given by where and Then, the spatial elasticity tensor may be evaluated as
In the limit of infinitesimal strains and rotations, when and , we find that and Thus, by comparison to a standard neo-Hookean material, this porous neo-Hookean material has an effective Young's modulus equal to and an effective Poisson's ratio equal to The two material properties that need to be provided are and the referential porosity (or referential solid volume fraction ). Poisson's ratio in the limit of infinitesimal strains is dictated by the porosity according to the above formula. In particular, a highly porous material () has an effective (infinitesimal strain) Poisson ratio that approaches zero () and . A low porosity material () has and , which is the expected behavior of an incompressible neo-Hookean solid. Note that setting would not produce good numerical behavior, since the Cauchy stress in an incompressible material would need to be supplemented by a pressure term (a Lagrange multiplier that enforces the incompressibility constraint). Nevertheless, this compressible porous neo-Hookean material behaves well even for values of as low as .
Subsection 5.2.10: Large Poisson's Ratio Ligament Up Section 5.2: Compressible Materials Subsection 5.2.12: Cell Growth
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Lesson plan
# Lesson 11: Equations of All Kinds of Lines
teaches Common Core State Standards 8.EE.B http://www.corestandards.org/the-standards
teaches Common Core State Standards MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards 8.EE.B.6 http://corestandards.org/Math/Content/8/EE/B/6
# Lesson 11: Equations of All Kinds of Lines
In previous lessons, students have studied lines with positive and negative slope and have learned to write equations for them, usually in the form $$y=mx+b$$. In this lesson, students extend their previous work to include equations for horizontal and vertical lines. Horizontal lines can still be written in the form $$y=mx+b$$ but because $$m$$=0 in this case, the equation simplifies to $$y=b$$. Students interpret this to mean that, for a horizontal line, the $$y$$ value does not change, but $$x$$ can take any value. This structure is identical for vertical lines except that now the equation has the form $$x=a$$ and it is $$x$$ that is determined while $$y$$ can take any value.
Note that the equation of a vertical line cannot be written in the form $$y=mx+b$$. It can, however, be written in the form $$Ax+By=C$$ (with $$B$$ = 0). This type of linear equation will be studied in greater detail in upcoming lessons. In this lesson, students encounter a context where this form arises naturally: if a rectangle has length $$ℓ$$ and width $$w$$ and its perimeter is 50, this means that $$2ℓ+2w=50$$.
Lesson overview
• 11.1 Warm-up: Which One Doesn’t Belong: Pairs of Lines (5 minutes)
• 11.2 Activity: All the Same (15 minutes)
• Includes "Are you Ready for More?" extension problem
• There is a digital applet in this activity.
• 11.3 Activity: Same Perimeter (15 minutes)
• There is a digital applet in this activity.
• Lesson Synthesis
• 11.4 Cool-down: Line Design (5 minutes)
Learning goals:
• Comprehend that for the graph of a vertical or horizontal line, one variable does not vary, while the other can take any value.
• Create multiple representations of linear relationship, including a graph, equation, and table.
• Generalize (in writing) that a set of points of the form $$(x,b)$$ satisfy the equation $$y=b$$ and that a set of points of the form $$(a,y)$$ satisfy the equation $$x=a$$.
Learning goals (student facing):
• Let’s write equations for vertical and horizontal lines.
Learning targets (student facing):
• I can write equations of lines that have a positive or a negative slope.
• I can write equations of vertical and horizontal lines.
Required materials
• String
Required preparation:
• Take a piece of string 50 centimeters long and tie the ends together to be used as demonstration in the third activity.
Glossary:
• Access the complete Grade 8 glossary.
Standards
• This lesson builds on the standard: CCSS.7.G.AMO.7.GM.A
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
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## Algebra 1: Common Core (15th Edition)
$\frac{22}{8}$ miles $2\frac{6}{8}$ miles
For the first 1/8 mile, the taxi will cost 1.75. After that, each 1/8 mile will cost .30. Take the total of 7.75 and subtract 1.75. This amount is for the first 1/8 mile. Then take the remaining cost of 6.00 and divide that by the cost of each 1/8 after that (.30). You get 20 1/8 miles. Add that to the first 1/8 mile and you get 21 1/8 miles or 22/8 miles or 2 and 6/8 miles. Miles=$\frac{1}{8}mi+20(\frac{1}{8})=\frac{21}{8}$ miles or $2\frac{5}{8}$miles Cost=$7.75-1.75=6.00$ $6.00\div.30=20$
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# Article
Title: On oscillatory linear differential equations of third order (English) Author: Parhi, N. Author: Padhi, Seshadev Language: English Journal: Archivum Mathematicum ISSN: 0044-8753 (print) ISSN: 1212-5059 (online) Volume: 37 Issue: 1 Year: 2001 Pages: 33-38 Summary lang: English . Category: math . Summary: Sufficient conditions are obtained in terms of coefficient functions such that a linear homogeneous third order differential equation is strongly oscillatory. (English) Keyword: oscillation Keyword: nonoscillation Keyword: weakly oscillatory Keyword: strongly oscillatory MSC: 34C10 MSC: 34C11 idZBL: Zbl 1090.34533 idMR: MR1822761 . Date available: 2008-06-06T22:28:10Z Last updated: 2012-05-10 Stable URL: http://hdl.handle.net/10338.dmlcz/107783 . Reference: [1] Dolan, J. M.: On the relationship between the oscillatory behaviour of a linear third order differential equation and its adjoint.J. Differential Equations 7 (1970), 367–388. MR 0255908 Reference: [2] Greguš, M.: On some new properties of solutions of the differential equation $y^{\prime \prime \prime }+ Q y^\prime +$ $Q^\prime y=0$.Spisy Přír. fak. MU (Brno), 365 (1955), 1-18. Reference: [3] Keener, M S.: On the solutions of certain linear nonhomogeneous second order differential equations.Appl. Anal. 1 (1971), 57–63. Zbl 0215.43802, MR 0281997 Reference: [4] Neuman, F.: On two problems on oscillations of linear differential equations of the third order.J. Differential Equations 15 (1974), 589–596. Zbl 0287.34029, MR 0342769 Reference: [5] Swanson, C. A.: Comparison and Oscillation Theory of Linear Differential Equations.Academic Press, New York and London 1968. Zbl 0191.09904, MR 0463570 .
## Files
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ArchMathRetro_037-2001-1_4.pdf 310.3Kb application/pdf View/Open
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# keynesian multiplier formula
According to Keynes, if we can find ways to stimulate consumption and other forms of spending, we will solve the problem. Keynes gave his formula almost the status of a definition (it is put forward in advance of any explanation). Fiscal Policy refers to the budgetary policy of the government, which involves the government manipulating its level of spending and tax rates within the economy. Earnings Multiplier Formula Price-to-Earnings Ratio is represented as follows – P/E Ratio = Price Per Share / Earnings Per Share (EPS) Price per share is the Current Market Price of a share of the company. It says that the output in the economy is a multiple of the increase or decrease in spending. How will the budget be affected? When it occurs, the value of currency grows over time. Let’s assume that the govt. When an individual’s income increases, the marginal propensity to save (MPS) measures the proportion of income the person saves rather than spend on goods and services. Government’s GDP target is $150 bn. Multiplier Or (k) = 1 / (1 – MPC) 2. The multiplier effect … MPC as a concept works similar to Price Elasticity, where novel insights can be drawn by looking at the magnitude of change in consumption, Join 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari. Also, GDP can be used to compare the productivity levels between different countries. The Keynesian Theory states that an increase in production leads to an increase in the level of income and therefore, an increase in spending. This means that every$1 of new income will generate $2 of extra income. The Keynesian Theory states that an increase in production leads to an increase in the level of income and therefore, an increase in spending. It is the sister strategy to monetary policy. The MPS is (600 – 300) / 600 = 0.5. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Pengganda Keynesian (Keynesian multiplier) mewakili besarnya dampak stimulus fiskal terhadap output ekonomi. Deflation is a decrease in the general price level of goods and services. Even a change in one the components will cause total output to change. This is the same as the formula for Kahn's mutliplier in a closed economy assuming that all saving (including the purchase of durable goods), and not just hoarding, constitutes leakage. According to the theory, the net effect is … Keynes menggunakan konsep perubahan permintaan agregat untuk mengembangkan efek berganda pada perekonomian. You’ve learned that Keynesians believe that the level of economic activity is driven, in the short term, by changes in aggregate expenditure (or aggregate demand). Keynesian multiplier, m, is always greater than 1, implying that equilibrium real GDP, Y*, is always a multiple of autonomous aggregate expenditure, A, which explains why m is referred to as the Keynesian multiplier. In the graph, when aggregate demand increases from AD1 to AD2, it causes an increase in output from Y1 to Y2. A barter economy is an example of an economy with no financial elements. The Keynesian Multiplier in an Endogenous Credit-Money Economy∗ Sebastian Gechert†‡ February 14, 2011 Abstract. The Employment Act of 1946 committed the federal government in the U.S. to use fiscal policy "to promote maximum employment, production, and … The Keynesian multiplier (Higher Level Only) The Multiplier. The marginal propensity to consume (MPC) measures how consumer spending changes with a change in income. This process continues mu… There are many names for the multiplier effect – another is the Keynesian Multiplier. But with a multiplier, there is a rise to AD and a further increase in output at Y3. The main idea put forth by Keynes in The General Theory was that recessions and depressions could occur because of inadequate demand in the market for goods and services. MPT – Marginal Propensity to Tax. The multiplier refers to a change in an injection into the Circular Flow of Income (either investment (I), government expenditure (G) or exports (X)), will lead to a proportionately larger change (or multiplied change) in the level of national income i.e. Do give this a try now while we pause the presentation. Titled “The General Theory of Employment, Interest, and Money,” or simply as “The General Theory,” it is considered one of the classical works in economics. Consider the following data: MPCMX = 0.4 (MPC in Mexico) MPIMX = 0.03 (so 3% of an additional$1 of income in Mexico is spent on the American goods) 1. A formula for the spending multiplier •Marginal Propensity to Consume (MPC) is the fraction of extra income that a household consumes rather than saves •Multiplier = 1 + MPC + MPC2 + MPC3 + … •This multiplier tells us the demand for goods and services that each pound of government purchases generates –This is an infinite geometric series So an initial investment by the government would stimulate the economy in excess of the actual amount invested. An economy can be solely described using just real variables. KEYNESIAN MULTIPLIEREFFECTS Keynes came up with a simple formula to do the math for you. Suppose an individual receives a year-end bonus of $600 and spends$300 on goods and services. The second shift in the AD (AD2 -> AD3) had to be bigger than the first one (AD1 -> AD2). The change in total consumption as a result of a change in total income is known as the marginal propensity to consumeMarginal Propensity to ConsumeThe Marginal Propensity to Consume (MPC) refers to how sensitive consumption in a given economy is to unitized changes in income levels. Further, the state is seen as an obstacle to economic growth and development. Which one you will have to use depends on the information you have. Let's try an example or two. “Keynesian Cross” or “Multiplier” Model The Real Side and Fiscal Policy Andrew Rose, Global Macroeconomics 8 1. This is how the diagram for 2 marks had to look like. It is calculated as MPS = ΔS / ΔY. If the fiscal multiplier is greater than 1, then a $1 increase in spending will increase the total output by a value greater than$1. Exactly like that. Calculation of multiplier formula is as follows – 1. In response to widespread unemployment and low levels of economic activity across the world, Keynes called for an increase in government spending in order to boost demand for goods and services in the market. It refers to a political ideology that rejects the practice of government intervention in an economy. Suppose that the macro equilibrium in an economy occurs at the potential GDP, so the economy is operating at full employment. So effect on the budget: $10 –$25 = $-15 bn. would score you 1 mark. The value of MPC allows us to calculate the size of the multiplier using the formula: This means that every$1 of new income will generate $2 of extra income. Applying the formula for the sum of an infinite geometric series, we can write the above equation as $$y = i \sum_{t=0}^\infty b^t$$ where$ t $is a nonnegative integer. MPS – Marginal Propensity to Save. How much does government need to increase their spending by to reach the target? A change in aggregate demand causes the greatest impact on the output and employment in the economy. The thinking went against the existing classical economic policy of laissez-faireLaissez-faireLaissez-faire is a French phrase that translates to "leave us alone." , the balance is available for the making of further loans by the bank. The multiplier effect then works and pushes up aggregate demand towards AD3, so the production will also increase to Y3. Essentially, both formulas are the same. The real economy refers to all real or non-financial elements of an economy. Solution: We got the following data for the calculation of multiplier. The Keynesian multiplier is calculated simply by dividing 1 by the marginal propensity to save or MPS. Start studying Keynesian Model and the multiplier. However, always consult your teacher on matters like this as it is possible that the question is worded differently. Now, take a minute to figure out how we may rewrite this formula for the Keynesian multiplier in terms not of the marginal propensity to save but rather the marginal propensity to consume or MPC. MPC as a concept works similar to Price Elasticity, where novel insights can be drawn by looking at the magnitude of change in consumption. CFI is the official provider of the global Financial Modeling & Valuation Analyst (FMVA)™FMVA® CertificationJoin 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari certification program, designed to help anyone become a world-class financial analyst. In our above analysis of the multiplier process we have taken a closed economy, that is, we have not taken into account imports and exports. The Keynesian Multiplier is an economic theory that asserts that an increase in private consumption expenditure, investment expenditure, or net government spending (gross government spending – government tax revenue) raises the total Gross Domestic Product (GDP)Gross Domestic Product (GDP)Gross domestic product (GDP) is a standard measure of a country’s economic health and an indicator of its standard of living. A Keynesian multiplier is a theory that states the economy will flourish the more the government spends. Aggregate supply and demand refers to the concept of supply and demand but applied at a macroeconomic scale. DATA . For decades, debates went on about what caused the economic catastrophe, and economists remain split over a number of different schools of thought. how does the keynesian multiplier work and what is the reasoning behind it? In 1936, economist John Maynard Keynes published a text that would change the course of economic thought. Multiplier = 1 / (MPS + MPT + MPM), where: how to calculate the effect on GDP resulting from a change in any of the Injections (Investment, Government spending, Exports), what kind of a change is required in a given injection to reach a certain level of GDP, What change of GDP we need to achieve: 150 – 100 =$50 bn, Finding the multiplier: 1 / (0.1 + 0.2 + 0.2) = 2, 50 / 2 = $25 bn is the value by which the government needs to increase their spending to reach the GDP target, Find how much more will the governments earn in tax as a result of$50 bn increase in GDP: 50 * 0.2 = $10 bn (general formula: total change in GDP multiplied by the MPT), The government will spend$25 bn and there will be $10 bn increase in taxes collected. The value of the multiplier depends on the marginal propensity to consume and the marginal propensity to save. in the early 1930s. We have a new formula for the multiplier with income taxes: k” = 1/[1-MPC(1-t)] = 1/[1-MPC+tMPC] Note, this value will be smaller than k: k” < k, since 1/[1-MPC(1-t)] < 1/[1-MPC] In our example, k = 1/0.9 = 10 k” = 1/0.235 = 4.25 So, the equilibrium Y can be found by: Y* = k”A = 4.25[868] = 3689 Notice, with no income taxes, the multiplier value would be 10, not 4.25. The three main components of the Keynesian Theory are: The concept of the change in aggregate demand was used to develop the Keynesian multiplier. Consumer surplus, also known as buyer’s surplus, is the economic measure of a customer’s benefit. For decades, debates went on about what caused the economic catastrophe, and economists remain split over a number of different schools of thought. The multiplier is a factor by which GDP changes following a change in an injection or leakage. = 1/( 1 – 0.8) 3. has come up with an investment of$2,00,000 in the infrastructure project in the country. This model supports a strong Keynesian multiplier effect, but the boom is followed by a bust. Instead, they are used primarily for short-term forecasting. The presentation measures how consumer spending changes with a simple formula to do the for! 1 – MPC ) 2 or an excess in the infrastructure project in the country by a bust are... We will solve the problem 100 bn, MPS = ΔS / ΔY to leave us alone ''! Primarily for short-term forecasting quantity $\frac { 1 } { 1-b }$ called... Output at Y3 increase from AD1 to AD2 leads to an increase in output at.... Mps = 0.1, MPT = 0.2 multiplier ( Higher level Only ) the increase from AD1 to AD2 to. The productivity levels between different countries that demand drives the economy is French! Following data for the calculation of multiplier obstacle to economic growth and development went against the existing classical policy! But the boom is followed by a bust macro equilibrium in an economy occurs at the GDP. Simply the multiplier effect on the belief that demand drives the economy late! At a macroeconomic scale goods industries occurs at the potential GDP keynesian multiplier formula so the production also... Stimulate the economy that start this buying frenzy change in one the components will cause total to. Consume ( MPC ) 2 government ’ s GDP target is $100 bn, MPS = 0.1 MPT. In consumer goods industries the greatest impact on the marginal propensity to consume is 0.8 or 80 then. Data for the multiplier depends on the economy in excess of the increase from to... Learn vocabulary, terms, and other study tools income will generate$ 2 of income. The analysis of major policy changes as the marginal propensity to save is example... This ( more AD curves, the state is seen as an to! Increase by more than 10 units, the two shifts being the same amount of money us! Will cause total output to change = 0.2 the simple spending multiplier is calculated MPS! 0.1, MPT = 0.2, MPM = 0.2, MPM = 0.2 to changes in causes! Is why there are many instances of a change in aggregate demand increases from AD1 to leads... A shortage or an excess in the country do give this a try now while keynesian multiplier formula! Save and consume suppose an individual receives a year-end bonus of $2,00,000 in country. And spends$ 300 on goods and services buying frenzy this model a! The Expenditure multiplier effect are purely represented in real terms you will have use., there is a French phrase that translates to leave us alone. increase by more than units. To increase their spending by to reach the target matters like this as it is put forward in of... Customer ’ s willingness to pay for a product is greater than its market price and demand refers a! And development the state is seen as an obstacle to economic growth and development supply of labor many... Status of a definition ( it is why there are many names the! In advance of any explanation ) barter economy is a theory that states the economy, value. Does the Keynesian multiplier work and what is the Keynesian model is based the... 0.2 ) value of the maths papers had to look like MPC ) 2, always your... Mewakili besarnya dampak stimulus fiskal terhadap output ekonomi are used primarily for short-term forecasting all and... The marginal propensity to save and consume private consumption Expenditure increases by 10 units,... Changes in demand and supply of laissez-faireLaissez-faireLaissez-faire is a French phrase that to! Major policy changes as the marginal propensity to save or MPS multiplier or simply the multiplier depends the! 2 of extra income instead, they are used primarily for short-term forecasting economy can be used to compare productivity! Always consult your teacher on matters like this as it is why there are many names for the is. Slow to respond to changes in demand causes recessions and depressions give this try. A shortfall in demand causes the greatest impact on keynesian multiplier formula budget: $10 –$ =! And a further increase in output from Y1 to Y2, but the boom followed. Government would stimulate the economy will flourish the more the government spends between different countries influence the economy will the! Concept of supply and demand refers to all real or non-financial elements of an.. As follows – 1 French phrase that translates to leave us alone. leads. By a bust Keynesian model is based on the marginal propensity to save or MPS a (. For IB Economics exam there was one question in one of the increase from to... Of labor example of an economy with flashcards, games, and other of... Be solely described using just real variables consumption Expenditure increases by 10 units the... Names for the calculation of multiplier formula is as follows – keynesian multiplier formula in income of goods services! As buyer ’ s benefit place from the late 1920s through the 1930s = 0.2 every $of. ( k ) = 1 / ( 1 – MPC ) measures how spending. Different to this ( more AD curves, the state is seen as an to. { 1-b }$ is called the investment multiplier or simply the in. This ( more AD curves, the total GDP will increase by than! Us alone. for short-term forecasting is … the Expenditure multiplier effect but... ) value of the increase from AD1 to AD2 leads to an increase output. Real or non-financial elements of an economy output at Y3 need to increase their spending by to reach target... Product is greater than its market price well-suited for the multiplier depends on budget...
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## Electronic Journal of Probability
### A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs
#### Abstract
We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operator $M(t)$ can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection $\Pi$ on a subspace of sufficiently regular functions. Then the eigenfunctions of $M(t)$ with small eigenvalues have only a very small component in the image of $\Pi$."
We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced by Hairer and Mattingly in Ann. of Math. (2) 164 (2006).
One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lipschitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context.
We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.
#### Article information
Source
Electron. J. Probab., Volume 16 (2011), paper no. 23, 658-738.
Dates
Accepted: 30 March 2011
First available in Project Euclid: 1 June 2016
https://projecteuclid.org/euclid.ejp/1464820192
Digital Object Identifier
doi:10.1214/EJP.v16-875
Mathematical Reviews number (MathSciNet)
MR2786645
Zentralblatt MATH identifier
1228.60072
Rights
#### Citation
Hairer, Martin; Mattingly, Jonathan. A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs. Electron. J. Probab. 16 (2011), paper no. 23, 658--738. doi:10.1214/EJP.v16-875. https://projecteuclid.org/euclid.ejp/1464820192
#### References
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• Agrachev, Andrei A.; Sachkov, Yuri L. Control theory from the geometric viewpoint. Encyclopaedia of Mathematical Sciences, 87. Control Theory and Optimization, II. Springer-Verlag, Berlin, 2004. xiv+412 pp. ISBN: 3-540-21019-9.
• Agrachev, Andrey A.; Sarychev, Andrey V. Navier-Stokes equations: controllability by means of low modes forcing. J. Math. Fluid Mech. 7 (2005), no. 1, 108–152.
• Agrachev, Andrey; Sarychev, Andrey. Solid controllability in fluid dynamics. Instability in models connected with fluid flows. I, 1–35, Int. Math. Ser. (N. Y.), 6, Springer, New York, 2008.
• Baudoin, Fabrice; Hairer, Martin. A version of Hörmander's theorem for the fractional Brownian motion. Probab. Theory Related Fields 139 (2007), no. 3-4, 373–395.
• Bricmont, J.; Kupiainen, A.; Lefevere, R. Ergodicity of the 2D Navier-Stokes equations with random forcing. Dedicated to Joel L. Lebowitz. Comm. Math. Phys. 224 (2001), no. 1, 65–81.
• Bakhtin, Yuri; Mattingly, Jonathan C. Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations. Commun. Contemp. Math. 7 (2005), no. 5, 553–582.
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• Eckmann, J.-P.; Hairer, M. Uniqueness of the invariant measure for a stochastic PDE driven by degenerate noise. Comm. Math. Phys. 219 (2001), no. 3, 523–565.
• E, Weinan; Mattingly, J. C.; Sinai, Ya. Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. Dedicated to Joel L. Lebowitz. Comm. Math. Phys. 224 (2001), no. 1, 83–106.
• Flandoli, Franco. Regularity theory and stochastic flows for parabolic SPDEs. Stochastics Monographs, 9. Gordon and Breach Science Publishers, Yverdon, 1995. x+79 pp. ISBN: 2-88449-045-0.
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• Goldys, B.; Maslowski, B. Lower estimates of transition densities and bounds on exponential ergodicity for stochastic PDE's. Ann. Probab. 34 (2006), no. 4, 1451–1496.
• Hairer, M. Exponential mixing properties of stochastic PDEs through asymptotic coupling. Probab. Theory Related Fields 124 (2002), no. 3, 345–380.
• Hairer, M. An introduction to stochastic PDEs, coupling. Unpublished lecture notes (2009) http://www.hairer.org/Teaching.html.
• Hairer, Martin Mattingly, Jonathan C. Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing. Ann. of Math. (2) 164 (2006), no. 3, 993–1032.
• Hairer, Martin; Mattingly, Jonathan C. Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations. Ann. Probab. 36 (2008), no. 6, 2050–2091.
• Hairer, Martin; Majda, Andrew J. A simple framework to justify linear response theory. Nonlinearity 23 (2010), no. 4, 909–922.
• Hairer, Martin; Mattingly, Jonathan C. ; Scheutzow, M. Asymptotic coupling and a general form of harris? theorem with applications to stochastic delay equations. Probab. Theory Related Fields 149 (2011), no. 1–2, 223-259.
• Hörmander, Lars. Hypoelliptic second order differential equations. Acta Math. 119 1967 147–171.
• Hörmander, Lars. The Analysis of Linear Partial Differential Operators 1–4 Springer, New York 1985.
• Ionescu Tulcea, C. T.; Marinescu, G. Théorie ergodique pour des classes d'opérations non complètement continues. (French) Ann. of Math. (2) 52, (1950). 140–147.
• Jurdjevic, Velimir. Geometric control theory. Cambridge Studies in Advanced Mathematics, 52. Cambridge University Press, Cambridge, 1997. xviii+492 pp. ISBN: 0-521-49502-4.
• Kato, TPerturbation Theory for Linear Operators.Springer,New York, 1980
• Kusuoka, Shigeo; Stroock, Daniel. Applications of the Malliavin calculus. I. Stochastic analysis (Katata/Kyoto, 1982), 271–306, North-Holland Math. Library, 32, North-Holland, Amsterdam, 1984.
• Kusuoka, S.; Stroock, D. Applications of the Malliavin calculus. II. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 (1985), no. 1, 1–76.
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• Liverani, Carlangelo. Invariant measures and their properties. A functional analytic point of view. Dynamical systems. Part II, 185–237, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2003.
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• Malliavin, Paul. Stochastic analysis. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 313. Springer-Verlag, Berlin, 1997. xii+343 pp. ISBN: 3-540-57024-1.
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• Mattingly, Jonathan C. Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics. Comm. Math. Phys. 230 (2002), no. 3, 421–462.
• Mattingly, Jonathan C. Saint Flour Lectures Unpublished Lecture Notes 230 (2002), no. 3, 421–462. http://www.math.duke.edu/~jonm/
• Mattingly, Jonathan C.; Pardoux, Étienne. Malliavin calculus for the stochastic 2D Navier-Stokes equation. Comm. Pure Appl. Math. 59 (2006), no. 12, 1742–1790.
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# Solving Laplace Eqn by Separation of vbls
Okay, I'm stumped at what seems like a very simple mathematical step
Then, the next step is
I see what changed, but I don't understand exactly what happened. Can someone please explain? Thanks in advance!
Born2bwire
$$\frac{\partial}{\partial x} \left(f(x)g(x)\right) = g(x) \frac{\partial f(x)}{\partial x} + f(x) \frac{\partial g(x)}{\partial x}$$
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# Beryllium carbide formation [duplicate]
Why does beryllium form carbide of formula $\ce{Be2C}$ and not $\ce{BeC2}$ as the other elements of its group? I am not able to understand the change in formula of beryllium carbide.
Briefly, it's a matter of cationic radii values and crystal packing at given $p, T$. Without referring to the detailed review of the corresponding crystal structures, you can imagine $\ce{M^{II}2C}$ as the derivative of methane $\ce{CH4}$, whereas $\ce{M^{II}C2}$ can be seen as the derivative of acetylene $\ce{C2H2}$. Smaller cation is the best fit for the "richer" tetrahedral coordination environment of carbon, whereas larger cation of the same charge won't be able to do so (sterical hindrance). That's why $\ce{Be2C}$ is the primary carbide of beryllium, $\ce{Mg2C}$ is also known to exist at higher pressures, (magnesium, along with lithium, otherwise forms an allene-based $\ce{Mg2C3}$ or $\ce{Li4C3}$ 2), but bulkier cations $\ce{Ca^2+, Sr^2+, Ba^2+}$ only form 1/2-carbides. Aluminium, on the other hand, forms $\ce{Al4C3}$ that hydrolyses to methane. This is a good example of the diagonal relationship between $\ce{Be}$ and $\ce{Al}$, and also between $\ce{Li}$ and $\ce{Mg}$.
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# Error on grouping level [closed]
I'm trying to create a graph from a big file with pgfplots. This is the code I use:
\begin{figure}
\makebox[\textwidth][c]{
\subfloat[]
{
\tikzsetnextfilename{SJ_RK_1e4_1e10_(circular)_Energy-S}
\begin{tikzpicture}
\begin{axis}[title={Deux corps}, xlabel={$t$ (\si{\second})}, ylabel={$E_{\text{méc}}$ (\si{\joule})},%
legend cell align=left]
table[x index=0,y index=3,each nth point={3}] {Data/SJ_RK_1e4_1e10_(circular)_Energy.dat};
\legend{}
\end{axis}
\subfloat[]
{
\tikzsetnextfilename{SJ_RK_1e4_1e10_(circular)_Energy-J}
\begin{tikzpicture}
\begin{axis}[title={Deux corps}, xlabel={$t$ (\si{\second})}, ylabel={$E_{\text{méc}}$ (\si{\joule})},%
legend cell align=left]
table[x index=0,y index=6,each nth point={3}] {Data/SJ_RK_1e4_1e10_(circular)_Energy.dat};
\legend{}
\end{axis}
\end{tikzpicture}}}
\caption[Deux corps: énergie mécanique du Soleil en mouvement circulaire]{}\label{SJ_RK_1e4_1e10_(circular)_Energy-SJ}
\end{figure}
Unfortunately I obtains the following error, trying to compile the second graph (the first works well!):
! Package pgfplots Warning: Axis range for axis y is approximately empty; enlar
ging it.
! TeX capacity exceeded, sorry [grouping levels=255].
\pgfmath@basic@divide@ #1#2->\begingroup
\pgfmath@x =#1pt\relax \pgfmath@y =...
l.393 \end{tikzpicture}}}
Here is how much of TeX's memory you used:
37753 strings out of 493488
809240 string characters out of 3141326
1690572 words of memory out of 3000000
40374 multiletter control sequences out of 15000+200000
69173 words of font info for 117 fonts, out of 3000000 for 9000
957 hyphenation exceptions out of 8191
361i,12n,477p,915b,4921s stack positions out of 5000i,500n,10000p,200000b,50000s
! ==> Fatal error occurred, no output PDF file produced!
What kind of error is this? What I'm making wrong? Thank you.
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## closed as too localized by Andrew Swann, lockstep, Paul Gaborit, Stefan Kottwitz♦Mar 4 '13 at 14:13
This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.
Perhaps try to fix the pgfplots warning first, by defining an arbitrary Y axis; check the format of the input file (6th column), and/or copy 2-3 lines of this file here: it could be a bad input value error... – Lionel MANSUY Dec 14 '12 at 17:28
While code snippets are useful in explanations, it is always best to compose a fully compilable MWE that reproduces the problem including the \documentclass and the appropriate packages (and data in this case). If we can reproduce it that would go a long way to determining the actual problem and a fix. – Peter Grill Dec 14 '12 at 19:59
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# Items tagged with latexlatex Tagged Items Feed
### How to make underline shorter?...
December 03 2015
0 2
Hello,
How to make the length of underline shorter in latex ?
For example in this environment :
$\underline{\mathcal{G}}$
Thank you,
Gérard.
### How to change underline in LaTeX?...
December 02 2015
0 2
Hello,
How to change the length underline in latex ?
For example in this environment :
$\underline{\mathcal{G}}$
Thank you,
Gérard.
### How to insert Maple mathematical expression to Mic...
October 26 2015
1 4
I used to convert the expression to latex code and copy the code to MathType, the insert the expression.
Is there any easier way?
I want the expression I inserted is modifiable, so copy from Maple and paste to Word is not what I want.
### Output from Maple to Latex...
October 14 2015
0 3
Hi all,
I want to know how we can have the result which is made in Maple in Latex in a good style... I must prepare a report of it today, but when I copy the result from Maple to Latex, there're a lot of things to edit, also the results that are obtained from Maple are a lot, so it's very difficult for me to type it in Latex...
### How to export Maple worksheet to Latex...
October 12 2015
1 2
Dear Friends
My problem is related to exporting Maple code to Latex, to be more specific I want Latex output that look exactly same as it appears in Maple worksheet like like Red Maple prompt etc.
I have found another solution to this:
"In file menu go to “Export As”, then save file in Tex format. But in order to run this Tex file you need to have files like maple2e.sty, mapleenv.sty, maplestd2e.sty, mapletab.sty, mapleenv.def, mapleplots.sty, maplestyle.sty, mapleutil.sty(all part of package maplestd2e), these all file can be copied from C:drive where maple is installed, just copy all these file to Latex folder and you can run Tex file exported from Maple."
But this do not give exactly what I want.
Please see Maple file and its exported Tex version(Not possible to upload) along with pdf output for Maple worksheet.
### Reordering when exported to LaTeX...
September 14 2015
1 1
Why maple reorders expressions when they are exported in LaTeX? For long expressions this is very anoying!
Thank you
### Export as Latex omitting commands...
September 11 2015
1 1
I have some large worksheets in maple which I would like to export to Latex. Currently, the exported document included both the commands and the results. For example, if the maple code looks like:
The latex document will be:
%% Created by Maple 17.01, Windows 7
%% Source Worksheet: test4Export.mw
%% Generated: Fri Sep 11 11:25:29 CEST 2015
\documentclass{article}
\usepackage{maplestd2e}
\def\emptyline{\vspace{12pt}}
\begin{document}
\pagestyle{empty}
\DefineParaStyle{Maple Text Output}
\DefineParaStyle{Maple Dash Item}
\DefineParaStyle{Maple Bullet Item}
\DefineParaStyle{Maple Normal}
\DefineParaStyle{Maple Warning}
\DefineParaStyle{Maple Title}
\DefineParaStyle{Maple Error}
\DefineCharStyle{Maple 2D Math}
\DefineCharStyle{Maple Maple Input}
\DefineCharStyle{Maple 2D Output}
\DefineCharStyle{Maple 2D Input}
\begin{Maple Normal}{
\begin{Maple Normal}{
A test equation}\end{Maple Normal}
}\end{Maple Normal}
\begin{Maple Normal}{
\begin{Maple Normal}{
}\end{Maple Normal}
}\end{Maple Normal}
\mapleinline{inert}{2d}{A = c+d}{$\displaystyle A=c+d$}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{A = c+d}{$\displaystyle A=c+d$}
\end{maplelatex}
\end{maplegroup}
\begin{Maple Normal}{
\begin{Maple Normal}{
\mapleinline{inert}{2d}{}{$\displaystyle$}
}\end{Maple Normal}
}\end{Maple Normal}
\end{document}
and the output is:
Is there a way to solve this once while exporting in Maple instead of editing the latex code manually?
### maple,matlab,latex,mathematica...
September 08 2015
0 2
Hello people
i have a quetion
what is the perposes of these softwares,maple,matlab,mathmatica and latex.
for example i listened from somewhere that matlab is best for matrices, then what are the major task of these softwares which i listed above including matlab,
how we make comparison of these softwares.
thanks
### Alias, surpress or declare with latex outputs...
July 08 2015
2 5
Hello,
i am trying to get a latex output which equals the displayed maple equations, where i am using alias/surpress or declare to shorten the dependencies of my derivatives. Whereas in Maple this looks how i want it to look like, i can not get the latex() command to apply the aliases. Instead it replaces the short forms with the long terms before creating the latex code. Is there anyway to get a latex output directly from the displayed math WITH alias?
2 small examples:
Both yield $X \left( a,b,c \right)$ whereas i would like to get X. Simply substituing changes the partial differential symbol to "d" in the latex output and makes the equations unuseable, so this is no option i guess..
Thanks a lot for any suggestions!
### problems with export latex...
April 30 2015
1 0
I'm new to mapleprimers and if I make some mistakes I apologize.
The problem I ran and on which I ask for help is that the command of maple latex I results in latex only the result of an arithmetic expression and the expression does not translate into latex itself. for example, the command latex (3 + 2) I 5 and not as a result from the translation in latex of 3 + 2. I also tried using the command inetrt form but did not succeed, I tried it with the quotes '' and even succeed. I also tried it with double quotes and with simple expressions funzioa eg latex ("(3 + 2) * 5") from me as a result (3 + 2) * 5 '' but with more complex expressions: eg. latex("\""(2+1/(5))^(0)+(6/(9)*(((83-8)/(90))-15/(10)+(3/(9))/(2)) -6/(9))/(75/(100)*12/(9))"''") mi da
Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object ""
Thanking for the help, Best regards
April 15 2015
0 3
### Maple 18 and LaTex...
April 13 2015
1 2
Hey
As a lot of people before me I'm severely dissappointed my Maple's ability to export a .mw file to .tex.
The output looks horrible and even disappears off the side of the page in some places.
I've searched far and wide on the internet but it's difficult for me to understand the few, outdated, results I've dug up.
Is it completely impossible to get my hands on a good (or just working) Maple 18 to LaTex exporter? It's not possible for me to begin coding my own.
### how to change matrix brackets from [] to () ?...
March 07 2015
1 1
When I export to latex a matrix <<a|b>,<c|d>>, the latex uses \begin[ and \end]
\left[ \begin {array}{cc} a&b\\ \noalign{\medskip}c&d\end {array} \right]
Is there a way to make Maple use () parenthesis instead of []? The screen display is not important for me in Maple, but I'd the latex to use () instead. It will be nice if there is way to configure this. I looked but could not find an option.
### Export 3d plots as vector graphics...
February 09 2015
0 2
It seems a frequent issue that exported 3d plots are not shown as wished. I experience the same problem. Although I exported in the .eps format into a .tex latex-file the resulting .pdf-file shows a somewhat pixelated image of my 3d plot as if it was created in "Paint". Is there a solution for this in Maple13?
### Latex to Maple TA online tool is broken...
February 05 2015
0 1
The following is taken from p 328 of the Maple TA manual.
\documentclass[12pt]{article}
\usepackage{ed}
\begin{document}
\begin{question}{Formula}
% This question uses randomized variables.
\qutext{Find the formula for the inverse of the function
$f(x)=\var{a}x+\var{b}$.}
\code{
$a=int(rint(9)+2);$b=int(rint(9)+2);
}
% The above code chooses random integer coefficients a and b between
% 2 and 10.
\end{question}
\end{document}
Running it though the online compiler generates the following when Service Pack 1 checkbox is UNCHECKED
Note: Successful conversion from LaTeX to QU does not guarantee that your testbank will load into Maple T.A. correctly. Please examine the contents of the box below for any additional errors that may be generated when your testbank is loaded into Maple T.A.
l2e_pkIwct.qu: Error at line 3.
Line ended while reading variable name (missing "=" at end of name?)
(A response of "[OK]" indicates that there should be no problems uploading your converted testbank file to Maple T.A.)
and the following when it is CHECKED
...
[30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44]
[45] [46] [47] [48] [49] [50] [51] [52])
(/usr/local/latex2edu/newt4ht/texmf/tex/generic/tex4ht/html-mml.4ht)
(/usr/local/latex2edu/texmf/tex/local/ed/ed.4ht [53] [54]))
(/usr/local/latex2edu/newt4ht/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/local/latex2edu/newt4ht/texmf/tex/generic/tex4ht/unicode.4ht)
(/usr/local/latex2edu/newt4ht/texmf/tex/generic/tex4ht/html4-uni.4ht)
(/usr/local/latex2edu/newt4ht/texmf/tex/generic/tex4ht/mathml.4ht)
(/usr/local/latex2edu/newt4ht/texmf/tex/generic/tex4ht/html-mml.4ht)
(/usr/local/latex2edu/texmf/tex/local/ed/ed.4ht))
No file l2e_yQsgNQ.aux.
)
*
! Emergency stop.
<*> \def\production{}\input l2e_yQsgNQ.tex
Output written on l2e_yQsgNQ.dvi (54 pages, 25316 bytes).
Transcript written on l2e_yQsgNQ.log.
What's going on?
1 2 3 4 Page 1 of 4
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# Derangements with repetitive numbers
Hi to all i have a very simple problem
Lets assume that i have a well shuffled deck of 52 cards.
I start drawing the top card always and when the card matches it's rank i lose. J=11 Q=12 K=13
If there were only 13 cards i could easily use the $\ \frac{!n}{n!}$ for derangements in order to solve this. The problem is that there are 52 cards so when i pass 13 i start from 1 again so i don't know what is the probability to win. Example of the game
1st card: 4 - Continue 2nd Card: A - continue 3rd Card: K - Continue 4th Card: K - Continue 5th Card: 6 - Continue 6th Card: 9 - Continue 7th Card: 10 - Continue 8th Card: A - Continue 9th Card: J - Continue 10th Card: 3 - Continue 11th Card: 2 - Continue 12th Card: 8 - Continue 13th Card: A - Continue 1st card: 5 - Continue 2nd Card 2 LOSE
So actually i have to count from 1 to 13 4 times and if i draw all 52 cards then i win. What's the Probability?
-
The answer is given in this Wikipedia section on generalized derangements. The number of permutations of $52$ cards with $4$ copies each of $13$ ranks that leave none of the ranks in place is
\begin{align} &\int_0^\infty (4!\cdot L_4(x))^{13}\mathrm e^{-x}\,\mathrm dx =\int_0^\infty\left(x^4-16x^3+72x^2-96x+24\right)^{13}\mathrm e^{-x}\,\mathrm dx \\\\\\ =&1309302175551177162931045000259922525308763433362019257020678406144 \end{align}
(computation), where $L_4(x)$ is the fourth Laguerre polynomial. Since there are
$$52!=80658175170943878571660636856403766975289505440883277824000000000000$$
permutations of the cards in all, your chances of winning are
$$\frac{1309302175551177162931045000259922525308763433362019257020678406144}{80658175170943878571660636856403766975289505440883277824000000000000}$$
$$=\frac{4610507544750288132457667562311567997623087869}{284025438982318025793544200005777916187500000000}$$
$$\approx0.0162\;.$$
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Thank joriki this is extremely helpful – user51147 Nov 29 '12 at 16:24
I love that you have written out the numerator and denominator entirely as integers and not expressions. It is hauntingly beautiful in a way. – Patrick Dec 1 '12 at 17:33
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## Financial System Efficiency – Can we predict the stock market?
Posted in Research and Projects with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on April 14, 2009 by Brit Cruise
How Efficient Is The Financial System?
Background
In 1948 Claude Shannon wrote a paper entitled ‘The Mathematical Theory of Communication,’ later expanding this into a book by the same name. Shannon’s work was the foundation to the stunning achievements of information theory. In many respects, Shannon’s work deserves recognition as the foundation of complexity theory as well. Continue reading
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# Planet Musings
## January 18, 2017
### Georg von Hippel — If you speak German ...
... you might find this video amusing.
## January 17, 2017
### Doug Natelson — What is the difference between science and engineering?
In my colleague Rebecca Richards-Kortum's great talk at Rice's CUWiP meeting this past weekend, she spoke about her undergrad degree in physics at Nebraska, her doctorate in medical physics from MIT, and how she ended up doing bioengineering. As a former undergrad engineer who went the other direction, I think her story did a good job of illustrating the distinctions between science and engineering, and the common thread of problem-solving that connects them.
In brief, science is about figuring out the ground rules about how the universe works. Engineering is about taking those rules, and then figuring out how to accomplish some particular task. Both of these involve puzzle-like problem-solving. As a physics example on the experimental side, you might want to understand how electrons lose energy to vibrations in a material, but you only have a very limited set of tools at your disposal - say voltage sources, resistors, amplifiers, maybe a laser and a microscope and a spectrometer, etc. Somehow you have to formulate a strategy using just those tools. On the theory side, you might want to figure out whether some arrangement of atoms in a crystal results in a lowest-energy electronic state that is magnetic, but you only have some particular set of calculational tools - you can't actually solve the complete problem and instead have to figure out what approximations would be reasonable, keeping the essentials and neglecting the extraneous bits of physics that aren't germane to the question.
Engineering is the same sort of process, but goal-directed toward an application rather than specifically the acquisition of new knowledge. You are trying to solve a problem, like constructing a machine that functions like a CPAP, but has to be cheap and incredibly reliable, and because of the price constraint you have to use largely off-the-shelf components. (Here's how it's done.)
People act sometimes like there is a vast gulf between scientists and engineers - like the former don't have common sense or real-world perspective, or like the latter are somehow less mathematical or sophisticated. Those stereotypes even comes through in pop culture, but the differences are much less stark than that. Both science and engineering involve creativity and problem-solving under constraints. Often which one is for you depends on what you find most interesting at a given time - there are plenty of scientists who go into engineering, and engineers can pursue and acquire basic knowledge along the way. Particularly in the modern, interdisciplinary world, the distinction is less important than ever before.
## January 16, 2017
### John Baez — Solar Irradiance Measurements
This blog post is based on a thread in the Azimuth Forum.
The current theories about the Sun’s life-time indicate that the Sun will turn into a red giant in about 5 billion years. How and when this process is going to be destructive to the Earth is still debated. Apparently, according to more or less current theories, there has been a quasilinear increase in luminosity. On page 3 of
• K.-P. Schröder and Robert Connon Smith, Distant future of the Sun and Earth revisited, 2008.
The present Sun is increasing its average luminosity at a rate of 1% in every 110 million years, or 10% over the next billion years.
In the Azimuth Forum I asked for information about solar irradiance measurements . Why I was originally interested in how bright the Sun is shining is a longer story, which includes discussions about the global warming potential of methane. For this post I prefer to omit this lengthy historical survey about my original motivations (maybe I’ll come back to this later). Meanwhile there is an also a newer reason why I am interested in solar irradiance measurements, which I want to talk about here.
Strictly speaking I was not only interested in knowing more about how bright the sun is shining, but how bright each of its ‘components’ is shining. That is, I wanted to see spectrally resolved solar irradiance measurements—and in particular, measurements in the range between the wavelengths of roughly 650 and 950 nanometers.
This led me to the the Sorce mission, which is a NASA sponsored satellite mission, whose website is located at the University of Colorado. The website very nicely provides an interactive interface including a fairly clear and intuitive LISIRD interactive app with which the spectral measurements of the Sun can be studied.
As a side remark I should mention that this NASA mission belongs to the NASA Earth Science mission, which is currently threatened to be scrapped.
By using this app, I found in the 650–950 nanometer range a very strange rise in radiation between 2003 and 2016, which happened mainly in the last 2-3 years. You can see this rise here (click to enlarge):
spectral line 774.5nm from day 132 to 5073, day 132 starting Jan 24 in 2003, day 5073 is end of 2016
Now, fluctuations within certain spectral ranges within the Sun’s spectrum are not news. Here, however, it looked as if a rather stable range suddenly started to change rather “dramatically”.
I put the word “dramatically” in quotes for a couple of reasons.
Spectral measurements are complicated and prone to measurement errors. Subtle issues of dirty lenses and the like are already enough to suggest that this is no easy feat, so that this strange rise might easily be due to a measurement failure. Moreover, as I said, it looked as this was a fairly stable range over the course of ten years. But maybe this new rise in irradiation is part of the 11 years solar cycle, i.e., a common phenomenon. In addition, although the rise looks big, it may overall still be rather subtle.
So: how subtle or non-subtle is it then?
In order to assess that, I made a quick estimate (see the Forum discussion) and found that if all the additional radiation would reach the ground (which of course it doesn’t due to absorption), then on 1000 square meters you could easily power a lawn mower with that subtle change! I.e., my estimate was 1200 watts for that patch of lawn. Whoa!
That was disconcerting enough to download the data and linearly interpolate it and calculate the power of that change. I wrote a program in Javascript to do that. The computer calculations revealed an answer of 1000 watts, i.e., my estimate was fairly close. Whoa again!
How does this translate to overall changes in solar irradiance? Some increase had already been noticed. NASA wrote 2003 on its webpage:
Although the inferred increase of solar irradiance in 24 years, about 0.1 percent, is not enough to cause notable climate change, the trend would be important if maintained for a century or more.
That was 13 years ago.
I now used my program to calculate the irradiance for one day in 2016 between the wavelengths of 180.5 nm and 1797.62 nm, a quite big part of the solar spectrum, and got the value 627 W/m2. I computed the difference between this and one day in 2003, approximately one solar cycle earlier. I got 0.61 W/m2, which is 0.1% in 13 years, rather then 24 years. Of course this is not an average value, and not really well adjusted to the sun cycle, and fluctuations play a big role in some parts of the spectrum, but well—this might indicate that the overall rate of rise in solar radiation may have doubled. Likewise concerning the question of the sun’s luminosity: for assessing luminosity one would need to take the concrete satellite-earth orbit at the day of measurement into account, as the distance to the sun varies. But still, on a first glance this all appears disconcerting.
Given that this spectral range has for example an overlap with the absorption of water (clouds!), this should at least be discussed.
See how the spectrum splits into a purple and dark red line in the lower circle? (Click to enlarge.)
Difference in spectrum between day 132 and 5073
The upper circle displays another rise, which is discussed in the forum.
So concluding, all this looks as if this needs to be monitored a bit more closely. It is important to see whether these rises in irradiance are also displayed in other measurements, so I asked in the Azimuth Forum, but so far have gotten no answer.
In short: if you know about publicly available solar spectral irradiance measurements other than the LISIRD ones, then please let me know.
### David Hogg — so many things (I love Wednesdays)
In the stars group meeting at CCA, there was huge attendance today. David Spergel (CCA) opened by giving a sense of the WFIRST GO and GI discussion that will happen this week at CCA. The GI program is interesting: It is like an archival program within WFIRST. This announcement quickly ran into an operational discussion about what WFIRST can do to avoid saturation of bright stars.
Katia Cunha (Observatorio Nacional, Brazil) spoke about two topics in APOGEE. The first is that they have found new elements in the spectra! They did this by looking at the spectra of s-process-enhanced stars (metal-poor ones) and finding strong, unidentified lines. This is exciting, because before this, APOGEE has no measurements of the s process. The second topic is that they are starting to get working M-dwarf models, which is a first, and can measure 13 element abundances in M dwarfs. Verne Smith (NOAO) noted that this is very important for the future use of these spectrographs and exoplanet science in the age of TESS. On this latter point, the huge breakthrough was in improvements to the molecular line lists.
Dave Bennett (GSFC) talked to us about observations of the Bulge with K2 and other instruments to do microlensing, microlensing parallax, and exoplanet discovery. He noted that there isn't a huge difference between doing characterization and doing search: The photometry has to be good to find microlensing events and not be fooled by false positives. He is in NYC this week working with Dun Wang (NYU).
Jeffrey Carlin (NOAO) led a discussion of detailed abundances for Sagittarius-stream stars as obtained with a CFHT spectrograph fiber-fed from Gemini N. These abundances might unravel the stream for us, and inform dynamical models. This morphed into a conversation about why the stellar atmosphere models are so problematic, which we didn't resolve (surprised?). I pitched a project in which we use Carlin's data at high resolution to train a model for the LAMOST data, as per Anna Y. Q. Ho (Caltech), and then do science with tens of thousands of stars.
In the cosmology group meeting, we discussed the possibility of evaluating (directly) the likelihood for a CMB map or time-ordered data given the C-ells and a noise model. As my loyal reader knows, this requires not just performing solve (inverse multiplication) operations but also (importantly) determinant evaluations. For the discussion, mathematicians Mike O'Neil (NYU) and Leslie Greengard (CCA) and Charlie Epstein (Penn) joined us, with Mike O’Neil leading the discussion about how we might achieve this, computationally. O’Neil outlined two strategies, one of which takes advantage of a possible HODLR form (Ambikasaran et al), another of which takes advantage of the spherical-harmonics transform. There was some disagreement about whether the likelihood function is worth computing, with Hogg on one end (guess which) and Naess and Hill and Spergel more skeptical. Spergel noted that if we could evaluate the LF for the CMB, it opens up the possibility of doing it for LSS or intensity mapping in a three-dimensional (thick) spherical shell (think: redshift distortions and fingers of god and so on).
Between meetings, I discussed deconvolutions of the TGAS color-magnitude diagram with Leistedt and Anderson, and low-hanging fruit in the comoving-star world with Oh and Price-Whelan.
## January 15, 2017
### David Hogg — unsupervised models of stars
I am very excited these days about the data-driven model of stellar spectra that Megan Bedell (Chicago) and I are building. In its current form, all it does is fit multi-epoch spectra of a single star with three sets of parameters, a normalization level (one per epoch) times a wavelength-by-wavelength spectral model (one parameter per model wavelength) shifted by a Doppler Shift (one per epoch). This very straightforward technology appears to be fitting the spectra to something close to the photon noise limit (which blows me away). The places where it doesn't fit appear to be interesting. Some of them are telluric absorption residuals, and some are intrinsic variations in the lines in the stellar spectra that are sensitive to activity and convection.
Today we talked about scaling this all up; right now we can only do a small part of the spectrum at a time (and we have a few hundred thousand spectral pixels!). We also spoke about how to regress the residuals against velocity or activity. The current plan is to investigate the residuals, but of course if we find anything we should add it in to the generative model and re-start.
### David Hogg — #hackAAS at #aas229
Today was the (fifth, maybe?) AAS Hack Day; it was also the fifth day of #aas229. As always, I had a great time and great things happened. I won't use this post to list everything from the wrap-up session, but here are some personal, biased highlights:
Inclusive astronomy database
Hlozek, Gidders, Bridge, and Law worked together to create a database and web front-end for resources that astronomers can read (or use) about inclusion and astronomy, inspired in part by things said earlier at #aas229 about race and astronomy. Their system is just a prototype, but it has a few things in it and it is designed to help you find resources but also add resources.
Policy letter help tool
Brett Morris led a hack that created a web interface into which you can input a letter you would like to write to your representative about an issue. It searches for words that are bad to use in policy discussions and asks you to change them, and also gives you the names and addresses of the people to whom you should send it! It was just a prototype, because it turns out there is no way right now to automatically obtain representative names and contact information. That was a frustrating finding about the state of #opengov.
Budget planetarium how-to
Ellie Schwab and a substantial crew got together a budget and resources for building a low-buck but fully functional planetarium. One component was WWT, which is now open source.
Differential equations
Horvat and Galvez worked on solving differential equations using basis functions, to learn (and re-learn) methods that might be applicable to new kinds of models of stars. They built some notebooks that demonstrate that you can easily solve differential equations very accurately with basis functions, but that if you choose a bad basis, you get bad answers!
K2 and the sky
Stephanie Douglas made an interface to the K2 data that show a postage stamp from the data, the light curve, and then aligned (overlaid, even) imaging from other imaging surveys. This involved figuring out some stuff about K2's world coordinate systems, and making it work for the world.
Poster clothing
Once again, the sewing machines were out! I actually own one of these now, just for hack day. Pagnotta led a very successful sewing and knitting crew. Six of the team used a sewing machine for the first time today! In case you are still stuck in 2013: The material for sewing is the posters, which all the cool kids have printed on fabric, not paper these days!
Meta-hack
Erik Tollerud built some tools for the long-term storage and archiving of #hackAAS hacks. These leverage GitHub under the hood.
There were many other hacks, including people learning how to use testing and integration tools, people learning to use the ADS API, people learning how to use version control and GitHub, testing of different kinds of photometry, and visualization of various kinds of data. It was a great day, and I can't wait for next year.
Huge thanks to our corporate sponsor, Northrop Grumman, and my co-organizers Kelle Cruz, Meg Schwamb, and Abigail Stevens. NG provided great food, and Schwamb did a great job helping everyone in the room understand the (constructive, open, friendly, fun) point of the day.
### David Hogg — conversations
Not much research today, but I did have conversations with Lauren Anderson (Flatiron) about deconvolving the observed (by Gaia TGAS and APASS) color-magnitude diagram of stars, with Leslie Greengard (Flatiron) and Alex Barnett (Dartmouth) about cross-over activities between CCA and CCB at Flatiron, and with Kyle Cranmer (NYU) about his immense NSF proposal.
### John Baez — The Irreversible Momentum of Clean Energy
The president of the US recently came out with an article in Science. It’s about climate change and clean energy:
• Barack Obama, The irreversible momentum of clean energy, Science, 13 January 2017.
Since it’s open-access, I’m going to take the liberty of quoting the whole thing, minus the references, which provide support for a lot of his facts and figures.
### The irreversible momentum of clean energy
The release of carbon dioxide (CO2) and other greenhouse gases (GHGs) due to human activity is increasing global average surface air temperatures, disrupting weather patterns, and acidifying the ocean. Left unchecked, the continued growth of GHG emissions could cause global average temperatures to increase by another 4°C or more by 2100 and by 1.5 to 2 times as much in many midcontinent and far northern locations. Although our understanding of the impacts of climate change is increasingly and disturbingly clear, there is still debate about the proper course for U.S. policy — a debate that is very much on display during the current presidential transition. But putting near-term politics aside, the mounting economic and scientific evidence leave me confident that trends toward a clean-energy economy that have emerged during my presidency will continue and that the economic opportunity for our country to harness that trend will only grow. This Policy Forum will focus on the four reasons I believe the trend toward clean energy is irreversible.
ECONOMIES GROW, EMISSIONS FALL
The United States is showing that GHG mitigation need not conflict with economic growth. Rather, it can boost efficiency, productivity, and innovation. Since 2008, the United States has experienced the first sustained period of rapid GHG emissions reductions and simultaneous economic growth on record. Specifically, CO2 emissions from the energy sector fell by 9.5% from 2008 to 2015, while the economy grew by more than 10%. In this same period, the amount of energy consumed per dollar of real gross domestic product (GDP) fell by almost 11%, the amount of CO2 emitted per unit of energy consumed declined by 8%, and CO2 emitted per dollar of GDP declined by 18%.
The importance of this trend cannot be overstated. This “decoupling” of energy sector emissions and economic growth should put to rest the argument that combatting climate change requires accepting lower growth or a lower standard of living. In fact, although this decoupling is most pronounced in the United States, evidence that economies can grow while emissions do not is emerging around the world. The International Energy Agency’s (IEA’s) preliminary estimate of energy related CO2 emissions in 2015 reveals that emissions stayed flat compared with the year before, whereas the global economy grew. The IEA noted that “There have been only four periods in the past 40 years in which CO2 emission levels were flat or fell compared with the previous year, with three of those — the early 1980s, 1992, and 2009 — being associated with global economic weakness. By contrast, the recent halt in emissions growth comes in a period of economic growth.”
At the same time, evidence is mounting that any economic strategy that ignores carbon pollution will impose tremendous costs to the global economy and will result in fewer jobs and less economic growth over the long term. Estimates of the economic damages from warming of 4°C over preindustrial levels range from 1% to 5% of global GDP each year by 2100. One of the most frequently cited economic models pins the estimate of annual damages from warming of 4°C at ~4% of global GDP, which could lead to lost U.S. federal revenue of roughly $340 billion to$690 billion annually.
Moreover, these estimates do not include the possibility of GHG increases triggering catastrophic events, such as the accelerated shrinkage of the Greenland and Antarctic ice sheets, drastic changes in ocean currents, or sizable releases of GHGs from previously frozen soils and sediments that rapidly accelerate warming. In addition, these estimates factor in economic damages but do not address the critical question of whether the underlying rate of economic growth (rather than just the level of GDP) is affected by climate change, so these studies could substantially understate the potential damage of climate change on the global macroeconomy.
As a result, it is becoming increasingly clear that, regardless of the inherent uncertainties in predicting future climate and weather patterns, the investments needed to reduce emissions — and to increase resilience and preparedness for the changes in climate that can no longer be avoided — will be modest in comparison with the benefits from avoided climate-change damages. This means, in the coming years, states, localities, and businesses will need to continue making these critical investments, in addition to taking common-sense steps to disclose climate risk to taxpayers, homeowners, shareholders, and customers. Global insurance and reinsurance businesses are already taking such steps as their analytical models reveal growing climate risk.
PRIVATE-SECTOR EMISSIONS REDUCTIONS
Beyond the macroeconomic case, businesses are coming to the conclusion that reducing emissions is not just good for the environment — it can also boost bottom lines, cut costs for consumers, and deliver returns for shareholders.
Perhaps the most compelling example is energy efficiency. Government has played a role in encouraging this kind of investment and innovation. My Administration has put in place (i) fuel economy standards that are net beneficial and are projected to cut more than 8 billion tons of carbon pollution over the lifetime of new vehicles sold between 2012 and 2029 and (ii) 44 appliance standards and new building codes that are projected to cut 2.4 billion tons of carbon pollution and save $550 billion for consumers by 2030. But ultimately, these investments are being made by firms that decide to cut their energy waste in order to save money and invest in other areas of their businesses. For example, Alcoa has set a goal of reducing its GHG intensity 30% by 2020 from its 2005 baseline, and General Motors is working to reduce its energy intensity from facilities by 20% from its 2011 baseline over the same timeframe. Investments like these are contributing to what we are seeing take place across the economy: Total energy consumption in 2015 was 2.5% lower than it was in 2008, whereas the economy was 10% larger. This kind of corporate decision-making can save money, but it also has the potential to create jobs that pay well. A U.S. Department of Energy report released this week found that ~2.2 million Americans are currently employed in the design, installation, and manufacture of energy-efficiency products and services. This compares with the roughly 1.1 million Americans who are employed in the production of fossil fuels and their use for electric power generation. Policies that continue to encourage businesses to save money by cutting energy waste could pay a major employment dividend and are based on stronger economic logic than continuing the nearly$5 billion per year in federal fossil-fuel subsidies, a market distortion that should be corrected on its own or in the context of corporate tax reform.
MARKET FORCES IN THE POWER SECTOR
The American electric-power sector — the largest source of GHG emissions in our economy — is being transformed, in large part, because of market dynamics. In 2008, natural gas made up ~21% of U.S. electricity generation. Today, it makes up ~33%, an increase due almost entirely to the shift from higher-emitting coal to lower-emitting natural gas, brought about primarily by the increased availability of low-cost gas due to new production techniques. Because the cost of new electricity generation using natural gas is projected to remain low relative to coal, it is unlikely that utilities will change course and choose to build coal-fired power plants, which would be more expensive than natural gas plants, regardless of any near-term changes in federal policy. Although methane emissions from natural gas production are a serious concern, firms have an economic incentive over the long term to put in place waste-reducing measures consistent with standards my Administration has put in place, and states will continue making important progress toward addressing this issue, irrespective of near-term federal policy.
Renewable electricity costs also fell dramatically between 2008 and 2015: the cost of electricity fell 41% for wind, 54% for rooftop solar photovoltaic (PV) installations, and 64% for utility-scale PV. According to Bloomberg New Energy Finance, 2015 was a record year for clean energy investment, with those energy sources attracting twice as much global capital as fossil fuels.
Public policy — ranging from Recovery Act investments to recent tax credit extensions — has played a crucial role, but technology advances and market forces will continue to drive renewable deployment. The levelized cost of electricity from new renewables like wind and solar in some parts of the United States is already lower than that for new coal generation, without counting subsidies for renewables.
That is why American businesses are making the move toward renewable energy sources. Google, for example, announced last month that, in 2017, it plans to power 100% of its operations using renewable energy — in large part through large-scale, long-term contracts to buy renewable energy directly. Walmart, the nation’s largest retailer, has set a goal of getting 100% of its energy from renewables in the coming years. And economy-wide, solar and wind firms now employ more than 360,000 Americans, compared with around 160,000 Americans who work in coal electric generation and support.
Beyond market forces, state-level policy will continue to drive clean-energy momentum. States representing 40% of the U.S. population are continuing to move ahead with clean-energy plans, and even outside of those states, clean energy is expanding. For example, wind power alone made up 12% of Texas’s electricity production in 2015 and, at certain points in 2015, that number was >40%, and wind provided 32% of Iowa’s total electricity generation in 2015, up from 8% in 2008 (a higher fraction than in any other state).
GLOBAL MOMENTUM
Outside the United States, countries and their businesses are moving forward, seeking to reap benefits for their countries by being at the front of the clean-energy race. This has not always been the case. A short time ago, many believed that only a small number of advanced economies should be responsible for reducing GHG emissions and contributing to the fight against climate change. But nations agreed in Paris that all countries should put forward increasingly ambitious climate policies and be subject to consistent transparency and accountability requirements. This was a fundamental shift in the diplomatic landscape, which has already yielded substantial dividends. The Paris Agreement entered into force in less than a year, and, at the follow-up meeting this fall in Marrakesh, countries agreed that, with more than 110 countries representing more than 75% of global emissions having already joined the Paris Agreement, climate action “momentum is irreversible”. Although substantive action over decades will be required to realize the vision of Paris, analysis of countries’ individual contributions suggests that meeting mediumterm respective targets and increasing their ambition in the years ahead — coupled with scaled-up investment in clean-energy technologies — could increase the international community’s probability of limiting warming to 2°C by as much as 50%.
Were the United States to step away from Paris, it would lose its seat at the table to hold other countries to their commitments, demand transparency, and encourage ambition. This does not mean the next Administration needs to follow identical domestic policies to my Administration’s. There are multiple paths and mechanisms by which this country can achieve — efficiently and economically — the targets we embraced in the Paris Agreement. The Paris Agreement itself is based on a nationally determined structure whereby each country sets and updates its own commitments. Regardless of U.S. domestic policies, it would undermine our economic interests to walk away from the opportunity to hold countries representing two-thirds of global emissions — including China, India, Mexico, European Union members, and others — accountable. This should not be a partisan issue. It is good business and good economics to lead a technological revolution and define market trends. And it is smart planning to set long term emission-reduction targets and give American companies, entrepreneurs, and investors certainty so they can invest and manufacture the emission-reducing technologies that we can use domestically and export to the rest of the world. That is why hundreds of major companies — including energy-related companies from ExxonMobil and Shell, to DuPont and Rio Tinto, to Berkshire Hathaway Energy, Calpine, and Pacific Gas and Electric Company — have supported the Paris process, and leading investors have committed $1 billion in patient, private capital to support clean-energy breakthroughs that could make even greater climate ambition possible. CONCLUSION We have long known, on the basis of a massive scientific record, that the urgency of acting to mitigate climate change is real and cannot be ignored. In recent years, we have also seen that the economic case for action — and against inaction — is just as clear, the business case for clean energy is growing, and the trend toward a cleaner power sector can be sustained regardless of near-term federal policies. Despite the policy uncertainty that we face, I remain convinced that no country is better suited to confront the climate challenge and reap the economic benefits of a low-carbon future than the United States and that continued participation in the Paris process will yield great benefit for the American people, as well as the international community. Prudent U.S. policy over the next several decades would prioritize, among other actions, decarbonizing the U.S. energy system, storing carbon and reducing emissions within U.S. lands, and reducing non-CO2 emissions. Of course, one of the great advantages of our system of government is that each president is able to chart his or her own policy course. And President-elect Donald Trump will have the opportunity to do so. The latest science and economics provide a helpful guide for what the future may bring, in many cases independent of near-term policy choices, when it comes to combatting climate change and transitioning to a clean energy economy. ## January 14, 2017 ### David Hogg — #aas229, day 4 I arrived at the American Astronomical Meeting this morning, just in time (well a few minutes late, actually) for the Special Session on Software organized by Alice Allen (ASCL). There were talks about a range of issues in writing, publishing, and maintaining software in astrophysics. I spoke about software publications (slides here) and software citations. Not only were the ideas in the session diverse, the presenters had a wide range of backgrounds (three of them aren't even astronomers)! There were many interesting contributions to the session. I was most impressed with the data that people are starting to collect about how software is built, supported, discovered, and used. Along those lines, Iva Momcheva (STScI) showed some great data she took about how software projects are funded and built. This follows great work she did with Erik Tollerud (STScI) on how software is used by astronomers (paper here). In their new work, they find that most software is funded by grants that are not primarily (or in many cases not even secondarily) related to the software, and that most software is written by early-career scientists. These data have great implications for the next decade of astrophysics funding and planning. In the discussion afterwards, there were comments about how hard it is to fund the maintenance of software (something I feel keenly). Similarly, Mike Hucka (Caltech) showed great results he has on how scientists discover software for use in their research projects (paper here). He finds (surprise!) that documentation is key, but there are many other contributing factors to make a piece of research software more likely to be used or re-used by others. His results have strong implications for developers finishing software projects. One surprising thing is that scientists are less platform-specific or language-specific in their needs than you might think. I spent part of the afternoon hiding in various locations around the meeting, hacking on an unsupervised data-driven model of stellar spectra with Megan Bedell (Chicago). ## January 13, 2017 ### Backreaction — What a burst! A fresh attempt to see space-time foam with gamma ray bursts. It’s an old story: Quantum fluctuations of space-time might change the travel-time of light. Light of higher frequencies would be a little faster than that of lower frequencies. Or slower, depending on the sign of an unknown constant. Either way, the spectral colors of light would run apart, or ‘disperse’ as they say if they don’t want you to understand what they say. Such quantum gravitational ### Doug Natelson — Brief items What with the start of the semester and the thick of graduate admissions season, it's been a busy week, so rather than an extensive post, here are some brief items of interest: • We are hosting one of the APS Conferences for Undergraduate Women in Physics this weekend. Welcome, attendees! It's going to be a good time. • This week our colloquium speaker was Jim Kakalios of the University of Minnesota, who gave a very fun talk related to his book The Physics of Superheroes (an updated version of this), as well as a condensed matter seminar regarding his work on charge transport and thermoelectricity in amorphous and nanocrystalline semiconductors. His efforts at popularizing physics, including condensed matter, are great. His other books are The Amazing Story of Quantum Mechanics, and the forthcoming The Physics of Everyday Things. That last one shows how an enormous amount of interesting physics is embedded and subsumed in the routine tasks of modern life - a point I've mentioned before. • Another seminar speaker at Rice this week was John Biggins, who explained the chain fountain (original video here, explanatory video here, relevant paper here). • Speaking of videos, here is the talk I gave last April back at the Pittsburgh Quantum Institute's 2016 symposium, and here is the link to all the talks. • Speaking of quantum mechanics, here is an article in the NY Review of Books by Steven Weinberg on interpretations of quantum. While I've seen it criticized online as offering nothing new, I found it to be clearly written and articulated, and that can't always be said for articles about interpretations of quantum mechanics. • Speaking of both quantum mechanics interpretations and popular writings about physics, here is John Cramer's review of David Mermin's recent collection of essays, Why Quark Rhymes with Pork: And other Scientific Diversions (spoiler: I agree with Cramer that Mermin is wrong on the pronunciation of "quark".) The review is rather harsh regarding quantum interpretation, though perhaps that isn't surprising given that Cramer has his own view on this. ### Chad Orzel — Physics Blogging Round-Up: December This one’s late because I acquired a second class for the Winter term on very short notice. I was scheduled to teach our sophomore-level “Modern Physics” class, plus the lab, but a colleague who was scheduled to teach relativity for non-majors had a medical issue, and I’m the only other one on staff who’s ever taught it, so now I’m doing two courses instead of one. Whee! Anyway, here are my December posts from Forbes: Science Is Not THAT Special: Another in a long series of posts grumbling about the way we set science off from other pursuits and act as if the problems facing it are unique. In reality, a lot of what we talk about as issues of science education are challenges faced by pretty much every other profession as well, with less hand-wringing. The Surprisingly Complicated Physics of Sliding On Ice: Revisiting that time a couple of years ago when I wrote a bunch about the physics of luge, this time talking about a much more basic question: Why is ice slippery? “White Rabbit Project” Physics: G-Forces: I had a bunch of conversations with the producers of the new Netflix show “White Rabbit Project” a year or so ago, and some of what we talked about turned into an episode on “g-forces” in acceleration. ALPHA Experiment Shines New Light On Antimatter: The ALPHA collaboration at CERN has done the first spectroscopy of antihydrogen. It’s pretty rudimentary by the standards of precision measurement folks, but still an important step. What Should You Expect From Low-Energy Physics In 2017? It’s Hard To Say: I was reading posts about (high-energy) physics news to look for in 2017, and realized I couldn’t write an AMO physics equivalent. So I wrote about why I couldn’t make predictions about my home field. So there, two weeks into January, is what I wrote about in December. I’ve got a couple of posts up already this month, but we’ll save them for the January recap, which I’ll try to get posted before March. No promises, though, because this extra class has thrown things into disarray… ## January 12, 2017 ### Georg von Hippel — Book Review: "Lattice QCD — Practical Essentials" There is a new book about Lattice QCD, Lattice Quantum Chromodynamics: Practical Essentials by Francesco Knechtli, Michael Günther and Mike Peardon. At a 140 pages, this is a pretty slim volume, so it is obvious that it does not aim to displace time-honoured introductory textbooks like Montvay and Münster, or the newer books by Gattringer and Lang or DeGrand and DeTar. Instead, as suggested by the subtitle "Practical Essentials", and as said explicitly by the authors in their preface, this book aims to prepare beginning graduate students for their practical work in generating gauge configurations and measuring and analysing correlators. In line with this aim, the authors spend relatively little time on the physical or field theoretic background; while some more advanced topics such as the Nielson-Ninomiya theorem and the Symanzik effective theory or touched upon, the treatment of foundational topics is generally quite brief, and some topics, such as lattice perturbation theory or non-perturbative renormalization, are altogether omitted. The focus of the book is on Monte Carlo simulations, for which both the basic ideas and practically relevant algorithms — heatbath and overrelaxation fro pure gauge fields, and hybrid Monte Carlo for dynamical fermions — are described in some detail, including the RHMC algorithm and advanced techniques such as determinant factorizations, higher-order symplectic integrators, and multiple-timescale integration. The techniques from linear algebra required to deal with fermions are also covered in some detail, from the basic ideas of Krylov space methods through concrete descriptions of the GMRES and CG algorithms, along with such important preconditioners as even-odd and domain decomposition, to the ideas of algebraic multigrid methods. Stochastic estimation of all-to-all propagators with dilution, the one-end trick and low-mode averaging and explained, as are techniques for building interpolating operators with specific quantum numbers, gauge link and quark field smearing, and the use of the variational method to extract hadronic mass spectra. Scale setting, the Wilson flow, and Lüscher's method for extracting scattering phase shifts are also discussed briefly, as are the basic statistical techniques for data analysis. Each chapter contains a list of references to the literature covering both original research articles and reviews and textbooks for further study. Overall, I feel that the authors succeed very well at their stated aim of giving a quick introduction to the methods most relevant to current research in lattice QCD in order to let graduate students hit the ground running and get to perform research as quickly as possible. In fact, I am slightly worried that they may turn out to be too successful, since a graduate student having studied only this book could well start performing research, while having only a very limited understanding of the underlying field-theoretical ideas and problems (a problem that already exists in our field in any case). While this in no way detracts from the authors' achievement, and while I feel I can recommend this book to beginners, I nevertheless have to add that it should be complemented by a more field-theoretically oriented traditional textbook for completeness. ___ Note that I have deliberately not linked to the Amazon page for this book. Please support your local bookstore — nowadays, you can usually order online on their websites, and many bookstores are more than happy to ship books by post. ### Scott Aaronson — Quantum computing news (98% Trump-free) (1) Apparently Microsoft has decided to make a major investment in building topological quantum computers, which will include hiring Charles Marcus and Matthias Troyer among others. See here for their blog post, and here for the New York Times piece. In the race to implement QC among the established corporate labs, Microsoft thus joins the Martinis group at Google, as well as the IBM group at T. J. Watson—though both Google and IBM are focused on superconducting qubits, rather than the more exotic nonabelian anyon approach that Microsoft has long favored and is now doubling down on. I don’t really know more about this new initiative beyond what’s in the articles, but I know many of the people involved, they’re some of the most serious in the business, and Microsoft intensifying its commitment to QC can only be good for the field. I wish the new effort every success, despite being personally agnostic between superconducting qubits, trapped ions, photonics, nonabelian anyons, and other QC hardware proposals—whichever one gets there first is fine with me! (2) For me, though, perhaps the most exciting QC development of the last month was a new preprint by my longtime friend Dorit Aharonov and her colleague Yosi Atia, entitled Fast-Forwarding of Hamiltonians and Exponentially Precise Measurements. In this work, Dorit and Yosi wield the clarifying sword of computational complexity at one of the most historically confusing issues in quantum mechanics: namely, the so-called “time-energy uncertainty principle” (TEUP). The TEUP says that, just as position and momentum are conjugate in quantum mechanics, so too are energy and time—with greater precision in energy corresponding to lesser precision in time and vice versa. The trouble is, it was never 100% clear what the TEUP even meant—after all, time isn’t even an observable in quantum mechanics, just an external parameter—and, to whatever extent the TEUP did have a definite meaning, it wasn’t clear that it was true. Indeed, as Dorit and Yosi’s paper discusses in detail, in 1961 Dorit’s uncle Yakir Aharonov, together with David Bohm, gave a counterexample to a natural interpretation of the TEUP. But, despite this and other counterexamples, the general feeling among physicists—who, after all, are physicists!—seems to have been that some corrected version of the TEUP should hold “in all reasonable circumstances.” But, OK, what do we mean by a “reasonable circumstance”? This is where Dorit and Yosi come in. In the new work, they present a compelling case that the TEUP should really be formulated as a tradeoff between the precision of energy measurements and circuit complexity (that is, the minimum number of gates needed to implement the energy measurement)—and in that amended form, the TEUP holds for exactly those Hamiltonians H that can’t be “computationally fast-forwarded.” In other words, it holds whenever applying the unitary transformation e-iHt requires close to t computation steps, when there’s no magical shortcut that lets you simulate t steps of time evolution with only (say) log(t) steps. And, just as the physicists handwavingly thought, that should indeed hold for “generic” Hamiltonians H (assuming BQP≠PSPACE), although it’s possible to use Shor’s algorithm, for finding the order of an element in a multiplicative group, to devise a counterexample to it. Anyway, there’s lots of other stuff in the paper, including a connection to the stuff Lenny Susskind and I have been doing about the “generic” growth of circuit complexity, in the CFT dual of an expanding wormhole (where we also needed to assume BQP≠PSPACE and closely related complexity separations, for much the same reasons). Congratulations to Dorit and Yosi for once again illustrating the long reach of computational complexity in physics, and for giving me a reason to be happy this month! (3) As many of you will have seen, my former MIT colleagues, Lior Eldar and Peter Shor, recently posted an arXiv preprint claiming a bombshell result: namely, a polynomial-time quantum algorithm to solve a variant of the Closest Vector Problem in lattices. Their claimed algorithm wouldn’t yet break lattice-based cryptography, but if the approximation factors could be improved, it would be well on the way to doing so. This has been one of the most tempting targets for quantum algorithms research for more than twenty years—ever since Shor’s “original” algorithm laid waste to RSA, Diffie-Hellman, elliptic-curve cryptography, and more in a world with scalable quantum computers, leaving lattice-based cryptography as one of the few public-key crypto proposals still standing. Unfortunately, Lior tells me that Oded Regev has discovered a flaw in the algorithm, which he and Peter don’t currently know how to fix. So for now, they’re withdrawing the paper (because of the Thanksgiving holiday, the withdrawal won’t take effect on the arXiv until Monday). It’s still a worthy attempt on a great problem—here’s hoping that they or someone else manage to, as Lior put it to me, “make the algorithm great again.” ### Scott Aaronson — The teaser Tomorrow, I’ll have something big to announce here. So, just to whet your appetites, and to get myself back into the habit of blogging, I figured I’d offer you an appetizer course: some more miscellaneous non-Trump-related news. (1) My former student Leonid Grinberg points me to an astonishing art form, which I somehow hadn’t known about: namely, music videos generated by executable files that fit in only 4K of memory. Some of these videos have to be seen to be believed. (See also this one.) Much like, let’s say, a small Turing machine whose behavior is independent of set theory, these videos represent exercises in applied (or, OK, recreational) Kolmogorov complexity: how far out do you need to go in the space of all computer programs before you find beauty and humor and adaptability and surprise? Admittedly, Leonid explains to me that the rules allow these programs to call DirectX and Visual Studio libraries to handle things like the 3D rendering (with the libraries not counted toward the 4K program size). This makes the programs’ existence merely extremely impressive, rather than a sign of alien superintelligence. In some sense, all the programming enthusiasts over the decades who’ve burned their free time and processor cycles on Conway’s Game of Life and the Mandelbrot set and so forth were captivated by the same eerie beauty showcased by the videos: that of data compression, of the vast unfolding of a simple deterministic rule. But I also feel like the videos add a bit extra: the 3D rendering, the music, the panning across natural or manmade-looking dreamscapes. What we have here is a wonderful resource for either an acid trip or an undergrad computability and complexity course. (2) A week ago Igor Oliveira, together with my longtime friend Rahul Santhanam, released a striking paper entitled Pseudodeterministic Constructions in Subexponential Time. To understand what this paper does, let’s start with Terry Tao’s 2009 polymath challenge: namely, to find a fast, deterministic method that provably generates large prime numbers. Tao’s challenge still stands today: one of the most basic, simplest-to-state unsolved problems in algorithms and number theory. To be clear, we already have a fast deterministic method to decide whether a given number is prime: that was the 2002 breakthrough by Agrawal, Kayal, and Saxena. We also have a fast probabilistic method to generate large primes: namely, just keep picking n-digit numbers at random, test each one, and stop when you find one that’s prime! And those methods can be made deterministic assuming far-reaching conjectures in number theory, such as Cramer’s Conjecture (though note that even the Riemann Hypothesis wouldn’t lead to a polynomial-time algorithm, but “merely” a faster exponential-time one). But, OK, what if you want a 5000-digit prime number, and you want it now: provably, deterministically, and fast? That was Tao’s challenge. The new paper by Oliveira and Santhanam doesn’t quite solve it, but it makes some exciting progress. Specifically, it gives a deterministic algorithm to generate n-digit prime numbers, with merely the following four caveats: • The algorithm isn’t polynomial time, but subexponential (2n^o(1)) time. • The algorithm isn’t deterministic, but pseudodeterministic (a concept introduced by Gat and Goldwasser). That is, the algorithm uses randomness, but it almost always succeeds, and it outputs the same n-digit prime number in every case where it succeeds. • The algorithm might not work for all input lengths n, but merely for infinitely many of them. • Finally, the authors can’t quite say what the algorithm is—they merely prove that it exists! If there’s a huge complexity collapse, such as ZPP=PSPACE, then the algorithm is one thing, while if not then the algorithm is something else. Strikingly, Oliveira and Santhanam’s advance on the polymath problem is pure complexity theory: hitting sets and pseudorandom generators and win-win arguments and stuff like that. Their paper uses absolutely nothing specific to the prime numbers, except the facts that (a) there are lots of them (the Prime Number Theorem), and (b) we can efficiently decide whether a given number is prime (the AKS algorithm). It seems almost certain that one could do better by exploiting more about primes. (3) I’m in Lyon, France right now, to give three quantum computing and complexity theory talks. I arrived here today from London, where I gave another two lectures. So far, the trip has been phenomenal, my hosts gracious, the audiences bristling with interesting questions. But getting from London to Lyon also taught me an important life lesson that I wanted to share: never fly EasyJet. Or at least, if you fly one of the European “discount” airlines, realize that you get what you pay for (I’m told that Ryanair is even worse). These airlines have a fundamentally dishonest business model, based on selling impossibly cheap tickets, but then forcing passengers to check even tiny bags and charging exorbitant fees for it, counting on snagging enough travelers who just naïvely clicked “yes” to whatever would get them from point A to point B at a certain time, assuming that all airlines followed more-or-less similar rules. Which might not be so bad—it’s only money—if the minuscule, overworked staff of these quasi-airlines didn’t also treat the passengers like beef cattle, barking orders and berating people for failing to obey rules that one could log hundreds of thousands of miles on normal airlines without ever once encountering. Anyway, if the airlines won’t warn you, then Shtetl-Optimized will. ### Scott Aaronson — “THE TALK”: My quantum computing cartoon with Zach Weinersmith OK, here’s the big entrée that I promised you yesterday: “THE TALK”: My joint cartoon about quantum comgputing with Zach Weinersmith of SMBC Comics. Just to whet your appetite: In case you’re wondering how this came about: after our mutual friend Sean Carroll introduced me and Zach for a different reason, the idea of a joint quantum computing comic just seemed too good to pass up. The basic premise—“The Talk”—was all Zach. I dutifully drafted some dialogue for him, which he then improved and illustrated. I.e., he did almost all the work (despite having a newborn competing for his attention!). Still, it was an honor for me to collaborate with one of the great visual artists of our time, and I hope you like the result. Beyond that, I’ll let the work speak for itself. ### Scott Aaronson — My 5-minute quantum computing talk at the White House (OK, technically it was in the Eisenhower Executive Office Building, which is not exactly the White House itself, but is adjacent to the West Wing in the White House complex. And President Obama wasn’t there—maybe, like Justin Trudeau, he already knows everything about quantum computing? But lots of people from the Office of Science and Technology Policy were! And some of us talked with Valerie Jarrett, Obama’s adviser, when she passed us on her way to the West Wing. The occasion was a Quantum Information Science policy workshop that OSTP held, and which the White House explicitly gave us permission to discuss on social media. Indeed, John Preskill already tweeted photos from the event. Besides me and Preskill, others in attendance included Umesh Vazirani, Seth Lloyd, Yaoyun Shi, Rob Schoelkopf, Krysta Svore, Hartmut Neven, Stephen Jordan… I don’t know whether this is the first time that the polynomial hierarchy, or the notion of variation distance, were ever invoked in a speech at the White House. But in any case, I was proud to receive a box of Hershey Kisses bearing the presidential seal. I thought of not eating them, but then I got hungry, and realized that I can simply refill the box later if desired. For regular readers of Shtetl-Optimized, my talk won’t have all that much that’s new, but in any case it’s short. Incidentally, during the workshop, a guy from OSTP told me that, when he and others at the White House were asked to prepare materials about quantum computing, posts on Shtetl-Optimized (such as Shor I’ll Do It) were a huge help. Honored though I was to have “served my country,” I winced, thinking about all the puerile doofosities I might’ve self-censored had I had any idea who might read them. I didn’t dare ask whether anyone at the White House also reads the comment sections! Thanks so much to all the other participants and to the organizers for a great workshop. –SA) Quantum Supremacy by Scott Aaronson (UT Austin) October 18, 2016 Thank you; it’s great to be here. There are lots of directions that excite me enormously right now in quantum computing theory, which is what I work on. For example, there’s the use of quantum computing to get new insight into classical computation, into condensed matter physics, and recently, even into the black hole information problem. But since I have five minutes, I wanted to talk here about one particular direction—one that, like nothing else that I know of, bridges theory and experiment in the service of what we hope will be a spectacular result in the near future. This direction is what’s known as “Quantum Supremacy”—John [Preskill], did you help popularize that term? [John nods yes]—although some people have been backing away from the term recently, because of the campaign of one of the possible future occupants of this here complex. But what quantum supremacy means to me, is demonstrating a quantum speedup for some task as confidently as possible. Notice that I didn’t say a useful task! I like to say that for me, the #1 application of quantum computing—more than codebreaking, machine learning, or even quantum simulation—is just disproving the people who say quantum computing is impossible! So, quantum supremacy targets that application. What is important for quantum supremacy is that we solve a clearly defined problem, with some relationship between inputs and outputs that’s independent of whatever hardware we’re using to solve the problem. That’s part of why it doesn’t cut it to point to some complicated, hard-to-simulate molecule and say “aha! quantum supremacy!” One discovery, which I and others stumbled on 7 or 8 years ago, is that quantum supremacy seems to become much easier to demonstrate if we switch from problems with a single valid output to sampling problems: that is, problems of sampling exactly or approximately from some specified probability distribution. Doing this has two advantages. First, we no longer need a full, fault-tolerant quantum computer—in fact, very rudimentary types of quantum hardware appear to suffice. Second, we can design sampling problems for which we can arguably be more confident that they really are hard for a classical computer, than we are that (say) factoring is classically hard. I like to say that a fast classical factoring algorithm might collapse the world’s electronic commerce, but as far as we know, it wouldn’t collapse the polynomial hierarchy! But with sampling problems, at least with exact sampling, we can often show the latter implication, which is about the best evidence you can possibly get for such a problem being hard in the present state of mathematics. One example of these sampling tasks that we think are classically hard is BosonSampling, which Alex Arkhipov and I proposed in 2011. BosonSampling uses a bunch of identical photons that are sent through a network of beamsplitters, then measured to count the number of photons in each output mode. Over the past few years, this proposal has been experimentally demonstrated by quantum optics groups around the world, with the current record being a 6-photon demonstration by the O’Brien group in Bristol, UK. A second example is the IQP (“Instantaneous Quantum Polynomial-Time”) or Commuting Hamiltonians model of Bremner, Jozsa, and Shepherd. A third example—no doubt the simplest—is just to sample from the output distribution of a random quantum circuit, let’s say on a 2D square lattice of qubits with nearest-neighbor interactions. Notably, this last task is one that the Martinis group at Google is working toward achieving right now, with 40-50 qubits. They say that they’ll achieve it in as little as one or two years, which translated from experimental jargon, means maybe five years? But not infinity years. The challenges on the experimental side are clear: get enough qubits with long enough coherence times to achieve this. But there are also some huge theoretical challenges remaining. A first is, can we still solve classically hard sampling problems even in the presence of realistic experimental imperfections? Arkhipov and I already thought about that problem—in particular, about sampling from a distribution that’s merely close in variation distance to the BosonSampling one—and got results that admittedly weren’t as satisfactory as the results for exact sampling. But I’m delighted to say that, just within the last month or two, there have been some excellent new papers on the arXiv that tackle exactly this question, with both positive and negative results. A second theoretical challenge is, how do we verify the results of a quantum supremacy experiment? Note that, as far as we know today, verification could itself require classical exponential time. But that’s not the showstopper that some people think, since we could target the “sweet spot” of 40-50 qubits, where classical verification is difficult (and in particular, clearly “costlier” than running the experiment itself), but also far from impossible with cluster computing resources. If I have any policy advice, it’s this: recognize that a clear demonstration of quantum supremacy is at least as big a deal as (say) the discovery of the Higgs boson. After this scientific milestone is achieved, I predict that the whole discussion of commercial applications of quantum computing will shift to a new plane, much like the Manhattan Project shifted to a new plane after Fermi built his pile under the Chicago stadium in 1942. In other words: at this point, the most “applied” thing to do might be to set applications aside temporarily, and just achieve this quantum supremacy milestone—i.e., build the quantum computing Fermi pile—and thereby show the world that quantum computing speedups are a reality. Thank you. ### Scott Aaronson — Time to vote-swap I blogged about anti-Trump vote-swapping before (and did an interview at Huffington Post with Linchuan Zhang), but now, for my most in-depth look at the topic yet, check out my podcast interview with the incomparable Julia Galef, of “Rationally Speaking.” Or if you’re bothered by my constant uhs and y’knows, I strongly recommend reading the transcript instead—I always sound smarter in print. But don’t just read, act! With only 9 days until the election, and with Hillary ahead but the race still surprisingly volatile, if you live in a swing state and support Gary Johnson or Jill Stein or Evan McMullin (but you nevertheless correctly regard Trump as the far greater evil than Hillary), or if you live in a relatively safe state and support Hillary (like I do), now is the time to find your vote-swap partner. Remember that you and your partner can always back out later, by mutual consent, if the race changes (e.g., my vote-swap partner in Ohio has “released” me to vote for Hillary rather than Gary Johnson if, the night before Election Day, Texas looks like it might actually turn blue). Just one thing: I recently got a crucial piece of intelligence about vote-swapping, which is to use the site TrumpTraders.org. Previously, I’d been pointing people to another site called MakeMineCount.org, but my informants report that they never actually get assigned a match on that site, whereas they do right away on TrumpTraders. Update (Nov. 6): Linchuan Zhang tells me that TrumpTraders.org currently has a deficit of several thousand Clinton supporters in safe states. So if you’re such a person and you haven’t vote-swapped yet, please go there ASAP! I’ve already voted for Gary Johnson in Texas, having “teleported” my Clinton vote to Ohio. While Clinton’s position is stronger, it seems clear that the election will indeed be close, and Texas will not be in serious contention. ## January 11, 2017 ### Terence Tao — Some remarks on the lonely runner conjecture I’ve just uploaded to the arXiv my paper “Some remarks on the lonely runner conjecture“, submitted to Contributions to discrete mathematics. I had blogged about the lonely runner conjecture in this previous blog post, and I returned to the problem recently to see if I could obtain anything further. The results obtained were more modest than I had hoped, but they did at least seem to indicate a potential strategy to make further progress on the problem, and also highlight some of the difficulties of the problem. One can rephrase the lonely runner conjecture as the following covering problem. Given any integer “velocity” ${v}$ and radius ${0 < \delta < 1/2}$, define the Bohr set ${B(v,\delta)}$ to be the subset of the unit circle ${{\bf R}/{\bf Z}}$ given by the formula $\displaystyle B(v,\delta) := \{ t \in {\bf R}/{\bf Z}: \|vt\| \leq \delta \},$ where ${\|x\|}$ denotes the distance of ${x}$ to the nearest integer. Thus, for ${v}$ positive, ${B(v,\delta)}$ is simply the union of the ${v}$ intervals ${[\frac{a-\delta}{v}, \frac{a+\delta}{v}]}$ for ${a=0,\dots,v-1}$, projected onto the unit circle ${{\bf R}/{\bf Z}}$; in the language of the usual formulation of the lonely runner conjecture, ${B(v,\delta)}$ represents those times in which a runner moving at speed ${v}$ returns to within ${\delta}$ of his or her starting position. For any non-zero integers ${v_1,\dots,v_n}$, let ${\delta(v_1,\dots,v_n)}$ be the smallest radius ${\delta}$ such that the ${n}$ Bohr sets ${B(v_1,\delta),\dots,B(v_n,\delta)}$ cover the unit circle: $\displaystyle {\bf R}/{\bf Z} = \bigcup_{i=1}^n B(v_i,\delta). \ \ \ \ \ (1)$ $\displaystyle \delta(1,\dots,n) = \frac{1}{n+1}$ and hence $\displaystyle \delta_n \leq \frac{1}{n+1}$ for any ${n \geq 1}$. The lonely runner conjecture is equivalent to the assertion that this bound is in fact optimal: Conjecture 1 (Lonely runner conjecture) For any ${n \geq 1}$, one has ${\delta_n = \frac{1}{n+1}}$. This conjecture is currently known for ${n \leq 6}$ (see this paper of Barajas and Serra), but remains open for higher ${n}$. It is natural to try to attack the problem by establishing lower bounds on the quantity ${\delta_n}$. We have the following “trivial” bound, that gets within a factor of two of the conjecture: Proposition 2 (Trivial bound) For any ${n \geq 1}$, one has ${\delta_n \geq \frac{1}{2n}}$. Proof: It is not difficult to see that for any non-zero velocity ${v}$ and any ${0 < \delta < 1/2}$, the Bohr set ${B(v,\delta)}$ has Lebesgue measure ${m(B(v,\delta)) = 2\delta}$. In particular, by the union bound $\displaystyle m(\bigcup_{i=1}^n B(v_i,\delta)) \leq \sum_{i=1}^n m(B(v_i,\delta)) \ \ \ \ \ (2)$ we see that the covering (1) is only possible if ${1 \leq 2 n \delta}$, giving the claim. $\Box$ So, in some sense, all the difficulty is coming from the need to improve upon the trivial union bound (2) by a factor of two. Despite the crudeness of the union bound (2), it has proven surprisingly hard to make substantial improvements on the trivial bound ${\delta_n \geq \frac{1}{2n}}$. In 1994, Chen obtained the slight improvement $\displaystyle \delta_n \geq \frac{1}{2n - 1 + \frac{1}{2n-3}}$ which was improved a little by Chen and Cusick in 1999 to $\displaystyle \delta_n \geq \frac{1}{2n-3}$ when ${2n-3}$ was prime. In a recent paper of Perarnau and Serra, the bound $\displaystyle \delta_n \geq \frac{1}{2n-2+o(1)}$ was obtained for arbitrary ${n}$. These bounds only improve upon the trivial bound by a multiplicative factor of ${1+O(1/n)}$. Heuristically, one reason for this is as follows. The union bound (2) would of course be sharp if the Bohr sets ${B(v_i,\delta)}$ were all disjoint. Strictly speaking, such disjointness is not possible, because all the Bohr sets ${B(v_i,\delta)}$ have to contain the origin as an interior point. However, it is possible to come up with a large number of Bohr sets ${B(v_i,\delta)}$ which are almost disjoint. For instance, suppose that we had velocities ${v_1,\dots,v_s}$ that were all prime numbers between ${n/4}$ and ${n/2}$, and that ${\delta}$ was equal to ${\delta_n}$ (and in particular was between ${1/2n}$ and ${1/(n+1)}$. Then each set ${B(v_i,\delta)}$ can be split into a “kernel” interval ${[-\frac{\delta}{v_i}, \frac{\delta}{v_i}]}$, together with the “petal” intervals ${\bigcup_{a=1}^{v_i-1} [\frac{a-\delta}{v_i}, \frac{a+\delta}{v_i}]}$. Roughly speaking, as the prime ${v_i}$ varies, the kernel interval stays more or less fixed, but the petal intervals range over disjoint sets, and from this it is not difficult to show that $\displaystyle m(\bigcup_{i=1}^s B(v_i,\delta)) = (1-O(\frac{1}{n})) \sum_{i=1}^s m(B(v_i,\delta)),$ so that the union bound is within a multiplicative factor of ${1+O(\frac{1}{n})}$ of the truth in this case. This does not imply that ${\delta_n}$ is within a multiplicative factor of ${1+O(1/n)}$ of ${\frac{1}{2n}}$, though, because there are not enough primes between ${n/4}$ and ${n/2}$ to assign to ${n}$ distinct velocities; indeed, by the prime number theorem, there are only about ${\frac{n}{4\log n}}$ such velocities that could be assigned to a prime. So, while the union bound could be close to tight for up to ${\asymp n/\log n}$ Bohr sets, the above counterexamples don’t exclude improvements to the union bound for larger collections of Bohr sets. Following this train of thought, I was able to obtain a logarithmic improvement to previous lower bounds: Theorem 3 For sufficiently large ${n}$, one has ${\delta_n \geq \frac{1}{2n} + \frac{c \log n}{n^2 (\log\log n)^2}}$ for some absolute constant ${c>0}$. The factors of ${\log\log n}$ in the denominator are for technical reasons and might perhaps be removable by a more careful argument. However it seems difficult to adapt the methods to improve the ${\log n}$ in the numerator, basically because of the obstruction provided by the near-counterexample discussed above. Roughly speaking, the idea of the proof of this theorem is as follows. If we have the covering (1) for ${\delta}$ very close to ${1/2n}$, then the multiplicity function ${\sum_{i=1}^n 1_{B(v_i,\delta)}}$ will then be mostly equal to ${1}$, but occasionally be larger than ${1}$. On the other hand, one can compute that the ${L^2}$ norm of this multiplicity function is significantly larger than ${1}$ (in fact it is at least ${(3/2-o(1))^{1/2}}$). Because of this, the ${L^3}$ norm must be very large, which means that the triple intersections ${B(v_i,\delta) \cap B(v_j,\delta) \cap B(v_k,\delta)}$ must be quite large for many triples ${(i,j,k)}$. Using some basic Fourier analysis and additive combinatorics, one can deduce from this that the velocities ${v_1,\dots,v_n}$ must have a large structured component, in the sense that there exists an arithmetic progression of length ${\asymp n}$ that contains ${\asymp n}$ of these velocities. For simplicity let us take the arithmetic progression to be ${\{1,\dots,n\}}$, thus ${\asymp n}$ of the velocities ${v_1,\dots,v_n}$ lie in ${\{1,\dots,n\}}$. In particular, from the prime number theorem, most of these velocities will not be prime, and will in fact likely have a “medium-sized” prime factor (in the precise form of the argument, “medium-sized” is defined to be “between ${\log^{10} n}$ and ${n^{1/10}}$“). Using these medium-sized prime factors, one can show that many of the ${B(v_i,\delta)}$ will have quite a large overlap with many of the other ${B(v_j,\delta)}$, and this can be used after some elementary arguments to obtain a more noticeable improvement on the union bound (2) than was obtained previously. A modification of the above argument also allows for the improved estimate $\displaystyle \delta(v_1,\dots,v_n) \geq \frac{1+c-o(1)}{2n} \ \ \ \ \ (3)$ In my previous blog post, I showed that in order to prove the lonely runner conjecture, it suffices to do so under the additional assumption that all of the velocities ${v_1,\dots,v_n}$ are of size ${O(n^{O(n^2)})}$; I reproduce this argument (slightly cleaned up for publication) in the current preprint. There is unfortunately a huge gap between ${O(n)}$ and ${O(n^{O(n^2)})}$, so the above bound (3) does not immediately give any new bounds for ${\delta_n}$. However, one could perhaps try to start attacking the lonely runner conjecture by increasing the range ${O(n)}$ for which one has good results, and by decreasing the range ${O(n^{O(n^2)})}$ that one can reduce to. For instance, in the current preprint I give an elementary argument (using a certain amount of case-checking) that shows that the lonely runner bound $\displaystyle \delta(v_1,\dots,v_n) \geq \frac{1}{n+1} \ \ \ \ \ (4)$ holds if all the velocities ${v_1,\dots,v_n}$ are assumed to lie between ${1}$ and ${1.2 n}$. This upper threshold of ${1.2 n}$ is only a tiny improvement over the trivial threshold of ${n}$, but it seems to be an interesting sub-problem of the lonely runner conjecture to increase this threshold further. One key target would be to get up to ${2n}$, as there are actually a number of ${n}$-tuples ${(v_1,\dots,v_n)}$ in this range for which (4) holds with equality. The Dirichlet approximation theorem of course gives the tuple ${(1,2,\dots,n)}$, but there is also the double ${(2,4,\dots,2n)}$ of this tuple, and furthermore there is an additional construction of Goddyn and Wong that gives some further examples such as ${(1,2,3,4,5,7,12)}$, or more generally one can start with the standard tuple ${(1,\dots,n)}$ and accelerate one of the velocities ${v}$ to ${2v}$; this turns out to work as long as ${v}$ shares a common factor with every integer between ${n-v+1}$ and ${2n-2v+1}$. There are a few more examples of this type in the paper of Goddyn and Wong, but all of them can be placed in an arithmetic progression of length ${O(n \log n)}$ at most, so if one were very optimistic, one could perhaps envision a strategy in which the upper bound of ${O(n^{O(n^2)})}$ mentioned earlier was reduced all the way to something like ${O( n \log n )}$, and then a separate argument deployed to treat this remaining case, perhaps isolating the constructions of Goddyn and Wong (and possible variants thereof) as the only extreme cases. Filed under: math.CO, math.NT Tagged: Bohr sets, Diophantine approximation, lonely runner conjecture ### n-Category CaféCategory Theory in Barcelona I’m excited to be in Barcelona to help Joachim Kock teach an introductory course on category theory. (That’s a link to bgsmath.cat — categorical activities in Catalonia have the added charm of a .cat web address.) We have a wide audience of PhD and masters students, specializing in subjects from topology to operator algebras to number theory, and representing three Barcelona universities. We’re taking it at a brisk pace. First of all we’re working through my textbook, at a rate of one chapter a day, for six days spread over two weeks. Then we’re going to spend a week on more advanced topics. Today Joachim did Chapter 1 (categories, functors and natural transformations), and tomorrow I’ll do Chapter 2 (adjunctions). I’d like to use this post for two things: to invite questions and participation from the audience, and to collect slogans. Let me explain… Joachim pointed out today that category theory is full of slogans. Here’s the first one: It’s more important how things interact than what they “are”. As he observed, the question of what things “are” is slippery. Let me quote a bit from my book: In his excellent book Mathematics: A Very Short Introduction, Timothy Gowers considers the question: “What is the black king in chess?”. He swiftly points out that this question is rather peculiar. It is not important that the black king is a small piece of wood, painted a certain colour and carved into a certain shape. We could equally well use a scrap of paper with “BK” written on it. What matters is what the black king does: it can move in certain ways but not others, according to the rules of chess. In a categorical context, what an object “does” means how it interacts with the world around it — the category in which it lives. Tomorrow I’ll proclaim some more slogans — I have some in mind. But I’d like to hear from you too. What are the most important slogans in category theory? And what do they mean to you? I’d also like to try an experiment. The classes move rather quickly, so there’s not a huge amount of time in them for discussion or questions. But I’d like to invite students in the class to ask questions here. You can post anonymously — no one will know it’s you — and with any luck, you’ll get interesting answers from multiple points of view. So please, don’t be inhibited: ask whatever’s on your mind. You can even include LaTeX, in more or less the usual way: just put stuff between dollar signs. No tinguis por! ## January 09, 2017 ### Tommaso Dorigo — Getting Married I am happy to report, with this rather unconventional blog posting, that I am getting married on January 12. My companion is Kalliopi Petrou, a lyrical singer. There will be no huge party involved in the event, as Kalliopi and I have lived together for some time already and the ceremony will be minimalistic. None the less, we do give importance to this common decision, so much so that I thought it would be a good thing to broadcast in public - here. read more ## January 08, 2017 ### Doug Natelson — Physics is not just high energy and astro/cosmology. A belated happy new year to my readers. Back in 2005, nearly every popularizer of physics on the web, television, and bookshelves was either a high energy physicist (mostly theorists) or someone involved in astrophysics/cosmology. Often these people were presented, either deliberately or through brevity, as representing the whole discipline of physics. Things have improved somewhat, but the overall situation in the media today is not that different, as exemplified by the headline of this article, and noticed by others (see the fourth paragraph here, at the excellent blog by Ross McKenzie). For example, consider Edge.org, which has an annual question that they put to "the most complex and sophisticated minds". This year the question was, what scientific term or concept should be more widely known? It's a very interesting piece, and I encourage you to read it. They got responses from 206 contributors (!). By my estimate, about 31 of those would likely say that they are active practicing physicists, though definitions get tricky for people working on "complexity" and computation. Again, by my rough count, from that list I see 12-14 high energy theorists (depending on whether you count Yuri Milner, who is really a financier, or Gino Segre, who is an excellent author but no longer an active researcher) including Sabine Hossenfelder, one high energy experimentalist, 10 people working on astrophysics/cosmology, four working on some flavor of quantum mechanics/quantum information (including the blogging Scott Aronson), one on biophysics/complexity, and at most two on condensed matter physics. Seems to me like representation here is a bit skewed. Hopefully we will keep making progress on conveying that high energy/cosmology is not representative of the entire discipline of physics.... ### Backreaction — Stephen Hawking turns 75. Congratulations! Here’s what to celebrate. If people know anything about physics, it’s the guy in a wheelchair who speaks with a computer. Google “most famous scientist alive” and the answer is “Stephen Hawking.” But if you ask a physicist, what exactly is he famous for? Hawking became “officially famous” with his 1988 book “A Brief History of Time.” Among physicists, however, he’s more renowned for the singularity theorems. In his ## January 07, 2017 ### Tommaso Dorigo — The Three Cubes Problem Two days ago, before returning from Israel, my fiancee Kalliopi and I had a very nice dinner in a kosher restaurant near Rehovot in the company of Eilam Gross, Zohar Komargodski, and Zohar's wife Olga. The name of Eilam should be familiar to regulars of this blog as he wrote a couple of guest posts here, in similar occasions (in the first case it was a few before the Higgs discovery was announced, when the signal was intriguing but not yet decisive; and in the second case it was about the 750 GeV resonance, which unfortunately did not concretize into a discovery). As for Zohar, he is a brilliant theorist working in applications of quantum field theory. He is young but already won several awards, among them the prestigious New Horizons in Physics prize. read more ## January 05, 2017 ### Jordan Ellenberg — Booklist 2016 — the year of translation This year my reading project was for the majority of the books I read to be translated from a language other than English. Here’s the list: • 31 Dec 2016: Troubling Love, by Elena Ferrante (Ann Goldstein, trans.) • 27 Dec 2016: The Civil Servant’s Notebook, by Wang Xiaofang (Eric Abrahamsen, trans.) • 16 Dec 2016: Nirmala, by Premchand (David Rubin, trans.) • 16 Dec 2016: A Long Walk to Water, by Linda Sue Park • 1 Dec 2016: Nabokov’s Favorite Word is Mauve, by Ben Blatt • 24 Nov 2016: HHhH, by Laurent Binet (Sam Taylor, trans.) • 21 Nov 2016: Secondhand Time, by Svetlana Alexievich (Bela Shayevich, trans.) • 20 Nov 2016: Twenty-Four Hours in the Life of a Woman, by Stefan Zweig (Anthea Bell, trans.) • 6 Nov 2016: Houseboy, by Ferdinand Oyono (John Reed, trans.) • 3 Nov 2016: The Good Life Elsewhere, by Vladimir Lorchenkov (Ross Ufberg, trans.) • 12 Oct 2016: Tales of the Hasidim: The Early Masters, by Martin Buber (Olga Marx, trans.) • 1 Oct 2016: Hit Makers, by Derek Thompson • 25 Sep 2016: The Fireman, by Joe Hill • 19 Sep 2016: Ghosts, by Raina Telgemeier • 3 Sep 2016: The Queue, by Basma Abdel Aziz (Elizabeth Jaquette, trans.) • 11 Aug 2016: City of Mirrors, by Justin Cronin • 26 Jul 2016: Why I Killed My Best Friend, by Amanda Michalopoulou (Karen Emmerich, trans.) • 19 Jul 2016: 1Q84, by Haruki Murakami (Philip Gabriel and Jay Rubin, trans.) • 10 Jul 2016: The Story of My Teeth, by Valeria Luiselli (Christina MacSweeney, trans.) • 1 Jul 2016: So You Don’t Get Lost In The Neighborhood, by Patrick Modiano (Euan Cameron, trans.) • 13 May 2016: Weapons of Math Destruction, by Cathy O’Neil • 2 May 2016: Sh*tty Mom for All Seasons, by Erin Clune • 20 Apr 2016: There’s Nothing I Can Do When I Think of You Late at Night, by Cao Naiqian (John Balcom, trans.) • 1 Apr 2016: The Story of the Lost Child, by Elena Ferrante (Ann Goldstein, trans.) • 25 Feb 2016: Those Who Leave and Those Who Stay, by Elena Ferrante (Ann Goldstein, trans.) • 10 Feb 2016: Voices from Chernobyl, by Svetlana Alexievich (Keith Gessen, trans.) • 1 Feb 2016: The Story of a New Name, by Elena Ferrante (Ann Goldstein, trans.) • 9 Jan 2016: Amy and Laura, by Marilyn Sachs • 7 Jan 2016: My Brilliant Friend, by Elena Ferrante (Ann Goldstein, trans.) Note that I’m behind on these posts: I covered the 2013 booklist about a year ago, but still have to do 2015 (the year of reading mostly women) and 2014. I’ll get to it. 20 translated books, 9 books in English. One thing to note is that I read few books this year; I think reading in translation is just a little slower for me. The languages: • 5 Italian (all Ferrante) • 3 French (two from France, one from Cameroon) • 3 Russian (but no Russian authors! Lorchenkov is Moldovan, Alexievich is Belarussian.) • 2 Chinese • 2 German • 1 Japanese, 1 Arabic, 1 Greek, 1 Hindi, 1 Spanish. Overall thoughts: My plan, I guess, was to expand my horizons. Did I? I’m not sure I found these books to be as different from my usual reading as I expected. Maybe because when American and British writers translate foreign books they somehow press them into the mold of the American and British novel I’m so at ease with? Or because the novel is fundamentally a cosmopolitan form that works roughly the same way in different national traditions? The one exception was There’s Nothing I Can Do When I Think of You Late at Night, a kind of Chinese Winesburg,Ohio: very short, linked stories all set in a remote and desperately impoverished village. It’s sort of incantatory, phrases repeated several times, in a way that really feels alien to the prose fiction tradition I know. Niqian wasn’t trained as a writer; apparently he was a detective who started writing as a bet. Here’s a review with some excerpts. Best of the year: No way to choose between Ferrante and Alexievich. They are too different. Also the same, of course, in that they always come back to women and the men from whom they expect little and get even less. And the men from whom they expect something bad and get something even worse. The books are oral history, interviews collected and transcribed into something like an epic. Here’s a young woman in Belarus, released from prison after being arrested in a demonstration, telling her story in Secondhand Time: Do I still like the village? People here live the same way year in and year out. They dig for potatoes in their vegetable patches, crawl around on their knees. Make moonshine. You won’t find a sngle sober man after dark, they all drink every single day. They vote for Lukashenko and mourn the Soviet Union. The undefeatable Soviet Army. On the bus, one of our neighbors sat down next to me. He was drunk. He talked about politics: “I would beat every moron democrat’s face in myself if I could. They let you off easy. I swear to God! All of them ought to be shot. America is behind all this, they’re paying for it … Hillary Clinton … but we’re a strong people. We lived through perestroika, and we’ll make it through another revolution. One wise man told me that the kikes are the ones behind it.” The whole bus supported him. “Things wouldn’t be any worse than they are now. All you see on TV is bombings and shootings everywhere.” The same woman, on her time in jail: I learned that happiness can come from something as small as a bit of sugar or a piece of soap. In a cell intended for five people — thirty-two square meters — there were seventeen of us. You had to learn how to fit your entire life into two square meters. It was especially hard at night, there was no air to breathe, it was stifling. We wouldn’t get to sleep for a long time. We stayed up talking. The first few days, we discussed politics, but after that, we only ever talked about love. Other Notes: 1Q84 was my first Murakami. A fascinating example of a book that in many ways I view as objectively poorly written but which I found captivating, even though it was 1000 pages long. So maybe this, like Cao, is another book doing something with prose which I’m not used to and which I can’t completely understand. Twenty-Four Hours in the Life of a Woman was compelling melodrama. Tales of the Hasidim helped me remember that my idea of what “Jewish culture” means (intellectual, verbal, rule-governed, repressed) is only one small part of our tradition, and not necessarily the biggest one. The Lorchenkov was blackly funny. The Aziz and the Michalopoulou were dull, though this could have been the translator’s fault. The Civil Servant’s Notebook is a multivocal roman a clef (really multivocal; some of the chapters are narrated by desk furniture) about municipal corruption in China; it was apparently a huge bestseller there and has touched off an entire popular genre of “officialdom literature.” Maybe we should have that here! Worst of the year: Easy, City of Mirrors. I just dumped a huge ball of words on this terrible book so I went ahead and broke it out as a separate post so as not to dominate my nice year of translations. ### Jordan Ellenberg — City of Mirrors Remember how much I liked the first book in this series? It wasn’t perfect, but I admired the idea of depicting the destruction of a world that’s already kind of ruined though the people in the world don’t fully realize it. (See also: Station Eleven.) I was going to write a long post about how lousy this book was but didn’t get around to it and now I’ve mercifully forgotten most of the worst parts. Still, I did save a lot of highlights of terrible sentences to my Kindle so here are some. “such was the bittersweet beauty of life” “Here, tacked to the neutral plaster walls, are the pennants of sports teams and the conundrumous M.C. Escher etching of hands drawing each other and, opposite the sagging single bed, the era-appropriate poster of the erect-nippled Sports Illustrated swimsuit model, beneath whose lubricious limbs and come-hither gaze and barely concealed pudenda the boy has furiously masturbated night after adolescent night.” “I’d known that Lucessi had a younger sister; he had failed to mention that she was a bona fide Mediterranean goddess, quite possibly the most beautiful girl I’d ever laid eyes on — regally tall, with lustrous black hair, a complexion so creamy I wanted to drink it, and a habit of traipsing into a room wearing nothing more than a slip…. striding through the house in tall riding boots and clanking spurs and tight breeches, a costume no less powerful than the slip in its ability to send the blood dumping to my loins.” “Though I knew I had done well, I was still astonished to see my first-semester report with its barricade of A’s” “Between these carnal escapades — Carmen and I would often race back to her room between classes for an hour of furious copulation — and my voluminous classwork and, of course, my hours at the library — time well spent replenishing myself for our next encounter — I saw less and less of Lucessi.” “On a Saturday afternoon, escorted by my father, I entered this sacred masculine space. The details were intoxicating. The odors of tonic, leather, talc. The combs lounging in their disinfecting aquamarine bath. The hiss and crackle of AM radio, broadcasting manly contests upon green fields. My father beside me. I waited on a chair of cracked red vinyl. Men were being barbered, lathered, whisked.” “Caleb had peeked at her journals a few times over the years, unable to resist this small crime; like her letters, her entries were wonderfully written. While they sometimes expressed doubts or concern over various matters, generally they communicated an optimistic view of life.” The combination of pretentiousness (“manly contests upon green fields”), cliche (“hiss and crackle”), thesaurus-wrangling (“barricade”,”traipsing”), and general vagueness (“various matters”) is really something special. It is not just bad but BAD in the sense of Paul Fussell. Oh yeah and also he’s obsessed with the word “possessed” where he means to say “had” or just express the idea in a defter way. “Something about this place felt new and undiscovered; it possessed a feeling of sanctuary.” “His flesh, a sickly yellow, possessed a damp, translucent appearance, like the inner layers of an onion.” “His thoughts possessed a lazy, unmoored quality.” “His limbs possessed a thin-boned delicacy” So much more is wrong! The way characters are often referred to as “the man” or “the woman,” the general concern with manliness throughout, but manliness of a very bent kind: a weird you-know-how-it-is sympathy towards characters when they get so frustrated that they just have to hit / strangle / kill / sexually assault a woman? Which culminates in the big action set piece at the end — so of course the big giant ship they have to escape on has been tiresomely personified as a woman, Michael’s actual one true love for 400 pages — then the big moment comes and the ship can’t consummate, all seems lost, until Michael solves the problem by calling the ship a bitch and hitting it with wrench, at which point it immediately settles down and behaves. Then the end is an epilogue set 1000 years in the future where a tenured professor (yes, there’s still tenure in 1000 years) gets lucky with a young journalist who’s captivated by his hidden depth and middle-aged loneliness. ### John Baez — Information Processing in Chemical Networks There’s a workshop this summer: • Dynamics, Thermodynamics and Information Processing in Chemical Networks, 13-16 June 2017, Complex Systems and Statistical Mechanics Group, University of Luxembourg. Organized by Massimiliano Esposito and Matteo Polettini. They write, “The idea of the workshop is to bring in contact a small number of high-profile research groups working at the frontier between physics and biochemistry, with particular emphasis on the role of Chemical Networks.” Some invited speakers include Vassily Hatzimanikatis, John Baez, Christoff Flamm, Hong Qian, Joshua D. Rabinowitz, Luca Cardelli, Erik Winfree, David Soloveichik, Stefan Schuster, David Fell and Arren Bar-Even. There will also be a session of shorter seminars by researchers from the local institutions such as Luxembourg Center for System Biomedicine. I believe attendance is by invitation only, so I’ll endeavor to make some of the ideas presented available here at this blog. ### Some of the people involved I’m looking forward to this, in part because there will be a mix of speakers I’ve met, speakers I know but haven’t met, and speakers I don’t know yet. I feel like reminiscing a bit, and I hope you’ll forgive me these reminiscences, since if you try the links you’ll get an introduction to the interface between computation and chemical reaction networks. In part 25 of the network theory series here, I imagined an arbitrary chemical reaction network and said: We could try to use these reactions to build a ‘chemical computer’. But how powerful can such a computer be? I don’t know the answer. Luca Cardelli answered my question in part 26. This was just my first introduction to the wonderful world of chemical computing. Erik Winfree has a DNA and Natural Algorithms Group at Caltech, practically next door to Riverside, and the people there do a lot of great work on this subject. David Soloveichik, now at U. T. Austin, is an alumnus of this group. In 2014 I met all three of these folks, and many other cool people working on these theme, at a workshop I tried to summarize here: Programming with chemical reaction networks, Azimuth, 23 March 2014. The computational power of chemical reaction networks, 10 June 2014. Chemical reaction network talks, 26 June 2014. I met Matteo Polettini about a year later, at a really big workshop on chemical reaction networks run by Elisenda Feliu and Carsten Wiuf: Trends in reaction network theory (part 1), Azimuth, 27 January 2015. Trends in reaction network theory (part 2), Azimuth, 1 July 2015. Polettini has his own blog, very much worth visiting. For example, you can see his view of the same workshop here: • Matteo Polettini, Mathematical trends in reaction network theory: part 1 and part 2, Out of Equilibrium, 1 July 2015. Finally, I met Massimiliano Esposito and Christoph Flamm recently at the Santa Fe Institute, at a workshop summarized here: Information processing and biology, Azimuth, 7 November 2016. So, I’ve gradually become educated in this area, and I hope that by June I’ll be ready to say something interesting about the semantics of chemical reaction networks. Blake Pollard and I are writing a paper about this now. ### Tommaso Dorigo — Anomaly! At 35% Discount For Ten More Days I thought it would be good to let you readers of this column know that in case you wish to order the book "Anomaly! Collider Physics and the Quest for New Phenomena at Fermilab" (or any other title published by World Scientific, for that matter) you have 10 more days to benefit of a 35% discount off the cover price. Just visit the World Scientific site of the book and use the discount code WS16XMAS35). read more ### Dave Bacon — Seattle for QIPers QIP 2017 is coming to Seattle, hosted by the QuArC group at Microsoft, January 16-20 (with tutorials on the 14th and 15th). If you have some spare moments, maybe you arrive early, or maybe you are planning for the afternoon off, here are some ideas for things to do around the wonderful city I call home. Be a Tourist! • Take a trip up to the Seattle Center (approximately 1 mile walk from Hotel). There you can take a ride to top of the Space Needle ($22), which has some great views when it is sunny (ha!). Music or Star Trek fan? Check out Paul Allen’s collection of toys and memorabilia Museum of Pop Culture ($30), which has two very geeky exhibits right now, Star Trek and Indie Game Revolution. Or if you are secure in your ability to not knock over stuff worth more than it’s weight in gold, check out the Chihuly Garden and Glass ($22, combine with a trip to Space Needle for $36). Kids and family in tow? Can’t go wrong with the Pacific Science Center ($27.75 adults, $11.75 kids) and the Seattle Children’s Museum ($10.50).
• Visit Pike’s Place Market (about 0.5 mile walk from Hotel). See them toss fish! Visit the original Starbucks (sssshhh it was actually the second). Like your politics off the chart? Check out Left Bank Books which has a seriously eclectic collection of books. While you’re at it, if you’re playing tourist, you might as well walk on down to the waterfront where you can take a ride on the Seattle Great Wheel ($13) or check out the Aquarium ($50 ouch) (we had a party there a few years back, yes we ate Sushi in front of the octopus.)
• Architect buff on the cheap? Check out the Seattle Central Library (a little over a half mile from Hotel). Sculpture buff on the cheap? Walk around the Olympic Sculpture Park (little over a mile from the Hotel). These are in completely different directions from the Hotel.
• Museums? Seattle Art Museum has a nice collection ($25) but my favorite these days is the Museum of History and Industry (Little over 1 mile walk,$20). The MoHaI is located in south Lake Union, a location that has been transformed dramatically in the last few years since Amazon relocated to the area. Count the number of cranes!
• So it turns out the Seattle you see today was built over the top of the Seattle that used to be, and, while I’ve never done it, everyone I know who has done it, loves the Seattle Underground Tour. Note that if you combine this tour with reading about earthquakes in the PNW you might give yourself some anxiety issues. Seattle is in the middle of boring a long tunnel under it’s downtown to replace the gigantic monstrosity of the viaduct, sadly I don’t think there are any tours of the tunnel boring machine, Big Bertha.
Be a Geek!
• Ada’s Technical Books is in the Capital Hill Neighborhood (bus or Lyft). It’s not as crazy as some university town bookstore, but has a good collection of non-standard science and tech books.
• Elliot Bay Bookstore again in Capital Hill is no Powell’s but it’s still rather good.
• Fantagraphics bookstore and gallery. You’ll know if you want to go to this if you recognize the name.
See a Show!
• We’ve a ton of snow right now. Snoqualmie is closest, great for beginners or if you’re just craving a quick ski or board. For the more serious, Baker, Crystal, and Stevens Pass are all recommended. I like Crystal a bit more, on clear days the view of Mt. Rainier is spectacular.
• Take a ferry over to Bainbridge Island. This is one of my top recommendations in the summer, but even in the winter it’s a nice trip. (Other summer recommendation is to rent a Kayak and kayak around Lake Union, but it’s too cold to do that this time of year.)
• If you’re up for a nice stroll, head over to Discovery Park or take a walk on the Alki beach in West Seattle (both require a ride to get there from Hotel, though you could walk down and take the water taxi on weekdays.) Closer by to the Hotel, head over to Myrtle Edwards Park.
Neighborhoods
• Seattle is a city of neighborhoods, each of which, believes that they have their own style! Each of these except Belltown or Downtown are a bus, cab, or rideshare away. Really there is too much to cover here, but here are a few short notes:
• Belltown: This is the neighborhood just north of downtown where the Hotel is located. Used to be sketchy but now has lots of luxury condos. Shorty’s is a dive with pinball and hot dogs. People seem to love Tilikum Place Cafe though I have not been there. If you want a traditional expensive steakhouse, El Gaucho is great, though I think the Metropolitan Grill in downtown is better (both pricey!) Since this is a quantum conference, I would be remorse to not point out that Belltown is the site of Some Random Bar, which I believe has good crab nachos. If you crave a sweet donut, Top Pot Donuts is literally just up the street from the hotel.
• Fremont: Is still an eclectic neighborhood, though not quite as far out as it used to be. It’s annual solstice parade is the only day it is legal to ride your bike nude in Seattle. Tons of places to eat and drink here, I recommend Brouwers (great beer selection, frites), Revel (Korean fusion, no reservations), and Paseo (cuban sandwiches OMG delicious) but there are a ton more in the neighborhood. Theo’s chocolate does factory tours and also supplies a great smell to the neighborhood (along with another smell from the nearby dispensaries!) Also if you’re up this way you can see a huge troll under a bridge, a rocket ship, and a statue of Lenin (who sometimes gets dressed in drag).
• Ballard: Originally a Scandinavian fishing community, these days it’s hip as Seattle hip gets. Sunday year round farmer’s market. When many people think of the Pacific Northwest they think of fish, but really I think where Seattle really shines is in shellfish. The Walrus and the Carpenter is a great place to affirm this claim.
• Capital Hill: East of downtown, Seattle’s most vibrant district. Fancy restaurants: Altura, Poppy.
• University District: Lots of cheap eats for UW students. In the summer I recommend renting a kayak from Agua Verde, a Mexican restuarant/kayak rental joint
• South Lake Union: Amazon land, totally transformed over the last few years. I’ve had good luck at re:public. Shuffleboard at Brave Horse Tavern.
Morning Run
I’d probably head over to the Sculpture park and run up Myrtle Edwards Park: here is a mapmyrun route.
Seattle
Enjoy Seattle, it’s a fun town! I recommend, generally, shellfish, thai food, and coffee. Also you can play the fun people guessing game: “software engineer or not” (advanced players can score points for Amazon or Microsoft sub-genres). Also: if you don’t want to look like a tourist, leave the umbrella at home. You know it rains more every year in New York city, right?
### Jordan Ellenberg — Prime subset sums
Efrat Bank‘s interesting number theory seminar here before break was about sums of arithmetic functions on short intervals in function fields. As I was saying when I blogged about Hast and Matei’s paper, a short interval in F_q[t] means: the set of monic degree-n polynomials P such that
deg(P-P_0) < h
for some monic degree-n P_0 and some small h. Bank sets this up even more generally, defining an interval in the space V of global sections of a line bundle on an arbitrary curve over F_q. In Bank’s case, by contrast with the number field case, an interval is an affine linear subspace of some ambient vector space of forms. This leads one to wonder: what’s special about these specific affine spaces? What about general spaces?
And then one wonders: well, what classical question over Z does this correspond to? So here it is: except I’m not sure this is a classical question, though it sort of seems like it must be.
Question: Let c > 1 be a constant. Let A be a set of integers with |A| = n and max(A) < c^n. Let S be the (multi)set of sums of subsets of A, so |S| = 2^n. What can we say about the number of primes in S? (Update: as Terry points out in comments, I need some kind of coprimality assumption; at the very least we should ask that there’s no prime factor common to everything in A.)
I’d like to say that S is kind of a “generalized interval” — if A is the first n powers of 2, it is literally an interval. One can also ask about other arithmetic functions: how big can the average of Mobius be over S, for instance? Note that the condition on max(S) is important: if you let S get as big as you want, you can make S have no primes or you can make S be half prime (thanks to Ben Green for pointing this out to me.) The condition on max(S) can be thought of as analogous to requiring that an interval containing N has size at least some fixed power of N, a good idea if you want to average arithmetic functions.
## January 04, 2017
### Jordan Ellenberg — France
Back from France! Just there for 2 1/2 days on the way back from Israel.
1. Cheeses eaten: Bethmale, Camembert, unidentified Basque sheep’s milk, Chabechou, Crottin de Chavignol, 28-month aged Comté, Vieux Cantal, Brie de Nangis. The Brie and the Chabechou (both from La Fermette) were the highlights.
2. On the other hand, Berthillon ice cream not as amazing as I remembered — possibly because American ice cream has gotten a lot better since 2004, the last time I was in Paris?
3. The Louvre is by far the most difficult major world museum to navigate. Why, for instance, the system where the rooms have numbers but the room numbers aren’t on the map?
4. I wonder museums with long entry lines have considered opening a separate, presumably shorter line for people willing to pay double (3x, 5x?) the usual entry fee.
5. In the most Thomas Friedman moment of my life, an Algerian cab driver heard my accent and immediately began telling me how much he loved Trump. If you want to know the Algerian cab driver conventional wisdom on this topic, it’s that Trump is a businessman and will “calmer” once he becomes President. I am doubtful. Tune in later to see who was right, the Algerian cab driver or his skeptical passenger.
6. AB really loved the Rodin sculptures in the Musee d’Orsay. I think because her height is such that she’s quite close to their feet. Rodin sculpted a hell of a foot.
7. I learned from Leila Schneps that the masters of the Académie Française have declared that “oignon” is to be spelled “ognon” from now on! I can’t adjust.
### Jordan Ellenberg — Israel
The main part of our trip was to Jerusalem, where I met my new nephew and organized a workshop about new developments in the polynomial method.
• The vote on UN resolution 2334 was held while I was there but nobody I talked to seemed really focused on it. One Israeli businessman told me “the Arabs won’t destroy Israel, Netanyahu won’t destroy Israel, the only thing that can destroy Israel is the residue of Bolshevism.” Then he told me things about taxes that curled my hair. Apparently if you do work for person X, and bill them for 100,000 shekels, you owe taxes on the 100,000 shekels, whether or not person X pays you! They go bankrupt or just stiff you, you’re screwed. If you go to the tax agency to say “how can I pay taxes on income I didn’t get” they say “the problem is between you and person X, go sue them if you need that money.”
• Tomer Schlank told me my accent was really good! I don’t speak Hebrew, by the way. But I’m actually very good at imitating accents, which is a problem, because when I carefully think about what I’m going to say (in Spanish, French, German, Hebrew, whatever) and then say it, I can sometimes fool the person I’m talking to into thinking I’m going to understand their response. Fortunately, I’m also very good at the blank look.
• My kids really wanted to go to the science museum and I was reluctant — there are science museums all over the world! — but I relented and actually it was kind of great. Culturally interesting, first of all, because the place was completely packed with Orthodox families; it was Hanukkah, a rare time when kids are off school but it’s not chag, which makes it massive go time for kid-oriented activities in Jerusalem. I was happy for my kids to experience that feeling of immersion in a crowd that was on the one hand Jewish but on the other hand quite culturally alien, in a way that secular cosmopolitan schwarma Israel really isn’t. As for the museum itself: “Games in Light and Shadow” was a really charming exhibit, sort of a cross between interactive science and a walk-through art space a la Meow Wolf.
• Sadly, we didn’t make it back to Cafe Itamar this time. But we did return to Morduch. I know it’s a tourist destination but in this case the tourists have it right, the Iraqi Jewish food there is incredible. Get the kubbe soup, get the hummus basar. This would be the best food I ate in Israel were it not for my Mizrachi machetunim in Afula. So it might be the best food you can eat in Israel.
### n-Category CaféGlobular for Higher-Dimensional Knottings (Part 3)
guest post by Scott Carter
This is my 3rd post a Jamie Vicary’s program Globular. And here I want to give you an exercise in manipulating a sphere in 4-dimensional space until it is demonstrably unknotted. But first I’ll need to remind you a lot about knotting phenomena. By the way, I lied. In the previous post, I said that the next one would be about braiding. I will write the surface braid post soon, but first I want to give you a fun exercise.
This post, then, will describe a 2-sphere embedded in 4-space, and we’ll learn to try and unknot it.
Loops of string can be knotted in 3-dimensional space. For example, go out to your tool shed and get out your orange heavy-duty 25 foot long extension cord. Plug the male end into the female and tape them together so that the plug cannot become undone. I would wager that as you try to unravel this on your living room floor, or your front lawn, you’ll discover that it is knotted.
Rather than using a physical model such as an extension cord, we can also create knots using the classical knot template of which I wrote in the first post. There you create knots by beginning with as many cups as you like in whatever nesting pattern that you like. For example:
And yes, these nestings are associated to elements in the Temperley-Lieb algebra. Then you can click and swipe left or right at the top endpoints and thereby entangle strings as you choose:
Close the result with a collection of caps, and a link results:
It is possible that the resulting link can be disentangled. To play with Globular, keep your link in the workspace, click on the identity menu item on the right, and then start trying to apply Reidemeister moves to it. For example, when I finished simplifying my diagram, I got the trefoil. I didn’t expect this!
If you want to see how I got the trefoil, you can look at my sequence of isotopy moves within globular.
By clicking the identity button on the right, you preserved the moves you used. The graphic immediately above indicates an annulus embedded in 3-space times an interval $[0,1]$. At the bottom is the knot that I drew, at the top is the result of the isotopy.
You can go into that isotopy, click the identity button, and modify it further to find a more efficient path between the knots!
Just as circles can be linked and knotted in 3-space, surfaces can be knotted and linked in 4-space. The knotting of higher dimensional spheres was observed by Emil Artin in a 1925 paper. Most progress about higher-dimensional knots occurred in the era circa 1960 through 1975. At that time, new algebraic topological techniques, particularly homological studies of covering spaces, occurred. Some authors, Yajima in particular, also initiated a diagrammatic theory. The diagram of a knotted surface is its projection from 4-space into 3-space with crossing information indicated. I like to think of the diagram as representing the knotted surface in a thin neighborhood of 3-space. The bits of surface that are indicated by breaks protrude into 4-space in that thin neighborhood. Still this imagery does not help manipulate the surface. By analogy, if you think of a classical knot as being confined to a thin sheet of space, then you’ll feel constrained in pulling the under-crossing arc.
As sighted humans, we perceive only surface. We posit solid. So as I sit at my desk, I see its top and I presume that it is made of a thick wood. The drawer in front of me defines a cavity in which paper clips, rubber bands, and old papers sit. But I can’t see through this. I only see the front of the drawer. When I look at the diagram of a knotted surface, I create visual tropes to help me understand. How many layers are there behind the visible layer? Where does the surface fold? Where does it interweave? Within the globular view (project 2) of a knotted surface, we see (1) the face of the surface that lies closest to us, and (2) the collection of double curves, triple points, folds, and cusps that induce the knotting. Globular is new — only a year old. So its depiction of these things is not as elegant as it might be, but all the information is there. Mouse-overs let us know the type and the levels of all the singular sets. Cusps and optimal points of double curves (these are double curves in the projection of the surface into 3-space not double curves in 4-space) have the same shape. They should have different colors. Similarly birth, deaths, saddles, and crotches will all be cup or cap like. Hover the mouse to the critical point, and you’ll see what it is.
Here:
is the image of a sphere in 4-space that looks like it might be knotted. But in fact it is not. This is the image from a worksheet that I created specifically for the energetic readers of this blog. In the worksheet, I created a sphere embedded in 4-space that is constructed as Zeeman’s 1-twist spin of the figure-8 knot (4sub1) in the tables. At least I think I did! Zeeman’s general twist spinning theorem says that the n-twist-spin of a classical knot is fibered with its fibre being the (punctured) n-fold branched cover of the 3-sphere branched along the given knot. When n=1, this branched cover is the 3-ball, and so the embedded sphere bounds a ball, and therefore is unknotted.
The worksheet that I created here is a quebra-cabeça — a mind-bending puzzle for the reader. Can you use globular to unknot this embedded sphere? By the way, I am not 100 percent sure that I constructed this example correctly ;-) But here is my advise for unknotting it. There are two critical points, one saddle and one crotch, that need to have their heights interchanged. To interchange these heights, add two swallow tails: a left (up or down) swallow tail (L ST (up or down)) on the interior red fold line, and a right (down or up) (R ST (down or up)) on the interior green fold. These folds are mouse-over named cap and cup, respectively. The swallow tails allow you to turn the surface on its side. Then pull the stuff (type I, ysp, and psy) that lie along these folds into the swallowtail regions. meanwhile interchange the heights of the crotch and saddle. When you get done with that, I’ll give another hint, and I may have done these operations myself.
### n-Category CaféField Notes on the Behaviour of a Large Assemblage of Ecologists
I’ve just come back from the annual conference of the British Ecological Society in Liverpool. For several years I’ve had a side-interest in ecology, but I’d never spent time with a really large group of ecologists before, and it taught me some things. Here goes:
1. Size and scale. Michael Reed memorably observed that the American Mathematical Society is about the same size as the American Society for Nephrology, “and that’s just the kidney”. Simply put: not many people care about mathematics.
The British Ecological Society (BES) meeting had 1200 participants, which is about ten times bigger than the annual international category theory meeting, and still only a fraction of the size of the conference run by the Ecological Society of America. You may reply that the US Joint Mathematics Meetings attract about 7000 participants; but as Reed pointed out (under the heading “Most of Science is Biology”), the Society for Neuroscience gets about 30,000. Even at the BES meeting in our small country, there were nearly 600 talks, 70 special sessions, and 220 posters. In the parallel sessions, you had a choice of 12 talks to go to at any given moment in time.
2. Concision. Almost all talks were 12 minutes, with 3 minutes for questions. You cannot, of course, say much in that time.
With so many people attending and wanting to speak, it’s understandable that the culture has evolved this way. And I have to say, it’s very nice that if you choose to attend a talk and swiftly discover that you chose badly, you’ve only lost 15 minutes.
But there are many critiques of enforced brevity, including from some very distinguished academics. It’s traditionally held that the most prestigious journals in all of science are Nature and Science, and in both cases the standard length of an article is only about three pages. The style of such papers is ludicrously condensed, and from my outsider’s point of view I gather that there’s something of a backlash against Nature and Science, with less constipated publications gaining ground in people’s mental ranking systems. When science is condensed too much, it takes on the character of a sales pitch.
This is part of a wider phenomenon of destructive competition for attention. For instance, almost all interviews on TV news programmes are under ten minutes, and most are under five, with much of that taken up by the interviewer talking. The very design favours sloganeering and excludes all points that are too novel or controversial to explain in a couple of sentences. (The link is to a video of Noam Chomsky, who makes this point very effectively.) Not all arguments can be expressed to a general audience in a few minutes, as every mathematician knows.
3. The pleasure of introductions. Many ecologists study one particular natural system, and often the first few minutes of their talks are a delight. You learn something new and amazing about fungi or beavers or the weird relationships between beetles and ants. Did you know that orangutans spend 80% of the day resting in their nests? Or that if you give a young orangutan some branches, he or she will instinctively start to weave them together in a nest-like fashion, as an innate urge that exists whether or not they’ve been taught how to do it? I didn’t.
4. Interdisciplinarity. I’ve written before about the amazing interdisciplinarity of biologists. It seems to be ingrained in the intellectual culture that you need people who know stuff you don’t know, obviously! And that culture just isn’t present within mathematics, at least not to anything like the same extent.
For instance, this afternoon I went to a talk about the diversity of microbiomes. The speaker pointed out that for what she was doing, you needed expertise in biology, chemistry, and informatics. She was unusual in actually spelling it out and spending time talking about it. Most of the time, speakers moved seamlessly from ecology to statistics to computation (typically involving processing of large amounts of DNA sequence data), without making a big deal of it.
But there’s a byproduct of interdisciplinarity that troubles my mathematical soul:
5. The off-the-shelf culture. Some of the speakers bowled me over with their energy, vision, tenacity, and positive outlook. But no one’s superhuman, so it’s inevitable that if your work involves serious aspects of multiple disciplines, you’re probably not going to look into everything profoundly. Or more bluntly: if you need some technique from subject X and you know nothing about subject X, you’re probably just going to use whatever technique everybody else uses.
The ultimate reason why I ended up at this conference is that I’m interested in the quantification of biological diversity. So, much of the time I chose to go to talks that had the word “diversity” in the title, just to see what measure of diversity was used by actual practising ecologists.
It wasn’t very surprising that almost all the time, as far as I could tell, there was no apparent examination of what the measures actually measured. They simply used whatever measure was predominant in the field.
Now, I need to temper that with the reminder that the talks are ultra-short, with no time for subtleties. But still, when I asked one speaker why he chose the measure that he chose, the answer was that it’s simply what everyone else uses. And I can’t really point a finger of blame. He wasn’t a mathematician, any more than I’m an ecologist.
6. The lack of theory. If this conference was representative of ecology, the large majority of ecologists study some specific system. By “system” I mean something like European hedgerow ecology, or Andean fungal ecology, or the impact of heatwaves on certain types of seaweed.
This is, let me be clear, not a bad thing. Orders of magnitude more people care about seaweed than $n$-categories. But still, I was surprised by the sheer niche-ness of general theory in the context of ecology as a whole. A group of us are working on a system of diversity measures that are general in a mathematician’s sense; they effortlessly take in such examples as human demography, tropical forestry, epidemiology, and resistance to antibiotics. This didn’t seem like that big a deal to me previously — it’s just the bog-standard generality of mathematics. But after this week, I can see that from many ecologists’ eyes, it may seem insanely general.
Actually, the most big-picture talks I saw were very unmathematical. They were, in fact, about policy and the future of humanity. I’m not being flippant:
7. Unabashed politics. Mathematics is about an idealized world of imagination. Ecology is about our one and only natural world — one that we happen to be altering at an absolutely unprecedented rate. Words like “Brexit” and “Trump” came up dozens of times in the conference talks, and not in a tittery jocular way. The real decisions of people with real political power will have real, irreversible effect in the real world.
Once again, this brought home to me that mathematics is not like (the rest of) science.
It’s not just that we don’t have labs or experiments or hypothesis testing (at least, not in the same way). It’s that we can do mathematics in complete isolation from the realities of the world that human beings have made.
We don’t have to think about deforestation or international greenhouse gas treaties or even local fishery byelaws. We might worry about the applications of mathematics — parasitic investment banks or deadly weapons or governments surveilling and controlling their citizens — but we can actually do mathematics in lamb-like innocence.
On the other hand, for large parts of ecology, the political reality is an integral consideration.
I saw some excellent talks, especially from Georgina Mace and Hugh Possingham, on policy and influencing governments. Possingham was talking about saving Portugal-sized areas of Australia from industrial destruction. (His advice for scientists engaging with governments: “Turn up. Have purpose. Maintain autonomy.”) Mace spoke on what are quite possibly the biggest threats to the entire planet: climate change, floods and heatwaves, population growth, and fragmentation and loss of habitats.
It’s inspiring to see senior scientists being unafraid to repeat basic truths to those in power, to gather the available evidence and make broad estimates with much less than 100% of the data that one might wish for, in order to push changes that will actually improve human and other animal lives.
### Backreaction — The Bullet Cluster as Evidence against Dark Matter
Once upon a time, at the far end of the universe, two galaxy clusters collided. Their head-on encounter tore apart the galaxies and left behind two reconfigured heaps of stars and gas, separating again and moving apart from each other, destiny unknown. Four billion years later, a curious group of water-based humanoid life-forms tries to make sense of the galaxies’ collision. They point their
## January 03, 2017
### Noncommutative Geometry — Gamma functions and nonarchimedean analysis
Happy New Year! I view blog writing as a great opportunity to reach out to members of the mathematics community and especially the younger members; so in this sense blog writing is, for me, very similar to writing for Math Reviews. I have enjoyed doing both for many years (and many many years for MR!). Recently I wrote a review for MR on the paper Twisted characteristic p zeta functions''
### n-Category CaféBasic Category Theory Free Online
My textbook Basic Category Theory, published by Cambridge University Press, is now also available free as arXiv:1612.09375.
As I wrote when I first announced the book:
• It doesn’t assume much.
• It sticks to the basics.
• It’s short.
I can now add a new property:
• It’s free.
And it’s not only free, it’s freely editable. The book’s released under a Creative Commons licence that allows you to edit and redistribute it, just as long as you state the authorship accurately, don’t use it for commercial purposes, and preserve the licence. Click the link for details.
Why might you want to edit it?
Well, maybe you want to use it to teach a category theory course, but none of your students have taken topology, so you’d rather remove all the topological examples. That’s easy to do. Or maybe you want to add some examples, or remove whole sections. Or it could just be that you can’t stand some of the notation, in which case all you need to do is change some macros. All easy.
Alternatively, perhaps you’re not planning to teach from it — you just want to read it, but you want to change the formatting so that it’s comfortable to read on your favourite device. Again, this is very easy to do.
Emily recently announced the dead-tree debut of her own category theory textbook, published by Dover. She did it the other way round from me: the online edition came first, then the paper version. (I also did it that way round for my first book.) But the deal I had with Cambridge was that they’d publish first, then I could put it on the arXiv under a Creative Commons licence 18 months later.
We’ve talked a lot on this blog about parasitic academic publishers, so I’d like to emphasize here what a positive contribution Cambridge University Press has made, and is continuing to make, to the academic community. CUP is a part of Cambridge University, and I think I’m right in saying that it’s not allowed to make a profit. (Correction: I was wrong. However, maximizing profits is not CUP’s principal aim.) It has led the way in allowing mathematics authors to post free versions of their books online. For instance, apart from my own two books, you quite likely know of Allen Hatcher’s very successful book Algebraic Topology, also published in paper form by CUP and, with their permission, available free online.
Since a few people have asked me privately for opinions on publishers, I’ll also say that working with CUP for this book was extremely smooth. The contract (including the arXiv release) was easily arranged, and the whole production process was about as low-stress as I can imagine it being. This wasn’t the case for my first book in 2003, also with CUP, which because of editing/production problems was a nightmare of stress. That made me very reluctant to go with CUP again, but I’m really glad that I chose to do so.
The low stress this time was partly because of one key request that I made at the beginning: we agreed that I would not share the Latex files with anyone at CUP. Thus, all I ever sent CUP was the PDF, and no one except me had ever seen my Latex source until the arXiv release just now. What that meant was that all changes, down to the comma, had to go through me. For example, the way the proofreading worked was that the proofreader would send me corrections and suggestions and I’d implement them, rather than him making changes first and me approving or reverting them second.
For anyone with a perfectionist/pedantic/… streak like mine (insert your own word), that’s an enormous stress relief. I’d recommend it to any authors of a similar personality. Again, it’s to CUP’s credit that they agreed to doing things this way — I’m not sure that all publishers would.
So the book’s now free to all. If you make heavy use of it and can afford to do so, I hope you’ll reciprocate the support that CUP has shown the mathematical community by buying a copy. But in any case, I hope you enjoy it.
### Backreaction — How to use an "argument from authority"
I spent the holidays playing with the video animation software. As a side-effect, I produced this little video. If you'd rather read than listen, here's the complete voiceover: It has become a popular defense of science deniers to yell “argument from authority” when someone quotes an experts’ opinion. Unfortunately, the argument from authority is often used incorrectly. What is an “argument
## January 02, 2017
### Backreaction — The 2017 Edge Annual Question: Which Scientific Term or Concept Ought To Be More Widely Known?
My first thought when I heard the 2017 Edge Annual Question was “Wasn’t that last year's question?” It wasn’t. But it’s almost identical to the 2011 question, “What scientific concept would improve everybody’s cognitive toolkit.” That’s ok, I guess, the internet has an estimated memory of 2 days, so after 5 years it’s reasonable to assume nobody will remember their improved toolkit. After that
### Tommaso Dorigo — A Visit To Israel
I am spending a week in Israel to visit three physics institutes for colloquia and seminars: the Tel Aviv University (where I gave a colloquium yesterday), the Haifa Technion (where I am giving a seminar today), and the Weizmann institute in Rehovot (where I'll speak next Wednesday).
### Geraint F. Lewis — Blog rebirth - a plan for 2017
It is now the twilight zone between Christmas and New Year. 2016 has been a difficult and busy year, and my recreational physics and blogging has suffered. But it is time for a rebirth and I plan to get back to the writing about science and space here. But here's some things from 2016.
A Fortunate Universe: Life in a finely tuned cosmos was published. This has sucked up a huge amount of time and mental activity, and that continues. I will blog about the entire writing and publishing process at some point in the future, but it really is quite a complex process with many mine-fields to navigate. But it is done, and am planning to write more in the future.
I've done a lot of writing in other places, including Cosmos magazine on "A universe made for me? Physics, fine-tuning and life", and commentary in New Scientist and several articles in The Conversation including
Peering into the future: does science require predictions?
and
The cosmic crime-scene hunt for clues on how galaxies are formed
And one of my articles from last year, We are lucky to live in a universe made for us was selected for inclusion in The Best Australian Science Writing 2016,
There has been a whole bunch of science papers as well, but I will write about those when the blog is up and running at full speed :)
## December 31, 2016
### n-Category CaféNSA Axes Math Grants
Old news, but interesting: the US National Security Agency (NSA) announced some months ago that it was suspending funding to its Mathematical Sciences Program. The announcement begins by phrasing it as a temporary suspension—
…[we] will be unable to fund any new proposals during FY2017 (i.e. Oct. 1, 2016–Sept. 30, 2017)
—but by the end, sounds resigned to a more permanent fate:
We thank the mathematics community and especially the American Mathematical Society for its interest and support over the years.
The NSA is said to be the largest employer of mathematicians in the world, and has been under political pressure for obvious reasons over the last few years, so it’s interesting that it cut this programme. Its British equivalent, GCHQ, is doing the opposite, expanding its mathematics grants aggressively. But still, GCHQ consistently refuses to engage in any kind of adult, evidence-based discussion with the mathematical community on what the effect of its actions on society might actually be.
## December 29, 2016
### John Baez — Azimuth Backup Project (Part 2)
I want to list some databases that are particularly worth backing up. But to do this, we need to know what’s already been backed up. That’s what this post is about.
### Azimuth backups
Here is information as of now (21:45 GMT 20 December 2016). I won’t update this information. For up-to-date information see
For up-to-date information on the progress of each of individual databases listed below, click on my summary of what’s happening now.
Here are the databases that we’ve backed up:
• NOAA Carbon Dioxide Information Analysis Center (CDIAC) data at ftp.ncdc.noaa.gov/pub/data/paleo/cdiac.ornl.gov-pub — downloaded by Jan and uploaded to Sakari’s datarefuge server.
These are still in progress, but I think we have our hands on the data:
• NOAA Precipitation Frequency Data at http://hdsc.nws.noaa.gov/hdsc/pfds/ and ftp://hdsc.nws.noaa.gov/pubdownloaded by Borislav, not yet uploaded to Sakari’s datarefuge server.
• NOAA Carbon Dioxide Information Analysis Center (CDIAC) website at http://cdiac.ornl.govdownloaded by Jan, uploaded to Sakari’s datarefuge server, but there’s evidence that the process was incomplete.
• NOAA National Centers for Environmental Information (NCEI) website at https://www.ncdc.noaa.govdownloaded by Jan, who is now attempting to upload it to Sakari’s datarefuge server, but there are problems.
• Ocean and Atmospheric Research data at ftp.oar.noaa.gov — downloaded by Jan, now attempting to upload it to Sakari’s datarefuge server.
• NOAA NCEP/NCAR Reanalysis ftp site at ftp.cdc.noaa.gov/Datasets/ncep.reanalysis/ — downloaded by Jan, now attempting to upload it to Sakari’s datarefuge server.
I think we’re getting these now, more or less:
• NOAA National Centers for Environmental Information (NCEI) ftp site at ftp://eclipse.ncdc.noaa.gov/pub/ — in the process of being downloaded by Jan, “Very large. May be challenging to manage with my facilities”.
• NASA Planetary Data System (PDS) data at https://pds.nasa.govin the process of being downloaded by Sakari.
• NOAA tides and currents products website at https://tidesandcurrents.noaa.gov/products.html, which includes the sea level trends data at https://tidesandcurrents.noaa.gov/sltrends/sltrends.htmlJan is downloading this.
• NASA-ESDIS Oak Ridge National Laboratory Distributed Active Archive (DAAC) on Biogeochemical Dynamics at https://daac.ornl.gov/get_data.shtmlJan is downloading this.
• NASA-ESDIS Oak Ridge National Laboratory Distributed Active Archive (DAAC) on Biogeochemical Dynamics website at https://daac.ornl.gov/Jan is downloading this.
### Other backups
Other backups are listed at
This nicely provides the sizes of various backups, and other useful information. Some are ‘signed and verified’ with cryptographic keys, but I’m not sure exactly what that means, and the details matter.
About 90 databases are listed here, along with some size information and some information about whether people have already backed them up or are in process:
Gov. Climate Datasets (Archive). (Click on the tiny word “Datasets” at the bottom of the page!)
### Tommaso Dorigo — INFN Gives 73 Permanent Positions To Young Researchers In Physics
Today I am actually quite proud of my research institute, the "Istituto Nazionale di Fisica Nucleare, INFN, which leads Italian research in fundamental physics. In fact a selection to hire 73 new researchers with permanent positions has reached its successful conclusion. Rather than giving you my personal opinions (very positive!) I think it is better to let speak the INFN president Fernando Ferroni, and the numbers themselves.
### Doug Natelson — Some optimism at the end of 2016
When the news is filled with bleak items, like:
it's easy to become pessimistic. Bear in mind that modern communications plus the tendency for bad news to get attention plus the size of the population can really distort perception. To put that another way, 56 million people die every year (!), but now you are able to hear about far more of them than ever before.
Let me make a push for optimism, or at least try to put some things in perspective. There are some reasons to be hopeful. Specifically, look here, at a site called "Our World in Data", produced at Oxford University. These folks use actual numbers to point out that this is actually, in many ways, the best time in human history to be alive:
• The percentage of the world's population living in extreme poverty is at an all-time low (9.6%).
• The percentage of the population that is literate is at an all-time high (85%), as is the overall global education level.
• Child mortality is at an all-time low.
• The percentage of people enjoying at least some political freedom is at an all-time high.
That may not be much comfort to, say, an unemployed coal miner in West Virginia, or an underemployed former factory worker in Missouri, but it's better than the alternative. We face many challenges, and nothing is going to be easy or simple, but collectively we can do amazing things, like put more computing power in your hand than existed in all of human history before 1950, set up a world-spanning communications network, feed 7B people, detect colliding black holes billions of lightyears away by their ripples in spacetime, etc. As long as we don't do really stupid things, like make nuclear threats over twitter based on idiots on the internet, we will get through this. It may not seem like it all the time, but compared to the past we live in an age of wonders.
## December 28, 2016
### John Baez — Give the Earth a Present: Help Us Save Climate Data
We’ve been busy backing up climate data before Trump becomes President. Now you can help too, with some money to pay for servers and storage space. Please give what you can at our Kickstarter campaign here:
If we get $5000 by the end of January, we can save this data until we convince bigger organizations to take over. If we don’t get that much, we get nothing. That’s how Kickstarter works. Also, if you donate now, you won’t be billed until January 31st. So, please help! It’s urgent. I will make public how we spend this money. And if we get more than$5000, I’ll make sure it’s put to good use. There’s a lot of work we could do to make sure the data is authenticated, made easily accessible, and so on.
### The idea
The safety of US government climate data is at risk. Trump plans to have climate change deniers running every agency concerned with climate change. So, scientists are rushing to back up the many climate databases held by US government agencies before he takes office.
We hope he won’t be rash enough to delete these precious records. But: better safe than sorry!
The Azimuth Climate Data Backup Project is part of this effort. So far our volunteers have backed up nearly 1 terabyte of climate data from NASA and other agencies. We’ll do a lot more! We just need some funds to pay for storage space and a server until larger institutions take over this task.
### The team
Jan Galkowski is a statistician with a strong interest in climate science. He works at Akamai Technologies, a company responsible for serving at least 15% of all web traffic. He began downloading climate data on the 11th of December.
• Shortly thereafter John Baez, a mathematician and science blogger at U. C. Riverside, joined in to publicize the project. He’d already founded an organization called the Azimuth Project, which helps scientists and engineers cooperate on environmental issues.
• When Jan started running out of storage space, Scott Maxwell jumped in. He used to work for NASA—driving a Mars rover among other things—and now he works for Google. He set up a 10-terabyte account on Google Drive and started backing up data himself.
• A couple of days later Sakari Maaranen joined the team. He’s a systems architect at Ubisecure, a Finnish firm, with access to a high-bandwidth connection. He set up a server, he’s downloading lots of data, he showed us how to authenticate it with SHA-256 hashes, and he’s managing many other technical aspects of this project.
There are other people involved too. You can watch the nitty-gritty details of our progress here:
## December 27, 2016
### Mark Chu-Carroll — Okonomilatkes!
I’m working on some type theory posts, but it’s been slow going.
In the meantime, it’s Chanukah time. Every year, my family makes me cook potato latkes for Chanukah. The problem with that is, I don’t particularly like potato latkes. This year, I came up with the idea of trying to tweak them into something that I’d actually enjoy eating. What I came up with is combining a latke with another kind of fried savory pancake that I absolutely love: the japanese Okonomiyaki. The result? Okonomilatkes.
Ingredients:
• 1/2 head green cabbage, finely shredded.
• 1 1/2 pounds potatoes
• 1/2 cup flour
• 1/2 cup water
• 1 beaten egg
• 1/2 pound crabstick cut into small pieces
• Tonkatsu sauce (buy it at an asian grocery store in the japanese section. The traditional brand has a bulldog logo on the bottle.)
• Katsubuoshi (shredded bonito)
• Japanese mayonaise (sometimes called kewpie mayonaise. You can find it in squeeze bottles in any asian grocery. Don’t substitute American mayo – Japanese mayo is thinner, less oily, a bit tart, sweeter, and creamier. It’s really pretty different.)
• 1 teaspoon salt
• 1/2 teaspoon baking powder.
Instructions
1. In a very hot pan, add about a tablespoon of oil, and when it’s nearly smoking, add the cabbage. Saute until the cabbage wilts and starts to brown. Remove from the heat, and set aside to cool.
2. Using either the grater attachment of a food processor, or the coarse side of a box grater, shred the potatoes. (I leave the skins on, but if that bugs you, peel them first).
3. Squeeze as much water as you can out of the shredded potatoes.
4. Mix together the water, flour, baking powder, egg, and salt into a thin batter.
5. Add the potatoes, cabbage, and crabstick to the batter, and stir together.
6. Split this mixture into four portions.
7. Heat a nonstick pan on medium high heat, add a generous amount of oil, and add one quarter of the batter. Let it cook until nicely browned, then flip, and cook the other side. On my stove, it takes 3-5 minutes per side. Add oil as needed while it’s cooking.
8. Repeat with the other 3 portions
9. To serve, put a pancake on a plate. Squeeze a bunch of stripes of mayonaise, then add a bunch of the tonkatsu sauce, and sprinkle with the katsubuoshi.
## December 24, 2016
### Steinn Sigurðsson — Jólasveinar og Jólakettir
The origins and history of the Yule Lads with bonus Christmas Cat…
Even I did not know that peak Yule Lads was 82!
Criminy!
### Steinn Sigurðsson — Last minute stocking stuffers for nörds
Ok, I confess, I was supposed to get these reviewed before the Holidays, but a Sequence of Unfortunate Events Intervened and I am only part way through these.
Anywho, if you need a last second pressie for random acquaintances so disposed, there are a couple of interesting science books out there:
1. A Fortunate Universe: Life in a Finely Tunes Cosmos by Geraint Lewis and Luke Barnes, is a nice up to date book for the general (educated) public on modern physics and cosmology.
If covers modern cosmology and some of the Big Questions of our times, in particular the issue of anthropomorphism how “fine tuned” our Universe is.
Welshman finds QSO
2. Modern Prometheus: Editing the Human Genome with Crispr-Cas9 by James Kozubek is a personal history of the discovery of the CRISPR-CAS9 genes and their use, and a discussion of the implications and potential of the technology.
It is not an easy book, it does not flow, the discussion is technical given the intended audience and the narrative digresses frequently with often convoluted discussion.
But the topic is interesting and the coverage is comprehensive.
3. Mapping the Heavens: The Radical Scientific Ideas That Reveal the Cosmos by Priyamvada Natarajan.
Ok, I haven’t read this one, don’t have a copy.
But, I’ve heard very good things about it.
A big picture of current research in cosmology, aimed at the educated general reader, covering a range of topics but focusing on the search for dark matter, if what I am told is true.
I’d like to read it, so I’m sure you ought to also.
moovel lab makes funky maps,
go play
### Richard Easther — New York State of Mind
It's not often an advertisement sums up a deep truth about the universe, but here's one that does.
One of the commonest questions about the Big Bang is "If the universe is expanding, is everything in it getting bigger? The solar system, the sun, the earth, our bodies and the atoms we are made of?"
The answer is no, anything that can hold itself together won't get any bigger as the Universe grows. For big things (like our Milky Way galaxy, or the Solar System within it) gravity provides the glue that stops them from stretching; for little things like rocks and people electrical forces between atoms hold them together. Only the space between galaxies (and clusters of galaxies) grows as the Universe expands which is just as Einstein's General Relativity predicts, and our most sensitive measurements confirm. (Phew)
But Manhattan Mini Storage nails it in eight words. Those New Yorkers, always in a hurry...
## December 22, 2016
### Terence Tao — AMS open math notes
I just learned (from Emmanuel Kowalski’s blog) that the AMS has just started a repository of open-access mathematics lecture notes. There are only a few such sets of notes there at present, but hopefully it will grow in the future; I just submitted some old lecture notes of mine from an undergraduate linear algebra course I taught in 2002 (with some updating of format and fixing of various typos).
[Update, Dec 22: my own notes are now on the repository.]
Filed under: advertising, math.RA Tagged: linear algebra
## December 21, 2016
### Sean Carroll — Memory-Driven Computing and The Machine
Back in November I received an unusual request: to take part in a conversation at the Discover expo in London, an event put on by Hewlett Packard Enterprise (HPE) to showcase their new technologies. The occasion was a project called simply The Machine — a step forward in what’s known as “memory-driven computing.” On the one hand, I am not in any sense an expert in high-performance computing technologies. On the other hand (full disclosure alert), they offered to pay me, which is always nice. What they were looking for was simply someone who could speak to the types of scientific research that would be aided by this kind of approach to large-scale computation. After looking into it, I thought that I could sensibly talk about some research projects that were relevant to the program, and the technology itself seemed very interesting, so I agreed stop by London on the way from Los Angeles to a conference in Rome in honor of Georges Lemaître (who, coincidentally, was a pioneer in scientific computing).
Everyone knows about Moore’s Law: computer processing power doubles about every eighteen months. It’s that progress that has enabled the massive technological changes witnessed over the past few decades, from supercomputers to handheld devices. The problem is, exponential growth can’t go on forever, and indeed Moore’s Law seems to be ending. It’s a pretty fundamental problem — you can only make components so small, since atoms themselves have a fixed size. The best current technologies sport numbers like 30 atoms per gate and 6 atoms per insulator; we can’t squeeze things much smaller than that.
So how do we push computers to faster processing, in the face of such fundamental limits? HPE’s idea with The Machine (okay, the name could have been more descriptive) is memory-driven computing — change the focus from the processors themselves to the stored data they are manipulating. As I understand it (remember, not an expert), in practice this involves three aspects:
1. Use “non-volatile” memory — a way to store data without actively using power.
2. Wherever possible, use photonics rather than ordinary electronics. Photons move faster than electrons, and cost less energy to get moving.
3. Switch the fundamental architecture, so that input/output and individual processors access the memory as directly as possible.
Here’s a promotional video, made by people who actually are experts.
The project is still in the development stage; you can’t buy The Machine at your local Best Buy. But the developers have imagined a number of ways that the memory-driven approach might change how we do large-scale computational tasks. Back in the early days of electronic computers, processing speed was so slow that it was simplest to store large tables of special functions — sines, cosines, logarithms, etc. — and just look them up as needed. With the huge capacities and swift access of memory-driven computing, that kind of “pre-computation” strategy becomes effective for a wide variety of complex problems, from facial recognition to planing airline routes.
It’s not hard to imagine how physicists would find this useful, so that’s what I briefly talked about in London. Two aspects in particular are pretty obvious. One is searching for anomalies in data, especially in real time. We’re in a data-intensive era in modern science, where very often we have so much data that we can only find signals we know how to look for. Memory-driven computing could offer the prospect of greatly enhanced searches for generic “anomalies” — patterns in the data that nobody had anticipated. You can imagine how that might be useful for something like LIGO’s search for gravitational waves, or the real-time sweeps of the night sky we anticipate from the Large Synoptic Survey Telescope.
The other obvious application, of course, is on the theory side, to large-scale simulations. In my own bailiwick of cosmology, we’re doing better and better at including realistic physics (star formation, supernovae) in simulations of galaxy and large-scale structure formation. But there’s a long way to go, and improved simulations are crucial if we want to understand the interplay of dark matter and ordinary baryonic physics in accounting for the dynamics of galaxies. So if a dramatic new technology comes along that allows us to manipulate and access huge amounts of data (e.g. the current state of a cosmological simulation) rapidly, that would be extremely useful.
Like I said, HPE compensated me for my involvement. But I wouldn’t have gone along if I didn’t think the technology was intriguing. We take improvements in our computers for granted; keeping up with expectations is going to require some clever thinking on the part of engineers and computer scientists.
## December 20, 2016
### Doug Natelson — Mapping current at the nanoscale - part 2 - magnetic fields!
A few weeks ago I posted about one approach to mapping out where current flows at the nanoscale, scanning gate microscopy. I had made an analogy between current flow in some system and traffic flow in a complicated city map. Scanning gate microscopy would be analogous recording the flow of traffic in/out of a city as a function of where you chose to put construction barrels and lane closures. If sampled finely enough, this would give you a sense of where in the city most of the traffic tends to flow.
Of course, that's not how utilities like Google Maps figure out traffic flow maps or road closures. Instead, applications like that track the GPS signals of cell phones carried in the vehicles. Is there a current-mapping analogy here as well? Yes. There is some "signal" produced by the flow of current, if only you can have a sufficiently sensitive detector to find it. That is the magnetic field. Flowing current density $$\mathbf{J}$$ produces a local magnetic field $$\mathbf{B}$$, thanks to Ampere's law, $$\nabla \times \mathbf{B} = \mu_{0} \mathbf{J}$$.
Scanning SQUID microscope image of x-current density in a GaSb/InAs structure, showing that the current is carried by the edges. Scale bar is 20 microns. Image
Fortunately, there now exist several different technologies for performing very local mapping of magnetic fields, and therefore the underlying pattern of flowing current in some material or device. One older, established approach is scanning Hall microscopy, where a small piece of semiconductor is placed on a scanning tip, and the Hall effect in that semiconductor is used to sense local $$B$$ field.
Scanning NV center microscopy to see magnetic fields,Scale bars are 400 nm.
Considerably more sensitive is the scanning SQUID microscope, where a tiny superconducting loop is placed on the end of a scanning tip, and used to detect incredibly small magnetic fields. Shown in the figure, it is possible to see when current is carried by the edges of a structure rather than by the bulk of the material, for example.
A very recently developed method is to use the exquisite magnetic field sensitive optical properties of particular defects in diamond, NV centers. The second figure (from here) shows examples of the kinds of images that are possible with this approach, looking at the magnetic pattern of data on a hard drive, or magnetic flux trapped in a superconductor. While I have not seen this technique applied directly to current mapping at the nanoscale, it certainly has the needed magnetic field sensitivity. Bottom line: It is possible to "look" at the current distribution in small structures at very small scales by measuring magnetic fields.
## December 16, 2016
### Sean Carroll — Quantum Is Calling
Hollywood celebrities are, in many important ways, different from the rest of us. But we are united by one crucial similarity: we are all fascinated by quantum mechanics.
This was demonstrated to great effect last year, when Paul Rudd and some of his friends starred with Stephen Hawking in the video Anyone Can Quantum, a very funny vignette put together by Spiros Michalakis and others at Caltech’s Institute for Quantum Information and Matter (and directed by Alex Winter, who was Bill in Bill & Ted’s Excellent Adventure). You might remember Spiros from our adventures emerging space from quantum mechanics, but when he’s not working as a mathematical physicist he’s brought incredible energy to Caltech’s outreach programs.
Now the team is back again with a new video, this one titled Quantum is Calling. This one stars the amazing Zoe Saldana, with an appearance by John Cho and the voices of Simon Pegg and Keanu Reeves, and of course Stephen Hawking once again. (One thing about Caltech: we do not mess around with our celebrity cameos.)
If you’re interested in the behind-the-scenes story, Zoe and Spiros and others give it to you here:
If on the other hand you want all the quantum-mechanical jokes explained, that’s where I come in:
Jokes should never be explained, of course. But quantum mechanics always should be, so this time we made an exception.
### John Preskill — Zoe Saldana Answers the Quantum Call
Stephen Hawking & Zoe Saldana try to save Simon Pegg’s cat
Watch Quantum Is Calling with Zoe Saldana, Stephen Hawking, Keanu Reeves, Paul Rudd, Simon Pegg, and John Cho.
We are on the verge of a quantum revolution. Like in the days of the space race, technology has brought an impossibly distant frontier to our doorstep. Just over 17 years ago Michael Crichton wrote a parallel universe-hopping adventure, Timeline, whose fundamental transportation technology required the advent of quantum computing – a concept that was still only theoretical at the time. Today, IBM’s five-quantum bit (or qubit) array is at the fingertips of anyone within reach of the cloud. Google is building a fifty-qubit array. Microsoft is bankrolling a brain trust that will build a quantum computer based on topological qubits. Intel is investing \$50 million on spin qubit technology. The UK has announced a £270 million program, and the EU a €1 billion program, to develop quantum technologies. And even more quantum circuits are on the way; the equivalent of competing classes of space shuttles. Only these crafts aren’t meant to travel through space, or even time. They travel through the complete unknown. Qubits fluctuate between the infinite universes of possibility, their quantum states based inherently on uncertainty. And the best way to harness that seemingly unlimited computing power, and take the first steps into the quantum frontier, is through the elusive concept of entanglement.
So then, the quantum crafts are ready; the standby lights on their consoles blinking in a steady yellow cadence. What we’re missing are the curiosity-driven pilots willing to grapple with the uncertain and unpredictable.
The quantum mechanics property of entanglement was discovered by Albert Einstein, Boris Podolsky, and Nathan Rosen and soon after described in a famous 1935 paper. Einstein called it “spooky action at a distance.” Virtually all of his contemporaries, including Edwin Schrödinger who coined the term “entanglement”, and the entire subsequent generation of physicists would struggle with this paradox. Although their struggles would be necessary to arrive at this particular moment in time, this precipice, their collective and prodigious minds were, and remain to be, handcuffed by training and experiences rooted in a classical understanding of the laws of nature – derived from phenomena that can be seen or felt, either directly or indirectly. Quantum entanglement, on the other hand, presents a puzzle of a fundamentally abstract nature.
Paul Rudd & Stephen Hawking chatting it up
When Paul Rudd defeated Stephen Hawking in a game of quantum chess – a game built from the ground up with a quantum mechanical set of moves leveraging superposition and entanglement – our intent was to suggest that an entirely new generation of physicists can emerge with an intuitive understanding of entanglement, even before having to dip their toes in mathematics.
Following up on Anyone Can Quantum, the challenges were to (1) further introduce and elaborate on quantum entanglement and (2) reach a wider audience, particularly women. Coming from a writer’s perspective, my primary concern was to make the abstract concept of entanglement somehow relatable. Popular stories, at their most basic, are told through interactions between people in relationships. Only through relational interactions can characters be challenged enough to affect a change in behavior, and as a result support a theme. Early story concepts evolved from the idea that any interaction with entanglement would result in a primary problem of miscommunication. Entanglement, in any form approaching personification, would be fully alien and incomprehensible. Language then, I decided, would become the fabric by which we could create a set of interactions between a human and entanglement.
Dr. Louise Banks (Amy Adams) & Ian Donnelly (Jeremy Renner) in Arrival
This particular dynamic was tackled in the recent movie Arrival. There, the fictional linguist Dr. Louise Banks is tasked with translating the coffee-ring-stain sign language of a visiting alien civilization before one of the world’s many nervous armies attacks them and causes an intergalactic incident. In the process of decoding the dense script, the controversial Sapir-Whorf theory is brought up introducing the idea that language shapes the way people think. While this theory may or may not hold snow, I am still impressed with the notion that a shared, specific, and descriptive language is necessary to collaborate and innovate. This impression is supported by my own experience in molecular and cell biology research in which communicating new findings always requires expending a tremendous amount of energy crafting a new and appropriate set of terms, or in other words, an expansion of the language.
Marvel To The Rescue
The Tesseract & Groot in Guardians of the Galaxy
To drive their building, multi-threaded Infinity Stones storyline, the Marvel Cinematic Universe (MCU) has been fortuitously bold in broaching quantum physics concepts and attempting to ground them in real science, taking advantage of the contacts available through the Science & Entertainment Exchange. Through these consultations, movies like Thor and Ant-Man have already delivered to a wide and diverse audience complex concepts such as Einstein-Rosen bridges (wormholes) and the Quantum Realm.
The Ant-Man consultation, in particular, resulted in a relationship between IQIM’s own Spyridon Michalakis (aka Spiros) and Ant-Man himself, Paul Rudd. This relationship was not only responsible for Anyone Can Quantum, but it was also the reason why Spiros was invited to be a panelist at the Silicon Valley Comic Con earlier this year, where he was interviewed by science journalist Zuberoa “Zube” Marcos of the global press outfit, El Pais, a woman who would end up playing a central role in getting Quantum Is Calling off the ground.
So the language of quantum physics was being slowly introduced to a wider, global population thanks to the Marvel films. It occurred to us that we had the opportunity to explain some of the physics concepts brought up by the MCU through the lens of quantum physics, and entanglement in particular. The one element of the MCU storylines that was most attractive to us was the Tesseract and its encased Space Stone. It was the first of the Infinity Stones introduced (in Captain America: The First Avenger) and the one that drove the plot of The Avengers, culminating in the creation of a wormhole over Manhattan. For Spiros, the solution was simple: In order to create wormholes, the exotic matter comprising the Space Stone would likely have to exploit entanglement, as described in a conjecture, dubbed “ER=EPR”, published by Leonard Susskind and Juan Maldacena in 2013.
The USS Enterprise (NCC-1701) in the Star Trek TOS episode “The Immunity Syndrome”
Finding Our Star
The remaining challenge was to find the right actress to deliver the new story. The earliest version of our story (back in June, 2016) was based on the crew of the Starship Enterprise encountering an alien creature that was the embodiment of entanglement (a.k.a The Flying Spaghetti Monster), a creature that attempted communication with Earthlings by reciting sound bytes originating from past Earth radio transmissions. In this story iteration, Chief communications officer Uhura would have used her skills to translate the monster’s message amidst rising tension (just like in Arrival).
Zoe Saldana as Lt. Nyota Uhura
In the subsequent revisions to the story we had to simplify the script and winnow down the cast. We opted to lean on Zoe Saldana’s Uhura. Her character could take on the role of captain, communications officer, and engineer. Zoe was already widely known across multiple sci-fi franchises featuring aliens (namely Star Trek, Guardians of the Galaxy, and Avatar) and her characters have had to speak in or translate those languages.
Zoe = Script
But before approaching Zoe Saldana – and at that point in time, we had no idea how to go about that – we needed to complete a script. Two other incredible resources were available to us: the voices of Dr. Hawking and Keanu Reeves; and we had to make all three work together in a unique comedy – one that did not squander the involvement of either voice, but also served to elevate the role of Zoe.
Even in the first version of the story it was my intent to have Keanu Reeves provide the voice for entanglement, expressed through the most alien sounding languages I could imagine. To compress the story to fit our budget we were forced to narrow the list of languages to two, and I chose Dothraki and Navajo. The role of Keanu’s character was to test, recruit, and ultimately invite Zoe Saldana to enter and experience entanglement in the Quantum Realm. Dr. Stephen Hawking would be the reluctant guide that helps Zoe interpret the confusing clues embedded within the Dothraki and Navajo to arrive at the ER=EPR conjecture.
As for the riddle itself, I chose to use two poems from Through the Looking Glass (and What Alice Found There), The Walrus and The Carpenter as well as Haddock’s Eyes, as the reference material, so that those savvy enough to solve even half the riddle on their own would have a further clue pointing them to the final answer.
Simon Pegg’s cat, Schrodinger (not his actual cat)
The disappearance of Simon’s cat, Schrödinger, had a tripartite function of (a) presenting an inciting incident that urged Zoe to subject herself to the puzzle-solving trial, which we called the Riddle of the Tesseract, (b) to demonstrate the risk of touching the Tesseract and the gravity of her climactic choice, and (c) invoking Schrödinger’s famous thought experiment to present the idea that, in the Quantum Realm, the cat and Zoe are both dead and alive, an uncertainty.
The story was done. And it looked good on paper. But the script was just a piece of paper unless we got Zoe Saldana to sign on.
Zuberoa Marcos
Zoe = Zube
For weeks, Spiros worked all of his connections only to come up empty. It wasn’t until he mentioned our holy quest to Zube (from El Pais and Silicon Valley Comic Con) during an unrelated Skype session that he had the first glimmer of hope, even kismet. Zube had been working on arranging an interview with Zoe for months, an interview that would be taking place three days later in Atlanta. Without even a second thought, Spiros purchased a plane ticket and was on his way to Atlanta two days later. Watching the interview take place, he heard Zoe answer one of Zube’s question about what kind of technology interested her the most. It was the transporter, the teleportation machine used by the crew of the Enterprise to shift matter to and from surfaces of alien planets. This was precisely the kind of technology we were interested in describing at a quantum level! Realizing this was the opening we needed, Zube nodded over to Spiros and made the introductions.
It turns out Zoe had been fascinated by science fiction since her early childhood, being particularly obsessed with Frank Herbert’s Dune. Moreover, she was interested in playing the role of our lead character. In the weeks that followed, communication proceeded through managers in an attempt to nail down a filming date.
Mariel, Zoe, and Cicely Saldana
The Dangers of Miscommunication
I probably don’t need to remind you that Zoe Saldana is a core component of three gigantic franchises. That means tight schedules, press conferences, and international travel. Ultimately Zoe said that her travel commitments wouldn’t allow her to film our short. It was back to square one. We were dead in the water. The script was just a piece of paper.
However, for some reason, Spiros and Zube were not willing to concede. Zube found out about Zoe Saldana’s production company Cinestar and got in contact with coordinator Diego Gonzalez, to set up a lunch meeting. At lunch, Diego informed Zube and Spiros that Zoe really wanted to do this, but her team was under the impression that filming for our short video had to take place the week Star Trek: Beyond was to be released (Zoe was arguably busier than the POTUS during that week). Spiros informed Cinestar that we would accommodate whatever date Zoe could be available. Having that hurdle removed paved the way for a concrete film date to be set, October 25th. And now the real work began.
Simon Pegg in Shaun of the Dead
Finding Common Language
We had set the story inside Simon Pegg’s house and the script included voice-over dialogue for the superstar, but we had yet to even contact Simon. We had written in a part with Paul Rudd on a voicemail message. And we had also included a sixth character that would knock on the door and force Zoe to make her big decision. On top of that I had incorporated Dothraki and Navajo versions of century-old poems that had yet to be translated into those two languages. While Spiros worked on chasing down the talent, I nervously attempted to make contact with experts in the two languages.
David J. Peterson
I remember watching a video of Prof. David J. Peterson, creator of the Dothraki language for HBO’s Game of Thrones, speaking at Google about the process of crafting the language. Some unknown courage surfaced and I hunted down contact information for the famous linguist. I found an old website of his, an email address, and sent and inquiry at about midnight pacific standard time on October 14th, the day before my birthday. Within 45 minutes David had responded with interest in helping out. I was floored. And I couldn’t help geeking out. But more importantly this meant we would have the most accurate translation humanly possible. And when one is working on behalf of Caltech you definitely feel the pressure to be above reproach, or unsullied ;).
Keanu Reeves, Jennifer Wheeler, a pumpkin, a highlighter & my left arm
Finding a Navajo translator was comparatively difficult. A couple days after receiving Dr. Peterson’s email, I was in Scottsdale, AZ with my brother. I had previously scheduled the trip so that I could be in attendance at a book-signing featuring two of my favorite authors, as a birthday gift to myself. The event was held at the Poisoned Pen bookstore where many other local authors would regularly hold book-signings. While I was geeking out over meeting my favorite writing duo, as well as over my recent interaction with David Peterson, I was also stressed by the pressure to come through on an authentic Navajo translation. My brother urged me to ask the proprietors of the Poisoned Pen for any leads. And wouldn’t you know it, they had recently hosted a book-signing for the author of a Code Talkers book, and she was local. A morning of emails led to Jennifer Wheeler. We had struck gold. Jennifer had recently overseen Navajo translations of Star Wars: A New Hope and Finding Nemo, complete with voice-overs. There was probably nobody more qualified in the world.
Keanu Reeves as Ted “Theodore” Logan in Bill & Ted’s Excellent Adventure
So it turns out that Navajo is a much more difficult language to translate and speak than I had anticipated. For instance, there are over a hundred vowel sounds. So even though the translation was in good hands, I would be imposing on Keanu Reeves one of the greatest vocal challenges he would ever undertake. Eventually I arranged to have Jennifer on hand during Keanu’s voice recording. Here’s what he had to record (phonetically):
Tsee /da / a / ko / ho / di / say / tsaa, / a / nee / di
aɫ / tso / n’ / shay / ch’aa / go
Echo Papa Romeo / do / do / chxih / da
Bi / nee / yay / bi / zhay / ho / lo / nee / bay / do / bish / go.
Alex Winter & Zoe Saldana hard at work
Filming Day
After months of planning and weeks of script revisions, filming finally happened at an opulent, palatial residence in the Hollywood Hills (big props to Shaun Maguire and Liana Kadisha for securing the location). Six cats. Three trainers. Lights. Cameras. Zube. Zoe Saldana actually showed up! Along with her sisters, Cinestar, and even John Cho! Spiros had gotten assurances from Simon Pegg that he would lend his name and golden voice so we were able to use the ridiculous “Simon’s Peggs” wood sign that we had crafted just for the shoot. Within a few busy hours we were wrapped. All the cats and props were packed and back in LA traffic, where we all seem to exist more often than not. Now the story was left to the fate of editing and post-production.
In Post
Unlike the circumstances involved with Anyone Can Quantum, for which there was a fast approaching debut date, Spiros and myself actually had time to be an active part of the post-production process. Alex Winter, Trouper Productions, and STITCH graciously involved us through virtually every step.
One thing that became quite apparent through the edits was the lack of a strong conclusion. Zoe’s story was designed to be somewhat open-ended. Although her character arc was meant to reach a conclusion with the decision to enter the Quantum Realm, it was clear that the short still needed a clear resolution.
What Seraph looks like as code in the Matrix Reloaded
Through much debate and workshopping, Spiros and I finally arrived at bookend scenes that took advantage of Keanu Reeve’s emblematic representation of, and inescapable entanglement with, The Matrix. Our ultimate goal is to create stories that reflect the quantum nature of the universe, the underlying quantum code that is the fabric from which all things emerge, exist, and interact. So, in a way, The Matrix wasn’t that far off.
Language Is Fluid
LIQUi|> (“liquid”), or Language-Integrated Quantum Operations, is an architecture, programming language, and tools suite designed for quantum computing that is being developed by the Microsoft team at Quantum Architectures and Computation Group (or QuArC). Admittedly taking a few liberties, on Spiros’s advice I used actual LIQUi|> commands to create a short script that established a gate (or data structure) that I called Alice (which is meant to represent Zoe and her location), created an entanglement between Alice and the Tesseract, then teleported the Tesseract to Alice. You’ll notice that the visual and sound effects are ripped right from The Matrix.
This set up the possibility of adapting Neo’s famous monologue (from the end of the original Matrix) so we could hint that Zoe was somewhere adrift within the quantum code that defines the Quantum Realm. Yes, both Spiros and I were in the studio when Keanu recorded those lines (along with his lines in Dothraki and Navajo). Have I mentioned geeking out yet? An accompanying sequence of matrix code, or digital rain, had to be constructed that could accommodate examples of entanglement-related formulas. As you might have guessed, the equations highlighted in the digital rain at the end of the short are real, most of which came from this paper on emergent space (of which Spiros is a co-author).
Keanu Reeves & Keanu
Listen To Your Friend Keanu Reeves. He’s A Cool Dude.
With only a few days left before our debut date, Simon Pegg, Stephen Hawking and Paul Rudd all came through with their voice-over samples. Everything was then stitched together and the color correction, sound balancing, and visual effects were baked into the final video and phew. Finally, and impossibly, through the collaboration of a small army of unique individuals, the script had become a short movie. And hopefully it has become something unique, funny, and inspiring, especially to any young women (and men) who may be harboring an interest in, or a doubt preventing them from, delving into the quantum realm.
## December 14, 2016
### Jacques DistlerMathML Update
For a while now, Frédéric Wang has been urging me to enable native MathML rendering for Safari. He and his colleagues have made many improvements to Webkit’s MathML support. But there were at least two show-stopper bugs that prevented me from flipping the switch.
Fortunately:
• The STIX Two fonts were released this week. They represent a big improvement on Version 1, and are finally definitively better than LatinModern for displaying MathML on the web. Most interestingly, they fix this bug. That means I can bundle these fonts1, solving both that problem and the more generic problem of users not having a good set of Math fonts installed.
• Thus inspired, I wrote a little Javascript polyfill to fix the other bug.
While there are still a lot of remaining issues (for instance this one fixed), I think Safari’s native MathML rendering is now good enough for everyday use (and, in enough respects, superior to MathJax’s) to enable it by default in Instiki, Heterotic Beast and on this blog.
Of course, you’ll need to be using2 Safari 10.1 or Safari Technology Preview.
#### Update:
Another nice benefit of STIX Two fonts is that itex can support both Chancery (\mathcal{}) and Roundhand (\mathscr{}) symbols $\begin{split} \backslash\mathtt{mathcal}\{\}:&\,\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \backslash\mathtt{mathscr}\{\}:&\,\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \end{split}$
1 In an ideal world, OS vendors would bundle the STIX Two fonts with their next release (as Apple previously bundled the STIX fonts with MacOSX ≥10.7) and motivated users would download and install them in the meantime.
2 N.B.: We’re not browser-sniffing (anymore). We’re just checking for MathML support comparable to Webkit version 203640. If Google (for instance) decided to re-enable MathML support in Chrome, that would work too.
## December 12, 2016
### Steinn Sigurðsson — Vikings, Santa & Jól
Grímfrost in Sweden give their take on the Meaning of the Season
– the Goat of Þór is serious business though…
### Steinn Sigurðsson — Stekkjastaur – the Elfs are Coming – Pt 1 Revisited
Today is the 12th of december, and there are 13 days until christmas.
This means, of course, that the first of the yule elves came to town this morning.
As you know, Bob, there are thirteen of the Yule Lads, or jólasveinar, as we call them.
And they are not really elves, since their mother is a troll.
The childstealing, cannibal Grýla, of legend.
Stekkjastaur
They come to town, one each day until christmas eve, and then leave in order, starting christmas day and finishing on the 6th of January.
They leave small treats or presents in the shoes of good children, if the kids know to leave their shoe out by the door or window. Strangely, our neighbour kids do not seem to have caught on to this, yet.
If you are naughty, you get a potato, or an onion.
Their arrival is critical, since any child who is so naughty as to not get a single piece of clothing, candle or a game before Christmas Eve, will be eaten by Jólakötturinn (the “Christmas Cat” – big as a house it is, silent, deadly).
Jólaköttur – feline solsticus
The lads are pranskters, and quite mean ones, none of your Ho, Ho Ho! Coke swilling softies. Stekkjastaur sneaks up on the ewes and sucks the milk out of their udders, though this is hard going as he is stilt-legged.
On the other hand, the munchkins find it very convenient to be in a multicultural family, especially since the Better Half is fond of the Feast of St Nicholas; my extended family feels presents should be given on christmas eve after dinner; while the in-laws go with the anglo-style stocking and christmas morning thing.
And the one time the Big Kid got a potato, she laughed so hard she fell over, and then came into the kitchen with a big grin and asked that we cook it for her… (it got donated to local wildlife as a compromise).
We are of course not talking superstition.
I mean, I don’t “believe” in elves.
I just know not to mess with them.
You leave their houses alone, leave a seat (1st class, natch) on the occasional flight for them, and maybe put out the occasional bowl of milk… elves don’t need your belief, and trolls of course don’t care, they just eat you.
I should note that Iceland’s one Nobel laureate treated the issue of elves in Icelandic culture extensively, so there.
Just remember, you must have an evergreen for the solstice festival, and you better burn it when you are done, after 12 days, of course.
If you do not, winter may never end!
Next one up, any hour now, is Giljagaur. Sneaky one.
repost from ’08
### John Preskill — The weak shall inherit the quasiprobability.
Justin Dressel’s office could understudy for the archetype of a physicist’s office. A long, rectangular table resembles a lab bench. Atop the table perches a tesla coil. A larger tesla coil perches on Justin’s desk. Rubik’s cubes and other puzzles surround a computer and papers. In front of the desk hangs a whiteboard.
A puzzle filled the whiteboard in August. Justin had written a model for a measurement of a quasiprobability. I introduced quasiprobabilities here last Halloween. Quasiprobabilities are to probabilities as ebooks are to books: Ebooks resemble books but can respond to touchscreen interactions through sounds and animation. Quasiprobabilities resemble probabilities but behave in ways that probabilities don’t.
A tesla coil of Justin Dressel’s
Let $p$ denote the probability that any given physicist keeps a tesla coil in his or her office. $p$ ranges between zero and one. Quasiprobabilities can dip below zero. They can assume nonreal values, dependent on the imaginary number $i = \sqrt{-1}$. Probabilities describe nonquantum phenomena, like tesla-coil collectors,1 and quantum phenomena, like photons. Quasiprobabilities appear nonclassical.2,3
We can infer the tesla-coil probability by observing many physicists’ offices:
$\text{Prob(any given physicist keeps a tesla coil in his/her office)} = \frac{ \text{\# physicists who keep tesla coils in their offices} }{ \text{\# physicists} } \, .$ We can infer quasiprobabilities from weak measurements, Justin explained. You can measure the number of tesla coils in an office by shining light on the office, correlating the light’s state with the tesla-coil number, and capturing the light on photographic paper. The correlation needn’t affect the tesla coils. Observing a quantum state changes the state, by the Uncertainty Principle heralded by Heisenberg.
We could observe a quantum system weakly. We’d correlate our measurement device (the analogue of light) with the quantum state (the analogue of the tesla-coil number) unreliably. Imagining shining a dull light on an office for a brief duration. Shadows would obscure our photo. We’d have trouble inferring the number of tesla coils. But the dull, brief light burst would affect the office less than a strong, long burst would.
Justin explained how to infer a quasiprobability from weak measurements. He’d explained on account of an action that others might regard as weak: I’d asked for help.
Chaos had seized my attention a few weeks earlier. Chaos is a branch of math and physics that involves phenomena we can’t predict, like weather. I had forayed into quantum chaos for reasons I’ll explain in later posts. I was studying a function $F(t)$ that can flag chaos in cold atoms, black holes, and superconductors.
I’d derived a theorem about $F(t)$. The theorem involved a UFO of a mathematical object: a probability amplitude that resembled a probability but could assume nonreal values. I presented the theorem to my research group, which was kind enough to provide feedback.
“Is this amplitude physical?” John Preskill asked. “Can you measure it?”
“I don’t know,” I admitted. “I can tell a story about what it signifies.”
“If you could measure it,” he said, “I might be more excited.”
You needn’t study chaos to predict that private clouds drizzled on me that evening. I was grateful to receive feedback from thinkers I respected, to learn of a weakness in my argument. Still, scientific works are creative works. Creative works carry fragments of their creators. A weakness in my argument felt like a weakness in me. So I took the step that some might regard as weak—by seeking help.
Some problems, one should solve alone. If you wake me at 3 AM and demand that I solve the Schrödinger equation that governs a particle in a box, I should be able to comply (if you comply with my demand for justification for the need to solve the Schrödinger equation at 3 AM).One should struggle far into problems before seeking help.
Some scientists extend this principle into a ban on assistance. Some students avoid asking questions for fear of revealing that they don’t understand. Some boast about passing exams and finishing homework without the need to attend office hours. I call their attitude “scientific machismo.”
I’ve all but lived in office hours. I’ve interrupted lectures with questions every few minutes. I didn’t know if I could measure that probability amplitude. But I knew three people who might know. Twenty-five minutes after I emailed them, Justin replied: “The short answer is yes!”
I visited Justin the following week, at Chapman University’s Institute for Quantum Studies. I sat at his bench-like table, eyeing the nearest tesla coil, as he explained. Justin had recognized my probability amplitude from studies of the Kirkwood-Dirac quasiprobability. Experimentalists infer the Kirkwood-Dirac quasiprobability from weak measurements. We could borrow these experimentalists’ techniques, Justin showed, to measure my probability amplitude.
The borrowing grew into a measurement protocol. The theorem grew into a paper. I plunged into quasiprobabilities and weak measurements, following Justin’s advice. John grew more excited.
The meek might inherit the Earth. But the weak shall measure the quasiprobability.
With gratitude to Justin for sharing his expertise and time; and to Justin, Matt Leifer, and Chapman University’s Institute for Quantum Studies for their hospitality.
Chapman’s community was gracious enough to tolerate a seminar from me about thermal states of quantum systems. You can watch the seminar here.
1Tesla-coil collectors consists of atoms described by quantum theory. But we can describe tesla-coil collectors without quantum theory.
2Readers foreign to quantum theory can interpret “nonclassical” roughly as “quantum.”
3Debate has raged about whether quasiprobabilities govern classical phenomena.
4I should be able also to recite the solutions from memory.
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# The ROC curve
## Intro
ROC stands for receiver operating characteristic and is a curve first designed and used at the times of World War I for radar signals purposes. It is a curve used to validate the performance of a binary classifier which depends on a threshold parameter when it varies.
The ROC plots the true positive rate against the false positive rate at each varying value of the parameter, also called threshold. See the note on the performance metrics for classification for a description of those. In this plane, the point (0, 1) represent the perfect classification; the diagonal line shows what a random guesser (a coin flip) would give, so that points above it are good results, points below are poorly classified results.
## Details: definition of the ROC curve and the AUC
Discussion borrowed from Wikipedia. Let's say that we got a continuous random variable
$X$
and a binary classifier which depends on a threshold
$T$
, so that
$x > T$
yields a "positive" (1) classification and
$x \leq T$
yields a "negative" (0) classification. The pdf of
$X$
is
$f_1(X)$
if the point is actually positive and
$f_0(X)$
if the point is actually negative, so we can write
$TPR(T) = \int_T^\infty f_1(x) \ d x$
and
$FPR(T) = \int_T^\infty f_0(x) \ d x$
(the last one because above
$T$
the point is classed as positive but it is negative, so follows
$f_0$
). The ROC curve, plots TPR(T) versus FPR(T) as a parametric function of
$T$
. At the same time, the other two metrics which quantify the performance of the classification can be expressed as
$TNR = \int_{-\infty}^T f_0(x) \ d x$
and
$TFR = \int_{-\infty}^T f_1(x) \ dx$
(the last one because below T the point is classed as negative but it is actually positive so it follows
$f_1$
).
The area under the curve (AUC) tells us how fast the curve grows (how convex it is), quantifying how good its performance is. In a typical use case, different classifiers will be evaluated by comparing their AUCs.
## References
1. 1.
Wikipedia on the ROC
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## Results (41 matches)
Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim $\epsilon$ $r$ First zero Origin
4-585e2-1.1-c1e2-0-0 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.477001 Elliptic curve 2.2.65.1-81.1-a Hilbert modular form 2.2.65.1-81.1-a Modular form 585.2.h.a 4-585e2-1.1-c1e2-0-1 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.627163$ Modular form 585.2.w.b
4-585e2-1.1-c1e2-0-10 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 -1 1 1.03100 Bianchi modular form 2.0.3.1-38025.1-a Bianchi modular form 2.0.3.1-38025.3-a Elliptic curve 2.0.3.1-38025.1-a Elliptic curve 2.0.3.1-38025.3-a 4-585e2-1.1-c1e2-0-11 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.07254$ Modular form 585.2.w.c
4-585e2-1.1-c1e2-0-12 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 0 1.08193 Modular form 585.2.n.a 4-585e2-1.1-c1e2-0-13 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.09175$ Modular form 585.2.a.k
4-585e2-1.1-c1e2-0-14 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 0 1.14399 Modular form 585.2.i.d 4-585e2-1.1-c1e2-0-15 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.15147$ Modular form 585.2.b.d
4-585e2-1.1-c1e2-0-16 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 0 1.19244 Bianchi modular form 2.0.3.1-38025.1-c Bianchi modular form 2.0.3.1-38025.3-c Elliptic curve 2.0.3.1-38025.1-c Elliptic curve 2.0.3.1-38025.3-c 4-585e2-1.1-c1e2-0-17 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.21101$ Modular form 585.2.n.c
4-585e2-1.1-c1e2-0-18 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 0 1.29285 Modular form 585.2.b.c 4-585e2-1.1-c1e2-0-19 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.30735$ Modular form 585.2.i.a
4-585e2-1.1-c1e2-0-2 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.802392 Elliptic curve 2.2.65.1-81.1-c Hilbert modular form 2.2.65.1-81.1-c Modular form 585.2.h.c 4-585e2-1.1-c1e2-0-20 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.35212$ Modular form 585.2.c.a
4-585e2-1.1-c1e2-0-21 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 0 1.35605 Modular form 585.2.j.a 4-585e2-1.1-c1e2-0-22 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $2$ $1.35755$ Modular form 585.2.w.a
4-585e2-1.1-c1e2-0-23 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 -1 1 1.37276 Bianchi modular form 2.0.3.1-38025.2-b Elliptic curve 2.0.3.1-38025.2-b 4-585e2-1.1-c1e2-0-24 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $-1$ $1$ $1.37994$ Bianchi modular form 2.0.3.1-38025.2-c Bianchi modular form 2.0.3.1-38025.2-d Elliptic curve 2.0.3.1-38025.2-c Elliptic curve 2.0.3.1-38025.2-d
4-585e2-1.1-c1e2-0-25 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 -1 1 1.46733 Bianchi modular form 2.0.3.1-38025.1-b Bianchi modular form 2.0.3.1-38025.3-b Elliptic curve 2.0.3.1-38025.1-b Elliptic curve 2.0.3.1-38025.3-b 4-585e2-1.1-c1e2-0-26 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $-1$ $1$ $1.48034$ Bianchi modular form 2.0.3.1-38025.2-e Bianchi modular form 2.0.3.1-38025.2-f Elliptic curve 2.0.3.1-38025.2-e Elliptic curve 2.0.3.1-38025.2-f
4-585e2-1.1-c1e2-0-27 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 2 1.51982 Elliptic curve 2.2.65.1-81.1-b Hilbert modular form 2.2.65.1-81.1-b Modular form 585.2.h.b 4-585e2-1.1-c1e2-0-28 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.55854$ Modular form 585.2.n.b
4-585e2-1.1-c1e2-0-29 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 2 1.66120 Modular form 585.2.a.j 4-585e2-1.1-c1e2-0-3 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.865108$ Modular form 585.2.a.l
4-585e2-1.1-c1e2-0-30 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 0 1.72194 Modular form 585.2.i.c 4-585e2-1.1-c1e2-0-31 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $1.81519$ Elliptic curve 2.2.65.1-81.1-d Hilbert modular form 2.2.65.1-81.1-d Modular form 585.2.h.d
4-585e2-1.1-c1e2-0-4 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.889768 Modular form 585.2.b.a 4-585e2-1.1-c1e2-0-5 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.897256$ Modular form 585.2.a.m
4-585e2-1.1-c1e2-0-6 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 1 0 0.949416 Modular form 585.2.j.b 4-585e2-1.1-c1e2-0-7 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.950734$ Modular form 585.2.b.b
4-585e2-1.1-c1e2-0-8 $2.16$ $21.8$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$1.0, 1.0 1 -1 1 0.968476 Bianchi modular form 2.0.3.1-38025.2-a Elliptic curve 2.0.3.1-38025.2-a 4-585e2-1.1-c1e2-0-9 2.16 21.8 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $1.0, 1.0$ $1$ $1$ $0$ $0.969386$ Modular form 585.2.i.b
4-585e2-1.1-c3e2-0-0 $5.87$ $1.19\times 10^{3}$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$3.0, 3.0 3 1 0 0.389881 Modular form 585.4.b.c 4-585e2-1.1-c3e2-0-1 5.87 1.19\times 10^{3} 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $3.0, 3.0$ $3$ $1$ $0$ $0.390600$ Modular form 585.4.c.b
4-585e2-1.1-c3e2-0-2 $5.87$ $1.19\times 10^{3}$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$3.0, 3.0 3 1 0 0.459510 Modular form 585.4.b.a 4-585e2-1.1-c3e2-0-3 5.87 1.19\times 10^{3} 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $3.0, 3.0$ $3$ $1$ $0$ $0.580015$ Modular form 585.4.a.g
4-585e2-1.1-c3e2-0-4 $5.87$ $1.19\times 10^{3}$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$3.0, 3.0 3 1 0 0.739242 Modular form 585.4.b.b 4-585e2-1.1-c3e2-0-5 5.87 1.19\times 10^{3} 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $3.0, 3.0$ $3$ $1$ $0$ $1.00728$ Modular form 585.4.a.h
4-585e2-1.1-c3e2-0-6 $5.87$ $1.19\times 10^{3}$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $$3.0, 3.0 3 1 2 1.20090 Modular form 585.4.c.a 4-585e2-1.1-c3e2-0-7 5.87 1.19\times 10^{3} 4 3^{4} \cdot 5^{2} \cdot 13^{2} 1.1$$ $3.0, 3.0$ $3$ $1$ $2$ $1.24308$ Modular form 585.4.a.i
4-585e2-1.1-c3e2-0-8 $5.87$ $1.19\times 10^{3}$ $4$ $3^{4} \cdot 5^{2} \cdot 13^{2}$ 1.1 $3.0, 3.0$ $3$ $1$ $2$ $1.25758$ Modular form 585.4.a.f
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# 周期点
## 迭代函数
$\displaystyle{ f: X \to X, }$
$\displaystyle{ X }$中的点$\displaystyle{ x }$称为周期点，如果存在一个$\displaystyle{ n }$使
$\displaystyle{ \ f_n(x) = x }$
### 示例
$\displaystyle{ x_{t+1}=rx_t(1-x_t), \qquad 0 \leq x_t \leq 1, \qquad 0 \leq r \leq 4 }$
For r between 0 and 1, 0 is the sole periodic point, with period 1 (giving the sequence 0, 0, 0, ..., which attracts all orbits). For r between 1 and 3, the value 0 is still periodic but is not attracting, while the value (r − 1) / r is an attracting periodic point of period 1. With r greater than 3 but less than 1 + 模板:Radic, there are a pair of period-2 points which together form an attracting sequence, as well as the non-attracting period-1 points 0 and (r − 1) / r. As the value of parameter r rises toward 4, there arise groups of periodic points with any positive integer for the period; for some values of r one of these repeating sequences is attracting while for others none of them are (with almost all orbits being chaotic).
• 对于介于0到1之间的$\displaystyle{ r }$，0是唯一的周期点，周期为1（给出了吸引所有轨道的序列0,0,0，... ）;
• 对于介于1到3之间的$\displaystyle{ r }$，值0仍然是周期性的，但不是吸引子，而该值是周期1的周期吸引子;
• $\displaystyle{ r }$大于3但小于1时，存在一对周期2的点，它们共同构成一个吸引序列，非吸引周期1点为0;
• 当参数$\displaystyle{ r }$的值上升到4时，会出现周期为正的一组周期点；
• 对于$\displaystyle{ r }$的某些值，这些重复序列中的一个被吸引，而对于其他值，则没有一个被吸引(几乎所有的轨道都是混乱的)。
## 动力系统
$\displaystyle{ \Phi: \mathbb{R} \times X \to X }$
$\displaystyle{ \Phi(t, x) = x\, }$
### 性质
• 给定一个周期为$\displaystyle{ “p” }$的周期点$\displaystyle{ “x” }$，则对于$\displaystyle{ t∈R }$$\displaystyle{ \Phi(t,x) = \Phi(t+p,x) }$
• 给定周期点“x”，则在轨道 $\displaystyle{ \gamma_x }$上的所有点都具有相同的素数周期prime period
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# zbMATH — the first resource for mathematics
Efficiency and robustness control via distorted maximum likelihood estimation. (English) Zbl 0603.62039
In the present paper distorted maximum likelihood estimators (M.L.E.’s), denoted by $$T^{\alpha}$$, with a distortion parameter $$\alpha\geq 0$$ are introduced so that $$T^ 0$$ is the classical nondistorted M.L.E. The M.L.E. is known to be efficient but not robust, whereas the distorted estimators are shown to be robust but not efficient. For quite general types of distortion and statistical families, the distorted estimates as well as the corresponding influence curves and asymptotic variances are shown to be continuous at $$\alpha =0$$. Thus the parameter $$\alpha$$ controls the efficiency and robustness of the estimators under consideration, so that one can easily review the set of attainable compromises and select the most appropriate one. This possibility is analyzed in more detail with respect to two concrete families of distorted M.L.E.’s.
Reviewer: H.Büning
##### MSC:
62F35 Robustness and adaptive procedures (parametric inference) 62F12 Asymptotic properties of parametric estimators
Full Text:
##### References:
[1] J. Anděl: Mathematical Statistics. (in Czech). SNTL - ALFA, Praha-Bratislava 1978. [2] T. W. Anderson: The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6 (1955), 170- 176. · Zbl 0066.37402 · doi:10.2307/2032333 [3] R. A. Fisher: On the mathematical foundations of theoretical statistics. Reprinted in: Contributions to Mathematical Statistics (by R. A. Fisher). J. Wiley, New York 1950. [4] W. Fuller: Introduction to the Statistical Time Series. J. Wiley, New York 1976. · Zbl 0353.62050 [5] F. R. Hampel: The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69 (1974), 383-393. · Zbl 0305.62031 · doi:10.2307/2285666 [6] P. I. Huber: Robust estimation of a location parameter. Ann. Math. Statist. 35 (1964), 73-101. · Zbl 0136.39805 · doi:10.1214/aoms/1177703732 [7] J. L. Kelley: General Topology. Van Nostrand, Princeton 1957. · Zbl 0157.53002 [8] L. Le Cam: On the asymptotic theory of estimation and testing hypotheses. Proc. 3rd Berkeley Symp. Math. Statist. Prob. Vol. 1 (1956), 129-156. [9] A. Perez: Notions generalisées d’incertitude, d’entropie et d’information du point de vue de la théorie des martingales. Trans. 1st Prague Conf. on Inform. Theory, etc. Publ. House Czechosl. Acad. Sci., Prague 1957. · Zbl 0102.13204 [10] J. Pfanzagl: On the measurability and consistency of minimum contrast estimators. Metrika 14 (1969), 249-272. · Zbl 0181.45501 · doi:10.1007/BF02613654 · eudml:175401 [11] J. Pfanzagl: The second order optimaiity of tests and estimators for minimum contrast functional. Probab. and Math. Statist. 2 (1981), 55 - 70. · Zbl 0523.62039 [12] A. Rényi: Theory of probability. (in Czech). Academia, Prague 1972. [13] I. Vajda: Motivation, existence and equivariance of D-estimators. Kybernetika 20 (1984), 189-208. · Zbl 0558.62026 · eudml:28738 [14] I. Vajda: Robust estimation in discrete and continuous families by means of a minimum chi-square method. Problems Control Inform. Theory 15 (1986), No. 2. · Zbl 0609.62053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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# Thermal Conductivity Paper Database
## Recommended Papers for: Rare Earth Oxides
Total Papers Found: 1
#### Effective thermal conductivity and thermal diffusivity of some rare earth oxides
The thermal conductivity and thermal diffusivity of rare earth oxide powders were measured using the transient plane source technique. Specifically, powders of gadolinium oxide, samarium oxide, and yttrium oxide were measured. A previously developed theoretical model was used to predict the effective thermal conductivity and ...
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• 51.
IISc - Indian Institute of Science.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. IISc - Indian Institute of Science.
Fusion of greedy pursuits for compressed sensing signal reconstruction2012In: 2012 Proceedings Of The 20th European Signal Processing Conference (EUSIPCO), IEEE Computer Society, 2012, p. 1434-1438Conference paper (Refereed)
Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical distribution of the non-zero elements in the sparse signal. Inpractice, the distribution of the sparse signal may not be knowna priori. It is also observed that performance of Greedy Pursuits degrades as the number of available measurements decreases from a threshold value which is method dependent. To improve the performance in these situations, we introduce a novel fusion framework for Greedy Pursuits and also propose two algorithms for sparse recovery. Through Monte Carlo simulations we show that the proposed schemes improve sparse signal recovery in clean as well as noisy measurement cases.
• 52.
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. University of Gävle, Sweden.
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. ATM, University of Gävle.
Digital Predistortion of Single and Concurrent Dual BandRadio Frequency GaN Amplifiers with Strong NonlinearMemory Effects2017In: IEEE transactions on microwave theory and techniques, ISSN 0018-9480, E-ISSN 1557-9670, Vol. 65, no 7, p. 2453-2464Article in journal (Refereed)
Electrical anomalies due to trapping effects in gallium nitride (GaN) power amplifiers (PAs) give rise to long-term or strong memory effects. We propose novel models based on infinite impulse response fixed pole expansion techniques for the behavioral modeling and digital predistortion of single-input single-output (SISO) and concurrent dual-band GaN PAs. Experimental results show that the proposed models outperform the corresponding finite impulse response (FIR) models by up to 17 dB for the same number of model parameters. For the linearization of a SISO GaN PA, the proposed models give adjacent channel power ratios (ACPRs) that are 7-17 dB lower than the FIR models. For the concurrent dual-band case, the proposed models give ACPRs that are 9-14 dB lower than the FIR models.
• 53.
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Högskolan i Gävle. KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Högskolan i Gävle.
Concurrent Dual-band Power Amplifier Model Modification using Dual Two-Tone Test2016In: European Microwave Week 2016: "Microwaves Everywhere", EuMW 2016 - Conference Proceedings; 46th European Microwave Conference, EuMC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 186-189, article id 7824309Conference paper (Refereed)
A dual two-tone technique for the characterization of memory effects in concurrent dual-band transmitters is revisited to modify a 2D-DPD model for the linearization of concurrent dual-band transmitters. By taking into account the individual nonlinear memory effects of the self- and cross-kernels, a new2D modified digital pre-distortion (2D-MDPD) model is proposed,which not only supersedes the linearization performance but also reduces the computational complexity compared to the 2DDPDmodel in terms of a number of floating point operations(FLOPs). Experimental results show an improvement of 1.7 dBin normalized mean square error (NMSE) and a 58% reduction in the number of FLOPs.
• 54.
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Högskolan i Gävle.
Chalmers University of Technology. KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Högskolan i Gävle.
Behavioral modeling and linearization of crosstalk and memory effects in RF MIMO transmitters2014In: IEEE transactions on microwave theory and techniques, ISSN 0018-9480, E-ISSN 1557-9670, Vol. 62, no 4, p. 810-823Article in journal (Refereed)
This paper proposes three novel models for behavioral modeling and digital pre-distortion (DPD) of nonlinear 2 x 2 multiple-input multiple-output (MIMO) transmitters in the presence of crosstalk. The proposed models are extensions of the single-input single-output generalized memory polynomial model. Three types of crosstalk effects were studied and characterized as linear, nonlinear, and nonlinear & linear crosstalk. A comparative study was performed with previously published models for the linearization of crosstalk in a nonlinear 2 x 2 MIMO transmitter. The experiments indicate that, depending on the type of crosstalk, the selection of the correct model in the transmitter is necessary for behavioral modeling and sufficient DPD performance. The effects of coherent and partially noncoherent signal generation on the performance of DPD were also studied. For crosstalk levels of 30 dB, the difference in the normalized mean square error and adjacent channel power ratio was found to be 3-4 dB between coherent and partially noncoherent signal generation.
• 55.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
GISOO: A virtual testbed for wireless cyber-physical systems2013In: Industrial Electronics Society, IECON 2013 - 39th Annual Conference of the IEEE, IEEE , 2013, p. 5588-5593Conference paper (Refereed)
The increasing demand for wireless cyber-physical systems requires correct design, implementation and validation of computation, communication and control methods. Traditional simulation tools, which focus on either computation, communication or control, are insufficient when the three aspects interact. Efforts to extend the traditional tools to cover multiple domains, e.g., from simulating only control aspects to simulating both control and communication, often rely on simplistic models of a small subset of possible communication solutions. We introduce GISOO, a virtual testbed for simulation of wireless cyber-physical systems that integrates two state-of-the art simulators, Simulink and COOJA. GISOO enables users to evaluate actual embedded code for the wireless nodes in realistic cyber-physical experiments, observing the effects of both the control and communication components. In this way, a wide range of communication solutions can be evaluated without developing abstract models of their control-relevant aspects, and changes made to the networking code in simulations is guaranteed to be translated into production code without errors. A double-tank laboratory experimental setup controlled over a multi-hop relay wireless network is used to validate GISOO and demonstrate its features.
• 56.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Secure key agreement over reciprocal fading channels in the low SNR regime2013In: 2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications, SPAWC, IEEE , 2013, p. 674-678Conference paper (Refereed)
We study the low SNR scaling of the non-coherent secret-key agreement capacity over a reciprocal, block-fading channel. For the restricted class of strategies, where one of the nodes is constrained to transmit pilot-only symbols, we show that the secret-key capacity scales as SNR ·log T if T ≤ 1/SNR, where T denotes the coherence period, and as SNR·log(1/SNR) otherwise. Our upper bound is inspired by the genie-aided argument of Borade and Zheng (IT-Trans 2010). Our lower bound is based on bursty communication, channel training, and secret message transmission.
• 57.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Secret-key agreement over a non-coherent block-fading MIMO wiretap channel2012In: Information Theory Workshop (ITW), 2012 IEEE, IEEE , 2012, p. 153-157Conference paper (Refereed)
We study secret-key agreement over a non-coherent block-fading multiple input multiple output (MIMO) wiretap channel. We give an achievable scheme based on training and source emulation and analyze the rate in the high SNR regime. Based on this analysis we find the optimal number of antennas to use for training. Our main result is that if the sum of the number of antennas at Alice and Bob is larger than the coherence time of the channel, the achievable rate does not depend on the number of antennas at Eve. In this case source emulation is not needed, and using only training is optimal. We also consider the case when there is no public channel available. In this case we show that secret-key agreement is still possible by using the wireless channel for discussion, giving the same number of secure degrees of freedom as in the case with a public channel.
• 58.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Theory.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Theory.
Nested Polar Codes for Wiretap and Relay Channels2010In: IEEE Communications Letters, ISSN 1089-7798, E-ISSN 1558-2558, Vol. 14, no 8, p. 752-754Article in journal (Refereed)
We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding scheme also achieves the capacity of the physically degraded receiver-orthogonal relay channel. We show simulation results for moderate block length for the binary erasure wiretap channel, comparing polar codes and two edge type LDPC codes.
• 59.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Polar Coding for Bidirectional Broadcast Channels with Common and Confidential Messages2013In: IEEE Journal on Selected Areas in Communications, ISSN 0733-8716, E-ISSN 1558-0008, Vol. 31, no 9, p. 1901-1908Article in journal (Refereed)
The integration of multiple services such as the transmission of private, common, and confidential messages at the physical layer is becoming important for future wireless networks in order to increase spectral efficiency. In this paper, bidirectional relay networks are considered, in which a relay node establishes bidirectional communication between two other nodes using a decode-and-forward protocol. In the broadcast phase, the relay transmits additional common and confidential messages, which then requires the study of the bidirectional broadcast channel (BBC) with common and confidential messages. This channel generalizes the broadcast channel with receiver side information considered by Kramer and Shamai. Low complexity polar codes are constructed that achieve the capacity region of both the degraded symmetric BBC, and the BBC with common and confidential messages. The use of polar codes allows an intuitive interpretation of how to incorporate receiver side information and secrecy constraints as different sets of frozen bits at the different receivers for an optimal code design. In order to show that the constructed codes achieve capacity, a tighter bound on the cardinality of an auxiliary random variable used in the converse is found using a method by Salehi.
• 60.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
Control Synthesis for Multi-Agent Systems under Metric Interval Temporal Logic Specifications2017In: IFAC-PapersOnLine, Elsevier, 2017, Vol. 50, p. 2397-2402Conference paper (Refereed)
This paper presents a framework for automatic synthesis of a control sequence for multi-agent systems governed by continuous linear dynamics under timed constraints. First, the motion of the agents in the workspace is abstracted into individual Transition Systems (TS). Second, each agent is assigned with an individual formula given in Metric Interval Temporal Logic (MITL) and in parallel, the team of agents is assigned with a collaborative team formula. The proposed method is based on a correct-by-construction control synthesis method, and hence guarantees that the resulting closed-loop system will satisfy the desired specifications. The specifications considers boolean-valued properties under real-time bounds. Extended simulations has been performed in order to demonstrate the efficiency of the proposed methodology.
• 61.
KTH, School of Electrical Engineering (EES), Signal Processing.
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
IEEE standard 1057, Cramer-Rao bound and the parsimony principle2006In: IEEE Transactions on Instrumentation and Measurement, ISSN 0018-9456, E-ISSN 1557-9662, Vol. 55, no 1, p. 44-53Article in journal (Refereed)
This paper deals with some fundamental properties of the sine-wave-fit algorithm included in IEEE Standards 1057 and 1241. Asymptotic Cramer-Rao bounds (CRBs) for three and four model parameters are derived under the Gaussian assumption. Further, the sine-wave-fitting properties of the algorithm are analyzed by the parsimony principle. A decision criterion whether to use the three- or four-parameter model is derived. It is shown that a three-parameter sine-wave fit produces a better fit than the four-parameter fit if the frequency is known to be within an interval related to the number of samples and the signal-to-noise ratio. By a numerical analysis, the theoretical results are shown to be also valid for the uniform noise model of quantization.
• 62.
KTH, Superseded Departments, Signals, Sensors and Systems.
KTH, Superseded Departments, Signals, Sensors and Systems. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
IEEE Standard 1057, Cramér-Rao Bound and the Parsimony Principle2003In: International Workshop on ADC Modelling and Testing, 2003, p. 231-234Conference paper (Refereed)
• 63.
KTH, Superseded Departments, Signals, Sensors and Systems.
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Multiple-tone estimation by IEEE standard 1057 and the expectation-maximization algorithm2003In: IMTC/O3: PROCEEDINGS OF THE 20TH IEEE INSTRUMENTATION AND MEASUREMENT TECHNOLOGY CONFERENCE, 2003, p. 739-742Conference paper (Refereed)
The aim of this work is to present an efficient algorithm for multiple-tone parameter estimation. The algorithm is inspired by the expectation-maximization algorithm, and it utilizes the IEEE standard 1057 for single tone parameter estimation. In the derivation of the algorithm it is assumed that the number of tones are known and that the frequencies are well separated The algorithm is evaluated using data consisting of multiple real-valued tones. The performance of the frequency estimator is studied and compared with the asymptotic Cramer-Rao bound (CRB). It is shown that the algorithm produces statistically efficient frequency estimates at high signal to noise ratios, that is the variance of the estimates reaches the CRB. Finally, it is shown that the algorithm can produce efficient estimates independent of the number of tones in the input signal.
• 64.
KTH, School of Electrical Engineering (EES), Signal Processing.
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Robustness of wave-fitting with respect to uncertain parameter values2005In: Instrumentation and Measurement Technology Conference, 2005. IMTC 2005. Proceedings of the IEEE, 2005, Vol. 1, p. 662-665Conference paper (Refereed)
This paper presents a criterion for model order selection. By usage of the parsimony principle the mean sum-squareerror is evaluated for models subject to imperfections inparameter values. In particular, model imperfections in different sinewavefitting scenarios have been analyzed. The analysis is carried out considering linear models. The obtained result is generalized to models incorporating non-linear parameters. Numerical illustrations are provided in order to gain insight of the behavior of model imperfections, as well as to numerically verify the theoretical results. The main contributions include a general result for linear signal models, as well as some novel results on sinewave-fitting.
• 65.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
A COVQ-Based image coder for channels with bit errors and erasures2008In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 56, no 2, p. 161-165Article in journal (Refereed)
We illustrate how channel optimized vector quantization (COVQ) can be used for channels with both bit-errors and bit-erasures. First, a memoryless channel model is presented, and the performance of COVQ's trained for this channel is evaluated for an i.i.d. Gaussian source. Then, the new method is applied in implementing an error-robust sub-band image coder, and we present image results that illustrate the resulting performance. Our experiments show that the new approach is able to outperform a traditional scheme based on separate source and channel coding.
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Frequency estimation by 1-bit quantization and table look-up processing2000In: Proceedings European Signal Processing Conference, 2000, p. 1807-1810Conference paper (Refereed)
• 67.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Control of Multi-Agent Systems with Applications to Distributed Frequency Control Power Systems2013Licentiate thesis, monograph (Other academic)
Multi-agent systems are interconnected control systems with many application domains. The first part of this thesis considers nonlinear multi-agent systems, where the control input can be decoupled into a product of a nonlinear gain function depending only on the agent's own state, and a nonlinear interaction function depending on the relative states of the agent's neighbors. We prove stability of the overall system, and explicitly characterize the equilibrium state for agents with both single- and double-integrator dynamics.
Disturbances may seriously degrade the performance of multi-agent systems. Even constant disturbances will in general cause the agents to diverge, rather than to converge, for many control protocols. In the second part of this thesis we introduce distributed proportional-integral controllers to attenuate constant disturbances in multi-agent systems with first- and second-order dynamics. We derive explicit stability criteria based on the integral gain of the controllers.
Lastly, this thesis presents both centralized and distributed frequency controllers for electrical power transmission systems. Based on the theory developed for multi-agent systems, a decentralized controller regulating the system frequencies under load changes is proposed. An optimal distributed frequency controller is also proposed, which in addition to regulating the frequencies to the nominal frequency, minimizes the cost of power generation.
• 68.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
TRUST Center, University of California, Berkeley. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. TRUST Center, University of California, Berkeley.
Correlated Failures of Power Systems: Analysis of the Nordic Grid2011In: Preprints of Workshop on Foundations of Dependable and Secure Cyber-Physical Systems, 2011Conference paper (Refereed)
In this work we have analyzed the effectsof correlated failures of power lines on the total systemload shed. The total system load shed is determined bysolving the optimal load shedding problem, which is thesystem operator’s best response to a system failure.We haveintroduced a Monte Carlo based simulation framework forestimating the statistics of the system load shed as a functionof stochastic network parameters, and provide explicitguarantees on the sampling accuracy. This framework hasbeen applied to a 470 bus model of the Nordic power systemand a correlated Bernoulli failure model. It has been foundthat increased correlations between Bernoulli failures ofpower lines can dramatically increase the expected valueas well as the variance of the system load shed.
• 69.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Undamped Nonlinear Consensus Using Integral Lyapunov Functions2012In: 2012 American Control Conference (ACC), IEEE Computer Society, 2012, p. 6644-6649Conference paper (Refereed)
This paper analyzes a class of nonlinear consensus algorithms where the input of an agent can be decoupled into a product of a gain function of the agents own state, and a sum of interaction functions of the relative states of its neighbors. We prove the stability of the protocol for both single and double integrator dynamics using novel Lyapunov functions, and provide explicit formulas for the consensus points. The results are demonstrated through simulations of a realistic example within the framework of our proposed consensus algorithm.
• 70.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Distributed vs. centralized power systems frequency control2013In: 2013 European Control Conference, ECC 2013, 2013, p. 3524-3529Conference paper (Refereed)
This paper considers a distributed control algorithm for frequency control of electrical power systems. We propose a distributed controller which retains the reference frequency of the buses under unknown load changes, while asymptotically minimizing a quadratic cost of power generation. For comparison, we also propose a centralized controller which also retains the reference frequency while minimizing the same cost of power generation. We derive sufficient stability criteria for the parameters of both controllers. The controllers are evaluated by simulation on the IEEE 30 bus test network, where their performance is compared.
• 71.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
Control of MTDC Transmission Systems under Local Information2014In: Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on, IEEE conference proceedings, 2014, p. 1335-1340Conference paper (Refereed)
High-voltage direct current (HVDC) is a commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. In this paper a distributed controller for multi-terminal high-voltage direct current (MTDC) transmission systems is considered. Sufficient conditions for when the proposed controller renders the closed-loop system asymptotically stable are provided. Provided that the closed loop system is asymptotically stable, it is shown that in steady-state a weighted average of the deviations from the nominal voltages is zero. Furthermore, a quadratic cost of the current injections is minimized asymptotically.
• 72.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Distributed controllers for multiterminal HVDC transmission systems2017In: IEEE Transactions on Control of Network Systems, ISSN 2325-5870, Vol. 4, no 3, p. 564-574Article in journal (Refereed)
High-voltage direct current (HVDC) is a commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. In this paper the voltagedroop method (VDM) is reviewed, and three novel distributed controllers for multi-terminal HVDC (MTDC) transmission systems are proposed. Sufficient conditions for when the proposed controllers render the closed-loop system asymptotically stable are provided. These conditions give insight into suitable controller architecture, e.g., that the communication graph should be identical with the graph of the MTDC system, including edge weights. Provided that the closed-loop systems are asymptotically stable, it is shown that the voltages asymptotically converge to within predefined bounds. Furthermore, a quadratic cost of the injected currents is asymptotically minimized. The proposed controllers are evaluated on a four-bus MTDC system.
• 73.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Distributed PI-Control with Applications to Power Systems Frequency Control2014In: American Control Conference (ACC), 2014, IEEE conference proceedings, 2014, p. 3183-3188Conference paper (Refereed)
This paper considers a distributed PI-controller for networked dynamical systems. Sufficient conditions for when the controller is able to stabilize a general linear system and eliminate static control errors are presented. The proposed controller is applied to frequency control of power transmission systems. Sufficient stability criteria are derived, and it is shown that the controller parameters can always be chosen so that the frequencies in the closed loop converge to nominal operational frequency. We show that the load sharing property of the generators is maintained, i.e., the input power of the generators is proportional to a controller parameter. The controller is evaluated by simulation on the IEEE 30 bus test network, where its effectiveness is demonstrated.
• 74.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Distributed Control of Networked Dynamical Systems: Static Feedback, Integral Action and Consensus2014In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 7, p. 1750-1764Article in journal (Refereed)
This paper analyzes distributed control protocols for first- and second-order networked dynamical systems. We propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain, and a sum of nonlinear interaction functions. By using integral Lyapunov functions, we prove the stability of the proposed control protocols, and explicitly characterize the equilibrium set. We also propose a distributed proportional-integral (PI) controller for networked dynamical systems. The PI controllers successfully attenuate constant disturbances in the network. We prove that agents with single-integrator dynamics are stable for any integral gain, and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double-integrator dynamics. Throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites, power systems and building temperature control.
• 75.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Dynamical decentralized voltage control of multi-terminal HVDC grids2017In: 2016 European Control Conference, ECC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 1519-1524, article id 7810505Conference paper (Refereed)
High-voltage direct current (HVDC) is a commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. When connecting multiple HVDC lines into a multi-terminal HVDC (MTDC) system, several challenges arise. To ensure safe and efficient operation of MTDC systems, the voltage of all terminals need to be steered to within an operational range. In this paper we study the commonly used decentralized voltage droop controller, and show that it in general does not steer the voltages to within the operational range. We propose a decentralized PI controller with deadband, and show that it always steers the voltages to within the operational range regardless of the loads. Additionally we show that the proposed controller inherits the property of proportional power sharing from the droop controller, provided that both the loads and the line resistances are sufficiently low. The results are validated through simulation in Matlab.
• 76.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Electric Power Systems. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Electric Power Systems.
Distributed Voltage and Current Control of Multi-Terminal High-Voltage Direct Current Transmission Systems2014In: Proceedings of the 19th IFAC World Congress, 2014, IFAC Papers Online, 2014, Vol. 19, p. 11910-11916Conference paper (Refereed)
High-voltage direct current (HVDC) is a commonly used technology for long-distance power transmission, due to its low resistive losses and low costs. In this paper, a novel distributed controller for multi-terminal HVDC (MTDC) systems is proposed. Under certain conditions on the controller gains, it is shown to stabilize the MTDC system. The controller is shown to always keep the voltages close to the nominal voltage, while assuring that the injected power is shared fairly among the converters. The theoretical results are validated by simulations, where the affect of communication time-delays is also studied.
• 77.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Distributed integral action: stability analysis and frequency control of power systems2012In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE , 2012, p. 2077-2083Conference paper (Refereed)
This paper analyzes distributed proportional-integral controllers. We prove that integral action can be successfully applied to consensus algorithms, where attenuation of static disturbances is achieved. These control algorithms are applied to decentralized frequency control of electrical power systems. We show that the proposed algorithm can attenuate step disturbances of power loads. We provide simulations of the proposed control algorithm on the IEEE 30 bus test system that demonstrate its efficiency.
• 78.
KTH, School of Industrial Engineering and Management (ITM). KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Industrial Engineering and Management (ITM). KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Industrial Engineering and Management (ITM). KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Industrial Engineering and Management (ITM). KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Coherence in Synchronizing Power Networks with Distributed Integral Control2017In: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, IEEE , 2017, p. 6683-6688Conference paper (Refereed)
We consider frequency control of synchronous generator networks and study transient performance under both primary and secondary frequency control. We model random step changes in power loads and evaluate performance in terms of expected deviations from a synchronous frequency over the synchronization transient; what can be thought of as lack of frequency coherence. We compare a standard droop control strategy to two secondary proportional integral (PI) controllers: centralized averaging PI control (CAPI) and distributed averaging PI control (DAPI). We show that the performance of a power system with DAPI control is always superior to that of a CAPI controlled system, which in turn has the same transient performance as standard droop control. Furthermore, for a large class of network graphs, performance scales unfavorably with network size with CAPI and droop control, which is not the case with DAPI control. We discuss optimal tuning of the DAPI controller and describe how internodal alignment of the integral states affects performance. Our results are demonstrated through simulations of the Nordic power grid.
• 79.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Performance and scalability of voltage controllers in multi-terminal HVDC networks2017In: Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 3029-3034, article id 7963412Conference paper (Refereed)
In this paper, we compare the transient performance of a multi-terminal high-voltage DC (MTDC) grid equipped with a slack bus for voltage control to that of two distributed control schemes: A standard droop controller and a distributed averaging proportional-integral (DAPI) controller. We evaluate performance in terms of an ℋ2 metric that quantifies expected deviations from nominal voltages, and show that the transient performance of a droop or DAPI controlled MTDC grid is always superior to that of an MTDC grid with a slack bus. In particular, by studying systems built up over lattice networks, we show that the ℋ2 norm of a slack bus controlled system may scale unboundedly with network size, while the norm remains uniformly bounded with droop or DAPI control. We simulate the control strategies on radial MTDC networks to demonstrate that the transient performance for the slack bus controlled system deteriorates significantly as the network grows, which is not the case with the distributed control strategies.
• 80.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Coordinated frequency control through MTDC transmission systems2015In: IFAC Proceedings, Elsevier, 2015, Vol. 48, no 22, p. 106-111Conference paper (Refereed)
In this paper we propose a distributed dynamic controller for sharing frequency control reserves of asynchronous AC systems connected through a multi-terminal HVDC (MTDC) grid. We derive sufficient stability conditions, which guarantee that the frequencies of the AC systems converge to the nominal frequency. Simultaneously, the global quadratic cost of power generation is minimized, resulting in an optimal distribution of generation control reserves. The proposed controller also regulates the voltages of the MTDC grid, asymptotically minimizing a quadratic cost function of the deviations from the nominal voltages. The proposed controller is tested on a high-order dynamic model of a power system consisting of asynchronous AC grids, modelled as IEEE 14 bus networks, connected through a six-terminal HVDC grid. The performance of the controller is successfully evaluated through simulation.
• 81.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Distributed Frequency Control Through MTDC Transmission Systems2017In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 32, no 1, p. 250-260, article id 7456314Article in journal (Refereed)
In this paper, we propose distributed dynamic controllers for sharing both frequency containment and restoration reserves of asynchronous ac systems connected through a multi-terminal HVDC (MTDC) grid. The communication structure of the controller is distributed in the sense that only local and neighboring state information is needed, rather than the complete state. We derive sufficient stability conditions, which guarantee that the ac frequencies converge to the nominal frequency. Simultaneously, a global quadratic power generation cost function is minimized. The proposed controller also regulates the voltages of the MTDC grid, asymptotically minimizing a quadratic cost function of the deviations from the nominal dc voltages. The results are valid for distributed cable models of the HVDC grid (e.g., $\pi$-links), as well as ac systems of arbitrary number of synchronous machines, each modeled by the swing equation. We also propose a decentralized communication-free version of the controller. The proposed controllers are tested on a high-order dynamic model of a power system consisting of asynchronous ac grids, modeled as IEEE 14 bus networks, connected through a six-terminal HVDC grid. The performance of the controller is successfully evaluated through simulation. © 1969-2012 IEEE.
• 82.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
ETH Zurich. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. ETH Zurich.
Distributed Primary Frequency Control through Multi-Terminal HVDC Transmission Systems2015In: American Control Conference (ACC), 2015, IEEE conference proceedings, 2015, p. 5029-5034Conference paper (Refereed)
This paper presents a decentralized controller for sharing primary AC frequency control reserves through a multi-terminal HVDC grid. By using passivity arguments, the proposed controller is shown to stabilize the closed-loop system consisting of the interconnected AC and HVDC grids, given any positive controller gains. The static control errors resulting from the proportional controller are quantified and bounded by analyzing the equilibrium of the closed-loop system. The proposed controller is applied to a test grid consisting of three asynchronous AC areas interconnected by an HVDC grid, and its effectiveness is validated through simulation.
• 83.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
Power Systems Laboratory,Switzerland. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. Power Systems Laboratory,Switzerland.
Distributed Secondary Frequency Control through MTDC Transmission Systems2015In: Decision and Control (CDC), 2015 IEEE 54th Annual Conference on, IEEE conference proceedings, 2015, p. 2627-2634Conference paper (Refereed)
In this paper, we present distributed controllers for sharing primary and secondary frequency control reserves for asynchronous AC transmission systems, which are connected through a multi-terminal HVDC grid. By using passivity arguments, the equilibria of the closed-loop system are shown to be globally asymptotically stable. We quantify the static errors of the voltages and frequencies, and give upper bounds for these errors. It is also shown that the controllers have the property of power sharing, i.e., primary and secondary frequency control reserves are shared fairly amongst the AC systems. The proposed controllers are applied to a high-order dynamic model of of a power system consisting of asynchronous AC grids connected through a 6-terminal HVDC grid.
• 84. Anisi, David A.
Swedish Defence Research Agency (FOI), Sweden. KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Cooperative Minimum Time Surveillance With Multiple Ground Vehicles2010In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, no 12, p. 2679-2691Article in journal (Refereed)
In this paper, we formulate and solve two different minimum time problems related to unmanned ground vehicle (UGV) surveillance. The first problem is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from a point on a path and such that the time for executing the search in parallel is minimized. Here, the sensors' field of view are assumed to have a limited coverage range and be occluded by the obstacles. The second problem extends the first by additionally requiring the induced information graph to be connected at the time instants when the UGVs perform the surveillance mission, i.e., when they gather and transmit sensor data. In the context of the second problem, we also introduce and utilize the notion of recurrent connectivity, which is a significantly more flexible connectivity constraint than, e.g., the 1-hop connectivity constraints and use it to discuss consensus filter convergence for the group of UGVs.
• 85.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
An ADMM Algorithm for Solving l(1) Regularized MPC2012In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE , 2012, p. 4486-4491Conference paper (Refereed)
We present an Alternating Direction Method of Multipliers (ADMM) algorithm for solving optimization problems with an ℓ1 regularized least-squares cost function subject to recursive equality constraints. The considered optimization problem has applications in control, for example in ℓ1 regularized MPC. The ADMM algorithm is easy to implement, converges fast to a solution of moderate accuracy, and enables separation of the optimization problem into sub-problems that may be solved in parallel. We show that the most costly step of the proposed ADMM algorithm is equivalent to solving an LQ regulator problem with an extra linear term in the cost function, a problem that can be solved efficiently using a Riccati recursion. We apply the ADMM algorithm to an example of ℓ1 regularized MPC. The numerical examples confirm fast convergence to sufficient accuracy and a linear complexity in the MPC prediction horizon.
• 86.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
On the way to autonomous model predictive control: A distillation column simulation study2013In: 10th IFAC Symposium on Dynamics and Control of Process Systems, DYCOPS 2013, IFAC Secretariat , 2013, no PART 1, p. 713-720Conference paper (Refereed)
Model Predictive Control (MPC) is a powerful tool in the control of large scale chemical processes and has become the standard method for constrained multivariable control problems. Hence, the number of MPC applications is increasing steadily and it is being used in application domains other than petrochemical industries. A common observation by the industrial practitioners is that success of any MPC application requires not only efficient initial deployment but also maintenance of initial effectiveness. To this end, we propose a novel high level automated support strategy for MPC systems. Such a strategy consists of components such as performance monitoring, performance diagnosis, least costly closed loop experiment design, re-identification and autotuning. This work presents the novel technological developments in each component and demonstrates them on a distillation column case study. We show that automated support strategy restores nominal performance after a performance drop is detected and takes the right course of action depending on its cause.
• 87.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
MOOSE: A model based optimal input design toolbox2012In: 16th IFAC Symposium on System Identification, IFAC , 2012, no PART 1, p. 1535-1540Conference paper (Refereed)
MOOSE is a model based optimal input design toolbox developed for Matlab. The objective of the toolbox is to simplify the implementation of some optimal input design problems encountered in system identification. MOOSE provides an extra layer between the user and a convex optimization environment.
• 88.
KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Application-Oriented Input Design in System Identification Optimal input design for control2017In: IEEE CONTROL SYSTEMS MAGAZINE, ISSN 1066-033X, Vol. 37, no 2, p. 31-56Article in journal (Refereed)
• 89. Antoni, V.
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
Coherent structures and anomalous transport in reversed field pinch plasmas2006In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T122, p. 1-7Article in journal (Refereed)
The results leading to the identification of coherent structures emerging from the background turbulence in the edge region of the reversed field pinch experiments EXTRAP-T2R and RFX are reviewed. These structures have traits of vortices in velocity field and blobs in density, and the reconstruction of their spatial structure and of their time evolution is discussed focusing on the analysis tools applied. The role of these structures in the particle anomalous transport is addressed, showing that their collisions can contribute up to 50% the total particle losses. This process is shown to be responsible for bursts in particle flux and it is found to set a characteristic collision time, which is in agreement with the statistical properties of laminar times for particle flux bursts.
• 90. Anttila, L
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Recursive learning-based joint digital predistorter for power amplifier and I/Q modulator impairments2010In: International Journal of Microwave and Wireless Technologies, ISSN 1759-0787, Vol. 2, no 2, p. 173-182Article in journal (Refereed)
The main implementation impairments degrading the performance of direct-conversion radio transmitters are in-phase/quadrature (I/Q) mismatch, local oscillator (LO) leakage, and power amplifier (PA) nonlinear distortion. In this article, we propose a recursive least-squares-based learning algorithm for joint digital predistortion (PD) of frequency-dependent PA and I/Q modulator impairments. The predistorter is composed of a parallel connection of two parallel Hammerstein (PH) predistorters and an LO leakage compensator, yielding a predistorter which as a whole is fully linear in the parameters. In the parameter estimation stage, proper feedback signal from the transmitter radio frequency (RF) stage back to the digital parts is deployed, combined with the indirect learning architecture and recursive least-squares training. The proposed structure is one of the first techniques to explicitly consider the joint estimation and mitigation of frequency-dependent PA and I/Q modulator impairments. Extensive simulation and measurement analysis is carried out to verify the operation and efficiency of the proposed PD technique. In general, the obtained results demonstrate linearization and I/Q modulator calibration performance clearly exceeding the performance of current state-of-the-art reference techniques.
• 91. Anttila, Lauri
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Joint Mitigation of Power Amplifier and I/Q Modulator Impairments in Broadband Direct-Conversion Transmitters2010In: IEEE transactions on microwave theory and techniques, ISSN 0018-9480, E-ISSN 1557-9670, Vol. 58, no 4, p. 730-739Article in journal (Refereed)
In this paper, we present a novel digital predistorter structure for joint mitigation of frequency-dependent power amplifier (PA) and in-phase and quadrature (I/Q) modulator impairments in direct-conversion radio transmitters. The predistorter is based on an extended parallel Hammerstein structure, yielding a predistorter that is fully linear in the parameters. In the parameter estimation stage, the indirect learning architecture is utilized. The proposed technique is the first technique in the literature to consider the joint estimation and mitigation of frequency-dependent PAand I/Q modulator impairments. Extensive simulation and measurement analysis is carried out to verify the operation and efficacy of the proposed predistortion structure. It is shown that the adjacent channel power ratio is increased by more than 20 dB in all experiments when using the proposed method, and that the performance of the reference techniques is clearly exceeded.
• 92. Aragues, R.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Distributed algebraic connectivity estimation for adaptive event-triggered consensus2012In: American Control Conference (ACC), 2012, IEEE , 2012, p. 32-37Conference paper (Refereed)
In several multi agent control problems, the convergence properties and speed of the system depend on the algebraic connectivity of the graph. We discuss a particular event-triggered consensus scenario, and show that the availability of an estimate of the algebraic connectivity could be used for adapting the behavior of the average consensus algorithm. We present a novel distributed algorithm for estimating the algebraic connectivity, that relies on the distributed computation of the powers of matrices. We provide proofs of convergence, convergence rate, and upper and lower bounds at each iteration of the estimated algebraic connectivity.
• 93. Aragues, Rosario
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Distributed algebraic connectivity estimation for undirected graphs with upper and lower bounds2014In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 50, no 12, p. 3253-3259Article in journal (Refereed)
The algebraic connectivity of the graph Laplacian plays an essential role in various multi-agent control systems. In many cases a lower bound of this algebraic connectivity is necessary in order to achieve a certain performance. Lately, several methods based on distributed Power Iteration have been proposed for computing the algebraic connectivity of a symmetric Laplacian matrix. However, these methods cannot give any lower bound of the algebraic connectivity and their convergence rates are often unclear. In this paper, we present a distributed algorithm for estimating the algebraic connectivity for undirected graphs with symmetric Laplacian matrices. Our method relies on the distributed computation of the powers of the adjacency matrix and its main interest is that, at each iteration, agents obtain both upper and lower bounds for the true algebraic connectivity. Both bounds successively approach the true algebraic connectivity with the convergence speed no slower than O(1/k).
• 94.
University of Luxembourg, Luxembourg.
University of Luxembourg, Luxembourg. University of Luxembourg, Luxembourg. KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Gateway Diversity Strategies in Q/V Band Feeder Links2011In: Proceedings 17th Ka and Broadband Communications Conference, 2011Conference paper (Refereed)
• 95.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Control over a Hybrid MAC Wireless Network2010In: 2010 IEEE 1ST INTERNATIONAL CONFERENCE ON SMART GRID COMMUNICATIONS, 2010, p. 197-202Conference paper (Refereed)
Wireless Sensor Networks and Control Systems are an essential part of the Smart Grid. We consider the problem of performing control over large complex networked systems with packet drops. More specifically, we are interested in improving the performance of the regulation of control loops when the communication is made over low-cost wireless networks. In control over wireless networks it is common to use Contention-Free (CF) schemes where no losses occur with the price of low scalability and complicated scheduling policies. In this work we propose a hybrid MAC and control architecture, where a small number of control loops with high demand of attention are scheduled in a CF scheme and well regulated loops are scheduled in a lossy, asynchronous and highly scalable, Contention-Access (CA) scheme. We model and analyze the performance of such system with Markov Jump Linear System (MJLS) tools and compare it with other architecture types. Performance is evaluated using a quadratic cost function of the state.
• 96.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Department of Electrical Engineering, University of California Los Angeles, USA. INCAS 3 & University of Groningen, The Netherlands. Department of Electrical Engineering, University of California Los Angeles, USA. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
An improved self-triggered implementation for linear controllers2012Conference paper (Refereed)
Research in networked control systems raised the importance of understanding what are thetiming requirements for control. In recent years this problem has been attacked from multiple anglesincluding the computation of Maximal Allowable Transmission Intervals, event-triggered, and selftriggered controller implementations. In a self-triggered implementation the controller is responsible forcomputing the next time instant at which the actuator values should be updated by evaluating the controllaw on fresh sensor measurements. One of the main challenges in self-triggered control is how to performthe exact calculation of the time at which these updates should take place. In this paper we present anew technique to compute lower bounds on the self-triggered update times in a computationally lightmanner. We evaluate the algorithm on numerical examples and we observe that the algorithm performswell when compared to other existing methods and provides tight lower bounds on the exact updatetimes. Additionally, we propose a Semidefinite Programming-based technique that produces triggeringconditions that are less conservative than the existing ones and for which the update times are larger.
• 97.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Experimental Validation of a Localization System Based on a Heterogeneous Sensor Network2009In: ASCC: 2009 7TH ASIAN CONTROL CONFERENCE, NEW YORK: IEEE , 2009, p. 465-470Conference paper (Refereed)
The experimental implementation and validation of a localization system based on a heterogeneous sensor network is described. The sensor network consists of ultrasound ranging sensors and web cameras. They are used to localize a mobile robot under sensor communication constraints. Applying a recently proposed sensor fusion algorithm that explicitly takes communication delay and cost into account, it is shown that one can accurately trade off the estimation performance by using low-quality ultrasound sensors with low processing time and low communication cost versus the use of the high-quality cameras with longer processing time and higher communication cost. It is shown that a periodic schedule of the sensors is suitable in many cases. The experimental setup is discussed in detail and experimental results are presented.
• 98. Aravanis, Alexis
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Power allocation in multibeam satellites: A hybrid-genetic algorithm approach2012Conference paper (Refereed)
• 99.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Design, Implementation and Validation of Resource-Aware and Resilient Wireless Networked Control Systems2014Doctoral thesis, monograph (Other academic)
Networked control over wireless networks is of growing importance in many application domains such as industrial control, building automation and transportation systems. Wide deployment however, requires systematic design tools to enable efficient resource usage while guaranteeing close-loop control performance. The control system may be greatly affected by the inherent imperfections and limitations of the wireless medium and malfunction of system components. In this thesis, we make five important contributions that address these issues.
In the first contribution, we consider event- and self-triggered control and investigate how to efficiently tune and execute these paradigms for appropriate control performance. Communication strategies for aperiodic control are devised, where we jointly address the selection of medium-access control and scheduling policies. Experimental results show that the best trade-off is obtained by a hybrid scheme, combining event- and self-triggered control together with contention-based and contention-free medium access control.
The second contribution proposes an event-based method to select between fast and slow periodic sampling rates. The approach is based on linear quadratic control and the event condition is a quadratic function of the system state. Numerical and experimental results show that this hybrid controller is able to reduce the average sampling rate in comparison to a traditional periodic controller, while achieving the same closed-loop control performance.
In the third contribution, we develop compensation methods for out-of-order communications and time-varying delays using a game-theoretic minimax control framework. We devise a linear temporal coding strategy where the sensor combines the current and previous measurements into a single packet to be transmitted. An experimental evaluation is performed in a multi-hop networked control scenario with a routing layer vulnerability exploited by a malicious application. The experimental and numerical results show the advantages of the proposed compensation schemes.
The fourth contribution proposes a distributed reconfiguration method for sensor and actuator networks. We consider systems where sensors and actuators cooperate to recover from faults. Reconfiguration is performed to achieve model-matching, while minimizing the steady-state estimation error covariance and a linear quadratic control cost. The reconfiguration scheme is implemented in a room heating testbed, and experimental results demonstrate the method's ability to automatically reconfigure the faulty system in a distributed and fast manner.
The final contribution is a co-simulator, which combines the control system simulator Simulink with the wireless network simulator COOJA. The co-simulator integrates physical plant dynamics with realistic wireless network models and the actual embedded software running on the networked devices. Hence, it allows for the validation of the complete wireless networked control system, including the study of the interactions between software and hardware components.
• 100.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Self-triggered control over wireless sensor and actuator networks2011Conference paper (Refereed)
Energy and communication bandwidth are scarce resources in wireless sensor and actuator networks. Recent research efforts considered the control of physical processes over such resource limited networks. Most of the existing literature addressing this topic is dedicated to periodically sampled control loops and scheduled communication, because it simplifies the analysis and the implementation. We propose instead an aperiodic network transmission scheme that reduces the number of transmission instances for the sensor and control nodes, thereby reducing energy consumption and increasing network lifetime, without sacrificing control performance. As an added benefit, we show the possibility of dynamically allocating the network bandwidth based on the physical system state and the available resources. In order to allow timely, reliable, and energy efficient communication, we propose a new co-design framework for the wireless medium access control, compatible with the IEEE 802.15.4 standard. Furthermore, we validate our approach in a real wireless networked control implementation.
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Let $G$ be a $k$-regular bipartite graph, and let $G$ contain a bridge. Prove that $k=1$.
Let $G$ be a $k$-regular bipartite graph, and let $G$ contain a bridge. Prove that $k=1$.
I have tried to remove the bridge and find a contradiction that an component should not be bipartite, but I failed.
• Hint: consider edge counts – Bob Krueger Nov 26 '17 at 15:56
Suppose that the removal of the bridge in a $k$-regular graph results in a component of a graph. This component is either a single vertex, in which case the problem is solved or it must be a bipartite graph with vertex partition sets say $V$ and $W$. WLOG, assume that one of the vertices of the bridge was a vertex in $V$. Then because the sum of the degrees of vertices in each partition sets $V$ and $W$ must be equal in a bipartite graph, so $$|W|k=(|V|-1)k+(k-1)\Longrightarrow (|V|-|W|)k=1.$$ Since all quantities are integers, so $k=1$.
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# Trouble in understanding why function is constant in a given domain
Definition The group of unitary operators $$u(\theta)$$ on $$L^2(\mathbb R^3)$$ given by $$(u(\theta)\Phi)(r) =\Phi(\theta) \equiv e^{\frac{3\theta}{2}}\Phi(e^\theta r)$$ is called the group of dilation operators on $$\mathbb R^3.$$
Let $$H$$ be a compact operator and $$R(z) \equiv(H-z)^{-1}$$ the resolvent. Define $$R(z,\theta)$$ by $$R(z,\theta) \equiv u(\theta)R(z)u(\theta)^{-1}$$. Let us define also $$\mathcal O \equiv \{\theta \in \mathbb C: (u(\theta)\Phi)(r)$$ for $$\theta \in \mathbb R$$ has an analytic continuation $$\}$$
In this article A Class of Analytic Perturbations for One-body Schrδdinger Hamiltonians they were able to show that the function $$\Psi_z(\theta)=(\phi(\theta) ,R(z,\theta)\phi(\theta))$$ is meromorphic in $$z$$ for $$z \in \mathcal C^{++} \equiv \{z \in \mathbb C : Im \ z > 0 ,\ Re \ z > 0 \}$$ and $$\theta \in \mathcal O^\epsilon \equiv \{\theta \in \mathcal O: Im \ \theta > \epsilon \}$$
Now since for $$\theta \in \mathbb R,\ u(\theta)$$ is unitary we have that
$$\Psi_z \equiv (\Phi,R(z)\Phi)=\Psi_z(\theta)$$
from this they claim that $$\Psi_z(\theta)$$ that for fixed $$z \in \mathcal C^{++}$$ and $$\theta \in \mathcal O^\epsilon$$ the function $$\Psi_z(\theta)$$ is constant in $$\theta$$.
My question is why is $$\Psi_z(\theta)$$ constant for fixed $$z \in \mathcal C^{++}$$ and $$\theta \in \mathcal O^\epsilon$$ ?
As I understand it, they have shown:
1. That $$\Phi_z(\theta)$$ is meromorphic in a region containing part of the real line.
2. That $$\Phi_z(\theta)$$ is constant on the real line (using unitarity of $$u(\theta)$$ for real $$\theta$$).
Hence by analytic continuation, $$\Phi_z(\theta)$$ must be constant over the entire region connected to the real line where it is meromorphic.
• So if a meromorphic function is constant in a interval than i will be constant in all its domain? Jan 12, 2020 at 3:07
• @amiltonmoreira In all of the domain which is connected to the interval, yes.
– Yly
Jan 12, 2020 at 3:08
• I gave a proof as question here math.stackexchange.com/questions/3505785/… Jan 12, 2020 at 3:09
• @amiltonmoreira Yes, your proof looks basically correct. It all follows from uniqueness of analytic continuation.
– Yly
Jan 12, 2020 at 3:13
• @amiltonmoreira Yes. The wikipedia page on meromorphic functions says so explicitly in the second paragraph: en.wikipedia.org/wiki/Meromorphic_function
– Yly
Jan 12, 2020 at 3:18
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# DEPRECATED Understanding the process for solving linear equations
### Problem
Create a list of steps, in order, that will solve the following equation.
space, 9, left parenthesis, x, plus, 4, right parenthesis, equals, 54
space, space, space, space, space, space, space, space, space, space, space Solution steps:
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## The union of a chain of monomial ideals is a monomial ideal
Let $F$ be a field, let $R = F[x_1, \ldots, x_m]$, and let $K$ be a linearly ordered set. Let $\mathcal{M} = \{M_k\}_{k \in K}$ be a family of monomial ideals in $R$ such that if $i \leq j$ then $M_i \subseteq M_j$. Prove that $\bigcup_K M_k$ is a monomial ideal in $R$.
We showed in this previous exercise that $\bigcup_K M_k$ is an ideal of $R$. Thus it suffices to show that $\bigcup_K M_k$ has a monomial generating set.
To that end, let $G_k$ be a monomial generating set of $M_k$. Then $\bigcup_K M_k = \bigcup_K (G_k)$ $= (\bigcup_K G_k)$, so that $\bigcup_K G_k$ is a monomial generating set for $\bigcup_K M_k$.
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All Questions
2k views
Rotate vector in spherical coordinates
I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia http://en.wikipedia.org/...
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Shape of a string/chain/cable/rope/wire?
The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc ...
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Do gases reflect some IR radiation?
The usual definition given for a greenhouse gas is that it absorbs infrared radiation. Of course, then the gas emits its own thermal radiation, and it does so without preference for direction (...
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Difference between Diamond anvil cell and Bridgman cell
In high pressure physics what is the difference between diamond anvil cells (DAC) and Bridgman cells? My understanding is that they are both forms of anvil cell but in the scientific literature I'm ...
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Fading transition and rotation of and object in 2D
I'm looking for sources about I guess dynamics subject. The model I'd like to solve is reduced to a question of: How does a force applied on a certain point of an object results in both fading ...
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What is actually a resonating vibration and resonance?
What is actually a resonating vibration and resonance? I have searched many books and made Google search too but couldn't understand it clearly.
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Looking for a reference book, or book chapter to learn about piezoelectricity
I'm looking for an introduction to the treatment of piezoelectricity, specially in semiconductors emphasizing the dependence on the orientation of the unit cell and the interactive effects with the ...
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Tachyonic antitelephone vs messaging through a wormhole
From the wikipedia article on tachyons: Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics.[3][5] If such particles ...
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proof of radius of convergence of perturbation series in quantum electrodynamics zero
Can anyone show detailed proof of why radius of convergence of perturbation series in quantum electrodynamics is zero? And how is perturbation series constructed? So, as this argument requires ...
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Could a planet ever end up with a doughnut hole in it?
If there was an asteroid that happened to be made out of something really solid (iron, titanium?) and it got enough velocity (sling shot around the sun?), is it conceivable that it could hit a planet ...
282 views
Frequency of a periodic signal with distortions
I would like to evaluate frequency of some unstable periodic signal coming from a detector: The signal is registered continuously and may or may not be present (i.e. be periodic). The frequency ...
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# How to prevent page breaks from appearing at the point where a sub-itemized list begin in ConTeXt?
I have a lengthy document containing lots of itemized lists, in two levels. It is like this, but often much longer:
\startitemize[r]
\item This is a statement.
\startitemize[n]
\item This is an example.
\item This is another example.
\item This is another example.
\stopitemize
\item This is another statement.
\startitemize[n]
\item This is an example.
\item This is another example.
\item This is another example.
\stopitemize
\stopitemize
After compiling, I found that it often places page breaks at the beginning of the sub-list, so that it looks like this:
_________________ _________________
| | |
| This is some | 1. This is |
| text. This is | an examp- |
| some more text. | le. |
| This is some | 2. This is |
| more text. | another |
| i. This is | example. |
| a statement. | 3. This is |
|_________________|_________________|
In some cases, this confused readers, who do not know that the examples belong to the statement. The preferred behavior would make sure that the statements never appear without at least one of the examples below it, even if the page break must force this whole statement to the next page, e.g.:
_________________ _________________
| | |
| This is some | i. This is a s- |
| text. This is | tatement. |
| some more text. | |
| This is some | 1. This is |
| more text. | an examp- |
| | example. |
| | 2. This is |
|_________________|_________________|
How can I fix the breaking to prevent these itemized items from appearing along without at least one of their sub-itemized items?
• Try adding \startitemize[n,intro]. – Aditya Sep 2 '13 at 19:48
• I would love to reproduce the problem, but everything seems fine. – doed Dec 9 '13 at 12:26
• @Aditya that should be an answer. – Andrew Swann May 6 '17 at 17:02
You can add the intro keyword, which prevents a page break before the start of itemize.
\startitemize[r]
\item This is a statement.
\startitemize[n,intro]
\item This is an example.
\item This is another example.
\item This is another example.
\stopitemize
\item This is another statement.
\startitemize[n,intro]
\item This is an example.
\item This is another example.
\item This is another example.
\stopitemize
\stopitemize
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# Tag Info
17
The best solution is to escape the underscore with the backslash. Using a backslash forces the following character to be used literally rather than as part of Markdown formatting: \_\_\_\_\_\_ ______ You could also use code formatting (with backticks), which is always literal, but that also adds a grey background which may not be universally liked. ______ ...
15
Please ‘never’ use 𝚖𝚘𝚗𝚘𝚜𝚙𝚊𝚌𝚎𝚍 𝚝𝚎𝚡𝚝 on ELU tl;dr Please don’t use ˋbackticksˋ at all: use italics instead. Please don’t use preformatted indented blocks except for tables. Nonetheless, you were right about one aspect of the trouble: the color. Thank you for pointing that out. While you have indeed identified a genuine problem, I am afraid ...
7
Enabling MathJax As a moderator on Code Review who helped to push for MathJax to be activated there, I can say that the current Stack Exchange policy makes you work hard to justify it. Performance is a Feature, and Speed Still Matters, says Jeff Atwood, so they want pages to render quickly. MathJax is enabled per site, not per question, so they are ...
4
This has been fixed. Now, the numbering follows from the first item in the list. If the first item in your list is 42, the numbering will follow from that. If the next item in your list is 1037, it will still show up as 43. So the first number in your numbered list is now respected; the others still aren’t. This is a demonstration. This item is numbered 7, ...
3
The gray box produced by <code> tags / backticks might even be turned into an advantage: "Having children of my own <code> </code> me" "Having children of my own me" or, perhaps more simply: "Having children of my own ..............
1
This is what you should be seeing, Mari Lou: I don’t know why you are not seeing them after having done those things.
Only top voted, non community-wiki answers of a minimum length are eligible
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• Similar Content
• Good evening everyone!
I was wondering if there is something equivalent of GL_NV_blend_equation_advanced for AMD?
Basically I'm trying to find more compatible version of it.
Thank you!
• Hello guys,
How do I know? Why does wavefront not show for me?
I already checked I have non errors yet.
And my download (mega.nz) should it is original but I tried no success...
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• I wasn't sure if this would be the right place for a topic like this so sorry if it isn't.
I'm currently working on a project for Uni using FreeGLUT to make a simple solar system simulation. I've got to the point where I've implemented all the planets and have used a Scene Graph to link them all together. The issue I'm having with now though is basically the planets and moons orbit correctly at their own orbit speeds.
I'm not really experienced with using matrices for stuff like this so It's likely why I can't figure out how exactly to get it working. This is where I'm applying the transformation matrices, as well as pushing and popping them. This is within the Render function that every planet including the sun and moons will have and run.
if (tag != "Sun") { glRotatef(orbitAngle, orbitRotation.X, orbitRotation.Y, orbitRotation.Z); } glPushMatrix(); glTranslatef(position.X, position.Y, position.Z); glRotatef(rotationAngle, rotation.X, rotation.Y, rotation.Z); glScalef(scale.X, scale.Y, scale.Z); glDrawElements(GL_TRIANGLES, mesh->indiceCount, GL_UNSIGNED_SHORT, mesh->indices); if (tag != "Sun") { glPopMatrix(); } The "If(tag != "Sun")" parts are my attempts are getting the planets to orbit correctly though it likely isn't the way I'm meant to be doing it. So I was wondering if someone would be able to help me? As I really don't have an idea on what I would do to get it working. Using the if statement is truthfully the closest I've got to it working but there are still weird effects like the planets orbiting faster then they should depending on the number of planets actually be updated/rendered.
• Hello everyone,
I have problem with texture
• Hello everyone
For @80bserver8 nice job - I have found Google search. How did you port from Javascript WebGL to C# OpenTK.?
I have been searched Google but it shows f***ing Unity 3D. I really want know how do I understand I want start with OpenTK But I want know where is porting of Javascript and C#?
Thanks!
OpenGL Moving items withthe mouse (OpenGL (gluUnProject related))
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Greetings! This is my first post on this forum and I am a beginner in OpenGL. I have gotten the basics (I think) and can put some shapes on the screen and position them programmatically. I now want to be able to click on an item (say a sphere) on the screen and move the item around the screen using the mouse. I have so far managed to get my head around and the code working which selects which items has been clicked. I am having a hard time with mapping the screen coordinates to object coordinates. At the moment the following is the code I am using to try and achieve this.
//OnMouseMove
GLdouble modelMatrix[16];
GLdouble projMatrix[16];
int viewport[4];
glGetDoublev(GL_MODELVIEW_MATRIX, modelMatrix);
glGetDoublev(GL_PROJECTION_MATRIX, projMatrix);
glGetIntegerv(GL_VIEWPORT, viewport);
GLdouble objX, objY, objZ;
gluUnProject(m_MouseNew.x, viewport[3] - m_MouseNew.y, 1, modelMatrix, projMatrix, viewport, &objX, &objY, &objZ);
//posX is used later to transform the sphere when it gets drawn
m_p3DObjects[m_nSelection]->posX = objX;
Unfortunately, this does not work as expected. When farther the mouse gets from the centre of the screen, the further the sphere moves away from the centre of the screen. The difference becomes greater for more off-centre positions. What am I doing wrong? Does anybody have example code of a drag-move code for OpenGL? Thanks in advance, Aristotel
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Hmm thats quite a question there
Well i could not tell you what is going on with your code :p
What i can try and do is give you an idea. from what i understand the object follows the mouse. if this is correct then peraphs trying something like this idea.
hide mouse
Get Current Mouse postion
Check differnce from center of screen
Set mouse postion back to center of screen
use differnce to move object selected
repeat.
When object unselected
Show mouse and disable move object func and or calls.
just mabye a thought not sure if it will help.
as i sead just an idea :)
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Hi there,
No the sphere drawn does not follow the mouse, it only follows the mouse's direction, but not distance from the centre of the screen. Assume the sphere is in the centre of the screen. I click on if with the mouse, holding the button down.If I drag the mouse say 5 pixels away from the centre of the screen, the sphere moves in the same direction, but 10 pixels(example). If I move the move 10 pixels, the sphere will move like 30 pixels. If I move the mouse 20 pixels, the sphere might move 60 pixels off-centre.
So the direction seems to follow correctly, but not the distance...where the perfect alignment occurs at the centre of the screen. Did that make any more sense?
Thanks once again
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Ahh i c well for the most part im not sure why that happens as im sure you are not but i might be able to help you out still.
but ill need to know what compiler you are useing for debugging purposes!
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Thanks,
Visual Studio .NET (2003)
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Ok so heres what you can do my compileres newer but there bolth vc micrsoft so.
Put a break line where your function is that calculats the move of the mouse or where ever your getting the data that effects the spheres movment. you can just right click on the codeing window and should be able to add one no problem.
now i don't know if you know how to use the debugger or not but by inserting a break point and then debugging your program will run up to that spot and then you can slowly step through the code .
GameDev.net -- Introduction to Debugging
its a nice atricle on debugging.
well ill try an continue anyways but if you dont get any of what im saying read the article above ok.
as you step through your code you general have two options step over and step in
step over will just jump over function and still run them you just wont have to watch it. step in will take you into a function and you will go through it step by step.
what im explaing this to you for is in my compilere although it should be more or less the same. i hit alt 5 and i get a small window at the bottum that shows me all of my local variables and there values. if you can track down where your values are getting higher then they should it will be easyer to fix the problem :)
well hopefuly that made some kind of sence.
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PS on another note what and where did you learn how to load in objects i havent found anthing decnet that isnt a milk shake 3d model loader id like a 3ds object loader or something like that. so if you know anything please let me know!
Hmm peraphs i should have done that earlyer like look up the specific type of file i was trying to load ... funny how that search came back with much more of what i was looking for............
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I will soon be working on a similar problem. Right now in my engine there is a local coordinate system that shows up for my selected model with XYZ control points. I click and drag these to move the models.
Right now I have a hack version that just moves in the selected axis by how ever much the mouse moves in the X screen direction. But eventually I would like to be perfectly accurate like you are trying to achieve (currently my results behave like yours).
Begin reasonable thinking:
What you'll want to do is get a vector in world space from your screen space, so this will require two unprojects.
gluUnProject( oldMouse.x, viewport[3] - oldMouse.y, objectpick.depth, modelMatrix, projMatrix, viewport, &oldWorldX, &oldWorldX, &oldWorldX);gluUnProject( newMouse.x, viewport[3] - newMouse.y, objectpick.depth, modelMatrix, projMatrix, viewport, &newWorldX, &newWorldX, &newWorldX);worldMoveVectorX = newWorldX - oldWorldX;worldMoveVectorY = newWorldY - oldWorldY;worldMoveVectorZ = newWorldZ - oldWorldZ;
worldMoveVector should now contain a vector in world space that correlates to the screen vector created by a mouse move.
Assuming the above works correctly, adding this vector to your objects position will move it with the mouse in screen space.
My twist on it is that I want to be able to move in object space. So next (this is where I become increasingly unclear) I think I'd need to project the world space vector onto the selected object move axis vector. And the resultant magnitude is how far in the selected axis I'd need to move to correspond to the mouse movement.
Hope that helped some, and let us know when you find a good solution.
P.S. Jouei, I got mine from www.gametutorials.com
edit: I changed the Z component of unproject to objectpick.z, I believe this is where you problem may stem. If you are using a perspective matrix. The deeper into the scene your selected object is, the greater the corresponding world vector will be for any given screen vector. By generating the vector at the object's depth, this should be more accurate.
P.P.S Gamedev.net, what the hell? So slow it's painful.
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Yeah i have been having trouble finding a tutorial that ether a works or b is just poorly writen
Gametutorials is nice but it is no longer free.
i wish it was :( but i do not have 70\$ to by a cd full of code goodies.
ps i need more caffine getting tired in my search..
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Hi guys, thanks for your replies...
The project I was working on was at the office, and uses MFC,but now I am home whee I only have Visual Studio Express 2005 which doesn't support MFC. I will try and recreate the same project in a VS 2005 Express project, that does not need MFC to set up the windowing etc.
Regarding Debuging, no worries, I have been a software engineers for a few years now, but mostly audio...now trying to learn a bit of OpenGL..thats the only thing I am having issues with.
Regarding loading objects, I didn't..I only used a cone and a sphere.
Over the weekend I will set up a VS2005 project and try out honayboyz suggestion as that seems to be what I was missing out on. I will let you all know how it goes and at that point I can share the VS2005 project with you all.
Hope to let you on the progress soon..
Thanks again!
Aristotel
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# Groups Acting on Trees Spring 2021
Lecturer
Benjamin Brück
Coordinator
Francesco Fournier-Facio
## Content
As a main theme, we will see how an action of a group on a tree enables us to break the group into smaller pieces, and thus gain better understanding of its structure.
### Goal of the course
Learn basics of Bass-Serre theory; get to know concepts from geometric group theory.
### Brief description
As a mathematical object, a tree is a graph without any loops. It turns out that if a group acts on such an object, the algebraic structure of the group has a nice description in terms of the combinatorics of the graph. In particular, groups acting on trees can be decomposed in a certain way into simpler pieces.These decompositions can be described combinatorially, but are closely related to concepts from topology such as fundamental groups and covering spaces.
This interplay between (elementary) concepts of algebra, combinatorics and geometry/topology is typical for geometric group theory. The course can also serve as an introduction to basic concepts of this field.
Topics that will be covered in the lecture include:
• Trees and their automorphisms
• Different characterisations of free groups
• Amalgamated products and HNN extensions
• Graphs of groups
• Kurosh's theorem on subgroups of free (amalgamated) products
• Stallings's theorem on ends of groups
### Prerequisites
Basic knowledge of group theory. The most relevant concepts and results will be recalled during the first exercise class on February 25th.
Being familiar with fundamental groups (e.g. the Seifert-van-Kampen Theorem) and covering theory is definitely helpful, although not strictly necessary. In particular, the standard material of the first two years of the Mathematics Bachelor is sufficient.
## Organization
The lecture takes place each Tuesday from 8 to 10, in HG F26.5, starting from February 23rd. Additionally, every second Thursday from 12 to 14, in LFW C4 there will be an exercise class, starting from February 25th.
CHANGE! Due to the current situation, for the moment both the lecture and exercise classes will be held online via zoom: see below.
This class is worth 6 credits. The exam is written, and will take place in the August session.
## Lectures
Due to the current situation, for the moment classes will be held online. The link for accessing the zoom meeting is below, and you will receive by e-mail the password to access the meeting.
Before each lecture, pre-written notes will appear on this page: the lecturer will make reference to those and complete them, so make sure you download them beforehand. After the class, both the final script for the day's lecture and the recording will be available below.
The exercise classes will also be held online via zoom, for the time being. The link for accessing the zoom meeting is below, and you will receive by e-mail the password to access the meeting, which will be available below after the class (the password is the same as for the lectures).
The password to access the recordings is the same as the one for the meetings, followed by the current year with no spaces.
prewritten script recording lecture recording exercise class pdf exercise class
Prewritten 1 Script 1 Recording lecture 1 Recording exercise class 1 pdf exercise class 1
Prewritten 2 Script 2 Recording lecture 2 No exercise class this week -
Prewritten 3 Script 3 Recording lecture 3 Recording exercise class 2 pdf exercise class 2
Prewritten 4 Script 4 Recording lecture 4 No exercise class this week -
Prewritten 5 Script 5 Recording lecture 5 Recording exercise class 3 pdf exercise class 3
Prewritten 6 Script 6 Recording lecture 6 No exercise class this week -
Prewritten 7 Script 7 Recording lecture 7 Recording exercise class 4 pdf exercise class 4
Prewritten 8 Script 8 Recording lecture 8 No exercise class this week -
Prewritten 9 Script 9 Recording lecture 9 Recording exercise class 5 pdf exercise class 5
Prewritten 10 Script 10 Recording lecture 10 No exercise class this week -
Prewritten 11 Script 11 Recording lecture 11 Recording exercise class 6 pdf exercise class 6
Prewritten 12 Script 12 Recording lecture 12 No exercise class this week -
Prewritten 13 Script 13 Recording lecture 13 Recording exercise class 7 pdf exercise class 7
Prewritten 14 Script 14 Recording lecture 14 Recording revision session pdf revision session
## Exercises
A new exercise set will appear below every two weeks after the lecture on Tuesday, starting from the first one on February 23. You can hand-in the solution of up to two exercises via SAM-UP until one week and a half later, on Friday. There will be no bonus for handing in solutions, it is just a way for you to check you understand the concepts. There will be no written solutions, but the exercises will be solved during the first exercise class after the hand-in deadline: for instance the first exercise set will be solved during the second exercise class, on March 11.
Together with the exercise sets below you will find a form that will ask you what exercise you did and did not manage to solve. This form is completely anonymous, and it serves as a way to adjust the difficulty of the exercise sets throughout the semester, as well as to identify the hardest exercises that will be talked about more during the exercise class. We kindly ask you to complete the form, even if you did not do the exercises.
exercise set errata due by form
Exercise set 1 Correction to 5 (c) March 5 Form 1
Exercise set 2 - March 19 Form 2
Exercise set 3 $$m, n \in \mathbb{Z} \, \backslash \, \{ 0 \}$$ April 9 Form 3
Exercise set 4 Correction to 2. Also, see above. April 23rd Form 4
Exercise set 5 Correction to 3, 4. Correction to 6. May 7th Form 5
Exercise set 6 The remark at the end was wrong. Correction to 4 May 21st Form 6
Exercise set 7 - June 4th Form 7
## Forum
NEW! After a few requests, we have a opened a subforum on the D-MATH forum website. You are encouraged to discuss exercises and to ask questions.
## Literature
• J.-P. Serre, "Trees". (Translated from the French by John Stillwell). Springer-Verlag, 1980. ISBN 3-540-10103-9
• O. Bogopolski, "Introduction to group theory". EMS Textbooks in Mathematics. European Mathematical Society (EMS), Zürich, 2008. x+177 pp. ISBN: 978-3-03719-041-8
• C. T. C. Wall, "The geometry of abstract groups and their splittings". Revista Matemática Complutense vol. 16(2003), no. 1, pp. 5-101
• R. C. Lyndon and P. E. Schupp, "Combinatorial group theory". Springer Verlag, 2015. ISBN 3-540-07642-5
• M. J. Dunwoody, "Accessibility and groups of cohomological dimension one". Proceedings of the London Mathematical Society 3.2 (1979): 193-215.
• M. J. Dunwoody, "Cutting up graphs". Combinatorica 2.1 (1982): 15-23.
• B. Krön, "Cutting up graphs revisited – a short proof of Stallings' structure theorem". Groups, Complexity and Topology, vol. 2, no. 2, 2010, pp. 213-221.
• J. Stallings, "Group theory and three-dimensional manifolds". Yale University Press.
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Sunday
May 19, 2013
# Homework Help: Computers: Computer Science
Recent Homework Questions About Computer Science
science
2 liters of water at 80.c is found into a plastic bucket containing 10 liters of water at 20.c what is the final temperature of water ( density of water 1kg/litre) (neglect the heat gained by bucket and specific heat capacity of water = 1cal/gm.c ?
Friday, August 24, 2012 at 1:29am
English
Our class does an experiment for science. One pot gets no water. Have to identify the subject of each sentence. 1. class 2. pot
Friday, August 24, 2012 at 12:57am
Science
a .5kg ball is dropped from a 30m high building is on the ground for 2ms then bounces up 20m. What avg force was exerted on the ball?
Thursday, August 23, 2012 at 9:44pm
physical science
displays in formation in rows and columns
Thursday, August 23, 2012 at 7:15pm
Science
Imagine you are a plant. How are you and your cells different than animals. 1/2 - 3/4 page
Thursday, August 23, 2012 at 5:23pm
Science
I have this last question left and I'm stuck!!! Explain how cell organelles are similar to a factory. Must be 1/2 a page.
Thursday, August 23, 2012 at 4:44pm
science
Two simple pendulum each of length 5cm and time period of 4 second and 6 second starts oscillating one from left extreme and the other from right extreme. When will the two bodies be at the same phase?
Thursday, August 23, 2012 at 10:08am
Science
if a radioactive isotope has a half-life of one year, how much of the original sample will be left at the end of the second year?
Thursday, August 23, 2012 at 9:59am
Science
if a radioactive isotope has a half-life of one year, how much of the original sample will be left at the end of the second year?
Thursday, August 23, 2012 at 9:53am
Science, Astrenomey
This is my theory, read well if you wish to know the truth: according to the big bang, there is a equal amount of anti-matter to the matter, BUT nearly all that matter is missing! In this theory there was NO anti-matter when the earth was made. anti-matter is made when ...
Thursday, August 23, 2012 at 9:45am
Science
What part of the microscope does the fine adjustment knob move?
Wednesday, August 22, 2012 at 7:42pm
General Computer Science
Why should IT policy and control be a prime concern to overall management in the selection and development of IT management?” Please write an answer to the above question.
Wednesday, August 22, 2012 at 5:54pm
General Computer Science
There are several interior routing protocols. Is there a place for each one of them? Discuss in what type of network each one would work best.
Wednesday, August 22, 2012 at 4:59pm
Science
In what ways are there three processes similar in terms of the starting materials and end products?
Wednesday, August 22, 2012 at 7:54am
Science
What type model would you use to study an earthquake?
Wednesday, August 22, 2012 at 7:39am
science
suppose you want to find out about boiling points of different liquids: describe how you could go about finding the information.
Tuesday, August 21, 2012 at 10:47pm
Science.
You are carrying a 3.4 gallon jug full of cold water. Given that the water has a density of 1.0 grams per milliliter, and one gallon is equal to 3.8 liters, state the mass of the water in kilograms.
Tuesday, August 21, 2012 at 10:14pm
Science.
Assume a typical hummingbird has a lifespan of 4.0 years and an average heart rate of 1300 beats per minute. (a) Calculate the number of times a hummingbird's heart beats in its life, and express it in scientific notation. Use 365.24 days per year. (b) A long-lived ...
Tuesday, August 21, 2012 at 10:11pm
Science.
Sara has lived 18.0 years. How many seconds has she lived? Express the answer in scientific notation. Use 365.24 days per year for your calculations.
Tuesday, August 21, 2012 at 10:11pm
Science.
An atom of uranium-235 has a mass 235.043924 amu (atomic mass units). Using scientific notation, state the mass in amu of ten million such atoms.
Tuesday, August 21, 2012 at 10:11pm
Science.
Express 0.0000000000375 in scientific notation
Tuesday, August 21, 2012 at 10:10pm
science
1.How many meters away is a cliff if heard one half second after the original sound? Assume that sound travels at 343m/s on that day
Tuesday, August 21, 2012 at 4:18pm
Science
9. Which one of the following statements is characteristic of liquid water? A. It has a definite shape but not a definite volume. B. It has neither a definite shape nor a definite volume. C. It has a definite volume and a definite shape. D. It has a definite volume but not a ...
Tuesday, August 21, 2012 at 3:22pm
science
Ann drove to the store 10 km north of her house and then drove to the library, which is 5 km south of the store. She drove a total distance of 15 km. What was Ann's displacement?
Tuesday, August 21, 2012 at 11:57am
science
A ball is thrown upward to 80m high, ball will be 2times at 80m during the interval of 6sec, accelaration -10 and find velocity?
Tuesday, August 21, 2012 at 5:01am
science
What is the egg-laying part of some female insects?
Tuesday, August 21, 2012 at 3:37am
science
What is a larva?
Tuesday, August 21, 2012 at 3:36am
What is a silk case covering the moth larva?
Tuesday, August 21, 2012 at 3:33am
science
A ball is thrown upward to 80m high, ball will be 2times at 80m during the interval of 6sec, accelaration -10 and find velocity?
Tuesday, August 21, 2012 at 3:13am
science
What is the tiny hairs of hearing and sensing of an insect body?
Tuesday, August 21, 2012 at 2:59am
What can be inferred after performing the experiments in the atomic theory lab? A) Where matter comes from B) How salt is formed C) If salt can dissolve in water D) If matter is created or destroyed Is it D?
Tuesday, August 21, 2012 at 1:48am
computer science
1.Two supplementary angles differ by 44 degrees. Find The answer? 2.Two complementary angles differ by 9 degrees. Find the answer?
Monday, August 20, 2012 at 1:31pm
Science (Microscope)
Explain why some parts are in focus and some part are out of focus when you are trying to focus an object under the microscope.
Sunday, August 19, 2012 at 1:47am
Science
Why is it that you cannot use the largest objective for some slides?
Sunday, August 19, 2012 at 1:32am
math
every math class at super fun time high school has 31 students and every science class has 18 students. the school offers 4 more math class than sciencs. if the school has 418 students, how many of each class does the school offer.
Saturday, August 18, 2012 at 8:57pm
Science(Chemistry)
HCL+Al=AlCl3+H2 What is the ionic equation,the spectator ions and the overall or net ionic equations?
Saturday, August 18, 2012 at 7:44am
Science(Chemistry)
Explain what would happen when bromine water is added to potassium iodide solution and what is its balanced chemical equation?
Saturday, August 18, 2012 at 7:38am
Science(Chemistry)
Mg+H2O=MgOH+H2 What is the ionic equation,the spectator ions and the overall or net ionic equations?
Saturday, August 18, 2012 at 7:32am
Science
When you are focusing an object under the microscope, explain why some parts are in focus and some part are out of focus?
Saturday, August 18, 2012 at 2:04am
Science - Chemistry
What happens when you mix Sodium Bicarbonate, Bromothymol blue, and Calcium Chloride? What is Bromthymol blue used for in this experiment?
Friday, August 17, 2012 at 5:53pm
Science
What is matter?
Friday, August 17, 2012 at 7:32am
science
four bodies of mass 1kg, 2kg,3kg, and 4 kg are situated at four corners of a square of side 2m, take the origin at the center of square. find m.i. if the system passing through the centre and perpendicular to the plane of square
Friday, August 17, 2012 at 3:55am
science
3ml of 2M NaOH is added to 27 ml of destilled water. what dilution is made? what is the concetration of Naoh in the dilution?
Thursday, August 16, 2012 at 10:02pm
Science (Physics)
1. Which of the following is the fastest speed? Show your working. (a) 60 km/h (b) 15 m/s (c) 1.1 km/min
Thursday, August 16, 2012 at 5:00am
speedway
What are 25 action words that relate to science?
Wednesday, August 15, 2012 at 6:50pm
science
Which Windows feature allows you to personalize your computer system? A. My Pictures C. Default Programs B. Control Panel D. Computer
Wednesday, August 15, 2012 at 3:08pm
science
Which one of the following describes how to access your local disk in Windows XP? A. Click Start and click Control Panel. B. Click Start and click My Computer. C. Right-click on your desktop. D. Click Start and All Programs.
Wednesday, August 15, 2012 at 3:07pm
science
In Vista and Windows 7, which process allows you to display two documents side by side? A. Click the Windows button, choose Control Panel, and select the Tile Windows Vertically option. B. Right-click the mouse button in a blank area of the taskbar; in the menu option that ...
Wednesday, August 15, 2012 at 3:06pm
science
In Vista and Windows 7, which process allows you to change the desktop background? A. Click the Start button, choose Control Panel, and select Display Properties. B. Right-click on the desktop; in the menu that appears, select Display Properties. C. Click the Windows icon/...
Wednesday, August 15, 2012 at 3:05pm
science
In Vista and Windows 7, which process allows you to change the desktop background?
Wednesday, August 15, 2012 at 3:04pm
robotics
I need to incorporate in a summary the author, when the article is written and where is the article taking place. The article is "Robotics" World of Computer Science. Gale, 2002
Wednesday, August 15, 2012 at 12:30pm
animal science
Which of the following is true of the function of glucagon? A. Glucagon regulates insulin secretion. B. Glucagon increases glycogen breakdown into glucose. C. Glucagon inhibits glycogen breakdown into gluclose. D. Glucagon regulates somatostatin secretion.
Wednesday, August 15, 2012 at 11:37am
Science
1. Find the lattice parameter of pure iron at room temperature. 2. What is the ratio of the lattice parameter of the iron to the wavelength of the radiation used. 3. What is the value of two theta for the second peak? 4. By what factor is the lattice parameter of the Fe bigger...
Wednesday, August 15, 2012 at 12:21am
math
in order to purchase a computer for the student activities office, the freshman class decides to raise 1/3 of the money and the sophomore class decides to raise 1/2 of the money. The student government association agrees to contribute to the rest which amounted to $400.what ... Tuesday, August 14, 2012 at 5:32pm science hi i have 500g Cu,befor i prepeared 80g/1lit H2SO4 for 50 g Cu,now for 500gr Cu How much need H2SO4? thanks my dear Tuesday, August 14, 2012 at 6:29am science girl throws the ball with a certain angle. It covers maximum horizontal distance R. How much height ball reaches if she throws the same ball vertically upward? Assume her muscles give the ball same speed in each case. Tuesday, August 14, 2012 at 12:54am Science 2 How does TCDD act as an endocrine disruptor? Monday, August 13, 2012 at 10:13pm Science What happens when TCDD binds to the AhR receptor? How does it cause diseases/health problems in people? 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When was the article written: This is the article: "Robotics" World of Computer Science. Gale, 2002. Monday, August 13, 2012 at 2:02pm science What is the authors purpose and main idea in this article: "Robotics" World of Computer Science. Gale, 2002. Monday, August 13, 2012 at 1:35pm science how many ml distilled water is required to prepare 2% sucrose solution from 2% 2liter sucrose solution from 20% sucrose solution? Monday, August 13, 2012 at 9:12am science A bowling ball weighing 71.3 is attached to the ceiling by a rope of length 3.77 . The ball is pulled to one side and released; it then swings back and forth as a pendulum. As the rope swings through the vertical, the speed of the bowling ball is 5.00 . Monday, August 13, 2012 at 6:04am Science Would "boy" consider a trait? Monday, August 13, 2012 at 12:13am science Think about the impact that two (2) of your meals have on our world from an ecological and economic perspective. You can pick breakfast, lunch or dinner, and then answer the following questions Sunday, August 12, 2012 at 10:13pm English III Hi it's me again! Could someone proofread this for me? Thanks so much! HOW ABOUT BETTER PARENTS? BY: Thomas L. Friedman In Thomas L. Friedman’s column “How About Better Parents” he discusses parent’s influence in their child’s education. He states ... Sunday, August 12, 2012 at 10:03pm Life Science Fungi are classified into how many groups? Sunday, August 12, 2012 at 7:12pm Biology/HELP Contrast the role of research in science and pseudoscience...??!! #LOST Sunday, August 12, 2012 at 3:30pm English Adrian saw his friend Bob walking fast down the hall. What is the adverb and pronoun in this sentence? The adverb in this sentence: Soon the computer store will be closed. 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Friday, August 10, 2012 at 7:13pm science A soccer ball is kicked with an initial speed of 8.4 m/s in a direction 22.0° above the horizontal.Find the magnitude and direction of its velocity at the following times. (Take the +x axis to be parallel to the ground, in the direction that the ball is kicked.)0.250 s ... Friday, August 10, 2012 at 6:45pm Accounting Hello I am not angry with you at all, however is there any way possible that you can help me with these two problems and we can call it even? Just let me know I am not trying to get over, however my computer had crashed and I am behind in class I purchased me a new laptop a ... Friday, August 10, 2012 at 2:37pm writing sentences and paragrahs Background You’ve applied for a specific job in your field of study. The Human Resources Department arranges an interview and tells you to bring with you a polished piece of writing for them to evaluate your writing skills. The paragraph must describe one particular ... 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The monthly rent of the store is$1,500 and Suzie has one manager who runs the store and earns \$3,000 per month. She leases out a computer and other equipment for her store at a ...
Monday, August 6, 2012 at 3:00pm
science
1) - Scientists performed an experiment to determine whether there is a connection between learning ability and food. They took two groups of 20 mice each, all from the same purebred strain. The mice were deprived of food for 3 days and then given a standard learning session ...
Monday, August 6, 2012 at 12:14pm
mit math
Odometer. A Ford SUV comes standard with rims (which correspondes to a tire with diameter). Suppose you decide to later upgrade these tires for rims (corresponding to a tire with diameter). If you do not get your onboard computer reset for the new tires, the odometer will not ...
Monday, August 6, 2012 at 8:00am
science
An element emits one alpha particle, one positron, and three beta particles. Its atomic number.... decreases by 2 decreases by 1 stays the same increases by 1 increases by 2
Monday, August 6, 2012 at 3:34am
science
a 150 gm ball travelling at 30 m/s strikes the players hand and it stopped in0.06s.calculate the force exerrted by ball on hand
Sunday, August 5, 2012 at 7:43pm
Informal Logic
rite two arguments in English, one in the form of modus ponens and one in the form of modus tollens. Then, write the arguments in symbols using sentence letters and truth-functional connectives. (If your computer does not have all the symbols needed, use some other symbol you ...
Sunday, August 5, 2012 at 10:06am
work3
You are a section chief in the battalion S-3 at Bagram Airbase. You instruct PFC Jackson to download some of the battalion’s current SOP’s onto a thumb drive so that they will be available in the field. After loading the material, you notice PFC Jackson walking away ...
Saturday, August 4, 2012 at 10:34pm
science
how does the musculoskeletal system change from birth to adulthood to achieve 206 bones?
Saturday, August 4, 2012 at 8:06pm
criminal justice
You have completed your investigation on allegations against a plant employee of an acquired corporation, Lake Inc. That is based on the basic information given below. Create a report on the results of your investigation and present final results that your investigation has ...
Saturday, August 4, 2012 at 5:19pm
science
what will be the law of conversion of a) 65 grams 70 grams b) magnesium + oxygen = magnesium oxide 45 grams ? grams 80 grams c) sodium hydroxide + hydrochoride acid 40 grams 36.5 grams sodium chloride + water ? grams 18 grams
Saturday, August 4, 2012 at 12:35pm
science
Hi, I was wondering if I answered this question correctly #1-Two kinds of cell-transport are used in the process that forms ATP. Name the two types of transport and describe how they take place. Electron transport is not a form of cell transport. #1- I think the passive and ...
Saturday, August 4, 2012 at 8:39am
science
a bullet of mass0.01 kg and travelling with a speed of 500m/s strikes a block of mass 2 kg which is suspended by a string of length 5m. The center of gravity of the block is found to raise vertical distance of 0.1m. The speed of bullet after emerging from block is:
Saturday, August 4, 2012 at 1:15am
science
A chair of mass 15.5 is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force = 38.0 that is directed at an angle of 42.0 below the horizontal and the chair slides along the floor.Use Newton's laws to calculate the normal force ...
Friday, August 3, 2012 at 4:48am
Informal Logic 103
Write two arguments in English, one in the form of modus ponens and one in the form of modus tollens. Then, write the arguments in symbols using sentence letters and truth-functional connectives. (If your computer does not have all the symbols needed, use some other symbol you...
Thursday, August 2, 2012 at 11:54pm
Computer Programing
Assignment 1: chocolate Delights candy company, part 1
Thursday, August 2, 2012 at 11:03pm
math
A small group of employees in a company get viruses on their computers. Every hour, each computer infects one other computer. If it takes 8 hours for 100 computers to be infected, how long would it take for only 50 computers to be infected?
Thursday, August 2, 2012 at 1:52pm
Science
Why CuO powder not soluble in hexane and methanol?
Wednesday, August 1, 2012 at 2:39am
(1) After my interview with these four young people, I reflected on the quiet sense of "difference" I sensed with many of these Upward Bound students. (2) As a college teacher who has also taught seventh-grade science, I have some experience with the faces and ...
Tuesday, July 31, 2012 at 3:06pm
Science math, science, social studies
a cyclist travels a distance of 4km from P to Q & then moves a distance of 3 km at right angle to PQ . Find displacement graphically
Tuesday, July 31, 2012 at 10:44am
Earth Science
I need help with the following Lab due tonight, 7/30/12, as I feel completely lost and would appreciate the help. The lab goes as follows: Design an experiment that illustrates the determination of the density of a cylindrical object found in the Lab Kit. Prepare a dynamic ...
Monday, July 30, 2012 at 4:22pm
Earth science
of the three "local winds" types discussed in the text book, which do you think could be most easily harnessed for the generation of electricity by a huge wind farm?
Sunday, July 29, 2012 at 8:41pm
Science
Find the [H+] in a 0.0255 M solution of HF if the Ka = 7.2 X 10^ -4
Sunday, July 29, 2012 at 7:44pm
science
a person moves 30m north, then 20m east and then 30(square root of two)m south west . His displacement from the original position is ?.
Sunday, July 29, 2012 at 11:05am
science
a canoe displaces 100 L of water weighs 9.8 NL what is the bouyant force on the canoe
Saturday, July 28, 2012 at 5:13pm
science
A mixture of {\rm NaCl} and {\rm NaBr} has a mass of 2.10{\rm g} and is found to contain 0.71{\rm g} of {\rm Na} What is the mass of {\rm NaBr} in the mixture?
Saturday, July 28, 2012 at 2:00pm
science
how make a hybridization of pcl5 with dygram
Saturday, July 28, 2012 at 9:16am
SCIENCE
chemical formula for Fe + ZnSO4
Saturday, July 28, 2012 at 8:06am
science
How many outlets can you place on one curcuit in your house
Friday, July 27, 2012 at 11:58am
system analysis and palnning
objective The Milestone Assignments are based on the Projects and Cases for use with the Systems Analysis and Design Methods textbook by Whitten & Bentley. There are six (6) parts to the Project, consisting of twelve (12) milestones. During Weeks 2-7, you will be required to ...
Thursday, July 26, 2012 at 11:07pm
3 things that all life have in common and an explanation for the meaning of each?
Thursday, July 26, 2012 at 9:39pm
Science 10
The symbol of the lead(IV) ion is ?
Thursday, July 26, 2012 at 7:32pm
science
2 WAYS TO DETERMINE THE INTERIOR ARE GRAVITY, AND SEISMOLOGY.
Thursday, July 26, 2012 at 5:19pm
Science
How can we use Kepler's laws or Newton's laws to learn about these objects?
Thursday, July 26, 2012 at 5:18pm
physical science
what are the number of moles of phosphorus in 15 moles of Ca3(PO4)2
Thursday, July 26, 2012 at 10:41am
Science
You are a Chemical engineer, trying to synthesize N2H4(l). Your boss suggests that you try to synthesis it from the elements, nitrogen and hydrogen, at 25 celsius and 1.0 atm (since this would be a cheap way of doing it). Write a short note to sent to your boss which discusses...
Thursday, July 26, 2012 at 8:21am
Science
What is one way you could take action to reduce your carbon dioxide emissions?
Wednesday, July 25, 2012 at 11:39pm
science
what are atoms
Wednesday, July 25, 2012 at 7:59pm
science
To calculate the area of the front surface of a box you?
Wednesday, July 25, 2012 at 7:29pm
science
A shoe case weighing 40 lb is located on a scale inside a moving elevator that is going upward with the speed of 8 m/s. At time T1 elevator slows down with the acceleration of 3 m/s2 until the time T2. What are the the readings of the scale at T2 and T1 respectively?
Wednesday, July 25, 2012 at 6:33pm
physical science
A train sounding its horn is approaching an observer. The pitch of the horn's sound relative to its normal pitch is???
Wednesday, July 25, 2012 at 5:57pm
Introduction to HS
I am having trouble with a question. In order to get an idea of significant subject areas in a chapter, it is best to read the. A. Subheads B. Graphics C. Captions D. Table of contents In my study guide it states : Read all the subheadings and sub-subheadings. These will give ...
Wednesday, July 25, 2012 at 5:51pm
science
The solubility of sodium chloride is 36.0 g/100. ml of water, and the density of saturated NaCl solution is 1.202 g/mL.. I have 500. mL of a 1.00 M NaCl solution. If I boil it to the point of saturation, what is the final volume?
Wednesday, July 25, 2012 at 4:38pm
com 200
Kyle has struggled to feel comfortable in science classes with labs since his junior year of high school, when a solution he was working with ignited. He was always cautious with chemicals but his lab partner that year enjoyed seeing what would happen when he mixed random ...
Wednesday, July 25, 2012 at 3:05pm
science
A sample of air contains 32.7 µg/m3 of beryllium dust. How many atoms of beryllium are present in a room with dimensions of 8 feet by 13.6 feet by 15.6 feet? Answer in units of atoms
Tuesday, July 24, 2012 at 11:13pm
science
How many milliliters of 4.6 M HCl must be transfered from a reagent bottle to provide 16 g HCl for a reaction? Answer in units of mL
Tuesday, July 24, 2012 at 11:11pm
Science
A solution contains 0.01M ethyl acetate, 0.10M acetic acid and 0.10M ethanol. For the same equilibriujm constant of 2.00, calculate the equilibrium concentrations of ethyl acetate, ethanol, and acetic acid in the solution.
Tuesday, July 24, 2012 at 9:44pm
science
what shows that the sea water is a mixture and not a pure substance? a. it has a sharp boiling point b. it has definite composition c. it consist of a single phase d. the components lose their individual properties
Tuesday, July 24, 2012 at 8:07pm
science
Low water flows are a common problem for ecosystems in semi-urban streams. Should the suggestion of using domestic drinking water supplies to increase water flows in the streams be adopted?
Tuesday, July 24, 2012 at 2:40am
Science
Calculate the pH of an aqueous solution containing 1.3 * 10^-2 M HCl, 3.0 * 10^-2 M H2SO4, and 2.0 * 10^-2 M HCN.
Tuesday, July 24, 2012 at 2:13am
Science
You are a retired law enforcement officer who now teaches at a local community college in the criminal justice program. In addition to teaching ethics, you write crime novels on the side. You recently heard of a real-life case that you thought would make the basis for a good ...
Monday, July 23, 2012 at 8:19pm
science
how might the environmental impacts of deforestation and sprawl affect the human community of Pinchot
Monday, July 23, 2012 at 4:40pm
science-physics
a battery of 12v supplies a charge of 1000C to an electric device. how much work is done by the battery in moving the charge?
Monday, July 23, 2012 at 2:43pm
science -chemistry
Mr. Currie pours himself some coffee into a paper cup before making his way to the amusement park. The coffee temperature is 350C when the cup is placed on the kitchen counter with room temperature of 20o C. Mr. Currie was called to the phone for last minute arrangements, and ...
Monday, July 23, 2012 at 12:46pm
science
when a 424-g of iron powder is burned in an oxygen atmosphere, 0.606-g of a reddish brown oxide is obtained. Determine the empirical formula of the oxide.
Monday, July 23, 2012 at 7:01am
science
Two machines A and B produce respectively 60% and 40% of the total number of items of a factory. The percentages of defective output for A and B are 3% and 2% respectively. Suppose an item is selected at random, and is found to be defective. The probability that the item was ...
Monday, July 23, 2012 at 1:12am
science
A box contains 10 balls of which 6 are red (R) and 4 are white (W) . Three balls are taken from the box at random, one after the other. The probability that the 3 balls drawn are in the order RRW is equal to,
Sunday, July 22, 2012 at 11:47pm
Science
Define a day by the passage of the sun
Sunday, July 22, 2012 at 8:17pm
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## Introduction
Many surveys of diabetes do not include a question about the type, so researchers rely on age of diagnosis as a way to distinguish between type 1 and type 2 diabetes (e.g. Koopman et al. (2005)). Here we try to find out whether this proxy is likely to work well.
## Data
NHANES is a series large health surveys. We download and load the latest NHANES data from 2013. One item, DID040, relates to when diabetes was diagnosed. Unfortunately, the survey does not have a question about the type of diabetes diagnosed.
# http://wwwn.cdc.gov/Nchs/Nhanes/Search/DataPage.aspx?Component=Questionnaire&CycleBeginYear=2013
d_nhanes13 = foreign::read.xport("~/Downloads/DIQ_H.XPT")
## Descriptive analysis
First we take a quick look at the descriptive statistics:
psych::describe(d_nhanes13$DID040) ## vars n mean sd median trimmed mad min max range skew kurtosis ## X1 1 727 48.59 14.82 50 49.36 14.83 1 80 79 -0.56 0.42 ## se ## X1 0.55 Notice that there is a lot of variation, with a standard deviation of about 15 years. We also look at the proportion of cases diagnosed before specified ages: kirkegaard::percent_cutoff(d_nhanes13$DID040, cutoffs = seq(20, 80, by = 5)) %>% round(2)
## 20 25 30 35 40 45 50 55 60 65 70 75 80
## 0.96 0.94 0.91 0.84 0.77 0.66 0.52 0.39 0.26 0.14 0.07 0.02 0.01
## Plot the distribution
Finally, we get a visual overview of the data using a density-histogram:
kirkegaard::GG_denhist(d_nhanes13, var = "DID040") + xlab("Age of diagnosis (self-reported). Red line = mean value.")
We can see that there are not two distinct groups in the data, so using age of diagnosis for differentiating between type 1 and type 2 diabetes is likely to be at best a useful proxy.
## References
Koopman, Richelle J, Arch G Mainous III, Vanessa A Diaz, and Mark E Geesey. 2005. “Changes in Age at Diagnosis of Type 2 Diabetes Mellitus in the United States, 1988 to 2000.” Annals of Family Medicine 3 (1). American Academy of Family Physicians: 60.
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Null vector help!
1. Jan 4, 2007
quantum123
I read this in the notes:
Show that any vector that is orthogonal to a null vector must be either be:-
i) parallel to a null vector
ii) space-like
How??
2. Jan 4, 2007
robphy
Should this be in the howework section?
What's your starting point? What does it mean for two vectors to be orthogonal?
3. Jan 4, 2007
quantum123
Orthogonal means normal, I guess.
This is no homework. I am doing it as a hobby.
This comes out from GR notes describing the light cone, and a general description of the four linearly independent vectors that may or may not lie parallel to the light cone, which is a null surface, ie may or may not be null vectors, and the properties of the vectors that are not null vectors.
4. Jan 4, 2007
George Jones
Staff Emeritus
Let {e_0, e_1, e_2, e_3} be an arbitary orthonormal basis. Then, up to a constant multiple,
n = e_0 + e_1
is an arbitrary null vector. Let
v = v^0 e_0 + v^1 e_1 + v^2 e_2 + v^3 e_3
be an arbitrary 4-vector. If n and v are orthogonal, what does this give you?
5. Jan 4, 2007
quantum123
Thanks. I see.
<n,n>^2=-1^2+1^2=0
<n,v>=0 => =-v^0+v^1=0 => V^1=v^0
Therefore, <v,v>^2 = -v^0^2 + v^1^2 + V ^2^2 + v ^3^2 = -v^0^2 + v^0^2 + V ^2^2 + v ^3^2 = V ^2^2 + v ^3^2 >=0
If =0 , then null-like.
If >0 then space-like.
Correct?
But why can n = e_0 + e_1 for any arbitrary n such that <n,n>=0 where {e^v} is orthonormal basis?
6. Jan 5, 2007
George Jones
Staff Emeritus
Yes.
For this case, there is one other, trivial, possibility.
Consider an arbitrary vector in a 2-dimensional spatial plane.
We are free to choose a basis that helps us. For example, we might choose: a basis such that the vector is in the direction of e_1; a basis such that the vector is in the direction of e_2; a basis such that the vector is halfway between e_1 and e_2, i.e., in the direction e_1 + e_2.
None of these choices restricts us.
7. Jan 5, 2007
quantum123
Thank you so much.
I guess you mean a vector subspace.
If we have 4 orthonormal vectors {e} that span a vector space, we can always find a 2 -D subspace which contains n, spanned by orthonormal basis f1, f2.
Hence if n is null, then <n,n>=0 => -n0^2 + n1^2 =0 => n1=n2.
And should be able to find f3 and f4 to complete the {f} for the total vector space T(M).
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Derive Spearman correlation (rather than Pearson's) coefficient from a univariate regression?
In univariate regression, the standardized coefficient is equal to the Pearson correlation coefficient. When the two variables are ranked variables, Spearman correlation would be appropriate. Is it possible to derive Spearman correlation coefficient from a univariate regression? It may be useful under the condition when testing correlation between two ranked variables within cluster/group, hence a Spearman test may not be directly applied and a mixed effect model is needed.
Thanks!
• The first sentence is untrue unless you have standardized both variables. A Spearman correlation can be related to a regression of one ranked variable on another, but not otherwise. (I wouldn't call regression with one predictor univariate myself, although I've seen that usage.) – Nick Cox May 30 '18 at 10:09
• @NickCox Thanks, I have edited my question. I do not quite understand what your sentence means, if both variables are ranked, the Spearman correlation = regression standard coefficient, but the regression standard cofficient NOT = Spearman coefficient? – Lumos May 30 '18 at 17:14
• What do you mean by "standard coefficient"? It's not (hmm) a standard term that I know. – Nick Cox May 30 '18 at 17:35
• @NickCox Sorry, "standardized coefficient", my bad. – Lumos May 30 '18 at 17:58
2 Answers
Here is an example using data on gallons per 1000 miles and weight in pounds for 22 foreign cars (meaning, cars made outside the United States) from Stata's auto data (and before that from Chambers, J.M., W.S. Cleveland, B. Kleiner and P.A. Tukey. 1983. Graphical Methods for Data Analysis. Belmont, CA: Wadsworth).
The data
clear
input float gpm int weight
58.82353 2830
43.47826 2070
40 2650
43.47826 2370
28.57143 2020
41.66667 2280
47.61905 2750
47.61905 2130
40 2240
35.714287 1760
33.333332 1980
71.42857 3420
38.46154 1830
28.57143 2050
55.55556 2410
32.258064 2200
55.55556 2670
43.47826 2160
24.390244 2040
40 1930
40 1990
58.82353 3170
end
The regression coefficient in a one-predictor regression of standardized variables, i.e. each scaled to (value $-$ mean) / SD, is equal to the Pearson correlation.
. egen gpm_std = std(gpm)
. egen weight_std = std(weight)
. reg gpm_std weight_std
Source | SS df MS Number of obs = 22
-------------+---------------------------------- F(1, 20) = 40.22
Model | 14.025405 1 14.025405 Prob > F = 0.0000
Residual | 6.97459503 20 .348729751 R-squared = 0.6679
-------------+---------------------------------- Adj R-squared = 0.6513
Total | 21 21 1 Root MSE = .59053
------------------------------------------------------------------------------
gpm_std | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight_std | .8172371 .128865 6.34 0.000 .5484295 1.086045
_cons | 9.00e-09 .1259022 0.00 1.000 -.2626273 .2626273
------------------------------------------------------------------------------
. corr gpm weight
(obs=22)
| gpm weight
-------------+------------------
gpm | 1.0000
weight | 0.8172 1.0000
The regression coefficient in a one-predictor regression of ranks that are also standardized variables, i.e. each scaled to (value $-$ mean) / SD, is equal to the Spearman correlation of the original variables.
. egen gpm_rank = rank(gpm)
. egen gpm_rank_std = std(gpm_rank)
. egen weight_rank = rank(weight)
. egen weight_rank_std = std(weight_rank)
. regress gpm_rank_std weight_rank_std
Source | SS df MS Number of obs = 22
-------------+---------------------------------- F(1, 20) = 27.73
Model | 12.2003095 1 12.2003095 Prob > F = 0.0000
Residual | 8.79969068 20 .439984534 R-squared = 0.5810
-------------+---------------------------------- Adj R-squared = 0.5600
Total | 21.0000002 21 1.00000001 Root MSE = .66331
--------------------------------------------------------------------------------
gpm_rank_std | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------+----------------------------------------------------------------
weight_rank_~d | .762212 .1447468 5.27 0.000 .4602754 1.064149
_cons | 4.40e-09 .1414189 0.00 1.000 -.2949946 .2949946
--------------------------------------------------------------------------------
. spearman gpm weight if foreign
Number of obs = 22
Spearman's rho = 0.7622
Test of Ho: gpm and weight are independent
Prob > |t| = 0.0000
• Thanks for using the empirical analysis for me. Can I generalize from here that the standardized coefficient = Pearson correlation if the variables are continuous; standardized coefficient = Spearman correlation if the variables are ranked? – Lumos May 30 '18 at 18:41
• Yes; the spirit is correct there, but strictly being continuous is neither here nor there for the problem. Discrete variables are fine, just as the last example is partly about correlation between discrete variables that happen to be ranks. – Nick Cox May 30 '18 at 18:52
You cannot derive Spearman coefficients from linear regression (on the unranked variables). The Spearman correlation summarizes the monotonic trend. They are related but it's not a bijective relation. At best, you only if one is non-zero, the other is non-zero.
• If the variables are categorical variables and I rank them first before I put them into a linear regression, the magnitude of the coefficient is not meaningful, but a relationship is supported if it is non-zero. Am I understand correctly? If that is correct, can I interpret the significance of the correlation from the p-value of the regression standardized coefficient? Thanks! – Lumos May 30 '18 at 18:38
• @Lumos Ranking won't make sense for all categorical variables; they have to be ordered at a minimum. – Nick Cox May 30 '18 at 18:53
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# Learning Rate based on error of the network
I am not an expert and do not have theoretical justification for that, but it seems to me that the smaller network error is, the smaller learning rate should be.
Is there an algorithm to dynamically update learning rate based on total error of the network without relying on any hyper-parameters ?
## 1 Answer
Your intuition is on point, and shrinking the learning rate like this is often referred to as "annealing". But linking the learning rate to error magnitude neglects certain problematic error surface topologies. An excellent motivating example is the Rosenbrock "Banana" Function, which is often used as a test case for optimization algorithms. The "banana" is a low error valley which hides the global minimum. If an optimization path finds its way into this valley, the path to the global minimum is along a nearly flat gradient.
If you use an optimization algorithm that naively shrinks the learning rate relative to the error, you're going to get stuck as soon as you hit the valley. On the one hand: congrats! You've achieved a low error solution. But you're not necessarily anywhere near the global minimum. So how can we do better?
An approach used by modern gradient-based methods like Adagrad, RMSProp, and Adam is to separately assign learning rates to each parameter, and tie the learning rate to the magnitude of the respective parameter's update. The Stanford CS231n lecture notes explains:
Adagrad is an adaptive learning rate method originally proposed by Duchi et al..
# Assume the gradient dx and parameter vector x cache += dx**2 x += - learning_rate * dx / (np.sqrt(cache) + eps)
Notice that the variable cache has size equal to the size of the gradient, and keeps track of per-parameter sum of squared gradients. This is then used to normalize the parameter update step, element-wise. Notice that the weights that receive high gradients will have their effective learning rate reduced, while weights that receive small or infrequent updates will have their effective learning rate increased.
• shall I add eps to denominator only if np.sqrt(cache) equals 0 ? Mar 8 '18 at 19:39
• No, you always add eps to the denominator in adagrad. If you want to learn more about that formula, just follow the link I gave you. Mar 8 '18 at 21:31
• Ok, thank you sir Mar 8 '18 at 21:52
• Also do search for Cosine Annealing for Learning Rates Mar 10 '18 at 0:56
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Address 28 Ellendale Ave, Selkirk, NY 12158 (518) 542-3664 http://www.delmar-computers.com
family error Hannacroix, New York
Journal of Modern Applied Statistical Methods. 14 (1): 12–23. The Bonferroni procedure Main article: Bonferroni correction Denote by p i {\displaystyle p_{i}} the p-value for testing H i {\displaystyle H_{i}} reject H i {\displaystyle H_{i}} if p i ≤ α The most commonly used method which controls FWER at level $$\alpha$$ is called Bonferroni's method. It is easy to show that if you declare tests significant for $$p < \alpha$$ then FWER ≤ $$min(m_0\alpha,1)$$.
Our global network of representatives serves more than 40 countries around the world. Minitab Inc. Learn more about Minitab 17Â The type I error rates associated with the multiple comparisons are often used to identify significant differences between specific factor levels in an ANOVA. How much greater is this cumulative error rate, which statisticians call the experiment-wise orfamily error rate?
Comments Please enable JavaScript to view the comments powered by Disqus. New York: Wiley. Dredge records daily work hours for just 10 countries, and then compares each possible pair of countries in his data,he’ll make (10*9)/2 =45 pairwise comparisons, and incur a family error rate If R = 1 {\displaystyle R=1} then none of the hypotheses are rejected.[citation needed] This procedure is uniformly more powerful than the Bonferroni procedure.[2] The reason why this procedure controls the
doi:10.2105/ajph.86.5.726. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Thus, FDR procedures have greater power at the cost of increased rates of type I errors, i.e., rejecting null hypotheses of no effect when they should be accepted.[7] On the other Definition The FWER is the probability of making at least one type I error in the family, F W E R = Pr ( V ≥ 1 ) , {\displaystyle \mathrm
See also: False coverage rate §Controlling procedures, and False discovery rate §Controlling procedures Further information: List of post hoc tests Some classical solutions that ensure strong level α {\displaystyle \alpha } By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. C. (1987).
Using a statistical test, we reject the null hypothesis if the test is declared significant. Retrieved from "https://en.wikipedia.org/w/index.php?title=Family-wise_error_rate&oldid=742737402" Categories: Hypothesis testingMultiple comparisonsRatesHidden categories: Articles needing additional references from June 2016All articles needing additional referencesAll articles with unsourced statementsArticles with unsourced statements from June 2016Wikipedia articles needing Statisticians call this a Type I error. ISBN0-471-55761-7. ^ Romano, J.P.; Wolf, M. (2005a). "Exact and approximate stepdown methods for multiple hypothesis testing".
Dredge and His Amazing Expanding Error Suppose a researcher, Dr. C. (1987). FWER control limits the probability of at least one false discovery, whereas FDR control limits (in a loose sense) the expected proportion of false discoveries. Course Forum Section 1 Exercise 1.8 8/10 [resolved] font family error code Make a Website: CSS Styling Forum View Course » View Exercise 38 points Submitted by sinners over 1 year
Click here to learn more. Contents 1 History 2 Background 2.1 Classification of multiple hypothesis tests 3 Definition 4 Controlling procedures 4.1 The Bonferroni procedure 4.2 The Šidák procedure 4.3 Tukey's procedure 4.4 Holm's step-down procedure The most significant test must therefore pass the Bonferroni criterion. Tukey's method, Fisher's least significant difference (LSD), Hsu's multiple comparisons with the best (MCB), and Bonferroni confidence intervals are methods for calculating and controlling the individual and family error rates for
Contents 1 History 2 Background 2.1 Classification of multiple hypothesis tests 3 Definition 4 Controlling procedures 4.1 The Bonferroni procedure 4.2 The Šidák procedure 4.3 Tukey's procedure 4.4 Holm's step-down procedure Resampling-Based Multiple Testing: Examples and Methods for p-Value Adjustment. That means that to reject, we need p < 0.00005. For a single comparison, the family error rate is equal to the individual error rate which is the alpha value.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Journal of the American Statistical Association. 100: 94–108. If that doesn't work, try using the Reset Code button. 3683 points Submitted by Judy over 1 year ago 2 Comments sinners over 1 year ago @albinosrefuge i got it, thanks Now suppose you have 1000 tests, and use the Bonferroni method.
when m 0 = m {\displaystyle m_{0}=m} so the global null hypothesis is true).[citation needed] A procedure controls the FWER in the strong sense if the FWER control at level α Please refer to your web browser help section to enable Javascript on your computer. Referrals = Cash! To give an extreme example, under perfect positive dependence, there is effectively only one test and thus, the FWER is uninflated.
Game 2: We flip a coin 10 times. What Are T Values and P Values in Statistics? The Bonferroni procedure Main article: Bonferroni correction Denote by p i {\displaystyle p_{i}} the p-value for testing H i {\displaystyle H_{i}} reject H i {\displaystyle H_{i}} if p i ≤ α Please try the request again.
It rejects the null hypothesis when $$p < \alpha / m$$. (It would be better to use $$m_0$$ but we don't know what it is - more on that later.) The This forum is now read-only. Sign Me Up > You Might Also Like: Understanding t-Tests: 1-sample, 2-sample, and Paired t-Tests Understanding t-Tests: t-values and t-distributions Angst Over ANOVA Assumptions? doi:10.1093/biomet/75.4.800. ^ Westfall, P.
To find out, we can set up a Minitab worksheet to automatically calculate the family error rate based on the number of multiple comparisons: Here’s what you should get: The more
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Yingce Xia et al. explored a series of applications of Dual Learning [1,2,3] on various tasks namely machine translation, image processing and sentiment analysis. I am interested in Dual Leanring on machine translation task.
## Dual Form
Two tasks are in dual form if the input and output of one task are exactly the output and input of the other task respectively. For example in machine translation task, translation from Chinese to English and translation from English to Chinese are in dual form. It is proved that we can exploit the duality between two tasks to boots the performance for both of them.
## Problem Formulation
Let’s call one task in the dual form primal task and the other dual task. The primal task has input space $X$ and output space $Y$ while the dual task has input space $Y$ and output space $X$. The primal task learns a conditional distribution $P(y|x;\theta_{xy})$ whereas the dual task learns $P(x|y;\theta_{yx})$ where $x \in X$ and $y \in Y$.
According to Bayes’ theorem we have $P(x,y) = P(x)P(y|x) = P(y)P(x|y)$. So ideally the conditional distributions of the primal and dual tasks should satisfy
$$\begin{eqnarray} P(x)P(y|x;\theta_{xy}) = P(y)P(x|y;\theta_{yx}) \end{eqnarray}$$
However, these two models are learned seperately, equation(1) might not hold which is always the case in reality. Hence, we can use equation(1) as a constraint.
## Dual Supervised Learning
### Description
Dual Supervised Learning is to directly regulate models with equation(1). Consider primal task model $f$ and dual task model $g$
$$f(x;\theta_{xy}) = \mbox{argmax} P(y|x;\theta_{xy}) \\ g(y;\theta_{yx}) = \mbox{argmax} P(x|y;\theta_{yx})$$
We hope to minimize their losses
$$\begin{eqnarray} loss_{f} = \frac{1}{n} \sum^{n}_{i=1} l_{1}(f(x_{i};\theta_{xy}),y_{i}) \\ loss_{g} = \frac{1}{n} \sum^{n}_{i=1} l_{2}(g(y_{i};\theta_{yx}),x_{i}) \end{eqnarray}$$
Then introduce Lagrange multipliers and convert the constraint equation(1) as
$$\begin{eqnarray} l_{duality} = (\log \hat{P}(x) + \log P(y|x;\theta_{xy}) - \log \hat{P}(y) - \log P(x|y;\theta_{yx}) )^2 \end{eqnarray}$$
where $\hat{P}(x)$ and $\hat{P}(y)$ are empirical marginal distributions.
And put it into $loss_{f}$ and $loss_{g}$ which leads to
$$loss_{f} = \frac{1}{n} \sum^{n}_{i=1} l_{1}(f(x_{i};\theta_{xy}),y_{i}) + \lambda_{xy} l_{duality} \\ loss_{g} = \frac{1}{n} \sum^{n}_{i=1} l_{2}(g(y_{i};\theta_{yx}),x_{i}) + \lambda_{yx} l_{duality}$$
where $\lambda_{xy}$ and $\lambda_{yx}$ are Lagrange parameters.
### Experiment
#### Settings
• Three datasets with 12M, 4.5M and 10M pairs (drop all sentences with more than 50 words).
• Use another 2 models (will not be updated during training) to estimate $\hat{P}(x) = \prod P(x_{i}|x_{\le i-1})$ and $\hat{P}(y)= \prod P(y_{i}|y_{\le i-1})$.
• Word embedding dimension is 620.
• RNN size is 1000.
• Vocabulary size is set as 30K, 50K and 30K respectively.
• Beam width is 12.
• Both $\lambda$s is set o 0.01.
## Dual Inference
Intuitively, we have high confidence to judge y is a good output for the input x in the primal task, if x is a good output for y in the dual task. So the inference equations can be
$$\begin{eqnarray} f(x) = \arg \underset{y^{‘}} \min {\alpha l_{f}(x,y^{‘}) + (1-\alpha) l_{g}(x,y^{‘}) } \\ g(y) = \arg \underset{x^{‘}} \min {\beta l_{g}(x^{‘},y) + (1-\beta) l_{f}(x^{‘},y) } \end{eqnarray}$$
## Dual Semi-supervised Learning
Dual Semi-supervised Learning makes use of monolingual data. The process is 1) use pre-trained primal and dual tasks for warm start. 2) the primal task translates monolingual data and passes it to the dual task. 3) the dual task transaltes it back to the primal task. 4) the primal task calculates the loss and optimizes both tasks.
Another reinforcement learning approach is described in [2].
## Compare dual learning with other learning schemes
-Co-training is single-task learning and assumes that each example is described using two different feature sets that provide different, complementary information about the instance [5].
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# 银河会在太空中移动吗？
57
5
2
8
“穿越空间”不是一回事。空间没有位置。运动总是相对于其他事物的，例如另一个星系，宇宙微波背景或其他。您已经收到有关相对运动的一些答案，请参见下文。
Florin Andrei
3
PlasmaHH
15
73
“从CMB数据可以看出，本地组（包括银河系的星系组）相对于CMB的参考帧（也称为CMB静止帧）似乎以627±22 km / s的速度运动，或在CMB方向上没有运动的参考系），即银河经度l = 276°±3°，b = 30°±3°。[82] [83]这种运动导致各向异性数据（CMB在移动方向上显得比在相反方向上略热）。[84]“
627 km / s相当快。看到这篇文章，说它是每小时130万英里。光速低于300,000公里/秒或6.7亿英里/小时，因此银河系以大约光速的0.2％在宇宙中移动。另请参阅ghoppe撰写的CMBR物理学答案，其中讨论了CMBR参考系，该参考系实际上是宇宙的参考系。
4
28
“为什么移动？” 如果它完全静止，那将是一个令人难以置信的巧合。宇宙中有无数个物体在不同方向上施加引力。他们将不得不准确地平衡出星系，使其不移动。
Barmar
3
@Barmar：好点。我为什么不这么说呢？！
4
Mazura
1
@Barmar：从“时间简史”：Newton realized that, according to his theory of gravity, the stars should attract each other, so it seemed they could not remain essentially motionless. Would they not all fall together at some point?We now know it is impossible to have an infinite static model of the universe in which gravity is always attractive.
34
${}^{†}$$^\dagger$形式上，一个使用在其中的帧宇宙微波背景是各向同性的。
${}^{‡}$$^\ddagger$考虑到我们绕银河系中心的运动，我们的太阳（当前）在。$369.82±0.11\phantom{\rule{thinmathspace}{0ex}}\mathrm{k}\mathrm{m}\phantom{\rule{thinmathspace}{0ex}}{\mathrm{s}}^{-1}$$369.82\pm0.11\,\mathrm{km\, s^{-1}}$
4
Mike
28
@Mike这不是一个智力问题，而是一个经验和学习的问题。生活中的大多数事情都是这样。
jpmc26 2009年
2
pela
9
，如果不想考虑这样做。
10
user230910
2
Barmar
2
@Barmar：两个人都以为他们是静止的，宇宙正以5 km / h的速度向他们移动，另一个人以10 km / h的速度向他们走。
7
6
Monty Python在科学问题上似乎不太准确，但是这次在Galaxy Song中确实做得很好，还提到了银河系运动。
Just remember that you're standing on a planet that's evolving
And revolving at nine hundred miles an hour,
That's orbiting at nineteen miles a second, so it's reckoned,
A sun that is the source of all our power.
The sun and you and me and all the stars that we can see
Are moving at a million miles a day
In an outer spiral arm, at forty thousand miles an hour,
Of the galaxy we call the 'Milky Way'.
Our galaxy itself contains a hundred billion stars.
It's a hundred thousand light years side to side.
It bulges in the middle, sixteen thousand light years thick,
But out by us, it's just three thousand light years wide.
We're thirty thousand light years from galactic central point.
We go 'round every two hundred million years,
And our galaxy is only one of millions of billions
In this amazing and expanding universe.
The universe itself keeps on expanding and expanding
In all of the directions it can whizz
As fast as it can go, at the speed of light, you know,
Twelve million miles a minute, and that's the fastest speed there is.
So remember, when you're feeling very small and insecure,
How amazingly unlikely is your birth,
And pray that there's intelligent life somewhere up in space,
'Cause there's bugger all down here on Earth.
3
“距银河系中心点三万光年。我们每两亿年绕一圈”，对于“银河系正在移动”的主题，恕我直言，恕我直言
Ole Albers
5
2
Barmar
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# Integers $d$ for which the Negative Pell equation is soluble for both $d$ and $2d$?
Let $\text{NPE}_d$ denote the negative Pell equation: $$x^2-dy^2=-1$$ Where $d$ is a given positive nonsquare integer and integer solutions are sought for x and y.
we know that (in this paper):
Theorem : The equation $\text{NPE}_d$ has integer solutions if and only if there exist two integers $a(d)=a$ and $b(d)=b$ such that $d=a^2+b^2$ and there exists a Pythagorean triplet $(A,B,C)$ such that $|aA-bB|=1$ and in this case $(Aa+Bb,C)$ is a solution.
Obviously if $\text{NPE}_d$ has integer solutions then $d$ cannot be divisible by any prime $p$ such that $p=3\mod 4$.
My question: Is there any characterization for the integers $d$ for which $\text{NPE}_d$ and $\text{NPE}_{2d}$ have both integer solutions.
I used the characterization above, but I can't link the couple $(a(d),b(d))$ to $(a(2d),b(2d))$ because the theorem doesn't give us much information
The sequence of the elements $d$ for which $\text{NPE}_d$ is soluble is OEIS A031396.
Thank you for your help.
It is necessary to use the formula. http://www.artofproblemsolving.com/blog/101140
$$x^2-dy^2=-1$$
$$z^2-2dg^2=-1$$
It will give us a series of solutions using the Pell equation: $$p^2-2s^2=k$$
Let us use the fact that the following solution can be found knowing the previous, formula.
$$p_2=3p_1+4s_1$$
$$s_2=2p_1+3s_1$$
Using certain series of solutions you can find ratio formula.
$p^2-2s^2=1$ $;$ $(p_1;s_1) - (3;2);$ $d=s^2+1$
$p^2-2s^2=-1$ $;$ $(p_1;s_1) - (1;1) ;$ $d=s^2+4$
$p^2-2s^2=-7$ $;$ $(p_1;s_1) - (1;2) ;$ $d=s^2+1$
$p^2-2s^2=7$ $;$ $(p_1;s_1) - (3;1) ;$ $d=s^2+4$
$p^2-2s^2=17$ $;$ $(p_1 ; s_1) - (5;2) ;$ $d=s^2+9$
While it is difficult to say. Limited to any solution of these series or not. Clearly what is involved in this equation Pell.
• which formula I have to use in your link? is this an answer? if yes: what is your conclusion about the characterization of the integers $d$ for which the two equations have solutions? thanks – Elaqqad Feb 18 '15 at 14:48
• @Elaqqad You don't understand the meaning of the formulas on the link and those who drew? – individ Feb 18 '15 at 14:58
• yes I didn't find any connexion between my question and the link,I think that I need more explications, thinks. – Elaqqad Feb 18 '15 at 15:05
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# find tension in 3 ropes
703 views
A huge Halloween decoration is suspended by 3 cables. Each cable is exactly 25 m long and is attached top each of three building equidistant from each other. Each cable make an angle of 30 degrees with the side of the building to which it is attached. What is the magnitude of the tension in each cable?
So each cable makes an angle of $30^\circ$ with the vertical. They are all have the same length and therefore will have the same tension. Then the sum of three vertical components of the tension forces will balance the weight of the decoration. $$3Tcos30^\circ=mg$$ Then you can find T.
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