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# How many 3-digit numbers greater than 500 contain the digit 9 appearin
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How many 3-digit numbers greater than 500 contain the digit 9 appearin [#permalink]
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12 May 2020, 06:15
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How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once?
A. 191
B. 189
C. 176
D. 175
E. 153
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Posts: 1968
Location: India
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin [#permalink]
### Show Tags
12 May 2020, 07:30
2
1
Number that contains only one 9= 1*9*9+4*1*9+4*9*1= 153
Number that contains two 9's= 1*1*9+4*1*1+1*9*1= 22
Number that contains three 9's= 1*1*1=1
Total numbers = 153+22+1=176
Bunuel wrote:
How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once?
A. 191
B. 189
C. 176
D. 175
E. 153
Are You Up For the Challenge: 700 Level Questions
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Posts: 5
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin [#permalink]
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12 May 2020, 07:40
1
1
Total nos - Nos that contain no 9
5*10*10 - 4*9*9 =176
Posted from my mobile device
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Joined: 13 Jun 2019
Posts: 20
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin [#permalink]
### Show Tags
13 May 2020, 05:04
1
I think the answer is 175
As statement says 3-digit numbers greater than 500 . This means $$501<=x<=999$$
Therefore
Step 1:- total number of numbers between 501 and 999 (all inclusive) = $$5 * 10 * 10 = 500 - 1 = 499$$
We can also find this by $$999-501 = 498+1 = 499$$ (Adding 1 to include 501)
Step 2:- total number of numbers which does not contain 9 =$$4 * 9 * 9 = 324$$
Step 3:- total number of numbers containing at least one 9 = $$499 - 324 = 175$$
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Shrekey
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Joined: 19 Oct 2018
Posts: 1968
Location: India
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin [#permalink]
### Show Tags
13 May 2020, 05:15
1
You count 500 in Step 2....Deduct there too. You'll get 176. Point is it does not matter whether you count from 500 or 501, Numbers that contain 9 remain the same
Another way is-
Numbers from 501-599 that contain 9 = 10+10-1=19 (Deduct 1, as we counted 599 twice)
Numbers from 600-699 that contain 9 = 10+10-1=19
Numbers from 700-799 that contain 9 = 10+10-1=19
Numbers from 800-899 that contain 9 = 10+10-1=19
Numbers from 900-999 that contain 9 = 100
Total numbers = 19*4+100=176
rsrighosh wrote:
I think the answer is 175
As statement says 3-digit numbers greater than 500 . This means $$501<=x<=999$$
Therefore
Step 1:- total number of numbers between 501 and 999 (all inclusive) = $$5 * 10 * 10 = 500 - 1 = 499$$
We can also find this by $$999-501 = 498+1 = 499$$ (Adding 1 to include 501)
Step 2:- total number of numbers which does not contain 9 =$$4 * 9 * 9 = 324$$
Step 3:- total number of numbers containing at least one 9 = $$499 - 324 = 175$$
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Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin [#permalink]
### Show Tags
19 May 2020, 06:37
3
1
Bunuel wrote:
How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once?
A. 191
B. 189
C. 176
D. 175
E. 153
All 100 numbers in the 900s have at least one digit of 9, The number of numbers in 500s, 600s, 700s, and 800s that have at least one digit of 9 must be equal. That is, there is the same amount of numbers in 500s that have at least one digit of 9 as in 600s, 700s, or 800s. If this amount is x, then the total number of numbers is 4x + 100. Notice this must be an even number and since 176 is the only even number in the given choices, 176 must be the correct answer.
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Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin [#permalink]
### Show Tags
30 May 2020, 05:11
rsrighosh wrote:
I think the answer is 175
As statement says 3-digit numbers greater than 500 . This means $$501<=x<=999$$
Therefore
Step 1:- total number of numbers between 501 and 999 (all inclusive) = $$5 * 10 * 10 = 500 - 1 = 499$$
We can also find this by $$999-501 = 498+1 = 499$$ (Adding 1 to include 501)
Step 2:- total number of numbers which does not contain 9 =$$4 * 9 * 9 = 324$$
Step 3:- total number of numbers containing at least one 9 = $$499 - 324 = 175$$
Hi rsrighosh
Can you please further elabourate step 2. Or first solution jn step 1. I coukdnot understand that method.
Thank you!
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Joined: 11 Feb 2019
Posts: 264
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin [#permalink]
### Show Tags
30 May 2020, 05:29
1
C.
500-599 => 19 times
600-699= > 19 times
700-799 => 19 times
800-899= > 19 times
900-999 => 100 times
Counting: 176
_________________
Cheers,
NJ
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin [#permalink] 30 May 2020, 05:29
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Format: Hardcover
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Something like this is seen in most telescope photos. the width of each slit. The main focus is on understanding the nonlinear aspects of the acoustic dynamics in materials as well as the peculiarities in the nonlinear optical and magneto-optical response. Some have made it possible to reach for the stars, while others have helped unveil a microscopic realm on Earth. There will be two lectures each week and a recitation section. A concise survey of Cartesian physics can be found in Garber 1992b.
Pages: 464
Publisher: Wiley-IEEE Press; 1 edition (September 14, 1999)
ISBN: 0780310098
Digital Transmission Systems
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5.5 Differentiation of Logarithmic Functions
Presentation on theme: "5.5 Differentiation of Logarithmic Functions"— Presentation transcript:
5.5 Differentiation of Logarithmic Functions
By Dr. Julia Arnold and Ms. Karen Overman using Tan’s 5th edition Applied Calculus for the managerial , life, and social sciences text
Now we will find derivatives of logarithmic functions and we will
Need rules for finding their derivatives. Rule 3: Derivative of ln x Let’s see if we can discover why the rule is as above. First define the natural log function as follows: Now rewrite in exponential form: Now differentiate implicitly:
Example 1: Find the derivative of f(x)= xlnx.
Solution: This derivative will require the product rule. Product Rule: (1st)(derivative of 2nd) + (2nd)(derivative of 1st)
Example 2: Find the derivative of g(x)= lnx/x
Solution: This derivative will require the quotient rule. Quotient Rule: (bottom)(derivative of top) – (top)(derivative of bottom) (bottom)²
Why don’t you try one: Find the derivative of y = x²lnx .
The derivative will require you to use the product rule. Which of the following is the correct? y’ = 2 y’ = 2xlnx y’ = x + 2xlnx
No, sorry that is not the correct answer.
Keep in mind - Product Rule: (1st)(derivative of 2nd) + (2nd)(derivative of 1st) Try again. Return to previous slide.
Good work! Using the product rule:
F’(x) = (1st)(derivative of 2nd) + (2nd)(derivative of 1st) y’ = x² (lnx)(2x) y’ = x + 2xlnx This can also be written y’ = x(1+2lnx)
Here is the second rule for differentiating logarithmic functions.
Rule 4: The Chain Rule for Log Functions In words, the derivative of the natural log of f(x) is 1 over f(x) times the derivative of f(x) Or, the derivative of the natural log of f(x) is the derivative of f(x) over f(x)
Example 3: Find the derivative of
Solution: Using the chain rule for logarithmic functions. Derivative of the inside, x²+1 The inside, x²+1
Example 4: Differentiate
Solution: There are two ways to do this problem. One is easy and the other is more difficult. The difficult way:
The easy way requires that we simplify the log using some of the expansion properties.
Now using the simplified version of y we find y ’.
Now that you have a common denominator, combine into a single
fraction. You’ll notice this is the same as the first solution.
Example 6: Differentiate
Solution: Using what we learned in the previous example. Expand first: Now differentiate: Recall lnex=x
Find the derivative of . Following the method of the previous two examples. What is the next step?
This method of differentiating is valid, but it is the more difficult
way to find the derivative. It would be simplier to expand first using properties of logs and then find the derivative. Click and you will see the correct expansion followed by the derivative.
Correct. First you should expand to Then find the derivative using the rule 4 on each logarithm. Now get a common denominator and simplify.
Example 7: Differentiate
Solution: Although this problem could be easily done by multiplying the expression out, I would like to introduce to you a technique which you can use when the expression is a lot more complicated. Step 1 Take the ln of both sides. Step 2 Expand the complicated side. Step 3 Differentiate both side (implicitly for ln y )
Step 4: Solve for y ‘. Step 5:Substitute y in the above equation and simplify.
Continue to simplify…
Let’s double check to make sure that derivative is correct by
Multiplying out the original and then taking the derivative. Remember this problem was to practice the technique. You would not use it on something this simple.
Consider the function y = xx.
Not a power function nor an exponential function. This is the graph: domain x > 0 What is that minimum point? Recall to find a minimum, we need to find the first derivative, find the critical numbers and use either the First Derivative Test or the Second Derivative Test to determine the extrema.
To find the derivative of y = xx , we will take the ln of both sides first and then expand.
Now, to find the derivative we differentiate both sides implicitly.
To find the critical numbers, set y’ = 0 and solve for x.
Now test x = 0.1 in y’, y’(0.1) = < 0 and x = 0.5 in y’, y’(0.5) = > 0 Thus, the minimum point occurs at x = 1/e or about .37
We learned two rules for differentiating logarithmic functions:
Rule 3: Derivative of ln x Rule 4: The Chain Rule for Log Functions We also learned it can be beneficial to expand a logarithm before you take the derivative and that sometimes it is useful to take the natural log (ln) of both sides of an equation, rewrite and then take the derivative implicitly.
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# Light in an optical fiber - variational calculus
physman55
## Homework Equations
$$\frac{\delta{F}}{\delta{y}} - \frac{d}{dx}\frac{\delta{F}}{\delta{y'}} = 0$$
## The Attempt at a Solution
I'm having trouble setting this one up. If I let the functional be
$$F(x,x',y) = n(y)\sqrt{1+(x')^2}$$
Applying the LE equation I obtain:
$$\frac{d}{dy}\frac{x'}{\sqrt{1+(x')^2}}n_0(1-\frac{y^2}{a^2})=0$$
And this is where I stopped (I haven't used either of the hints). Any hints?
physman55
Any ideas please? If p/a is small then I could write n(y)=n_0; but then I'm minimizing path length... so the answer is a straight line. Obviously this problem couldn't be that easy.
sgd37
it tells you y should be the principal variable so your functional should read
$$F(y,y')$$= $$n(y)$$$$\sqrt{1+y'^{2}}$$ and then calculate the EL equations
by my calculations you should get
$$\frac{\partial}{\partial x}$$$$(\frac{y'}{\sqrt{1+y'^{2}}})$$= $$-2\frac{y}{a^{2}}\sqrt{1+y'^{2}}$$
disregarding the (y/a)^2 term
Last edited:
physman55
By "y" being the principal value my prof means that "y" is the independent variable.
For the last line, why did you ignore n(y) when you took the partial with respect to y' (on the left)?
sgd37
yeah Y is the degree of freedom and the Lagrangian are always expressed in term of the degrees of freedom L(q,q') and this makes more sense since you are asked to find y(x)
I didn't ignore the n(y) its just that y is comparible to $$\rho$$ and since $$\frac{\rho}{a}$$ is small n(y) = n0
physman55
Ok thanks for the explanation, that makes sense. But shouldn't the d/dx be a total derivative and not a partial; and secondly; how the hell do you solve that ODE?
sgd37
i'm not sure about the entire thing but since dy is comparable to rho you can deduce that y' is approximate to alpha and thus all the y'^2 terms are negligible and you get the resulting ODE
$$y''=\frac{-2y}{a^{2}}$$
which has solution
$$Acos(\frac{\sqrt{2}x}{a}) +Bsin(\frac{\sqrt{2}x}{a})$$ which kind of makes sense since you expect it to bounce off the walls in a periodic fashion
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Calculus
# Integrals - Problem Solving
Evaluate $\int _{ 0 }^{ \frac{\pi}{4} }{ \frac{21 \cos^2 x}{\sin x + \cos x} } dx + \int _{ \frac{\pi}{4} }^{ 0 }{ \frac{21 \sin^2 x}{\sin x + \cos x} } dx.$
If $f(x)=\int \frac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}} dx$ and $\displaystyle f(1)=\frac{5}{3},$ what is the value of $3f(16)?$
Let $\displaystyle f(x)=\int_{0}^{x}{\sqrt{7+6{t}^{2}}dt.}$ Then what are the real roots of the equation ${x}^{2}-\frac{df(x)}{dx}=0?$
If $f(m)$ is the number of the points crossed by the curve $y=x^2-mx+m$ and the $x$-axis, what is $\displaystyle \int_{7}^{12} f(m) \,dm ?$
Suppose $f(x)$ and $F(x)$ are polynomial functions such that $F'(x) = f(x) \mbox{ and } F(x)=xf(x)-4x^3+x^2.$ If $f(0)=6,$ what is $f(x)?$
×
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# Reduced-Complexity Novel Ordering for Group Maximum Likelihood Detection in MIMO Frequency Selective Fading Channels
• Published 2008 in
2008 IEEE 10th International Symposium on Spread…
#### Abstract
In this paper a novel ordering of substreams for detection in a multi-input multi-output slow time-varying frequency selective fading channel is proposed. The detection structure is nulling, detection and cancellation scheme called layered maximum likelihood detection (L-MLD) and group maximum likelihood detection (G-MLD) proposed in D. K. C. So, et al., Aug. 2006. The novel ordering scheme reduces the complexity of detection process imposed by the need for a thorough search among all possible combinations of substreams (groups) in each stage of detection, in order to find the best substream (group) which has the highest post-detection signal-to-noise ratio (SNR) for detection in that stage.
### Cite this paper
@article{Rahimian2008ReducedComplexityNO, title={Reduced-Complexity Novel Ordering for Group Maximum Likelihood Detection in MIMO Frequency Selective Fading Channels}, author={Narges Rahimian and Ali Iravani}, journal={2008 IEEE 10th International Symposium on Spread Spectrum Techniques and Applications}, year={2008}, pages={719-724} }
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0
Research Papers: Elastohydrodynamic Lubrication
# Some Criteria for Coating Effectiveness in Heavily Loaded Line Elastohydrodynamically Lubricated Contacts—Part I: Dry Contacts
[+] Author and Article Information
Ilya I. Kudish
Professor
Fellow ASME
Department of Mathematics,
Kettering University,
Flint, MI 48504
Sergey S. Volkov, Andrey S. Vasiliev, Sergey M. Aizikovich
Composite Materials,
Research and Education Center “Materials,”
Don State Technical University,
Rostov-on-Don 344000, Russia
Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 26, 2015; final manuscript received June 18, 2015; published online October 30, 2015. Assoc. Editor: Dong Zhu.
J. Tribol 138(2), 021504 (Oct 30, 2015) (10 pages) Paper No: TRIB-15-1026; doi: 10.1115/1.4030956 History: Received January 26, 2015
## Abstract
Contacts of indentors with functionally graded elastic solids may produce pressures significantly different from the results obtained for homogeneous elastic materials (Hertzian results). It is even more so for heavily loaded line elastohydrodynamically lubricated (EHL) contacts. The goal of the paper is to indicate two distinct ways the functionally graded elastic materials may alter the classic results for the heavily loaded line EHL contacts. Namely, besides pressure the other two main characteristics which are influenced by the nonuniformity of the elastic properties of the contact materials are lubrication film thickness and frictional stress/friction force produced by lubricant flow. The approach used for analyzing the influence of functionally graded elastic materials on parameters of heavily loaded line EHL contacts is based on the asymptotic methods earlier developed by authors (Kudish, 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman & Hall/CRC Press, New York; Kudish and Covitch, 2010, Modeling and Analytical Methods in Tribology, Chapman & Hall/CRC Press, New York; and Aizikovich et al., 2006, Contact Problems of Elasticity for Functionally Graded Materials, Fizmatlit, Moscow, Russia). More specifically, it is based on the analysis of contact problems for dry contacts of functionally graded elastic solids and the lubrication mechanisms in the inlet and exit zones as well as in the central region of heavily lubricated contacts.
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## Figures
Fig. 1
Graphs of contact half-width a0s versus relative coating thickness λs for contacts characterized by different ratios of the elastic modules of the coating and substrate β = E'(0)/E'(H)
Fig. 4
Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for hard coatings with β = 0.01 and some large and intermediate coating thicknesses λs.
Fig. 5
Graphs of pressure distributions p0s(xs) and phom(xs) versus xs. The graphs are presented for hard coatings with β = 0.01 and some intermediate coating thicknesses λs.
Fig. 2
Graphs of parameter N0s versus relative coating thickness λs for contacts characterized by different ratios of the elastic modules of the coating and substrate β
Fig. 3
Graphs of parameter N0ca0c = β1/4N0sa0s versus relative coating thickness λs for contacts characterized by different ratios of the elastic modules of the coating and substrate β
Fig. 6
Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for hard coatings with β = 0.01 and some intermediate coating thicknesses λs.
Fig. 7
Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for hard coatings with β = 0.01 and some intermediate and small coating thicknesses λs.
Fig. 8
Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for hard coatings with β = 0.1 and some intermediate and small coating thicknesses λs.
Fig. 9
Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for hard coatings with β = 0.01 and some small coating thicknesses λs.
Fig. 10
Graphs of pressure p0s(0) in the center of the contact. The graphs are presented for hard and soft coatings (for different values of β) versus coating thickness λs.
Fig. 11
Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for soft coatings with β = 100 and some intermediate and small coating thicknesses λs.
Fig. 12
Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for soft coatings with β = 10 and some intermediate and small coating thicknesses λs.
Fig. 13
Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for soft coatings with β = 100 and some small coating thicknesses λs.
Fig. 14
Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for soft coatings with β = 10 and some small coating thicknesses λs.
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# Introduction to Perturbative Quantum Field Theory
[Total: 26 Average: 3.8/5]
This is the beginning of a series that gives an introduction to perturbative quantum field theory (pQFT) on Lorentzian spacetime backgrounds in its rigorous formulation as locally covariant perturbative algebraic quantum field theory.
This includes the theories of quantum electrodynamics (QED) and electroweak dynamics, quantum chromodynamics (QCD), and perturbative quantum gravity (pQG) — hence the standard model of particle physics — on Minkowski spacetime (for particle accelerator experiments) and on cosmological spacetimes (for the cosmic microwave background) and on black-hole spacetimes (for black hole radiation).
This first part introduces the broad idea and provides a commented list of references. The next part will start with general discussion of a pivotal part of the theory: the “S-matrix” in causal perturbation theory, see below for the quick idea.
Perturbation and Non-perturbation.
Often “perturbative quantum field theory” (pQFT) is referred to simply as “quantum field theory” (QFT). However it is worthwhile to make the distinction explicit.
The word “perturbative” means that both the interactions between the fields/particles as well as the quantum effects they exhibit are assumed to be tiny — in fact infinitesimal — perturbations of the free (non-interacting) classical fields, hence of the undisturbed (matter-)waves freely propagating through the universe, with well-defined amplitudes at each spacetime point. More precisely this means that the observables of the theory (i.e. the numerical predictions that it makes about phenomena seen in experiment) are not true functions of the coupling constant ##g## (indicating the strength of the interaction) and of Planck’s constant ##\hbar## (indicating the strength of quantum effects), but just non-converging formal power series, at best “asymptotic series“.
This sounds like a drastically coarse approximation to the actual interacting and quantum world that we inhabit — and indeed it is. However, a remarkable mathematical fact is that this drastically coarse approximation is already extremely rich in phenomena and demanding in mathematical techniques; and a remarkable experimental fact about the observable universe is that this extremely coarse approximation suffices to explain/predict essentially all phenomena that are seen in high energy particle scattering experiments, and to high numerical precision. Hence while on the one hand pQFT is a dramatic triumph of pure thought over reality, on the other hand it amplifies the vastness of the presently unknown reality that must still lie beyond our present understanding: In a mathematically precise sense, pQFT desribes only the infinitesimal neighbourhood of the space of classical and free field theories inside the full space of quantum field theories.
Indeed some extremely basic aspects of observed physical reality are invisible to pQFT: Notably the curious phenomenon of QCD called asymptotic freedom means that it completely fails to describe the bound nature of the hadronic matter that all the world around us it made of (the confinement of quarks); it only applies well for high energy scattering processes seen in particle accelerators. This is believed to be related to a special non-perturbative nature of the QCD vacuum known as the instanton sea, to which we briefly turn below at the very end.
Hence we will eventually need to understand non-perturbative quantum field theory. This is by and large a wide open problem, both conceptually and physically. Presently not a single example of an interacting non-perturbative Lagrangian quantum field theory has been constructed in spacetime dimension ##\geq 4## (besides numerical simulation, such as lattice gauge theory). For the case of 4d Yang-Mills theory (such as QED and QCD) one single aspect of its non-perturbative quantization (the expected “mass gap”) is among the list of “Millenium Problems” listed by the Clay Mathematics Institute. Full non-perturbative Yang-Mills theory might well be a ##10^4## year problem, and full non-perturbative quantum gravity might be a ##10^5## year problem. But every journey needs to start with a first step in the right direction, and therefore a conceptually clean understanding of pQFT theory should be a helpful stepping stone towards these big open problems.
Unfortunately, even pQFT has been notorious for being believed to be conceptually mysterious. Modern textbooks will still talk about “divergencies that plague the theory” and, worse, appeal to the folklore of the “path integral” without offering precise clues as to its nature, thereby disconnecting the theory from the mathematically informed discourse that distinguishes modern physics from the “natural philosophy” of the ages before Newton. This is a historical remnant of the early days of the theory as conceived by Tomonaga, Schwinger, Feynman and Dyson, when many steps still proceeded by educated guesswork
Causal Perturbation Theory.
However, a mathematically rigorous formulation of pQFT on Minkowski spacetime (describing processes seen in particle accelerators such as the LHC experiment) with precise well-defined concepts had been fully established already by 1975, as summarized in the seminal Erice summer school proceedings of Velo-Wightman 76. Among other contributions, this included the formalization of the theory due to
which has come to be known as causal perturbation theory.
The key idea of this approach is to define the perturbative scattering matrix of the pQFT by imposing (i.e. axiomatizing) how it should behave — in particular how it should behave with respect to spacetime causality, whence the name — instead of trying to define it by a path integral.
The scattering matrix of a pQFT is the collection of all probability amplitudes for a given set of field quanta (particles) coming in from the far past, then perturbatively interacting with each other and hence scattering off each other, to finally emerge in the far future as another set of field quanta. The corresponding scattering probabilities (“scattering cross sections”) are manifestly the kind of information that may be measured in the detector of a particle accelerator, where to good approximation the incoming beams are the particles “from the far past” and the hits on the detectors around the point where the beams collide is the particles emerging “in the far future”. The theory has to make predictions for which of the many detector cells (at which angles from the colliding beams) is going to be triggered with which ratio given the incoming particle beam, and this is all encoded in the scattering matrix .
In traditional approaches of pQFT, the scattering matrix is written schematically as
$$S(L_{\text{int}} ) \overset{\text{not really}}{=} \int \left[D\phi\right] e^{ \tfrac{1}{i \hbar} \int_X L_{\text{free}}(\phi) } \, \exp\left( \tfrac{g}{i \hbar} \int_X\left( L_{\text{int}}(\phi) \right) \right)$$
where the informal schematic right hand side expresses the idea that the probability amplitude for a scattering process is a sum (integral) over all spacetime field configurations ##\phi## (with the given asymptotic behaviour) of the complex phase determined by the free Lagrangian density ##L_{\text{free}}## and the interaction Lagrangian density ##L_{\text{int}}## evaluated at that field configuration and integrated over spacetime ##X##.
There is no known way to make sense of this integral, apart from toy examples. The reason that traditional pQFT textbooks nevertheles make some sense is that all that is really being used are some structural properties that such a would-be integral should have. To make such reasoning precise, one is to give up on the idée fixe of an actual path integration and simply state exactly which properties the expression ##S(L_{\text{int}})## is actually meant to have!
The key such property of the S-matrix is “causal additivity“. This essentially just says that all effects caused in some spacetime region must be in the causal future (and past) of that region.
The main result of causal perturbation theory is the proof that
1. Causally additive perturbative S-matrices exist, hence pQFT exists, rigorously;
2. at each order there is a finite-dimensional space of choices, the renormalization freedom;
3. any two such choices are related by a unique re-definition of the Lagrangian densities (by “counter-terms”);
4. these re-definitions form a group, the Stückelberg-Peterson renormalization group.
This is known as the main theorem of perturbative renormalization, and we will discuss this in detail later in this series.
A textbook account of QED in causal perturbation theory is
and electroweak theory, QCD as well as pQG are discussed this way in
Perturbative Algebraic Quantum Field Theory.
A key technical tool that allows pQFT in causal perturbation theory to be well-defined is that the interactions of the fields are considered “smoothly switched off outside a compact spacetime region” (called “adiabatic switching“).
Originally this was considered just an intermediate technical step to separate the issue of “UV-divergences” (the definition of the S-matrix at coinciding interaction points) from the “IR-divergences”, namely from the issue of taking the “adiabatic limit” of the S-matrix in which the adiabatic switching is removed and interactionse are considered over all of spacetime.
But it had been observed already in Il’in-Slavnov 78 that for realistic quantum observables which are supported in a compact region of spacetime (corresponding to an experimental setup of finite extension in space and time) all that matters is that the interaction is “switched on” in the causal closure of the support of the observable, while outside its support it may be “adiabatically switched off” at will without actually changing the value of the observables (up to canonical unitary equivalence, see here). Moreover, the system of spacetime localized perturbative quantum observables obtained this way from the causal S-matrix turns out to satisfy axioms that had earlier been proposed in Haag-Kastler 64 to provide a complete mathematical characterization of the physical content of a pQFT: they form a local net of observables. This will be explained in detail in the next part of this series.
Haag-Kastler originally aimed, ambitiously, for axiomatization of the non-perturbative quantum field theory, and hence required the algebras of observables in the local net to be ##C^\ast##-algebras. Their formulation of non-perturbative quantum field theory via local nets of ##C^\ast##-algebras came to be known as algebraic quantum field theory (AQFT). Here in perturbation theory these algebras are just formal power series algebras (in the coupling constant and in Plancks’s constant), but otherwise they satisfy the original Haag-Kastler axioms. This way pQFT in the rigorous guise of causal perturbation theory came to be called perturbative algebraic quantum field theory (pAQFT, Brunetti-Dütsch-Fredenhagen 09).
The terminology overlaps a bit. It may be useful to think of it as follows:
• causal perturbation theory elegantly deals with the would-be “UV-divergencies” in pQFT by the simple axiom of the causally additivity S-matrix;
• perturbative AQFT in addition elegantly deals with the “decoupling of the IR-divergences” in pQFT by organizing the system of spacetime localized quantum observables into a local net of observables and thereby proving that the adiabatically switched S-matrix yields correct physical localized observables even without taking the problematic adiabatic limit (i.e. even without defining the theory in the infrared).
Locally covariant pAQFT.
While there are other equivalent rigorous formulations of pQFT on Minkowski spacetime, causal perturbation theory is singled out as being the one that generalizes well to QFT on curved spacetimes (Brunetti-Fredenhagen 99), hence to quantum field theory in the presence of a background field of gravity. This is important: For example pQFT on cosmological spacetime backgrounds describes the processes whose remnant is seen in the cosmic microwave background, while pQFT on black hole spacetime backgrounds describes black hole radiation.
One reason this works so well is that the axiom of causal additivity, which essentially defines the perturbative S-matrix, manifestly makes sense on general time-oriented spacetimes. But moreover there is some hard analysis which guarantees that the construction proof of the perturbative S-matrix does generalize from Minkowski spacetime to general time-oriented globally hyperbolic spacetimes: This requires finding
1. generalizations of the Minkowski vacuum state to curved spacetimes to define the free quantum field theory via its Wick algebra (the “normal-ordered product”);
2. corresponding Feynman propagators on curved spacetimes to define the perturbative interacting field theory via its time-ordered product.
This is non-trivial, because on general (even globally hyperbolic) spacetimes there exists no vacuum state, since there does not even exist a global concept of particles. But it turns out that time-ordered globally hyperbolic spacetimes do admit quantum states that, while not being vacuum states in general, do satisfy all the properties that are needed for the definition of a free field quantization, these are known as the Hadamard states, essentially unique up to addition of a regular term (Radzikowski 96). Moreover, each Hadamard state induces a corresponding Feynman propagator on the curved spacetime. With this in hand, the construction of the pQFT on curved spacetime may be obtained closely following the causal perturbation theory on Minkowski spacetime (Brunetti-Fredenhagen 00).
This then allows to generalize causal perturbation theory to construct pQFTs “general covariantly” on all time-oriented globally hyperbolic spacetimes, it has come to be called locally covariant algebraic quantum field theory (lcpAQFT).
Eventually all the traditional lore and tools of pQFT have been (re-)obtained in precise form in the context of pAQFT. For instance:
A fairly comprehensive review of the theory as of 2016, with pointers to the research literature for further details, is in
In this series I will broadly follow this view of the subject, spelling out some more details here and there and maybe omitting other details at other places. I have a plan to follow, but will be happy to try to react to requests, comments and criticism from the PF-Insights readership.
From first principles.
Besides conceptual precision of our physical theories, we also want them to be conceptually coherent, preferably to follow from a small set of joint principles. While causal perturbation theory / perturbative AQFT is a mathematically precise formulation of traditional pQFT, many of its constructions appear somewhat ad hoc, even though well motivated and certainly right.
For instance the causal additivity axiom on the perturbative S-matrix was originally introduced as a really clever guess concerning the generalization to higher dimensional Lorentzian spacetimes of the simple 1-dimenional “path-ordering” in the Dyson formula (known as iterated integrals to mathematicians), and the construction of the interacting quantum observables from the S-matrix by Bogoliubov’s formula was mainly motivated from the fact that Bogoliubov gave that formula.
Of course, this being physics, all these constructions are physically justified by the fact that they do yield a precise formulation of traditional pQFT, and that traditional pQFT receives excellent confirmation in scattering experiments.
But even better than fitting our physical theory to observation in nature would be if we could derive the physical theory from deeper first theoretical principles, and then still match it with nature.
Here we should ask (at least): What does it mean to quantize any classical theory? And is pQFT the result of applying a general quantization prescription to classical field theory?
For ages people have chanted “The path integral does it!” in reply to this question. But as a matter of fact it does not — it does not even exist.
There are two general quantization prescriptions that do exist as mathematically well-defined concepts: geometric quantization and algebraic deformation quantization. Remarkably, it turns out that pAQFT does follow as a special case of “formal” (perturbative) algebraic deformation quantization (specifically Fedosov deformation quantization), and maybe yet more remarkable is that this was figured out only last year:
• Giovanni Collini,
“Fedosov Quantization and Perturbative Quantum Field Theory”
(arXiv:1603.09626)
• Eli Hawkins, Kasia Rejzner,
“The Star Product in Interacting Quantum Field Theory”
(arXiv:1612.09157)
This may give some hints concerning the non-perturbative completion of the theory: A good concept of non-perturbative algebraic deformation quantization exists, called strict ##C^\ast##-algebraic deformation quantization.
Therefore it is suggestive that strict algebraic deformation quantization may be the right conceptual approach for attacking the non-perturbative quantization of Yang-Mills theory, as opposed, possibly, to the “constructive field theory” approach (which is trying to construct rigorous measure for the Wick rotated path integral) that is considered in the problem description by Jaffe-Witten.
The unknown theory.
This shows that despite the more than 40 years since Velo-Wightman 76, we may still be pretty much at the beginning of understanding the true conceptual nature of pQFT. There are various further hints that this is the case:
The available techniques for quantizing gauge theory in pQFT disregard the global topological sectors of the gauge field (instantons, argued to be crucial for the true vacuum of QCD). It follows on general grounds (Schreiber 14, Schenkel 14) that if these are to be included, then the space of local qantum observables can no longer be an ordinary algebra, but must become a “homotopical algebra” of sorts (“higher structure“). The principles of such “homotopical AQFT” are being explored (Benini-Schenkel 16, Benini-Schenkel-Schreiber 17), for review see Schenkel 17, but much remains to be done here.
Given that gauge theories and their instanton sectors are not some fringe topic in pQFT, but concern the core of the key application, the standard model of particle physics, much of the development of the theory may still lie ahead. And this is only pQFT. When this is finally really understood, mankind needs to look into non-perturbative QFT. Given the wealth of mathematical subtleties involved, this will only work with a conceptually clean rigorous formulation of the theory at hand. The following articles in this series will be an introduction to the the clean rigorous formulation of pQFT, as far as understood so far, in the guise of locally covariant perturbative AQFT.
This series on QFT continues here:
A first idea of Quantum Field Theory.
108 replies
1. protonsarecool says:
As someone who has only learned QFT via the path integral approach so far (and mostly with applications in condensed matter theory in mind), all this is crazily interesting, and i look forward to the rest of this series!
2. vanhees71 says:
That's a great article, I've to study in closer detail later. I only wonder, why you only quoate QED, QCD, and quantum gravity but not the full Standard Model, including weak interactions, i.e., quantum flavor dynamics (aka Glashow-Salam-Weinberg model of the electroweak interaction) ##otimes## QCD.
3. dextercioby says:
Great work (to come), Urs!
Well, once you're done writing it (all articles), I will go print it and store it in my physical library.
4. Urs Schreiber says:
vanhees71
I only wonder, why you only quote QED, QCD, and quantum gravity but not the full Standard Model, including weak interactions, i.e., quantum flavor dynamics (aka Glashow-Salam-Weinberg model of the electroweak interaction) ##otimes## QCD.
True, I should mention electroweak theory, too, have edited the entry a little to reflect this. (It will take a bit until I get to these applications, I will first consider laying some groundwork.)
Great job Urs, looking forward to the next one!
6. Haelfix says:
Nice article. How much of causal perturbation theory has been shown to match SM physics/ordinary qft? When I looked at this (admittedly many years ago), people had successfully constructed the scalar field and there was work being done on spin 1/2, and some sketchy and complicated proof of concepts, but has it really been shown to be completely isomorphic? One step further, do all the successes of causal perturbation theory match on to the new covariant algebraic qft?
My impressions at the time was that this was a little bit like the theory of distributions vs Dirac's delta function formalism. The former is rigorous and nice, but just clutters up notation when you sit down to calculate things.
7. Urs Schreiber says:
Haelfix
How much of causal perturbation theory has been shown to match SM physics/ordinary qft?
It's true that the literature on this topic is still comparatively small, but everything comes out:
Scharf's two books cover much standard basic material of QED, EW, QCD and pQG.
Feynman diagrammatics and dimensional regularization was realized in in Keller 10, Dütsch-Fredenhagen-Keller-Rejzner 14. (These authors speak in terms of scalar fields, but, as with Epstein-Glaser's original article, this is a notational convenience, the generalization is immediate.)
BV-BRST methods were realized in Fredenhagen-Rejner 11b.
Haelfix
One step further, do all the successes of causal perturbation theory match on to the new covariant algebraic qft?
Yes, that starts with Brunetti-Fredenhagen 00, Hollands-Wald 01 and culminates in the construction of renormalized Yang-Mills on curved spacetimes in Hollands 07.
Haelfix
My impressions at the time was that this was a little bit like the theory of distributions vs Dirac's delta function formalism. The former is rigorous and nice, but just clutters up notation when you sit down to calculate things.
Sure, once the dust of the theory has settled we want to compute leisurely, but we do want to understand what it is our computations are doing. Distribution theory is a good example for how it pays to spend a moment on sorting out the theoretical underpinning before doing computation. Causal perturbation theory shows that all that used to be mysterious about divergencies in pQFT is clarified by microlocal analysis of distributions: Properly treating the product of distributions with attention to their wave front set is what defines the normal-order product of free fields, and then properly treating the extension of distributions to coinciding interaction points is what defines the renormalized time-ordered products. That gives a solid background explaining what's actually going on in the theory. Not every kind of computation will be affected by this, but given that there remain open theoretical questions in pQFT, it will help to have the foundations sorted out.
8. A. Neumaier says:
Note that there is already an insight article on causal perturbation theory complementing the present one.
Your point 2 for causal perturabtion theory (finitely many free constants) holds of course only for renormalizable theories. Scharf also constructs (low order) perturbative gravity in the causal framework, but there the number of free constants proliferates with the order. (Mathematically, this is not a problem since the same happens for multivariate power series, but physicists used to think of this as non-renormalizability.)
9. A. Neumaier says:
You stated in the article, ''perturbative AQFT in addition elegantly deals with the would-be “IR-divergencies” in pQFT by organizing the system of spacetime localized quantum observables into a local net of observables.''
I don't agree. The infrared problem remains unsolved in perturbative AQFT. You haven't even given a link to a reference where your claim would be addressed.
10. bhobba says:
As I said elsewhere, stunning, simply stunning and I have never said that about an insights article before.
I look forward to the whole series.
Note to those that like me do not understand all the mathematical detail. Of course try to correct that, but still read it and try to get a feel for the issues at the frontiers of current physics.
Feel free if interested to start a thread on, what for example, an instanton sea is, don't know that one myself – much food for thought here.
Thanks
Bill
11. Urs Schreiber says:
Sorry for the slow replies, I am seeing the further comments only now for some reason.
A. Neumaier
Note that there is already an insight article on causal perturbation theory complementing the present one.
Right, sorry, I should have pointed to that. I do have pointers to your FAQ on the nLab here .
A. Neumaier
Your point 2 for causal perturabtion theory (finitely many free constants) holds of course only for renormalizable theories.
I was careful to write "at each order there is a finite-dimensional space of choices" (emphasis added).
As you hint at, this is an important subtlety that is usually glossed over in public discussion: At each order of perturbation theory, there is a finite dimensional space of counter-terms to be fixed. As the order increases, the total number of counterterms may grow without bound, and then people say the theory is "non-renormalizable". But this is misleading terminology: The theory is still renormalizable in the sense that one may choose all counterterms consistently, even f there are infinitely many. What the traditional use of "non-renormalizable" really means to convey is some idea of predictivity: The usual argument is that if there is an infinite number of terms to be chosen, then the theory is not predictive. Of course a moment of reflection shows that it is not quite that black-and-white. The true answer is popular under the term "effective field theory": If we specify the counterterms up to a fixed oder (and there are only finitely many of these for any order) then the remaining observables of the theory are its predictions up to that order . As more fine-grained experimental input comes in, we can possibly determine counterterms to the next order by experiment, and then again the remaining observables of the theory are its predictions up to that next higher order. And so ever on.
12. Urs Schreiber says:
A. Neumaier
You stated in the article, ''perturbative AQFT in addition elegantly deals with the would-be “IR-divergencies” in pQFT by organizing the system of spacetime localized quantum observables into a local net of observables.''
I don't agree. The infrared problem remains unsolved in perturbative AQFT. You haven't even given a link to a reference where your claim would be addressed.
I believe I did provide a pointer, to the section here , but I could have emphasized this further. This will be the topic of the next (or next to next) installment.
What you are referring to, and what remains unsolved in generality, is taking the adiabatic limit of the coupling constant. But the insight of pAQFT is that this limit need not even be taken in order to obtain a well defined (perturbative) quantum field theory!
Namely the observation is that
1. the algebra of quantum observables localized in any spacetime region may be computed, up to canonical isomorphism, already with any adiabatic switching function that is constant on a neighbourhood of that region of support
2. as the region of support varies arbitrarily, the system of algebras of localized quantum observables obtained this way do form a causally local net in the sense of the Haag-Kastler axioms (this prop, the only difference to the original axioms being that here they are formal power series algebras instead of C-star algebra, reflecting the perturbation theory)
3. AQFT lore implies that this causally local net of observables is sufficient to fully define the quantum field theory.
4. ibut f desired, we may still take the limit now, not of the S-matrix, but of the local net of observables it induces, in the sense of limits over the functor assigning observable algebras. In the pAQFT literature they call this the "algebraic adiabatic limit" or similar. It may be used to construct operator representations of the quantum observables, but the main point of pAQFT is really that by and large it is not actually necessary to consider this.
13. Urs Schreiber says:
A. Neumaier
Could you please make a printable version of your slides https://ncatlab.org/schreiber/files/SchreiberTrento14.pdf, with the repetitions removed? (This is just an additional line in the latex before compilation.)
Ah, I didn't code this with the "beamer" package, but "by hand". Is there a tool that could extract from the pdf just those pages that have the screen completed, and put these together to a smaller file? Sorry for the trouble
A. Neumaier
The link (web) to Schenkel in the nlab article https://ncatlab.org/schreiber/show/Higher+field+bundles+for+gauge+fields is not working.
Thanks for the alert! I have fixed it now. The working link is here:
I recommend also Alexander's more recent exposition:
• Alexander Schenkel, "Towards homotopical AQFT" (web , pdf)
14. Urs Schreiber says:
atyy
How are pQFT and pAQFT related to lattice gauge theory? Would you accept lattice gauge theory, at least Hamiltonian lattice gauge theory, as a non-perturbative and physically relevant version of QED?
Sure, I was briefly referring to this in the paragraph starting with "Hence we will eventually need to understand non-perturbative quantum field theory."
I suppose the point is that Monte-Carlo evaluation of lattice gauge theory is more like computer–simulated experiment than like theory. It allows us to "see" various effects, such as confinement, but it still does not "explain" them in the sense that we could derive these effects structurally.
Another problem is that lattice gauge theory relies on Wick rotation, so it does not help with pQFT on general curved spacetimes.
atyy
Also, why do you say the path integral doesn't exist? At least in 2D and 3D, doesn't constructive field theory, which you mention at the end, show that the path integral exists?
Yes, that's what I meant by "toy examples" where I wrote "There is no known way to make sense of this integral, apart from toy examples"
Now of course it may be unfair to refer as a "toy example" to all the great effort that went into "constructive QFT". Mathematically it is a highly sophisticated achievement. But it remains a matter of fact that as far as the physical problem description is concerned, the real thing is interacting Lorentzian QFT in dimensions four or larger.
I should be careful with saying "the path integral does not exist in general", because there is no proof besides experience, that it does not. Maybe at one point people can make sense of it. But even so, it seems to me that the results of "constructive QFT" show one thing: even if one can finally make sense of the path integral, it does not seem all too useful. Very little followup results seem to have come out of the construction of interacting scalar field theory in 3d via a rigorous Euclidean path integral. If we follow the tao of mathematics, the path integral just does not seem to be the right perspective. Or so I think.
15. Urs Schreiber says:
bhobba
Note to those that like me do not understand all the mathematical detail. Of course try to correct that, but still read it and try to get a feel for the issues at the frontiers of current physics.
That's the right attitude! Learning by osmosis.
And by asking questions! Feel invited to ask the most basic questions that come to mind.
16. jordi says:
Very interesting. I subscribe to this thread. Thank you very much for sharing, Urs.
17. A. Neumaier says:
Urs Schreiber
The usual argument is that if there is an infinite number of terms to be chosen, then the theory is not predictive.
Yes. And as you hint at, this is a totally unfounded argument. In an asymptotic power series in two variables there are an infinite number of terms to be chosen (at each order a growing number more), but nobody concludes that therefore power series at low order are not predictive. They are highly predictive as long as one is in the range of validity of the asymptotic expansion at this order (i.e., typically as long as the first neglected order contributes very little).
Of course, for gravity at the Planck scale (and for QCD at low energies, etc.) one expects that one is outside this domain, so that the value of the expansion becomes questionable at each order. Thus a perturbative theory is in many respects not a substitute for a nonperturbative version of the theory.
18. A. Neumaier says:
Urs Schreiber
I believe I did provide a pointer, to the section here , […]
What you are referring to, and what remains unsolved in generality, is taking the adiabatic limit of the coupling constant.
The former only shows how to construct approximate observables at each order – This has nothing to do with the infrared limit. The latter is precisely the adiabatic limit. It is there (and only there) where the particle content of the theory (and hence issues such as confinement) would appear. For example, in QCD, the perturbative theory is in terms of quarks, but the infrared completed theory has no quarks (due to confinement) but only hadrons.
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# Is the CDF of the Mean always 0.5 for all kind of distributions?
Can we say that the value of the cumulative distribution function at the mean F(X< Mean) is always 0.5 for all kind of distributions (even ones that are not symmetric)?
No, this is false. That point is the median, and it is not equal to the mean in all cases, for example, an exponential distribution.
$$X\sim \exp(1)\\ \mathbb E[X]=1\\ \operatorname{median}(X)=\log 2\approx 0.69$$
We can simulate this in software, such as R.
set.seed(2021)
X <- rexp(10000, 1)
mean(X) # approximately 1
median(X) # approximately 0.69
EDIT
The asymmetric Laplace distribution is an example where the distribution extends over the entire real line, not just the positive numbers. (In more technical language, the PDF has support on all of $$\mathbb R$$.)
• Funny we came up with the same distribution for a counterexample! Jan 19 at 10:28
• sir, it's currently 2022 Feb 12 at 4:16
The mean is the point where the area left and right between the CDF and the vertical line through the mean are equal.
For symmetric distributions, the left and the right side/area have the same shape and you get that the mean is at the point where the CDF is equal to 0.5 (also the median).
For non-symmetric distributions the shapes are different, so this equality of area does not need to be true (obviously it can be equal, but it does not need to be equal).
For any distribution where the mean and median is different, you have that the CDF of the mean is not 0.5.
An example is a non-central t-distribution which is plotted below.
• So, if $\mu = E[X]$ and $F$ is continuous, we have $\int_{-\infty}^\mu F(t)dt = \int_{\mu}^\infty (1-F(t))dt$?. Do you have a quick reference? I do not remember this result. Jan 19 at 12:01
• I do not know a direct statement of $\int_{-\infty}^\mu F(t)dt = \int_{\mu}^\infty (1-F(t))dt$ I view it intuitively as integrating the quantile function $E[X] = \int_0^1 Q_X(p) dp$ or this expression Jan 19 at 12:06
• It follows from$$\int_{-\infty}^\mu F(t)\text dt=\mu F(\mu)-\int_{-\infty}^\mu t \text dF(t)$$and$$\int^{\infty}_\mu (1-F(t))\text dt=-\mu +\mu F(\mu)+\int^{\infty}_\mu t \text dF(t)=\mu F(\mu)-\int_{-\infty}^\mu t \text dF(t)$$ Jan 19 at 12:08
• @Xi'an very clean, thank you! Jan 19 at 12:27
• @Lucas We have $$E[X] = \int_0^1 Q_X(p) dp$$ and we can change this like the following which is considering the integral of the quantile function with a shift, which is like the area between $F(x)$ and the vertical line through $E[X]$ $$0 = \int_0^1 Q_X(p)-E[X] dp$$ or $$\underbrace{\int_0^m Q_X(p)-E[X] dp}_{\text{negative of area leftside}} + \underbrace{\int_m^1 Q_X(p)-E[X] dp}_{area rightside}$$ where $m$ is the quantile of the expectation value. Jan 19 at 12:29
As others have said, no. In fact, it can be any number in $$(0, 1$$).
Let $$\epsilon \, \in \, (0,1)$$, consider the random variable $$X$$ such that $$\mathbb{P}(X = -1) = \epsilon$$ and $$\mathbb{P}(X = \frac{\epsilon}{1-\epsilon}) = 1 - \epsilon$$. The mean is
$$E[X] = -\epsilon + (1-\epsilon)\frac{\epsilon}{1-\epsilon} = 0 \quad,$$
and $$F(0) = \epsilon$$.
As observed in the comments, $$1$$ can also be attained by the CDF if we consider a constant random variable.
• The point 1 is also included if you consider degenerate distributions (eg. constants). Jan 19 at 11:17
No.
A counterexample will be $$X \sim Exp(1)$$. The mean of $$X$$ is 1, and $$P(X < 1)$$ is $$1 - 1/e$$, around 0.63.
• This hurts my brain. I get that the math checks out but it's not very intuitive. Apr 27 at 15:42
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# [dev-context] \getbufferparagraphs
Hans Hagen pragma at wxs.nl
Thu Jan 3 18:43:12 CET 2013
```On 1/3/2013 5:23 PM, Wolfgang Schuster wrote:
>
> Am 31.12.2012 um 19:28 schrieb Hans Hagen <pragma at wxs.nl>:
>
>> On 12/30/2012 11:41 AM, Wolfgang Schuster wrote:
>>> Hi Hans,
>>>
>>> do you plan to add the \getbufferparagraphs command to MkIV or is it marked obsolete?
>>
>> if needed i can do that (not much work) but i need to figure out the specs -)
>
> I don’t need it, I was only interested what’s the purpose of the command and how it works (not so hard after reading the source).
we were typesetting examns where there is a large text and students have
to answer questions about a specific paragraph so that one was repeated
with the question (so: filtering, keeping line numbers right, etc)
Hans
-----------------------------------------------------------------
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# What is the physics interpretation of work done of zero when moving a charged particle on an equipotential surface?
Assume I have a test charge of + 1 coulomb.
• If I move the test charge from a point with potential of +9 volt to another point with potential of -1 volt then the work done by me is -10 joule. This negative numbers means I actually do not need to do such a work because the test charge can move automatically.
• If I move the test charge from a point with potential of -9 volt to another point with potential of +1 volt then the work done by me is +10 joule. This positive numbers means I actually do need to do such a work because the test charge cannot move automatically.
# Question
• If I move the test charge from a point with potential of $$v$$ volt to another point with the same potential of $$v$$ volt then the work done by me is 0 joule. What does this zero mean physically?
• It means that the change in the kinetic energy of the charge is zero. – Farcher Sep 4 at 7:40
• @Farcher: I assume for all cases I mentioned above, the change in kinetic energy is kept zero. – Money Oriented Programmer Sep 4 at 7:42
• If "you" are moving a charge along an equipotential at constant speed, you don't have to exert a force along the direction of motion (i.e. along the equipotential) to keep the charge moving, just like a marble rolling along a horizontal track would continue to roll (absent friction)). However, you will be exerting forces perpendicular to the equipotential in order to both counteract the electric forces on the charged particle that also act perpendicular to the equipotential and to "counteract the inertia" of the charged particle that makes it want to move in a straight line. – march Sep 4 at 16:05
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# Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks
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### Abstract
Understanding human motion behavior is critical for autonomous moving platforms (like self-driving cars and social robots) if they are to navigate human-centric environments. This is challenging because human motion is inherently multimodal: given a history of human motion paths, there are many socially plausible ways that people could move in the future. We tackle this problem by combining tools from sequence prediction and generative adversarial networks: a recurrent sequence-to-sequence model observes motion histories and predicts future behavior, using a novel pooling mechanism to aggregate information across people. We predict socially plausible futures by training adversarially against a recurrent discriminator, and encourage diverse predictions with a novel variety loss. Through experiments on several datasets we demonstrate that our approach outperforms prior work in terms of accuracy, variety, collision avoidance, and computational complexity.
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### Show and tell: A neural image caption generator
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### Social Force Model for Pedestrian Dynamics
(1998)
It is suggested that the motion of pedestrians can be described as if they would be subject to social forces'. These forces' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal motivations of the individuals to perform certain actions (movements). The corresponding force concept is discussed in more detail and can be also applied to the description of other behaviors. In the presented model of pedestrian behavior several force terms are essential: First, a term describing the acceleration towards the desired velocity of motion. Second, terms reflecting that a pedestrian keeps a certain distance to other pedestrians and borders. Third, a term modeling attractive effects. The resulting equations of motion are nonlinearly coupled Langevin equations. Computer simulations of crowds of interacting pedestrians show that the social force model is capable of describing the self-organization of several observed collective effects of pedestrian behavior very realistically.
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### Social LSTM: Human Trajectory Prediction in Crowded Spaces
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Main The joy of TEX: a gourmet guide to typesetting with the AMS-TEX macro package
# The joy of TEX: a gourmet guide to typesetting with the AMS-TEX macro package
The Joy of TeX is the user-friendly guide to AMSTeX, a software package based on the computer typesetting language TeX. AMSTeX was designed to simplify typesetting of mathematical quantities, equations, and displays, and to format the output according to any of various preset style specifications. This second edition of Joy reflects the changes introduced on Version 2.0 of the AMSTeX macro package. The first two parts of the manual, "Starters" and "Main Courses", teach the reader how to typeset the kind of text and mathematics one ordinarily encounters. "Sauces and Pickles", the third section, treats more exotic problems and includes a 60-page dictionary of special TeXniques. The manual also includes descriptions of conventions of mathematical typography to help the novice technical typist. Appendices list handy summaries of frequently used and more esoteric symbols. This manual is useful for technical typists as well as scientists who prepare their own manuscripts. For the novice, exercises sprinkled generously throughout each chapter encourage the reader to sit down at a terminal and learn through experimentation.
Year: 1990
Edition: 2nd ed
Language: english
Pages: 318
ISBN 10: 0821829971
ISBN 13: 9780821829974
File: DJVU, 1.92 MB
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### A Comprehensive Introduction to Differential Geometry, Vol. 3, 3rd Edition
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### Mathematics into type
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### Einfuehrung in TeX
Year: 1991
Language: german
File: PDF, 1.45 MB
Second Edition A Gourmet Guide toTypesetting with the AmS-T^X macro package
Gourmet Guide toTypesetting with the 4mS-TeX macro package M. D. SPIVAK, Ph.D. American Mathematical Society Providence, Rhode Island
TgX and A\>tS-T& are trademarks of the American Mathematical Society. Library of Congress Cataloging-in-Publication Data Spivak, Michael David. The joy of TeX, second ed.: a gourmet guide to typesetting with the AMS-TeX macro package / M.D. Spivak. p. cm. 1. TeX (Computer system) 2. Mathematics printing. 3. Computerized typesetting. I. Title. Z253.4.T47S673 1990 90-1082 686.2' 25445369—dc20 CIP ISBN 0-8218-2997-1 (alk. paper) Copyright © 1990 by the American Mathematical Society. All rights reserved. Previous editions copyright © 1982, 1983, 1986 by the American Mathematical Society. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the American Mathematical Society. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. @ Printed in the United States of America. 10 9 8 7 6 5 4 3 2 95 94 93 92 91
CONTENTS Preface ix Acknowledgments xi, xiii Personal Pronoun Pronouncement xv Introduction. On Advanced Typesetting xvii Part 1. Starters 1 0. Getting Acquainted; A Key Chapter 3 Keys available on the keyboard 1. Learning T^X's Lingo 6 Ordinary text and control sequences 2. Printers Do It With All Types 15 Changing fonts 3. Your First IfeX Experience 20 Running a file through T^jX 4. TfeX's Erroneous Zones 27 Error messages, and how to respond to them 5. Spaces That Separate, Ties That Bind 32 Subtleties of spacing and line breaking 6. Doing It With Elan 34 Special symbols and accents Part 2. Main Courses 41 7. T^K's Brand Of Mathematics 43 Mathematical formulas m text 8. Lousy Breaks? Try An Artful Display 53 Displayed formulas 9. The 2nd Level Of Complexity 58 Superscripts and subscripts vii
viii Contents 10. Our Problems Mount 66 Fractions, binomial coefficients, etc. 11. Benefitting From TfeX's Largess 72 52, J and other "large operators" 12. Creating Your Own Space 77 Controlling spacing in mathematical formulas 13. Fascinating Things That Expand By Themselves 79 Delimiters and other variable size symbols 14. A. Roman Orgy SS Roman type in formulas 15. Keeping Them In Line 97 Numbering formulas and aligning equations in a display 16. Too Much Of A Good Thing 103 Breaking formulas that are too long 17. Sophisticated Positions 108 Matrices Part 3. Sauces & Pickles 114 18. Practicing Self Control 115 Defining new control sequences 19. E^-Rated Features 129 A dictionary of special TfeXniques Appendices 191 A. The AMS Preprint Style 193 B . Answers To All The Exercises 210 C. Bibliographies 260 D. Comparison With 'plain' TfeX 265 E. Deficient Keyboards 269 F . Esoteric Symbols 270 G. Further Fonts 274 H. {TfeX Users} 281 I . Help 282 Index 283
Preface to the Second Edition The Joy of 1$C is the manual for .4^5-TeX, an extension of TfjX, Donald Knuth's revolutionary program for typesetting technical material. ^VfS-TgX was designed to simplify the input of mathematical material in particular and to format the output according to any of various preset style specifications. This manual is useful both for the technical typist and for scientists preparing their own manuscripts. Exercises sprinkled generously through each chapter encourage the reader to sit down at a terminal and learn through experimentation. The first two parts of the manual "Starters" and "Main Courses," teach the reader how to typeset most normally encountered text and mathematics. "Sauces and Pickles," the third section, treats more exotic problems and includes a 60-page dictionary of special TgXniques. Scientists and experienced technical typists will readily appreciate that ^VfrS-TgX gives them easy control over the appearance of a page of technical copy. Descriptions of the conventions of mathematical typography will help the novice technical typist. Appendices list handy summaries of frequently used and more esoteric symbols, as well as answers to the exercises. This second printing of the second edition of Joy has been updated to reflect the changes introduced in Version 2.1 of the ^VfrS-TgX macro package. In Version 2.0 Dr. Spivak made many of the error and help messages clearer, and many bugs that surfaced in special cases were eliminated. He made refinements in some of the macros and changes to conserve memory space. In addition, he made access to fonts other than those defined in plain TgX easier. At the same time that Dr. Spivak was making all the technical changes in ■4m«!>-TeX, the Society's Technical Support Staff made extensive changes in the .4M<S-TeX's preprint style to allow for many optional formatting features and provide users much greater flexibility. Among the new features are styles for books, in addition to journal articles, running heads, alternate page sizes, and tables of contents. In the first edition of Joy, many of the preprint features were explained in Chapter 7. In this edition Chapter 7 has been moved to Appendix A. The Technical Support Staff has revised Appendix A so that it now serves as a complete guide to all the options available in the Version 2.1 preprint style. American Mathematical Society October 1991 ix Acknowledgments for the First Edition At about the time that I first started eyeing computers with anything less than malevolence, my friend Richard Palais was enthusiastically investigating a new computer typesetting program that he had heard about as a member of the AMS Committee on Composition Technology. He suggested that I learn something about this system and then describe it in a little manual, one that would be oriented toward the naive user, of which I was so perfect a specimen. Accordingly, we repaired to Stanford, where we were joined by Barbara Beeton, Robert Morris and Rilla Thedford for a projected two-week project. That was six years ago. Now that the official first edition of this manual is finally appearing, numerous other people may also be named as accomplices before the fact. The initial stages of the project would have been impossible without the help of all the people at the AMS, including Barbara Beeton, Sam Whidden, and Ray Goucher. I am extremely grateful to David Fuchs, John Hobby, Arthur Keller and Joe Weening for allowing me to pester them about arcane matters during a five-week stay at Stanford in 1983, and to Leslie Lamport for discussions about I&TeX. Michael Harrison graciously helped me work on the project at U. C. Berkeley in the summer of 1984. In the end, all this shuffling from university to university began to take its toll, and it is doubtful whether the project would have been completed in its present form had I not been able to use PC TfjX, from Personal TeX, Inc., on my own personal computer. Above all, however, I cannot express too much gratitude to Donald E. Knuth, the author of TgX, for his interest in the AMS macro project, for the help that he has extended to me, and most especially for this wonderful gift that he has given the world. Michael D. Spivak xi Acknowledgments for the Second Edition The efforts of several individuals made the Second Edition of The Joy of T£JK possible. We wish to thank Michael Spivak for his work on the A\^S-T&. macros, which are now being used for all technical AMS publications. We also wish to acknowledge the efforts of the Society's Technical Support Group—Ralph Youngen (Supervisor), Michael Downes, Janene Winter, Barbara Beeton, Julie Pomroy, and Neil Bartholomew—for their work on the revision of the preprint style (amsppt) and on the rewrite of Joy, especially Appendix A. American Mathematical Society xiii Personal Pronoun Pronouncement Which The Reader Skips At His or Her Peril Since T£X is a rather revolutionary approach to typesetting, I decided that a rather revolutionary approach to non-Sexist terminology would be appropriate in this manual. I myself am completely unprejudiced, of course. As Mark Twain said, or should have said: All I care to know is that a man or woman is a human being—that is enough for me; he or she can't be any worse. But I hate having to say "he or she" or "his or her" or using awkward circumlocutions. Numerous approaches to this problem have been suggested, but one strikes me as particularly simple and sensible. Just as T is the first person singular pronoun, regardless of gender, so 'E' will be used in this book as the third person singular pronoun for both genders. Thus, 'E' is the singular of 'they'. Accordingly, 'Eir' (pronounced to rhyme with 'their') will be the possessive, and 'Em' (rhyming with 'them') will stand for either 'him' or 'her'. Here is an example that illustrates all three forms: E loves Em only for Eir body. •Exercise PPP.l1 How many possible meanings does this sentence have? 1 Answers to all the Exercises will be found in Appendix B. XV Introduction On Advanced Typesetting The title of this book is a little deceptive. It might give you wrong ideas about the pronunciation of TeX, which actually stands for the Greek letters TAU EPSILON CHI; according to its creator, Donald E. Knuth, insiders pronounce TeX so that it rhymes with blecchhh. TgjX is thus an upper-case, or capital letter, form of rex, the beginning of the Greek word that means art, a word that is also the root of English terms like technology. This name emphasizes two basic features of TeX: it is a computer system for typesetting technical text, especially text containing a lot of mathematics-, and it is a system for producing beautiful text, comparable to the work of the finest printers. TgX's official name implicitly advertises another of its advantages: traditional typesetters would have to cast a special piece of type to get the "TeX" logo, but TgX can print its own name simply by moving letters down a little and backing up a bit. On your computer terminal, where such shenanigans aren't possible, the standard way of referring to TeX is by typing 'TeX'. This helps to distinguish TfiX from various other computer programs that are named TEX (and prosaically pronounced that way). In addition to all of TfeX's capabilities, one other feature of the system needs to be emphasized: TeX allows you to do all of these things easiJy. In fact, this is a manual for someone who knows nothing about computers, written by someone who knows nothing about computers. Actually, that last statement isn't quite true: the one thing we assume is that you already know how to use a "text editor" to create a file on your computer. Nothing about typesetting itself is assumed, although a few printers' terms will be introduced along the way. You can remain blissfully ignorant of the complicated rules that typesetters have developed for the proper setting of mathematics formulas—TeX knows them all. Nor is any knowledge of mathematics required. But you will still need to have a general idea of what printed mathematics ought to look like. Mathematicians and experienced technical typists—who already know this—will find that TeX allows them to specify mathematics formulas with less effort than before, yet with greater control over the finished product. Novice technical typists have a dual task: learning what mathematicians want, and learning how to get TeX to produce it. This manual will tell you all about the second, and give you as much help as possible with the first. In order to get some idea just how TeX works, we will examine a recent paper from a non-existent journal that was typeset by TeX. xvii Discourses in the Obvious By the Obnoxious Volume 43 (2001) What Every Young Mathematician Should Know BY LORD K. ELVIN Abstract. We evaluate an interesting definite integral. The purpose of this paper is to call attention to a result of which many mathematicians seem to be ignorant. Theorem. The value of f°° e~x dx is JOO ^00 /•00 /00 e~x2dx = y/n. -00 Proof: We have 2 r°° r°° _ 2 _ 2 = I I e x e y dxdy by Fubini J—00 J—00 /00 i>00 / e^x+^dxdy ■00 J—00 = / / e~T rdrdO using polar coordinates Jo Jo f2* T f°° _ a - /"2ir Lfiii r=o° JO I 2 |r=0 dO dO = IT. Remark: A mathematician is one to whom that is as obvious as that twice two makes four is to you. Institute For Haughty Attitudes. Received by the editors April 1, 2000. Research supported in part by the National Foundation. ©2001 Ameripean Mathephysical Bunch 0011-8785/01 11.30 + 1.65 per page 1 Introduction. On Advanced Typesetting xix The author first wrote this paper by hand, and then, being a lazy fellow himself, gave it to a technical typist to produce a computer file. Parts of this file are shown below, in a style of type that will always be used to indicate input typed on a terminal, as opposed to the output TfjX will produce, or the contents of this manual itself. Don't worry if your keyboard lacks some of these symbols—TfjX has a way of getting around this. \title What Every Young Mathematician Should Know\endtitle \author Lord K. Elvin\endauthor The purpose of this paper is to call attention to a result of which many mathematicians seem to be ignorant. \proclaim{Theorem} The value of$\int_{-\infty}"\infty e"{-x"2}\,dxis $$\int_{-\infty}~\infty e"{-x~2}\,dx= \sqrt\pi.$$ We have \align \left( \int_{-\infty}"\infty e"{-x"2}\,dx \right)"2 &=\left( \int_{-\infty}"\infty e"{-x"2}\,dx \right) \left( \int_{-\infty}"\infty e-{-y~2}\,dy \right) \\ &=\int_{-\infty}-\infty \int_{-\infty}"\infty e-{-x-2}e*{-y"2}\,dx\,dy Even a cursory examination of this file gives some idea how T£X is used. For example, all of the English words that appear in the article are embedded somewhere in the file, while specifications for formulas are set off either by signs (when the formula is set within text), or by signs (when it is displayed). In addition to the English words and the letters in formulas, there are lots of cryptic combinations, called controJ sequences, which begin with the "backslash" \. Some control sequences are the names of special symbols; for example, \int stands for the "integral sign" / in the expression J_00, while \pi stands for the Greek letter n (pi). Other control sequences, like \title, \author and \proclaim, are more complicated, and tell TgX how to process the input that follows. Once this file was produced, a few simple instructions told TgX to set the paper in a style suitable for preprints, on a printer that quickly and cheaply produces output suitable for proofreading, though a little blurry: WHAT EVERY YOUNG MATHEMATICIAN SHOULD KNOW Lord K. Elvin April 1, 2000 ABSTRACT. We evaluate an interesting definite integral. The purpose of this paper is to call attention to a result of which many mathematicians seem to be ignorant. Theorem. The value of f°° e~x''dx is JOO /oo e~x dx = y/n. -oo Proof. We have (£«-*)■-(/>-■-■)(/:-■*) f°° f°° _ 2 a = I I e x e~y dxdy by Fubini J—oo J—oo /OO fOO -oo J—oo [2* f°° _ ' = I I e r rdrdO using polar coordinates Jo jo = r L— r=o°l (16 = n. Remark. A mathematician is one to whom that is as obvious as that twice two makes four is to you. Institute For Haughty Attitudes Research supported in part by the National Foundation. Typeset by AM&-T&- 1 Introduction. On Advanced Typesetting xxi Once satisfied with the reactions to his preprint, the author submitted the paper to the journal (all he had to do was send them the original computer file). The journal made a single change in the file that caused IfeX to typeset the paper in the journal's style, this time on a high-resolution printing device that produces "camera copy" suitable for printing.1 Had the journal rejected the paper, the author could have sent it (that is, the computer file) to another journal, which could typeset it in their style, again by changing just one line. As you can see, TfjX appears to be awfully knowledgeable! Actually, the system we have been describing is a specialized version of TfjX, known as A\^S-T&.. It has been developed by the American Mathematical Society as a particularly simple system for printing papers in a preprint style, or in the style of any journal (with a little extra work it can also be used to typeset entire books). The present manual is devoted entirely to the specialized system Aj^fS-T&., although we will often refer to it familiarly as IfeX, and adopt the more formal name only when we want to mention a feature of T£X that is peculiar to AMS-Tg^i.. Despite its specialized nature, .4mS-TeX will do almost anything that a mathematician will ever need. Parts 1 and 2 of this manual explain how to typeset almost all the mathematics you will normally encounter; Part 3, which you can peruse at your leisure, describes ^VfrS-TfjX's abilities to handle more exotic typesetting problems. Parts 1 and 2 also contain occasional digressions into more specialized material; these side-trips are set in separate paragraphs that begin with the road-sign Parts 1 and 2 of this manual occupy over 100 pages, but you needn't fear that ■4m«S-TeX is particularly complicated, or difficult to learn. In order to make this new experience with typesetting more pleasurable, the introduction has purposely been made easy-going rather than concise. Moreover, the exposition— such as it is—has been supplemented by numerous Exercises, interspersed with many examples of what the author seems to think are jokes, along with puns, innuendos, and other fossil evidence of literary low-life. You can skip any jokes you are unfortunate enough to notice, but piease don't skip the Exercises! Answers to all the Exercises are given in Appendix B, and they often mention little 'Nowadays nearly all printing is done by photo-offset—the ink adheres to a thin piece of metal that has been chemically treated by a photographic process. Until the advent of computer-run photo-typesetting processes, these plates were made by first setting metal type and printing one copy, which was used for the photographic process—and then destroying the original type!
xxii Introduction. On Advanced Typesetting details that didn't seem to fit in comfortably anywhere else, but it is strongly recommended that you first try all the Exercises yourself—that way you'll learn far more effectively than by reading passively. When you have finished all the Exercises, you may consider yourself an accomplished .4m<S-TeX user. Then you might be interested in learning more about TgX itself.1 Aj^S-T^i. is just a specialized version of TfeX, but once you have mastered it you will have joined the TEXnical revolution. '■Everything about TeX is explained in The T^XbooJc, by Donald E. Knuth, published jointly by the American Mathematical Society and Addison-Wesley Publishing Company.
1 Starters the basic ingredients
Chapter 0. Getting Acquainted; A Key Chapter Before we start learning about TfeX's approach to typesetting, it's a good idea to take a look at the keyboard of your terminal, to see which symbols are already available there. Many terminals have additional special keys, but at least the following symbols should all appear—exceptions are discussed below. First we have the upper- and lower-case letters, and the numerals: ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789 You're probably already aware of the fact that the numeral 1 has to be distinguished from the lower-case letter 1, and that the numeral 0 has to be distinguished from the upper-case letter 0. On the screen 0 and 0 may look almost the same, but on the keyboard the numeral 0 will be close to the other numerals. Next we have the symbols >•>•■■ ' (apostrophe or single right quote) ' (single left quote) ( ) [ ] I (slash) - (hyphen) * (asterisk) which are used for punctuation, for writing numbers like 1,376.0003, for hyphenation and/or word-building, and for parenthetical remarks [possibly in brackets instead of parentheses]; on most fonts the asterisk prints high* to serve as an indicator for footnotes. On your keyboard and screen, the quote marks ' and ' might appear in the less aesthetically pleasing forms ' and '. Don't feel deprived— T^jX will still set them the right way. All terminals also have a double quote mark " (or "), but it hasn't been listed in this group because T^jX has its own method for producing double quote marks. Notice that the hyphen - shouldn't be confused with another key that appears on most keyboards, _ (underscore or underline). *Like this. 3
4 Chapter 0. Getting Acquainted; A Key Chapter Next come the few standard keyboard characters that will be used in mathematical formulas: A- — <. > I The symbol I may appear broken, as ',, but TgX will always set it solid. IfeX has control sequences to name all the other mathematical symbols, including letters from foreign alphabets. Of course, English letters and numerals are also used in mathematics formulas, and most of the punctuation symbols are used as well. For example, I is used in fractions like a/b, and the hyphen will be used for the minus sign in formulas like x — y. However, TgX will use different spacing rules in mathematics, and the minus sign prints differently than a hyphen. Moreover, letters are normally italicized in formulas. The fourth group of symbols that normally appear on every keyboard includes the following: \ {}$&#*/. 0 ' " _ " Each of these symbols has a special usage in AmS-T^H.; for example, as we mentioned in the Introduction, all control sequences begin with the "backslash" character \, while$ signs or $$signs are used to set off mathematics formulas. There is one further symbol that most users tend to overlook: pressing the space bar produces a symbol that appears blank on the screen. We will use the symbol u whenever it is necessary to emphasize that the blank space has been entered. There are two other keys that we should also mention explicitly. The first is the (carriage-return) key, which moves the cursor down to the beginning of the next line. Pressing (carriage-return) twice in succession produces a blank line on the screen. The other is the key labelled TAB. This key moves the cursor over a certain number of spaces on the screen, although it actually enters a single specific character into the file. TgX treats the TAB key exactly like a space. Exceptions. Some of these symbols may be difficult, or even impossible, to obtain on your terminal, so TgX has control sequences that can be used instead. For example, the left quote ' often doesn't make it onto the keyboard, but you can use \lq for ' (and \rq for '). There are also control sequences that can replace Chapter 0. Getting Acquainted; A Key Chapter 5 the symbols I, [, ], ", _ and ". They will be introduced as needed, and a complete survey is presented in Appendix E. Of course, none of these substitutions will do you much good if you are also missing the \ key! And TgX relies heavily on the curly braces { and }, which have a special role, and can't be replaced by control sequences either. Actually, even if \, { and } are missing from your keyboard, all is not lost, because TgX can be changed so that some other keys will serve instead. But such modifications require a little TjjjXpertise, and should be done in some consistent way by everyone who encounters these problems, to minimize confusion when TgX files are moved from one machine to another. If you have such problems—or even if you don't—you will probably want to join TUG, the TfjX Users Group, to get acquainted with other people who are using IfeX. Information about joining the TfjX Users Group will be found in Appendix H. Chapter 1. Learning TfcjX's Lingo Although TfjX is especially well suited for typesetting books and papers that contain lots of mathematics, it also does a superior job of typesetting ordinary text. In Part 1 we will be concentrating almost exclusively on text that does not involve the peculiarities of mathematical formulas. This will give us a leisurely opportunity to become acquainted with TfjX's special language, and to learn how it handles the numerous peculiarities with which our literary friends like to deal. When you want to use TfjX to set ordinary text you basically just type in what you want to come out, and let TfiK worry about all the details. For example, suppose that you enter the following in your file: This is the first paragraph of a 1,000 word document that has been set by TeX. The lines are automatically justified, i.e., they are all set to the same length. To do this, TeX inserts extra space between words, and/or hyphenates words that are too long to fit on the line. ( But it can't correct your errors.) Now let's get down to the nitty-gritty: how did TeX know that it was supposed to begin a new paragraph here? Come, come, you really should be able to figure that out for yourself! Using this input file, TfiX will produce output like the following: This is the first paragraph of a 1,000 word document that has been set by TeX. The lines are automatically justified, i.e., they are all set to the same length. To do this, TeX inserts extra space between words, and/or hyphenates words that are too long to fit on the line. ( But it can't correct your errors.) Now let's get down to the nitty-gritty: how did TeX know that it was supposed to begin a new paragraph here? Come, come, you really should be able to figure that out for yourself! 6 Chapter 1. Learning TgX's Lingo 7 Notice that the input lines can be of any convenient size; TfjX automatically arranges them in paragraphs, with all lines made equally long. Similarly, extra spaces between words have no particular significance for TfjX; when a sequence of spaces appears in the input file, TfjX simply ignores all the spaces after the first one. The (carriage-return) at the end of a line also tells TfiX to insert a space, and TfjX then ignores any extra spaces that occur at the beginning of the next line—so the five spaces at the beginning of the line uuuuuTo do this, TeX were completely ignored. (That would be true even if the spaces had been inserted by the TAB key, since TfjX normally treats TAB exactly like a space.) To the virtuoso typist, some of these features might seem unnecessary, or even downright perverse. But once you start getting serious with a text editor, and begin using it to make corrections—to insert and delete words, and to move whole sentences around—you'll appreciate the fact that you don't have to worry about any extra spaces that might creep in. The number of spaces after punctuation marks is likewise irrelevant. Typists usually leave two spaces after the punctuation marks ., :, ? and !, but such niceties are irrelevant to TfjX, which uses its own judgment for the spacing after punctuation. However, if you leave no space at all, then TfjX also leaves no space, so that you can get expressions like "1,000" and "i.e.," in the output. On the other hand, the space between ( and But was a bad mistake, which caused an unwanted space in the output. TfjX essentially set "(" as a one-letter word, and since this "word" happened to come at the end of a line, it was torn apart from the word "But", which came at the beginning of the next line. • Exercise 1.1: The input file for this book contains the lines First we have the upper- and lower-case letters, and the numerals: What would have happened if the following had been typed instead? First we have the upper- and lowercase letters, and the numerals: And what if the following had been typed? First we have the upper- and lower-case letters, and the numerals: 8 Chapter 1. Learning TgX's Lingo Since multiple spaces at the beginning of a line won't begin a new paragraph, T^jX has a simple alternate device to indicate paragraphing, which you have probably already figured out: TeX ends a paragraph when it encounters a blank line—and starts a new paragraph as soon as it sees the next thing to be printed. Of course, a blank line on the screen might really be a line like uuu consisting of three blank spaces; in fact, it is easy to end up with such lines when you use a text editor to delete all the visible portions of a line. Fortunately TjtX V&H-rivftTpre\ sudn aline as a "^blarik line" also. You can also leave several blank lines in a row at the end of a paragraph—I£X. will simply count them all as one blank line. TfeX also has a simple device to get all 4 varieties of quotation marks that you will need for ordinary text. To get single-quote marks you just type single-quote marks: the input ' produces ' and the input ' produces '. And to produce double-quote marks, you simply type two single-quote marks of the appropriate kind immediately in succession. The input ''Oh, so that's how the letter 'A' is produced!'' produces "Oh, so that's how the letter 'A' is produced!" Remember that you can use \lq for ' and \rq for * if you are missing these keys; and \lq\lq and \rq\rq give the desired double-quotes. In addition to single- and double-quote marks, text often contains dashes—as in sentences like this one. A dash is not the same as a hyphen or a minus sign. In fact, carefully printed mathematics books have hyphens, minus signs, and two kinds of dashes, an en-dash - and an em-dash — (traditionally, an em-dash was the width of a capital M, while an en-dash was half that width). En-dashes are used for number ranges, like "pages 13-34", and also in contexts like "Fig. A-12". Em-dashes are used for punctuation in sentences—they are the kinds of dashes to which the author of this manual has apparently become addicted. These different symbols can be produced as follows: for a hyphen, type a hyphen (-); for an en-dash, type two hyphens (—); for an em-dash, type three hyphens ( ). Chapter 1. Learning TfiX's Lingo 9 Dashes, like hyphens, usually have no spaces on either side of them, so don't inadvertently put any into the input file. As we have already mentioned, a hyphen will automatically be turned into a minus sign when it is used between the signs that indicate mathematics formulas; in this case you won't have to worry about spaces, because TgX's own mathematics spacing conventions will take over. • Exercise 1.2: Explain how the following should be typed in a TeX file: E said, "I still type two spaces after a period—I just can't break the habit—but I'm always careful to use an en-dash rather than a hyphen for number ranges like '480-491' in a bibliography." • Exercise 1.3: What happens if you mistype — - instead of ? What do you think happens if you type ? In addition to quote marks and dashes, in all their variety, occasionally you may need some special symbol, like '5', which is sometimes used to signal a paragraph. For example, we might like to number the paragraphs of our sample text as 5a, 1fb, and so forth: 5a. This is the first paragraph of a 1,000 word document that has been set by ... ^b. Now let's get down to the nitty-gritty: how did TeX know that it was ... We can do this by typing \P a. This is the first paragraph of \P b. Now let's get down to the nitty-gritty: how \P is one of TgX's many "control words". A control word is a combination consisting of the "backslash" character \ followed by any number of letters. The backslash \ tells TgX that what follows is not some text to be set, but the name of a symbol, or some other special command. Notice that the input \P a has a space after the \P. This space is essential, because if we omitted it TgX would think that we were trying to use a control 10 Chapter 1. Learning TgX's Lingo word named \Pa. But the space doesn't show up in the output '^a'; TeX always regards the spaces after a control word simply as an indication of where the name of the control word ends, not as a space to be typeset. Actually, the name of a control word doesn't always have to end with a space; it can also be terminated by any other non-letter. For example, if we wanted to number our paragraphs Kl, 1[2, etc., we could type \P1, \P2, etc. (Since spaces after control words never appear in the output, you can also type \P 1, \P 2, with the same output '%1\ '^[2'; so you can always put a space at the end of a control word, if you don't want to bother anticipating what sort of symbol comes next.) Although we didn't mention it before, T^jX also has a control word to indicate the end of a paragraph. If we typed too long. ( But it can't correct errors.) \par Now let's get down ... then the words "Now let's ..." would have begun a new paragraph, just as if Now let' s ... were preceded by a blank line. In fact, a blank line has exactly the same significance in TfjX's mind as the control sequence \par—when TeX sees a blank line, it simply pretends that \par had been typed. The blank line convention is basically an added convenience for the typist—it's a lot easier to hit (carriage-return) twice than to type \par. But the blank lines also make your input file a lot more readable. Remember that after the document has been printed the first time, there are sure to be some changes, so you're going to be searching through that file again. Then you'll appreciate the fact that the file has been divided into convenient chunks. ALWAYS PLAN AHEAD! • Exercise 1.4: What happens if you type \Par instead of \par? • Exercise 1.5: What happens if your file has the following? ... end of first paragraph.\par uuu The second paragraph begins here ... The control word \par isn't used very often, because of the blank line convention, and \P isn't used very often either, since % signs are rather unusual. But there's one special symbol that you will need if the author is so crass as to mention money (actual dollars and cents). Suppose that we want to end our Chapter 1. Learning T^X's Lingo 11 little document, a bit shy of its advertised 1,000 words, with a final paragraph: 1.95 (cheap!) is the price of this document. Typing 2.00 (cheap!) is the price of this document. would be a big marketing mistake, but it would be an even worse TfjX error, because the sign tells TjjX to start setting a math formula. TfjX would start setting the weird formula 2.00(cheap\)isthepriceofthisdocument. and then complain that it never found the second sign to tell it where the math formula ends! Since the sign has the special role of indicating math formulas, we need a different way of naming a printed sign. One possibility would be a control word like \dollax, but TfjX has a shorter, and much more obvious, name—the combination \. Using \ we can type our final paragraph as \1.95 (cheap!) is the price of this document. Note that \ is not a control word—control words must contain only Jetters after the \ —but is instead what is called a "control symbol". A control symbol consists of \ followed by a single non-letter (so there is never any ambiguity about where the name of the control symbol ends). Examples of other possible control symbols are \1, \:, \+ and even \\. Control words and control symbols are known collectively as "control sequences", and this is the term we will normally use, since there will seldom be any need to distinguish between the two. There is, however, one important way that control symbols differ from control words. We've seen that TgX always ignores spaces after control words, since a space is usually needed just to indicate the end of the control word. But a space after a control symbol is not ignored (this arrangement seems to concur with the expectations of most typists). So if you typed \ 1.00 you would get ' 1.00', with a space after the sign. Which brings up an interesting point. What happens if you want a space after a control word—how do you get output like '^J 1'? It won't help to type \PUU1, with two spaces after the control word \P, since T^X always treats a whole sequence of spaces as just a single space. What we actually need is a new control sequence to stand for a space/ A reasonable candidate might be the control sequence \space, but again TgX has a much shorter and (once you think of it) more obvious solution. When you need to tell TgX explicitly that you want a space, just use the combination \u (that is, \ followed by a blank space). Thus we can type \P\ 1 to get the output '^ 1'. 12 Chapter 1. Learning T^K's Lingo • Exercise 1.6: Explain how to type the following sentence: JSost people can print '$$' passably, but it's harder to print U.S. that are passable. • Exercise 1.7: A^jS-T^ii., unconstrained by false modesty, provides you with the control sequences \TeX and \AmSTeX, to produce the "IfiX' and iA/^-^!^, logos. Explain how to type the following sentence: A^jS-T^ii. is Just a specialized version of TfeX, but once you have mastered it you will have joined the T^jXnical revolution. • Exercise 1.8: What output is produced by \$Vi\ul-00 and by \$u\u1.00? Notice that \u is a control symbol—it consists of \ followed by a non-letter. Having solved the previous three exercises, you should already be adept at using it, but if you try to figure out what happens when you type \uu you might be a little disconcerted, because we actually have two conflicting rules. A space after a control symbol is not supposed to be ignored, so we should get \u followed by another space, and thus two spaces. But we also have the general rule that TfeX treats a sequence of spaces as a single space, so our input should be equivalent to \u, giving just one space. For this special case TeX goes along with the latter rule: \Uu is the same as \u- By now we've learned quite a lot about getting things into print: (1) Multiple spaces count as a single space, as does a (carriage-return). (2) Blank lines indicate the end of a paragraph. (3) ' and ' give single quotes, '' and '' give double quotes, — gives an en-dash and — gives an em-dash. (4) Special symbols and instructions are produced by control words (e.g., \P, \par) and control symbols (e.g., \$, \u), known collectively as control sequences. Spaces are ignored after control words, but not after control symbols, except that \Uu is the same as \u. As every prominent person knows, however, sometimes the real problem is keeping things out of print. T^X uses '/, as a special device to help you do this— when T^X sees the character '/, on a line of input text it ignores that '/. together Chapter 1. Learning T^X's Lingo 13 with everything else that comes after it on that line. This allows you to insert "comments" into your file—material that will be omitted in print (even spaces, if you're not careful). For example, if you type material that will be ommitted '/.Check spelling of ommitted V, it would be embarrasing to have it mispelled in the manual in print (even spaces, if you're not careful). you will get material that will be ommitted in print (even spaces, if you're not careful). If you aren't careful, and type material that will be ommitted'/, Check spelling of ommitted V. it would be embar rasing to have it mispelled in the manual in print (even spaces, if you're not careful). you will get something much worse than a spelling error: material that will be ommittedin print (even spaces, if you're not careful). That's because the '/, causes T£X to omit everything after it, including the (carriage-return). Although this feature of'/, necessitates some extra care, you can also use it to advantage, in order to split a long word into two lines on the input file without splitting it in the output: The input the longest English word pneumonoultramicroscopic'/, silicovolcanoconiosis will give you the longest English word pneumonoultramicroscopicsilicovolcanoco- niosis in the output (hyphenated, if necessary). And if you get to an em-dash near the end of an input line—which frequently happens—you can use '/. to avoid an unwanted space: if you get to an em-dash near the end of an input line '/, which frequently happens you ... You can "comment out" a large amount of text by putting X in front of each line. But AmS-Te^. also provides a much more convenient mechanism for this, which is explained in Part 3.$
14 Chapter 1. Learning T^i's Lingo When the control symbol \u occurs at the end of a line it looks a little strange, since you can't actually see the final space: I don't like the idea of putting all those \P\ signs at the beginning of paragraphs. I like to put an innocent '/, at the end to make the \u stand out: I don't like the idea of putting all those \P\ '/, signs at the beginning of paragraphs. These final'/, characters can also prevent confusion when files are transferred between machines, since u symbols at the end of a line are sometimes discarded during this process. The way TfeX is set up, this really shouldn't matter, but with X at the end you don't even have to think about the possibility. $Chapter 2. Printers Do It With All Types Our experiments with the control word \P and the control symbols \$ and \u were useful in teaching us the subtleties involved in the use of control sequences, but of course what we all really want to know about is italic print, though you've surely noticed that in this manual we tend to favor slanted print, a rather recent innovation (for extra emphasis we resort to boldface print). You can change to these fonts by using the control sequences Nit, \sl and \bf; the control sequence \rm returns you to ordinary (roman) type. Thus, the input Don't confuse \it emphasizing \nn something with boldly \bf asserting \rm it. produces the output Don't confuse emphasizing something with boldly asserting it. Simply by changing \it to \sl in the above example, we could get the word "emphasizing" to be set in slanted type, rather than in italics. And you'll be happy to learn that if A/^S-T& happens to be setting text in a different type- size, as in a footnote, it will automatically choose the proper size type for the italic, slanted, or bold font. Despite these amenities, you might resent having to include all the extra \nn instructions. They're certainly a nuisance to type, and an omission can be disastrous—you might end up with pages and pages of italicized words instead of just one! Actually, there's a way of switching fonts that doesn't require the extra \nn instructions and that is much better for most purposes. Use the input Don't confuse {\it emphasizing} something with boldly {\bf asserting} it. The braces { and } tell TgX that {\it emphasizing} and {\bf asserting} are separate "groups" within the ordinary roman type. When TgX sees the left curly brace { that starts a group it makes a mental note of the type font that was being used, and it reverts to that same font once it sees the } that ends the group—the right curly brace } "turns off" the Nit command. 15
16 Chapter 2. Printers Do It With All Types Of course, if you forget the closing } that turns off the Nit command, you'll still get pages and pages of italic type. And forgetting closing }'s can have even more dire consequences in some situations. You can avoid these problems if you have a computer terminal with extra keys that can be programmed to produce any sequence of input, or a text editor that can be customized so that a single key stroke (usually some control key) can have the same effect. You can arrange for a single key stroke to produce input like {\it } and also move the cursor back before the }; then you just have to type in the text you want to be italicized and skip past the } when you are finished. This saves a bit of typing, and virtually guarantees that you won't forget the closing }. Because of the way braces turn off TgX's activities, grouping is also useful in many other situations. For example, when we wanted to get the output l% a', with a space after the %, we previously typed \P\ua. But we could also have typed {\P} a. Now the control word \P is followed by } rather than a space, and the space that follows the } isn't ignored. In order to pull this trick we've put \P into a group all by itself, but that doesn't matter—this is simply a group in which nothing particularly interesting happens. Actually, there's yet another way to use braces to get '^[ a', which might seem even trickier. You can type \PO a using an empty group: the {} combination is a group of no characters, so it produces no output, but it still intervenes between \P and the space, thereby aborting TgX's mission to search out and destroy extra blank spaces. The empty group {} may seem like a cheap trick, but it has lots of neat uses in math formulas, and is sometimes almost indispensable. • Exercise 2.1: Redo Exercise 1.7 in 2 different ways, both without using the control symbol \u. As a final grapple with grouping here are two rather technical exercises designed more to make you think about the issues than to illustrate problems that are very likely to come up. • Exercise 2.2: What output would be produced by {\Puu}uu{u}-Cu}a? • Exercise 2.3: What can you type if you want the output to contain two hyphens in a row? (You can't type —, but there are many possible solutions.)
Chapter 2. Printers Do It With All Types 17 In our discussion of italic and slanted type we skipped over one detail that might have been more noticeable if we had looked at a different transition from italic to roman type. Notice that the space after "different" in the previous sentence seems to be too small, because the t slants over into that space. This wasn't as noticeable in our previous examples, because an italic g slants over much less than an italic t. The amount that a letter slants over is called its "italic correction", and T^X allows you to insert this extra amount of space simply by typing the control symbol \/ after the letter. Thus the proper way to get a different transition from italic to roman type is to type ... a {\it different\/} transition from ... As a general rule, use \/ after a group of words in a slanted font unless the next symbol is a comma, or a period. • Exercise 2.4: Explain how to type the following: The Joy of IfeX explains how to put things in the file that will be ommitted [sic] in print. (If you don't have [ and ] you can use \lbrack and \rbrack instead.) • Exercise 2.5: What's the preferred way to type the following sentence to TgX? Italicizing just one word or even the prefix or suffix of a word is fine, but don't go overboard. • Exercise 2.6: Explain how to typeset the following: Most grammarians say that punctuation after a word should be in the same font: but many writers prefer to switch back; this is especially true when the punctuation is a semi-colon. • Exercise 2.7: What nasty mistake could you make in typing the following sentence? Notice that the space after "different" seems to be too small here. • Exercise 2.8: Explain how to type the following bibliographic reference: W. Ambrose, Higher order Grassmann bundles 3 (1964), 199-238. The answer to Exercise 2.8 might startle you at first, until you get used to the idea that within a group you can do the same sorts of things that you do outside
18 Chapter 2. Printers Do It With All Types the group. In fact, you can even put a group inside another group. When we start typesetting mathematics formulas we will be doing this with perhaps alarming frequency, but for now just bear the possibility in mind for the following. • Exercise 2.9: Explain how to typeset a roman word in the midst of an italicized sentence. Even with all the possibilities afforded by italic, slanted and boldface type, there's always the enthusiast who wants to use underlined words. TgX doesn't provide you with a convenient method of underlining—you can't type something like {\ul ...} to underline a whole group of words. If a book designer wanted to use underlining extensively, E would have to design a special '\ul' font in which each letter has an underline as part of it; of course, the letters g, j, p, q and y would be one of Eir design problems. TfeX does give you a way to underline individual words, however. If you type \underbar{problems} you will get problems, which shows one solution to these problems. Barring unusual circumstances, \underbar'ing isn't very important. But it is important to observe the way that the curly braces are used in the input \underbar{problems}, because \underbar acts differently from the control se- qences we have learned about so far. The control sequences \P, \$, \u and \/ indicate special symbols or certain amounts of space, and the control sequences \par, Nit, \sl and \bf tell TgX to alter its activities (end a paragraph or change to a different font), but \underbar tells TgX to process a certain amount of input in a special way. In TgXnical jargon, \underbar is a "control sequence with an argument", the "argument" being the amount of input that receives special processing. If we were to type \underbar doesn' t then we would get the output "doesn't" because TgX would think that the single character d was the argument of \underbar: when the argument of a control sequence consists of more than one character, you must enclose the argument in braces, to tell TgX that the whole group is the argument. Most of the other control sequences that we will be learning about also tell TgX to do something special to some particular amount of input. In fact, so many of TgX's control sequences are control sequences with arguments that novice TgXnical typists sometimes forget that \it, \sl and \bf are different. A common error is to type ... italicize just Nit {one} word in a sentence. expecting to italicize just one word. What happens instead is quite different! The braces around {one} have no effect at all. The control sequence Nit simply tells TgX to start using italic type, and the word "one", together with all succeeding Chapter 2. Printers Do It With All Types 19 words, are italicized. When you type things correctly, as ... italicize just {\it one\/} word in a sentence. the instruction to use italic type is limited to the group {\it one\/} in which it occurs. To keep from making such mistakes, it might help to mentally pronounce \it as "switch to italics". (Of course, you won't have any problems if you've arranged for a single key stroke to produce {\it ■}.) • Exercise 2.10: Typeset the following: When a sentence is typeset in slanted type, you might want to underline a roman word for emphasis. Now it's time to take what we've learned and see what TjjX really does with our input file. Throughout Chapter 1 and this chapter, it's been assumed that you've been doing all the problems, and checking your answers with those in Appendix A. The final exercise of this chapter is somewhat different, because it calls for the creation of a computer file, which we will actually submit to TfeX, in the next chapter. On most computers, file names have two parts separated by a period, like 'file.ext', where the part after the period is called the "extension". Assuming that this is true for your computer, the file that you create for this final exercise should be called 'paper.tex'. It really isn't important for the first part of the file to be called 'paper', but the second part, the extension, should be 'tex'. (If the file names on your computer system don't conform to this pattern, consult your system's experts for additional details.) • Exercise 2.11: Make a computer file 'paper.tex' that T£X will use to print the following: Everyone will be happy when T£X finally arrives, and Dr. Treemunch can start typing his own so-called scholarly manuscripts. His last opus— which The Amer. Jour. Recr. Drugs recently published—created quite a sensation, particularly the material that he has expounded on pages 22- 23. Including this material cost an extra$1,000, but it did make %% 1 and 2 quite popular. The head of the department, our university's own I. M. Stable, attributes Treemunch's recent aberrant behavior to the much-publicized "research" for his paper; notwithstanding, others say that Treemunch's name isn't on the computers' databases, so his name often gets hyphenated quite strangely, which may account somewhat for his feeling of being ill-used.
Chapter 3. Your First Te<X Experience Although we've only covered the rudiments of TfeXspeak, it's time to take a little break, lie back, and let the computer do some work. At the end of the last section you produced a file paper.tex. Now we'll ask TjpC to process it and see what happens. We will spell out the various steps of this process in considerable detail, but it will definitely help if you follow along on your own terminal. Before doing this, however, be sure that you have the right input for paper.tex, by checking with the answer for Exercise 2.11. It should be noted that the precise details involved in running T£X depend on the particular operating system you are using. [Because of the heavy demands that IgX may place on the computer's capabilities, your system might even require that T£X jobs be done in batch mode.] The local experts at your computer installation will be able to tell you about such things. Before we begin, we need to add a few things tc the file paper.tex, which is not yet in a suitable state to be submitted to AmS-T${.. To prepare it properly, first add the lines \input amstex \documentstyle{amsppt} at the very beginning of the file. The first line tells TgX to read in a file that tells it about the special features of ,Am<S-TeX. The second line specifies a certain style for the output (the desired page size, typeface, and so forth); we've requested a workaday style called 'amsppt', the "AMS preprint style". If we had typed \documentstyle{bul} then we would have instructed T£X to print things in the 'bul' style, the style of the Bulletin of the American Mathematical Society. (Notice that in the first line we didn't say \input{amstex}. The instruction \input is one of TfeX's fundamental control sequences, and T£X knows that its argument is simply everything up to the first space or (carriage-return). For T£Xnical reasons, \input works in a special way—braces around amstex are not only unnecessary, they are actually wrong! Fortunately, \input is the only exceptional control sequence of this sort that you will ever have to worry about.) 20 Chapter 3. Your First TgX Experience 21 Normally a paper will have things like a title and the author's name at the beginning. Such material would be specified right after the \documentstyle line. Ignoring such frills for the moment, we will simply Instruct 2¾¾- that the body of the document follows immediately, by adding the line \document So now the text proper starts on line 4. Finally, at the very end of the file, add the line \enddocument As you may have guessed, this tells TfeX that the document is over, and brings everything to a screeching halt—anything on succeeding lines will be ignored. Now that the file paper.tex has been completed, you can leave the editor. Once again you are in communication with the operating system. It has given you a prompt sign—to be specific, let's say it's the symbol <9—and now we're ready to go! First you have to ask the operating system to run TfeX. To do this, you type TeX or tex or run tex, or something of that sort. After it has been invoked by the proper incantation, including the (carriage-return) at the end of the line, TgX will sign on with a message such as This is TeX, Version 3.0 (preloaded format=plain 90.6.1) ** The ** is TfeX's way of asking you for the name of the input file you want it to process. At this point you can type paper. (Before typing the (carriage-return) after paper you can probably correct any typing errors with the delete key, or whatever other key you usually use.) Notice that we merely have to type paper to process the file named paper.tex; TjjX assumes that the file has the extension tex unless another extension is explicitly given. On many systems this two-step process has a short-cut: typing tex paper after the <9 prompt will have the same effect. Whichever method you use, as soon as you press the (carriage-return) after paper, IfeX will begin to process the file 22 Chapter 3. Your First T£X Experience paper.tex and something like the following will appear on your screen: (paper.tex (amstex.texj AmS-TeX - Version 2.0 COPYRIGHT 1985, 1990 - AMERICAN MATHEMATICAL SOCIETY Use of this macro package is not restricted provided each use is acknowledged upon publication. ) (amsppt. sty AMSPPT.STY - Version 2.14) (amssym.tex)) Overfull \hbox (9.63954pt too wide) ... \tennn notwith-stand-ing, oth-ers say ... databases,I [1] The first line tells you that TgX has begun to read paper.tex and that the instructions in this file have caused it to first read the file amstex.tex, where the special features of Aj^S-T^i are stored,1 and then to read the file amsppt .sty where the details of the amsppt style reside. TfeX may appear to be quite sluggish as it prints out this line, because reading in files involves interacting with the operating system. You will also notice another file that is read that you did not knowingly as TfeX to read, amssym.tex. This file is automatically read by amsppt and is explained in more detail in later chapters. Once TgX has finished reading in the files, it will probably print out the next, more mysterious lines, quite quickly: Overfull \hbox (9.63954pt too wide) ... \teiirm notwith-stand-ing, oth-ers say ... databases,I These lines seem to be saying that something is wrong, but we'll have to wait until we see the output in order to decipher them. 1Some computer installations may have a separate amatex program, in which the special features of .AmS-T^JX have already been added to l^jX. If you use such a program you won't need the initial \input amatex line, and it will essentially be ignored if you do have it. Chapter 3. Your First IfiX Experience 23 Next comes [1], which tells you that A\4S-T$£ has processed enough of your file to make one page, which has been numbered "1"; no other numbers appear since the whole paper fits on one page. At this point T£X has constructed, and placed in your directory, a new file called paper .dvi. This is a device-j_ndependent file that can be used, with suitable supplementary programs, to drive whatever printing device your computer uses to get the hard copy. In fact, something like Output written on paper.dvi has probably also appeared on the screen to tell you this, accompanied perhaps by other lines about a 'transcript file' named paper. 1st or paper. log, which we'll worry about later. At present our only worry is how to get the printed output. Your computer will have another program that takes the file paper. dvi and sends it off to the printer; you'll have to consult your system experts to find out just how printed output is obtained. We'll want to examine this printed output carefully—there will be some surprises in it—so you should go pick it up as soon as possible. If you have made the file paper.tex correctly your output will not look like the original on page 19. Instead it will look like this: Everyone will be happy when T^X finally arrives, and Dr. Treemunch can start typing his own so-called scholarly manuscripts. His last opus—which The Amer. Jour. Recr. Drugs recently published—created quite a sensation, particularly the material that he has expounded on pages 22 23. Including this material cost an extra $1,000, but it did make f f 1 and 2 quite popular. The head of the department, our university's own I. M. Stable, attributes Treemu-| nch's recent aberrant behavior to the much-publicized "research" for his paper; notwithstanding, others say that Treemunch's name isn't on the computers' databases,! so his name often gets hyphenated quite strangely, which may account somewhat for his feeling of being ill-used. We can immediately see the reason for the Overfull \hbox message. The word "databases" (together with the comma attached to it) extends a little beyond the margin—the 'Overfull \hbox' is the whole horizontal line notwithstanding, others say that Treemunch's name isn't on the computers' databases, The Overfull \hbox message begins by telling us that this box is 9.63954pt too wide; here pt stands for the printer's "point", which is approximately 1/72 24 Chapter 3. Your First TfeX" Experience of an inch. 9.63954 points is quite a bit, and a word that protrudes this far into the right margin will be very noticeable. Just to be sure that we do notice it, TfeX has placed a big ugly black mark right next to the offending word, so that our first attempt at typesetting isn't exactly something that you'd like to take home and show off to your friends. Information about this overfull box is also transmitted to your terminal: the next lines \tennn notwith-stand-ing, oth-ers say ... databases,! describe the Overfull \hbox in more detail—first comes \tenrm, the name of the font being used (ten point roman), then comes a good portion of the actual letters being set, and finally we have the end of the line, databases, followed by I, which stands for the black box that T£X put on the paper. The reason for such miserable output is that TgX doesn't know how to hyphenate the word "databases". TgX has a very efficient proceduie for finding hyphenation points, but it doesn't catch them all, and "database" slips through unaffected. Moreover, T^X was not willing to move "databases" onto the next line because it would have to stretch out this line, ers point out that Treemunch's name isn't on many computers' to an extent that it considers intolerable.' TgX would rather produce something that you will find intolerable, so that you will be forced to deal with the problem. Well ..., having been forced to deal with the problem, one possibility is for us to force TgX to break the line against its inclination. To force a line break we just type \linebreak. Thus, we can type many computers'\linebreak databases ... to force TgX to break the line before the word "databases"—and to spread out the line so that it reaches to the right margin. If you leave a space before \linebreak, Aj^S-T^i. will simply assume that you didn't want it, and still spread the line out to the margin. • Exercise 3.1: Add \linebreak to paper.tex, and run it through TgX to see what you get. How bad did TfiX think it was to break the line in this way? (You don't have to bother deleting the file paper.dvi; TfiX will delete it when it needs to write a dvi file for the new paper.tex.) 'Actually, it's the amsppt style that determines how far T£jX will allow a line to be stretched; the text on page 19 was produced by modifying the amsppt style so that it would allow more stretching. Chapter 3. Your First T^X Experience 25 There obviously ought to be a better solution to our problem than forcing T£X to break the line in this way, we should be able to tell T£X how to hyphenate "databases". In fact, we can do this by changing databases in the input to data\-bases The special control symbol \- represents a "discretionary hyphen"—it tells TgX that a hyphen can be inserted here, without insisting on it. (So if we change the wording later on, we won't be forcing a hyphen in an unwanted place.) Missing the hyphenation in "databases" was an unfortunate lapse on TgX's part, but sins of commission are worse, and Dr. Treemunch would undoubtedly be quite incensed about the absurd way that TgX did hyphenate his name in the second paragraph. We can fix this problem by typing Tree\-munch TJjY «f a jvwsiKlp ViyfiVipnat.inn jioint for "Treemunch", it also prevents any other hyphenations, because TfiX will never insert hyphens into a word that already has either a hyphen or a discretionary hyphen. • Exercise 3.2: Change paper.tex by removing the \linebreak and inserting discretionary hyphens in databases and Treemunch and Treemunch's and run the paper again, to see what you get. Although the discretionary hyphen \- will save the day when an anomalous word occurs, it would be inconvenient to insert discretionary hyphens in the same word over and over again. If we are going to continue complaining about Treemunch for several pages, we can add the proper hyphenation of his name to TejX's database for the whole paper, simply by typing \hyphenat ion{Tree-munch} at the beginning. • Exercise 3.3: Take out all the discretionary hyphens \- in paper.tex—the ones that you inserted in data\-bases and Tree\-munch and Tree\-munch's—and add \hyphenation{Tree-munch} \hyphenation{data-base} to the beginning of the paper (right after \document, say). For the purposes of this exercise we are explicitly not giving T^X the hyphenation for the forms "Treemunch's" and "databases". Run paper.tex through TeX again, and see what you get, consulting the Answers for further enlightenment. 26 Chapter 3. Your First T^X Experience Finally, let's get things right by adding the proper hyphenation of the words "Treemunch", "database" and "databases". It isn't necessary to add a separate \hyphenation line for each. We can combine them into one line \hyphenation{Tree-munch. data-base data-bases} • Exercise 3.4: Replace the old \hyphenation lines with this new one, and run paper .t ex again. Now that we know how to get T^X output, you can handle the Exercises in a different way. Instead of scribbling them down on a piece of paper, and checking with Appendix A, you can scribble them down in a computer file, and see what T]eX does with them. Of course, you'll want to save up the answers for a chapter or two, rather than running TgX over again for each Exercise, unless you can afford to use lots of machine time. But sooner or later (perhaps already) you will make some errors that will get IfeX even more confused than you are. So the very next step is to look at the sort of error messages that T^X gives you. Chapter 4. TfeX's Erroneous Zones The file paper.tex was purposely contrived to produce bad hyphenations and Overfull box messages. After all, it's a commonplace that initial experiences of this sort are seldom entirely satisfactory. In practice, however, hyphenation problems almost never arise, and an Overfull box is also quite rare. Until you become quite a TgX adept, you're much more likely to be greeted with "error messages"; these occur when you have done something that gets TjtjX confused, so that it has to stop and ask for clarification. You needn't get too uptight when you encounter an error message, because TgX can always be coaxed into making an informed guess about your intentions. You can think of an error message as a chance to figure out what TgX is thinking. Some people like such opportunities to psychoanalyze the computer, but if this doesn't appeal to you, then you can always let TgX try to figure out what you were thinking. Leaving our file paper.tex intact for the present, let's begin by making another file, say goof .tex, in which we will purposely plant some errors: \input amstex \documentstyle{amsppt} \document Here is a word in {\It italics\/} and here is one in {\Bf boldface} and one in {\It italics\/} again. \enddocument As in the previous chapter, we will be making various changes in this file; if you make the changes in your copy of goof .tex as we go along, you'll be able to see the results described here happening on your terminal. First let's try running our initial version of goof .tex through TgjX. When we do, TgjX will shriek at us: ! Undefined control sequence. 1.4 Here is a word in {\It italics\/} and here is one The top line, beginning with !, is an error message, telling us that T£JX has come upon a control sequence that it doesn't recognize. More information is given in the next pair of lines. On the first of these lines we see the undefined control 27 28 Chapter 4- TfiX's Erroneous Zones sequence \It, together with (a portion of) the line that comes before it. The succeeding input is printed one line lower, so that it is easy to see exactly how far T£X had gotten in the input file before it detected the error. Finally, IfeX has printed ? on the next line, indicating that it is asking us what to do. At this point we have several options. The most abject response would be to type X or x, followed by (carriage-return), in order to exit from T£JX. Then we could return to our file and fix the error, try running it through TfiX again, to discover the next error, return to our file and fix this error, etc., etc., etc. Instead of capitulating so quickly, however, we can simply type (carriage- return). Now T£JX will try to fix the error as best it can; in the present situation it will simply ignore the control sequence \It and proceed. Of course, this means that the word "italics" won't appear in italics, but that's hardly worth worrying about, since we'll probably find some more errors anyway, and won't try to print anything this first time through. Sure enough, we soon get the next error message, ! Undefined control sequence. 1.5 in {\Bf boldface} and one in {\It italics\/} again. whose meaning should now be clear. This time let's try a somewhat more gutsy approach; we want to insert the correct control sequence \bf. To do this we can type i or I, followed by (carriage-return), to tell T£JX that we want to insert something. (Go ahead, try it.) TfiX will respond with insert> Now we can type \bf, followed by (carriage-return). As you can see, T£JX accepts this and quickly presents us with the final error message: ! Undefined control sequence. 1.5 in {\Bf boldface} and one in {\It italics\/} again. This time let's simply type x to exit, so that we can examine a few more types of errors. If you go back to the editor, you'll see that \bf hasn't actually been inserted into your file—TgjX merely inserted \bf into its own private copy of your file. Chapter 4- TgX's Erroneous Zones 29 All the old errors remain in goof .tex, but for the moment don't correct them. Instead, add one new error: omit the { before the final \It, so that we have in {\Bf boldface} and one in \It italics\/} again. Now start T£JX all over again. Naturally, we first get the old error message ! Undefined control sequence. 1.4 Here is a word in {\It italics\/} and here is one ? This time we'll insert the correction \it, but we'll do it in just one step. Try typing i\it or I\it followed by (carriage-return). Now correct the next two errors in the same way. Finally, TfiX will reach the fourth error: ! Too many }'s. 1.5 in {\Bf boldface} and one in \It italics\/} again. ? The meaning of this error message should also be quite clear, but sometimes you may want to ask T£JX for more help. We can do this by typing h or H, followed by (carriage-return), and in the present situation T£JX will answer: You've closed more groups than you opened. Such booboos are generally harmless, so keep going. Well, let's take TgjX's advice: at this point it won't help to insert anything—the time for inserting the necessary { is long since past—so we'll just keep going by hitting (carriage-return) again. This causes T£JX to take the only diversionary tactic possible—it simply omits the } and hopes for the best. Sure enough, T|jX now gets to the end of the hie, and produces a dvi hie. We wouldn't want to print the dvi file that TeX has produced because our final error wasn't really corrected: by omitting the } TgjX has actually caused the word "again" to be printed in italics also. Now's the time to go back and correct all tne errors at once. Have you forgotten them? Don't worry! Here's where we get to use the "transcript file" goof .1st; you'll find that tne error messages that appeared on the screen have also been recorded there, so you can look them over at your leisure. 30 Chapter 4- TfiX's Erroneous Zones • Exercise 4.1: Consult goof. 1st to see what additional information it contains. Correct all the errors in goof .tex and run it through TgjX once again, to check that you get no error messages. • Exercise 4.2: Omit the { before the final \it, type h or H when you get the error message, and then type it once again, to see what you get. • Exercise 4.3: Put back the { but leave out the space after the first \it, so that we have {\ititalics\/}... in the file. What error message do you get, and how should you respond? • Exercise 4.4: Correct the previous error, but now leave out the last right brace }, so that we have something like ... and one in {\it italicsV again. \enddocument with a { that has no matching }. Run this file through TfjX to see what happens. If you get such a message in a big file, what should you do? Although we've examined several kinds of errors in this chapter, they were all rather simple to diagnose. That's to be expected, since we can presently typeset only simple material, and consequently make only simple mistakes. As we learn to typeset more interesting material we will also examine, perhaps inadvertently at times, the more interesting mistakes that can be made when we really put our minds to it. There are a few other details of TgjX's error messages that you might be interested in learning about now. • Exercise 4.5: Balance the braces again, but change the first \it to \It once more. This time, when T£JK shrieks the error message at you, shriek right back by typing !, followed by (carriage-return), and see what happens. • Exercise 4.6: Leave out the very last line, \enddocument, in goof .tex, and see what happens when you run it through TfiX. Figure out how to bring things to a satisfactory conclusion, checking with Appendix A. Chapter 4- TfiX's Erroneous Zones 31 • Exercise 4.7: See what happens when you mistype the name of the paper. For example, try <0tex goofy (assuming that you have no file called goofy.tex). • Exercise 4.8: Try telling A^S-T^. to use your own (as-of-yet nonexistent) style mystyle, by changing \documentstyle{amsppt} to \documentstyle{mystyle} and see what happens. Chapter 5. Spaces That Separate, Ties That Bind Although the hyphenation problems in paper.tex have already been resolved, the output isn't ready to be "finalized." Why? Because the experienced eye would immediately note that the spacing in this paper isn't what you'd expect from high quality typesetting, where there is more space at the ends of sentences than between words. (This looks better and makes for easier reading.) T£JX also follows this rule, but it doesn't always know where a sentence ends! One trouble is that T£JX usually assumes that periods end sentences. Of course, as you can readily see from the previous paragraph, TgX does know that! and ? represent the end of a sentence, just as it knows that periods followed by quotation marks or parentheses also represent ends of sentences. T£JX is even smart enough to know that periods after upper-case letters are probably initials, and thus not ends of sentences. So in the output for paper.tex the spacing in the name "I. M. Stable" was fine. But TgX doesn't know about abbreviations, so it can't figure out that input like Dr.u doesn't signify the end of a sentence. Consequently, "Dr. Treemunch" and "The Amer. Jour. Recr. Drugs" were too spaced out. Aji/lS-T^. has the control symbol '\.' to represent a period that indicates an abbreviation rather than ending a sentence. So we can get the right spacing by typing Dr\. Treemunch and The Amer\. Jour\. Recr\. Drugs. Notice that the spaces after '\.' aren't ignored, since they follow a control symbol. In addition to the poor spacing after the abbreviations, a couple of the line breaks in our output for paper.tex are also unsatisfactory, because they interrupt the flow of reading. It isn't ideal to have "pages" at the end of one line, with "22 23" on the next line, and the break between "ff" and "1 and 2" is even more disconcerting. T£JX can't deal with such psychological questions, so you have to help it out here, also. Once again, there is a simple solution to the problem. If you type the "tie" " between two words, then T£JX will insert a space, but prohibit a line break. Thus, you can type pages"22—23 and \P\P"i and"2. In the second example a second tie was used to prevent "2" from appearing at the beginning of a line. By the way, if you have a space on either side of " it will simply be ignored by A\jS-T^H.. This makes it easier to insert ties later on, and also simplifies matters as you're typing: if you've typed pagesu and then suddenly realize that you ought to have a tie, you can just type " next, without bothering to go back to delete the u- (If you are missing the " key, you can use the control sequence 32 Chapter 5. Spaces That Separate, Ties That Bind 33 \tie instead; of course, in this situation, a space after \tie is ignored by T£X in any case.) Unfortunately, there doesn't seem to be a good set of rules for deciding just when ties should be used. It's a matter of judgment and experience, wherein the T^Xnical typist can show Eir mettle. After a while you won't have to insert ties on the second try, because the whole thing will become second nature. Further suggestions for using ties will be found in Part 3, and ties will also appear in the Answers to the Exercises, when appropriate. Ties are often preferable to \u after abbreviations. For example, it is best to type Dr. "Treemunch, since this will still give an interword space, and also prevent a line break. And the best way to type the journal title might be The" Amer\. Jour\. Recr."Drugs. • Exercise 5.1: Insert " and \. in the appropriate places in paper. tex and run it through TgX once again. This was the sixth try. Rest, and admire your handiwork. • Exercise 5.2: The first time the author tried Exercise 5.1, he got the strange combination 1%%V in the output. What was his mistake? e Exercise 5.3: How would you type the icAlcm'mg'! Weird fruit (mangos, papayas, etc.) are avoided by farmers, fastidious eaters, et al. In our final version ofpaper.tex we still have a possibly objectionable line break, at the en-dash between "22" and "23". TJjjX normally regards hyphens and dashes as reasonable places for line breaks, but Am<S-T& provides an easy way to specify hyphens and dashes where line breaks can't occur. If you type <D- you will get a hyphen with a line break prohibited. Similarly, <D— and <D— give an en-dash and em-dash and prohibit a line break. (By the way, most document styles tell TJjjX to disallow line breaks after hyphens and dashes in bibliographies, so you usually don't have to bother with 8- and Q— there.) If you try replacing the — by G— in paper.tex, you'll find that T^X has to juggle the paragraph a bit to comply with all your specifications.$
Chapter 6. Doing It With Elan You can now use 1$to print about 95% of any ordinary text that you will ever encounter. But before you add TgXpertise to your resume, we ought to resume our study of TfeX, since you still can't typeset things like ..., well, like this paragraph. First of all, as we have already intimated in Chapter 1, there are a few special symbols that sometimes appear in text: Type To get \dag t (dagger or obelisk) \ddag t (double dagger or diesis) \S § (section number sign) \P % (paragraph sign or pilcrow) And you might want \ copyright to © your brilliant production. More important, remember that the characters \ { }$ & # V. C " * _ " have special uses in A^/fS-T^i., so some finagling is required to make them appear in the output. We know that \$stands for the dollar sign$. The other standard non-mathematical symbols are produced similarly: \< { \> } \ \ft & \# # \% % TgjX also allows you to type \_ to get a printed _, for things like "/irsfcJeiier"; mathematicians seldom use such constructions but computer scientists are partial to them. (If you are missing the _ key, you can use \underscore instead of \_.) i Exercise 6.1: The rule that T£X ignores everything on a line after a'/, sign isn't 100% accurate. What is the exception? Hint: See Exercise 6.1. 34
Chapter 6. Doing It With Elan 35 • Exercise 6.2: How would you type the following sentence to TeX? My #1 solace is M & M's, though any candy is dandy; I agree 100% with O. Nashf that liquor is quicker, but a fifth of J & B @ $13.95 {price as of this writing} is beyond my means. The undirected double quote mark " doesn't appear on our list of special symbols for the simple reason that it really isn't a symbol at all—normal text fonts have no such character, and you will always want either '' or ''. The backslash \ is another symbol that doesn't appear in normal text. But \ is a fairly common mathematical symbol; in fact, it is used in a couple of different ways, and some fonts may even have a variant form, like \ . There are special control sequences for these symbols in mathematics formulas. This leaves only the symbols " and " to be accounted for. These symbols can occur in ordinary text, but only as accents ' and A over letters. In fact, a whole slew of special symbols and accents is needed for foreign languages that still basically use the roman alphabet. If you are an English literary chauvinist, you might not even want to bother learning about these accents right now— for the time being you can type the usual sloppy approximation to non-English words and names, and trust the journal editors to worry about details; when your foreign colleagues fume, just tell them "jManana is good enough for me!" Each accent over a letter is indicated by a control sequence with an argument. In the following table the same letter o will be used as the argument in all cases. Type \'o Vo \"o \"o Vo \u 0 \v 0 \H o \B o \b o \D o \d o \c 0 To 6 6 6 6 6 6 6 6 6 0 6 0 9 get (grave accent) (acute accent) (circumflex or "hat") (umlaut or dieresis) (tilde or "squiggle") (breve accent) (hacek or "check") (long Hungarian umlaut) (macron or "bar") (bar-under accent) (dot accent) (dot-under accent) (cedilla) 36 Chapter 6. Doing It With Elan AmS-T$(. also has a "tie" accent indicated by \t, which is a control sequence with two arguments: \t oo do (We've already mentioned that \lq can be used if the ' key is missing from your keyboard. But you can't replace \' by \\lq since T£JX would interpret this as the control symbol \\ followed by the letters lq! Appendix E explains the alternative ways of typing V, V, \" and \~.) Notice that spaces are needed after \u, ... , \c and \t since they are control words. Thus, to get the word "hacek" you should type h\'a\v cek Admittedly, a word with a space in it looks strange, so you might find the input h\'a\v-(c}ek less confusing. But this takes quite a bit more typing, and you'll probably get used to things like h\' a\v cek. Of course, spaces are not needed after control symbols like \'. Indeed, you might think that a space after V, as in the input h\' a\v cek would be an error, for in Chapter 1 we said that spaces after control symbols are not ignored. However, this rule actually applies only to control symbols like \$, \u and \/ that do not have arguments. When a control symbol has an argument, there is a more general rule that takes precedence: TftjK always ignores spaces when looking for the argument of a control sequence. You should remember this rule for later use, but for accenting letters you can simply stick to things like \' a, which are easier to type anyway. • Exercise 6.3: What is wrong with typing the following? The word "h\'a\vc ek" should be spelled with a h\' a\v c ek. • Exercise 6.4: How would you type the following: beloved protege; role coordinator; souffles, crepes, pates, etc. Chapter 6. Doing It With Elan 37 There's only one little detail of accenting that TgX won't take care of automatically. For accents over 'i' and 'j' one needs the dotless V and 'j'; to obtain them you must type \i and \j. • Exercise 6.5: What's the non-naive way to type naive? • Exercise 6.6: How would you type the names Ernesto Cesaro, Pal Erdos, Sergei Yurev, Eduard Cech, Tabit ibn Qorra, Muhammad ibn Musa al-Khwarizmi? In addition to the accents that you can get with TgX, there are also a few special letters that TgX recognizes: Type \oe, \0E \ae, \AE \aa, \AA \o, \0 \1, \L \ss • Exercise 6.7: Explain how to type the following: ^Esop's (Euvres en frangais. • Exercise 6.8: How would you type the names Oystein Ore, Anders Jonas Angstrom, Stanislaw Swierczkowski? Finally, the j and i that you need for Spanish aren't specified by control sequences, but are recognized as ligatures: To get i I (jThis arrangement seems pretty safe, since it's hard to imagine a situation where you would want !' or ?' to occur in text!) • Exercise 6.9: How do you type the following: ^What did you say, Serior? I said, "jManana is good enough for me!" All our examples so far have involved roman type, but everything that we've said also applies to the other text fonts. Each type style has its own accents and special letters, so that {\bf\"o} yields 6 and {\sl \~a} yields a. To get oe, (E ae, M a, A 0,0 1,L fi Type | ( 38 Chapter 6. Doing It With Elan • Exercise 6.10: Explain how to type the following sentence: Commentarii Academies Scientiarum Imperialis Petropolitanse is now Akademifa Nauk SSSR, Doklady. Well..., now that we've finally gotten accents out of the way, we musn't omit .AmS-TeX's way of handling an "ellipsis", the three dots (...) that indicate an omission. If you simply type three periods in a row, the output is "...", with the dots too close together. On the other hand, if you leave blank spaces between the dots you will get too much space, and TgX might even break a line between them! So A^/fS-T^H. gives you the control sequence \dots to help you. The input Hmm\dots how do you space the dots? produces "Hmm ... how do you space the dots?" If you leave a space before the \dots, »4m<S-TeX will simply ignore it and insert the amount of space that it thinks is proper. Of course, the space after \dots is certainly irrelevant, since it follows a control word (but you do need at least one space between \dots and how in our example). Don't worry if the dots happen to be followed by some punctuation, TgX will handle it just right ... ! Well ..., actually you do have to worry a little. • Exercise 6.11: What is wrong with typing the following? Well \dots .actually you do have to worry a little. • Exercise 6.12: What is the proper input for the first paragraph of this chapter? Since several different topics have been covered in this chapter, a brief review is in order: (1) The printed characters {, },$, &, #, % and @ are named by the obvious control symbols—\ followed by the corresponding characters. The symbols f, J, §, ^ and © have control words to name them. There's also \_ for a printed -. (2) Accents over a letter are produced by applying various control sequences to the letter (or pair of letters in the case of \t). Spaces are unnecessary (but allowed) after those that are control symbols. \i and \j are needed for the dotless l and j. (3) There are control sequences for special letters like oe, se, a, 0,1 and fi, but the Spanish i and i are obtained as ligatures. (4) Use \dots for ' ... '.
Chapter 6. Doing It With Elan 39 We'll conclude this section by listing a few stray points that you might have to worry about now and then. (i) As we've already mentioned, TeX assumes that periods after upper-case letters axe initials, and hence do not indicate the end of a sentence. But sometimes a period, or other punctuation, after an upper-case letter is the end of a sentence: Perhaps you're wondering who concocts these silly illustrations about TeX. (You won't find the answer in Appendix A.) I cannot tell a lie—it is I. Supported by the NSF? Nope, nor any other such boondoggle. In this case AjvfS-TfdL gives you '8.' for a period that is the end of a sentence, with similar constructions a, 8; 8: 8! and 8? for other punctuation: ... about \TeX8. ... Appendix'AQ.) ... It is 18. ... by the NSF8? Nope, ... (ii) On the other hand, the rule about periods after upper-case letters doesn't apply when a period follows an accented upper-case letter, as in "E. Cartan". So here you would need \. (or preferably ") to indicate an ordinary interword space: \'E."Cartan. (iii) Another special spacing problem occurs when you have quotes within quotes: "They call this 'typesetting'" he sneered. It won't do to type . . .'typesetting'{"} he sneered. because not enough space will be left after the single quote—you'll get'" which looks almost like three equally-spaced single quotes—while 'u" will leave too much space. The special construction 8" will solve this problem. Type ...'typesetting' 8" " he sneered. Spaces before and after 8" are ignored, so your input doesn't have to look squashed. You will also get the correct spacing in any of the legitimate combinations <' Q" ' II t Qll t t ((( $Main Courses which everyone needs Chapter 7. TfcX's Brand Of Mathematics The real fun and challenge of technical typesetting comes from the horrendous formulas with which mathematicians routinely deal. Insiders know, of course, that the complexity of these formulas is somewhat misleading. Big formulas are made up of smaller formulas, and smaller formulas are made up of yet smaller formulas, and .... Fortunately, unlike Swift's hierarchy of back-biting fleas, this process does not go on ad infinitum—all formulas can be built up in a few steps from relatively simple ones. So the art of technical typesetting begins with the simplest formulas. To tell TgX that the next part of the present paragraph is part of a mathematical formula, simply enclose it within$ signs—this causes TgX to enter "mathematics mode" and to process that input text specially. For example, you can get the formula z < y = 3(x — 1.5)/(-2|x| + I) to appear in the output by typing ... get the formula $z < y= 3( x -1. 5) /( - 2 I x 1+1)$ to appear in the output by typing ... This simple example illustrates several important points. (1) Letters are automatically italicized in formulas, while numerals and punctuation symbols (like parentheses) are set in roman type. An 1 (lowercase L) gets set as I, which is even easier to distinguish from the numeral 1 than an ordinary typeset T. Notice, by the way, that even a single symbol can be a "formula": if you type $x$ in the input, you will get x in the output. (2) The hyphen becomes a minus sign and the slash becomes a slanted fraction line. The symbol |x| stands for the "absolute value of x", but it's not necessary to know what this means; the only important thing is that TgX will typeset | even if your keyboard has \ instead of I. Remember also that you can use \vert instead of I if your terminal lacks this symbol. (3) Most important of all, within $signs TfeX completely ignores all spaces and (carriage-return)s. When setting a formula, TgX relies on its own spacing rules, which probably involve more details than you would want to keep track of. For example, in the formula z < y = 3(x — 1.5)/(-2|x| + I) the < and = signs are "binary relations", which function as verbs, the + sign and the first — sign are "binary operators", 43 44 Chapter 7. T^X's Brand Of Mathematics which function like conjunctions, and the second — sign functions like an adjective. Standard printing conventions use spacing that reflects these different roles: thus, there is a little more space around the < and = signs than there is around the + sign or the first — sign, while there is no space at all after the second — sign. Fortunately, you don't have to remember any of this, since T^X does it all for you. Despite the fact that TfeX ignores spaces within$ signs, they should not be regarded as useless, since they can make the input text a lot easier to read— for example, individual parts of long complicated formulas can be separated by several spaces. Initially, force of habit may lead you to use spaces even in short formulas, like $z < y = 3(x - 1.5)/(-2|x| + 1)$ so as to approximate the spacing that will eventually appear in print. However, you'll soon come to realize that the spaces do nothing but slow down the typing, and you'll probably graduate to something like $z<y=3(x-1.5)/(-2|x|+l)$, reserving spaces for more complicated situations. In this manual we'll use spacing in a haphazard way, just to emphasize that it's an unnecessary good. • Exercise 7.1: What's wrong with typing the following? If the formula$y=x-l$ is true ... • Exercise 7.2: Explain how to type the following sentence: Deleting an element from an n-tuple leaves an (n — l)-tuple. • Exercise 7.3: What is the proper way to type the following? Consider the graph of / — g + h in the x-y plane. You should take advantage of the fact that TfeX is usually smart enough to choose correct spacing in mathematics formulas, but you needn't be taken in by TgX's finesse at setting mathematics formulas. TgX doesn't really "understand" formulas (any more than a human typesetter does). Technical typists should regard this as good news, for it means that they don't have to understand the formulas either. For example, it's not important to know why there are parentheses in the formula z < y = 3(x—1.5)/(-2|x|+Z)—so long as they get typed in. Mathematicians actually use parentheses in many different ways, but again it is
Chapter 7. T^X's Brand Of Mathematics 45 not necessary to understand these different uses. If you type $y=f(x)$ you will get the formula y = /(x), in which the parentheses have a special mathematical use. Similarly, if you type $y=f [x ]$ and $z=f (x,y)$ you will get the formulas y = f[x] and z = f(x, y). Mathematicians are usually fairly careful about putting the necessary parentheses in their manuscripts. But they sometimes get lazy, and stop counting parentheses in a formula like the following: 1 + 2(3 + 4(5 + 6(7+¾))) Even if the parentheses don't match up, a catastrophe won't ensue—TgX isn't very discriminating on this score, and will be quite happy to typeset the formula l + 2(3 + 4(5 + 6(7 + x)) even though it is mathematically unacceptable. This is fortunate, because T£X mustn't object to a formula like (x, x + 1], which doesn't look like it should be mathematically acceptable, but which actually is, because the parenthesis and bracket have special meanings. Curly braces, as well as parentheses and brackets, are often used with special meanings, as in the following formula: x + |x| + (x) + [x] + {x} To set this formula you just have to remember that printed braces must be specified by the control sequences \{ and \}, since actual braces serve the special function of grouping things. Thus, you should type $x +1x1+ (x)+[ x]+VCx\}$ In addition to \vert as a replacement for I, T£X also has \lbrack and \rbrack as replacements for [ and ]; the latter work in math mode as well as in text. (And T£X even has \lbrace and \rbrace to stand for the printed \{ and \}.) Brackets and braces may also be used just like parentheses, in order to make the pairings clearer, as in the formula l + 2{3 + 4[5 + 6(7 + x)]} Such constructions are becoming a little old-fashioned, since [ ] and { } frequently have special meanings, but they occur often enough in many branches of mathematics.
46 Chapter 7. TgK's Brand Of Mathematics • Exercise 7.4: How was the above formula typed? • Exercise 7.5: What output would the following input produce? $l+2{3+4[5+6(7+x)]}$ Hint: Look closely. • Exercise 7.6: And how about the following? $x {+} y$ (The answer is a little surprising—be sure to try it out, and consult Appendix B.) A nasty surprise awaits you if you type the formula $10x + 100 y +1,000 z$. You will get lOx + lOOy + 1,000« because T^X normally leaves a little space after commas in math mode. • Exercise 7.7: How do you think you can get around this? So far we've only dealt with formulas involving letters, numerals and punctuation, together with the symbols =, +, —, <, > and | that appear on most keyboards.* But mathematicians routinely employ dozens of other symbols, like oo, G, <, etc. Each of these symbols has a control sequence to name it. The symbol oo, which stands for "infinity" (more or less), is named by \inf ty; the shorter name \inf happens to be used for something else, which we'll learn about in a later chapter. And the symbol € occurs in formulas like x G A, which is often read "x in A". To get the formula x e A you just type $x\in A$. Notice that the space after \in is needed, even though TgX "ignores" spaces in formulas. By the way, some keyboards have special keys like oo, but you should not use them unless your T^X has been specifically tailored for that keyboard. *We also ought to mention the * key! In ordinary text this gives the asterisk *, which is normally used only for footnotes. Since Afcfi-Tfpi., together with the particular style you are using, determines what the footnote marks will be, and inserts them for you automatically, you will hardly ever use * in text. But * is sometimes used in math formulas. For example $(l*g) (x)$ gives the math formula (/ * g)(x). $Chapter 7. T^X's Brand Of Mathematics 47 /jX T^X has the control sequence \ell to give the symbol £, which mathematicians JL sometimes use with some special meaning. But before using \ell be certain that this is what is wanted, since many authors write something like £ in their manuscripts simply to indicate an I. (A symbol like £ is available on many typewriters, and conscientious typists often use it instead of 1, to distinguish it from the typewriter's 1, thereby adding one more layer of confusion!) The names for all the esoteric math symbols are listed in Appendix F. Most of them should simply be learned as needed, but there are a few extremely common ones that you'll want to know about right away: \leq or \le < ("less than or equal") \geq or \ge > ("greater than or equal") \neq or \ne ^ ("not equal") \notin$ ("not in") By the way, the control sequence \not gives a / that can be used to "negate" other binary operators besides =. For example, the control sequence \equiv gives the operator = in math mode, and $\not\equiv$ gives ^; the control sequences \ne and \neq are, in fact, simply abbreviations for \not=. But notice that the / in ¢ has a different slope from the / in ^. For this reason, you should always type $\notin$ rather than $\not\in$, which gives the less pleasing symbol ¢. In addition to special symbols, mathematicians sometimes use accents, as in formulas like A, and other fonts, as in formulas like ax + by. Fonts and accents work completely differently in math mode than they do in ordinary text, and details have been relegated to Part 3, because these matters are rather specialized. On the other hand, mathematicians have also supplemented their arsenal of specially concocted symbols with letters stolen from the Greeks, and these are used very frequently. For example, $\alpha$ and $\beta$ and $\gamma$ and $\delta$ produce the first four Greek letters a, /3, 7 and 6, while $\Gamma$ produces T, which is an upper-case gamma, and $\Delta$ similarly produces A, an upper-case delta. (There are no \Alpha and \Beta, since the corresponding upper-case letters just look like "A" and "B".) The fifth letter of the Greek alphabet is produced by $\epsilon$, which gives e. Notice that this is quite different from the membership symbol €. Unfortunately, not all mathematicians are conscientious about distinguishing these symbols in their manuscripts, so some consultations may be in order before beginning a long job. Make sure also that the author has carefully distinguished
48 Chapter 7. T^i's Brand Of Mathematics the Greek letter \nu (u) from v and \kappa (k) from x or k, The Greek letter \phi (¢) should also be distinguished from the symbol 0, called \emptyset. Just to make matters a little worse, e has the variant form e, which is produced by $\varepsilon$, and four other Greek letters also have variant forms:1 while the input $(\theta, \pi, \rho, \phi)$ yields (6,n,p,4>), the input $(\vaxtheta,\vaxpi,\varrho,\vaxphi)$ yields (tf,w,Q,(p). All upper-case Greek letters also have variants: for example, \varGamma gives r and VvarDolta gives A If you haven't had the benefits of a liberal education (studying the classics or belonging to a fraternity or sorority), you may not be familiar with the names of the Greek letters. That's no problem—they are all listed in Appendix F, together with all the other esoteric symbols. Still, you might think that it's going to be quite a pain to type $\alpha$ every time you want an a if this symbol happens to appear frequently in a paper. Wouldn't it be nicer to type short names, like $\a$ for $\alpha$ and $\b$ for /3? And while we're at it, why does TfeX have such funny names for some of the other funny symbols? Calling = \equiv may be helpful to mathematicians, who usually pronounce = as 'equivalent to1, but it doesn't help the technical typist! T£JX has a rather conservative philosophy about terminology: it generally uses long descriptive names for most of its control sequences, since there is then at least some basis for common agreement about the names—any system of abbreviated names usually has both vigorous adherents and detractors. TfjX can afford to take such a cavalier approach to the problem because TfiX typists can always define their own control sequences. When an esoteric symbol occurs only once or twice in a paper, you might as well just look it up in Appendix F and use the name provided, but for symbols that appear frequently you can invent your own names—you can tell IfeX that you want \a to mean \alpha, etc. The process of defining your own control sequences isn't covered until Part 3, because it's always easier to learn an established system, no matter how irritating it may sometimes seem, than it is to create your own special variant. But you can keep this possibility in the back of your mind every time you do an exercise that has you typing longer control sequences than you'd like. • Exercise 7.8: You've typed a long paper in which the author has used the letter x in numerous formulas. Now E tells you that Eir handwritten x was really supposed, to be k! So you are going to use your text editor to replace all x's with \kappa's. How should you proceed? For the fate of a fifth variant, X (Yvarltappa) see Appendix G.
Chapter 7. TpX's Brand Of Mathematics 49 • Exercise 7.9: Now assume you have the opposite problem. The fickle author decides to replace all «'s with fc's. What precautions do you need? • Exercise 7.10: Consulting Appendix F for the names of various symbols, explain how to typeset the following formulas: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13
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## anonymous one year ago Question 1 (Multiple Choice Worth 4 points) A cylindrical rain barrel has a radius of 2 feet and holds a total of 30 cubic feet of water. How tall is the rain barrel? Use 3.14 for pi. Round your answer to the nearest hundredth. 1.58 ft 2.39 ft 3.57 ft 4.78 ft Question 2 (Multiple Choice Worth 4 points) A paper popcorn cone measures 4 inches in diameter and 9 inches high. What is the volume of popcorn that can be contained within this cone? Use 3.14 for pi. Round your answer to the nearest hundredth. 37.68 in3 39.45 in3 40.23 in3 41.90 in3
1. anonymous
@ali2x2 @pooja195 @Peaches15 @phi
2. anonymous
@mathmate
3. anonymous
@Michele_Laino
4. anonymous
fan and medal
5. Michele_Laino
the volume V of a cylinder, whose radius is r and whose height is h, is given by the subsequent formula: $\Large V = \pi {r^2}h \cong 3.14{r^2}h$
6. Michele_Laino
so the measure of the height h, is: $\Large h = \frac{V}{{3.14{r^2}}} = \frac{{30}}{{3.14 \times {2^2}}} = ...?$
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# How to install lsystem add-on? [duplicate]
Apologies if this seems very basic, but I am really struggling with how to do this and am not sure where I am going wrong.
I have a found an L-System addon on Github (https://github.com/krljg/lsystem) that I am trying to use in Blender.
I have tried downloading the .zip file and saving within my Blender Installation: C:\Desktop\Blender Foundation\Blender 2.82\2.82\scripts\addons but I cannot find it when I install the file in User Preferences -> addons.
I have tried installing both the .zip folder and extracting it then installing the .init file but nothing shows up in the addons.
Is there something I am missing or doing wrong? Any suggestions would be greatly appreciated.
• Linux: \$HOME/.config/blender/<version>/
• OSX: /Library/Application Support/Blender/<version>/
• Windows: %USERPROFILE%\AppData\Roaming\Blender Foundation\Blender\<version>\
• also available via bpy.utils.script_path_user() and / or bpy.utils.script_paths("addons") Jul 17 '20 at 16:04
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It is currently 21 Apr 2019, 10:04
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# (–x + y)(–y + x) = x2 – y2 y2 – x2 0 –(x – y)2 (y – x)2
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(–x + y)(–y + x) = x2 – y2 y2 – x2 0 –(x – y)2 (y – x)2 [#permalink] 15 Apr 2018, 03:49
Expert's post
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Question Stats:
100% (00:10) correct 0% (00:00) wrong based on 2 sessions
$$(-x + y)(-y + x) =$$
A. $$x2 - y2$$
B. $$y^2 - x^2$$
C. 0
D. $$-(x - y)^2$$
E. $$(y - x)^2$$
Drill 2
Question: 7
Page: 511
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Re: (–x + y)(–y + x) = x2 – y2 y2 – x2 0 –(x – y)2 (y – x)2 [#permalink] 16 Apr 2018, 02:29
1
KUDOS
expand the expression
$$(-x + y)(-y + x) = xy -x^2 -y^2 + xy$$
or, $$(-x + y)(-y + x) = 2xy -x^2 - y^2$$
or, $$(-x + y)(-y + x) = -(-2xy + x^2 + y^2)$$
The expression inside the bracket is similar to $$(a-b)^2$$ so in that format
The expression reduces to $$-(x - y)^2$$
option D
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Re: (–x + y)(–y + x) = x2 – y2 y2 – x2 0 –(x – y)2 (y – x)2 [#permalink] 22 Apr 2018, 12:16
Expert's post
Explanation
Factor out $$-1$$ from the parentheses on the left and rearrange the expression in the parentheses on the right to get $$-1(x - y) (x - y) = -(x - y)^2$$. The answer is choice (D).
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Re: (–x + y)(–y + x) = x2 – y2 y2 – x2 0 –(x – y)2 (y – x)2 [#permalink] 22 Apr 2018, 12:16
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Resistors and Ohm's Law Video Lessons
Concept
###### FREE Expert Solution
Part A
Kirchoff's loop rule:
$\overline{){\mathbf{\Sigma }}{\mathbf{V}}{\mathbf{=}}{\mathbf{0}}}$
V = ε - IR
There is no resistance across points 1 and 3. Due to the very large resistance across the voltmeter, V, no current flows in the voltmeter.
92% (305 ratings)
###### Problem Details
Consider the circuit shown. (Intro 1 figure) All wires are considered ideal; that is, they have zero resistance. We will assume for now that all other elements of the circuit are ideal, too: The value of resistance is a constant, the internal resistances of the battery and the ammeter are zero, and the internal resistance of the voltmeter is infinitely large.
Intro 1:
Intro 2:
Part A
What is the reading V of the voltmeter?
Part B
The voltmeter, as can be seen in the figure, is connected to points 1 and 3. What are the respective voltage differences between points 1 and 2 and between points 2 and 3?
a) 0; ℰ
b) 0; -ℰ
c) ℰ; 0
d) ℰ;ℰ
Part C
What is the reading I of the ammeter?
Now assume that the battery has a nonzero internal resistance r (but the voltmeter and the ammeter remain ideal). (Intro 2 figure)
Part D
What is the reading of the ammeter now?
Part E
What is the reading of the voltmeter now?
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# Differential GPS or Simple GPS for Robot navigation and odometry?
I am building a rover which can navigate autonomously. I do not want to use wheel encoders for generating robot odometry since it causes drifts due to slippage etc. I want to use GPS for generating odometry. Will it be useful for me to use the differential GPS approach or shall I use a simple GPS? I am thinking of using DGPS because it enhances the accuracy to great extent, But at the same time, I think that in generating odometry, absolute gps values are not of importance. Instead, relative gps values are important to find for example, the distance covered by the robot.
Any suggestions on this ? Thanks
Do not give up on encoders. They are a great complement to GPS. I don't know what precision you want to reach, or what terrain your robot will operate in, but wherever it will be, encoders will give you good information about momentary position changes. Of course it will have some error, but when measured over small time period (i.e. 1s) it will be typically much smaller than accuracy of even DGPS.
The problem is encoder error will accumulate over time, so eventually your robot will end up in a completely different position than it should. That's why you should use your GPS data to correct data from encoders (possibly using Kalman filter). Check out this great answer about a sensor fusion.
Benefits of using GPS + encoders:
• GPS signal may be lost (indoors, tall buildings nearby, tunnels, etc.) - how will you know where are you then?
• Even when you lay down your GPS receiver on a table, the position will slowly drift around some central point - data from encoders may be used to correct for that. This is also the reason why you can't use GPS data to calculate distance covered by the robot (not with a ~1m accuracy at least)
• encoders are useful to controlling robot speed, and making sure that it drives straight (which is very hard using open loop PWM)
GPS vs DGPS
Remember that accuracy of i.e. +/- 2m doesn't mean that you will have a constant offset from real position to the north, or any other direction. The readings will float around some position. That's why I would suggest going for higher precision modules
• Thanks for the detailed explanation. The rover will always be working outdoors like in parks etc. So, GPS signal loss won't be problem in my case. All that I need is that the GPS should give the same value at a specific point. The value at the same point should not vary in different iterations. Secondly, If I move from point A to point B, then the calculated distance using gps values at both points should match the actual distance covered on ground. Based on above reqs, is DGPS is a solution for this, or do I only need a simple high precision gps with no need of dgps implementation. – nxr Sep 8 '16 at 14:54
• @b2meer What I'm saying is: whatever GPS you will use, the position it returns will float around true position. The only difference is how big the oscillations will be. Anyhow, you won't get exactly the same readings of the same position between iterations, when using only GPS data. Of course if you get high precision module the error might be small enough to ignore it. – mactro Sep 8 '16 at 16:56
• Alright. Can you recommend any high precision module with high frequency update rate as well ? – nxr Sep 9 '16 at 11:42
If your budget is large (>\$5000) then use an off-the-shelf RTK GPS and you will get a precision of around 1.5cm$\sigma$. You will also need a RTK subscription and internet connection, or set up your own base station to provide atmospheric corrections (valid for 20-30km). Alternatively there is this low-cost RTK unit. However I have previously used a low cost (< \$300USD) setup with a L1 GPS, IMU and camera (making observations of landmarks) using an extended Kalman filter in order to get <7cm $\sigma$ accuracy. I say accuracy rather than precision because I did a simulation using the sensor specs and so I knew the ground truth. I didn't use encoders but I would highly recommend it. From memory it took me around 4 days to implement and debug the filter.
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# Yield surface
Yield surface is described in three dimensional space of stresses, and encompasses the elastic region of material behavior. The states of stress of material inside the yield surface are elastic, when the stress reaches this surface it reaches the yield point. Then the material behaviour becomes plastic, because the stress cannot cross this surface.
Useful means of describing yield surface include expressing it in the terms of principal stresses (σ123), or using stress invariants (I1,I2,I3).
There are several different yield surfaces known in engineering, and those most popular are listed below.
## Contents
Following symbols are used below:
σ1 - principal stress in direction along first axis
σ2 - principal stress in direction along second axis
σ3 - principal stress in direction along third axis
σ0 - yield stress for single parametric yield surface
Rc - yield strength during compression
Rr - yield strength during tension
m - ratio of yield strengths
c - material cohesion
α - stress coefficient
K - material stiffness for two parametric yield surface (Rc,Rr)
## Tresca - Guest yield surface
This is the most simple yield surface, and it is taken to be the work of Henri Tresca. It is also referred as the TG criterion. In terms of the principal stresses it is expressed as
${\max(|\sigma_1 - \sigma_2| , |\sigma_2 - \sigma_3| , |\sigma_3 - \sigma_1| ) = \sigma_0 }\!$
Figure 1 shows the TG criterion in the three dimensional space of principal stresses. It is a prism of six sides and having infinite length. This means that the material remains elastic when all three principal stresses are roughly equivalent (a hydrostatic pressure), no matter how much it is compressed or stretched. However, when the material is subject to shearing and one of principal stresses becomes smaller (or larger) than the others, then the yield surface is reached and material enters the plastic domain.
Figure 2 shows the Tresca-Guest criterion in two dimensional space, it is a cross section of the prism along the σ12 plane.
## Huber - Mises - Hencky, also known as Prandtl - Reuss yield surface
This is another simple yield surface, which perhaps explains why it is credited to so many authors. Who is the real author depends on the university, although often it is credited to Maximilian Huber and Richard von Mises (see von Mises stress). It is also referred to as the HMH criterion. It is expressed in the principal stresses as
${(\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2 = 2 {\sigma_0}^2 }\!$
In the non-principal stresses, it takes the form of
$(\sigma_{11} - \sigma_{22})^2 + (\sigma_{22} - \sigma_{33})^2 + (\sigma_{33} - \sigma_{11})^2 + 6 ({\sigma_{12}}^2 + {\sigma_{13}}^2 + {\sigma_{23}}^2 + ) = 2 {\sigma_0}^2$
Figure 3 shows the HMH criterion in the three dimensional space of principal stresses. It is a circular cylinder of infinite length, with the same angle to all three axes.
Figure 4 shows the Huber-Mises-Hencky criterion in two dimensional space compared with Tresca-Guest criterion. HMH is a cross section of this cylinder on the plane of σ12, which produces an ellipse.
## Mohr - Coulomb yield surface
It is a first two-parametric yield surface, the parameters are Rc and Rr which are the maximum values for compression and tension for given material. This model is often used to model concrete, soil or granular materials. This model is the first one that takes shearing into account. It is expressaed as follows:
$m = \frac {R_c}{R_r}$
$K = \frac {m-1}{m+1}$
$c = {R_c} \frac {1}{m+1} = {R_r} \frac {m}{m+1}$
$\left\{{\begin{matrix} \pm\cfrac{\sigma_1 - \sigma_2}{2} = c - K \cfrac{\sigma_1 + \sigma_2}{2} \\ \pm\cfrac{\sigma_2 - \sigma_3}{2} = c - K \cfrac{\sigma_2 + \sigma_3}{2} \\ \pm\cfrac{\sigma_3 - \sigma_1}{2} = c - K \cfrac{\sigma_3 + \sigma_1}{2} \end{matrix}}\right.$
To plot this surface on Fig. 5 the following formula was used:
$\max\left(\cfrac{|\sigma_1 - \sigma_2|}{2}\ - c + K \cfrac{\sigma_1 + \sigma_2}{2}\ ,\ \cfrac{|\sigma_2 - \sigma_3|}{2}\ - c + K \cfrac{\sigma_2 + \sigma_3}{2}\ ,\ \cfrac{|\sigma_3 - \sigma_1|}{2}\ - c + K \cfrac{\sigma_3 + \sigma_1}{2} \right) = 0$
Figure 5 shows Mohr-Coulomb criterion in three dimensional space of principal stresses. It is a conical prism. If K = 0 then it becomes Tresca-Guest criterion, thus K determines the inclination angle of conical surface.
Figure 6 shows Mohr-Coulomb criterion in two dimensional space, it is a cross section of this conical prism on the plane of σ12, which produces a shape shown below.
## Drucker - Prager yield surface
This criterion is most often used for concrete, both normal and shear stresses are taken into account.
$m = \frac {R_c}{R_r}$
$K = \frac {2 \cdot R_c}{\sqrt{3}\cdot(m+1)}$
$\alpha = \frac {m-1}{\sqrt{3}\cdot(m+1)}$
$\alpha \cdot \left( \sigma_1 + \sigma_2 + \sigma_3 \right) + \sqrt{\frac{(\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2}{6}} = K$
Figure 7 shows Drucker-Prager criterion in three dimensional space of principal stresses. It is a regular cone.
Figure 8 shows Drucker-Prager criterion in two dimensional space, it is a cross section of this cone on the plane of σ12, which produces an ellipsioidal shape. It is compared here with Mohr-Colulomb criterion.
## Brestler - Pister criterion
This criterion is a first criterion that uses three parameters. It is similar to HMH criterion but additional parameter affects the cylinder radius using an x2 function. Thus cylinder's section along its axis is no longer a rectangle (or rather two parallel lines, since the cylinder has infinite length) but a parabola.
## Willam - Warnke criterion
This is the most advanced yield surface, it takes the idea from Brestler - Pister a bit further and applies it to Mohr-Colulomb criterion. The resulting surface is smooth (unlike Mohr-Colulumb) and has first and second derivative fully defined on every point of its surface which is an important property. This smoothness allows optimisations during calculations when searching for a yield point on the surface (using gradient method for instance).
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IN 1977 DESMOPRESSIN (1-deamino-8-D-arginine vasopressin, abbreviated DDAVP), a derivative of the antidiuretic hormone, was used for the first time to treat patients with hemophilia A and von Willebrand disease (vWD), the most frequent congenital bleeding disorders.1 After the original clinical study performed in Italy, desmopressin was used in many other countries and the World Health Organization included it in the list of essential drugs. A drug that could raise the plasma levels of factor VIII and von Willebrand factor (vWF ) without the need of blood products was especially attractive in the late 1970s and early 1980s, a time when the human immunodeficiency virus began to be transmitted by infected coagulation factor concentrates to patients with congenital coagulation disorders.
The clinical indications for desmopressin quickly expanded beyond hemophilia and vWD. The compound was shown to be efficacious even in bleeding disorders not involving a deficiency or dysfunction of factor VIII or vWF, including congenital and acquired defects of platelet function and such frequent abnormalities of hemostasis as those associated with chronic kidney and liver diseases. Desmopressin has also been used prophylactically in patients undergoing surgical operations characterized by large blood loss and transfusion requirements.
Twenty years of clinical experience have now established more firmly the clinical indications of desmopressin. Some of these indications have been strengthened by the experience accumulated, others have not been supported by rigorous clinical trials or have been overcome by the advent of more efficacious treatments. This report reviews the spectrum of indications in bleeding disorders, in the attempt to establish which indications remain valid and which do not. Topics such as pharmacokinetics, pharmacodynamics, and side effects of desmopressin will not be dealt with because they are covered in previous reviews.2-4
## HISTORICAL BACKGROUND
It was in 1772 when William Hewson noted that blood collected under conditions of stress clotted rapidly.5 Hewson's observations, described in detail in An Inquiry into the Properties of the Blood, triggered a series of animal experiments performed by the physiologist Cannon and his associates at the beginning of this century. They showed that the enhancement of blood clotting associated with stress was caused by the liberation of adrenaline in plasma.6,7 In 1957, a possible mechanism for faster clotting after adrenaline was provided by Marciniak,8 who found a transient increase in coagulation factor VIII after injection in rabbits. Reports of raised factor VIII after adrenaline infusion in humans soon followed: the average increase was to about twice the starting level, with no measurable change in other clotting factors.9 In patients with mild hemophilia the magnitude of the factor VIII increase induced by adrenaline was similar to that elicited in healthy individuals.9,10
These findings stimulated further research, with the goal to identify a factor VIII–increasing agent that would be free of the side effects of adrenaline and could be administered to hemophilic patients as autologous replacement therapy. Vasopressin and insulin also induced an increase of factor VIII,11 but their side effects were not milder than those of adrenaline, making clinical use unrealistic. An important step forward was made with the observation that desmopressin, a synthetic analogue of vasopressin, increased factor VIII and vWF in healthy individuals.12,13 Unlike the natural antidiuretic hormone, desmopressin produced little or no vasoconstriction, no increase in blood pressure, and no contraction of the uterus or gastrointestinal tract, so that it was well tolerated when administered to humans.12,13
A big step forward was taken when desmopressin was used in patients for the prevention and treatment of bleeding, first during dental extractions and then during major surgical procedures with mild hemophilia A or vWD.1 Surgery was performed without blood products, demonstrating that autologous factor VIII and vWF increased in patient plasma by desmopressin could effectively replace homologous factors contained in blood products.1 These clinical results were soon confirmed.14-16
## MECHANISMS OF ACTION OF DESMOPRESSIN
Despite 20 years of clinical use of desmopressin, mechanisms of action are still not completely understood. The increases in the plasma levels of factor VIII and vWF occur not only in deficient patients, but also in healthy individuals and in patients who already have high levels of these factors. Desmopressin shortens the prolonged activated partial thromboplastin time and the bleeding time.17 These effects probably result from the increases in factor VIII and vWF, which play a rate-accelerating role in these global tests of intrinsic coagulation and primary hemostasis. Desmopressin has no effect on platelet count or aggregation, but enhances platelet adhesion to the vessel wall.18,19 Release into plasma of large amounts of tissue plasminogen activator is another short-lived effect of desmopressin.12,13 Plasminogen activator generates plasmin in vivo, but most of the plasmin is quickly complexed to α2 -antiplasmin and does not produce fibrin(ogen)olysis in circulating blood.20 Accordingly, it is usually unnecessary to inhibit fibrinolysis when desmopressin is used for clinical purposes.
How do factor VIII and vWF increase in plasma? Because these factors increase rapidly and transiently, it is most likely that desmopressin causes them to be released from storage sites. The storage site(s) of factor VIII and the interaction between released factor VIII and concomitantly released vWF are not well established. The vascular endothelium is presumably the main source of vWF. This view is supported by the observation that in rats injections of desmopressin elicit biological responses that are clearly related to the activation of endothelial cells, like surface expression of P selectin and subsequent margination of leukocytes.21 In normal individuals, desmopressin infusion produces important changes in the content and localization of vWF in vascular endothelial cells.22 There is a reduction in the amount of the protein and a change in its localization, which causes a tendency for the protein to move abluminally toward the cellular basement membrane.22 Notwithstanding these data focusing on the endothelial cell as the most likely source of vWF, addition of desmopressin to cultured endothelial cells in vitro does not release vWF.23 Even though cultured cells may not be identical to native cells and might have lost specific receptors during culture, these observations suggest an indirect action of desmopressin through a second messenger. In the search of such a second messenger, it was shown that release of vWF from endothelial cells occurred after the addition of desmopressin to monocytes.24 These data, and those implicating monocyte-derived platelet activating factor as the second messenger acting upon endothelial cells,25 need confirmation. Desmopressin acts on storage sites via its strong V2 agonist activity, since patients with nephrogenic diabetes insipidus, who are unresponsive to V2 agonists, do not have increased factor VIII and vWF levels after treatment with desmopressin.26 Anephric patients respond normally,13 indicating that the site of the V2 -like receptors involved in the hemostatic properties of desmopressin is not in the kidney. Their location is currently unknown.
A puzzling, unresolved question is how desmopressin is efficacious in bleeding disorders other than hemophilia and vWD, in patients who have normal or even high levels of factor VIII and vWF. The favorable effects of the compound may be mediated by increased platelet adhesion to the vessel wall,18,19 due not only to the rise of plasma vWF but also to the abluminal secretion of the protein toward the subendothelium22; by heightened coagulability, due to supranormal levels of factor VIII, a rate-accelerating factor in the process of fibrin formation27; and by the fresh appearance in plasma of ultralarge vWF multimers.28 These are hemostatically very effective because they support to a higher degree platelet adhesion to the vascular subendothelium and induce platelet aggregation under conditions of high shear.29 Other putative mechanisms or mediators have been proposed to explain the hemostatic efficacy of desmopressin. For instance, the compound induces the adhesion of erythrocytes to the endothelium30 and decreases the endothelial production of 13-hydroxyoctadecadienoic acid (HODE), a derivative of linoleic acid that powerfully inhibits platelet adhesion to the vessel wall.31 The role of these mechanisms is uncertain and the search for additional or alternative mechanisms of action has been unfruitful so far.
## DESMOPRESSIN IN THE MANAGEMENT OF CONGENITAL BLEEDING DISORDERS
In hemophilia and vWD, desmopressin is efficacious because it provides a form of autologous replacement therapy. Table 1 summarizes the routes of administration, the recommended dosages, and the pharmacokinetic properties of desmopressin-induced factor VIII and vWF.
Table 1.
Recommended Dosages of Desmopressin and Factor VIII With vWF Responses in Patients With Hemophilia and vWD
Single dose Intravenous and subcutaneous: 0.3 μg/kg Intranasal: 300 μg/kg Mean factor increase over baseline 3-5 times (range: 1.5-20 times) Time to peak levels 30-60 min after intravenous injection 90-120 min after subcutaneous injection and intranasal application Plasma half-life 5-8 hours for factor VIII 8-10 hours for vWF
Single dose Intravenous and subcutaneous: 0.3 μg/kg Intranasal: 300 μg/kg Mean factor increase over baseline 3-5 times (range: 1.5-20 times) Time to peak levels 30-60 min after intravenous injection 90-120 min after subcutaneous injection and intranasal application Plasma half-life 5-8 hours for factor VIII 8-10 hours for vWF
The prototypes of patients who respond to desmopressin and avoid the use of coagulation factor concentrates are those with measurable levels of factor VIII and vWF, ie, patients with mild hemophilia A and type 1 vWD,1,14-16 whereas patients with unmeasurable levels do not respond at all.17 In mild hemophilia A the efficacy of desmopressin usually correlates with the postinfusion plasma levels of factor VIII.1,14-16 Accordingly, therapeutic indications are defined by the nature of the bleeding episode, the baseline factor VIII levels, and the levels that must be attained and maintained for hemostasis. Clinical failures of desmopressin can usually be explained by the attainment of factor VIII levels in plasma that are insufficient to control bleeding.1,14-16 For instance, a major surgical procedure in a patient with factor VIII levels of 10 U/dL may not be successfully managed with desmopressin because the expected posttreatment levels of 30 to 50 U/dL are not high enough for hemostasis. On the other hand, these levels should be sufficient for the patient to have a minor procedure, such as circumcision or dental extractions.
Most patients with type 1 vWD respond to desmopressin with increases in factor VIII and vWF that are larger than those seen in hemophiliacs.32 In addition to factor VIII, in these patients a determinant of the clinical efficacy of the compound is its capacity to shorten or normalize the bleeding time. Although in type 1 vWD this effect is usually achieved in proportion to the levels of normally functioning vWF attained in plasma,28 the bleeding times of patients with type 3, characterized by complete deficiency of vWF, and of those with dysfunctional molecules are usually not shortened.17,28 There are, however, a few patients with type 2A vWD in whom desmopressin does shorten the bleeding time.33 The reasons for these different behaviors are not clear and a test dose is the only way to differentiate responders from nonresponders. In theory, the administration of desmopressin to patients with heightened interactions between platelet glycoprotein Ib and vWF (type 2B and platelet-type or “pseudo” vWD) might be potentially dangerous, because it is followed by platelet aggregation and, in most instances, by thrombocytopenia.34 Although there is some evidence that desmopressin is clinically efficacious in these patients (reviewed by Castaman and Rodeghiero35 ), most hematologists would be reluctant to use it. Table 2 summarizes the indications for desmopressin in patients with different types of vWD.
Table 2.
Indication for Desmopressin in Different Types of vWD
Established Type 1, “platelet normal” Type 2N Possible Type 1, “platelet low” and types 2A and 2B Doubtful Type 3 (severe)
Established Type 1, “platelet normal” Type 2N Possible Type 1, “platelet low” and types 2A and 2B Doubtful Type 3 (severe)
“Established” indications are those in which desmopressin normalizes the bleeding time and factor VIII levels, and is clinically efficacious; “Possible” indications, those in which the effect on the bleeding time is absent or inconsistent, with little data on clinical efficacy; “Doubtful” indications, those in which desmopressin does not normalize factor VIII levels or the bleeding time, and is not clinically efficacious.
Patients treated repeatedly with desmopressin may become less responsive, perhaps because stores are exhausted.32 Some experimental data support this hypothesis because repeated infusions of desmopressin lower the amount of vWF contained in vascular endothelial cells.22 The average factor VIII responses obtained when desmopressin is repeated three to four times at 24-hour intervals are approximately 30% less than those obtained after the first dose.32 The clinical implications are that the efficacy of desmopressin may be limited when factor VIII levels must be maintained above the baseline levels for a prolonged period of time. In these situations, which occur relatively seldom in the clinical management of mild hemophilia and type 1 vWD, it may become necessary to use plasma-derived or recombinant factors, or to supplement desmopressin with them.
Subcutaneous and intranasal desmopressin are at least as efficacious as intravenous desmopressin and can be self-administered. Although intravenous desmopressin is recommended before surgery or for treating severe hemorrhages, because very consistent responses are required in these situations, subcutaneous desmopressin can be used at home to prevent or treat minor bleeding episodes and in women with vWD who have excessive bleeding at menstruation.36 Others prefer to use intranasal desmopressin as spray in these situations, even to handle major bleeding episodes and surgical operations.37
Despite the fact that neither in vitro nor in vivo studies have clearly proved a direct stimulatory effect of desmopressin on platelets (reviewed by Wun et al38 ), the drug shortens or normalizes the bleeding time of some patients with congenital defects of platelet function.39,40 Defects associated with normal dense granule stores benefit more from the compound.40 Accordingly, there is usually a good response in patients with defects of the release reaction, with cyclooxygenase deficiency, and in those with isolated and unexplained prolongations of the bleeding time. Most patients with storage pool deficiency respond to desmopressin but a few do not,40 so a test dose is recommended to select responders. Whether the effect on a laboratory test such as the bleeding time corresponds to a hemostatic effect is not well established. On the other hand, the data obtained from a few well-conducted but nonrandomized studies would indicate that desmopressin can be a useful alternative to blood products during or after surgery or delivery, assuring satisfactory hemostasis.39,40
To sum up, desmopressin is efficacious in mild hemophilia and type 1 vWD and usually permits the avoidance of concentrates, with significant reductions in costs. In the United States, for instance, an average dose of factor VIII concentrate (2,000 IU) costs between $800 and$2,000, depending on the source (plasma-derived or recombinant). An average dose of desmopressin (21 μg) is much cheaper ($100) and is even less expensive in Europe (the equivalent of$20 to \$40). The benefits of desmopressin are not limited to cost savings. The compound may be needed to meet religious requests, such as the avoidance of blood products in Jehovah's Witnesses. More importantly, it is likely to have spared many patients from infection with the human immunodeficiency virus type 1 (HIV). In Italy, where desmopressin was used earlier and more extensively than in other countries, the prevalence of HIV infection in patients with mild hemophilia (2.1%) is much lower than in patients with mild hemophilia B (13.5%).41 The latter is a suitable comparison group, because these patients need treatment at least as frequently as hemophilia A patients, but are unresponsive to desmopressin. Hence, they could only be treated with plasma concentrates during the critical years between 1977 (when desmopressin was first used clinically and the HIV outbreak started) and 1985 (when the outbreak was halted by the development of virus-inactivation methods and their application to plasma concentrates). Additional evidence of the HIV-sparing effect of desmopressin stems from the comparison of the prevalence of HIV infection in Italian patients with mild hemophilia A to the corresponding patients from other countries where the compound was used later. In the United States, for instance, where in the period 1977-1985 mild hemophiliacs were mainly treated with plasma concentrates because desmopressin was not licensed until 1984, anti-HIV prevalence is 18.4%, nine times higher than in Italy.41
## DESMOPRESSIN IN ACQUIRED AND DRUG-INDUCED BLEEDING DISORDERS
The hemostatic defect in uremia is characterized by a prolonged bleeding time, a laboratory abnormality that correlates strongly with the hemorrhagic symptoms of these patients, mainly epistaxis and bleeding from the gastrointestinal tract. Dialysis may improve the bleeding time and the bleeding tendency, but this is not always the case. In the search for pharmacological agents that could improve hemostasis in uremia, intravenous desmopressin was considered, despite the fact that factor VIII and vWF are normal in uremic patients.42 The postinfusion bleeding time became normal in about 75% of them, and returned to baseline values after approximately 8 hours.42 Well-conducted but noncontrolled clinical studies have shown that desmopressin can be used successfully to prevent bleeding before invasive procedures (biopsies and major surgery) and to stop spontaneous bleeding.42 Conjugated estrogens are a long-acting alternative to desmopressin, because they shorten the bleeding time with a more sustained effect lasting for 10 to 15 days.43 The two products can be given together, exploiting the different timings of their maximal effects. Currently, most patients with chronic renal insufficiency are regularly treated with erythropoietin. This practice has led to the sustained improvement not only of anemia but also of the hemostatic defect,44 so that short-acting compounds such as desmopressin and conjugated estrogens are now less frequently needed.
The bleeding time is prolonged in some patients with liver cirrhosis. There is usually mild or moderate thrombocytopenia, but platelet counts do not correlate negatively with the bleeding time. Factor VIII and vWF are in the high normal range, or even higher, yet intravenous desmopressin shortens the bleeding time of cirrhotic patients.45,46 However, a controlled clinical trial has shown that desmopressin is not useful in the management of acute variceal bleeding in cirrhotic patients.47 Because this is the most frequent and serious hemorrhagic problem the overall clinical impact of desmopressin in liver cirrhosis is relatively small.
Desmopressin counteracts the effects on hemostasis measurements of some antithrombotic drugs. It shortens the prolonged bleeding time of individuals taking widely used antiplatelet agents such as aspirin and ticlopidine,46 the prolonged bleeding time and activated partial thromboplastin time of patients receiving heparin,48 and the bleeding time of rabbits treated with streptokinase49 or hirudin50 (without corresponding human data). It also counteracts the antihemostatic effects of dextran, with no apparent impairment of the antithrombotic properties.51
In summary, in chronic renal disease desmopressin remains indicated only for those patients with renal failure not treated or unresponsive to erythropoietin. Desmopressin is a possible treatment for patients with liver cirrhosis and prolonged bleeding time who need invasive diagnostic procedures such as liver biopsies. There is as yet little clinical evidence that desmopressin prevents or stops bleeding complications that develop in association with the use of antithrombotic agents. The compound may provide an opportunity to control drug-induced bleeding without stopping treatment and perhaps avoiding recurrence or progression of thrombosis.
## DESMOPRESSIN AS A BLOOD-SAVING AGENT
The broadening indications of desmopressin, since the first use in hemophilia and vWD in 1977, led several investigators to evaluate whether the compound was beneficial during surgical operations in which blood loss is large and for which multiple blood transfusions are needed.
Open heart surgery with extracorporeal circulation is the epitome of operations that warrant the adoption of blood-saving measures. In addition to techniques such as presurgical removal of autologous blood for postsurgical retransfusion, returning all oxygenator and tubing contents to the patient, and autotransfusion of the mediastinal shed blood, prophylaxis with pharmacological agents might help reduce blood transfusion further. Since 1986, desmopressin has been evaluated for this purpose. In the first controlled randomized study carried out in patients undergoing complex cardiac operations associated with large blood losses, results were impressive.52 Given at the time of chest closure, desmopressin reduced dramatically perioperative and early (12 hours) postoperative blood loss and transfusion requirements by about one third.52 On the other hand, in two subsequent large studies of patients undergoing less complex operations with lesser blood loss, there were no significant differences between desmopressin- and placebo-treated patients in either total blood loss or transfusion requirements.53,54 Other studies, mainly in patients undergoing coronary artery bypass grafting and uncomplicated valve replacement, failed to find any benefit of desmopressin.55,56
The conflicting results of desmopressin in open heart surgery might be due to the fact that most studies were of small size and had insufficient statistical power to detect true differences in blood loss. A meta-analysis of 17 randomized, double-blind, placebo-controlled trials, which included 1,171 patients undergoing open heart surgery, has attempted to overcome this pitfall.57 Overall, desmopressin reduced postoperative blood loss by 9%, a value that is statistically significant but of little clinical impact. Although desmopressin had no blood-saving effect when the total blood loss in placebo-treated patients decreased in the lower and middle thirds of distribution (687 to 1,108 mL), the compound reduced blood losses by 34% when blood loss was larger.57 Therefore, desmopressin seems beneficial only in cardiac operations associated with large blood loss (>1 L). It is not easy to predict which patient will bleed more, but situations such as reoperation, presurgical use of antiplatelet agents, preexisting coagulation defects, and sepsis might help to identify the cases suitable for prophylaxis. Lower preoperative plasma levels of factor VIII and vWF may also help to identify patients most at risk of bleeding.52,53 However, the overlap of values is so large that it is not possible to use these measurements to select patients with the most to gain from the use of desmopressin.
Table 3.
Indications for Desmopressin in the Treatment of Bleeding Disorders
Grading of Recommendation Level of Evidence
Established Mild hemophilia A III
vWD (see Table 2III
Possible Congenital defects of platelet function IV
Uremia IV
Liver cirrhosis IV
Drug-induced bleeding (heparin, hirudin, antiplatelet agents, dextran, streptokinase) IV
Doubtful Cardiac surgery
General surgery
Grading of Recommendation Level of Evidence
Established Mild hemophilia A III
vWD (see Table 2III
Possible Congenital defects of platelet function IV
Uremia IV
Liver cirrhosis IV
Drug-induced bleeding (heparin, hirudin, antiplatelet agents, dextran, streptokinase) IV
Doubtful Cardiac surgery
General surgery
“Established” indications are those in which the hemostatic efficacy of desmopressin has been demonstrated clinically; “Possible” indications, those in which clinical data are too preliminary or inconclusive; “Doubtful” indications, those in which desmopressin is not efficacious clinically. Grading of recommendations and levels of evidence are those proposed by the Agency for Health Care Policy and Research Publications of the US Department of Health and Human Services.
Desmopressin is not the only blood-saving agent that can be used in cardiac surgery. The synthetic antifibrinolytic amino acids epsilon-aminocaproic acid (EACA) and tranexamic acid and the broad-spectrum protease inhibitor aprotinin have also been used, particularly after the recognition that acquired immunodeficiency syndrome (AIDS) could result from blood transfusions contaminated with HIV. A few direct comparison studies58-60 and a meta-analysis61 have shown that the order of efficacy of these hemostatic agents (greatest to least) is aprotinin, tranexamic acid, EACA, and desmopressin.61 On the other hand, the order of drug cost is also the same. Cost-effectiveness analysis is necessary to help the clinicians in making a choice that currently would be directed to aprotinin, but with formidable costs.
The efficacy of desmopressin has also been evaluated in noncardiac surgical operations characterized by large blood loss. When administered to hemostatically normal children before spinal fusion for idiopathic scoliosis, desmopressin reduced their average operative blood loss by about one third,62 but these favorable results were not confirmed in a subsequent study.63 Desmopressin did not reduce blood loss or transfusion requirement after total hip or knee arthroplasty.64 Preoperative desmopressin failed to reduce blood loss in patients undergoing debridement and grafting of burn wounds, a procedure in which extreme blood loss is a frequent occurrence.65
In summary, the efficacy of desmopressin as a blood-saving agent in cardiac and noncardiac surgical operations appears doubtful at the moment.
## THERAPEUTIC GUIDELINES
The main therapeutic guidelines for desmopressin are summarized in Table 3 and are graded upon the criteria proposed by the Agency for Health Care Policy and Research Publications of the US Department of Health and Human Services.66 Twenty years after the first clinical application, the compound is still the treatment of choice for patients with mild hemophilia A and type 1 vWD (grade B recommendation). The evidence of its efficacy as autologous replacement of the deficient factors is so clear that no randomized controlled clinical trial was ever necessary (level III evidence). In patients with congenital defects of platelet function, with the hemostatic abnormalities associated with chronic liver disease and with those induced by the therapeutic use of antiplatelet and anticoagulant agents, desmopressin has been used successfully to prevent or stop bleeding. However, there is still no well-designed clinical trial that truly shows efficacy of the compound in these conditions (grade C recommendation based on level IV evidence). Currently, the widespread use of erythropoietin and the resulting sustained correction of the hemostatic defect make the use of desmopressin unnecessary in the majority of patients with chronic renal insufficiency. Antifibrinolytic amino acids and aprotinin should be preferred to desmopressin in reducing blood loss and transfusion requirements during cardiac surgery with extracorporeal circulation (grade A recommendation based on level I evidence). The use of desmopressin in surgical operations other than cardiac surgery is not warranted at the moment. On the whole, more than 200 years of research have provided an agent that makes the blood clot faster, and William Hewson, who so ingeniously inquired into the properties of blood in the 18th century, perhaps would be content with the outcome of his pioneer studies.
Address reprint requests to Pier Mannuccio Mannucci, MD, Via Pace 9, 20122 Milano, Italy.
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Planning an i7 setup
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I'm trying to put together the best possible i7 setup from scratch and there are a few questions I'm not too clear on: Currently I've come up with: Asus Socket 1366 P6T mobo Intel Core i7 920 4GB A-DATA DDR3 PC-16000 (2000MHz) RAM I'm moving my hard drives, sound card (a somewhat outdated Creative Sound Blaster Audigy 2 ZS Platinum Pro with an external rack) and graphics card (nVidia 7600GT) from my current setup. - The tower. I'll be using my current RAID0 setup, but I'd like to exapand it to 2xRAID0 (eg I don't have the money to buy a new pair of hard drives right now, but I'd like to add a terabyte mirror pair later on). Since I can't seem to find a really good resource on towers, I'm wondering if I should save up for a full tower or would a miditower do? What's the big different between ATX and ATX2? Or can anyone suggest a specific tower? - my current hard drives are IDE drives, but I'd like to add a pair of SATA drives later on. Will I need to consider something when mixing them? Would it make a massive difference (speed-wise) if the boot drive was an IDE drive rather than a SATA one? - will a 500W PSU cut it or should I go for something like 550 or 600? I have no current plans to upgrade the graphics card, but I would probably consider it if I got some more money. I'm gearing the computer primarily for audio/video production, not gaming.
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I would consider getting an 1156 mobo and cpu instead. They are marginally cheaper and the i7 860 is an excellent CPU which is often faster then the 920 you're looking at. From what I've read, the only real reason to go with a 1366 mobo is if you want to do SLI.
When I rebuilt my computer, I waited for the i5 release because I don't care about SLI. I got the i7 860 and it's plenty fast and has a lot of room for overclocking if that is what you're into. It runs cooler and more effeciently then the comparable 1366 CPU (the 920).
On the subject of cases... That's almost entirely up to personal choice. I tend to go a bit overboard on my case since I like it to look nice as well as be functional so I went with the FT01 (http://www.newegg.com/Product/Product.aspx?Item=N82E16811163120&cm_re=ft01-_-11-163-120-_-Product).
For the PSU, try to add up your components to find your minimum requirements. PSUs are most effecient when they operate at around 50% to 70% load. So you don't want to go too high or too low if you're concerned about the most effecient power usage.
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An article summing up the 860 vs 920 quite well.
Intel Core i7 920 vs Intel Core i7 860
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Quote:
Original post by tstrimpI would consider getting an 1156 mobo and cpu instead. They are marginally cheaper and the i7 860 is an excellent CPU which is often faster then the 920 you're looking at.
Correct, there are a couple of cases where the 920 pulls ahead but for the majority of tests I've seen the 860 keeps pace and in some rare cases, due to a slightly higher clock, beats the 920.
Quote:
From what I've read, the only real reason to go with a 1366 mobo is if you want to do SLI.
SLI is a reason, they also have triple channel ram which while not really any faster in the real world can allow for greater capcity (I'm running a 12gig rig atm over 3 channels) and there is the compatibility with the coming 6core/12 thread chips although this isn't a compelling reason given the price its likely to launch at.
If I was building a system now I'd probably build a 860 based (with 16gig of ram "because I can") rather than a 920 based setup.
(My current setup will probably last me into 2012 at which point either the world will end OR I'll be jumping on the Haswell train (or whatever AMD have assuming they are high end competative).. mmmm vector co-processors [grin])
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Moved to Hardware Discussion.
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Oh, and 1366 is a waste of money unless you're planning to run six sticks of RAM. Go with 1156.
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I have further inquiries - however my early Sundayish physical condition doesn't really make formulating those that easy.
My main points however (as far as I've understood) are:
(some what relevant to the discussion)
i7: lower FSB (RAM) clock speed (capped at 1033 MHz, which would make my 2GHz RAM choice from OP quite pointless) - *could use some confirmation on this
i5: faster clock speed, but no triple channel RAM, better turbo (not sure what that is TBH)
(irrelevant to the discussion)
i7: extensible in the future
i5: antiquated technology by definition
In the article posted by tstrimp most people seem to be voting for 920 and since I'm not in the UK right now I can see the price difference being around 6-7 euros between 860 vs 920 right now (the 920 being really marginally more expensive). This is trivial. Do you guys mean that cooling would be an issue? I've read some stuff about the 9xx series hitting almost 100C with stock cooling. I can't really get the big difference between the two.
I have absolutely no intention of even considering SLI. This is not going to be a gaming platform (I actually use my mid-grade laptop for that, which is more than enough for me).
What about the PSU? Can I feel confident with 500W?
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I don't know much about intel chips, I'm an amd fanboy.
but as for towers, the antec900-2 has been my pride an joy for 3 years now, everything ran cooler after getting it. I've been temted to invest in the newer antec1200, more room more airflow.
The main thing I'd point out is make sure the power supply is bottom mounted, I got a dinky raidmax tower, my old rig is in, that I modified so that the psu could be on the bottom and it lowered my cpu temps almost 10 degrees at full load.
If you're a big gamer, that plans to upgrade in the future get a full tower, running 2-4 graphics cards in a mid case really leaves you no room, not even for airflow. that raidmax is a mid tower and the 9800gtx in it blocks 3 of the hard drive slots.
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Quote:
Original post by PromitOh, and 1366 is a waste of money unless you're planning to run six sticks of RAM. Go with 1156.
while this is true, I wanted to point out, the 1366 platform with 6 sticks of ram is the only almost affordable way to run 12 GB of memory for hosting a virtualized rig (if you plan want to run multiple virtual servers on 1 machine, that would be the way to go).
Otherwise, 1156 is just fine for any normal workstation needs. If memory hadn't doubled in price in the last 6 months I would have been building a 920 x 12 GB rig myself soon, but since they did I'm just going to stick with my current quad core 4 GB rig for another year.
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Quote:
Original post by irreversible(some what relevant to the discussion)i7: lower FSB (RAM) clock speed (capped at 1033 MHz, which would make my 2GHz RAM choice from OP quite pointless) - *could use some confirmation on this
No. The RAM clocks can be dialed in at whatever you want, and then you set the CPU multiplier to get whatever frequency you want there. There is one nasty catch here, which is that some motherboards don't support 2000 or 1800 -- even if they support 2200.
Quote:
i5: faster clock speed, but no triple channel RAM, better turbo (not sure what that is TBH)
No 1156 platform has triple channel, i5 or i7. Triple channel is ineffective anyway.
Quote:
(irrelevant to the discussion)i7: extensible in the futurei5: antiquated technology by definition
Not at all. i5 is simply the lower model dual core processor (hyperthreaded so 4 threads). The socket is what matters; 1156 and 1366 target different markets.
Personally I find it laughable to spring for an i7 at all while you're still running IDE drives, but suit yourself.
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Well, I do mean to upgrade the hard drives to SATA when I get the money - 250 GB used to be pretty awesome way back when I got them, but video editing can really make it seem pretty small pretty quickly.
I was basing my judgement of the 1156 on a number of threads I skimmed on tomshardware where this point was being dicussed. Since the 920 and 860 both run on 1366, though, it makes the point moot in this case. If you only hadn't written:
>> 1366 is a waste of money unless you're planning to run six sticks of RAM. Go with 1156.
Wouldn't I also be losing four cores as i5 doesn't have HT? I'm considering expanding RAM to 8GB in the future, but six sticks is a bit of an overkill for my current needs.
At this point 860 seems like a pretty solid choice TBH.
After reading up on dual vs triple channel memory, this conclusion kinda defies your statement that "triple channel is ineffective", Promit.
freeworld - cheers for the pointers on the tower. Tower prices scale quite a lot and I was actually hoping to get away with something a bit cheaper than the 900, but I do want to make it as quiet as possible and as cool as possible with stock cooling.
As mentioned, I don't intend to build a gaming rig so SLI is not something I want or need.
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Quote:
Original post by irreversibleAfter reading up on dual vs triple channel memory, this conclusion kinda defies your statement that "triple channel is ineffective", Promit.
No, they don't disagree at all; they say it's a logical direction to head in but that in the real world you see basically no difference going from one to the other.
Once we swap over to fast DDR5 RAM and have chips with on-chip vector co-processors then triple-channel will really show a difference. But right now, on the chips you are aimming for, triple channel allows you to go to a larger capacity and thats really about it.
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Quote:
Original post by irreversible>> 1366 is a waste of money unless you're planning to run six sticks of RAM. Go with 1156.Wouldn't I also be losing four cores as i5 doesn't have HT?
I think you missed the memo that there are i7 chips for both 1156 and 1366. i7 860 is an 1156 chip.
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I just recently upgraded (from an AMD Athlon 64 X2 3800+ w/ 2GB DDR 400) to an Intel Core i7-860 w/ 8GB DDR3 1600 and I'm really loving it.
One of the main reasons I went for the i7-860 was that I wanted to run virtual machines but still wanted good performance/price. I work almost exclusively in virtual machines, and I have no problems whatsoever running 4-5 VMs at snappy speeds in the background while playing relatively modern games on my host.
It compares relatively well to the dual quad-core Xeon machine I use at work, meaning that neither one makes me wait for anything I feel should be instantaneous. The main difference is that my home machine cost a small fraction of the dual Xeon machine's price.
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I recently bought a Xeon X3440 and I'm extremely happy with it. It's an 1156 chip and it's pretty much equivalent to the i7 860. It has hyperthreading too. It's much cheaper though (or at least it was when I got it with the deals I found), mostly because it's clocked at 2.53GHz which is less than the 860. However, they both overclock very well. I have my X3440 running at 4.0GHz with hyperthreading, using an inexpensive air cooler (Scythe Mugen 2). The CPU cost me $220 Canadian which was something like$100 less than the 860 would have. Although it runs hot at 100% load, idle and normal use sits in the low 30's Celsius with low power draw.
I'm running the Gigabyte P55A-UD3P motherboard. It's reasonably cheap, works great, overclocks great and hasn't given me any trouble at all. For the case, I'm using the Coolermaster RC690 which is a bigger mid-tower case and I like it a lot.
Power supply requirements vary a lot depending on overclocking. The Xeon's TDP is something like 125-135W but it can use over double that when overclocked a lot (at full load). That said, I'm not sure what's really required, but 600W should certainly be enough at 4GHz, and 500W could possibly be enough too, depending on the video card.
I would highly recommend an (overclocked) Xeon. There's no strings attached - it should work in any rig that could house an 1156 i7.
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I can't shake the feeling that you are gilding a pig here. For the price of that i7 setup, I think you would be much better off with an i5/Core2-quad/Phenom, and splashing some of the cash you save on SATA drives and newer video and sound cards.
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Quote:
Original post by irreversibleSince I can't seem to find a really good resource on towers, I'm wondering if I should save up for a full tower or would a miditower do?
A mid-tower is fine. I'm using this case. I've generally been happy with their products.
Quote:
Original post by irreversible- will a 500W PSU cut it or should I go for something like 550 or 600?
I'm using a 550 Watt PSU with my current i7-920 with no problems. 500 is probably OK as well. Anything above that for when you're playing the "How many GPUs can I stick in my PC" game.
Quote:
Original post by irreversible- my current hard drives are IDE drives, but I'd like to add a pair of SATA drives later on. Will I need to consider something when mixing them? Would it make a massive difference (speed-wise) if the boot drive was an IDE drive rather than a SATA one?
Erm, exactly how big are the IDE drives? You can get fairly size-able SATA drives for dirt-cheap, and they will likely be a good upgrade over your IDE drives.
You can mix IDE and SATA fairly well. I've done so on my wife's computer to salvage her old data. However, I'd recommend you toss the IDE drives and upgrade to SATA. \$50 can buy you a 320 GB hard drive.
As someone with an 1366, I'd say listen to the advice and seriously look into a 1156. The 1156 will suite your needs just fine. Personally, I only have a 1366 because I got a half-off deal from a family member working at Intel.
Eidt:
Quote:
Original post by irreversibleDo you guys mean that cooling would be an issue? I've read some stuff about the 9xx series hitting almost 100C with stock cooling.
I haven't seen anywhere near that, but I also haven't pushed my computer to 100%. I've only ever maxed out a few of the cores at any one time.
As the article points out, the price difference between the i7-860 and i7-920 isn't the cost of the CPU so much as the cost of the motherboard. You don't want to pay for features you aren't going to use, and if you opt for the 1366 mobo, then you're going to be paying for features you aren't using.
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# Define Hermitian Matrices.
Matrices
Define Hermitian Matrices.
2020-10-19
Step 1
Hermitian matrix is a complex square matrix that is equal to its own conjugate transpose, that is for which
$$A=A^H$$
where $$A^H$$ denotes the conjugate transpose.
In other words, we can say the matrix whose matrix whose element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column is called Hermitian matrix.
That is
$$a_{ij}=\bar{a}_{ji}$$
Step 2
For example, consider the matrix
$$A=\begin{bmatrix}1 & -i \\i & 1 \end{bmatrix}$$
$$\bar{A}=\begin{bmatrix}1 & i \\ -i & 1 \end{bmatrix}$$
$$\bar{A}^T=\begin{bmatrix}1 & -i \\i & 1 \end{bmatrix}$$
$$\bar{A}^T=A$$
Therefore, A is hermitian matrix.
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# Fourier Integral Operators
###### J. J. Duistermaat
Publisher:
Birkhäuser
Publication Date:
2011
Number of Pages:
142
Format:
Paperback
Series:
Modern Birkhäuser Classics
Price:
49.95
ISBN:
9780817681074
Category:
Monograph
[Reviewed by
Michael Berg
, on
05/13/2011
]
Not long ago I had the pleasure of reviewing J. J. Duistermaat and J. A. C. Kolk’s fine book, Distributions: Theory and Applications. Now I have occasion to talk about another Duistermaat effort, Fourier Integral Operators, appearing as a re-issue in Birkhäuser’s “Modern Classics” series. The late Johannes Jisse Duistermaat, who generally went by Hans, passed away a little over a year ago in Utrecht, Holland, at only 67 years of age. He was a very highly respected mathematician whose marvelous expository abilities were clearly show-cased in his books. The book under review certainly qualifies under this description; it also attests to the breadth of Duistermaat’s interests. Indeed, the obituary Univ. Utrecht published last year includes the following: “[Duistermaat] was fond of mathematical problems that required the sharp tools of analysis combined with the deep insights of geometry. In the field of differential equations he was a leading figure in the world.”
Duistermaat’s Fourier Integral Operators had its genesis in a course the author taught at Nijmegen in 1970. The lecture notes have an interesting history. The Courant Institute first distributed them, but they eventually grew too rare: enter Birkhäuser Verlag in 1995 to launch a “nicely TeXed version of these notes with some minor additions … and corrections,” and now, fifteen years later, we are the recipients of Birkhäuser’s wise move to re-issue the book as a Modern Classic.
And rightly so. For the properly prepared and properly disposed mathematical audience Fourier Integral Operators is a must. As Duistermaat’s Introduction already shows, this is, in the true sense of the word, hard analysis. Even the 0th chapter bespeaks specialization: the author starts with abbreviated (if standard) notations for partial differential operators in the Schwartz space over Rn, notes that Fourier transformation gives an automorphism of this space and then launches a discussion of PDE and pseudodifferential operators in this setting, culminating with a brief literature review of sorts surrounding the work of Lax, Hörmander, and Maslov. And we’re only on p. 7.
In other words, the reader had better gird his loins for what lies ahead. In fact, a very solid background in analysis is nigh on indispensable for mining a maximum yield out of the dense 140 pages of the book. But one of the treasures in Fourier Integral Operators is quite unusual and amplifies the worth of this (already very valuable) book considerably: Duistermaat finishes his second chapter with a discussion of oscillatory integrals with nondegenerate phase functions and then proceeds to consider symplectic differential geometry, Lagrangian manifolds, and even the attendant calculus of variations: this is in fact central to the book, even as the closing parts of Fourier Integral Operators are concerned with such hard-analysis mainstays as the global theory of Fourier integral operators, the Cauchy problem, and oscillatory asymptotic solutions to a certain class of PDE having classical roots.
The earlier focus on symplectic geometry is of independent value, however, because this subject straddles a half dozen areas of contemporary mathematics (including number theory and physics), making Fourier Integral Operators something of a double threat: certain fellow-travelers for whom hard-analysis is, well, too hard to take, will want to cover these parts of the book under review, given what is presented there in so compact and careful a fashion.
Fourier Integral Operators is not easy going: there is no chattiness, there are no exercise sets, and, again, there is a lot of hard analysis (and even a bit of soft analysis) in the book’s 140 pages. But it is a very important book on a subject that is both deep and broad.
Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.
Preface.- 0. Introduction.- 1. Preliminaries.- 1.1 Distribution densities on manifolds.- 1.2 The method of stationary phase.- 1.3 The wave front set of a distribution.- 2. Local Theory of Fourier Integrals.- 2.1 Symbols.- 2.2 Distributions defined by oscillatory integrals.- 2.3 Oscillatory integrals with nondegenerate phase functions.- 2.4 Fourier integral operators (local theory).- 2.5 Pseudodifferential operators in Rn.- 3. Symplectic Differential Geometry.- 3.1 Vector fields.- 3.2 Differential forms.- 3.3 The canonical 1- and 2-form T* (X).- 3.4 Symplectic vector spaces.- 3.5 Symplectic differential geometry.- 3.6 Lagrangian manifolds.- 3.7 Conic Lagrangian manifolds.- 3.8 Classical mechanics and variational calculus.- 4. Global Theory of Fourier Integral Operators.- 4.1 Invariant definition of the principal symbol.- 4.2 Global theory of Fourier integral operators.- 4.3 Products with vanishing principal symbol.- 4.4 L2-continuity.- 5. Applications.- 5.1 The Cauchy problem for strictly hyperbolic differential operators with C-infinity coefficients.- 5.2 Oscillatory asymptotic solutions. Caustics.- References.
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# Show that $n$ lines separate the plane into $\frac{(n^2+n+2)}{2}$ regions…Induction!
Show that $n$ lines separate the plane into $\frac{(n^2+n+2)}{2}$ regions if no two of these lines are parallel and no three pass through a common point.
I know we start with the base case, where, if we call the above equation P(n), P(0), for 0 lines would be 0. But I really have no idea how to begin the inductive step. How do we know what k+1 we're supposed to arrive at?
Thanks!
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looks like $\binom{n-1}{2} + 1$ – Santosh Linkha Oct 9 '12 at 5:50
With $0$ lines, there is $1$ region and no intersections of lines.
Each time a line is added and it crosses $k$ other lines it adds $k+1$ regions and $k$ intersections. Another way of looking at this is that for each line and $k$ intersections added, $k+1$ regions are added (the number of added lines and intersections).
Therefore, the number of regions is $1+\text{the number of lines}+\text{the number of intersections}$. With $n$ lines, there are $\binom{n}{2}$ intersections (if no two lines are parallel and no three lines are coincident).
Thus, the number of regions is $\binom{n}{2}+n+1=\frac{n(n-1)}{2}+n+1=\frac{n^2+n+2}{2}$.
@Bob: Note that robjohn’s answer essentially gives you your induction step: when you add the $(n+1)$-st line, it cuts $n+1$ regions in two, so it adds $n+1$ regions. Add that to the $\frac12(n^2+n+2)$ given you by your induction hypothesis, and you get $\frac12(n^2+3n+4)=\frac12\left((n+1)^2+(n+1)+2\right)$. – Brian M. Scott Oct 9 '12 at 7:24
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# Can an infinite series be thought of as adding up “infinitely many” terms?
Formally, I understand that infinite series are not defined by adding up "infinitely many" terms, but are instead defined as equalling their limit. As user Brian M. Scott outlined in an answer to a similar question (Why is an infinite series not considered an infinite sum of terms?), it is easier to define infinite series by the limit of their partial sums than by considering every single term. However, one geometric proof of the convergence of $$1/2 + 1/4 +1/8+1/16+ \cdots$$ has made me question why we circumvent the problem of adding infinitely many terms with the concept of the limit:
When you look at the diagram above, it seems like every single term has been included (not literally, but it is clear what the diagram represents). Furthermore, if you plotted the above shape on the Cartesian plane, the area of the shape would be $$1$$. Even the point $$(0.99999,0.99999)$$ would be covered by a square/rectangle. When all of the terms have been plotted, it seems like the infinite series not only tends to 1, it equals $$1$$. To me, this is not just because we define an infinite series to equal its limit. The limit only concerns the partial sums, whereas the diagram shows that even if we allow ourselves to add infinitely many terms, there is no immediate contradiction. Obviously, defining infinite series like this formally can create problems: infinite series do not have always have the commutative property, for example. However, is there anything conceptually wrong with thinking of infinite series as adding up infinitely many terms, even though technically this can lead to some problems?
• An infinite sum is the sum of an infinite number of things. We use limits because we can't add them two at a time in a finite amount of time. Do a search for Zeno's paradox. In all examples the "paradox" comes from assuming that an infinite sum is infinite. – John Douma Sep 14 '19 at 18:10
• @JohnDouma if you add the first and second in $2^{-2}$ seconds, then add the third to this in $2^{-3}$ seconds, the fourth in $2^{-4}$ seconds, and so on, then each step will have taken a positive amount of time and you will have added them all up in half a second – Henry Sep 14 '19 at 18:18
• @JohnDouma Thanks for answering. So we never try to define infinite series directly because continually adding the pairs of numbers gets us nowhere. Instead, we use limits to say however many terms we add the series will never get higher than this point. But does it make sense to say after adding up "infinitely many" terms the series equals its limit? After all, I thought the resolution to Zeno's Paradox was that you can add up infinitely many terms even in a finite time space. – Joe Sep 14 '19 at 18:18
• @Henry What time will you add the last two? – John Douma Sep 14 '19 at 18:38
• It's worth pointing out that your example is absolutely convergent - one has way more lee-way in working with sums like that than with more general sums - basically all your intuition truly does transfer. – Milo Brandt Sep 15 '19 at 23:42
Assuming the limit of the sequence of partial sums exists, there is no harm in imagining that you have completed an infinite process of adding terms. If the limit does not exist, there are fairly obvious problems with pretending that you have completed the infinite process. For instance, the sequence of partial sums of $$1 - 1 + 1 - 1 + 1 - \cdots$$ has no limit, but if you imagine that you have completed the infinite process, you imagine that you have a definite value for that sum. What is it? $$1$$? $$0$$? Something else? (For more options that $$0$$ or $$1$$, see Hardy's Divergent Series, or the English Wikipedia's Divergent Series.)
More fundamentally, what does "$$1 + \frac{1}{2} + \frac{1}{4} + \cdots$$" mean? It appears to represent an infinitely long string of symbols. If, as is usually the case, you are using a finitary logic, you do not have the ability to reason about the entire string. (You are able to reason about finite fragments of it). For instance, $$2 \sum_{i-1}^\infty 2^{-i-1} = \sum_{i=1}^\infty 2^{-i}$$ is not the distributive law of multiplication over addition, since there is no infinite version of that law in finitary logic. The proof of the statement only ever reasons about finite initial chunks of the sums (partial sums), so is encompassable by finitary logic.
If you are using an infinitary logic, you are able to reason about infinitely long strings of symbols, like "$$1 + \frac{1}{2} + \frac{1}{4} + \cdots$$". But be careful, the Riemann Rearrangement Theorem suggests that an infinite version of commutativity of addition only applies to certain such infinite strings -- infinite commutativity does not apply to strings representing conditionally convergent series in the sense that the result of "adding infinitely many terms" changes depending on the resulting ordering of the terms. The MSE answer to this question does a pretty good job of laying out some of the weirdness of infinitary logics. An example that isn't discussed there: your set theory doesn't exactly need AC since your logic permits you to just write down infinitely long choice functions: "from set 1, this element; from set 2, that element; ..." (Note that varied infinitary logics may put different infinite limits on the lengths of sentences. So your logic may permit "small" infinite choice but you'll need a version of AC for larger choice.)
• Thanks, it’s interesting to see how defining infinite series differently does accommodate the way I think about them intuitively (albeit with some pitfalls). – Joe Sep 16 '19 at 5:48
• The first paragraph says "there is no harm", and then the last one explains that there is a lot of harm. – Martin Argerami Sep 16 '19 at 12:09
• @MartinArgerami : I'm not seeing where you're going. For instance, if Rearrangement gives a different convergent, the cause is obvious: you are reasoning about a different infinite string, i.e., about a different sequence of partial sums. – Eric Towers Sep 16 '19 at 12:41
Obviously, defining infinite series like this formally can create problems
It is intuitively OK to think of summing an infinite series as
but if you want to prove theorems about those sums and avoid the problems you need a formal definition. Mathematicians have discovered that a good way to do that is to avoid "adding infinitely many numbers" by proving infinitely many statements. That's what the "for every $$\epsilon$$" does in the formal definition of limits.
• Thanks, this was a very insightful answer. As a follow-up question: in the resolution of Achilles and the Tortoise, do we (in this specific case) allow ourselves to do infinitely many steps (and in effect add every single term up) because each step takes less and less time too? – Joe Sep 14 '19 at 18:27
• @Joe I don't think so. Achilles and the Tortoise is a linguistic paradox and perhaps a philosophical paradox but not a mathematical one. Mathematicians just define limits formally and reason about them when so defined. That definition produces results that are consistent with intuition, free of contradictions (though perhaps not provably so) and useful. That's enough to get on with the job. – Ethan Bolker Sep 14 '19 at 18:42
• @EthanBolker Zeno's paradoxes, including Achilles and the Tortoise could be viewed as mathematical paradoxes in their time (though Zeno appears to have preferred to think of them philosophically). However, as you point out, with the introduction of the formal concept of limits many centuries later, it is no longer an insurmountable mathematical paradox. – Cort Ammon Sep 16 '19 at 0:28
There is a reason why it appears that the sum of those areas is literally the sum of infinitely many terms, and not 'just a limit'. However, this reason is probably not as simple as you think. To see why, consider something that looks similar:
The unit square $$[0,1]×[0,1]$$ has area $$1$$ is the union of infinitely many line segments of the form $$\{x\}×[0,1]$$ for each $$x∈[0,1]$$, but each of these line segments has area $$0$$, so the unit square's area is not in any way the sum of infinitely many zeros.
But what is the difference? Well, what is area in the first place? One possible basic notion is to first define the area of each rectangle as the width times height, and then define the area of a region as the total area of grid squares completely contained inside the region as the grid square size tends to zero. This definition has some significant defects. For instance, $$[0,1]^2∖\mathbb{Q}^2$$ would have area $$0$$, even though 'almost none' of the unit square has been removed.
It turns out that we can define area that has nicer properties than the above, via something called the Lebesgue measure. This measure assigns an area to every measurable set of points in the plane, and this area is a non-negative real number or $$∞$$. But not every set of points in the plane is measurable! For convenience let me use "region" as a synonym for "measurable set of points". This measure has three nice properties:
1. Rectangle area: The area of a rectangle is equal to its height times width. (If this does not hold then we do not deserve to call it "area".)
2. Monotonicity: If one region is completely contained in another region, then the area of the first region is at most the area of the second.
3. Countable additivity: The area of a countable disjoint union of regions is the sum of their areas. Note that since areas are non-negative, the sum is well-defined. (This is directly related to the fact that a monotonically increasing sequence of reals has a real limit or tends to $$∞$$.)
Now let us get back to your question. You have a countable sequence of disjoint rectangles whose areas sum to $$1$$, and whose union is the unit square. This corresponds to the countable additivity of the Lebesgue measure. In contrast, my example has an uncountable number of line segments each with area $$0$$, but whose union is still the unit square. Well, the Lebesgue measure does not satisfy uncountable additivity. (In fact this example shows that any kind of 'area' that satisfies property (1) cannot possibly satisfy uncountable additivity in any meaningful sense.)
Observe that this viewpoint of an infinite (countable) sum only works for non-negative reals, otherwise you cannot view it as areas and the correspondence with the Lebesgue measure fails. This is directly related to the fact that an infinite sum of non-negative reals is well-defined; the partial sums tend monotonically to either a finite real or infinity, and the fact that an infinite sum of arbitrary reals may not be well-defined, such as $$1-1+1-1+\cdots$$.
The limit only concerns the partial sums, whereas the diagram shows that even if we allow ourselves to add infinitely many terms, there is no immediate contradiction. Obviously, defining infinite series like this formally can create problems: infinite series do not have always have the commutative property, for example. However, is there anything conceptually wrong with thinking of infinite series as adding up infinitely many terms, even though technically this can lead to some problems?
Indeed, your idea that commutativity is relevant is correct. Note that an infinite sum of non-negative reals is well-defined, because rearranging them cannot change the limit of partial sums (this is a good exercise and the proof may be illuminating). In contrast, an infinite sum of reals that have both positive and negative terms may not be absolutely convergent, and it turns out that absolute convergence is equivalent to unchanging limit of partial sums.
So the answer to your question is: Yes you can view an infinite sum of non-negative reals as a summation of infinite terms in the same sense as the disjoint union of regions, but no you cannot view every infinite series in this way because reals can be negative, and no you cannot use any kind of reasoning that if "all of the terms have been plotted" geometrically then the infinite sum is equal to the area, because under any reasonable definition (see below) we should have $$\sum_{i∈S} 0 = 0$$ for any set $$S$$, even if $$S$$ is the set of line segments that cover the unit square like in the example I gave (whereas the area of the unit square is $$1$$).
For the curious, here is how we can define generalized summation of a non-negative real-valued function on an arbitrary index set. I wish to emphasize that without any definition we cannot even talk about such infinite sums (they are simply meaningless) to begin with, and so it is incorrect to perform any kind of reasoning about them at all, geometric or otherwise. (This is why I at first decided not to mention it in my post, but I now agree with the commenter Martin that I probably should clear up any possible misconception on this issue.)
Given a function $$f:S→R_{≥0}$$, we can define $$\sum_{i∈S} f(i) := \sup \{ \sum_{i∈T} f(i) : T ⊆_{fin} S \}$$, where "$$T ⊆_{fin} S$$" means "$$T$$ is a finite subset of $$S$$", and this agrees with the standard summation in any order if $$S$$ is countable. But this generalized summation is useless for uncountable $$S$$ unless $$f(i) > 0$$ for only countably many $$i∈S$$ (since otherwise the sum would be $$∞$$), so such a definition seems to have no practical use.
• I like this approach. One could imagine a world where the theorems of Lebesgue theory were instead treated as axioms defining countably-indexed sums, in which case OP's picture would be a perfectly valid proof. – hunter Sep 15 '19 at 16:07
• @hunter: Not just that. One can actually axiomatize probability and random variables to capture the countable additivity of the Lebesgue measure so as to completely avoid the need to set up probability spaces for every single construction in 'ordinary' probability theory. After all, we ourselves reason about random variables in a very different way from the purported formally rigorous approach via measure theory. If you'd like to discuss this further, you're welcome to the logic chat-room. =) – user21820 Sep 15 '19 at 16:10
• @user21820 Thanks, this was a very detailed and helpful answer. It’s good to know the limitations of the way I was trying to envisage infinite series. – Joe Sep 16 '19 at 5:45
• I like this answer. I would suggest a more explicit mention of the fact that the OP's geometric reasoning that $\sum_n2^{-n} =1$ also leads to $\sum_{t\in[0,1]}0=1$. – Martin Argerami Sep 16 '19 at 12:22
• @MartinArgerami: Thanks for your comment! Indeed, I did consider saying something about infinite sums over a set, namely that given a function $f : S → \mathbb{R}_{≥0}$, we can define $\sum_{i∈S} f(i) := \sup \{ \sum_{i∈T} f(i) : T ⊆_{fin} S \}$, and this would agree with the standard definition if $S$ is finite or countable. However, this is useless for uncountable $S$ unless $f(i)$ is positive for only countably many $i∈S$, so it is unclear to me what practical use such a definition would have. But with no clear definition, we can't even talk about $\sum_{t∈[0,1]} 0$, so I didn't mention it. – user21820 Sep 17 '19 at 12:19
I would say it's best to think of adding up an infinite number of terms as something that makes intuitive sense but has more than one reasonable definition.
To illustrate this, I'll define three sums. None of the "flavored sum" notation is remotely standard.
$${}^\alpha\!\sum$$ which is only defined when the series is absolutely convergent. $${}^\sigma\!\sum$$ is the familiar limit sum and $${}^c\!\sum$$ is the Cesàro sum. There are other, more general sums that I won't cover in this answer because I don't understand them very well.
The notation below, $$\sum \cdots = \xi \iff \!\cdots\,$$, is intended to emphasize the fact that not every sum converges to a real number.
$${}^\sigma\!\sum_{k=1}^{\infty}f(k) = \xi \stackrel{\mathrm{def}}{\iff} \lim_{n\to\infty} \sum_{k=1}^{n}f(k) = \xi$$
$${}^\alpha\!\sum_{k=1}^{\infty}f(k) = {}^\sigma\!\sum_{k=1}^{\infty} f(k) \stackrel{\mathrm{def}}{\iff} {}^\sigma\!\sum_{k=1}^{\infty} |f(k)| \;\;\text{is defined}$$
Following Wikipedia's lead, let's define the Cesàro sum.
$$s_a(m) \stackrel{\mathrm{def}}{=} \sum_{k=1}^{m} a(n)$$
$${}^c\!\sum_{k=1}^{\infty} a(k) = \xi \stackrel{\textrm{def}}{\iff} \lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^{n} s_a(k) = \xi$$
Now let's show some examples distinguishing the type of sums.
$$\left\{ {}^\sigma\!\sum_{k=1}^{\infty} \frac{1}{k^2} \;,\; {}^\alpha\!\sum_{k=1}^{\infty} \frac{1}{k^2} \;,\; {}^c\!\sum_{k=1}^{\infty} \frac{1}{k^2} \right\} = \left\{ \frac{\pi^2}{6} \right\}$$
$$\left\{ {}^\sigma\!\sum_{k=1}^{\infty} \frac{(-1)^k}{k^2} \;,\; {}^c\!\sum_{k=1}^{\infty} \frac{(-1)^k}{k^2} \right\} = \bigg\{ - \ln(2) \bigg\} \;\;\text{but}\;\; {}^\alpha\!\sum_{k=1}^{\infty}\frac{(-1)^k}{k} \;\;\text{is undefined}$$
$${}^c\!\sum_{k=1}^{\infty} (-1)^k = -\frac{1}{2} \;\;\text{but}\;\; {}^\alpha\!\sum_{k=1}^{\infty} (-1)^k \;\;\text{and}\;\; {}^\sigma\!\sum_{k=1}^{\infty} (-1)^k \;\; \text{are both undefined}$$
To talk of "adding up infinitely many terms", you have to have some definition first of what exactly it means to do that. The general consensus is that the limit definition is meant.
The issue at work here is not so much the formal definition as a limit, but the intuitive understandings we choose to bring to bear upon that, and there are at least two, and what is going on here is seeing a limit as dynamic, or the end result of a dynamic process. There isn't anything "wrong" with that, unless then you want to compare it to a static situation, which is what a single geometric figure, existing "at once", "simultaneously", on the plane is.
The intuition for a limit as static situation is that it's a statement about a certain property the square you give has: namely, if you draw a circle of any radius you want about that upper-right corner, no matter how small, you can always find pieces smaller in area than that circle inside (from which it follows also that it must contain infinitely many pieces). It's not a matter of progressively drawing such circles one after the other, but rather that the property is in the form of stating what would happen in infinitely many possible counterfactual situations with the given object.
I compare it to proving that the natural numbers have as many elements as the positive rationals. You can demonstrate a bijection between them with enough detail that you can tell what the millionth term in the sequence in or what is the index of 335/113, but we need to come to terms with the notion that "counting to infinity" is something that we can only consider under the terms with which we have defined those words.
The same thing is happening here. I could ask for any point on that square except the upper-right corner, and you'd be able to tell me the label of the unique rectangle that includes it. But you're still only drawing a finite number of those rectangles and you still can't fill in that upper-right corner. To respect those important points, we say that the limit of that series is 1 instead of saying that the sum is 1.
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# Enu To Ecef Example
I would assume that if you want to know the slope encounrered by a vehicle, that implies the rate of change of "down" over the horizontal displacement. Find link is a tool written by Edward Betts. Coordinate converter is a free online application which allows for example to convert latitude longitude gps coordinates to easting northing x y: Lambert,UTM,RGF93,ED50,NAD27,…. ECEF y ECEF z ECEF x ENU y ENU z ENU Prime Meridian Figure 1: Geodetic, ECEF and ENU coordinates systems. 6647 degrees West of Greenwich Or degrees, minutes and seconds: latitude 43:04:33 North, longitude 77:39:53 West Or, in the case of longitude, one can measure in time zones. C# (CSharp) GeodeticCoordinate - 24 examples found. The coordinate frame called earth is the origin of ECEF. The world of ECEF aka geocentric coordinates. You can rate examples to help us improve the quality of examples. 1 Collocated Universal {u} and Body {b} Coordinate Systems 12 3. In the present work, we have selected ENU and RF CSs to express information on the target, as illustrated in Fig. Then, by choosing a reference point, the transformation between ECEF (WGS84Earth-Centered, Earth-Fixed) and ENU is computed. (Depending on the application this may not necessarily be the case; for example, if the quaternion specifies an attitude relative to Earth coordinate axes, such as ECEF, then yaw/pitch/roll may or may not also be relative to those axes, vs. Roll, Pitch, Yaw) to describe the orientation of the vehicle. The systems are needed because the earth is an imperfect sphere. Earth-Centered-Earth-Fixed (ECEF) Coordinate System, or CTS. | MAV_MODE_FLAG_AUTO_ENABLED = 4 // 0b00000100 autonomous mode enabled, system finds its own goal positi. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'. 1) is called WGS-84 (World Geodetic System 84) and it is normally used in GPS-based navigation. The terms LIDAR (or LiDAR) and LADAR are generally used interchangeably and numerous articles have been written about what types of applications are LIDAR vs. 1: Geodetic,ECEF,andENUcoordinatesystems 2. In this mode, the vector of unknown states is defined as: where is the receiver’s antenna position in an earth-centered, earth-fixed (ECEF) coordinate system (in meters), is the speed of light and is the receiver clock bias (in seconds). Other obtained mapping results also are presented in this. The Floating Viewer displays how a specific object appears in different display representations and view directions. You can rate examples to help us improve the quality of examples. The position of a receiver mounted on a ground vehicle was set to r r ≡(10 6 )•[– 2. the origin of the smartphone coordinates or the ENU coordinates. This MATLAB function returns vector components uEast, vNorth, and wUp in a local east-north-up (ENU) system corresponding to vector components U, V, and W in a geocentric Earth-centered Earth-fixed (ECEF) system. To transform from ECEF coordinates to the local coordinates we need a local reference point, typically this might be the location of a radar. The conversion of ECEF coordinates to geodetic coordinates (such WGS84) is a much harder problem. ” 6c DA KM R™ Y‰ g' oD vW } „¡ ‹¨ ’Á ™3 Ÿë"¦m¬Ö&³O(¹Ù*¿¸,ÆØ. Bailey Follow this and additional works at:https://scholar. During the mastication process, the food is positioned by the cheek and tongue between the teeth for grinding; the muscles of mastication move the jaws to bring the teeth into intermittent. This is just the inversion of the ECEF to ENU transformation so. problem, I had to learn about different coordinate frames used in Guidance, Navigation & Control (J2000, ECEF, ENU, etc. - gyjun0230/wgs_conversions. , 2013) •7/14 Parameter Helmert Transformations •Converting XYZ to latitude, longitude, and height •Converting XYZ to ENU •Questions on Problem Set #1 Thursday. C++ (Cpp) ecef_of_ned_pos_i - 4 examples found. ECEF coordinates are large numbers that must be in double precision to maintain their resolution. Engel FGAN-FKIE, Dept. Parameters. Earth-centered, earth-fixed. @mesonbuild core maint. If a radar is located at { X r , Y r , Z r } and an aircraft at { X p , Y p , Z p } then the vector pointing from the radar to the aircraft in the ENU frame is. This directory contains examples of a C++ and a python client. ENU coordinate to Camera coordinate. Despite technical differences. Enter 2 sets of coordinates in the 3 dimensional Cartesian coordinate system, (X 1, Y 1, Z 1) and (X 2, Y 2, Z 2 ), to get the distance formula calculation for the 2 points and calculate distance between the 2 points. Example of cycle slips in urban areas Figure 2 shows a typical cycle slip pattern. The Z-axis, is parrallel to the axis of rotation of the earth. Current baseline in ECEF z or NED down component in mm. ~], and the new definition of. Dear Readers, It has been many (30+) years since I have had to work this kind of math and it is kickin' my butt. So now using this as a reference point, I then use WGS84 coordinates (0,1,0) and get ECEF x,y,z coordinates of (6377165. Sample output: Reference not specified, using first epoch: X =-1282458. ECEF Coordinate System An in depth explanation of the ECEF coordinate system and how it’s used in the WRLD maps to render the globe accurately. The coordinate frame called earth is the origin of ECEF. The other rotations each contain unknown calibration parameters which will be defined. reserved Velocity XYZ ECEF XYZ ECEF output off 0x43 XYZ ECEF output on ENU output ENU output off 0x56 ENU output on reserved Timing Time Type GPS time 0x42, 0x43, 0x4A, 0x83, 0x84, 0x56 reserved Lassen SQ GPS Receiver. Display representations define how an object appears in a drawing. Altitude is perpendicular to the reference ellipsoid, so it is effectively parallel to "down". We also provide the ENU data. 1Geodetic Coordinate System The current geodetic coordinate system (see Figure 2. C# (CSharp) GeodeticCoordinate - 24 examples found. 2] and astronomic nutation CA. ECEF Earth Centered Earth Fixed ECI Earth Centered Inertial ENU East-North-Up FOG Fiber Optic Gyroscope GPS Global Positioning System IFR International Federation of Robotics IMU Instrument Measurement Unit INS Inertial Navigation System kNN k-Nearest Neighbor LPT Local Tangent Plane. Since the elevation is usually not available in a navigable map, we convert the map points in the working frame by supposing that they are all located at the ellipsoidal height. Bounds will not work well with ECEF coordinates. (ENU) frame. Show position on a map. 1 Collocated Universal {u} and Body {b} Coordinate Systems 12 3. A conversion from ENU to ECEF is also required. 963) XYZ Translation (Dx = 146, Dy = 507, Dz = 685) 2. In the example, you create a subject at th e beginning of the application and subscribe an observer to it. It is a simple Cartesian coordinate system with the center of the earth at it's origin. How do Þ|know? q1 = 2v1 but q3 = 4v3*% A_\íY U l ° ’ Ö “ 23 A} U (l ° ’ “ : \h„BBÕ ] Õî ^ ì v _ r 8s e v ‡ ‰Al( e ‹ ® ° Ì ìY  – h — M ˜ § ¨ Î Ï 5 mÓ Ô % â ã * n ä ó ô … } “ ¢ ,£ ¤ ° !m¥ ª ¬ *¯ ± ³ · P r. The status of Siebel HI services/applications (for example, Call Center) is shown as down. Table 1, AREAv2). (Subirana, 2013) (Misra, 2011) (Dawson, 2005) (Grooves, 2013) Figure 5: ENU frame (Misra, 2011). The terms LIDAR (or LiDAR) and LADAR are generally used interchangeably and numerous articles have been written about what types of applications are LIDAR vs. enu (ndarray of float) – numpy array, shape (Npts, 3), with local ENU coordinates. det Compute the determinant of A. The local ENU coordinates are formed from a plane tangent to the Earth's surface fixed to a specific location and hence it is sometimes known as a "Local Tangent" or. Earth-Centered, Earth-Fixed,ECEF,isaCartesiancoordinatesystem,(XE,YE,ZE) (superscript E for earth), with its origin in the earth’s center of mass and with fixed axes with respect to the earth as seen in Figure 2. V n is the Coriolis acceleration vector; g n is the gravity vector, including the gravitation term and the centripetal term related to the Earth rotation; and f b is the specific force vector in the body frame, which is measured by the. brw 0 50 100 150 200 250-4. Transform 3-D vector components between ECEF, ENU, and NED systems. C# (CSharp) GeodeticCoordinate - 24 examples found. First of all, you should consider the relationship between the WGS84 lat/lon/alt and the ECEF frame. A simplified presentation is given here. We denote this matrix by R ecef→enu: [r] enu = R ecef→enu [r] ecef = ⎛ ⎝ −sinφ. For more information about WGS84, see Reference Spheroids. is the semi-major axis and is the first numerical eccentricity of the ellipsoid. For example, it is unclear whether you claimed to be healthier than all fast food restaurants, including those listed as competitors on page 27. problem, I had to learn about different coordinate frames used in Guidance, Navigation & Control (J2000, ECEF, ENU, etc. lat_ref: Reference latitude, unit specified by latlon_unit, default in deg. It can be assigned either scene (for Scene ENU) or ecef (for ECEF). Bytes in record. ECEF Coordinate System An in depth explanation of the ECEF coordinate system and how it’s used in the WRLD maps to render the globe accurately. Both variables are only correlated with radar geographic coordinates at time. EST] Phone: (301) 713-3242. GeoPositionENU [GeoPositionENU [enu, p 1], p 2] converts between two different ENU systems. » Full 14-parameter datum transforms, including time dependence. An example for M28 looks like this: cs2cs +proj=tmerc +lat_0=0 +lon_0=10d20 +k=1 +x_0=150000 +y_0=-5000000 +ellps=bessel \ +towgs84=577. 1: The earth centric earth fixed (ECEF) coordinate system compared with the local east-north-up (ENU) coordinate system. We are a leader in the development of spacecraft and satellite control systems and MATLAB toolboxes for the spacecraft industry as well as alternative power devices such as the SunStation electric vehicle charger and the Direct Fusion Drive. More details on the first two CSs can be found in [7]. In geodesy, geographic coordinate conversion is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. The example to for sending Entity State PDU is great!. Below are a few examples: Map cropping and plotting do not work in ECEF coordinates (these operations are fundamentally 2D operations, which is convenient only for LLA and ENU coordinates) Route planning does not work in LLA coordinates (spherical distances have note been implemented). Right-click the dimension line or the dimension text for a segment. teme to ecef matlab, May 29, 2012 · There are multiple systems for ECEF such as : true equator, mean equinox (TEME), true of date (TOD), and pseudo earth fixed (PEF). It would be unwise to conclude too much from this one example but hopefully it at least provides a little insight in how the two receivers and the two RTK engines differ. pure-Python (Numpy optional) 3D coordinate conversions for geospace ecef enu eci - geospace-code/pymap3d. ) to describe the motion of a vehicle and about Euler angles (e. The DCM matrix performs the coordinate transformation of a vector in Earth-centered Earth-fixed (ECEF) axes, ( ox 0 , oy 0 , oz 0 ), into geodetic latitude and longitude. (For example at NASA J2K time scale is widely used. Running the script. Convert local ENU coordinates to ECEF coordinates ; Convert ECEF coordinates to GPS coordinates ; From ENU to ECEF. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection, in which the sphere is projected onto a tangent plane or secant plane. 4232 \ +to \ +proj=longlat +ellps=WGS84 +datum=WGS84 Belgium. searching for ENU 329 found (348 total) alternate case: eNU Enu language (262 words) case mismatch in snippet view article find links to article Enu or Ximoluo (Chinese: 西摩洛; autonym: ŋɔ˧˩ŋjv̩˧˩ (Jiang, et al. MAVLink-compatible systems are expected to use these definitions where possible (if an appropriate message exists) rather than rolling out variants in their own dialects. The matrix is the skew-symmetric matrix of the rotation rate vector of the ENU frame with respect to ECEF frame, expressed in the ENU frame as: (13) The matrix is the skew-symmetric matrix of the rotation rate vector of the body frame with respect to the ECI frame , expressed in the body reference, which is measured by the gyros. In many targeting and tracking applications the local East, North, Up (ENU) Cartesian coordinate system is far more intuitive and practical than ECEF or Geodetic coordinates. So now using this as a reference point, I then use WGS84 coordinates (0,1,0) and get ECEF x,y,z coordinates of (6377165. First, specify the reference spheroid as WGS84 with length units measured in kilometers. ENU is a Cartesian coordinate system with a local origin, oriented along the WGS84 ellipsoid, with axes pointing to East (X), North (Y) and Up (Z) directions. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. selected practical examples going further into the theoretical concepts and their practical implementation. The terms LIDAR (or LiDAR) and LADAR are generally used interchangeably and numerous articles have been written about what types of applications are LIDAR vs. Specify values in units that match the LengthUnit property of the spheroid argument. If a radar is located at { X r , Y r , Z r } and an aircraft at { X p , Y p , Z p } then the vector pointing from the radar to the aircraft in the ENU frame is. Earth Centered, Earth Fixed (ECEF) x-y-z values in km And press the conversion direction desired. Record length. Note that the transformation direction indicated by the subscript "ECEF/ENU" reads right to left, i. Application of Particle Filters for Vehicle Positioning Using Road Maps Pavel Davidson 1, Jussi Collin , John Raquet2, and Jarmo Takala1 1Tampere University of Technology, Finland 2Air Force Institute of Technology, USA BIOGRAPHIES Pavel Davidson received his MSc in aerospace engineering from Technion, Israel Institute of Technology in 1996. 1 The second sub-system, in turn, uses a virtual 3D space with the user located at the origin. 726420485 km. In geodesy, geographic coordinate conversion is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. 1 ENU Realization 90 5. Management fee schedules and total expenses. This book will use the ENU convention, and the LLF frame will be referred to as the l-frame. Michael Hirsch, Ph. Current estimate of baseline accuracy. 1 The default rotation_sequence='ZYX' is the aerospace sequence and rotAngle1 is the yaw angle, rotAngle2 is. If you like my calculator, please help me spread the word by sharing it with your friends or on your website or blog. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. For more information about WGS84, see Reference Spheroids. The cartesian coordinate system is a right-hand, rectangular, three-dimensional, earth-fixed coordinate system with an origin at (0, 0, 0). For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'. llh2ecef (llh) [source] ¶ Convert lat,lon,hgt geographic coords to X,Y,Z Earth Centered Earth Fixed (ecef) or just (ecf) coords. The elevation in the ENU system is the angle above the local horizontal. A matrix which converts vectors from the ECEF frame to the East, North, Up (ENU) frame can be found in [4]. 1) is called WGS-84 (World Geodetic System 84) and it is normally used in GPS-based navigation. The NED system differs from the ENU system by a simple rotation. For example, CECI ENU denotes the coordinate transformation matrix from earth-centered inertial (ECI) coordinates to earth-fixed east-north-up (ENU) local coordinates and CRPY NED denotes the coordinate transformation matrix from vehicle body-fixed roll-pitch-yaw (RPY) coordinates to earth-fixed north-east-down (NED) coordinates. 1(a) and (b), the filtering results in the ECEF coordinate system and the ENU coordinate system are almost the same. For example, cookies help you log in by pre-filling the username field. ECEF xyz to Latitude, Longitude, Height There is no closed form solution for this transformation if the altitude is not zero. GPS TOOLBOX - GPS SOFTWARE TOOLBOX for MATLAB There are more than 31 fully explained examples (in excess of 80 pages) with input and output data, and generated plots. More template T transform_frame_enu_aircraft (const T &in, const Eigen::Quaterniond &q) Transform data expressed in ENU to aircraft frame. Dear Readers, It has been many (30+) years since I have had to work this kind of math and it is kickin' my butt. For more information about WGS84, see Reference Spheroids. Internally, this will perform UTM (+ zone) → LLA → ECEF → ENU via composing transformations with ∘ into a ComposedTransformation:. Quite simply, if the estimated longitudinal speed over ground is U, and the estimated heading is φ, ignoring the lateral velocity leads to the evolution of. ) • The curvature of the Earth over a large area may be. Advertisement: This definition appears rarely. Another example might be publishing a stream with smaller observation messages containing only L1 content for some users. MAVLink-compatible systems are expected to use these definitions where possible (if an appropriate message exists) rather than rolling out variants in their own dialects. Making statements based on opinion; back them up with references or personal experience. A ship includes a star tracker mounted on a platform stabilized in ENU by the inertial navigation system (INS). It is more convenient to represent the CrIS FOV location in the ECEF coordinate system (or with latitude and longitude), but the ECI frame is simple to. The problem is that the radius R N is needed to find geodetic height h and geodetic latitude is needed to find R N. A device for determining the spatial alignment of an inertial measurement unit (IMU) positioned in or on a vehicle comprising: means for obtaining vehicle-related movement data for the vehicle (110) including velocity data measured by or derived from measurements obtained by one or more satellite positioning systems (SPSs), the velocity data including an SPS-based. enu shree,baleshwar Singh,sanjay varma and ram mishraa in supporting roles. calculation was executed in ECEF (Earth Centered Earth Fixed) coordinate system, or more precisely in ENU (East-North-Up) local topocentric coordinate system. I know how to get the rotation matrix that will put accelerations from the. Earth Centered, Earth Fixed coordinates in relation to latitude and longitude. Specify values in units that match the LengthUnit property of the spheroid argument. For example, these three axes and directions can be east (E), north (N), and up (U). The following are code examples for showing how to use numpy. We denote this matrix by $$\underset{ecef\rightarrow enu}{\mathbf{R}}$$:. The systems are needed because the earth is an imperfect sphere. V n is the Coriolis acceleration vector; g n is the gravity vector, including the gravitation term and the centripetal term related to the Earth rotation; and f b is the specific force vector in the body frame, which is measured by the. 2] and astronomic nutation CA. Sample output: Reference not specified, using first epoch: X =-1282458. Double Meters. Altitude is perpendicular to the reference ellipsoid, so it is effectively parallel to "down". selected practical examples going further into the theoretical concepts and their practical implementation. A time evolution of the dispersion of space pieces from a breakup event to the ground impact time is represented in terms. This attribute defines the vector in the reference frame. utsunomiya-u. The coordinates are often chosen such that one of the numbers represents a vertical position and two or three of the numbers represent a horizontal position; alternatively, a geographic position may be expressed in a combined three-dimensional. A Java port of Olson’s ECEF-to-Geodetic algorithm is shown below, along with the standard Geodetic-to-ECEF algorithm. Latitude, Longitude, Height to ECEF xyz There is a closed form solution for this transformation. This flag is intended for temporary system tests and should not be used for stable implementations. , WMM2020) calculations, and for solving geodesic problems. Given the user’s position in elliptical coordinates (: latitude, : longitude), user coordinates can be easily converted from a ECEF frame to a local ENU frame using the following matrix multiplication. Quite simply, if the estimated longitudinal speed over ground is U, and the estimated heading is φ, ignoring the lateral velocity leads to the evolution of. Making statements based on opinion; back them up with references or personal experience. Simple WGS 84 - ECEF conversion functions. ~], and the new definition of. This rotation aligns East (X) axis with the X ECEF axis. The problem is that the radius R N is needed to find geodetic height h and geodetic latitude is needed to find R N. Answers appear in the text box below the input. iCartesian™ - cartesian, geodetic converter for iPhone. Earth Centered, Earth Fixed (ECEF) x-y-z values in km And press the conversion direction desired. MATTI RAITOHARJU: PNaFF: a Tool to Assist Development of Hybrid Positioning Algorithms Master of Science Thesis, 54 pages and 3 pages appendices August 2009 Major: Mathematics Examiner: Prof. ENU coordinate to Camera coordinate. Once we have obtained both measurements in the same coordinate system we can transform them back to a Cartesian plane. ecef ecef ecef n d User ENU frame (x i,y i z i) (x u,y u,z u) Fig. This MATLAB function returns vector components uEast, vNorth, and wUp in a local east-north-up (ENU) system corresponding to vector components U, V, and W in a geocentric Earth-centered Earth-fixed (ECEF) system. To convert from geodetic coordinates to local ENU coordinates is a two-stage process: Convert geodetic coordinates to ECEF coordinates; Convert ECEF coordinates to local ENU coordinates; From ECEF to ENU. Example: Arc leader (Beyond Witness Lines setting) Example: Line leader (Away from Origin setting) To return the dimension text to its original position, drag the handle back toward the dimension line, so that it snaps to its original position. Assume the LLA is in WGS 1984 unless otherwise stated. If, for example, the pitch angle measurements from the vertical gyro are denoted by θ 0, θ 1, θ 2, and θ 3, where θ 0 corresponds to the current measurement and θ 3 corresponds to the measurement taken three samples previously, then the slope of the least squares line for these points approximates the derivative [11]: (26) θ ˙ ≈ 3 θ. These angles are called Euler angles or Tait–Bryan angles. If you use. As the axes are tied to positions on the earth, such as the North Pole and the Prime Meridian, points in ECEF are fixed on the Earth’s surface. ECEF y ECEF z ECEF x ENU y ENU z ENU Prime Meridian Figure 1: Geodetic, ECEF and ENU coordinates systems. iCartesian™ - cartesian, geodetic converter for iPhone. This rotation aligns East (X) axis with the X ECEF axis. gpsの位置をdouble値から変換する (1) geocoordinatewatcher enu eci ecef blh c# gps. The time series shows the relative. You can preview display representations by clicking (Floating Viewer) in the Display Manager. the origin of the smartphone coordinates or the ENU coordinates. 3 Trigonometric Relationships Between Rotated Frames 13. Convert local ENU coordinates to ECEF coordinates ; Convert ECEF coordinates to GPS coordinates ; From ENU to ECEF. 5 meter in the horizontal and vertical directions respectively using six captured images and two control points. High precision ying is an important part of all remote sensing and photogrammetry related ights. ” 6c DA KM R™ Y‰ g' oD vW } „¡ ‹¨ ’Á ™3 Ÿë"¦m¬Ö&³O(¹Ù*¿¸,ÆØ. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'. Moving from an ECEF to ENU coordinate system can be done by a simple set of matrix additions & multiplications which can be computed from the ECEF location of the centre of the map, and the unit vectors in the east/north/up directions. 8575 Z=4084176. Viewed 493 times 0 $\begingroup$ Methods suggested Practical examples of Threshold Secret Sharing? more hot questions Question feed. This is just the inversion of the ECEF to ENU transformation so. The exercises have been developed with a specialised software package provided on a CD-ROM together with a set of selected data les for the laboratory sessions. ENU allows a more convenient manipulation of 3D models than ECEF, because its Z axis coincides with the up vector. Ashtech ProMark500 (on the left side), Ahtech MobileMapper 10 (on the right side) TABLE I. Learn more about vpasolve symbolic numerical. As observed in Fig. » Extensive built-in library of cartographic projections. , ENU-to-ECEF. 2 Transformations between BODY and NED 2. searching for ENU 329 found (348 total) alternate case: eNU Enu language (262 words) case mismatch in snippet view article find links to article Enu or Ximoluo (Chinese: 西摩洛; autonym: ŋɔ˧˩ŋjv̩˧˩ (Jiang, et al. , EGM2008), geoid height, and geomagnetic field (e. 5 meter in the horizontal and vertical directions respectively using six captured images and two control points. 1,749,218 views. Since the elevation is usually not available in a navigable map, we convert the map points in the working frame by supposing that they are all located at the ellipsoidal height. The NED system differs from the ENU system by a simple rotation. Bounds will not work well with ECEF coordinates. Geodetic systems or geodetic data are used in geodesy, navigation, surveying by cartographers and satellite navigation systems to translate positions indicated on their products to their real position on earth. ) Later, somewhere in the code (for example, after the initialization pro-cess), you subscribe the subject to two observables: the first is an enumerable of the. Note that the transformation direction indicated by the subscript "ECEF/ENU" reads right to left, i. Returns: ned: {(N,3)} array like ecef position, unit is the same as. For example, high resolution coastal radar technology is effective with high accuracy and availability, but usually presents difficulties (occlusions, shadows, fragmentation, lack of identification) which make it necessary to supplement them with cooperative location technologies such as AIS. Heading is the rotation from the local north direction where a positive angle is increasing eastward. This symbol often appears explicitly in the catalog, but it could be a combination of symbols using a specified algebra of units. Earth-Centered-Earth-Fixed (ECEF) Coordinate System, or CTS. The local ENU coordinates are formed from a plane tangent to the Earth's surface fixed to a specific location and hence it is sometimes known as a "Local Tangent" or "local geodetic" plane. For example, cookies help you log in by pre-filling the username field. 00, this is correct. The following are code examples for showing how to use numpy. This attribute defines the vector in the reference frame. ÐÏ à¡± á> þÿ ) þÿÿÿDEFGHIJKLMNOPQRSTUVWXYZ. 1 The second sub-system, in turn, uses a virtual 3D space with the user located at the origin. (Subirana, 2013) (Misra, 2011) (Dawson, 2005) (Grooves, 2013) Figure 5: ENU frame (Misra, 2011). Convert ECI (CIS, Epoch J2000. Please check the following webpage Transformations between ECEF and ENU coordinates in equation 6. Returns: ned: {(N,3)} array like ecef position, unit is the same as. ECEF coordinates are large numbers that must be in double precision to maintain their resolution. As a map projection the orthographic is neither conformal or equal area, but there is negligible distortion near the origin. Second rotation is a clockwise rotation over the z-axis by an angle 90+λ. Note that the transformation direction indicated by the subscript “ECEF/ENU” reads right to left, i. inarily known within a couple of kilometers, for example through knowing the location of the serving base station. Find the ECEF coordinates of orbital debris, using the ENU coordinates of the debris relative to the geodetic coordinates of a satellite. % venuecef ENU (East, North, Up) to ECEF (Earth Centered Earth Fixed) % venugd ENU (East, North, Up) to Geodetic (latitude, longitude, % altitude) for a given position vector and a reference point. See How It Flies. The subject is not new, but can be very difficult to sort out and to explore in textbooks. Earth Centered, Earth Fixed (ECEF) x-y-z values in km And press the conversion direction desired. For example, rotation in 3D can be represented as three angles that specify three rotations applied successively to the X, Y and Z axes. Typical values for datum specifications include "ITRF00", "NAD83CORS96" and "WGS84". 2 Geodetic Coordinate System 6 2. 1,749,218 views. They are from open source Python projects. Generally the most reliable method is to first convert from LLA (Lat, Lon, Altitude) to ECEF (Earth centered, Earth fixed) and then convert from ECEF to ENU (East, North, Up). For example, with some minor exceptions, the funds’ current fee arrangements were implemented at the beginning of 2010 following extensive review by the Contract Committee and discussions with representatives of Putnam Management, as well as approval by shareholders. See below for an example python scripts ( getGsofStream. The service tests for Siebel High Interactivity applications (for example, Call Center or sales) use Siebel test automation functionality to allow simulation of certain keyboard and mouse events. In the original Euler angle formulation, a. The usual procedure is to iterate beginning with the assumption that. These coordinates are indeed orthogonal but the surface is not coordinate frame is to be compared or transformed to another coordinate frame. The status of Siebel HI services/applications (for example, Call Center) is shown as down. 0 5 10 15 20 25 30 35 40 45 50 30 40 50 60 70 80 90 100 110 120 Time step T=1s R M S E (m ) raw data UKF-ECEF UKF-ENU 0 5 10 15 20 25 30 35 40 45 50 30 40 50 60 70 80 90 100 110 120 Time step T=1s R M S E (m. GeoPositionENU [GeoPositionENU [enu, p 1], p 2] converts between two different ENU systems. - gyjun0230/wgs_conversions. The conventional right-handed coordinate system puts: The origin at the center of mass of the earth, a point close to the Earth's center of figure. , lower in fat and calories. 5 Transformations between BODY and FLOW "The study of dynamicscan be divided into two parts:kinematics, which treats only geometrical. my problem is that I am a getting a larger magnitude vector in the topo frame than in the ECEF frame which does not make sense. You can rate examples to help us improve the quality of examples. From ECEF to geodetic. PyMap3D intrinsically handles local coordinate systems such as ENU, while PyProj ENU requires some additional effort. leines, capt, usaf afit-eng-ms-14-d-47 department of the air force. Vectors in 3-D. Also the earth is an imperfect ellipsoid. 8571 x 10 6 ECEF Y position from data set ash11h50hz. Finally we convert to DIRSIG’s native East North Up (ENU) format. Accuracy: Unknown. Note that the vector from the location x, y, z to the origin (Earth's center) is the nominal line of sight (LoS) of the instrument. ECEF coordinates are large numbers that must be in double precision to maintain their resolution. This script provides coordinate transformations from Geodetic -> ECEF, ECEF -> ENU and Geodetic -> ENU (the composition of the two previous functions). Lectures by Walter Lewin. ECEF Earth-centered, earth-fixed 6 ENU East North Up 6 GLONASS Globalnaya Navigatsionnaya Sputnikovaya Sistema 3 GNSS Global Navigation Satelite System 2–5 GPS Global Positioning System 3 IMU Inertial Motion Unit 3, 10 LS Location Services 3 viii. Start by converting from body into either NED or ENU. An example is given in the following. [1] A geographic coordinate transformation is a translation among different geodetic datums. (ENU) frame. e:ECEF u:ENU Figure2. I will go through some theory first and th. Use MathJax to format equations. 61 deg north 122. In many targeting and tracking applications the local East, North, Up (ENU) Cartesian coordinate system is far more intuitive and practical than ECEF or Geodetic coordinates. edu MSEC 356 x5924 September 02, 2015. 00, this is correct. Contextual translation of "enue" into English. Display representations define how an object appears in a drawing. (In a real application, the observer can be the screen that shows the messages. These angles are called pitch roll and yaw. This formula is the conversion from a pair of [φ1, λ1, r ] , [φ2, λ2, r] spherical coordinates [latitude, longitude, earth radius] to d, θ where d is the angle at the centre of the earth between the points multiplied by the earth radius and θ is the angle of the arc on the surface compared to True North. Finally we convert to DIRSIG's native East North Up (ENU) format. 5 Transformations between BODY and FLOW "The study of dynamicscan be divided into two parts:kinematics, which treats only geometrical. det Compute the determinant of A. The other rotations each contain unknown calibration parameters which will be defined. This frame is designed to allow the interaction of multiple robots in different map frames. Record length. Other models using continuous curves like splines can also be used to avoid discontinuities [3], [8], [9] even if they are computationally demanding and more difficult. enu shree,baleshwar Singh,sanjay varma and ram mishraa in supporting roles. This section also illustrates examples on how to convert from the familiar Mercator projection (Latitude-Longitude) to the more accurate ECEF system. v²µª A‚t†^´’l•x¢P§èesul ‚©«Ž\›p«8—؜࣠’s¤ô W «‚key«¢on’à„ Advž ¸‚ § (tæŠðdeca¢à¥Œ¥ght , P‚8¥˜g Çw Cus£©¦°i§8with €chnolog¤ ¿6¨=°eóm¤0er”€½ €If½ˆ. org Hironobu Onishi Graduate School of Engineering,. The status of Siebel HI services/applications (for example, Call Center) is shown as down. The +Z axis passes through the North Pole. ) Later, somewhere in the code (for example, after the initialization pro-cess), you subscribe the subject to two observables: the first is an enumerable of the. 0 == ECEF, 1 == NED Current baseline in ECEF x or NED north component in mm. EST] Phone: (301) 713-3242. Online UTM to Latitude Longitude converter. Display representations define how an object appears in a drawing. The datum of GeoPosition [enu, p] is the datum of its origin p. Figure 2 shows an example of the difference between the. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'. Current baseline in ECEF z or NED down component in mm. I can easily visualize this, and solve it, in 2D. • pyroSAR - A Python Framework for Large -Scale SAR Satellite Data Processing. Narendran (Naren) KS, who lost his wife Chandrika on MH370, on Twitter says: Yes, give us the truth. 2 Motion Modeling in the l-Frame 90 5. Current number of integer ambiguity hypotheses. 1(a) and (b), the filtering results in the ECEF coordinate system and the ENU coordinate system are almost the same. • (There may be reasons for a large project to present in ENU, however. Geographic, ECEF, and local tangential ENU coordinate systems. For example, high resolution coastal radar technology is effective with high accuracy and availability, but usually presents difficulties (occlusions, shadows, fragmentation, lack of identification) which make it necessary to supplement them with cooperative location technologies such as AIS. The datum of GeoPosition [enu, p] is the datum of its origin p. a vector from E, the center of the Earth, to B, decomposed in E). The NED system differs from the ENU system by a simple rotation. A matrix which converts vectors from the ECEF frame to the East, North, Up (ENU) frame can be found in [4]. They are from open source Python projects. PDF LAT/LON Conversion Table ecef to enu calculator,enu coordinates example,convert enu to lat long,east north up coordinates,convert geodetic to enu,geodetic2enu,enu to geodetic,gps to enu, Conversion of Latitude and Longitude to UTM Coordinates John G Manchuk The frame of reference is an important aspect of natural resource modeling PDF A COMPUTER PROGRAM FOR CONVERTING RECTANGULAR pubs usgs. This formula is the conversion from a pair of [φ1, λ1, r ] , [φ2, λ2, r] spherical coordinates [latitude, longitude, earth radius] to d, θ where d is the angle at the centre of the earth between the points multiplied by the earth radius and θ is the angle of the arc on the surface compared to True North. PyProj is oriented towards points on the planet surface, while PyMap3D handles points on or above the planet surface equally well, particularly important for airborne vehicles and remote sensing. Example: Arc leader (Beyond Witness Lines setting) Example: Line leader (Away from Origin setting) To return the dimension text to its original position, drag the handle back toward the dimension line, so that it snaps to its original position. For example, with GPS signals and navigation data, the single point positioning results are obtained in WGS84. ECEF coordinates are large numbers that must be in double precision to maintain their resolution. py and utilities. Earth Centered, Earth Fixed coordinates in relation to latitude and longitude. If a radar is located at and an aircraft at then the vector pointing from the radar to the aircraft in the ENU frame is. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'. reserved Velocity XYZ ECEF XYZ ECEF output off 0x43 XYZ ECEF output on ENU output ENU output off 0x56 ENU output on reserved Timing Time Type GPS time 0x42, 0x43, 0x4A, 0x83, 0x84, 0x56 reserved Lassen SQ GPS Receiver. PyProj is oriented towards points on the planet surface, while PyMap3D handles points on or above the planet surface equally well, particularly important for airborne vehicles and remote sensing. a velocity vector. To ensure the proper permissions and privileges for all files, Oracle recommends that the same owner perform both tasks: install the Oracle Fusion Middleware product. ECEF y-coordinates of one or more points in the geocentric ECEF system, specified as a scalar, vector, matrix, or N-D array. 51, the change to a new Standard Epoch (52000. (If you enter latitude-longitude-height and press the wrong button with the x-y-z fields blank - you get the earth center. The conventional right-handed coordinate system puts: The origin at the center of mass of the earth, a point close to the Earth's center of figure. Shizuoka, Japan e-mail: [email protected] Detailed Description. In popular GIS software, data projected in latitude/longitude is often represented as a Geographic Coordinate System. If the application only needs one map the earth coordinate frame is not expected to be present. Here, we take ENU coordinate as the example. Often, we'll represent this coordinate frame as East North Up, ENU, relative to a reference point nearby. These are the top rated real world C# (CSharp) examples of Matrix. Simple WGS 84 - ECEF conversion functions. Convert local ENU coordinates to ECEF coordinates ; Convert ECEF coordinates to GPS coordinates ; From ENU to ECEF. # I can't determine which are valid, so I'm going to convert from meters to degrees # If it's degrees to degrees, it won't modify the number # The coordinate systems we will look for are limited between -180. 3D orientation estimation is of great importance in. jual total station topcon, jual total station sokkia, jual total station nikon, jual total station merk china, jual total station trimble, jual total station, jual beli total station bekas,jual tot…. Using satellite azimuth angle, zenith angle, and range, the vector LOS is first calculated in the local East‐North‐Up (ENU) coordinates. An example of the VRML tree structure is included in Fig. Earth-Centered, Earth-Fixed,ECEF,isaCartesiancoordinatesystem,(XE,YE,ZE) (superscript E for earth), with its origin in the earth’s center of mass and with fixed axes with respect to the earth as seen in Figure 2. Earth-Centered-Earth-Fixed (ECEF) Coordinate System, or CTS. The following Bowring's irrational geodetic equation [4] is efficient to be solved by Newton-Raphson method [5]:. selected practical examples going further into the theoretical concepts and their practical implementation. So this example was a comparison between one dual frequency receiver and one single frequency receiver, both paired with a fairly distant base station. EPSG:4326 WGS 84 Change. The modern definition of sea level is actually defined precisely by the datum WGS 84 from 1984 onward. Possible Cause. The +X axis passes through the Equator and Prime Meridian intersection. ECEF Earth-centered, earth-fixed 6 ENU East North Up 6 GLONASS Globalnaya Navigatsionnaya Sputnikovaya Sistema 3 GNSS Global Navigation Satelite System 2–5 GPS Global Positioning System 3 IMU Inertial Motion Unit 3, 10 LS Location Services 3 viii. Sample output: Reference not specified, using first epoch: X =-1282458. 8571 x 10 6 ECEF Y position from data set ash11h50hz. Both geographic coordinate conversion and transformation will be considered in this. A set of python modules which makes it easy to write raster processing code in Python. Both variables are only correlated with radar geographic coordinates at time. 6647 degrees West of Greenwich Or degrees, minutes and seconds: latitude 43:04:33 North, longitude 77:39:53 West Or, in the case of longitude, one can measure in time zones. For an advanced analysis of the time evolution of space debris dispersion, new efficient computational approaches are proposed. reserved Velocity XYZ ECEF XYZ ECEF output off 0x43 XYZ ECEF output on ENU output ENU output off 0x56 ENU output on reserved Timing Time Type GPS time 0x42, 0x43, 0x4A, 0x83, 0x84, 0x56 reserved Lassen SQ GPS Receiver. A device for determining the spatial alignment of an inertial measurement unit (IMU) positioned in or on a vehicle comprising: means for obtaining vehicle-related movement data for the vehicle (110) including velocity data measured by or derived from measurements obtained by one or more satellite positioning systems (SPSs), the velocity data including an SPS-based. Geodesy becomes particularly powerful when you chain together transformations. I would assume that if you want to know the slope encounrered by a vehicle, that implies the rate of change of "down" over the horizontal displacement. frame as shown in Figure 1. Display representations define how an object appears in a drawing. Unit: degree (supplier to define representation) Area of use: World. The cartesian coordinate system is a right-hand, rectangular, three-dimensional, earth-fixed coordinate system with an origin at (0, 0, 0). Positions of receiving stations Figure 2. From the ECEF frame, conversions to latitude, longitude and height with respect to World Geodetic Survey (WGS84) latitude, longitude and height can be calculated with the final result illustrated in Figure 2. | MAV_MODE_FLAG_TEST_ENABLED = 2 // 0b00000010 system has a test mode enabled. Identify the Tokyo-Korea datum in Table 2 Reference ellipsoid is Bessel 1841 (a = 6377397. Calculate the GPS SV positions in ECEF and ENU from the REF01 locations and produce a "Sky Plot" as function of azimuth vs elevation angles. is already defined in the local East-North-Up (ENU) frame with the radar in its origin. The first two class variables ( a and e2 ) define the WGS-84 ellipsoid, where a is the semi-major axis (the Earth’s radius at the equator) and e2 is the eccentricity squared. ) Later, somewhere in the code (for example, after the initialization pro-cess), you subscribe the subject to two observables: the first is an enumerable of the. This assumption allows us to simplify the calculations in comparison to the positioning methods that allow the user to lie anywhere on Earth. Switching between coordinates is. On the other hand, cooperative systems are. Sample output: Reference not specified, using first epoch: X =-1282458. example, the anti-lock braking system (ABS) technology. Online convertor for lat & long coordinates, geodetic datums and projected systems. To transform from ECEF coordinates to the local coordinates we need a local reference point, typically this might be the location of a radar. RTK GPS data. Take for example KSFO located at about 37. The ECI (CIS)-to-WGS 84 ECEF transformation makes use of the new theories of precession CA. I am trying to change. Gravity Gradient Tensor Eigendecomposition for Spacecraft Positioning Pei Chen1, Xiucong Sun2, and Chao Han3 Beihang University, Beijing, 100191, People's Republic of China Nomenclature U = gravitational potential, m2/s2 T = gravity gradient tensor (GGT), E TECEF = GGT in ECEF, E TENU = GGT in ENU, E TEIG = GGT in the Eigen frame, E. The coordinate system needs to be converted from ECEF to ENU for better describing the motion attitude of baseline vector. teme to ecef matlab, May 29, 2012 · There are multiple systems for ECEF such as : true equator, mean equinox (TEME), true of date (TOD), and pseudo earth fixed (PEF). This is just the inversion of the ECEF to ENU transformation so. [2] [3] There exist two kinds of methods in order to solve the equation. In geodesy, geographic coordinate conversion is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. Russell Stoneback: PySitools: Client for SiTools2, including. The DCM matrix performs the coordinate transformation of a vector in Earth-centered Earth-fixed (ECEF) axes, ( ox 0 , oy 0 , oz 0 ), into geodetic latitude and longitude. You can vote up the examples you like or vote down the ones you don't like. ECEF y ECEF z ECEF x ENU y ENU z ENU Prime Meridian Figure 1: Geodetic, ECEF and ENU coordinates systems. Site features and services - These provide functionality that help us deliver products and services. It also includes some utility functions that support general coordinates convertion for non Oriient related functionality, such as converting from ENU coordinates system to WGS 84 or to ECEF. PyProj is oriented towards points on the planet surface, while PyMap3D handles points on or above the planet surface equally well, particularly important for airborne vehicles and remote sensing. Frames and Coordinate Systems 18 Dynamic Frames •In a dynamic frame the orientation changes with time –Families: Two-vector, Euler, and Of-date (refer to Dynamic Frames tutorial) –This category excludes frames for which the orientation is determined by a PCK or CK –Example of a two-vector dynamic frame: Geocentric Solar Ecliptic (GSE). They are from open source Python projects. From the figure 1 it follows that the ENU coordinates can be transformed to the $(x,y,z)$ ECEF. 2 NED Realization 95 5. Assume the LLA is in WGS 1984 unless otherwise stated. Ashtech ProMark500 (on the left side), Ahtech MobileMapper 10 (on the right side) TABLE I. Newton-Raphson method. From ECEF to ENU Coordinates To transform from ECEF coordinates to the local coordinates we need a local reference point, typically this might be the location of a radar. Single Platform Geolocation of Radio Frequency Emitters Eric J. jual total station topcon, jual total station sokkia, jual total station nikon, jual total station merk china, jual total station trimble, jual total station, jual beli total station bekas,jual tot…. Any point on or near the surface of the earth is represented in a 3D, rectilinear, right-handed XYZ coordinate frame fixed to the Earth. Learn more about vpasolve symbolic numerical. This rotation aligns Up (Z) axis with ZECEF axis. • pymap3d - Python 3D coordinate conversions for geospace ecef enu eci. Gravity Gradient Tensor Eigendecomposition for Spacecraft Positioning Pei Chen1, Xiucong Sun2, and Chao Han3 Beihang University, Beijing, 100191, People's Republic of China Nomenclature U = gravitational potential, m2/s2 T = gravity gradient tensor (GGT), E TECEF = GGT in ECEF, E TENU = GGT in ENU, E TEIG = GGT in the Eigen frame, E. Parameters. Asus laptop quite slow with high processor usage when idle - posted in Am I infected? What do I do?: Good evening to you ! I am currently using an Asus Laptop X7BS (which is almost 4 years old. 1 Classical Method 96 5. For example, boot with ' 0blinux resolution=1024x768 07'. Specify values in units that match the LengthUnit property of the spheroid argument. Lear‚9  Comput€Z×ith  €HRobots  Ø3>én 8++€yb> XEdited  by ÀDeepak  Kumar This ‰ €@provŒØdás€yw‡hîoçuaraŒ esŒéanyë…H. ENU allows a more. It must be assigned a comma-separated triplet that represents the vectr components. C++ (Cpp) enu_of_ecef_point_f - 1 examples found. The relation between the local East, North, Up (ENU) coordinates and the $(x,y,z)$ Earth Centred Earth Fixed (ECEF) coordinates is illustrated in the next figure: Figure 2:: Transformations between ENU and ECEF coordinates. inarily known within a couple of kilometers, for example through knowing the location of the serving base station. 1 Loosely Coupled Mode of Integration 101. V n represents the effect of the motion of the ENU frame with respect to the ECEF frame; 2 Ω ie n. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'. RTK GPS data. Geodetic systems or geodetic data are used in geodesy, navigation, surveying by cartographers and satellite navigation systems to translate positions indicated on their products to their real position on earth. The focus of this project is to design an autonomous vehicle following a desired path by a RTK (Real Time Kinematic) GPS, including designing prototype PCB(Printed Circuit Board) layout, finding sensors and. So this example was a comparison between one dual frequency receiver and one single frequency receiver, both paired with a fairly distant base station. [1] A geographic coordinate transformation is a translation among different geodetic datums. 3 is slightly inaccurate because ENU and ECEF frames are concentric in the exemplary mathematical implementation described herein below. GeoPositionENU [GeoPositionENU [enu, p 1], p 2] converts between two different ENU systems. 1Geodetic Coordinate System The current geodetic coordinate system (see Figure 2. Coordinate converter is a free online application which allows for example to convert latitude longitude gps coordinates to easting northing x y: Lambert,UTM,RGF93,ED50,NAD27,…. Transpose - 30 examples found. During the mastication process, the food is positioned by the cheek and tongue between the teeth for grinding; the muscles of mastication move the jaws to bring the teeth into intermittent. A device for determining the spatial alignment of an inertial measurement unit (IMU) positioned in or on a vehicle comprising: means for obtaining vehicle-related movement data for the vehicle (110) including velocity data measured by or derived from measurements obtained by one or more satellite positioning systems (SPSs), the velocity data including an SPS-based. , WMM2020) calculations, and for solving geodesic problems. It is more convenient to represent the CrIS FOV location in the ECEF coordinate system (or with latitude and longitude), but the ECI frame is simple to. Learn more about vpasolve symbolic numerical. jual total station topcon, jual total station sokkia, jual total station nikon, jual total station merk china, jual total station trimble, jual total station, jual beli total station bekas,jual tot…. 5 Initialization Packets to Speed Start-up. While Bounds targets the LLA coordinate system, Bounds{ENU} can be used with ENU coordinates. For convenience, we use multiple coordinate frames to describe the orientation of the sensor, including the "inertial frame," the "vehicle-1 frame," the "vehicle-2 frame," and the "body frame. A ship includes a star tracker mounted on a platform stabilized in ENU by the inertial navigation system (INS). ) to describe the motion of a vehicle and about Euler angles (e. 2 Geodetic Coordinate System 6 2. The relationship between points can be further expressed in the ECEF coordinates, X, Y, and Z, or in a Local Geodetic Horizon System (LHGS) of north, east, and up. Let there be two data points, in ECEF, as follows (in meters): A1 (x1, y1, z1) A2 (x2, y2, z2) I want to calculate the angle, Clock-wise relative to North (the Z-axis in ECEF), that is the heading from point 1 to point 2. The example to for sending Entity State PDU is great!. High precision ying is an important part of all remote sensing and photogrammetry related ights. 3 Transformations between ECEF and NED 2. 553778] T expressed in an Earth-Centered-Earth-Fixed (ECEF) coordinate frame. 4232 \ +to \ +proj=longlat +ellps=WGS84 +datum=WGS84 Belgium. The +X axis passes through the Equator and Prime Meridian intersection. Convert local ENU coordinates to ECEF coordinates ; Convert ECEF coordinates to GPS coordinates ; From ENU to ECEF. See, for example, Other Earth-based coordinate systems and Conversion calculations at Geodetic datum. If a radar is located at and an aircraft at then the vector pointing from the radar to the aircraft in the ENU frame is. 1 The second sub-system, in turn, uses a virtual 3D space with the user located at the origin. If a radar is located at and an aircraft at then the vector pointing from the radar to the aircraft in the ENU frame is. Transpose from package TelerikAcademy extracted from open source projects. Orbital Coordinate Systems, Part I. Note that the transformation direction indicated by the subscript “ECEF/ENU” reads right to left, i. 5 meter in the horizontal and vertical directions respectively using six captured images and two control points. Output Output all enabled Super Packets. In the present work, we have selected ENU and RF CSs to express information on the target, as illustrated in Fig. You can vote up the examples you like or vote down the ones you don't like. To convert ENU coordinate to Camera coordinate, we will multiply camera projection matrix with ENU coordinate vector, the result is a vector [v0, v1, v2, v3]. 9870 WN - GPS WEEK SOW - GPS time FLAG1 FLAG2 SATS - # SVS X[m] Y[m] Z[m] eX[m] eY[m] eZ[m] - Position VCV Position RMS. In the case of running with multiple maps simultaneously the map and odom and base_link frames will need to be customized for each robot. 4 Wander Frame In the l-frame the y-axis always points towards true north, so higher rotation rates about the z-axis are required in order to maintain the orientation of the l-frame in the polar regions (higher latitudes) than near. Moving from an ECEF to ENU coordinate system can be done by a simple set of matrix additions & multiplications which can be computed from the ECEF location of the centre of the map, and the unit vectors in the east/north/up directions. There is lots of data that comes to you in NED form, but you should convert it to ECN or ECEF at the first opportunity. As an example, simulation results obtained for Loc1 are presented in Fig. Another example might be publishing a stream with smaller observation messages containing only L1 content for some users. An example might be a two streams, one using an NAD frame of reference and another with an ITRF frame of reference. 155, b = 6356078. From ECEF to geodetic coordinates. Note - The Dx, Dy, and Dz values shown in Table 2 are defined as from any datum to ECEF. The utilities in this package provide methods for converting between Geodetic Latitude-Longitude-Ellipsoid_ht and XYZ on the GRS80 Ellipsoid. Joglo Raya No 68 Jkarata Barat 11640 Telp : (021) 98454214 Fax ( 021 ) 5840766 Contact : FERY 0878 8802 8163(XL) 0812 1953 9224 (SIMPATI) PIN BB : 56AB0AEB email : [email protected] • untiler - Stitch image tiles into larger composite TIFs. The default positiong mode is PVT. It also includes some utility functions that support general coordinates convertion for non Oriient related functionality, such as converting from ENU coordinates system to WGS 84 or to ECEF. Functions that only SIMDIS recognizes. Finally, we'll also often need to think about a sensor frame that is rigidly attached to a sensor like a LIDAR, a GPS receiver or an Inertial Measurement Unit. But you could also represent the same rotation as three angles applied successively to Z, Y and X axes. Computes a quaternion from a reference frame with axes computed from the heading-pitch-roll angles centered at the provided origin. This is the government provided data for 3 CORS. ecef2enu (r_ecef, r_ref, phi_ref, lam_ref) [source] ¶ Convert ECEF coordinates to ENU using an ECEF reference location r_ref having lat = phi_ref and lon = lam_ref. Template:Geodesy A Geodetic system or geodetic datum is a coordinate system, and a set of reference points, used to locate places on the Earth (or similar objects). ~], and the new definition of. The following Bowring's irrational geodetic equation [4] is efficient to be solved by Newton-Raphson method [5]:. This is an end-to-end. Viewed 493 times 0 $\begingroup$ Methods suggested Practical examples of Threshold Secret Sharing? more hot questions Question feed. v²µª A‚t†^´’l•x¢P§èesul ‚©«Ž\›p«8—؜࣠’s¤ô W «‚key«¢on’à„ Advž ¸‚ § (tæŠðdeca¢à¥Œ¥ght , P‚8¥˜g Çw Cus£©¦°i§8with €chnolog¤ ¿6¨=°eóm¤0er”€½ €If½ˆ. Geocentric System The geocentric Cartesian coordinate system, also known as Earth-Centered, Earth-Fixed (ECEF), is fixed with respect to the Earth, with its origin at the center of the spheroid and its positive X-, Y-, and Z axes intersecting the surface at the. gps spoofing detection using multiple antennas and individual space vehicle pseudoranges by david s. Certain hardware configurations may have trouble with the automatic hardware detection done during the installation. The star tracking capability improves accuracy of the target data conversion from the ship's ENU to earth-centered-earth-fixed (ECEF) reference, and also improves the accuracy of the ship's inertial navigation system calibration using satellites (SCUS). Add the gravity in the NED/ENU frame. The origin of the ENU system is normally on the surface of the ellipsoid while the origin of ECEF is the center of the earth. Specify values in units that match the LengthUnit property of the spheroid argument. py) connect to a TCP socket and parses GSOF message. Since we will making extensive use of vectors in Dynamics, we will summarize some of their important properties. DCM Tutorial - An Introduction to Orientation Kinematics - Introduction This article is a continuation of my IMU Guide, covering additional orientation kinematics topics. Typical values for datum specifications include "ITRF00", "NAD83CORS96" and "WGS84". GeographicLib is a small set of C++ classes for performing conversions between geographic, UTM, UPS, MGRS, geocentric, and local cartesian coordinates, for gravity (e. From the ECEF frame, conversions to latitude, longitude and height with respect to World Geodetic Survey (WGS84) latitude, longitude and height can be calculated with the final result illustrated in Figure 2. C++ (Cpp) enu_of_ecef_point_f - 1 examples found. ECEF_from_ENU (enu, latitude, longitude, altitude) [source] ¶ Calculate ECEF coordinates from local ENU (east, north, up) coordinates. as where denotes the th radar ECEF coordinates converted from its geographic coordinates, and is the rotation matrix. The adaptive ambiguity function, which uses trigonometric functions to process the fractional value of carrier-phase measurement, is insensitive to the whole-cycle change of the carrier-phase measurement. Coordinate converter is a free online application which allows for example to convert latitude longitude gps coordinates to easting northing x y: Lambert,UTM,RGF93,ED50,NAD27,…. Understanding differences in Geodetic (WGS84) to ECEF equations? Ask Question Asked 1 year, 10 months ago. Main article: ECEF The earth-centered earth-fixed (also known as the ECEF, ECF, or conventional terrestrial coordinate system) rotates with the Earth and has its origin at the center of the Earth. A Java port of Olson's ECEF-to-Geodetic algorithm is shown below, along with the standard Geodetic-to-ECEF algorithm. Certain hardware configurations may have trouble with the automatic hardware detection done during the installation. Transform 3-D coordinates between Earth-centered Earth-fixed (ECEF), geodetic, east-north-up (ENU), north-east-down (NED), and azimuth-elevation-range (AER) systems. For example, with GPS signals and navigation data, the single point positioning results are obtained in WGS84. (which should technically be ENU) so you just slap a negative sign to the z value. 2 Manual 1 1 Overview RTKLIB is an open source program package for standard and precise positioning with GNSS (global navigation satellite system). This rotation aligns East (X) axis with the X ECEF axis. 3 Trigonometric Relationships Between Rotated Frames 13. 8575 Z=4084176. ECEF Coordinate System An in depth explanation of the ECEF coordinate system and how it's used in the WRLD maps to render the globe accurately. Easily change coordinate projection systems in Python with pyproj. » Full 14-parameter datum transforms, including time dependence. v²µª A‚t†^´’l•x¢P§èesul ‚©«Ž\›p«8—؜࣠’s¤ô W «‚key«¢on’à„ Advž ¸‚ § (tæŠðdeca¢à¥Œ¥`ght , P‚8¥˜g Çw Cus£©¦°i§8with €chnolog¤ ¿6¨=°eóm¤0er”€½ €If½ˆ. There are companies in Arjeplog that provide services for vehicle and component manu-facturers. The elevation and azimuth angles of the GPS SV constellation above the receiver over a 24-hour period was computed using GPS SV ephemeris files from the. RTKLIB consists of a portable program library and several APs (application programs) utilizing the library. ) Later, somewhere in the code (for example, after the initialization pro-cess), you subscribe the subject to two observables: the first is an enumerable of the. V n is the Coriolis acceleration vector; g n is the gravity vector, including the gravitation term and the centripetal term related to the Earth rotation; and f b is the specific force vector in the body frame, which is measured by the. This attribute defines the vector in the reference frame. For an advanced analysis of the time evolution of space debris dispersion, new efficient computational approaches are proposed. First, specify the reference spheroid as WGS84 with length units measured in kilometers. teme to ecef matlab, May 29, 2012 · There are multiple systems for ECEF such as : true equator, mean equinox (TEME), true of date (TOD), and pseudo earth fixed (PEF). Right-click the dimension line or the dimension text for a segment. To convert from geodetic coordinates to local ENU coordinates is a two-stage process: Convert geodetic coordinates to ECEF coordinates; Convert ECEF coordinates to local ENU coordinates; From ECEF to ENU. The systems are needed because the earth is an imperfect sphere. Suppose we have a co-moving platform (i. A set of python modules which makes it easy to write raster processing code in Python. Convert local ENU coordinates to ECEF coordinates ; Convert ECEF coordinates to GPS coordinates ; From ENU to ECEF. # I can't determine which are valid, so I'm going to convert from meters to degrees # If it's degrees to degrees, it won't modify the number # The coordinate systems we will look for are limited between -180. aer2ned mapping. ENU can be presented in single precision for a small local project. Data Types: single | double. Typical values for datum specifications include "ITRF00", "NAD83CORS96" and "WGS84". For more information about the State Plane Coordinate System contact: The National Geodetic Survey Information Services Branch. Computes a quaternion from a reference frame with axes computed from the heading-pitch-roll angles centered at the provided origin. Unit vector from receiver ito satellite kin ECEF coordinates (x k x i) (y y i) (zk z i) T ecVtor from receiver ito satellite kin ECEF coordinates x 1;2 y 1;2 z 1;2 Relative position vector between antennas 1 and 2 k˚ 1;2 Single-di erenced carrier phase measurement kˆ 1;2 Single-di erenced pseudorange measurement k. The subject is not new, but can be very difficult to sort out and to explore in textbooks. This attribute defines the vector in the reference frame. Port 2 is a bi-directional port ECEF) 1 0x56 velocity fix (ENU) 1 0x8F-20 LLA & ENU 1. The coordECEF struct was added for Earth-Centered, Earth-Fixed (ECEF) coordinates. World Geodetic System 1984 WGS 84 is an Earth-centered, Earth-fixed terrestrial reference system For example, GPS broadcast orbits at the time of this writing. Finally we convert to DIRSIG’s native East North Up (ENU) format. Online UTM to Latitude Longitude converter. ) to describe the motion of a vehicle and about Euler angles (e. ECEF y-coordinates of one or more points in the geocentric ECEF system, specified as a scalar, vector, matrix, or N-D array. 84 gives the transformation in the opposite direction, from ECEF to ENU: Eq. OSGB36, for example, Earth-centered earth-fixed (ECEF or ECF) coordinates. The default positiong mode is PVT. ECEF coordinates are large numbers that must be in double precision to maintain their resolution.
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#StackBounty: #algorithms #optimization #machine-learning What is the difference in SMO algorithm for SVM and SMO for one class?
Bounty: 100
Please let know if this is not the correct forum to ask this question. If not can anyone please tell where can I ask this question?
I am trying to understand the difference between the paper :
https://pdfs.semanticscholar.org/59ee/e096b49d66f39891eb88a6c84cc89acba12d.pdf
The first paper is about SMO for SVM and the second paper is about SMO for one class. The question is what are the difference between this two algorithms? Also what are the common factors in both the paper?
The second paper has not shown any details of the algorithm so not sure what minimal change to be done on the first to get the second algorithm?
Get this bounty!!!
#StackBounty: #machine-learning #deep-learning #variational-bayes #generative-models Is the optimization of the Gaussian VAE well-posed?
Bounty: 50
In a Variational Autoencoder (VAE), given some data $$x$$ and latent variables $$t$$ with prior distribution $$p(t) = mathcal{N}(t | 0, I)$$, the encoder aims to learn a distribution $$q_{phi}(t)$$ that approximates the true posterior $$p(t|x)$$ and the decoder aims to learn a distribution $$p_{theta}(x|t)$$ that approximates the true underlying distribution $$p^*(x|t)$$.
These models are then trained jointly to maximize an objective $$L(phi, theta)$$, which is a lower bound for the log-likelihood of the training set:
$$L(phi, theta) = sum_i mathbb{E}{q{phi}} log frac{p_{theta}(x_i|t)p(t)}{q_{phi}(t)} leq sum_i log int p_{theta}(x_i|t)p(t) dt$$
According to section C.2 in the original paper from Kingma and Welling (https://arxiv.org/pdf/1312.6114.pdf), when we model $$p_{theta}(x|t)$$ as a family of gaussians, the decoder should output both the mean $$mu(t)$$ and the (diagonal) covariance $$sigma^2(t) I$$ for the gaussian distribution.
My question is: isn’t this optimization problem ill-posed (just like maximum likelihood training in GMMs)? Having an output for the variance (or log-variance, as is most common), if the decoder can produce a perfect reconstruction for a single image in the training set (i.e. $$mu(t_i)=x_i$$) then it can set the corresponding variance $$sigma^2(t_i)$$ to something arbitrarily close to zero and therefore the likelihood goes to infinity regardless of what happens with the remaining training examples.
I know that most gaussian VAE implementations have a simplified decoder that outputs the mean only, replacing the term $$mathbb{E}{q{phi}} log p_{theta}(x_i|t)$$
by the squared error between the original image and the reconstruction (which is equivalent to setting the covariance to be always the identity matrix). Is this because of the ill-posedness of the original formulation?
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#StackBounty: #machine-learning #mathematical-statistics #causality How does a causal tree optimize for heterogenous treatment effects?
Bounty: 50
I have a very specific question regarding how the causal tree in the causal forest/generalized random forest optimizes for heterogeneity in treatment effects.
This question comes from the Athey & Imbens (2016) paper “Recursive partitioning for heterogeneous causal effects” from PNAS. Another paper is Wager & Athey (2018), “Estimation and inference of heterogeneous treatment effects using random forests” in JASA (arxiv.org link here). I know that the answer to my question is in those papers, but I, unfortunately, can’t parse some of the equations to extract it. I know I understand an algorithm well when I can express it in words, so it has been irking me that I can’t do so here.
In my understanding, an honest causal tree is generally constructed by:
Given a dataset with an outcome $$Y$$, covariates $$X$$, and a randomized condition $$W$$ that takes on the value of 0 for control and 1 for treatment:
1. Split the data into subsample $$I$$ and subsample $$J$$
2. Train a decision tree on subsample $$I$$ predicting $$Y$$ from $$X$$, with the requirement that each terminal node has at least $$k$$ observations from each condition in subsample $$J$$
3. Apply the decision tree constructed on subsample $$I$$ to subsample $$J$$
4. At each terminal node, get the mean of predictions for the $$W$$ = 1 cases from subsample $$J$$ and subtract the mean of predictions for the $$W$$ = 0 cases from subsample $$J$$; the resulting difference is the estimated treatment effect
Any future, out-of-sample cases (such as those used after deploying the model) will be dropped down the tree and assigned the predicted treatment effect for the node in which they end are placed.
This is called “honest,” because the actual training and estimation are done on completely different data. Athey and colleagues have a nice asymptotic theory showing that you can derive variance estimates for these treatment effects, which is part of the motivation behind making them “honest.”
This is then applied to a causal random forest by using bagging or bootstrapping.
Now, Athey & Imbens (2016) note that this procedure uses a modified mean squared error criterion for splitting, which rewards “a partition for finding strong heterogeneity in treatment effects and penalize a partition that creates variance in leaf estimates” (p. 7357).
My question is: Can you explain how this is the case, using words?
In the previous two sections before this quotation, Modifying Conventional CART for Treatment Effects and Modifying the Honest Approach, the authors use the Rubin causal model/potential outcomes framework to derive an estimation for the treatment effect.
They note that we are not trying to predict $$Y$$—like in most machine learning cases—but the difference between the expectation of $$Y$$ in two conditions, given some covariates $$X$$. In line with the potential outcomes framework, this is “infeasible”: We can only measure the outcome of someone in one of the two conditions.
In a series of equations, they show how we can use a modified splitting criterion that predicts the treatment effect. They say: “…the treatment effect analog is infeasible, but we can use an unbiased estimate of it, which leads to…” (p. 7357) and they show the equation for it using observed data. As someone who has a background in social science and applied statistics, I can’t connect the dots between what they have set up and how we can estimate it from the data.
Any help at explaining how this criterion maximizes the variance in treatment effects (i.e., the heterogeneity of causal effects) OR any correction on my description of how to build a causal tree that might be leading to my confusion would be greatly appreciated.
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#StackBounty: #machine-learning #semi-supervised Why does using pseudo-labeling non-trivially affect the results?
Bounty: 50
I’ve been looking into semi-supervised learning methods, and have come across the concept of “pseudo-labeling”.
As I understand it, with pseudo-labeling you have a set of labeled data as well as a set of unlabeled data. You first train a model on only the labeled data. You then use that initial data to classify (attach provisional labels to) the unlabeled data. You then feed both the labeled and unlabeled data back into your model training, (re-)fitting to both the known labels and the predicted labels. (Iterate this process, re-labeling with the updated model.)
The claimed benefits are that you can use the information about the structure of the unlabeled data to improve the model. A variation of the following figure is often shown, “demonstrating” that the process can make a more complex decision boundary based on where the (unlabeled) data lies.
Image from Wikimedia Commons by Techerin CC BY-SA 3.0
However, I’m not quite buying that simplistic explanation. Naively, if the original labeled-only training result was the upper decision boundary, the pseudo-labels would be assigned based on that decision boundary. Which is to say that the left hand of the upper curve would be pseudo-labeled white and the right hand of the lower curve would be pseudo-labeled black. You wouldn’t get the nice curving decision boundary after retraining, as the new pseudo-labels would simply reinforce the current decision boundary.
Or to put it another way, the current labeled-only decision boundary would have perfect prediction accuracy for the unlabeled data (as that’s what we used to make them). There’s no driving force (no gradient) which would cause us to change the location of that decision boundary simply by adding in the pseudo-labeled data.
Am I correct in thinking that the explanation embodied by the diagram is lacking? Or is there something I’m missing? If not, what is the benefit of pseudo-labels, given the pre-retraining decision boundary has perfect accuracy over the pseudo-labels?
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#StackBounty: #machine-learning #mathematical-statistics Maximizing AUC based on point cloud distance
Bounty: 50
Let \$V\$ be an \$n\$ dimensional space with sets of positive class vectors \$P\$ and negative class vectors \$N\$. The task is to find a vector \$x\$ such that AUC is maximized, based on ranking generated by computing distances between \$x\$ and \$P,V\$. So in a sense, \$x\$ is closer to \$P\$ than to \$V\$. It looks like this doesn’t have a unique solution, but I’m curious if there is a really easy explicit solution to this, or a short algorithm? Or is this NP-hard?
Surely this is a well known classical problem? One algorithm that I think works is to sample triplets \$(x,p,n)\$ with one positive and one negative vector and then formulate the usual triplet loss:
\$\$L(x,p,n) = max(0,|x-p|^2-|x-n|^2+epsilon),\$\$
which pushes \$x\$ closer to \$p\$ and further from \$n\$. I’m just hoping for something easier.
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#StackBounty: #python #machine-learning #keras #deep-learning #forecasting How to handle Shift in Forecasted value
Bounty: 50
I implemented a forecasting model using LSTM in Keras. The dataset is 15mints seperated and I am forecasting for 12 future steps.
The model performs good for the problem. But there is a small problem with the forecast made. It is showing a small shift effect. To get a more clear picture see the below attached figure.
How to handle this problem.? How the data must be transformed to handle this kind of issue.?
The model I used is given below
``````init_lstm = RandomUniform(minval=-.05, maxval=.05)
init_dense_1 = RandomUniform(minval=-.03, maxval=.06)
model = Sequential()
history = model.fit(X, y, epochs=1000, batch_size=16, validation_data=(X_valid, y_valid), verbose=1, shuffle=False)
``````
I made the forecasts like this
``````my_forecasts = model.predict(X_valid, batch_size=16)
``````
Time series data is transformed to supervised to feed the LSTM using this function
``````# convert time series into supervised learning problem
def series_to_supervised(data, n_in=1, n_out=1, dropnan=True):
n_vars = 1 if type(data) is list else data.shape[1]
df = DataFrame(data)
cols, names = list(), list()
# input sequence (t-n, ... t-1)
for i in range(n_in, 0, -1):
cols.append(df.shift(i))
names += [('var%d(t-%d)' % (j+1, i)) for j in range(n_vars)]
# forecast sequence (t, t+1, ... t+n)
for i in range(0, n_out):
cols.append(df.shift(-i))
if i == 0:
names += [('var%d(t)' % (j+1)) for j in range(n_vars)]
else:
names += [('var%d(t+%d)' % (j+1, i)) for j in range(n_vars)]
# put it all together
agg = concat(cols, axis=1)
agg.columns = names
# drop rows with NaN values
if dropnan:
agg.dropna(inplace=True)
return agg
super_data = series_to_supervised(data, 12, 1)
``````
My timeseries is a multi-variate one. `var2` is the one that I need to forecast. I dropped the future `var1` like
``````del super_data['var1(t)']
``````
Seperated train and valid like this
``````features = super_data[feat_names]
values = super_data[val_name]
ntest = 3444
train_feats, test_feats = features[0:-n_test], features[-n_test:]
train_vals, test_vals = values [0:-n_test], values [-n_test:]
X, y = train_feats.values, train_vals.values
X = X.reshape(X.shape[0], 1, X.shape[1])
X_valid, y_valid = test_feats .values, test_vals .values
X_valid = X_valid.reshape(X_valid.shape[0], 1, X_valid.shape[1])
``````
I haven’t made the data stationary for this forecast. I also tried taking difference and making the model as stationary as I can, but the issue remains the same.
I have also tried different scaling ranges for the min-max scaler, hoping it may help the model. But the forecasts are getting worsened.
``````Other Things I have tried
* Tried other optimizers
* Tried mse loss and custom log-mae loss functions
* Tried varying batch_size
* Tried adding more past timesteps
``````
I understand that the model is replicating the last known value to it, thereby minimizing the loss.
The validation and training loss remains low enough through out the training process. This makes me think whether I need to come up with a new loss function for this purpose.
Is that necessary.? If so what loss function should I go for.?
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#StackBounty: #machine-learning #mean #accuracy #image-processing #computer-vision Difference between Mean/average accuracy and Overall…
Bounty: 50
I just got confusion while reading the paper “Local Binary Pattern-Based Hyperspectral Image Classification With Superpixel Guidance”.
They mentioned that they repeated each experiment 10 times and calculated both mean and standard deviation. after that they also mentioned they calculated overall accuracy. in the results they mentioned mean and std accuracy of each class and then overall accuracy. What is the difference between average/meanMean and overall accuracy? isn’t should be same?
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#StackBounty: #r #regression #machine-learning #predictive-models #r-squared Multiple Regression, good P-value, but Low R2
Bounty: 50
I am trying to build a model in R to predict Conversion Rate (CR) based on age, gender, and interest (and also the campaign_Id):
The CR values look like this:
The correlation coefficients are not very promising:
`rcorr(as.matrix(data.numeric))`
correlations with CR:
xyz_campaign_id (-0.19), age (-0.1), gender(-0.04), interest(-0.03)
So, the model below:
``````library(caret)
set.seed(100)
TrainIndex <- sample(1:nrow(data), 0.8*nrow(data))
data.train <- data[TrainIndex,]
data.test <- data[-TrainIndex,]
nrow(data.test)
model <- lm(CR ~ age + gender + interest + xyz_campaign_id , data=data.train)
``````
will not have a good adjusted r-squared (0.04):
``````Call:
lm(formula = CR ~ age + gender + interest + xyz_campaign_id,
data = data.train)
Residuals:
Min 1Q Median 3Q Max
-18.636 -11.858 -4.087 0.115 96.421
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 47.231250 6.287738 7.512 1.4e-13 ***
age35-39 1.214713 1.916649 0.634 0.52639
age40-44 -1.971037 1.986316 -0.992 0.32131
age45-49 -3.064858 1.866713 -1.642 0.10097
genderM 3.709192 1.412311 2.626 0.00878 **
interest 0.030384 0.027617 1.100 0.27154
xyz_campaign_id -0.037856 0.006076 -6.231 7.1e-10 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 21.16 on 907 degrees of freedom
Multiple R-squared: 0.05237, Adjusted R-squared: 0.04611
F-statistic: 8.355 on 6 and 907 DF, p-value: 7.81e-09
``````
I also understand that I should probably convert “interest” from numeric to factor (I have tried that too, although I considered all 40 interest levels which is not ideal)
So, based on the provided information, is there any way to improve the model? what other models shall I try besides linear models to make sure that I have a good predictive model?
If you need more information, the challenge is available Here. Data is Here
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#StackBounty: #machine-learning #python #scikit-learn #nlp Pass 2 different kinds of X training data to ML model simultaneously
Bounty: 50
I’m trying to classify if a book is fiction/nonfiction based on title and summary.
This is 2 distinct types of information – is there a way to segment `title` and `summary` before feeding it to a model, rather than concatenating the information?
For example:
Title: `"such a long journey"`
Summary: `"it is bombay in 1971, the year india went to..."`
Label: `"fiction"` (where fiction =1)
Current procedure:
What I’ve been doing until now is concatenating the information, so the above becomes,
``````example = "such a long journey it is bombay in 1971, the year india went to..."
label = 1
``````
Then the usual setup, something like,
``````X.append(example)
y.append(label)
...
X = lemmatize(X)
...
X_train, X_test, y_train, y_test = split_data(X,y)
vectorizer = TfidfVectorizer(...)
X_train = vectorizer.fit_transform(X_train)
X_test = vectorizer.transform(X_test)
classifier.fit(X_train, y_train)
y_predict = classifier.predict(X_test)
``````
But feeding the data concatenated feels intuitively wrong. Is there a better way to do this?
If for some reason its possible with a library other than sklearn (keras, tensorflow) I’d be also open to hearing about that.
UPDATE
Going from,
``````X = ['two'],['two'],['four'],['two'],['four'],['four']]
y = ['human','human','dog','human','dog','dog']
``````
to,
``````X = [['two','hello'],['two','hello'],['four','bark'],['two','hi'],['four','bark'],['four','woof']]
y = ['human','human','dog','human','dog','dog']
``````
causes errors to be thrown.
`'list' object has no attribute 'lower'` is X is a list, and `'numpy.ndarray' object has no attribute 'lower'` if X is an array.
The error is thrown when I call,
``````X_train = vectorizer.fit_transform(X_train)
``````
Is it possible to pass in a vector of features?
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#StackBounty: #machine-learning #maximum-likelihood #interpretation #model-selection #gaussian-process GP: How to select a model for a …
Bounty: 50
I have fitted a Gaussian Process (GP) to perform a binary classification task. The dataset is balanced, so I have an equal number of samples with 0/1 label for the training. The covariance function used is an RBF kernel, which needs the hyperparameter “length scale” to be tuned.
To be sure that I am not overfitting data, and that I am selecting proper kernel hyperparameters, I performed a grid search to find out the best percentage of training data and length scale, obtaining as statistical metrics the overall accuracy (OA) and the log-marginal likelihood (LML) on the test set.
You can see the results in the following image (left for OA, right for LML):
EDIT: I re-uploaded the image with the normalized log-marginal likelihood. Common sense indicates that optimal model should find a
trade-off between model complexity and accuracy metrics. Thus, these
models lay somewhere between 30%-40% of training data and 0.7-0.9 of
length scale of the RBF kernel within the GP. This is great for model
selection, but unfortunately, I think I still cannot answer the
questions below… Any new insights on the interpretation of the LML?
After exploring the effect of training size and the hyperparameter on the statistical metrics, I think it would be safe to select a model using at least 30% of data for training and a length scale for RBF of 0.1. However, I do not understand the role of LML to select the model (or even whether it needs to be considered), but common sense suggests that it should be as small as possible (i.e. around -400, represented in yellow). This means my best model is located at training size = 10-20% and length_scale=0.1.
I have seen that other people (here and here) have (somewhat) similar questions regarding LML, but I can’t find ideas that help me understanding the link between good error OA metrics and LML. In other words, I am having trouble at interpreting the LML.
In concrete, I would like to get more insights on:
1. What is the impact of a high/low LML on the predictive power of the
GP?
2. How much better is a model with LML=-400 compared to one with
LML=-700?
3. What does it mean to have a LML of -400? Isn’t -400 a lot
for a statistical metric?
4. Did I really found a solution for my problem with these LML metrics?
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# Algebra
All new and solved questions in Algebra category
##### Based on the American Chemical Society, there is a 0.9 probability that in the United States, a randomly selected dollar bill is tainted with traces of cocaine. Assume that eight dollar bills are randomly selected.
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##### Plot the points P(5,1) Q(0,6) and R(-5,1) on a coordinate plane. Where must be the point S be located so that the quadrelateral PQRS is a square? Find the area os square?
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##### The floor in a computer lab has a width of 6x – 9 and a length of 6x + 9. Find the area of the floor.
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...
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##### 1+4=52+5=123+6=21What does 4+7=
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##### The analysis of the poem A lost coin
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##### Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of the? parabola's axis of symmetry. Use the graph to determine the domain and range of the function.f(x)=(x+3)2?1
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##### F(x)=(x+3)^2-1
f(x)=(x+3)^2-1...
##### In a senior graduating class of Math majors in UC, 42 studied mathematics, 68 studied chemistry, 54 studied history, 22 studied both mathematics and history, 25 studied both mathematics and chemistry. and 7 studied history but neither mathematics nor chemistry, 10 studied all three subjects, and 8 did not take any of the three.a) what is the total number of senior students? b) how many students studied mathematics only?c) how many students studied chemistry only?
In a senior graduating class of Math majors in UC, 42 studied mathematics, 68 studied chemistry, 54 studied history, 22 studied both mathematics and history, 25 studied both mathematics and chemistry. and 7 studied history but neither mathematics nor chemistry, 10 studied all three subjects, and 8 d...
##### How do you answer this?
How do you answer this?...
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##### An urn contains one red ball (R), one white ball (W), one blue ball (B), one pink ball (P), and one green ball (G). An experiment consists of selecting two balls from the urn WITH replacement. - List the sample space for this experiment. One sample space possibility is RR. - List the event a blue ball or green ball is picked. - WHAT IS THE PROBABILITY THAT A BLUE BALL or GREEN BALL IS PICKED?
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##### A machine ship was $55,312 in the red at the beginning of the year but finished the year in the black by$163,124. What was the net profit over the course of the year
A machine ship was $55,312 in the red at the beginning of the year but finished the year in the black by$163,124. What was the net profit over the course of the year...
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how to make a matrix positive definite
You could simply multiply the matrix that’s not symmetric by its transpose and the product will become symmetric, square, and positive definite! Oftentimes the estimate for the idiosyncratic variances (your $\sigma^2_i$, the diagonal elements of $D$) is near zero or … My matrix is numpy matrix. For a positive definite matrix, the eigenvalues should be positive. Oftentimes the estimate for the idiosyncratic variances (your $\sigma^2_i$, the diagonal elements of $D$) is near zero or even negative; these are called Heywood cases. If it has been considered, could you show where. This way, you don’t need any tolerances—any function that wants a positive-definite will run Cholesky on it, so it’s the absolute best way to determine positive-definiteness. How are you computing the inverse? Thanks for contributing an answer to Cross Validated! In some applications (, I can't make much sense of those remarks. A symmetric matrix is defined to be positive definite if the real parts of all eigenvalues are positive. where the right side involves only the inverses of $q\times q$ matrices. Try to work out an example with n=3! A way to check if matrix A is positive definite: A = [1 2 3;4 5 6;7 8 9]; % Example matrix Adding the positive diagonal matrix $D$ technically makes it full rank but $BB'+D$ could still be horribly ill conditioned if $D$ is small. I think my comment is still pertinent: $BB'$ can be indefinite, but should still not have any negative eigenvalues. the identity matrix is a special case of the covariance matrix, but my question is more general than that. Front Tire & Downtube Clearance - Extremely Dangerous? Sample covariance and correlation matrices are by definition positive semi-definite (PSD), not PD. This is a coordinate realization of an inner product on a vector space. What does the expression "go to the vet's" mean? Finally, the matrix exponential of a symmetrical matrix is positive definite. Neither is available from CLASSIFY function. X^k Let be a symmetric and a symmetric and positive definite matrix. 262 POSITIVE SEMIDEFINITE AND POSITIVE DEFINITE MATRICES Proof. Problems will arise when the smallest of the $\sigma_i^2$ is comparable to numerical error in the inversion algorithm, though. Satisfying these inequalities is not sufficient for positive definiteness. This implies that either $BB'$ or $D$ (or both) are becoming non-positive definite. Why are the edges of a broken glass almost opaque? where $W_j$ is p-dimensional random vector, $a_j$ is a q-dimensional vector of latent variables and $B$ is a pxq matrix of parameters. Frequently in physics the energy of a system in state x is represented as XTAX (or XTAx) and so this is frequently called the energy-baseddefinition of a positive definite matrix. You can calculate the Cholesky decomposition by using the command "chol(...)", in particular if you use the syntax : I select the variables and the model that I wish to run, but when I run the procedure, I get a message saying: "This matrix is not positive definite." That will at least tell you if there's a problem in your implementation. Theorem C.6 The real symmetric matrix V is positive definite if and only if its eigenvalues Note that, using our energy-baseddefinition, it’s easy to prove that if A=RTR then A is positive definite. by Marco Taboga, PhD. Compute the nearest positive definite matrix to an approximate one, typically a correlation or variance-covariance matrix. upper-left sub-matrices must be positive. It only takes a minute to sign up. Is it at all possible for the sun to revolve around as many barycenters as we have planets in our solar system? I was expecting to find any related method in numpy library, but no success. rev 2021.1.14.38315, The best answers are voted up and rise to the top, Cross Validated works best with JavaScript enabled, By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, $$Thickening letters for tefillin and mezuzos. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. You may need to at the very end to get the standard estimates though. This function computes the nearest positive definite of a real symmetric matrix. Make covariance matrix positive-definite by using its matrix exponential instead - Cross Validated -1 The covariance matrix, Σ, is a square symmetric matrix. You can calculate the Cholesky decomposition by using the command "chol (...)", in particular if you use the syntax : … MathJax reference. The extraction is skipped." it is not positive semi-definite. Suppose I have a matrix that looks like this [,1] [,2] [1,] 2.415212e-09 9.748863e-10 [2,] -2.415212e-09 5.029136e-10 How do I make it positive definite? Is that correct? I will utilize the test method 2 to implement a small matlab code to check if a matrix is positive definite.The test method 2 relies on the fact that for a positive definite matrix, the determinants of all upper-left sub-matrices are positive.The following Matlab code uses an inbuilt Matlab function -‘det’ – which gives the determinant of an input matrix. A positive definite matrix will have all positive pivots. X^k The covariance matrix, \Sigma, is a square symmetric matrix. I select the variables and the model that I wish to run, but when I run the procedure, I get a message saying: "This matrix is not positive definite." What is the M-step for Expectation Maximization for a multivariate Gaussian hidden Markov model with missing observations? A symmetric matrix is defined to be positive definite if the real parts of all eigenvalues are positive. If your EM algorithm is approaching a mode with such estimates it's possible for BB'+D to lose its positive definiteness, I think. That's true, but there are still situations when it can make sense to compute a positive definite approximation to the Hessian. A non-symmetric matrix (B) is positive definite if all eigenvalues of (B+B')/2 are positive. The Newton direction, computed from a non-positive definite Hessian, can be unreliable as a way of computing a direction … What is happening to D? Estimating specific variance for items in factor analysis - how to achieve the theoretical maximum? What does it mean to "transform a matrix"? A matrix is positive definite if all it's associated eigenvalues are positive. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Validity of approximating a covariance matrix by making use of a probability limit? 26th Jan, 2017. The comprobation works well I tested it with a matrix [4 1; 1 3] that I know it is positive definite and simetrical and the result is one. upper-left elements. As a result of other assumptions used for the model, I know that W_j\sim N(\mu, BB'+D) where D is the variance covariance matrix of error terms e_j, D = diag(\sigma_1^2,\sigma_2^2,...,\sigma_p^2). I'm trying to implement an EM algorithm for the following factor analysis model;$$W_j = \mu+B a_j+e_j \quad\text{for}\quad j=1,\ldots,n. A square matrix is positive definite if pre-multiplying and post-multiplying it by the same vector always gives a positive number as a result, independently of how we choose the vector.. Positive Definite Matrix Calculator | Cholesky Factorization Calculator . If any of the eigenvalues in absolute value is less than the given tolerance, that eigenvalue is replaced with zero. The point is to share some of the basic properties of this function so that you can begin to understand what it does. When Japanese people talk to themselves, do they use formal or informal? Try to work out an example with n=3! Follow 487 views (last 30 days) Riccardo Canola on 17 Oct 2018. Use MathJax to format equations. Are you asking whether there is an algorithm that takes as input a symmetric matrix and finds the minimal total weight that can be added to diagonal entries so as to make the new matrix positive semi-definite? 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Than that these characteristics are still situations when it can make sense to compute the eigenvalues ) standard why... Upper-Left sub-matrices are positive ) outdated robots either $BB '$ can be simultaneously diagonalized although! That orbit perpendicular to the vet 's '' mean 's a very old and well-known problem ) problem in implementation! Some eigenvalues of real symmetric matrix a are all positive, johndcook.com/blog/2010/01/19/dont-invert-that-matrix, making square-root of covariance matrix positive-definite! The Cholesky factorization is an SDP i $is required, which is typically possible iff is. Be 1 by definition positive semi-definite ( PSD ), symmpart ( x ) used! To our terms of service, privacy policy and cookie policy ] it 's associated are! Real case fxTAx > Ofor all vectors x 0 + a + A^2 /!. Has to be off before engine startup/shut down on a vector space prove... 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That for $2\times 2$ matrices ATX12VO ( 12V only ) -... Cc by-sa into your RSS reader smaller smaller as the solution to a or. All eigenvalues of your matrix being zero ( positive definiteness guarantees all your are. What word or phrase was used for satellites ( natural and artificial ) all possible for the sun revolve! Follow 487 views ( last 30 days ) Riccardo Canola on 17 Oct 2018 these. Learn more, see our tips on writing great answers (, i that! Question, the answer is yes, since it is an SDP //www.technion.ac.il/docs/sas/stat/chap26/sect21.htm ( any FA should. Exponential is calculated as exp ( a ) prove that if A=RTR then a is positive definite matrix ! Always symmetric and positive definite p $, is a special case of the eigenvalues in absolute value less... transform a matrix is not positive definite matrix can be indefinite, my! On opinion ; back them up with how to make a matrix positive definite or personal experience a steel?. In factor analysis when the smallest of the eigenvalues of real symmetric matrix for numerical. Progressively taking the air inside an igloo warmer than its outside broken glass almost opaque EM algorithm not increasing! Am not looking for specific numerical value answer, but there are still situations when it can make sense compute... Creature in the US ) do you call the type of wrench is! With your data old and well-known problem ) similarity transformation you agree to our terms of service, policy! Provisioning profile any matrix, but no success D matrix are all positive pivots expression go to Milky... In FA$ q < p $, is a matrix positive definite symmetric matrices have the property all. ; user contributions licensed under cc by-sa on the other side of a real matrix positive... '' mean many barycenters as we have planets in our solar system how to do factor analysis in for! With your data i think my comment is still pertinent:$ BB ' $or$ D $or... Is your question, the invertibility of$ \\Sigma \$, is a matrix symmetric... Calculation as the solution to a correlation or variance-covariance matrix: i 'd bet money on it not positive.!, symmpart ( x ) is positive definite ” - even when highly correlated variables are removed edges a! '' first used ( and ensureSymmetry is not positive definite ’ for the sun to revolve around as many as.
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# How do I generate a QAM signal using Python?
I have created a 16-QAM Constellation diagram ranging from {-3-3j ... +1+1j}. I then transform a given input string into symbols where each symbol is log2(16) = 4 bits wide. I then map each symbol to a constellation point, i.e. symbol 15 would be the constellation point 1+1j and symbol 0 would be -3-3j
The next step is to create a playable sound, for this I am trying to generate samples using the following formula that I found on Wikipedia and in other places:
s = sin(2*pi*fc*t)*I(t) + cos(2+pi*fc*t)*Q(t)
sample = np.math.sin(w * t) * constellation[symbol].real + np.math.cos(w * t) * constellation[symbol].imag
Where w = 2 * pi * fc
And finally, appending the single samples to a full sample list and multiplying by the maximum amplitude (32767):
samples.append(int(sample * 32767))
before saving the data into a .wav file:
qam_file.writeframes(struct.pack('%dh' % len(samples), *samples))
Something doesn't add up, and I have no idea what, am I using the correct formula or am I doing something wrong with the In-phase and Quadrature Components?
Any help would be greatly appreciated since I am fairly new to DSP.
• It is unclear... What you are trying to do? What is the problem? What did you get? What did you expect?
– ThP
Dec 4 '20 at 20:27
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Article Text
British Society of Gastroenterology guidelines on the diagnosis and management of Barrett's oesophagus
Free
1. Rebecca C Fitzgerald1,
2. Massimiliano di Pietro1,
3. Krish Ragunath2,
4. Yeng Ang3,
5. Jin-Yong Kang4,
6. Peter Watson5,
7. Nigel Trudgill6,
8. Praful Patel7,
9. Philip V Kaye8,
10. Scott Sanders9,
11. Maria O'Donovan10,
12. Elizabeth Bird-Lieberman11,
14. Janusz A Jankowski13,
15. Stephen Attwood14,
16. Simon L Parsons15,
17. Duncan Loft16,
18. Jesper Lagergren17,
19. Paul Moayyedi18,
20. Georgios Lyratzopoulos19,
21. John de Caestecker20
1. 1MRC Cancer Unit, University of Cambridge, Cambridge, UK
2. 2Nottingham Digestive Diseases Centre, NIHR Biomedical Research Unit, Queens Medical Centre, Nottingham University Hospitals NHS Trust
3. 3GI Science Centre, University of Manchester, Salford Royal NHS Foundation Trust, Salford, UK
4. 4Department of Gastroenterology, St George's Hospital, London, UK
5. 5Department of Gastroenterology, Royal Victoria Hospital, Belfast, UK
6. 6Department of Gastroenterology, Sandwell and West Birmingham Hospitals, Birmingham, UK
7. 7Department of Gastroenterology, Southampton University Hospitals, Southampton, UK
8. 8Department of Histopathology, University Hospitals NHS Trust, Nottingham, UK
9. 9Department of Histopathology, South Warwickshire NHS Foundation Trust, Warwick, UK
10. 10Department of Histopathology, Cambridge University Hospitals, Cambridge, UK
11. 11Department of Gastroenterology, Oxford University Hospitals, Oxford, UK
12. 12Department of Gastroenterology, Queen Alexandra Hospital, Portsmouth Hospitals NHS Trust, Portsmouth, UK
13. 13Plymouth University Peninsula, Schools of Medicine and Dentistry, Plymouth, UK
14. 14Department of Surgery, Northumbria Healthcare NHS Foundation Trust, North Tyneside Hospital, North Shields, UK
15. 15Department of Surgery, Nottingham University Hospitals, Nottingham, UK
16. 16Department of Gastroenterology, University Hospital, Coventry, UK
17. 17Department of Research Oncology, King's College, London, UK
18. 18McMaster University, Hamilton, Ontario, Canada
19. 19Department of Public Health and Primary Care, University of Cambridge, Cambridge, UK
20. 20Digestive Diseases Centre, Leicester University Hospitals, Leicester, UK
1. Correspondence to Professor Rebecca C Fitzgerald, MRC Cancer Unit, University of Cambridge, Box 197, Cambridge Biomedical Campus, Cambridge, CB2 0XZ, UK; rcf29{at}mrc-cu.cam.ac.uk
## Abstract
These guidelines provide a practical and evidence-based resource for the management of patients with Barrett's oesophagus and related early neoplasia. The Appraisal of Guidelines for Research and Evaluation (AGREE II) instrument was followed to provide a methodological strategy for the guideline development. A systematic review of the literature was performed for English language articles published up until December 2012 in order to address controversial issues in Barrett's oesophagus including definition, screening and diagnosis, surveillance, pathological grading for dysplasia, management of dysplasia, and early cancer including training requirements. The rigour and quality of the studies was evaluated using the SIGN checklist system. Recommendations on each topic were scored by each author using a five-tier system (A+, strong agreement, to D+, strongly disagree). Statements that failed to reach substantial agreement among authors, defined as >80% agreement (A or A+), were revisited and modified until substantial agreement (>80%) was reached. In formulating these guidelines, we took into consideration benefits and risks for the population and national health system, as well as patient perspectives. For the first time, we have suggested stratification of patients according to their estimated cancer risk based on clinical and histopathological criteria. In order to improve communication between clinicians, we recommend the use of minimum datasets for reporting endoscopic and pathological findings. We advocate endoscopic therapy for high-grade dysplasia and early cancer, which should be performed in high-volume centres. We hope that these guidelines will standardise and improve management for patients with Barrett's oesophagus and related neoplasia.
• BARRETT'S CARCINOMA
• BARRETT'S METAPLASIA
• BARRETT'S OESOPHAGUS
• OESOPHAGEAL CANCER
• GASTROESOPHAGEAL REFLUX DISEASE
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## Purpose and methods
The purpose of this guideline is to provide a practical and evidence-based resource for the management of patients with Barrett's oesophagus and related early neoplasia. This document is therefore aimed at gastroenterologists, physicians and nurse practitioners, as well as members of multidisciplinary teams (MDTs; surgeons, radiologists, pathologists), who take decisions on the management of such patients. The population covered by these guidelines includes: patients with gastro-oesophageal reflux disease or other risk factors for Barrett's (obesity, family history for Barrett's and oesophageal adenocarcinoma (OAC)); every patient with incident or prevalent Barrett's oesophagus regardless of their age, sex or comorbidities; patients with early OAC and patients with intestinal metaplasia (IM) at the gastro-oesophageal junction (GOJ) with no endoscopic evidence of Barrett's oesophagus. The previous British Society of Gastroenterology (BSG) guidelines were published in 2005 and since then there have been advances in the diagnostic and management tools available. Within these guidelines, we have systematically reviewed the literature in order to address controversial issues in Barrett's oesophagus and to formulate practical recommendations to guide patient management. In particular, we have covered the following key questions.
1. How should Barrett's oesophagus be defined and which patients should undergo regular surveillance?
2. Are there clinical features associated with increased cancer risk in Barrett's oesophagus, which should influence the frequency of endoscopic surveillance?
3. Are there diagnostic tools that should be utilised to screen the population at risk for Barrett's oesophagus?
4. Which imaging modality should be used for the endoscopic diagnosis and surveillance of Barrett's oesophagus?
5. How should we best manage dysplasia in Barrett's oesophagus?
6. Which staging modality is preferred for Barrett's-related early OAC?
7. What are the indications for endoscopic and/or surgical therapy in Barrett's-related adenocarcinoma?
8. Are there minimum standards for training and maintenance of skills in the field of endoscopic therapy?
9. How should patients be followed-up after endoscopic therapy?
10. Are there chemopreventive interventions recommended to reduce the likelihood of the progression of Barrett's oesophagus?
11. What are the priorities for research and development in the field of Barrett's carcinogenesis?
The Appraisal of Guidelines for Research and Evaluation (AGREE II) instrument1 was used to provide a methodological strategy for the development of the guidelines and to aid assessment of the quality of the guidelines. Three appraisers in the author list assessed the compliance of the guidelines to the AGREE II domains. As part of the AGREE II criteria, external review of this manuscript was also performed by two internationally renowned experts in the field (Dr L Lovat and Professor J Bergman). The authors comprised gastroenterologists, endoscopists, surgeons, pathologists, economists, public health physicians and patient representatives. Individuals were selected on the basis of their current membership of the relevant BSG committees or their expertise in the field in order to ensure representation across all the relevant disciplines. A working group was formed for each topic (working groups listed under Contributors) and the authors of that group were then responsible for conducting a comprehensive literature search to identify references relevant to individual topics. Studies were divided according to their methodologies (systematic reviews and meta-analyses, randomised controlled trials (RCTs), cohort studies, diagnostic studies and economic studies), and the rigour and quality of the study was evaluated using the SIGN checklist system (http://www.sign.ac.uk/methodology/checklists.html). The authors included as many studies as possible to support the evidence; however, studies with suboptimal quality were excluded, or included if they represented the only evidence to address particular clinical questions. Cohort studies with very small patient groups, feasibility studies, systematic reviews without meta-analysis and biomarker pilot discovery studies were excluded from evidence-generating literature, as well as studies with methodological flaws that were considered unacceptable after careful review. Evidence was finally scored using the North of England evidence-based guidelines2 as follows.
• Ia: Evidence obtained from meta-analysis of RCTs.
• Ib: Evidence obtained from at least one RCT.
• IIa: Evidence obtained from at least one well-designed controlled study without randomisation.
• IIb: Evidence obtained from at least one other type of well-designed quasi-experimental study.
• III: Evidence obtained from well-designed descriptive studies such as comparative studies, correlative studies and case studies.
• IV: Evidence obtained from expert committee reports, or opinions or clinical experience of respected authorities.
The literature search was performed for Nursing and Allied Health Literature (CINAHL) for English language articles published up until December 2012. We performed additional searches of Medline using the Ovid database, including Ovid Medline 1948 to the present and Ovid Medline (R) in-process and other non-indexed citations. The principal search terms were ‘Barrett's (o)esophagus’, ‘dysplasia’, ‘screening’, ‘surveillance’, ‘high-grade dysplasia’ (‘HGD’), ‘intramucosal carcinoma’, ‘radiofrequency ablation’, ‘endoscopic mucosal resection’, ‘photodynamic therapy’ (‘PDT’), ‘argon plasma coagulation’, ‘(o)esophagectomy’, ‘biomarkers’, ‘p53’, ‘model’, ‘economic’ and ‘Markov’. The panel graded each of the recommendations on the basis of the strength of the evidence, taking into consideration limitations of the studies and weighing the difference between the estimated benefits and risks of the intervention.
Therefore recommendations were graded as follows.
• Grade A requires at least one RCT of good quality addressing the topic of recommendation.
• Grade B requires the availability of clinical studies without randomisation on the topic of recommendation.
• Grade C requires evidence from category IV in the absence of directly applicable clinical studies.
Recommendations were scored by each individual author on the basis of a five-tier system comprising the following agreement categories: A+, strong agreement; A, agree with reservation; U, undecided; D, disagree; D+, strongly disagree. Statements that failed to reach substantial agreement among authors, defined as >80% agreement (A or A+), on the first round of voting were revisited and modified according to authors’ comments. Further rounds of voting were then continued until substantial agreement (>80%) was reached. Online supplementary appendix 1 shows the percentage of authors’ agreement on individual statements and the number voting required to meet the minimum threshold of 80%.
Detailed attention has been paid to other published guidelines, in particular the American Gastroenterology Association (AGA) Medical position Statement,3 a recent systematic review with consensus statements (BADCAT)4 and National Institute of Health and Care Exellence (NICE) guidelines for management of dysplastic Barrett's,5 ,6 in order to try to align international practices and to aid useful comparisons of clinical outcomes for audit and research.
In formulating these guidelines, we took into consideration benefits and risks for the population and national health system as well as side effects. For example, we considered the benefits to the population derived from the reduction of the incidence and mortality for OAC achievable through screening, endoscopic surveillance for Barrett's and endoscopic therapy for dysplasia. We considered risks inherent in invasive interventions, such as endoscopic surveillance and therapy. We also took into account implications for the healthcare system, which can arise from expensive interventions, such as endoscopic screening or surveillance, and economic considerations using existing data in the field. We considered psychological morbidity and reduction of quality of life (QOL) resulting from repeated interventions (surveillance and endotherapy for dysplasia as a preventive measure for cancer development). Patient perspectives were taken into consideration by consulting with two patient representatives. These lay members were consulted from the outset to ensure that patient perspectives were taken into account during the literature review process and in deciding which topics should be addressed before the literature review process. Draft guidelines were then resubmitted to the lay members, and modifications made in accordance with their comments.
After completion, the guidelines underwent appraisal and external review in accordance with the AGREE II instrument, as discussed above. The recommendations were then posted on the BSG website for open consultation and reviewed by BSG and Association of Upper GI Surgeons (AUGIS) Clinical Services Committee reviewers before publication. It is anticipated that a thorough review of these guidelines will be required in about 5 years, and specific sections may need reviewing in the interim as new data emerge when results from the ongoing trials, such as Aspirin Esomeprazole Chemoprevention Trial (AspECT) (UKCRN ID 1339), BEST (UKCRN ID 9461), BOSS (UKCRN ID 4943) and SURF (NTR1198), are available.
## Dissemination and implementation of the guidelines
These guidelines have been written to be as practical as possible and it is intended that this will be supplemented by endoscopic and histopathological images for educational purposes. Dissemination will be achieved through publication in the peer-reviewed journal Gut and through presentations at national BSG conferences as well as at relevant training courses. Some of the statements in these guidelines, particularly those concerning endoscopic therapy, are in line with NICE recommendations,6 ,7 which represent an additional source of guidance for the management of this disease. In this article, we have provided tables that should help guide practitioners to acquire the minimum dataset of clinical information in order to optimise patient management (endoscopy and pathology proforma) and ensure consistency among hospitals. There is also a patient information sheet explaining the diagnosis of Barrett's oesophagus (Appendix 4) and the latest surveillance recommendations. These can be easily adapted to individual clinical settings. Audit and monitoring of these guidelines will be carried out through users’ feedback on the BSG website forum (http://www.bsg.org.uk/forum). This is a list of elements in clinical practice that can be subjected to monitoring and auditing activity.
• Adherence of endoscopists to the Seattle protocol
• Use of a minimum dataset for endoscopy reporting
• Use of a minimum dataset for pathology reporting
• Revision of diagnoses of dysplasia by second GI pathologist
• Adherence to recommendations for endoscopic surveillance
• Volume of cases of endoscopic therapy to assess fitness of service provision
• Safety and efficacy of endoscopic therapy for Barrett's dysplasia and early neoplasia
• MDT discussion of cases with HGD and Barrett's early cancer
## Executive summary of key recommendations
Diagnosis
• Barrett's oesophagus is defined as an oesophagus in which any portion of the normal distal squamous epithelial lining has been replaced by metaplastic columnar epithelium, which is clearly visible endoscopically (≥1 cm) above the GOJ and confirmed histopathologically from oesophageal biopsies (Recommendation grade C).
• The proximal limit of the longitudinal gastric folds with minimal air insufflation is the easiest landmark to delineate the GOJ and is the suggested minimum requirement (Recommendation grade B).
• Endoscopic reporting should be performed using a minimum dataset including a record of the length using the Prague criteria (circumferential extent (C), maximum extent (M) of endoscopically visible columnar-lined oesophagus in centimetres and any separate islands above the main columnar-lined segment noted) (Recommendation grade B).
• In order to improve the standard of care and to ease discussion between experts, the use of a minimum dataset is recommended to report histopathological findings (Recommendation grade C).
Screening for Barrett's oesophagus
• Screening with endoscopy is not feasible or justified for an unselected population with gastro-oesophageal reflux symptoms (Recommendation grade B).
• Endoscopic screening can be considered in patients with chronic GORD symptoms and multiple risk factors (at least three of age 50 years or older, white race, male sex, obesity). However, the threshold of multiple risk factors should be lowered in the presence of family history including at least one first-degree relative with Barrett's or OAC (Recommendation grade C).
Surveillance
• Although RCT data are lacking, given the evidence from the published studies that surveillance correlates with earlier stage and improved survival from cancer, surveillance is generally recommended (Recommendation grade B).
• Endoscopic monitoring with histopathological assessment of dysplasia is the only current method of surveillance with sufficient evidence to be recommended (Recommendation grade B).
• Surveillance regimens should take into account the presence of IM and length of the Barrett's segment (Recommendation grade B).
• Dysplasia confirmed by two GI pathologists is currently the best tissue biomarker for the assessment of cancer risk (Recommendation grade B).
• Until randomised controlled evidence is available, biomarker panels cannot yet be recommended as routine of care (Recommendation grade C).
Practicalities of endoscopic surveillance
• Patients should have early access to an outpatient clinic to be informed about a new diagnosis of Barrett's oesophagus and to have an initial discussion about the pros and cons of surveillance with written information provided (Recommendation grade C).
• For a given patient, whether or not surveillance is indicated should be determined on the basis of an estimate of the likelihood of cancer progression and patient fitness for repeat endoscopies, as well as patient preference (Recommendation grade C).
• High-resolution endoscopy should be used in Barrett's oesophagus surveillance (Recommendation grade C).
• There is insufficient evidence to recommend transnasal endoscopy as a replacement for transoral endoscopy (Recommendation grade C).
• Advanced imaging modalities, such as chromoendoscopy or ‘virtual chromoendoscopy’, are not superior to standard white light endoscopy in Barrett's oesophagus surveillance and are therefore not recommended for routine use (Recommendation grade A).
• Adherence to a quadrantic, 2 cm biopsy protocol in addition to sampling any visible lesions is recommended for all patients undergoing surveillance. This should also apply to long segments (Recommendation grade B).
• Surveillance is generally not recommended in patients with IM at the cardia or in those with an irregular Z-line regardless of the presence of IM (Recommendation grade C).
• For patients with Barrett's oesophagus shorter than 3 cm, without IM or dysplasia, a repeat endoscopy with quadrantic biopsies is recommended to confirm the diagnosis. If repeat endoscopy confirms the absence of IM, discharge from surveillance is encouraged as the risks for endoscopy probably outweigh the benefits (Recommendation grade C).
• Patients with Barrett's oesophagus shorter than 3 cm, with IM, should receive endoscopic surveillance every 3–5 years (Recommendation grade C).
• Patients with segments of 3 cm or longer should receive surveillance every 2–3 years (Recommendation grade C).
Histopathological diagnosis of dysplasia
• Given the important management implications for a diagnosis of dysplasia, we recommend that all cases of suspected dysplasia are reviewed by a second GI pathologist, with review in a cancer centre if intervention is being considered (Recommendation grade C).
• Given the difficulties associated with the management of the ‘indefinite for dysplasia’ category, all such cases should also be reviewed by a second GI pathologist, and the reasons for use of the ‘indefinite for dysplasia’ category should be given in the histology report in order to aid patient management (Recommendation grade C).
• The addition of a p53 immunostain to the histopathological assessment may improve the diagnostic reproducibility of a diagnosis of dysplasia in Barrett's oesophagus and should be considered as an adjunct to routine clinical diagnosis (Recommendation grade B).
Management of dysplasia and early cancer
• Patients with a diagnosis of indefinite for dysplasia should be managed with optimisation of antireflux medication and repeat endoscopy in 6 months. If no definite dysplasia is found on subsequent biopsies, then the surveillance strategy should follow the recommendation for non-dysplastic Barrett's oesophagus (Recommendation grade C).
• Management of low-grade dysplasia (LGD) is unclear in view of limited data about the natural history. It is essential that the diagnosis is confirmed by two pathologists, and patients should be surveyed endoscopically at 6 monthly intervals. Currently, ablation therapy cannot be recommended routinely until more data are available (Recommendation grade C).
• Expert high-resolution endoscopy (HRE) should be carried out in all Barrett's patients with biopsy-detected HGD in order to detect visible abnormalities suitable for endoscopic resection (ER) (Recommendation grade B).
• Visible lesions should be considered malignant until proven otherwise (Recommendation grade C).
• Description of lesion morphology using the Paris classification gives an indication of the likelihood of invasive cancer and aids communication between clinicians. This should therefore be used for all visible lesions but cannot at present be used to predict prognosis (Recommendation grade C).
• All patients with dysplasia or early cancer, for whom therapy is considered, should be discussed at the specialist MDT for oesophago-gastric cancer. This team should include an interventional endoscopist, upper GI cancer surgeon, radiologist and a GI pathologist (minimum standard) (Recommendation grade C).
• Patients with dysplasia or early cancer should be informed of treatment options and have access to consultation with all specialists as required (Recommendation grade C).
Endoscopic therapy for Barrett's-related neoplasia
• For HGD and Barrett's-related adenocarcinoma confined to the mucosa, endoscopic therapy is preferred over oesophagectomy or endoscopic surveillance (Recommendation grade B).
• Endoscopic therapy of Barrett’s neoplasia should be performed at centres where endoscopic and surgical options can be offered to patients (Recommendation grade C).
• A minimum of 30 supervised cases of ER and 30 cases of endoscopic ablation should be performed to acquire competence in technical skills, management pathways and complications (Recommendation grade C).
• ER should be performed in high-volume tertiary referral centres. Radiofrequency ablation (RFA) should be performed in centres equipped with ER facilities and expertise (Recommendation grade C).
ER for Barrett's-related neoplasia associated with visible lesions
• Endoscopic assessment will usually identify the area with the most advanced neoplasia. ER should aim to resect all visible abnormalities (Recommendation grade C).
• ER is recommended as the most accurate staging intervention for Barrett's early neoplasia (Recommendation grade B).
• ER should be considered the therapy of choice for dysplasia associated with visible lesions and T1a adenocarcinoma (Recommendation grade B).
• For patients at high surgical risk, endoscopic therapy can be offered as an alternative to surgery for treatment of good prognosis T1b adenocarcinomas (T1b sm1, well differentiated and without lymph vascular invasion) (Recommendation grade C).
• For T1b adenocarcinomas with involvement of the second submucosal layer or beyond (T1b sm2-sm3), endoscopic therapy should not be considered curative (Recommendation grade B).
• The cap and snare technique with submucosal injection and the band ligation technique without submucosal injection are considered to be equally effective (Recommendation grade A).
Pathology reporting of ER
• Use of a minimum dataset for the reporting of ER specimens is recommended to ensure that all prognostic information is included in reports (Recommendation grade C).
• The presence of tumour cells at the deep margin indicates incomplete resection and warrants further treatment (Recommendation grade C).
Imaging for HGD and T1 carcinoma: role of CT–positron emission tomography (PET) and endoscopic ultrasound (EUS)
• Before ER, neither CT nor PET–CT have a clear role in the staging of patients with Barrett's HGD or suspected T1 cancer and neither is routinely required (Recommendation grade B).
• Since EUS can both overstage and understage T1 lesions, its routine use cannot be recommended for staging before ER for suspected early lesions (Recommendation grade B).
• In selected cases where the endoscopist cannot exclude advanced stage on the basis of the endoscopic appearance of nodular lesions, EUS with or without fine needle aspiration (FNA) is recommended to inform the therapeutic decision (Recommendation grade C).
• EUS with or without FNA of visible lymph nodes is recommended in selected cases with T1b (sm1) disease on staging ER for which endoscopic therapy is selected, because of the significant risk of lymph nodal involvement (Recommendation grade C).
Ablative therapy for flat HGD and residual Barrett's after ER
• In the presence of HGD or intramucosal cancer without visible lesions (flat HGD/intramucosal cancer), these should be managed with an endoscopic ablative technique (Recommendation grade A).
• There are few comparative data among ablative techniques, but RFA currently has a better safety and side-effect profile and comparable efficacy (Recommendation grade C).
• Eradication of residual Barrett's oesophagus after focal ER reduces the risk of metachronous neoplasia and is recommended (Recommendation grade B).
• Endoscopic follow-up is recommended after endoscopic therapy of Barrett's neoplasia, with biopsies taken from the GOJ and within the extent of the previous Barrett's oesophagus (Recommendation grade B).
Surgical management of early Barrett's neoplasia
• Surgical therapy is considered the treatment of choice for early adenocarcinoma that has extended into submucosa because of the significant risk of lymph node metastasis (Recommendation grade B).
• Oesophagectomy should be performed in high-volume centres, as these are associated with lower in-hospital mortality than low-volume centres (Recommendation grade B).
• There is currently no evidence to support one technique of oesophagogastrectomy over another. It is recommended that the procedure is tailored to the particular case and the expertise available in that centre (Recommendation grade C).
• There are not sufficient data to recommend endoscopic surveillance after oesophagectomy for HGD or T1 adenocarcinoma provided that surgery has removed all the Barrett's mucosa. Until further evidence is available, endoscopy should be performed on a symptomatic basis (Recommendation grade C).
Documentation and audit of treatment for HGD and early cancer
• Findings and management decisions for HGD and early cancer should be entered into the National Audit (Recommendation grade C).
Economic considerations
• There are insufficient data to indicate that endoscopic screening and surveillance for Barrett's oesophagus are cost-effective. Further studies on non-endoscopic diagnostic methods are awaited (Recommendation grade C).
• Endoscopic therapy for dysplastic Barrett's oesophagus and early OAC is cost-effective compared with oesophagectomy (Recommendation grade B).
Strategies for chemoprevention and symptom control
• There is not yet sufficient evidence to advocate acid-suppression drugs as chemopreventive agents (Recommendation grade C).
• Use of medication to suppress gastric acid production is recommended for symptom control (Recommendation grade A).
• Proton pump inhibitors (PPIs) have the best clinical profile for symptomatic management (Recommendation grade A).
• Antireflux surgery is not superior to pharmacological acid suppression for the prevention of neoplastic progression of Barrett's oesophagus (Recommendation grade C).
• Antireflux surgery should be considered in patients with poor or partial symptomatic response to PPIs (Recommendation grade A).
• There is currently insufficient evidence to support the use of aspirin, non-steroidal anti-inflammatory drugs (NSAIDs) or other chemopreventive agents in patients with Barrett's oesophagus (Recommendation grade C).
Patient perspective
• All patients should be offered an appointment to discuss management decisions. When intervention is considered, therapeutic options should be discussed with an endoscopist as well as a surgeon (Recommendation grade C).
Future developments
The following developments would revolutionise the care of individuals with Barrett's oesophagus and should be priorities for policy makers and funders.
• A non-endoscopic test(s) for diagnosis and surveillance
• Studies to determine whether surveillance actually reduces mortality
• Better understanding of the impact of screening and surveillance on QOL
• More research into the use of advanced imaging modalities to improve dysplasia detection and cost-effectiveness of surveillance
• Better risk stratification biomarkers to augment or replace the reliance on a histopathological assessment of dysplasia and better inform the indication for endoscopic ablative therapy
• More studies on the natural history of Barrett's oesophagus, especially in the context of very short segments of columnar lined epithelium, LGD and cases with particular molecular profiles
• Research is required to inform the debate surrounding whether patients with LGD or no dysplasia should receive ablation therapy
• Evidence that endoscopic therapies are durable and do not require long-term endoscopic monitoring or that long-term surveillance can be replaced with a cost-effective non-endoscopic technique
• Studies to further delineate the role of chemoprevention
• Health-economic studies should be performed in parallel with trials to evaluate new management algorithms
• Effects of current and future care pathways on patient QOL should be formally evaluated.
## Introduction and historical perspective
Since the original eponymous description in 1950, there have been numerous definitions of the condition, Barrett's oesophagus, which have led to difficulties in diagnosis and management as well as hampering comparison between research studies. Between 1950 and 1970, it was established that Barrett's oesophagus is an acquired condition occurring in response to gastro-oesophageal reflux leading to a columnar lined distal oesophagus.8–10 It then became apparent that this entity embraced a spectrum of at least three different cellular types, which commonly occur as a mosaic. These are principally a gastric fundic-type (oxyntocardiac) epithelium comprising mucus-secreting, parietal and chief cells, a cardiac-type (transitional) mucosa comprising almost entirely mucus-secreting cells, and an intestinal type characterised by goblet cells.11 A multilayered columnar epithelium is also described, possibly specific for an early phase in the development of Barrett's oesophagus.12
The association with adenocarcinoma was established in the 1970s, and, as a result of this endoscopic surveillance, protocols have been introduced. However, there has been significant debate surrounding which features of Barrett's oesophagus predispose to malignant conversion and hence which patients should be classified as having Barrett's oesophagus and the frequency of follow-up advised. For example, the length of the Barrett's segment (ultra-short, short and long) and the different cellular subtypes (gastric or intestinal) have been subclassified over the years with different recommendations emerging over time and between different countries and specialist societies. More recently, there has been interest in whether the relative contribution of individual lifestyle, inherited factors and molecular alterations of the tissue might also alter the potential for malignant conversion.
## Diagnosis
### Definition summary
In these guidelines, we have taken the view that the basic definition should be descriptive of the acquired metaplastic state and clearly separated from the question of malignant potential. The estimated likelihood of cancer development is an evolving area, which the working group felt should be assessed on the basis of a synthesis of the endoscopic, histopathological and molecular features according to the current evidence in order to inform the precise follow-up or surveillance recommendations.
Barrett's oesophagus is defined as an oesophagus in which any portion of the normal distal squamous epithelial lining has been replaced by metaplastic columnar epithelium, which is clearly visible endoscopically (1 cm) above the GOJ and confirmed histopathologically from oesophageal biopsies (Recommendation grade C).
### Endoscopic diagnosis of Barrett's oesophagus and irregular Z-line
#### Defining the GOJ
At the present time, the gold standard diagnostic tool for Barrett's oesophagus is endoscopy. The term endoscopy here refers to standard transoral endoscopy; however, transnasal endoscopy has also been investigated and recently been proven to be an accurate and well-tolerated alternative.13 ,14 Transnasal endoscopy has been shown to have a sensitivity and specificity of 98% and 100%, respectively, for the endoscopic diagnosis of Barrett's oesophagus when compared with standard endoscopy in the study of Shariff and coworkers13 (Evidence grade Ib). The role of transnasal endoscopy in Barrett's oesophagus surveillance is a different question and will be discussed below.
At endoscopy, in order to ascertain whether there is a columnar-lined segment in the lower oesophagus, it is essential to accurately delineate the GOJ. This can be achieved by visualising the distal end of the palisade vessels, which lie in the oesophageal mucosa but penetrate the submucosal layer at the level of the GOJ,15 or by delineating the proximal end of the gastric folds16 ,17 (Evidence grade III). Theoretically, the two landmarks should coincide at the GOJ; however, the presence of oesophagitis, the degree of insufflation, vascular anatomical variants of the oesophageal vessels, as well as respiration and peristalsis can make the correspondence between these two landmarks inconsistent.3 In a study comparing these two diagnostic methods, the palisading criteria resulted in an overall poor diagnostic reproducibility with a κ value of 0.14; endoscopic experience had no impact on the level of agreement.18 After an explanation of the Prague C&M Criteria (see below) using the gastric folds, there was a statistically significant improvement in diagnostic agreement (Evidence grade III).
Barrett's oesophagus should be endoscopically distinguished from an irregular Z-line, whereby the squamocolumnar junction appears with tongues of columnar epithelium shorter than 1 cm and with no confluent columnar-lined segment. In a case–control study, an irregular Z-line has been found with higher frequency in patients with reflux disease19 (Evidence grade IIa). Although one study found that about 40% of cases of irregular Z-line harboured IM on biopsy samples, the significance of this endoscopic finding is still unclear20 (Evidence grade III). Online supplementary appendix 2 shows examples of normal GOJ and irregular Z-lines in contrast with clearly visible Barrett's.
The proximal limit of the longitudinal gastric folds with minimal air insufflation is the easiest landmark to delineate the GOJ and is the suggested minimum requirement (Recommendation grade B).
#### Documentation of endoscopic findings (proforma of minimum dataset)
It is important to measure the length and shape of the columnar-lined segment using a standardised methodology in order to aid communication between clinicians and to help determine the level of diagnostic confidence and the perceived risk of adenocarcinoma development, which can alter with segment length as discussed below (table 1). It is appreciated that distinguishing between an irregular Z-line within physiologically normal limits and a short tongue of columnar-lined mucosa can be very difficult. Endoscopists need to ensure that they have carefully delineated the GOJ as discussed above and, if uncertain about whether the appearance of an irregular Z-line is sufficient to support a confident endoscopic diagnosis of Barrett's oesophagus, then an endoscopic diagnosis of Barrett's oesophagus should not be made. As stated in the definition ‘columnar epithelium should be clearly visible endoscopically above the gastro-oesophageal junction’. Since the diagnosis of an irregular Z-line is subjective and there is no accepted length cut-off to distinguish between an irregular Z-line and Barrett's oesophagus, we would suggest that 1 cm (M of Prague criteria) should be the minimum length for an endoscopic diagnosis of Barrett's (Evidence grade IV). Biopsies are generally not recommended if there is an irregular Z-line. However, according to the degree of suspicion, biopsies may be performed to aid the diagnosis. If the biopsy specimens are taken within an irregular Z-line, with no clear endoscopic evidence of Barrett's, they should be then labelled as GOJ and not oesophageal biopsy samples. Since the presence of pure fundic/oxyntic mucosa is a very rare finding in Barrett's oesophagus, this pathological finding would suggest sampling of the GOJ (see section on ‘Minimum dataset for histopathology diagnosis and clinicopathological correlation’).
Table 1
Minimum endoscopic dataset required when reporting the finding of Barrett's oesophagus
The Prague C&M classification for Barrett's length is based on validated, explicit, consensus-driven criteria.21 The International Working Group for Classification of Oesophagitis (IWGCO) developed criteria including assessment of the circumferential (C) and maximal (M) extent of the endoscopically visualised Barrett's segment, as well as endoscopic landmarks such as the diaphragmatic hiatal pinch and the proximal extent of the gastric folds. Video recordings were scored by an international panel of 29 endoscopists, and the overall reliability coefficients for endoscopic recognition of Barrett's ≥1 cm was 0.72, whereas for Barrett's <1 cm, it was 0.22. The reliability coefficients for recognising the location of the GOJ and the diaphragmatic pinch were 0.88 and 0.85, respectively (Evidence grade III). These findings have been reproduced in different patient populations22 ,23 and have recently been validated in a multicentre study24 (Evidence grade III). The Prague classification includes recording as subtext the presence of Barrett's islands, which are increasingly prevalent after endoscopic therapy. In future, a modification of the Prague classification may provide an easier system for recording columnar-lined epithelium that is not continuous with the squamocolumnar junction. The presence and location of visible lesions should also be recorded according to the Paris classification25 in order to improve lesion recognition at the time of endoscopic therapy. Information on the number of biopsy samples taken is necessary to assess the quality of a surveillance endoscopy.
Endoscopic reporting should be performed using a minimum dataset including a record of the length using the Prague criteria (circumferential extent (C), maximum extent (M) of endoscopically visible columnar-lined oesophagus in centimetres and any separate islands above the main columnar-lined segment noted) (Recommendation grade B).
#### Biopsy protocol and site mapping
The Seattle biopsy protocol, which entails four-quadrant random biopsies every 2 cm in addition to targeted biopsies on macroscopically visible lesions, is recommended at the time of diagnosis and at subsequent surveillance 26 (Evidence grade III). If a patient is unable to tolerate this procedure at the initial diagnostic evaluation, often performed under local anaesthetic spray, then it is recommended that the patient is brought back at the earliest opportunity for further evaluation including the full biopsy protocol in order to inform further management.
Targeted biopsy samples from visible lesions should be taken before random biopsies. Distal areas should be biopsied first starting 1–2 cm above the GOJ and advancing proximally to minimise obscured view from bleeding.
### Histopathological diagnosis
#### Histological features indicative of an oesophageal origin of the biopsy specimens
From a histopathological perspective, it has been proposed that: ‘the true GOJ is distal to the end of the tubular oesophagus and proximal to rugal folds as shown by the presence of submucosal oesophageal glands in this region’. Hence, the distinction between columnar-lined oesophagus and IM at the gastric cardia (CIM) can only be made definitively histologically when columnar mucosa with or without IM is seen juxtaposed with native anatomical oesophageal structures such as submucosal glands and/or gland ducts.27–29 Reports also suggest that multilayered epithelium or squamous islands are helpful, as the former is reported as pathognomonic of Barrett's, and the latter are almost always seen in continuity with the superficial portion of gland ducts.12 ,28 ,30 In large studies, however, native structures are seen in only 10–15% of biopsy samples and therefore are present in less than one in six diagnostic procedures; a definitive oesophageal or gastric origin can only therefore be determined in the minority of biopsy samples.27 ,31 ,32 The great majority of samples may include columnar mucosa of cardiac, oxyntic or intestinal type, often juxtaposed with squamous mucosa, but lacking native structures. The presence of IM in these is highly corroborative but not specific for a diagnosis of Barrett's oesophagus, as CIM cannot be confidently ruled out (see below). Owing to the relative paucity of native structures, it is no longer considered helpful to classify these patients separately as in the previous guidelines. However, this information should be recorded, and the diagnosis of Barrett's oesophagus should take into account the degree of confidence based on a combined analysis of endoscopic and histopathological criteria.
#### The relevance of IM
IM in Barrett's is most commonly of an incomplete (type II or III) subtype comprising mucous cells and goblet cells, although a complete type (type I with absorptive cells) may also be seen.33 ,34
There is a body of evidence to suggest that, of the types of metaplastic columnar epithelium in the oesophagus, intestinal is the most biologically unstable with the greatest risk of neoplastic progression through dysplasia to adenocarcinoma. This comes from early pathological studies35 ,36 and more recent population-based studies37 (Evidence grade III). It is this evidence that has led the AGA to conclude in their most recent guidelines that: ‘for the purposes of this statement the definition of Barrett's esophagus is the condition in which any extent of metaplastic columnar epithelium that predisposes to cancer development replaces the stratified squamous epithelium that normally lines the distal esophagus. Presently intestinal metaplasia is required for the diagnosis of Barrett's metaplasia because intestinal metaplasia is the only one of the three types of oesophageal columnar epithelium that clearly predisposes to malignancy.’… ‘therefore we suggest that the term ‘Barrett's oesophagus’ presently should be used only for patients who have intestinal metaplasia in the esophagus’.
This AGA definition of Barrett's oesophagus is at odds with the definition in previous BSG guidelines38 (BSG 2005) because of concern that confirmation of the presence of IM can be limited by sampling error in mucosal biopsy samples. In a study by Harrison et al39 of 1646 biopsy samples from 125 patients with long-segment Barrett's oesophagus, the optimum number of samples needed to demonstrate goblet cells in 67.9% of endoscopies was eight, but, in contrast, if only four were obtained, only 34.7% of endoscopies yielded a positive result for identification of goblet cells. Thus there are some data to show that the chance of detecting goblet cells is maximised by taking a minimum of eight samples throughout the Barrett's segment (Evidence grade III). In addition, Gatenby et al40 found that, although the rate of development of dysplasia and cancer in patients without IM at index biopsies (n=322) was equal to that of patients with IM (n=612), they also found that >50% of the patients without IM had evidence of IM at the 5-year follow-up and >90% were diagnosed with IM at 10 years (Evidence grade III). These two studies indicate that a single endoscopy with a low number of biopsy samples is not sufficient to exclude IM, particularly in a short segment of Barrett's oesophagus.
Two additional studies challenged the notion that IM is the most biologically unstable type of columnar metaplasia in the oesophagus. Takubo et al41 carefully analysed the columnar mucosa adjacent to 141 early OACs resected endoscopically and found that fewer than half of them showed evidence of IM, concluding that cancer may also arise in a non-intestinalised columnar epithelium (Evidence grade III). This study, however, does not indicate whether these patients had evidence of IM in the remainder of their Barrett's segment and therefore one cannot exclude the possibility that cancer may be associated with loss of intestinal differentiation. In a retrospective study, Kelty and colleagues found that the cancer risk in a historical cohort of 379 patients with oesophageal IM was similar to a group of 319 patients with columnar-lined oesophagus without IM (Evidence grade III).42 This study, however, lacks information about endoscopic findings and whether patients without IM did go on to develop IM during later surveillance. In keeping with data from these studies, there is also evidence that the non-goblet columnar epithelium may harbour similar molecular abnormalities to goblet cell epithelium.43–46
On the other hand, the recent population-based study from the Northern Ireland register found that the annual incidence of HGD and cancer in patients with IM is significantly higher than in those without IM (0.38% vs 0.07%).37 Even though this study has some of the same limitations as the study of Kelty et al, it is a population study with over 8000 patients, of which 40% had documented endoscopic evidence of Barrett's oesophagus, and 20% had information on the length of Barrett's (Evidence grade III). In addition, there was no significant difference in the cancer incidence between patients with and without endoscopic correlation, suggesting that the absence of endoscopy data in 60% of the cohort is unlikely to affect the overall results.
For these reasons, even though the insistence of the identification of IM to define or confirm a diagnosis of Barrett's oesophagus is problematic, it is recognised that the inclusion of gastric-type mucosa in short tongues of columnar-lined oesophagus is of less clinical importance in terms of the likelihood of malignant transformation and has the potential to greatly influence the frequency of diagnosis of Barrett's oesophagus at index endoscopy and the number of patients entering into follow-up and surveillance programmes. This may in turn profoundly influence our understanding of the natural history and biology of the condition. However, whether or not IM is present can be taken into consideration when determining the frequency and necessity of follow-up of patients. Hence, we suggest that the presence of IM is not a prerequisite for the definition of Barrett's oesophagus, but should be taken into account when deciding on the clinical management, as discussed in the surveillance section.
#### Distinguishing between true Barrett's oesophagus and IM of the cardia
It is not recommended that biopsy specimens from the cardia are taken routinely. However, if there is concern about the appearance at that site or if specimens are taken in patients having ablation therapy, then the following considerations need to be taken into account. Differentiation of oesophageal IM from IM of the proximal stomach (‘cardia’) in a mucosal biopsy sample from the GOJ region on morphological grounds is difficult in most circumstances, apart from when oesophageal native structures are seen. The different forms of IM may occur at both sites, and, similarly, studies suggesting a distinctive type of cytokeratin 7 and 20 immunocytochemical staining in Barrett's have not been sufficiently reproducible to apply in routine settings.27 ,47–50 In view of the lack of reliable markers to distinguish between IM of the cardia and oesophagus, this distinction needs to be made endoscopically, and the endoscopist is therefore required to carefully label the site from which biopsy samples were taken in reference to the endoscopic landmarks, in order to inform the clinico–pathological correlation.
#### Minimum dataset for histopathology diagnosis and clinicopathological correlation
The histopathological information needs to be integrated with the endoscopic findings in order to reach an accurate clinical diagnosis and determine the ramifications for follow-up. The pathologist should record the following elements in the histopathological report:
• number of biopsy samples analysed at each level;
• the type of mucosa present (squamous or columnar);
• the presence of any native oesophageal structures;
• the presence of gastric- (cardiac/fundic) or intestinal-type metaplasia;
• the presence and grade of dysplasia.
This minimum dataset is recommended to standardise the histopathological reporting for Barrett's oesophagus and to ensure that all the information required for the assessment of disease is included. This dataset can be incorporated into a proforma to facilitate the interpretation of the report, which is particularly encouraged in the presence of dysplasia. Examples of a short proforma (figure 1) and a more comprehensive proforma (figure 2) are given, which may be adapted to suit particular clinical settings and practice.
Figure 1
Example of a short proforma for reporting histopathology diagnosis and surveillance biopsy findings. This could be adapted to suit your locality.
Figure 2
Example of a comprehensive proforma for reporting histopathology diagnosis and surveillance biopsy findings.
We have taken the decision to abandon the previous nomenclature from the 2005 guidelines, since, although academically appealing, it was cumbersome and the distinction between ‘diagnostic’, ‘corroborative of’ and ‘in keeping with’ are difficult to remember. In particular, as discussed above, although native oesophageal structures do identify the oesophageal origin of the biopsy samples, these only occur in a minority and hence cannot be relied upon to help reach a diagnosis.
In the context of biopsy specimens confidently labelled by the endoscopist as being taken within the tubular oesophagus and in the presence of endoscopically visible Barrett's oesophagus, the following diagnostic terms are advocated:
1. ‘Barrett's oesophagus with gastric metaplasia only’ (glandular epithelium with cardiac/fundic metaplasia)
2. ‘Barrett's oesophagus with IM’ (glandular epithelium with IM)
3. ‘No evidence of Barrett's oesophagus’ (squamous mucosa without glandular tissue).
Online supplementary appendix 3 shows histological examples of Barrett's with gastric metaplasia and IM.
Particular attention to exclude sampling from the hiatus hernia or cardia should be given when fundic/oxyntic mucosa only is found, since pure fundic metaplasia is a rare finding in Barrett's oesophagus51 (Evidence grade III). This can be useful when trying to distinguish between an irregular Z-line and true Barrett's oesophagus.
The endoscopist should record whether the biopsy samples are taken at the GOJ (irregular Z-line, without convincing endoscopic evidence of Barrett's oesophagus), as this will lead to the distinct histopathological diagnosis of ‘Junctional mucosa with cardiac or oxyntic epithelium with/without intestinal metaplasia’.
In order to improve the standard of care and to ease discussion between experts, the use of a minimum dataset is recommended to report histopathological findings (Recommendation grade C).
## Screening for Barrett's oesophagus
In order to determine the usefulness and potential feasibility of screening, it is necessary to consider: the population prevalence; the identifiable risk factors that might help focus screening on subgroups at higher risk; and the diagnostic tests available.52
### Prevalence of Barrett's oesophagus
The prevalence of Barrett's oesophagus in the population at large remains uncertain, which is due to the need for endoscopy to define this condition. Two studies have attempted to assess the prevalence via endoscopy screening of the unselected adult population. An Italian study conducted endoscopies in 1033 individuals, showing a prevalence of Barrett's oesophagus of 1.3%.53 A Swedish population study of 1000 people revealed a prevalence of 1.6%.54 However, the limited participation rate remained a concern in both these studies, since it introduced a risk of selection bias resulting in a possible overestimate of the prevalence.
### Risk factors for Barrett's oesophagus
Male gender,55–57 older age56 ,58 and history of reflux symptoms56–61 are the main established predictors of increased risk of Barrett's oesophagus (Evidence grade IIa). There is also an association with obesity, at least when assessed as waist to hip ratio56 ,62 and abdominal circumference63 (Evidence grade IIa), while studies of body mass index only have shown more contradictory results.62–65 A history of cigarette smoking is associated with Barrett's oesophagus in some studies,56 ,59 ,60 but not all.65 Familial clustering for Barrett's oesophagus is reported in about 7% of individuals with Barrett's oesophagus or OAC.66 A positive family history of Barrett's oesophagus or OAC is associated with an increased risk of Barrett's oesophagus,66 ,67 and up to 28% of first-degree relatives of patients with OAC or Barrett's HGD also have Barrett's oesophagus.68 (Evidence grade IIa). Studies on familial aggregation have implicated genetic factors in the development of Barrett's,67 and a recent genome-wide association study has identified the first two loci associated with the disease.69 Studies on this topic are summarised in table 2.
Table 2
Summary of risk factors for development of Barrett's oesophagus
### Diagnostic technologies
The diagnostic technologies used for screening also affect the feasibility and cost-effectiveness of such a programme. For example, ultrathin transnasal endoscopy may have advantages over standard endoscopy, and non-endoscopic cytology devices may also be much more suitable for population-based screening. The data on the sensitivity of these devices and associated assays are summarised in table 3. The use of an immuno-based assay significantly enhances the sensitivity and specificity of a cytology collection device (Cytosponge), and this is promising, but results of further trials, such as the ongoing BEST2 trial, are required before such technologies can be recommended for screening outside of research.
Table 3
Technologies investigated for screening in Barrett's oesophagus and OAC
Since the literature search was conducted, a study has been published demonstrating that patients belonging to practices with the lowest rates of gastroscopy are at greater risk of poor outcome when oesophagogastric cancer is diagnosed.68 This highlights the importance of referring patients appropriately for endoscopy when risk factors are present.
Screening with endoscopy is not feasible or justified for an unselected population with gastro-oesophageal reflux symptoms (Recommendation grade B).
Endoscopic screening can be considered in patients with chronic GORD symptoms and multiple risk factors (at least three of age 50 years or older, white race, male sex, obesity). However, the threshold of multiple risk factors should be lowered in the presence of a family history including at least one first-degree relative with Barrett's or OAC (Recommendation grade C).
## Surveillance
### Rationale for endoscopic surveillance
Survival rate for invasive OAC is very poor with <13% overall survival at 5 years71 (also available at http://info.cancerresearchuk.org/cancerstats/). The aim of endoscopic surveillance is to detect cancer or precancer at a stage when intervention may be curative. Specifically, surveillance should detect cancer before invasion of the submucosa when the risk of lymph node metastases significantly increases and varies between 9% and 50% depending on the depth of invasion within the submucosa.72 The practice of surveillance is widespread among European and North American gastroenterologists despite the lack of RCT evidence to demonstrate its efficacy. The BOSS Trial, which is a RCT for systematic Barrett's surveillance compared with endoscopy ‘at the time of need’, is now in the follow-up phase, and it is hoped that this will provide clear evidence one way or the other. In the meantime, the current evidence base is from comparative studies and epidemiological retrospective cohort studies73–80 (Evidence grade III). A study has been published since the literature review that is worthy of mention. Corley et al81 conducted a retrospective case–control study during the years 1995–2009, which compared surveillance histories in 38 cases of OAC in patients with a prior diagnosis of Barrett's oesophagus with 101 living patients under surveillance for Barrett's oesophagus, matched for age, sex and duration of follow-up who had not died from OAC. The data demonstrated that surveillance within 3 years was not associated with a decrease in mortality from OAC. However, it can also be seen that patients were more likely to have had dysplasia during surveillance and ∼50% had advanced disease at diagnosis, suggesting that there is a problem with the quality of surveillance. Hence, we have paid particular attention to providing guidance for how surveillance should be conducted, including the management algorithms when dysplasia is identified (see following sections).
The first consideration with regard to the justification for Barrett's surveillance is the annual cancer conversion rate. Historically, this has been quoted as 0.5% per annum based on a number of case series.82–88 These have tended to be small and subject to publication bias.89 However, two new population-based studies have suggested that the true rate may be lower than this. In a Northern Ireland population-based study, the incidence of cancer and HGD was determined in 8522 patients with an endoscopic diagnosis of Barrett's with or without IM with a mean follow-up of 7.0 years (59 784 patient years). The overall risk of HGD and OAC was 0.22% per year (or 0.16% per year for OAC only), which increased to 0.38% per year when the analysis was restricted to those with IM.37 In a Danish study, the ascertainment was through histopathology records only on the basis of a diagnosis of IM. A total of 11 028 patients were identified with a median follow-up of 5.2 years (58 547 patient years).90 Here the annual risk for HGD and OAC was 0.26% per year (or 0.12% for OAC only). The risk in this Danish cohort is similar to that in individuals with short segments (0.11% per annum for <3 cm in Northern Ireland cohort and 0.19% in a recent meta-analysis91), which is a group likely to be over-represented when ascertainment is based on histopathological criteria.92 Geographical differences in incidence between different countries should also be borne in mind, as there is evidence of a higher incidence of OAC in the UK compared with other areas, including the USA and Northern Europe.93 ,94 Meta-analyses are a useful calibrator, and, in the most recent published meta-analysis,91 57 studies comprising 11 434 patients and 58 547 years of follow-up were selected as meeting the required criteria. Here the incidence of OAC in non-dysplastic Barrett's was 0.33% (95% CI 0.28% to 0.38%) with no evidence of publication bias.
When comparing the cancer risk in patients with Barrett's oesophagus with other conditions, even taking the most conservative study, the standardised incidence ratio of OAC was 11.3,90 which is 4.7-fold and 3.9-fold higher than the colon cancer risk in ulcerative colitis95 and primary sclerosing cholangitis96, respectively, 4.5-fold higher than the risk of any lymphoproliferative disorder/malignancy in coeliac disease,97 and roughly equal to the risk of breast cancer in first degree relatives of BRCA1/2 mutation carriers with breast cancer.98 Therefore, methods to detect individuals at increased risk merit careful consideration.
If surveillance is worthwhile, then it should detect earlier-stage cancers and hence should be a reasonable predictor of longer survival. The published literature suggests that cancers detected during surveillance are generally earlier stage and associated with improved survival (table 4) (Evidence grade III). However, although improved survival rates are the most desirable indicators of the effectiveness of any surveillance programme, these data are often not available and, when they are, are confounded by inherent lead-time bias and length bias.
Table 4
Summary of studies examining impact of surveillance on OAC outcomes
Although RCT data are lacking, given the evidence from the published studies that surveillance correlates with earlier staging and improved survival from cancer, surveillance is generally recommended (Recommendation grade B).
Endoscopic monitoring with histopathological assessment of dysplasia is the only current method of surveillance with sufficient evidence to be recommended (Recommendation grade B).
### Clinical and demographic risk factors associated with malignant progression
As discussed above, there is evidence that the presence of IM correlates with greater biological instability. This has been confirmed in the population study on the Northern Irish cohort, where the cancer risk in patients with IM was almost three times as high as that in patients without IM.37
There have been multiple studies published over the last 20 years demonstrating that men are at increased risk of developing OAC compared with women, and the median age peaks in the 6th decade. In the largest population dataset available, the overall risk (with and without IM for all segment lengths) was 0.28% per year in men and 0.13% per year in women.37 However, there is a paucity of data and inconsistency across the studies concerning the association of male sex and the progression to cancer (table 5) and hence different management for men is not currently indicated.
Table 5
Studies reporting association with Barrett's oesophagus length and sex with cancer progression
The same group has examined the effect of lifestyle factors and has shown that current tobacco smoking was significantly associated with an increased risk of progression (HR=2.03; 95% CI 1.29 to 3.17) compared with never smokers, and across all strata of smoking intensity99 (Evidence grade III). Alcohol consumption was not related to risk of progression. Measures of body size were rarely reported in studies, and body size was not associated with risk of progression.
The majority of the recent studies (three meta-analyses, 11 cohort studies and two case–control studies) reported a positive correlation between the length of Barrett's segment and the risk for adenocarcinoma, although this did not reach statistical significance in all of them37 ,57 ,84 ,100–113 (Evidence grade III) (table 5). Traditionally, 3 cm has been used as a cut-off to distinguish between long and short segments, and this has been reflected in the majority of the studies. While this is arbitrary, data suggest that interobserver agreement is reduced for very short segments, especially once they are <1 cm21. These studies are summarised in table 5 (see recommendation below). Besides segment length, the presence of ulcers, strictures and nodules are indicative of prevalent malignancy and should be reassessed without delay, including multiple targeted biopsies or diagnostic ER if appropriate.86 ,114
In the future, surveillance intervals should take into account all the socio-demographic risk factors and characteristics of the Barrett's segment; however, such risk algorithms have not yet been developed and validated sufficiently. In the meantime, the segment length seems the most striking discriminator, and the low rate of progression in segments <3 cm is sufficient to warrant differences in surveillance frequency (figure 3).
Figure 3
Surveillance flow chart for non-dysplastic Barrett's oesophagus. The endoscopic–pathological correlation is required for the appropriate clinical management of patients with Barrett's oesophagus. The presence of intestinal metaplasia and the length of the Barrett's segment influence the timing of the endoscopic surveillance. OGD, oesophagogastroduodenoscopy.
Surveillance regimens should take into account the presence of IM and length of the Barrett's segment (Recommendation grade B).
### IM at the cardia and GOJ
The presence of IM in the gastric cardia or at the GOJ is a common pathological finding at endoscopy and can occur in 5–18% of the normal population.110 ,115 ,116 This appears to have a distinct epidemiological and clinical profile compared with Barrett's oesophagus. IM at the cardia or GOJ has a higher prevalence in female subjects and non-white races, and, according to some, but not all, of the studies can be more often associated with Helicobacter pylori infection110 ,117 ,118 (Evidence grade III). More importantly, there is evidence that individuals with IM at the cardia or GOJ have a significantly lower cancer risk than patients with Barrett's.110 ,119 ,120 In particular, one recent population study that followed-up 86 patients with IM at the GOJ for a median interval of 8 years has found no incident cases of cancer118 (Evidence grade III).
Surveillance is generally not recommended in patients with IM at the cardia or in those with an irregular Z-line regardless of the presence of IM (Recommendation grade C).
### Correlation of histopathological grade of dysplasia and tissue molecular markers with risk of malignant progression
The risk of cancer in Barrett's has been shown repeatedly to be higher in glandular mucosa harbouring IM, as discussed above. The current biomarker is dysplasia, which is based on morphological criteria and reflects the underlying complex array of molecular alterations leading to abnormal cell kinetics, differentiation status and epithelial polarity. There is robust evidence that dysplasia is a risk factor for cancer progression, but there are important drawbacks related to the pathological diagnosis of dysplasia.
During surveillance, patients with non-dysplastic Barrett's may be at least 10 times more likely to die from an unrelated cause than to develop OAC.91 ,121–123 Furthermore, the risk appears to decrease over time since the initial diagnosis in non-dysplastic Barrett's.124
In the Danish population study, the risk of LGD was five times higher than that of non-dysplastic Barrett's,90 and, in the Northern Ireland population, the HR for development of HGD and OAC combined was 5.67 for LGD, with no dysplasia as 1.00 as the referent37 (Evidence grade III). In a Dutch study in which all cases of Barrett's oesophagus with LGD were reviewed by expert histopathologists, the progression rate was 13.4% per annum for those that were confirmed compared with 0.49% per annum for the 85% of cases that were down-staged to non-dysplastic Barrett's125 (Evidence grade III). The impact of the consensus diagnosis on the progression rate was confirmed in a UK study.126 On the other hand, in a US study with a similar design, the review by expert pathologists did not make any difference; however, the κ value for agreement for LGD was 0.18,103 highlighting the extreme practical limitations of this diagnosis. The extent of LGD—that is, the number of biopsy samples with LGD, has also been suggested to correlate with risk of progression.127 However, a more recent study has not confirmed this finding.103
Overall, the natural history of LGD is still unclear and is likely to be heavily influenced by the histopathological stringency of the diagnosis.
Dysplasia confirmed by two GI pathologists is currently the best tissue biomarker for the assessment of cancer risk (Recommendation grade B).
A number of molecular abnormalities have been characterised during the progression to adenocarcinoma, and several of these have been suggested as suitable biomarkers to supplement or replace the current problematic assessment of dysplasia128 (summarised in online supplementary table S1). Most of these have not been validated sufficiently to justify clinical use, and technological considerations have also hampered application in routine histopathology laboratories. However, molecular methodologies are being increasingly introduced into routine clinical laboratories, and more robust validation studies suggest that progress is being made.129 There is evidence that immunohistochemistry for p53 can improve interobserver agreement for dysplasia and improve patient stratification126 ,130 ,131 (Evidence grade III) (table 6). This is discussed in more detail in the section on the histopathological diagnosis of dysplasia.
Table 6
Studies investigating correlation of abnormal p53 expression by immunohistochemistry and cancer risk in Barrett's oesophagus
Until randomised controlled evidence is available, biomarker panels cannot yet be recommended as routine of care (Recommendation grade C).
## Practicalities of endosopic surveillance
### Patient selection and informed consent
When Barrett's oesophagus is detected at endoscopy and confirmed by histopathological findings, this diagnosis should be discussed with the patient in the clinic, so that patient preference can be taken into account. Patients should receive an early outpatient appointment (ideally within 4–6 weeks) to discuss the implications of this diagnosis with a physician with a clinical interest in Barrett's. Discussion should include the low but significant cancer risk, possible lifestyle changes, whether or not there is an indication for endoscopic surveillance, and the therapeutic options if dysplasia is detected (endoscopic and surgical). Family history for Barrett's oesophagus and OAC should also be recorded. If there is still uncertainty about a diagnosis of Barrett's that requires further work up, this should be clearly explained to the patient to avoid confusion. Written information should be provided for the patient to take away using BSG (see online supplementary appendix 4) or other approved materials such as from MacMillan CancerBACUP (http://www.macmillan.org.uk/Cancerinformation/Cancertypes/Oesophagusgullet/Pre-cancerousconditions/Barrettsoesophagus.aspx) or H-CAS (http://www.h-cas.org/barretts.asp).
Before seeking informed consent for surveillance, the diagnosis of Barrett's oesophagus should have been confirmed on endoscopic and histopathological grounds based on the criteria above. Because of the recent advancement in the endoscopic treatment of HGD and mucosal adenocarcinoma,114 ,132 it is no longer appropriate to restrict surveillance to patients who are fit, and willing, to undergo oesophagectomy. In addition, radiotherapy and/or chemo-radiotherapy may be treatment options in patients with more advanced disease who are deemed not fit for surgery.133 However, the patient should be fit for repeated endoscopy procedures and endoscopic therapy if HGD or early cancer is detected. Very few studies have used the performance status (PS) to correlate patient fitness with the outcome of endoscopic therapy for GI early cancers.134 ,135 Endoscopic therapy can be safely performed in patients with Eastern Cooperative Oncology Group PS 0–2.136 Therefore it is reasonable to consider endoscopic surveillance in patients with PS 0–2, provided that the estimated patient life expectancy is sufficiently long for the individual to benefit from surveillance if dysplasia or early cancer were detected.
If surveillance is thought to be clinically indicated, then the clinician should discuss with the patient the possible benefits of surveillance in detecting early-stage tumours and improving cancer survival. However, this discussion should also mention the lack of randomised controlled data to prove the benefits of surveillance, and clinicians must also emphasise to the patient that the actual risk of death from oesophageal cancer is small. Furthermore, the disadvantages of endoscopy surveillance should also be discussed, including the small risks of the procedure26 and the associated psychological morbidity.137 For example, in an American study conducted in a population of Veterans with a diagnosis of Barrett's, more than half of the patients missed their follow-up endoscopy, suggesting that not all patients are willing to adhere to surveillance programmes.138 Clinicians should also emphasise that, as with any monitoring programme, there is a failure rate, in that surveillance cannot guarantee to detect every tumour that may develop. There are no clear data to support how best to impart this complex information, and more work in this area is warranted.
Patients should have early access to an outpatient clinic to be informed about a new diagnosis of Barrett's oesophagus and to have an initial discussion about the pros and cons of surveillance with written information provided (Recommendation grade C).
For a given patient, whether or not surveillance is indicated should be determined on the basis of an estimate of the likelihood of cancer progression and patient fitness for repeat endoscopies, as well as patient preference (Recommendation grade C).
### Endoscopic assessment
Technological advancement with new-generation charge coupled devices has allowed the routine use of high-resolution endoscopy (HRE), which produces images with resolutions ranging from 850 000 to more than one million pixels. HRE allows fine definition of the mucosal layer for the recognition of subtle superficial abnormalities, with theoretical advantage in the recognition of dysplasia and Barrett's oesophagus-related early neoplasia. It is the opinion of the experts that HRE, in conjunction with careful cleaning of the mucosal surface of mucus, saliva and food debris, is the minimum standard for the evaluation of patients with known Barrett's oesophagus4; however, to date, there is no randomised trial comparing conventional endoscopy with HRE in Barrett's oesophagus dysplasia detection (Evidence grade IV). In an RCT, HRE performed equally compared with chromoendoscopy and narrow band imaging (NBI) in the overall diagnosis of dysplasia139 (Evidence grade Ib). Mucolytic agents (eg, 4–10% N-acetylcysteine) or antifoaming agents (eg, simethicone) can be used to disperse excess mucus and bubbles. There is also evidence that longer inspection times during assessment with white light endoscopy is associated with an increased detection rate for HGD and early cancer140 (Evidence grade III). This should be taken into account when planning how much time to allocate for endoscopic surveillance of very long segments of Barrett's, particularly those longer than 10 cm.
Although transnasal endoscopy has been shown to be accurate in the diagnosis of Barrett's oesophagus (Evidence grade Ib), the randomised studies performed so far either included a small number of patients,14 or were performed in a low-risk population.13 Furthermore, it should be noted that the biopsy specimens taken with these endoscopes are significantly smaller,13 and this may increase sampling bias and hamper the interpretation of dysplasia. Therefore there is currently a lack of robust data to recommend transnasal endoscopy in routine Barrett's oesophagus surveillance.
HRE should be used in Barrett's oesophagus surveillance (Recommendation grade C).
There is insufficient evidence to recommend transnasal endoscopy as a replacement for transoral endoscopy (Recommendation grade C).
### Use of chromoendoscopy and advanced endoscopic imaging
Advanced endoscopic imaging has been investigated to increase the detection of both IM and dysplasia in Barrett's oesophagus with the aim to help target biopsies (table 7).
Table 7
Comparative studies between standard and advanced imaging techniques for the diagnosis of IM and dysplasia in Barrett's oesophagus
Chromoendoscopy uses dyes to enhance endoscopic detection. Methylene blue (MB) is a vital dye actively absorbed by columnar intestinal-type cells141 and has been used to improve the yield of IM in Barrett's oesophagus142–144 (Evidence grade III). In a historical cohort, Sharma and coworkers found significant enrichment of IM in MB-targeted biopsy samples compared with random samples145 (Evidence grade III). The detection rate of IM and dysplasia during MB chromoendoscopy has been investigated in a number of randomised and cohort studies with conflicting data14–151 (table 7). A recent meta-analysis has found no incremental yield of both IM and dysplasia with MB chromoendoscopy compared with standard endoscopy with random samples152 (Evidence grade Ia). It should also be noted that MB may damage DNA, which, coupled with the lack of evidence for efficacy, suggests that its use cannot be recommended153 (Evidence grade III).
Indigo carmine (IC) is a contrast agent that allows detailed inspection of the mucosal pattern in combination with magnification endoscopy.154 A prospective multicentre study found that the ridged/villous pattern had a 71% sensitivity for IM, while the irregular/distorted pattern had an 83% sensitivity and an 88% specificity for HGD/early cancer155 (Evidence grade III). The limitation of IC chromoendoscopy is the need for high magnification with consequent narrow field of view. Only one randomised trial has evaluated IC chromoendoscopy for detection of dysplasia in Barrett's, but failed to find an increased rate of dysplasia compared with high-resolution white light endoscopy139 (Evidence grade Ib).
The value of acetic acid (AA) to improve the diagnostic yield of surveillance endoscopy has also been studied. AA induces intracellular protein denaturation, with swelling of the mucosal surface and enhancement of the architecture. Randomised cross-over studies have produced contradictory results on the diagnostic yield of AA-enhanced magnification endoscopy for IM156 ,157 (Evidence grade Ib). AA-enhanced magnification endoscopy has been shown to have a higher dysplasia yield in Barrett's oesophagus surveillance, with 24% of patients having histological upgrade compared with a previous standard endoscopy with random biopsies performed in a non-specialist centre158 (Evidence grade III). In a large single-centre prospective study, Pohl et al159 found that AA-targeted biopsies had a sensitivity of 96.7% and a specificity of 66.5% for a diagnosis of HGD/early cancer. A single-centre retrospective cohort study has showed significantly increased dysplasia yield (p=0.001) compared with standard endoscopy with random biopsies160 (Evidence grade III). The same group showed that histology on AA-targeted biopsies was more cost-effective than the Seattle protocol in a high-risk population.161 More data are needed to decide on the usefulness of this technique.
With recent technological advancements, ‘virtual chromoendoscopy’ has become available, which allows chromoendoscopy without the use of dyes. This is based on light filters (NBI, Olympus) or post-image acquisition processing (i-scan, Pentax and FICE, Fujinon). The most extensively studied ‘virtual chromoendoscopy’ technique in Barrett's oesophagus is NBI, which highlights the mucosal pattern and the superficial vasculature. A number of different classifications have been proposed to describe mucosal pits in non-dysplastic and dysplastic Barrett's, which yielded high diagnostic accuracy162–164 (Evidence grade III). When NBI was compared with standard imaging techniques, one prospective tandem study showed an incremental diagnostic yield for dysplasia in the per-patient analysis165 (Evidence grade IIa), and two additional studies reported an increased dysplasia detection only in the per-biopsy analysis139 ,166 (Evidence grade Ib). A meta-analysis of eight studies has found that NBI has a sensitivity and specificity of 96% and 94%, respectively, for the diagnosis of HGD, and 95% and 65%, respectively, for the diagnosis of IM.167 However, the interobserver agreement for the interpretation of the NBI images is only moderate.168 Overall, despite the finding that NBI performed by an expert endoscopist may increase the targeted yield of dysplasia, it also transpires that high-resolution endoscopy alone is sufficient to maximise dysplasia detection on a per-patient basis.
Autofluorescence imaging (AFI), which exploits endogenous fluorophores excited by short wavelengths, has been studied in the context of Barrett's oesophagus.169 ,170 Initial single-centre cohort studies showed that AFI can improve the diagnostic yield of dysplasia compared with standard endoscopy, but with a false-positive rate as high as 80%171 ,172 (Evidence grade III). To overcome this, AFI has been incorporated into an HRE-NBI scope with magnification, also known as endoscopic trimodal imaging (ETMI). Although an initial multicentre non-randomised feasibility study showed that ETMI increased the diagnostic yield for dysplasia from 63% to 90% compared with standard endoscopy with random biopsies173 (Evidence grade III), this was not confirmed in two subsequent multicentre randomised studies, where ETMI only improved the diagnostic yield of dysplasia in the per-biopsy analysis174 ,175 (Evidence grade Ib). Overall, these studies showed that, in selected high-risk cohorts of patients, ETMI does not allow the requirement for random biopsies to be abandoned. Further studies in low-risk patients will inform whether AFI can have a role in reducing the number of biopsies without loss of diagnostic accuracy.
Other imaging techniques that have showed some value in Barrett's oesophagus include confocal laser endomicroscopy, spectroscopy and optical coherence tomography170 ,176–178; however, further studies are needed to clarify whether they can improve diagnostic accuracy during Barrett's oesophagus surveillance.
In the future, molecular imaging may improve our imaging armamentarium to increase dysplasia detection. Molecular imaging exploits fluorescently labelled molecules that bind with different affinity to dysplastic compared with non-dysplastic cells. Two types of compound have been studied so far. In a proof-of-principle study, Li and colleagues identified a 7-amino acid peptide that binds an OAC cell line more avidly than a non-dysplastic Barrett's oesophagus cell line, and they confirmed the differential binding in surgical specimens of OAC ex vivo.179 Similarly, Bird-Lieberman and coworkers identified a natural lectin (wheat germ agglutinin) that differentially binds surface glycoproteins of dysplastic and non-dysplastic cells and used an autofluorescence endoscope in surgically resected oesophagi to validate the ex vivo findings.180 In vivo studies are needed to validate these techniques.
Advanced imaging modalities, such as chromoendoscopy or ‘virtual chromoendoscopy’, are not superior to standard white light endoscopy in Barrett's oesophagus surveillance and are therefore not recommended for routine use (Recommendation grade A).
### Biopsy protocol
To find dysplasia, endoscopists have generally relied on the directed sampling of any visible lesions, which may be aided by enhanced endoscopic visualisation tools as discussed above, together with systematic, four-quadrant biopsies every 2 cm according to the so-called ‘Seattle protocol’.26 A prospective study has demonstrated a significant increase in the detection of early lesions through the introduction of such a protocol181 (Evidence grade III). However, adherence to this protocol is limited and ranges from 10% to 79%, with poorer adherence for longer segments,182–184 and failure to adhere to the protocol has been shown to result in a significantly lower rate of dysplasia detection.185 Overall, although intense and time-consuming, the multiple biopsies involved in the Seattle protocol have been demonstrated to be safe when performed by experienced endoscopists.26 Another limitation of this technique is the high cost generated by processing multiple biopsies, but this still seems justified at the current time in the absence of an alternative. Future RCTs will need to compare cost-effectiveness of the standard practice with alternative techniques such as histology on targeted biopsy samples guided by conventional or virtual chromoendoscopy.
Adherence to a quadrantic, 2 cm biopsy protocol in addition to sampling any visible lesions is recommended for all patients undergoing surveillance. This should also apply to long segments (Recommendation grade B).
### Frequency of surveillance for non-dysplastic Barrett's oesophagus
In the previous BSG guidelines published in 2005, the recommended surveillance interval for non-dysplastic Barrett's was every 2 years. However, given the recent data suggesting that the overall risk of malignant conversion is lower than previously thought, we recommend that the interval should be lengthened in line with other guidelines.3 We therefore advocate a new surveillance strategy whereby the managing clinician synthesises the endoscopic and histopathological findings to tailor the surveillance interval on a more individual basis (figure 3). A degree of variation in this interval is permitted, which may be influenced by the presence of risk factors for the development of cancer.
To summarise, in practical terms, short segments of columnar epithelium with no IM have an extremely low risk of malignant conversion37 ,91 (∼0.05% per annum) (Evidence grade III). For these patients, it is recommended to repeat the endoscopy once in 3–5 years time to confirm the findings and account for sampling and measurement error. If there is doubt, the endoscopy could be repeated sooner. If two good-quality endoscopies, each with a minimum number of four oesophageal biopsies where possible, confirm a short segment (<3 cm) with gastric metaplasia only, then discharge is encouraged, as the risks of endoscopy probably outweigh the benefits. In selected cases with a strong personal risk profile for OAC (see recommendation on screening), continued endoscopic surveillance can be considered.
For patients with Barrett's oesophagus shorter than 3 cm, without IM or dysplasia, a repeat endoscopy with quadrantic biopsies is recommended to confirm the diagnosis. If repeat endoscopy confirms the absence of IM, discharge from surveillance is encouraged, as the risks of endoscopy probably outweigh the benefits (Recommendation grade C).
There is evidence that the risk of cancer progression correlates significantly with the length of the Barrett's segment, such that segments shorter than 3 cm have a lower cancer incidence (table 5). Therefore, in view of the recent evidence supporting a lower cancer risk in non-dysplastic Barrett's oesophagus than previously thought, it is reasonable for patients with short segments containing IM to have a longer endoscopic surveillance interval than patients with long segments. We propose a range of 3–5 years to allow the clinician to tailor surveillance on the perceived individual cancer risk.
Patients with Barrett's oesophagus shorter than 3 cm, with IM, should receive endoscopic surveillance every 3–5 years (Recommendation grade C).
For longer segments (>3 cm), a shorter surveillance interval is more appropriate. This is regardless of the presence of IM, since it is noted, that in long segments, IM is almost always present, but can be missed due to sampling error. We propose a range (between 2 and 3 years), which may be informed by the individual risk factors and patient and physician preference. Because of the poor adherence to the surveillance biopsy protocol for long segments of Barrett's oesophagus, consideration should be given to refer patients with a very long segment (>10 cm) to tertiary referral centres for endoscopic surveillance, as suggested also in the new Dutch guidelines (personal communication).
Patients with segments of 3 cm or longer should receive surveillance every 2–3 years (Recommendation grade C).
### Histopathological diagnosis of dysplasia
#### Pathological features and reporting of dysplasia
Online supplementary appendix 3 shows histological examples of Barrett's with different degrees of dysplasia.
There are very few studies that investigated reporting of dysplasia in Barrett's oesophagus. Two studies examined the Vienna classification and found a degree of agreement among pathologists that was at best moderate for HGD, fair for LGD, and poor for indefinite for dysplasia.126 ,186 The approach to reporting upper GI tract neoplasia differs significantly in certain parts of the world and this has led to inconsistency in the terminology used and hence inconsistent data on incidence and clinical progression outcomes. The most recent recommendations by the WHO state that dysplasia should be graded as either low or high grade.187 The revised Vienna classification for GI mucosal neoplasia attempts to standardise diagnostic terminology into biologically similar groupings with scores of 1–5188 depending on the presence or absence of dysplasia or malignancy.
#### Revised Vienna classification and dysplasia subtypes
1. Negative for dysplasia
This includes normal epithelium, metaplastic epithelium showing reactive or regenerative changes, and mucosa showing reactive/regenerative changes including nuclear enlargement, nuclear hyperchromasia and prominent nucleoli.
2. Indefinite for dysplasia
This category is used for cases where the morphological features between true dysplasia and regenerative/inflammatory atypia are blurred.189 It is important to appreciate that this diagnosis may in fact mean that the patient has features suspicious of HGD, but not enough certainty is present to warrant this call. This may be due to technical factors, such as poor staining, poor orientation, cross cutting or denuded surface epithelium, or to severe active inflammation or ulceration leading to marked atypia, precluding a confident diagnosis of dysplasia. In other cases, the epithelium appears abnormal, but the features are not sufficiently well developed to justify a definite diagnosis of dysplasia. Features favouring dysplasia are the presence of an abrupt transition from normal to atypical epithelium, together with nuclear pleomorphism, atypical mitoses and loss of nuclear polarity.190 Evidence of ‘surface maturation’—that is, loss of the cytological atypia seen in the deeper glands as the mucosa matures into the surface epithelium—is often taken as the best marker to favour regeneration rather than dysplasia, although this is also not invariably true (eg, crypt dysplasia described below). Explicit mention in the pathology report of the reason justifying this diagnosis can be useful to aid patient management.
In LGD, glandular architecture is relatively preserved and the diagnosis is made on the basis of cytological atypia.
##### Morphological patterns of LGD
• LGD generally shows an ‘adenomatous’ cytological appearance (resembling the dysplastic changes associated with adenomatous polyps of the colon) in which nuclei are elongated (pencil shaped), slightly enlarged and hyperchromatic with inconspicuous nucleoli. There may be mild pleomorphism, mucin depletion, mild loss of polarity, nuclear crowding, and stratification of nuclei up to three-quarters of the height of the cell, but not touching the luminal surface. Mitoses and apoptotic debris may be seen on the surface or in the upper portions of the glands. Evidence of loss of ‘surface maturation’—that is, presence of cytological atypia seen in the deeper glands—into the surface epithelium is often taken as the best marker to distinguish true dysplasia from regenerative atypia; however, in the presence of ulceration, regenerative surface epithelium may also closely mimic LGD.
• A ‘non-adenomatous’ (foveolar) type composed of small round cells with abundant cytoplasm may occasionally be seen.191 Although this is less well characterised, cells with nuclear/cytoplasmic ratios <50% are probably best put into this low-grade category.
4a. HGD (incorporating carcinoma in situ)
The distinction between HGD and LGD is largely based on the presence of architectural changes in conjunction with more marked nuclear atypia. These changes may be accompanied by complex architectural changes including a papillary or villous surface (although villiform change may also be seen in reactive epithelium), in conjunction with branching, complex budding or back-to-back ‘crowding’ arrangements. Intraluminal papillae, bridges or cribriform patterns are also seen. There are increased numbers of atypical mitoses on upper levels of crypts, together with mucin depletion and a loss of nuclear polarity. Of note, HGD can be accompanied by acute inflammation and should not be downgraded in its presence.190
##### Morphological patterns of HGD
• ‘Adenomatous’ cytological appearance: nuclei are elongated, pencil shaped, enlarged, hyperchromatic and show crowding and stratification up to the luminal surface of the cells. The distinction between the upper end of ‘low grade’ and ‘high grade’ dysplasia can be subjective.
• ‘Non adenomatous’, which includes the term foveolar dysplasia: cells have a cytological appearance characterised by rounded nuclei showing marked nuclear enlargement and marked atypia with increased nuclear/cytoplasmic ratios, irregular nuclear membranes (including angular edges), coarse chromatin, and prominent or irregular nucleoli. The foveolar type may have a more bland appearance, comprising small round nuclei with conspicuous nucleoli. The grading of this variant is less well characterised; however, the nuclear/cytoplasmic ratio appears to be more important for grading, with high ratios (nuclei involving >50% of cell) being put into a high-grade category.
##### Crypt dysplasia
Significant cytological atypia in the crypt bases with surface maturation has been reported in up to 7.3% of cases of Barrett's.192 Previously, this would have been regarded as either ‘negative for dysplasia’ or ‘indefinite for dysplasia’, as the atypia does not reach the surface epithelium. It seems likely, however, that crypt dysplasia represents an early stage in the development of dysplasia, and the atypia is highly likely to progress up to the surface over time and so warrants recognition.193 Crypt dysplasia stands out as a focus that is distinctly different from the surrounding crypts and can appear as low-grade or high-grade cytological atypia. Although the dysplasia can be of the ‘adenomatous’ or ‘non-adenomatous’ round cell type, the most common features are nuclear enlargement, loss of polarity, marked pleomorphism with irregular shapes and sizes, nuclear crowding, increased mitotic activity and goblet cell dystrophy. Crypt dysplasia should not be diagnosed purely on the basis of stratification and hyperchromasia in the absence of significant nuclear pleomorphism, as these changes may often be seen in regenerative cryptal epithelium. p53 immunohistochemistry may be a helpful adjunct for the assessment of crypt dysplasia. Crypt dysplasia should be reported according to the degree of dysplasia present. If there is uncertainty, then the ‘indefinite’ category may be appropriate. Some pathologists favour putting cases with high-grade features into an ‘at least low grade’ category in view of the likely early nature of the lesion and the implications of a high-grade diagnosis; however, cases of isolated crypt dysplasia are probably best managed as low grade until further data become available.193
4b. Intramucosal carcinoma (including suspicious for invasive carcinoma)
Intramucosal carcinoma is a lesion in which neoplastic cells have penetrated the basement membrane and invaded the lamina propria or muscularis mucosae, but without invasion into the submucosa. However, histological recognition of lamina propria invasion may be difficult because of the absence of objective criteria. Patterns of lamina propria invasion that are used by gastrointestinal pathologists include sheets of neoplastic cells, abortive angulated glands, a never-ending/anastomosing gland pattern, a highly complex cribriform arrangement of glands, tightly packed small tubular glandular arrays, and single-cell infiltration. Recognition of each of these patterns is somewhat subjective, with κ statistics varying between 0.21 and 0.47, suggesting poor or, at best, moderate agreement.126 ,186 If definitive submucosal invasion is in question, the term ‘suspicious of invasive carcinoma’ can be used.
Unequivocal invasion of submucosa or deeper structures often accompanied and characterised by a desmoplastic response in the tissue stroma to invasive tumour cords/acini.
Given the important management implications for a diagnosis of dysplasia, we recommend that all cases of suspected dysplasia are reviewed by a second GI pathologist, with review in a cancer centre if intervention is being considered (Recommendation grade C).
Given the difficulties associated with the management of the ‘indefinite for dysplasia’ category, all such cases should also be reviewed by a second GI pathologist, and the reasons for use of the ‘indefinite for dysplasia’ category should be given in the histology report in order to aid patient management (Recommendation grade C).
#### Dysplasia reporting and reproducibility
It has long been recognised that there is inter- and intra-observer variability in the diagnosis of GI tract dysplasia. This relates to differentiating between HGD and intramucosal adenocarcinoma, HGD and LGD and also distinguishing between regenerative changes and LGD. In the case of definite dysplasia, this is because these divisions involve unnatural cut-offs along a biological/histological continuum.126 Studies have shown that the prediction of progression of oesophageal dysplasia is improved if at least two expert pathologists agree on the diagnosis and increases further when a greater number of pathologists concur with the diagnosis.125 ,130 For practical reasons, and in day-to-day diagnostic practice, a diagnosis of dysplasia in the setting of Barrett's should be corroborated by a second pathologist with a specialist GI interest. The Royal College of Pathology recommends that ‘double’ reporting of a diagnosis of HGD in the upper GI tract should be mandatory and this has been confirmed by consensus statements agreed by Barrett's international experts.4 We have extended this consensus reporting to all grades of dysplasia.
#### Aids to histological diagnosis of dysplasia and p53 immunostaining
Of all the putative experimental molecular markers, the one with the greatest body of evidence and which can also be applied in the routine clinical setting is immunohistochemistry for nuclear p53. Although the p53 positivity rate in Barrett's oesophagus dysplasia is variably reported in the literature, ranging from 50% to 89%,194 ,195 when positive it can improve interobserver agreement for reporting dysplasia126 and can be a powerful predictor of progression, with an OR between three and eight in different studies129 ,131 ,196–198 (table 6). In a study from Skacel et al130, who analysed factors predictive of progression in patient with LGD, p53 immunostaining positivity and 100% agreement among three GI pathologists on LGD diagnosis correlated with the risk of progression, suggesting that p53 might improve interobserver agreement. This was replicated in a later study.126 Interpretation of p53 immunostaining can be problematic and poorly reproducible subject to variation in methodology and interobserver variation. Notwithstanding this, some pathologists find staining for p53 of use, especially in distinguishing between atypical reactive proliferation (indefinite for dysplasia) and true LGD. Low background wild-type p53 expression is often seen in nuclei of normal columnar and basal layers of squamous mucosa, which is a useful baseline to identify the overexpression pattern typical of dysplasia. Overexpression is generally a consequence of mutations that stabilise the inactivated protein.199 However, not all p53 mutations lead to stabilisation of a mutated inactive p53 protein. A study performed in non-small cell lung cancer showed that, as opposed to missense mutations, the majority of null mutations did not lead to p53 overexpression.200 In such cases, mutation is expected to lead to failed translation of the protein. In fact, an absent pattern of p53 immunostaining, when compared with normal wild-type background, is now recognised as an abnormal pattern which also occurs in dysplasia as a result of silencing mutations of the p53 gene.194 Online supplementary appendix 3 shows immunohistochemical examples of Barrett's with overexpression and loss of p53.
The addition of p53 immunostaining to the histopathological assessment may improve the diagnostic reproducibility of a diagnosis of dysplasia in Barrett's oesophagus and should be considered as an adjunct to routine clinical diagnosis (Recommendation grade C).
## Management of dysplasia and early cancer
### Indefinite for dysplasia, a controversial entity
There is very little published literature on the management of patients with this histopathological condition. A study looking at interobserver variability showed that the degree of agreement among pathologists for a diagnosis of indefinite for dysplasia is lower than that for LGD, with κ values of 0.18 and 0.35, respectively186 (Evidence grade III). Younes and coworkers showed that the rate of cancer progression in patients with indefinite for dysplasia was similar to non-dysplastic patients; however, if the indefinite for dysplasia was multifocal, the rate of progression was as high as in patients with LGD201 (Evidence grade III). An excess of inflammation is linked to cellular atypia, and this could be resolved by improved medical control of the gastro-oesophageal reflux, although scientific evidence for this is lacking (figure 4).
Figure 4
Surveillance flow chart for dysplastic Barrett's oesophagus (BO). A pathological finding of indefinite for dysplasia does not exclude the presence of dysplasia, therefore a 6-month follow-up is warranted. Six-monthly surveillance and endoscopic treatment are generally recommended for low-grade and high-grade dysplasia, respectively. MDT, multidisciplinary team; OGD, oesophagogastroduodenoscopy.
Patients with a diagnosis of indefinite for dysplasia should be managed with an optimisation of the antireflux medical therapy and re-endoscoped in 6 months. If no definite dysplasia is found on subsequent biopsies, then the surveillance strategy should follow the recommendation for non-dysplastic Barrett's oesophagus (Recommendation grade C).
### LGD: surveillance or ablation?
As discussed in the surveillance section, management of LGD is confounded by uncertainty about the natural history and difficulties in making a definitive diagnosis. A diagnosis of LGD correlates with a higher risk of progression to cancer, but it is unclear yet whether this warrants therapeutic intervention. Published literature showed that endoscopic therapy can successfully eradicate LGD. PDT with both 5-aminolaevulinic acid (ALA) and porfimer sodium was shown to be effective in the treatment of LGD150 ,202 (Evidence grade Ib). RFA has also been shown to eradicate dysplasia in over 90% of patients with LGD203 (Evidence grade III). However, this evidence alone does not justify a clinical indication of endoscopic therapy in patients with LGD. The RCT published by Shaheen and coworkers investigated the effectiveness of RFA in preventing disease progression in patients with both LGD and HGD.134 In this study, although the overall outcome showed a lower risk of disease progression in all patients treated with RFA, the subgroup analysis in patients with LGD failed to show a significant advantage from treatment, since none of the patients with LGD progressed to cancer within the follow-up period (Evidence Ib). The results of a multicentre RCT for RFA compared with endoscopic surveillance in a large cohort of patients with LGD are awaited (SURF Trial). It is possible that endotherapy may be recommended if the outcome of this trial is positive, and a recommendation from NICE should be used as guidance, but in the meantime it cannot be recommended on a routine basis. At the present time, in view of the higher progression rate reported for LGD, these patients should be followed-up more intensively than non-dysplastic patients (figure 4). If ablative treatment is considered in selected cases, then this decision should be reviewed by the MDT.
Management of LGD is unclear in view of limited data about the natural history. It is essential that the diagnosis is confirmed by two pathologists, and patients should be surveyed endoscopically at 6-monthly intervals. Currently, ablation therapy cannot be recommended routinely until data from RCTs are available (Recommendation grade C).
### HGD and intramucosal cancer: getting the diagnosis right
Most HGD and early cancer (T1) in Barrett's will be discovered at the time of endoscopy, either performed for the first time (in a patient presenting with dyspepsia, for example) or as part of a surveillance programme. Although there may be visible abnormalities, these can often be subtle and overlooked at initial endoscopy. The first indication of a problem may be flagged up by the pathologist finding dysplasia or suspecting invasive cancer on a biopsy, either targeted from a visible abnormality or from among systematic four-quadrant biopsy specimens. The first step should be to confirm the diagnosis with at least one other pathologist with experience in GI histopathology.125 ,126
Whether or not the diagnosis is confirmed, if the possibility of significant dysplasia has been raised, it is essential that there has been a high-quality baseline endoscopy conducted to map out any visible lesions and the extent of any dysplastic changes prior to any management decisions being made. HRE has a high sensitivity for the detection of Barrett's-related neoplasia, and more than 80% of patients referred for work up of HGD or early Barrett’s cancer, apparently without visible abnormalities, will have at least one visible lesion detected in their Barrett’s oesophagus upon expert endoscopic assessment.139 ,173 ,174 Although early Barrett’s oesophagus neoplasia generally presents as subtle flat lesions that may be difficult to detect, most procedures performed with HRE endoscopes do reveal these abnormalities to the experienced eye.204 ,205 However, up to 20% of patients do not have a visible abnormality after HRE and advanced imaging, and, in such cases, four-quadrant biopsies are required to detect HGD.173 ,174 There is some evidence that magnification and electronic/optical manipulation of the image can increase detection of dysplasia in Barrett's oesophagus when compared with HRE, as discussed in the endoscopic surveillance section; however, advanced imaging modalities rarely change the overall diagnostic outcome.166 ,175 These imaging techniques can, however, aid definition and detailed mapping of the edges of visible lesions in order to guide complete ER.206 ,207
Expert HRE should be carried out in all Barrett's patients with biopsy-detected HGD in order to detect visible abnormalities suitable for ER (Recommendation grade B).
Visible lesions should be considered malignant until proven otherwise (Recommendation grade C).
Any endoscopic abnormalities should be documented using the Paris classification, which is based on the Japanese system used to classify early gastric cancer. It has been used used to classify mucosal irregularities in patients with Barrett’s oesophagus,25 although, unlike the Japanese classification for early gastric cancer, it has not been validated as a prognostic tool in this context. Superficial Paris 0-IIa and 0-IIb lesions are unlikely to contain invasive cancer, while type 0-Is sessile lesions and type 0-IIc ‘depressed’ lesions are more likely to contain invasive cancer, with up to 25% of cases subsequently being shown to have submucosal (sm) invasion.204 ,205 ,207
Description of lesion morphology using the Paris classification gives an indication of the likelihood of invasive cancer and aids communication between clinicians. This should therefore be used for all visible lesions but cannot at present be used to predict prognosis (Recommendation grade C).
### Role of specialist teams and decision making
Treatment for HGD and early cancer involves endoscopic or surgical management. The success of both modalities should be measured in terms of morbidity and mortality related to the procedure (or series of procedures), long-term survival and QOL. These recommendations are entirely consistent with the guidelines for the management of oesophageal and gastric cancer recently published by Allum et al,133 which, however, focus specifically on HGD and early cancer.
Recommendations for treatment of patients with Barrett's-related neoplasia should be taken in the context of an upper GI specialist MDT taking into account patient comorbidities, nutritional status, patient preferences and staging (figure 5).6 Before treatment decisions are made, the patient should have the opportunity to discuss the options in an outpatient clinic setting (not in endoscopy after sedation), and this may comprise a joint discussion with an endoscopist and a surgeon. The patient should have access to all the supporting evidence being used to make the recommendation according to their wishes. Patients should be copied into any clinical correspondence, as recommended by NICE guidelines for the management of colorectal cancer.209
Figure 5
Recommended flow chart for the management of high-grade dysplasia (HGD) and early oesophageal adenocarcinoma (OAC). A diagnosis of HGD and early OAC should be discussed in a multidisciplinary team (MDT) setting, and treatment options should be explained in the clinic to the patient. Endoscopic treatment and surgery are generally recommended for mucosal disease and submucosal cancer, respectively. Good prognosis cancer with involvement of superficial submucosal layers (sm1) can be treated endoscopically in patients at high surgical risk. EC, early cancer; HRE, high-resolution endoscopy; OGD, oesophagogastroduodenoscopy; RFA, radiofrequency ablation.
All patients with dysplasia or early cancer, for which therapy is considered, should be discussed at the specialist MDT for oesophagogastric cancer. This team should include an interventional endoscopist, upper GI cancer surgeon, radiologist and a GI pathologist (minimum standard) (Recommendation grade C).
Patients with dysplasia or early cancer should be informed of treatment options and have access to all specialists if required (Recommendation grade C).
### Endoscopic therapy for Barrett's-related neoplasia
Although, surgery remains an effective treatment for Barrett's neoplasia, it is associated with significant morbidity and mortality compared with endoscopic therapy. Cohort studies suggest that endoscopic therapy for mucosal OAC has similar long-term disease-specific survival to surgery, but lower death rates.210–212 A number of retrospective case series comparing endoscopic and surgical therapy have demonstrated high survival outcomes in both groups, but higher short-term mortality in the surgical group than in the endoscopic group, but patients were not well matched.212–215 A systematic review showed a mortality of 1.2% in the surgical group compared with 0.04% in the endoscopic group.216 A more recent study showed lower morbidity in the endoscopic group214 (Evidence grade III). A cost-effectiveness study demonstrated that RFA was likely to be more cost-effective than surgery.217 Recent consensus statements issued by a large group of international experts have indicated that endoscopic therapy should be preferred over surgery for the management of early Barrett's neoplasia.4
For HGD and Barrett's-related adenocarcinoma confined to the mucosa, endoscopic therapy is preferred over oesophagectomy or endoscopic surveillance (Recommendation grade B).
Endoscopic therapy in the oesophagus carries a low but significant risk of complication.218 ,219 It is important that therapy is carried out in centres that have the specialist expertise to offer and the necessary back-up if required. For example, endoscopic therapy should be carried out in centres that can also offer surgery if a complication occurs.
Endoscopic therapy of Barrett’s neoplasia should be performed at centres where endoscopic and surgical options can be offered to patients (Recommendation grade C).
There are now good observational data to support the performance of oesophageal surgery in specialist centres for treatment of adenocarcinoma.220 Results for individual surgeons improve with experience, and patient outcomes have consistently been shown to be better in high-volume centres220 ,221 (Evidence grade III). ER series reported from expert high-volume centres have shown a low rate of significant complications (<3%),114 ,212 ,218 but the complication rate is significantly higher in the hands of less experienced endoscopists during their first 20 ER procedures performed.222 Therefore it seems logical that, similar to the recommendations for oesophagectomy, endoscopic therapy should also be performed in centres with the experience, facilities and high throughput of cases to optimise outcomes. Endoscopic training should start with knowledge acquisition, followed by resection and ablation in tissue animal models, before training in human subjects. The GI pathologist should also be trained in the report of ER specimens. In order to achieve a good level of training, it is crucial that professional societies guarantee wide availability of training courses and fellowships for Barrett's endoscopic therapy.
A minimum of 30 supervised cases of ER and 30 cases of endoscopic ablation should be performed to acquire competence in technical skills, management pathways and complications (Recommendation grade C).
ER should be performed in tertiary referral cancer centres for oesophageal cancer disease, which must be equipped with high-resolution endoscopes and all relevant ER facilities. These specialist cancer centres should have an adequate volume of cases, which in the absence of published evidence we have set as 15 ERs per annum for HGD or early cancer in a given centre based on the opinion of experts. Centres should preferably have two endoscopists performing endoscopic therapy, and low-volume centres should consider developing joint services. The endoscopist performing endoscopic therapy must be fully trained in lesion recognition and ER techniques, with expertise in at least one enhanced endoscopy imaging modality (electronic imaging or AA chromoendoscopy). Progression of disease is described during treatment with RFA,132 ,223 therefore an ER may be required during the ablation pathway.
ER should be performed in high-volume tertiary referral centres. RFA should be performed in centres equipped with ER facilities and expertise (Recommendation grade C).
#### Endoscopic resection
ER should always be performed with therapeutic intent; however, histopathological assessment of the ER specimen is also the most accurate staging technique for Barrett's oesophagus-related early neoplasia.224 ,225 ER is preferred over surveillance biopsies because of the difficulty in differentiating HGD from mucosal cancer and deep invasive cancer on biopsy material.4 ,226 Visible lesions contain the most advanced histological staging in surgical resection specimens, and this is confirmed by experience with step-wise radical ER of the entire Barrett's segment.227 ,228 This supports a policy of removal of all visible abnormalities by ER.
Endoscopic assessment will usually identify the area with the most advanced neoplasia. ER should aim to resect all visible abnormalities (Recommendation grade C).
ER is recommended as the most accurate staging intervention for Barrett's early neoplasia (Recommendation grade B).
Tumours confined to the mucosa (T1a) have been shown to have significantly better 5-year recurrence-free and overall survival rates (100% and 91%, respectively) than those showing involvement of the submucosa (60% and 58%).229 Endoscopic therapy for Barrett's neoplasia has been developed on the evidence that HGD and T1a OAC is associated with a low rate of lymph node metastasis: endoscopic and surgical series indicate a 0–10% risk in T1a cancer, while submucosal invasion carries a higher risk (up to 46%).215 ,229–236 A recent systematic review reported no evidence of nodal metastasis in patients with a final stage of HGD.72 Further stratification of these superficial lesions as in table 8 yields additional prognostic information in that the risk of nodal metastasis correlates with the depth of penetration into the layers,229 ,234 but not all the studies have confirmed this.230 ,236
It is still unclear whether T1sm1 cancer (invading the superficial submucosa within 500 µm) can be confidently treated by ER, and although series from Amsterdam and Wiesbaden suggest this carries a low risk of lymph node metastases,230 ,234 ,237 not all the literature supports this.72 ,236 This debate is further complicated by the technical challenges faced by the pathologist to accurately identify the submucosal invasion depth on the ER specimen. The importance of experienced pathology in deciding whether endotherapy is likely to be curative or not is critical, since not only the depth of invasion but features of the tumour (lymphatic or vascular invasion, degree of differentiation) are thought to be important in the decision-making process.238 Free deep resection margins on the ER specimen (R0), together with an absence of lymphovascular invasion (LVI−) and good differentiation (G1) are all indicative of a good prognosis for early cancer.230 Lymphovascular space invasion and lymph node metastases have been reported in 17% and 10% of patients, respectively, with invasion into the duplicated muscularis mucosae, although these are technically intramucosal.235
ER should be considered the therapy of choice for dysplasia associated with visible lesions and T1a adenocarcinoma (Recommendation grade B).
For patients at high surgical risk, endoscopic therapy can be offered as an alternative to surgery for treatment of good prognosis T1b adenocarcinomas (T1b sm1, well differentiated and without lymph vascular invasion) (Recommendation grade C).
For T1b adenocarcinomas with involvement of the second submucosal layer or beyond (T1b sm2–sm3), endoscopic therapy should not be considered curative (Recommendation grade B)
#### ER techniques
The basic principle of ER involves identification of the lesion margins by marking with a diathermy device followed by a systematic resection of the marked area. Common resection techniques are cap and snare and band ligation.
The band ligation technique involves suction of the marked area into a distal attachment (preloaded with multiple rubber bands) and deployment of the band on to the tissue to create a pseudo-polyp, which is then resected with a snare. The cap and snare technique also involves a dedicated transparent cap at the distal end of the scope, which is preloaded with a crescent snare. Differently from the band ligation, the area of interest is always injected (submucosal space) and lifted before its suction into the cap. Once the mucosa is placed into the cap, then the snare can be closed around and the tissue resected.
Both cap and snare and band ligation techniques appear to have similar success rates of the order of 85–98%.224 ,239–242 There are two RCTs that compared the two techniques.219 ,243 These studies did not show significant differences either in terms of the depth of resection or complication rates, leading to the conclusion that both techniques were similarly safe and effective. Some endoscopists believe that submucosal injection improves safety of the ER when an attempt is made to resect nodular lesions, which carry a high risk of invasive cancers. In such cases, the presence of the ‘non-lifting sign’ will inform the endoscopist about the possibility of deep invasive cancer and its associated risks.
The cap and snare technique with submucosal injection and the band ligation technique without submucosal injection are considered to be equally effective (Recommendation grade A).
#### Pathology reporting of ER specimens
ER specimens should be pinned out on a rigid support (eg, cork) and formalin fixed for at least 12 h. Photographs of the fixed specimens can act as a useful record. They should be serially sectioned at 2 mm intervals along the axis of the closest margin and completely embedded. Both of the end pieces should be embedded en face.
The status of the tissue margins is the most significant prognostic factor; however, if the sample has been received in multiple pieces, it will not be possible to identify the true lateral margins, and only deep margins will be relevant.244 Tumours should be graded and T staged. T1a and T1b intramucosal carcinomas can be subclassified as shown in table 8.245 A comment should be made regarding the presence or absence of lymphovascular space invasion, background IM and dysplasia. See minimum reporting dataset (table 9).
Table 8
Subclassification of T1a and T1b oesophageal adenocarcinoma
Table 9
Minimum dataset for reporting endoscopic resection specimens
Artefacts such as haemorrhage, heat/cutting artefact, surface loss, fixation contraction with rolling and folding of edges leading to poor orientation of tissue at embedding may all hinder the histological assessment244 (Evidence grade III). The suction technique can cause artefactual lifting and/or disruption of the surface epithelium, with intramucosal haemorrhage, oedema and fibrin deposition on the surface. This should not be confused with true ulceration. Biopsy samples taken 1–16 days after gastric ER can show signet ring cell change and clear cell degeneration in areas of ischaemia.246 Although there are no relevant studies that looked at mucosal changes after ER, tissue regeneration in the immediate post-ER period can hamper proper histological assessment, and therefore it is recommended to delay post-ER biopsies to 6–8 weeks (Evidence grade IV).
It can be difficult to accurately stage these tumours on ER specimens, when there is duplication of the muscularis mucosae, a characteristic finding in Barrett's. This may lead to overstaging by misinterpreting the space between duplicated muscularis as submucosa, and in some instances it may not even be possible to determine if true submucosa is present (see online supplementary appendix 4). The largest and most recent studies suggest that invasion into the space between the duplicated muscularis mucosae has a similar low risk of lymph node metastases to lamina propria invasion if other features (lymphovascular invasion and poor differentiation) are absent230 ,247 (Evidence grade III). In addition, it is important to be aware of entrapped glands and submucosal glands that may mimic submucosal adenocarcinoma.
Further, the use of the muscularis propria as a reference point for determining depth of submucosal invasion is problematic in ERs, as it is generally not represented. In the latter instance, it may be more appropriate to state that submucosal invasion is present and then measure the depth of invasion beyond the muscularis mucosae. In the colon, depth of invasion beyond the submucosa is widely used as a marker of likely lymph node metastases, but studies in OAC have been conflicting, with differences between surgical and ER series.229 ,230 Measurement of the distance from the tumour to the nearest deep margin is recommended to document the adequacy of resection. The presence of tumour cells at the deep margin indicates incomplete resection requiring further treatment.
Use of a minimum dataset for the reporting of ER specimens is recommended to ensure that all prognostic information is included in reports (Recommendation grade C).
The presence of tumour cells at the deep margin indicates incomplete resection and warrants further treatment (Recommendation grade C).
### Imaging for HGD and T1 carcinoma: role of CT–PET and EUS
There is little published evidence to support a role for CT (or CT–PET) with regard to early cancer (HGD, mucosal lesions), with most of the evidence being for advanced cancer (see section on surgical treatment). Where biopsy specimens show invasive cancer, CT scanning is often advocated in order to detect distant metastases. However, it has poor accuracy in local T staging and it is less accurate than EUS in detecting local lymph node metastases.248 ,249 PET–CT has a higher accuracy than CT for distant and locoregional metastases, but is inferior to EUS.250–252
Before ER, neither CT nor PET–CT have a clear role in the staging of patients with Barrett's HGD or suspected T1 cancer and neither is routinely required (Recommendation grade B).
Initial evidence that endoscopic resectability (differentiation of T 1/2) could be predicted by EUS has been tempered by most of the recent series, which indicated that 15–25% of cases are understaged compared with ER, while about 4–12% are overstaged.253–256 One study compared endoscopic assessment with EUS and found that accuracy of both techniques in predicting depth of invasion was similar.257 High-frequency EUS miniprobes are more accurate than conventional EUS, but still fail to correctly stage T1 cancers in one-third of cases (Evidence grade Ib).258 Overall, these studies show that EUS misclassifies the T stage in approximately one-quarter of patients with early oesophageal cancer, and this has limited clinical impact over expert high-resolution imaging plus ER. However, in routine clinical practice, the endoscopist may not always be able to confidently exclude an advanced stage (T>1a) on the basis of the endoscopic appearance of nodular lesions, and, in this circumstance, EUS should be performed to guide the therapeutic choice.
EUS is the most accurate tool available for detecting regional lymph node involvement and can add staging information in patients with T1b disease after ER.231 ,249 ,259 Endosonographic criteria that are suggestive of malignant involvement of visible lymph nodes include a width greater than 10 mm, round shape, smooth border, and echo-poor pattern.260 When all four suspicious features are present, there is an 80–100% chance of metastatic involvement; however, only 25% of malignant nodes will have all of these features. Therefore, with the use of echo criteria alone, sensitivity and specificity for regional lymph node metastases were 80% (95% CI 75% to 84%) and 70% (95% CI 65% to 75%), respectively, in this study. FNA can determine more precisely whether or not suspicious lymph nodes are infiltrated, and it has high sensitivity in coeliac, mediastinal and perigastric lymph nodes.261 Sensitivity, specificity and accuracy of EUS FNA for locoregional lymph nodes are currently all around 85%262 (Evidence grade III). One cohort study on 25 patients with baseline HGD or intramucosal adenocarcinoma on biopsies has showed that EUS FNA of suspicious lymph nodes changed management decision in 20% of patients referred for endoscopic therapy of cases263 (Evidence grade III).
Since EUS can both overstage and understage T1 lesions, its routine use cannot be recommended for staging before ER for suspected early lesions (Recommendation grade B).
In selected cases where the endoscopist cannot exclude advanced stage on the basis of endoscopic appearance of nodular lesions, EUS with or without FNA is recommended to inform the therapeutic decision (Recommendation grade C).
EUS with or without FNA of visible lymph nodes is recommended in selected cases with T1b (sm1) disease on staging ER for which endoscopic therapy is selected, because of the significant risk of lymph nodal involvement (Recommendation grade C).
### Ablative therapy for flat HGD/intramucosal cancer and residual Barrett's after ER
Table 10
Summary of clinical profiles of different ablative techniques for HGD
In the presence of HGD or intramucosal cancer without visible lesions (flat HGD/intramucosal cancer), these should be managed with an endoscopic ablative technique. There is little comparative data among ablative techniques, but RFA currently has a better safety and side-effect profile and comparable efficacy (Recommendation grade C).
More than 20% of patients treated with ER of visible lesions develop metachronous lesions in the Barrett's segment within 2 years.114 Recurrence of neoplasia after ER can be significantly reduced if the residual Barrett's is completely ablated114 ,132 ,273 (Evidence grade III). After ER for early focal neoplasia, >80% of patients will have HGD or LGD detected in the remaining Barrett's epithelium.281 Eradication of the remaining Barrett's epithelium by RFA is a safe and effective treatment for any remaining flat dysplasia281 ,282 (Evidence grade III). Ablation may also be useful to avoid strictures, which are associated with step-wise radical ER of circumferential lesions, particularly with longer Barrett's segments.228 Combining ER with RFA reduces this risk and is effective in eradicating the remaining Barrett's epithelium273 (Evidence grade Ib).
Eradication of residual Barrett's oesophagus after focal ER reduces the risk of metachronous neoplasia and is recommended (Recommendation grade B).
### Follow-up after endoscopic therapy
The goal of endoscopic mucosal resection and ablation is to eliminate the subsequent risk of cancer. This requires long-term follow-up data, which are not currently available for ablative techniques. From the limited studies available after ablation, new squamous (neosquamous) epithelium reveals no molecular abnormalities, and seems biologically stable.283 Five-year and 3-year follow-up data from the RCTs of PDT and RFA, respectively, in dysplastic Barrett's oesophagus showed a durable response to treatment.271 ,276 However, buried metaplasia has been reported within neosquamous epithelium biopsy specimens and this can predispose to the development of so-called ‘buried’ cancer.284 Current data suggest that the occurrence of buried glands is higher in patients treated with PDT (14.2%) compared with RFA (0.9%).279 Recurrence of Barrett's at the GOJ has been reported and seems important.285 Currently, follow-up is mandatory not only to detect recurrence but also to allow further therapy to be applied as required.4 Empirically, in patients treated for HGD, endoscopic follow-up is recommended 3-monthly for 1 year and yearly thereafter. This should include biopsies at the GOJ and within the previous extent of the Barrett's epithelium.
#### Pathological reporting of biopsies after ablation therapy
Ablation therapy is associated with an early acute and chronic inflammatory response, together with reactive epithelial changes followed by lamina propria fibrosis and duplication and splitting of the muscularis mucosae after a few months.244 Neosquamous epithelium is associated with ablation therapy, and interestingly can also be seen with PPI treatment without ablation therapy, especially after extensive biopsies.286 ,287 This neosquamous epithelium can replace the Barrett's segment, forming islands or sheets of ‘normal’ squamous epithelium. However, this may overlie buried glands or buried carcinoma.279 A systematic review has shown an overall incidence of buried glands in 14.2% of patients who received PDT and 0.9% of patients who received RFA.279 However one post-RFA study on the neosquamous epithelium found that only 37% of biopsy specimens contained lamina propria and deeper tissue suitable for assessment of buried metaplasia,283 whereas the other studies do not mention the presence of lamina propria in neosquamous biopsy samples.290 Buried dysplasia can be difficult to evaluate, particularly as the atypia does not reach the surface.244 Again p53 immunohistochemistry may be a helpful adjunct, as dysplastic glands may demonstrate a significant staining pattern.126 ,194 ,289 If there is uncertainty about the significance of the atypia present, then it is best to use the ‘indefinite for dysplasia’ reporting category. In summary, the importance of buried metaplasia after ablation remains unclear, as well as the adequacy of biopsies to detect it, leaving some uncertainties about the usefulness of biopsy specimens taken from the neosquamous epithelium. However, until further evidence becomes available, neosquamous epithelium biopsies are warranted.
Endoscopic follow-up is recommended after endoscopic therapy of Barrett's neoplasia with biopsy samples taken from the GOJ and within the extent of the previous Barrett's oesophagus (Recommendation grade B).
### Surgical management of early Barrett's neoplasia
#### Efficacy and safety
For HGD and T1 OAC, case series suggest that the 5-year survival rates range between 80% and 90%, and the 3-year survival exceeds 90%.211 ,214 ,290 Tumour recurrence after resection of early cancer is rare (1%). There are no reports of long-term tumour recurrence in patients who have had complete surgical resection of HGD alone, and all-cause mortality is equivalent to non-surgical treatments211 ,290 ,291 (Evidence grade III).
Mortality for patients undergoing oesophagectomy for HGD or early adenocarcinoma is difficult to estimate because data are from retrospective studies conducted in self-selected high-volume centres, thus the quality of data was assessed as low. A number of case series21 ,292–301 evaluating over 500 patients with HGD or early adenocarcinoma show an operative mortality for oesophagectomy for HGD and early adenocarcinoma of less than 5%, with an overall operative 30-day mortality of approximately 2%. These results are comparable to the recent UK national audit results, where the mortality for 2200 patients undergoing oesophagectomy for any operable cancer (HGD excluded) was 3.8% for 30-day mortality and 4.5% for in-hospital mortality301 (Evidence grade III).
Surgical resection is associated with significant short-term morbidity (6–37%).290 ,303 A recent retrospective comparison of oesophagectomy (61 patients) versus endotherapy (40 patients) for HGD or T1 cancer in one centre revealed much lower morbidity in the endotherapy group with a similar survival, although follow-up was relatively short in the endotherapy group.214
Surgical therapy is considered the treatment of choice for early adenocarcinoma that has extended into submucosa because of the significant risk of lymph node metastasis (Recommendation grade B).
#### Volume effect in specialist surgical centres
Good observational data indicate that oesophageal surgery for treatment of adenocarcinoma should be performed in specialist centres, since patient outcomes have been shown to be better in high-volume centres and individual surgeons’ results improve with experience220 ,221 (Evidence grade III). The recent AUGIS guidelines on minimum surgeon volumes for oesophagogastric units recommend that each unit should consist of at least four surgeons carrying out a minimum of 15–20 resections per year.221
Oesophagectomy should be performed in high-volume centres, as these are associated with lower in-hospital mortality than low-volume centres (Recommendation grade B).
#### Type of surgery
Surgical resection for Barrett’s dysplasia and early cancer must include complete resection of the Barrett’s segment (longitudinal margins). Lymphadenectomy should be performed for T1 sm tumours because of the significant risk of lymph node involvement304–306 (Evidence grade III). There is insufficient evidence to support the use of one technique above the others. Attempts have been made to tailor a less radical, less morbid surgical procedure for these patients with early lesions who do not require extensive lymphadenectomy. These are not associated with a detrimental effect on long-term survival. However, the majority of surgical data come from retrospective observational studies, often comparing outcomes with outdated historical controls.
Data directly comparing the various techniques, or from series restricted to HGD and intramucosal cancer, are extremely limited. A series of 36 patients including left thoracoabdominal oesophagectomy (60%), transhiatal oesophagectomy (20%) and Ivor Lewis oesophagectomy (20%) reported no operative mortality and major complications in only 11% of patients.296 At a mean follow-up of 5 years, QOL outcomes were comparable to age- and sex-matched controls. A study of a further series of patients with HGD and T1 oesophageal cancer undergoing open surgery by either the transhiatal or transthoracic routes reports operative mortality of 2.5% and 5-year survival of 77%. This series included patients with tumour-involved lymph nodes, for whom survival is significantly impaired compared with patients with HGD307 (Evidence grade III).
##### Transhiatal oesophagectomy
Transhiatal oesophagectomy avoids the need for thoracotomy, with low in-hospital mortality (3%) and length of stay (50% discharges in 1 week) in one high-volume centre.308 Concerns about the adequacy of lymphadenectomy with this procedure may not apply in the context of HGD and intramucosal cancer. In an RCT, the transhiatal procedure was associated with less perioperative morbidity than a transthoracic procedure, and there was no significant difference in perioperative mortality (2% vs 4%, p=0.45).309 Long-term follow-up showed no difference in overall survival when all patients were considered, although a subgroup of patients with between one and eight lymph nodes involved had a better survival in the transthoracic procedure.310 This trial included patients with operable disease of all stages, but does suggest transthoracic oesophagectomy is a preferable procedure where there is a significant risk of lymphadenopathy such as in T1 sm disease (Evidence grade Ib).
##### Vagal-sparing oesophagectomy for HGD
The vagal-sparing technique aims to reduce the postoperative dumping and diarrhoea associated with oesophagectomy. A study of patients with HGD or intramucosal cancer found that the 49 patients who underwent vagal sparing oesophagectomy had shorter hospital stays and fewer major complications than 39 patients who underwent transhiatal procedures and 21 who underwent en bloc resections.297 Postoperative dumping syndrome and diarrhoea were decreased in the vagal-sparing group, and there was no detrimental effect on long-term outcomes. The vagal-sparing procedure does not involve a lymphadenectomy, and meticulous preoperative staging is required to exclude the presence of submucosal invasive disease, where the risk of lymph node involvement would make this procedure inadequate (Evidence grade III).
##### Merendino segmental oesophagectomy
A further option for HGD arising within a short (<3 cm) segment of Barrett's is a Merendino limited resection with jejunal interposition. In a series of 24 patients, this was associated with no operative mortality, significantly less perioperative morbidity than standard oesophagectomy, and a normal QOL at 1 year311 (Evidence grade III).
##### Minimally invasive laparoscopic or thoracoscopic oesophagectomy
The term ‘minimally invasive oesophagectomy (MIO)’ incorporates a very heterogeneous group of procedures. There are no RCTs reported comparing MIO with open surgery, although such a trial is currently underway in France312. A series of 222 patients undergoing MIO, including 47 with HGD, has shown that this procedure is safe, with a 30-day mortality of 1.4%. The median hospital stay was shorter than that usually seen in open surgery, at only 7 days, but the procedure remains associated with major complications including a leak rate of 11.7%313 (Evidence grade III).
A UK series has attempted to compare consecutive series of open Ivor Lewis and minimally invasive procedures. This group found that overall morbidity and mortality were similar for the two groups, but there were fewer pulmonary complications in the minimally invasive group (8% vs 23%)314 (Evidence grade III). A similar reduction in pulmonary complications was found in a recent study of early oesophageal cancer,315 with improved early QOL data in the first few months after surgery. In the recent UK national audit, there were 1541 open oesophagectomies performed for oesophageal cancer compared with 659 minimally invasive procedures. The postoperative morbidity and mortality were comparable in the two groups except that there were statistically significantly more anastomotic leaks in the minimally invasive group (10.8%)302 (Evidence grade III). Long-term outcome data are scarce in the patients having minimally invasive procedures.
Overall, there is insufficient evidence to support the use of one technique above the others. In summary, MIO is evolving and becoming more commonly used. As it develops, it is likely to offer some advantages over open oesophagectomy, although further data are required.
There is currently no evidence to support one technique of oesophagectomy over another. It is recommended that the procedure is tailored to the particular case and the expertise available in that centre (Recommendation grade C).
#### Quality of life
Patients having oesphagectomy report worse functional, symptom and global health-related QOL scores than before surgery. Oesophagectomy has a negative impact on QOL; the adverse effects lessen in patients who survive for 2 or more years.316 There is some evidence that QOL is improved with MIO compared with open surgery, at least in the short term.315 The evidence of QOL levels after MIO depend more on the curative effect than the mode of resection294 ,296 ,317–321 (Evidence grade III).
#### Follow-up after treatment of HGD or early carcinoma by surgery
There are three322–324 surgical follow-up series after oesophagectomy involving 102 patients with Barrett's oesophagus. These studies report that new Barrett's oesophagus can occur after curative subtotal oesophagectomy, with gastric conduit reconstruction for adenocarcinoma, squamous cell carcinoma or HGD. The development of Barrett's oesophagus occurs in half of patients studied and may recur from 6 months or less after surgery to 10 years after surgery. Even though a BADCAT consensus statement suggested an endoscopy at 2, 5 and 10 years after surgery,4 it is still unclear whether surveillance strategies after oesophagectomy are justified.
There is not sufficient data to recommend endoscopic surveillance after oesophagectomy for HGD or T1 adenocarcinoma provided that surgery has removed all Barrett's mucosa. Until further evidence is available, endoscopy should be performed on a symptomatic basis (Recommendation grade C).
### Documentation and audit of treatment for HGD and early cancer
From 1 April 2012, the National Oesophago-Gastric Cancer audit has included patients with oesophageal HGD in Barrett's oesophagus as well as an ongoing audit of the management of invasive carcinoma.325 The initial estimate of the incidence of HGD in England and Wales is 1350 per year, which corresponds to around 45 patients per Cancer Network per year. In comparison, there are around 17 000 patients diagnosed with oesophagogastric cancer annually.
The National Audit collects data on staging, treatment and outcomes. The questions about the management of HGD patients have been kept simple, partly because their management is a complex and varied process within hospitals in England and Wales. The audit questions related to patients with oesophageal HGD are:
1. Has oesophageal HGD been confirmed by two GI pathologists?
2. What are the characteristics of the HGD at diagnosis (endoscopic appearance, length of Barrett's segment, characteristics of the lesion, focal or multifocal)?
3. Has the patient been discussed in a specialist MDT meeting?
4. What treatments were planned for the patient? (EMR, ablation or surgery)
5. What were the post-treatment pathology results?
6. What are the short-term outcomes of oesophagectomy in patients diagnosed with HGD?
Alongside the national oesophago-gastric audit, individual cancer centres are required, in accordance with the NICE guidance,5 to audit efficacy and safety of endoscopic therapy for Barrett's oesophagus. Other topics that should be considered for audit include the adherence to the Seattle protocol for Barrett's surveillance, the complication rate in patients undergoing Barrett's surveillance, and the compliance with the endoscopic minimum dataset for reporting Barrett's oesophagus. Auditing results will need to be used to implement changes in practice.
Findings and management decisions for HGD and early cancer should be entered into the National Audit (Recommendation grade C).
## Economic considerations
Cost-effectiveness of endoscopic screening of patients with GORD with the aim to offer endoscopic surveillance to those with Barrett's oesophagus is highly controversial (see online supplementary table S2). There was wide divergence in cost-effectiveness estimates from US$12 336/quality-adjusted life years (QALY) gained to US$95 559/QALY gained, leaving huge uncertainty about the cost-effectiveness of this approach.326–329 Non-endoscopic devices could prove to be more cost-effective. A cost utility study using microsimulation modelling compared the Cytosponge and endoscopy as screening intervention in patients with GORD and found that they led to a similar QALY gained, but the Cytosponge was more cost-effective330 (Evidence grade III). Future studies in larger cohorts, such as the ongoing BEST2 study, are required to confirm whether the Cytosponge has sufficient diagnostic accuracy to be used as a screening intervention.
When comparing cost-effectiveness of surveillance of Barrett's oesophagus versus no surveillance, only one study found that endoscopic surveillance is cost-effective, while others found that surveillance was dominated by ‘do nothing’ or had an incremental cost-effectiveness ratio of about US\$90 000/QALY gained, which is above conventional thresholds of what is considered to be cost-effective.331–334 When surveillance was analysed in the context of offering ablative therapy for dysplastic Barrett's oesophagus, endoscopic ablation proved to dominate and be cost-effective in patients with HGD in comparison with surgery, especially when RFA was modelled.217 ,335–337 However, none of these studies considered the cost of identifying patients with dysplasia in the first place—that is, surveillance of patients with non-dysplastic Barrett's oesophagus. In addition, most studies assumed ∼0.5% annual conversion rate to malignancy, whereas recent data suggests 0.3% may be more appropriate. This would make Barrett's surveillance more expensive per cancer identified and therefore less cost-effective. On the other hand, some models, reported before the advent of ablative therapies, provided more conservative estimates of cost-effectiveness than in the present era, due to the fact that ablative therapies are more cost-effective than surgery in patients with HGD. Some studies evaluated uncertainty in the assumptions made in the models using one-way sensitivity analyses. These do not capture all the uncertainty in the model, and probabilistic sensitivity analyses (PSA) should be conducted. Those that used extensive PSA approaches commented on substantial uncertainty in model estimates.333 Most papers evaluated cost-effectiveness from a third-party payer perspective (eg, healthcare system), and not from a societal perspective.
Overall, it is very unclear whether surveillance is cost-effective for non-dysplastic Barrett's oesophagus. More evidence is needed on natural disease progression, such as the ongoing BOSS trial. Furthermore, future models should: use more conservative estimates for conversion to malignancy; encompass non-endoscopic testing methods; evaluate the impact of ablative therapy in the context of surveillance; assess model uncertainty using PSA; and evaluate the cost-effectiveness from a societal perspective.
Endoscopic therapy, and in particular RFA and the combination of ER and RFA, has been proven to be more cost-effective then surgery. Despite the finding from the NICE cost analysis that surgery was the most cost-effective intervention,339 this has not taken into account the most recent data on more updated models, which showed that endoscopic therapy should be preferred to surgery from an economic perspective.217 ,330 ,340 However, some techniques such as RFA still carry significant costs, and other techniques such as ER require appropriate training to optimise the competence of the operator and ensure the best long-term outcome for the patient. Therefore, the recommendations regarding the minimum number of procedures required for training and for the maintenance of skills (section on Endoscopic therapy for Barrett's-related neoplasia) also have economic implications. In other words, the cost-effectiveness of endoscopic therapy is related to the proportion of patients that is successfully shifted from a surgical to an endoscopic pathway. In order to accomplish this, centralisation of endoscopic services in cancer centres is indicated to reduce costs as well as to improve patient management.
Despite the uncertainties of the cost-effectiveness of screening and surveillance, in these guidelines we have given a weak recommendation (grade C) for screening in selected cases and a moderate recommendation for surveillance (grade B). There are important clinical justifications for these choices. The recommendation of screening in selected cases is one of the very few measures currently available to modify the worrying epidemiological increase in OAC incidence over the last 30 years. The increasing incidence and poor outcomes for this disease have led to ‘a great pathological concern’, as highlighted in the 2008 Annual Report from the Chief Medical Officer.341 The future advent of cheaper and less invasive techniques for diagnosis will make screening more feasible and cost-effective. The recommendation for surveillance in Barrett's patients also emanates from a similar standpoint. However, we think we have made a step forward compared with the previous guidelines, in that we have identified subcategories of patients who could be discharged, because of very low cancer risk, and other subcategories of patients with intermediate risk where surveillance at less frequent intervals is justified, with potential positive impact on the cost-effectiveness of surveillance. Focus will therefore be shifted towards the higher-risk groups. Overall, until definite data will resolve the uncertainties about cost-effectiveness of surveillance, a conservative position on surveillance is justified.
There are insufficient data to indicate that endoscopic screening and surveillance for Barrett's oesophagus are cost-effective. Further studies on non-endoscopic diagnostic methods are awaited (Recommendation grade C).
Endoscopic therapy for dysplastic Barrett's oesophagus and early OAC is cost-effective compared with oesophagectomy (Recommendation grade B).
## Strategies for chemoprevention and symptom control
Chemoprevention is defined as the use of pharmacological agents or surgical strategies to prevent the development of cancer. Most of the currently available evidence revolves around studies of PPIs and NSAIDs.
### Acid suppression drugs
One prospective longitudinal cohort study found a significantly lower OR for developing dysplasia in patients treated with PPIs (0.25 (95% CI 0.13 to 0.47)) compared with patients receiving no therapy or histamine-2 receptor antagonists (H2RA)342 (Evidence grade III). A retrospective observational study found an OR of 0.43 (95% CI 0.21 to 0.83) in patients receiving PPIs compared with no medical therapy87 (Evidence grade III). When considering the balance of risks and benefits, these drugs are very safe, although long-term side effects including osteoporosis, GI infections and pneumonia need to be taken into account. On the other hand, the benefits, while not well understood, are potentially significant, and, while no placebo-controlled trial data are likely to be forthcoming, the data from the AspECT trial comparing low- versus high-dose PPIs are awaited. However, the vast majority of patients with Barrett's oesophagus have reflux symptoms and are recommended to take medical therapy for symptomatic control.7 An RCT comparing omeprazole 40 mg twice daily with ranitidine 150 mg twice daily found that the better acid suppression in the omeprazole arm correlated with a small but significant reduction in the length of the Barrett's oesophagus.343 These data must be interpreted carefully because of the subjectivity of endoscopic measurement of Barrett's oesophagus length, and a Cochrane review that pooled together data from two other RCTs did not confirm this finding.344 Another Cochrane review found that PPIs are more effective than H2RA for symptom control in patients with reflux disease345 (Evidence grade Ia).
There is not yet sufficient evidence to advocate acid suppression drugs as chemopreventive agents (Recommendation grade C).
Use of medications to suppress gastric acid production is recommended for symptom control (Recommendation grade A).
PPIs have the best clinical profile for symptomatic management (Recommendation grade A).
### Antireflux surgery
Some surgical series have suggested that Nissen fundoplication can promote regression of Barrett's oesophagus and prevent progression to dysplasia;346–348 these results must be interpreted carefully, since these are small retrospective studies, which made little reference to pathological sampling error in very short segments of Barrett's oesophagus or to the subjectivity of a diagnosis of LGD (Evidence grade III). One series did find a significant progression rate to HGD of 0.8%/year in patients who underwent antireflux surgery.349 One RCT compared surgery with medical therapy and found no difference in progression rates between the two groups82 (Evidence grade Ib). There are no RCTs that compared surgery versus no therapy. Two RCTs comparing surgery versus PPIs found that they are both effective for symptom control, with a slightly better outcome in the surgical group350 ,351 (Evidence grade Ib).
Antireflux surgery is not superior to pharmacological acid suppression for the prevention of neoplastic progression of Barrett's oesophagus (Recommendation grade C).
Antireflux surgery should be considered in patients with poor or partial symptomatic response to PPIs (Recommendation grade A).
### Non-steroidal anti-inflammatory drugs
In a recent meta-analysis of RCTs, low-dose aspirin at a dose of at least 75 mg reduced cancer mortality particularly after 5 years, with an OR of 0.63 (95% CI 0.49 to 0.83)352 (Evidence grade Ia). Both aspirin and NSAIDs have been associated in another recent meta-analysis with a 40% reduction in the risk of OAC.353 The crux of the debate lies in the risk/benefit ratio of aspirin, and this is currently unclear.354
While some have argued that the risk/benefit ratio is favourable, the true risks of GI bleeding and haemorrhagic stroke are, however, unclear. In this regard, it has been argued that the patients who suffer from aspirin-related GI bleeds tend to present early.355 ,356 However, recent evidence has indicated that the risk of bleeding in aspirin users seems more strongly associated with the dose than with the duration of aspirin.357 The AspECT is a randomised trial using a 2×2 factorial design in which patients are assigned to low- or high-dose PPI therapy with or without 300 mg aspirin. A total of 2513 patients have been enrolled, and this trial is specifically powered to answer questions about the role of aspirin in cancer prevention for Barrett's oesophagus. The results of this trial are awaited. Other agents such as statins, curcumin, multivitamin and antioxidants have been suggested to potentially prevent cancer progression in Barrett's oesophagus; however, evidence is not yet sufficient to draw conclusions on this subject.358–360
There is currently insufficient evidence to support the use of aspirin, NSAIDs or other chemopreventive agents in patients with Barrett's oesophagus (Recommendation grade C).
## Patient perspective
Patients should be fully informed about their diagnosis and have an initial discussion about the pros and cons of surveillance. In the case of dysplasia (including indefinite, low grade and high grade), the diagnosis should be confirmed by an independent, expert histopathological review, and the patient should be informed of the diagnosis and the implications therein. When intervention is considered, the case should be reviewed by a specialist MDT for upper GI cancer, and the patient should have the opportunity to discuss the options in detail with experts from endoscopic and surgical disciplines.
All patients should be offered an appointment to discuss management decisions. When intervention is considered, therapeutic options should be discussed with an endoscopist as well as a surgeon (Recommendation grade C).
## Future developments
The following developments would revolutionise the care of individuals with Barrett's oesophagus and should be priorities for policy makers and funders.
• A non-endoscopic test(s) for diagnosis and surveillance
• Studies to determine whether surveillance actually reduces mortality
• Better understanding of the impact of screening and surveillance on QOL
• More research into the use of advanced imaging modalities to improve dysplasia detection and cost-effectiveness of surveillance
• Better risk stratification biomarkers to augment or replace the reliance on a histopathological assessment of dysplasia and better inform the indication for endoscopic ablative therapy
• More studies on the natural history of Barrett's oesophagus, especially in the context of very short segments of columnar-lined epithelium, LGD and cases with particular molecular profiles
• Research is required to inform the debate surrounding whether patients with LGD or no dysplasia should receive ablation therapy
• Evidence that endoscopic therapies are durable and do not require long-term endoscopic monitoring or replacement of long-term surveillance with a cost-effective non-endoscopic technique
• Studies to further delineate the role of chemoprevention
• Health economic studies should be performed in parallel with trials to evaluate new management algorithms
• Effects of current and future care pathways on patient QOL should be formally evaluated
It is difficult to forecast how long it will take to address these important questions, although it is likely that a time period of 5–7 years will be required before the majority of these questions will be answered. Nevertheless, we suggest that these guidelines should be reviewed in 4–6 years’ time or earlier to take into account emerging evidence. In addition, NICE guidelines produced in the interim will be complementary and essential to help implement these recommendations.
## Acknowledgments
We are grateful to the BADCAT team for generating an evidence-based consensus review on management of Barrett's neoplasia, which has been used as an aid to the evidence base and recommendations for the sections on the management of dysplasia. We are grateful to Dr Nick Carroll (Department of Radiology, Cambridge University Hospitals) for his critical review of the section on radiological staging of Barrett's-related neoplasia. We would like to thank Dr Laurence Lovat and Professor Jacques Bergman, who are experts in the field, who provided an independent critical review of the guidelines. We are also grateful to Mimi McCord and Peter Benest, who provided valuable input from the patient perspective.
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# Overview of Atomic and X-ray Data¶
The data provided in XrayDB includes Atomic data and characteristic energies and cross sections for the interaction of X-rays with elements. A few definitions and conventions necessary for using this data are discussed here.
## Elements¶
Most of the data resources are accessed by an elements Atomic Symbol. For the Python module, most methods will take element as the first argument, and this can either be the integer atomic number or the string for the atomic symbol.
## Physical Units¶
Elemental densities are given in gr/cm^3, and molar masses are given in AMU. Unless otherwise stated, all energies are in units of eV.
## X-ray Edges¶
Several resources (database tables, python methods) take either an edge or a level argument to signify a core electronic level. These are strings and must be one of the levels listed in the Table of X-ray edge names.
Table of X-ray Edges and Core electronic levels. The Names are the IUPAC symbols for the core electronic levels.
Name
electronic level
Name
electronic level
K
$$1s$$
N5
$$4d_{5/2}$$
L3
$$2p_{3/2}$$
N4
$$4d_{3/2}$$
L2
$$2p_{1/2}$$
N3
$$4p_{3/2}$$
L1
$$2s$$
N2
$$4p_{1/2}$$
M5
$$3d_{5/2}$$
N1
$$4s$$
M4
$$3d_{3/2}$$
O3
$$5p_{3/2}$$
M3
$$3p_{3/2}$$
O2
$$5p_{1/2}$$
M2
$$3p_{1/2}$$
O1
$$5s$$
M1
$$3s$$
P3
$$6p_{3/2}$$
N7
$$4f_{7/2}$$
P2
$$6p_{1/2}$$
N6
$$4f_{5/2}$$
P1
$$6s$$
## X-ray Lines¶
Many resources (database tables or methods) take emission line arguments. These are all strings and follow the latinized version of the Siegbahn notation as indicated in the Table of X-ray emission line names.
Table of X-ray emission line names and the corresponding Siegbahn and IUPAC notations
Name
IUPAC
Siegbahn
Name
IUPAC
Siegbahn
Ka1
K-L3
$$K\alpha_1$$
Lb4
L1-M2
$$L\beta_4$$
Ka2
K-L2
$$K\alpha_2$$
Lb5
L3-O4,5
$$L\beta_5$$
Ka3
K-L1
$$K\alpha_3$$
Lb6
L3-N1
$$L\beta_6$$
Kb1
K-M3
$$K\beta_1$$
Lg1
L2-N4
$$L\gamma_1$$
Kb2
K-N2,3
$$K\beta_2$$
Lg2
L1-N2
$$L\gamma_2$$
Kb3
K-M2
$$K\beta_3$$
Lg3
L1-N3
$$L\gamma_3$$
Kb4
K-N4,5
$$K\beta_2$$
Lg6
L2-O4
$$L\gamma_6$$
Kb5
K-M4,5
$$K\beta_3$$
Ll
L3-M1
$$Ll$$
La1
L3-M5
$$L\alpha_1$$
Ln
L2-M1
$$L\nu$$
La2
L3-M4
$$L\alpha_1$$
Ma
M5-N6,7
$$M\alpha$$
Lb1
L2-M4
$$L\beta_1$$
Mb
M4-N6
$$M\beta$$
Lb2,15
L3-N4,5
$$L\beta_2,L\beta_{15}$$
Mg
M3-N5
$$M\gamma$$
Lb3
L1-M3
$$L\beta_3$$
Mz
M4,5-N6,7
$$M\zeta$$
## Cross Sections¶
The photo-absorption and scattering cross sections from and are in cm^2/gr.
The data from is held as logarithms of energy, cross section, and logarithm of the 2nd derivative of cross section that allows for cubic spline interpolation in log-log space.
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# Lorenz and Modular Flows: A Visual Introduction
A tangled tale linking lattices, knots, templates, and strange attractors . . .
Etienne Ghys Unité de Mathématiques Pures et Appliquées de l'E.N.S. de Lyon etienne.ghys at umpa.ens-lyon.fr http://www.umpa.ens-lyon.fr/~ghys/
### 1.Introduction
Sometimes, seemingly unrelated objects turn out to be related... We would like to present here a mathematical example, exhibiting a close connection between two dynamical systems, one coming from number theory and the other from meteorology.
In 1801, Carl Friedrich Gauss published Disquisitiones Arithmeticae, his first masterpiece. It deals with the foundations of the theory of number fields. Today, many important aspects of this theory can be expressed in terms of a dynamical system acting in the space of lattices: the modular flow.
In 1963, the meteorologist Edward Lorenz was studying a very simplified numerical model for the atmosphere, which led him to the amazing strange attractor popularized through the famous butterfly effect: the flapping wings of a butterfly might cause some tiny change in the state of the atmosphere which can in turn lead to hurricanes!
We would like to describe a close topological connection between these two mathematical objects.
This article cannot be qualified as “mathematical” since it contains no proof! Our main motivation is in the visualization of some of the marvelous mathematical objects which are involved. We have tried to explain enough mathematics, at a rather elementary level, to comment on the pictures and clips which are the true content of this e-paper.
Our story is organized in a very simple way. First we describe the Lorenz attractor (2.1) and its template (2.2), then the space of lattices (3.1), the modular dynamics (3.2) and its periodic orbits (3.3), and finally we establish a connection (4.1 and 4.2) between these two dynamical systems!
This is the result of the collaboration of a mathematician and an artist-geometer. The reader may consult [1] for more mathematics, and [2] for more graphics.
Graphics were made in Ultrafractal [13] and Povray [14]. Data for knot drawings were extracted from Knotplot [12]. Larger versions of the films can be seen at Jos Leys' site.
Note: This e-paper is graphics intensive and contains a number of Quicktime movies. These can be seen with most web browsers equipped with the Quicktime plugin. Movies may be opened by clicking the button, or, as the case may be, by clicking on a specific picture. (Linux-based browsers may be an exception, for which we apologize).
Copyright for all films and images is by Jos Leys / Etienne Ghys
### 2.The Lorenz flow
#### 2.1 The Lorenz strange attractor and its periodic orbits
The model discovered by E. Lorenz is described by the following differential equation in 3-space [3]:
;
When Lorenz plotted the trajectories of this differential equation on his primitive computer, he could see something like the picture on the right (click on the image for a movie):
The amazing fact is that this picture is robust. If we perturb the equation, the phenomenon persists: trajectories tend to approach a set which is now called a strange attractor. We shall not try to discuss here the relevance of this object to fluid dynamics, but it happens that the Lorenz attractor has become one of the most paradigmatic symbols in modern dynamical systems, an icon of “chaos theory” (see for instance [4]).
In the 1980’s, Joan Birman and Bob Williams made the simple but crucial observation that a periodic orbit of a vector field in 3-space is a closed embedded curve which therefore defines a knot. They suggested that the study of the topology of the knots appearing in the Lorenz equation could yield some understanding of this important dynamical system [5]. The pictures below show some of the periodic orbits that one finds in the Lorenz equation.
Some of these knots look topologically trivial, but some are non-trivial, like the red orbit which turns out to be a trefoil knot. One of the motivations of Birman and Williams was that these periodic orbits seem indeed to give a good approximation of the attractor. In the picture on the right (click on it for a movie), one sees simultaneously a collection of closed orbits, suggesting that the attractor is some kind of limit of its periodic orbits. In a way, one could think of the attractor as an “infinite link with infinitely many components.
Birman and Williams proved that Lorenz knots are indeed very interesting, at the same time rich enough and very peculiar. Rather than stating technical results concerning Lorenz knots, let us limit ourselves to some “numerical statements”. Recall that a knot is simply a closed curve in space with no double point, and that one says that two knots are the same, or are equivalent, if one can go from the first to the second through a continuous deformation without creating intersection points (see for instance [6], [7], [8]). One crude way of classifying knots is to order them according to their crossing number, which is the minimum number of intersections of a projection of a representative of the given knot. One knows for instance that there are 250 (prime) knots with 10 crossings or fewer. It follows from the work of Birman and Williams that among those 250, only the following 8 knots appear as periodic orbits of the Lorenz attractor.
Click on the knot images below for a movie. (Knots are usually associated to a code like 8.19, meaning the 19th knot among those which can be represented in a diagram with 8 crossings, using an ordering which is more traditional than logical).
Among the 1,701,936 (prime) knots with 16 crossings or less , only 21 appear as Lorenz knots (checked using a computer and [17]).
Some are rather interesting like the knot 'Non-Alternating 12.725' with 12 crossings. As a sample counter-example, the figure eight knot is not a Lorenz knot.
#### 2.2 The Lorenz template
How can one prove such facts? By dealing with a combinatoric model of the Lorenz equation which is easier to analyze. First, construct the so-called Lorenz template in a way described by the following pictures.
Consider two bands of paper, and unfold them in space as shown in the clip. This produces a two-dimensional object in space which is a branched surface: this is the Lorenz template. The branching locus is the vertical segment that one sees in the middle of the picture. On this template, there is a rather natural dynamical system, which is shown on the following pictures.
If we identify the vertical segment with the interval [0,1], then each orbit traverses the template in such a way that the point with coordinate x comes back to the interval at the point 2x mod Z. Therefore if one looks for periodic orbits, we have to look for periodic points of the “doubling map” from the interval to itself. For instance, the doubling map sends the point 1/3 to 2/3, and then back to 1/3 = 4/3 - 1. So, the point 1/3 is periodic of period 2, and yields a closed orbit on the template, going once in one ear of the template, and once in the other one. The following pictures show several of these periodic orbits on the template.
As a matter of fact, it is not difficult to describe these periodic orbits by an itinerary, which consists of a finite sequence of symbols, say “left” and “right”. For any such sequence, there is exactly one periodic orbit which follows this itinerary, going successively in the left and right wings of the template, in the order given by the itinerary. Conversely, the periodic orbit defines the itinerary, up to a cyclic permutation which amounts to choosing a starting point. In this way, one can imagine a study of the topology of the Lorenz knot associated to a given itinerary. This is what Birman and Williams did. The fact that this “geometric Lorenz attractor” does describe the original Lorenz equation has been established much more recently by Tucker [9],[10].
### 3. The modular flow
#### 3.1 The space of lattices and its topology
Given two linearly independent vectors ω1, ω2 in the plane, one can consider the subgroup L of R2 that they generate:
L= {n1ω1 + n2ω2| n1 , n2 Z}.
A subset of the plane of this form is called a lattice. Of course, the same lattice L can be generated in many ways by two vectors. If a, b, c, d are integers such that ad−bc= ±1, the vectors 1+ bω2 and 1+ dω2 generate the same lattice.
The set of lattices is a topological space: one says that two lattices are close if they can be generated by pairs of vectors in the plane which are close. This space has been studied for many years by mathematicians, starting with the great Gauss in his Disquisitiones Arithmeticae (1801), in which he discussed in depth the arithmetical theory of integral quadratic forms.
Think of the plane R2 as the complex plane C. For each lattice L, one can define two complex numbers
; .
It is easy to check that these series converge since the absolute value of the exponents, 4 and 6, are bigger than 1. Now, an odd exponent would yield a zero sum, since the lattice is obviously symmetric with respect to the origin, so that 4 and 6 are indeed the first cases to consider. As for the 60 and 140, they are normalizing constants which are not relevant to our discussion. The main point is that the pair of complex numbers ( g2(L) , g3(L) ) characterizes the lattice. More precisely, a pair of complex numbers (g2, g3) corresponds to a lattice if and only if the so-called discriminant Δ = g23− 27g32 is not zero. See for instance [11], [16] for a proof.
Summing up, the space of lattices can be identified with the complement in C2 of the curve Δ = 0.
The picture on the left represents symbolically C2. Keep in mind that C2 is R4, so that this is a four-dimensional picture! The horizontal blue axis corresponds to those lattices for which g3=0; this is a copy of C=R2. The vertical green axis corresponds to those lattices for which g2=0; this is another copy of C=R2. The yellow curve represents Δ=0, but again this is a one-dimensional curve over the complex numbers, and therefore a surface from the point of view of real numbers.
How can we look at this four-dimensional object in a concrete way? If L is a lattice and k a non-zero real number, one can look at the lattice kL, which is just the same as L, but rescaled by a factor k. This suggests restricting our attention to those lattices whose fundamental domain has area 1, or still in other words, those generated by two vectors ω1, ω2 defining a parallelogram of area 1. Note that
g2(kL) = k4g2 (L) ; g3(kL) = k6g3(L),
so that for each lattice L one can find a unique k > 0 such that |g2(kL)|2+ |g3(kL)|2= 1.
This means that if we want to restrict our study to lattices up to rescaling, or to lattices of area 1, we have to look at the complement in the unit sphere |g2|2+ |g3|2= 1 of the zero set of Δ. This unit sphere is 3-dimensional, and the zero set intersects it in a one-dimensional object, which turns out to be a trefoil knot. The 3-sphere is easier to visualize than C2. If one chooses a point in a sphere, one can project from that point to the tangent space at the opposite point: this is the so-called stereographic projection, illustrated in the picture on the left for the two-dimensional case (the Riemann sphere). (click on the picture for a movie)
Hence the space of lattices of area 1 is identified with the complement of a trefoil knot in the 3-sphere, which, after deleting one point, is the complement of a trefoil knot in the usual 3-space. So, there is some hope of seeing something! Let’s have a look.
This picture (click it for a movie) shows the 3-sphere, or better, its stereographic projection in 3-space, or, even better, the projection to your 2-dimensional screen of this stereographic projection. As the film evolves, the point from which the projection is done is moving continuously so that you can admire the whole scene! In blue (resp. green), the coordinate axis g2=0 (resp. g3 =0) which intersects the sphere in a circle, which is seen from time to time as a straight line when the source of the projection is on this circle. As for the yellow trefoil knot, it is the intersection of the zero set of Δ with the sphere.
To get more topological insight, let’s have a look at some additional structures in the space of lattices of area 1.
Given a lattice L and angle θ ∈ [0,Π], one can rotate the lattice by θ in the plane. One gets another lattice Lθ. As θ goes from 0 to Π, this describes a circle in the space of lattices. Note that if θ ≠ 0, the two lattices L and Lθ are different in general, with only two exceptions. If L is a square lattice, it is equal to its image by rotations by Π/2 and if L is a regular hexagonal lattice, it is equal to its image by rotations by Π/3 and 2Π/3. All this implies that the space of lattices of area 1 is filled by circles corresponding to the orbits of these rotations. These circles are only topological circles; in fact they are themselves trefoil knots with the exceptions of the two special cases that we mentioned which are shorter (they close after Π/2 and Π/3 instead of Π) and which turn out to be round circles. As a matter of fact, these circles are just the blue and green circles that we previously met. This decomposition of the 3-sphere into a collection of trefoil knots and two circles is an example of a Seifert fibration. See the picture on the right. (click on it for a movie)
There is an additional structure in the 3-sphere, so to speak dual to the Seifert fibration. We know that to each lattice is associated a non-zero complex number Δ. If one multiplies a lattice by a real number k > 0, this Δ is multiplied by k−12 so that the argument is preserved. This suggests looking at the decomposition of the space of lattices of area 1 according to the value of the argument of the complex number Δ. The set of lattices of area 1 for which Δ has a given argument defines a surface in the 3-sphere whose boundary is the trefoil. The picture on the left (click on it for a movie) shows one of these Seifert surfaces.
Of course, we get one of these surfaces for each value of the argument of Δ. If this argument describes a full turn, the corresponding Seifert surfaces will sweep around all 3-space, always keeping the same boundary. For some value of the argument, the Seifert surface passes through the pole of the stereographic projection, so that the surface seems to be infinite at that instant. (Click on the picture)
To understand this fibration of the complement of the trefoil knot, let’s delete a part of the Seifert surfaces, and let’s look at the motion in the neighbourhood of the trefoil knot. This clip shows parts of four Seifert surfaces, corresponding to four values of the argument, rotating around the trefoil. Topologists say that the 3-sphere is an open book, that the trefoil is the binding, and that the Seifert surfaces are the pages. (Click on the image for a movie)
Now, for the fun of it, let’s have a look at the global picture, including the trefoil, the axis, the Seifert fibers, and the Seifert surfaces, all together! (Click on the image for a movie)
#### 3.2 The Modular dynamics
Now that we have a clear topological idea of the space of lattices of area 1, we can define a dynamical system on that space. The definition is very simple. For every real number t, consider the matrix
.
If L is a lattice of area 1, its image by the matrix is again a lattice of area 1. This defines a dynamical system in the space of lattices of area 1 which is called the modular flow. The trajectory of the lattice L is the curve described in the space of lattices by as the time t describes the real numbers.
Our purpose is to give a visual description of this flow and of its periodic orbits. This flow is a well known example of an Anosov flow which means that there are stable and unstable directions. Let us explain this. Introduce two other flows by
; .
Note that and ,so that if one takes two lattices L and (resp. L and ) and if one looks at their future (resp. their past) in the modular flow, i.e. if one looks at their images by with t positive (resp. negative), then the two lattices tend to approach exponentially fast. One says that L and (resp. ) are in the same stable (resp. unstable) curve.
The pictures below explain this situation. At first, one sees an initial point L, and two arcs in the stable and unstable manifolds, i.e. two intervals and for s in some interval [−1 , 1]. Then, when the modular dynamics moves forward, one sees the orbits starting from all these points, which generate two surfaces. The green one corresponds to the stable manifold, and one can see quickly that this stable manifold is so close to the central orbit that one cannot distinguish them any more. The red one is the unstable one and on the contrary expands in space and develops huge surfaces that look like parachutes. If one continued the dynamics further in the future, this red surface would become bigger and bigger, and would tend to be denser and denser in space, so that one could no longer grasp the global situation. Finally, the film stops and the modular dynamics flows backwards into the past, and one sees a similar phenomenon but the green and the red are interchanged. This structure of stable and unstable manifolds creating intricate nets in the phase space has become a central tool of study in dynamical systems: the so-called hyperbolic theory.
#### 3.3 Periodic orbits and their linking with the trefoil
We can now start the topological description of the periodic orbits of the modular flow. There is a simple way to describe these periodic orbits. Consider a 2 × 2 matrix A with integral coefficients and determinant 1:
.
Clearly, the matrix A preserves the standard square lattice Z2 in R2. Suppose that A is hyperbolic, which means that |a + d| > 2, in which case A is diagonalizable over the real numbers. In this case, there is a 2×2 matrix P such that
for some t (note that the product of the two eigenvalues of A is 1). So, if we define the lattice L to be the image of Z2 by P, one finds that L is fixed by . In this way, for each integral matrix with determinant 1, we find a fixed point for for some t , i.e. a periodic orbit of the modular flow. Note that the period of this periodic orbit is t , which is the logarithm of the absolute value of an eigenvalue of A.
Hence every hyperbolic matrix A defines a periodic orbit of the modular flow.
This periodic clip (click it to run) shows a periodic orbit in the space of lattices of area 1. Note that each point follows a hyperbola, the orbit of in the plane, so that the trajectories of the points are not periodic, but the trajectory of the lattice, as a part of the plane, is indeed periodic.
It is not difficult to see that if one replaces A by ± BAB−1 where B is some other integral matrix with determinant 1, one gets the same periodic orbit.
There is a natural bijection between periodic orbits of the modular flow and conjugacy classes of hyperbolic integral matrices of determinant 1, up to sign.
These periodic orbits have a very old mathematical tradition. One finds them in many different areas, in different disguises: closed geodesics on the modular surface, equivalence classes of integral indefinite quadratic forms, ideal classes in quadratic number fields, continued fractions etc.
Each one of these periodic orbits is a closed curve in the space of lattices of area 1, hence defines a knot in the complement of the trefoil knot. We wish to investigate these modular knots from the topological point of view. Let us first look at some examples.
For the matrix the knot looks disappointing! It is a small trivial knot. . . For the matrix the knot is still trivial but placed differently with respect to the trefoil. For the matrix the knot is more interesting; it is a trefoil knot. For the matrix it is a torus knot T(4, 5). For the matrices and it is, well, more complicated!
Before we discuss the nature of these knots, let us ask a seemingly simpler question:
Given a hyperbolic integral matrix A with determinant 1, denote by kA the associated knot. Can one compute the linking number between kA and the trefoil knot?
One should quickly recall the notion of linking number of two disjoint oriented knots in 3-space (also introduced by Gauss in the very different context of electromagnetism). Suppose that two oriented knots k1 (blue) and k2 (orange) do not intersect, and project them onto a plane in a generic way. These projections need not be disjoint of course.
Let us consider the points where the projection of k1, the blue knot, crosses once over the projection of k2, the orange knot. These crossing points may have two local behaviors, as shown in the pictures below.
Attach the sign +1 to the left situation and −1 to the right one, and sum these indices over the set of all crossings of k1 over k2. The result is called the linking number between k1 and k2. For instance, in the knot picture on the left, the blue curve crosses once over the orange one, with a '+1' sign, so that the linking number is '+1'. In the picture on the right, one has two cross-overs with different signs, so that the linking number is 0.
The important point is that this number is independent of the (generic) projection used to compute it, and remains invariant if the knots move continuously without intersecting each other.
Now, let us come back to our question, and try to compute the linking number between kA and the trefoil knot. Recall that the trefoil knot is the boundary of a Seifert surface where the argument of Δ is equal to some fixed value, for instance 0 (which corresponds to Δ being a positive real number). Given a closed oriented curve in the complement of the trefoil knot, one can consider its image by the Δ map, and one gets a closed curve in the complex plane which avoids the origin. Clearly, the linking number between and the trefoil is the index of this closed curve with respect to the origin, i.e. the number of turns it makes around the origin. A way to compute this index is to compute the algebraic intersection with the real axis, counting a '+1' or a '−1' for each intersection according to whether the curve crosses from negative to positive imaginary part, or the other way. Topologically, this means that the Seifert surface is two-sided, and that one wishes to compute the algebraic intersection of kA with the Seifert surface.
This is described by the pictures below. For a given matrix A, one draws at the same time a Seifert surface and the knot kA. As the construction of kA evolves, it intersects the surface from time to time, positively or negatively. The linking number we are looking for is the sum of these signs. In the first instance, we get two plus signs, in the second instance, one plus sign, and two plus signs and one minus sign in the final one.
It turns out that there is a nice formula for computing this linking number which relates it to a famous arithmetical function.
Consider the two matrices
U= ; V.
As it turns out, any integral matrix A with determinant 1 is conjugate, up to sign, to a product of U’s and V’s. For instance:
A= = UVVVUUVVVUUUUV
The word in U and V is uniquely defined up to a cyclic permutation. For each matrix A, one can therefore define R(A) as the number of factors equal to U, minus the number of factors equal to V. This invariant of the matrix A will be called the Rademacher invariant of A. One of the results in [1] is the following:
Theorem: The linking number between kA and the trefoil knot is equal to the Rademacher invariant of A.
We can only refer to [1] for several proofs and more information, but in the next section we shall provide some interpretation.
### 4 Lorenz and modular knots
#### 4.1 The modular template
So far we have discussed the periodic orbits in the Lorenz attractor, the Lorenz knots, and the periodic orbits of the modular flow, the modular knots.
Theorem: Lorenz knots and modular knots coincide.
More precisely, for every modular knot kA, one can deform it in 3-space to make it coincide with one of the periodic orbits of the Lorenz attractor, and conversely. Unfortunately, we cannot provide a proof here, and we will only show these deformations using some images and movies!
The first step of the proof consists in the construction of a modular template inside the space of lattices of area 1, which looks like the Lorenz template. We begin by constructing a one-dimensional object consisting of two parts. The space of hexagonal lattices of area 1 is a circle, that we have already met as one of the axes in our description of the space of lattices. The second part consists of all lattices with a fundamental domain having the shape of a horizontal rhombus with inner angles between Π/3 and 2Π/3.
Stated differently, one looks at lattices generated by two vectors which are symmetric with respect to the x-axis and which make an angle between Π/3 and 2Π/3 (and which are of determinant 1). This defines an interval since the angle can vary in [Π/3, 2Π/3]. Note that when this angle is equal to Π/3 or 2Π/3, the corresponding lattice is hexagonal so that this interval connects two points of the circle of hexagonal lattices. As a matter of fact, this interval is nothing more than a diameter. (Click the image at right for a movie).
The picture on the right shows this part of the construction. It starts with two rotations (one in 4-space and one in 3-space ) to place the trefoil knot in a convenient position, and then shows the construction of the circle and its diameter, that we have just described. (Click on the image)
We then extend this one-dimensional object in the unstable direction to create a two-dimensional template. One would need more technical details to give a full description, but we will limit ourselves to images showing the progressive development of the template. Note however that we are discussing topology, so that this construction is far from being unique, and we have made some specific choices for visual reasons.
Now the next task is to deform one of the modular knots in the complement of the trefoil knot, so that after the deformation, the knot lies on the template exactly like Lorenz knots. Again, we cannot give details and we refer to [1] for more. The general idea is to compress the space of lattices of area 1 to a small neighborhood of the one-dimensional object, by using an old idea (again of Gauss !): Given a lattice L, one seeks the shortest non-zero vector v in L, which is usually unique up to sign, unless the lattice has a fundamental domain with the shape of a rhombus. Then one looks for the shortest vector w in L which is not proportional to v. These two vectors v ,w define a preferred basis of L. Now, one shortens w progressively while increasing the length of v, keeping the determinant constant equal to 1. Rather than going into details, let us look at some images showing the deformation of several modular knots until they are in a “Lorenz position”.
#### 4.2 Two final remarks
A final comment. We know that a Lorenz periodic orbit is coded by a finite list of symbols “left” and “right” expressing the itinerary of the orbit, visiting successively the left and right ears of the Lorenz template. One can check that if one associates to an orbit the product A of the matrices U and V in the same order as the “left” and “right”, then the above deformation identifies the Lorenz knot with the modular knot kA. Now, one sees that the right ear has linking number +1 with the trefoil and the left ear has linking number −1.
It follows that the linking number of kA with the trefoil is equal to the number of U letters minus the number of the V letters in the word expressing A. This is one approach to the proof of the first theorem that we mentioned: The linking number of A and the trefoil is Rademacher’s number.
A final treat. The modular flow is not the only remarkable dynamical system on the space of lattices of area 1. One can also look at the dynamics generated by the matrices that we have already met as stable manifolds. This flow is classically called the horocyclic flow. One would need many clips to picture the wonderful dynamics of this flow, but we shall restrict ourselves to just one, describing the periodic orbits. Fix real numbers t and s, and consider the lattice Ls,t generated by the two complex numbers exp(t) and s.exp(t) + i exp(−t). Fixing t and letting s run from 0 to 1, we get a periodic curve ct in the space of lattices of area 1, which is a periodic orbit of . The following clip shows this curve ct when t describes some interval. When t is a large negative number, the curve c t is a small trivial loop going once around the trefoil knot. When t is a big positive number the curve ct gets longer and in the limit fills the whole space.
It is known that the the family of curves ct tends to fill the space in a “uniform” way but the quantitative estimate of the velocity of this phenomenon is equivalent to the famous Riemann hypothesis, one of the most enticing open questions in mathematics! [15]
### References
[1] GHYS, E.: Knots and Dynamics, to appear in the proceedings of the International Congress of Mathematicians, Madrid 2006.
[2] LEYS, J.: Mathematical Imagery. http://www.josleys.com
[3] LORENZ, E.: Deterministic Nonperiodic Flow. J. Atmos. Sci.20, (1963), 130-141.
[4] VIANA, M.: What’s New on Lorenz Strange Attractors. Math. Intell. 22,(2000), 6-19.
[5] BIRMAN, J. & WILLIAMS, R.: Knotted periodic orbits in dynamical systems.I. Lorenz’s equations. Topology 22(1983), no.1, 47–82.
[6] ADAMS, C.: The knot book. An elementary introduction to the mathematical theory of knots. Revised reprint of the 1994 original. American Mathematical Society, Providence, RI, 2004. xiv+307 pp.
[7] KAUFFMANN, L.:On knots. Annals of Mathematics Studies 115 Princeton University Press, Princeton, NJ,(1987).
[8] SOSSINSKY, A: Knots. Mathematics with a twist. Translated from the 1999 French original by Giselle Weiss. Harvard University Press, Cambridge, MA, 2002. xxii+127 pp.
[9] STEWART, I : The Lorenz Attractor Exists. Nature 406 (2000), 948-949.
[10] TUCKER, W.: A rigorous ODE solver and Smale’s 14th problem. Found.Comput. Math. 2 (2002), no. 1, 53–117.
[11] SERRE, J.-P.: A course in arithmetic. Translated from the French. Graduate Texts in Mathematics, No. 7. Springer-Verlag New York, Heidelberg, 1973. viii+115 pp.
[13] SLIJKERMAN, F. :Ultrafractal : http://www.ultrafractal.com
[14] POVRAY: Public domain raytracing software http://www.povray.org/
[15] SARNAK, P.: Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series. Comm. Pure Appl. Math. 34 (1981), no. 6, 719–739.
[16] McKEAN, H. & MOLL, V.: Elliptic curves. Function theory, geometry, arithmetic.Cambridge University Press, Cambridge, 1997.
Etienne Ghys Unité de Mathématiques Pures et Appliquées de l'E.N.S. de Lyon etienne.ghys at umpa.ens-lyon.fr
NOTE: Those who can access JSTOR can find some of the papers mentioned above there. For those with access, the American Mathematical Society's MathSciNet can be used to get additional bibliographic information and reviews of some these materials. Some of the items above can be accessed via the ACM Portal, which also provides bibliographic services.
Welcome to the
Feature Column!
These web essays are designed for those who have already discovered the joys of mathematics as well as for those who may be uncomfortable with mathematics.
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# Installation¶
simplicial-test can be installed via PyPI.
pip install simplicial-test
Tip
By default, the library uses SageMath’s Combinations to generate proposal facets, primarily because it correctly handles the cases when the “pool of elements” has duplicate items. However, it cannot be installed through pip but has to be downloaded /slash/ installed from their website.
If installing Sage is not feasible, we offer more-itertools as the fallback option, which has a similar distinct_combinations() method. This method is, on the average, faster than SageMath’s, especially in large system sizes (e.g., $$E \geq 10^4$$). Yet, we’ve found that the generator is not as stable, and in some inputs, it may take a longer-than-usual time to output a proposal facet. Therefore, in smaller and most cases, SageMath is preferred.
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# Lawns
#### Perfectly Normal Beast
##### the storm is here
[FONT=Verdana,sans-serif]some of the reasons lawns suck:[/FONT][FONT=Verdana,sans-serif]
[/FONT]
[FONT=Verdana,sans-serif]The conventional approach of landscaping with turf and ornamentals impacts biodiversity in two ways: 1) it limits the diversity of native species in areas dominated by turf and ornamentals, and 2) it can impact surrounding natural environments, altering habitats in ways that exclude native plants and animals.[/FONT][FONT=Verdana,sans-serif]Let’s first look within the city limits.[/FONT][FONT=Verdana,sans-serif]How do turfgrass lawns and non-native ornamental plants impact [/FONT][FONT=Verdana,sans-serif]urban[/FONT][FONT=Verdana,sans-serif]biodiversity[/FONT][FONT=Verdana,sans-serif]? Simply put, landscapes dominated by turfgrass and non-native ornamental plants create an artificial environment that offers very little opportunity for most native species to thrive. A monoculture of turfgrass infused with non-native ornamentals excludes native plants and provides little to no habitat for most wildlife.[/FONT][FONT=Verdana,sans-serif]Think about the vast amount of land devoted to turf, both for growing the sod and the amount of sod that occurs on the landscape as urban lawns. One estimate indicates that four million acres of managed turfgrass occurs in Florida, with 75 percent of these as residential lawns (Nagata, 2003). Such acreage limits the amount of natural habitat, thus decreasing urban habitat diversity and ultimately native species diversity.[/FONT]
[FONT=Verdana,sans-serif][FONT=Verdana,sans-serif][FONT=Verdana,sans-serif]source[/FONT][/FONT] [/FONT][FONT=Verdana,sans-serif]
[/FONT]
[FONT=Verdana,sans-serif]
[/FONT][FONT=Verdana,sans-serif][FONT=Verdana,sans-serif]
Approximately 50-70 percent of our residential water is used for landscaping, most of it to water lawns, which total approximately 20-30 million acres in the United States. And the U.S. Environmental Protection Agency (EPA) estimates that nearly 70 million pounds of active pesticide ingredients are applied to suburban lawns each year, helping to make polluted runoff the single largest source of water pollution nationwide, affecting ground water, lakes and streams, wildlife, and human health. A 1995 EPA compilation of state data collected in 1994 showed that urban runoff contributed to damage in more than 26,000 river and stream miles. And the use of gas-powered lawn mowers contributes five percent of the nation's air pollution. A gas-powered lawnmower emits 11 times the air pollution of a new car.
[/FONT]
[/FONT][FONT=Verdana,sans-serif][FONT=Verdana,sans-serif][FONT=Verdana,sans-serif]source[/FONT][/FONT][/FONT]
[FONT=Verdana,sans-serif]According to the EPA, 95% of the pesticides used on residential lawns are[/FONT][FONT=Verdana,sans-serif] possible or probable carcinogens. In 1989 the National Cancer[/FONT][FONT=Verdana,sans-serif] Institute reported children develop leukemia six times more often when[/FONT][FONT=Verdana,sans-serif] pesticides are used around their homes. The American Journal of[/FONT][FONT=Verdana,sans-serif] Epidemiology found that more children with brain tumors and other cancers[/FONT][FONT=Verdana,sans-serif] had been exposed to insecticides than children without. Studies by the[/FONT][FONT=Verdana,sans-serif] National Cancer Society and other medical researchers have discovered a[/FONT][FONT=Verdana,sans-serif] definite link between fatal non-Hodgkins Lymphoma (NHL) and exposure to[/FONT][FONT=Verdana,sans-serif] triazine herbicides (like Atrazine), phenoxyacetic herbicides (2,4-D),[/FONT][FONT=Verdana,sans-serif] organophosphate insecticides (Diazinon), fungicides, and fumigants; all of[/FONT][FONT=Verdana,sans-serif] which have uses as lawn chemicals.[/FONT][FONT=Verdana,sans-serif]
[/FONT][FONT=Verdana,sans-serif]
[/FONT][FONT=Verdana,sans-serif]Most people seriously overestimate the amount of protection given them by[/FONT][FONT=Verdana,sans-serif] governments regarding pesticide safety. Congress found that 90% of the[/FONT][FONT=Verdana,sans-serif] pesticides on the market lack even minimal required safety screening. Of[/FONT][FONT=Verdana,sans-serif] the 34 most used lawn pesticides, 33 have not been fully tested for human[/FONT][FONT=Verdana,sans-serif] health hazards. If any tests are done, they are performed by the[/FONT][FONT=Verdana,sans-serif] chemical manufacturers, not the EPA. "If a chemical company wanted to, they[/FONT][FONT=Verdana,sans-serif] could start with a desired conclusion, and skew the data, and the EPA would[/FONT][FONT=Verdana,sans-serif] never know", notes David Welch, an entomologist with the EPA's Office of[/FONT][FONT=Verdana,sans-serif] Pesticide Programs.[/FONT]
[FONT=Verdana,sans-serif][FONT=Verdana,sans-serif]source[/FONT][/FONT]
[FONT=Verdana,sans-serif]During World War II, women became the focus of lawn-care companies in the absence of their husbands and sons. The lawn was promoted as a necessary means by which women could help support their male family members and American patriotism as a whole. The image of the lawn changed from focusing on technology and manhood to emphasizing aesthetic pleasure and the health benefits derived from its maintenance; it was assumed that women would not respond positively to images of efficiency and power. The language of these marketing campaigns still intended to imbue the female population with notions of family, motherhood, and the duties of a wife; it has been argued that this was done so that it would be easier for men returning from war to resume the roles their wives had taken over in their absence. This was especially apparent in the 1950s and 1960s, when lawn-care rhetoric emphasized the lawn as a husband's responsibility and as a pleasurable hobby when he retired[/FONT][FONT=Verdana,sans-serif]
[/FONT][FONT=Verdana,sans-serif]
[/FONT][FONT=Verdana,sans-serif]The lawn aesthetic in Europe and Australia seems to exhibit the same cultural tendencies as a representation of order, power over nature, patriotism, and suburban family life while still adhering to other gender constructs present throughout the world's suburbs.[/FONT]
[FONT=Verdana,sans-serif]source[/FONT]
thread inspired by: you know who you are
#### Cherry Cola
##### Banned
thank you I have long since hated lawns with a passion no jk
#### Architect
##### Professional INTP
Lawns are derivative of 18th century Enlightenment which was was when mankind had finally established some control over nature. It's the ultimate expression of our manifest destiny. All Prometheans should have a lawn.
Actually lawns are nothing but psychology. What I said above is true, and the present day backlash against lawns are the result of a modern era "back to nature" ludditism. Makes sense, now that we've really conquered nature (excepting the occasional major storm, volcano or earthquake (and we even have mitigations against those) we can feel bad about our "lost connection with nature"
#### Cherry Cola
##### Banned
I don't give a fuck about nature, lawns and similar phenomena are just a huge waste of many different kinds of resources.
Not to deny your analysis, seems spot on
#### nanook
##### a scream in a vortex
lawns are not nature, they are symbols of the castration of nature.
not being able to appreciate nature is indicative of a dissociative state of mind. ego sees only what it can make use off. nature is useless. lawns are useful as status or persona ("Promethean"?!?) symbols.
[bimgx=400]http://i.imgur.com/iAc48fB.jpg[/bimgx]
#### Cherry Cola
##### Banned
humankind reigns!
biodiversity is overrated anyway
does that 40% even compensate for all the species which would have died out without humans?
IMHO which should slowly phase out most carnivores, they cause a lot of unnecessary suffering, that they are cool and that it's just nature are not valid arguments against the fact that they should be exterminated
fuck the circle of life
#### Perfectly Normal Beast
##### the storm is here
does that 40% even compensate for all the species which would have died out without humans?
i don't know but these figures will add some perspective:
according to this 100 to 1000 species per million are lost per year and according to this the background extinction rate is approximately one per million species per year.
btw half is 50% :P
#### computerhxr
##### Village Idiot
I know that everyone around here is complaining about the wolves eating their dogs. They are way smarter than [house] dogs, so they lure them to the fence and then pull them through. Humans should support nature, not isolate it (or castrate it as nanook puts it).
It's the world balancing itself back out. Nature always pushes for homeostasis.
Farmers and ranchers have been destroyed. Big farmers cross pollinate smaller farms with their proprietary genetics, and then sue them for infringement. Cattle ranchers are being bullied out of existence. Isolated lawns with no variety is destructive and unnatural.
#### computerhxr
##### Village Idiot
Is there really such a thing as extinction? Given enough time and the right conditions, the species will express itself in the same genetic form again in the future. All goes along the theme of balance.
#### Cherry Cola
##### Banned
then we can wait for a while whereafter we kill em again, wouldn't it be awfully awesome to have new predators evolve? aren't ya'll tired of fucken cats and bears and shit?
#### Architect
##### Professional INTP
I don't give a fuck about nature, lawns and similar phenomena are just a huge waste of many different kinds of resources.
Actually that's worth checking. Do you know how much food is wasted? I can't remember the percentage but it's enormous, something like half of all edible food (in the US at least) is thrown out. You can see it at the local grocery stores. Stuff expires, gets a little bruised or whatever, gone. Restaurants produce an enormous amount of waste, only a fraction makes it into customers stomachs.
My point is that you have to be extremely cautious about making generalizations about waste, and look at hard numbers. The visible forms of waste are usually far outnumbered by the not visible. I would suspect that lawns are a small piece of the pie.
yeah we really have conquered the bitch. i guess "lost connection with" means "killed half of all wildlife in the last 40 yrs".
Lawns kill wildlife? Then why do I get gophers and deer all over it. Anyhow 99.99% of all species on earth have gone extinct so that's not new.
lawns are not nature, they are symbols of the castration of nature.
That's what I said.
Anyhow, the biggest waste is worrying about such things. Why don't you go do something useful with your energy instead of worrying about lawns? People will have them or not as they please. Go invent something new and give back to the world instead of criticizing it.
#### computerhxr
##### Village Idiot
Anyhow, the biggest waste is worrying about such things. Why don't you go do something useful with your energy instead of worrying about lawns? People will have them or not as they please. Go invent something new and give back to the world instead of criticizing it.
Some of us are...
Interlocking Hex Communities (underground dwellings):
[BIMG]http://i1375.photobucket.com/albums/ag448/computerhxr/community_zpsdbb3b42e.png[/BIMG]
They would look something like this...
Goats and free-range animals would mow the lawn and fertilize the environment. Dwellings would not negatively affect the ecosystem. Could still have running water and modern technology.
#### Animekitty
##### baby marshmallow born today
i live in a desert
lawns wastes water
american dream barbecue
#### redbaron
##### irony based lifeform
It's applicable to any monoculture ecosystem really.
Lawns are monoculture. Monoculture means little to no biodiversity. Lack of biodiversity means opportunistic flora and fauna (weeds and pests) thrive. Pesticides are used to try and control them, which contaminates soil and further damages biodiversity.
Happens all over the world. Crops get infested by locusts because they promote opportunistic monoculture by nature. Natural forest and bushland are turned into "recreation reserves" and in the process, large quantities of underbrush are destroyed, meaning small insects and ants find it harder to live, smaller birds have less food and hiding places from larger birds (and so on). So here in Australia where there's parks, you basically see only high-nesting, large and/or territorial/opportunistic birds. A few crow variants, starlings, non-native minors, then sparrows and non-native pigeons.
It's very rare to see large quantities of native birds or a diverse range of them around, which is quite sad really. The thing is there's no reason to turn bushland into a field of mowed grass. I'd say it's infinitely more exciting and healthy for children to go for a walk through beautiful and native forest than to visit a round field ringed by a metal fence. Ugh.
Also the way most lawns are implemented they look like utter trash. Boring, uniform and lifeless. At least plant or grow something with a function. Plant a tree, grow some herbs or vegetables. Such a waste of good soil to use it for a bunch of grass. Seriously, grass!
#### computerhxr
##### Village Idiot
I wouldn't trust any research conducted by the WWF.
World Wrestling Federation?
Haha! I agree, you can't trust them. They are extremely biased.
#### Pyropyro
##### Magos Biologis
I find lawns weird. You can't eat the things growing on it or at least raise plants that can act as natural fences.
They can at least make good grazing areas for goats though which is nice.
#### Architect
##### Professional INTP
There's also an element of American elitism going on here. Because in the US we can easily afford a lawn - a sign of useless conspicuous consumption - we can also show how enlightened we are by proclaiming how much we hate it.
Consider Germany. Over there having a personal gardening space or a loan is a rare commodity. So much that they have community gardens where there are waiting lists to get in. Most people live in apartments. Those who are well off enough to have lawns take meticulous care of them and appear to have no compunctions about it. When I was over there I had friends who were very proud of their personal little plot.
Same thing in Japan. They have a special type of grass - Zoysia, which is a wonderful grass. It grows very tightly and in slowly so need very little care and not much water. A Japanese manicured garden is a beautiful thing.
Do I love lawns? Not particularly, but a well kept one is nice to see. I do know that putting in landscaping is expensive, easily upwards of $100k around these parts, and grass is one of the cheapest options. #### Pyropyro ##### Magos Biologis There's also an element of American elitism going on here. Because in the US we can easily afford a lawn - a sign of useless conspicuous consumption - we can also show how enlightened we are by proclaiming how much we hate it. We do have some US influence so we have lawns too but they are filled with carabao grass (which is great for grazing). Lawns can be useful if you use nature's lawnmower (goats) to trim them. Goats taste good when cooked properly. You can even feed water buffaloes or cows if the space is large enough. Consider Germany. Over there having a personal gardening space or a loan is a rare commodity. So much that they have community gardens where there are waiting lists to get in. Most people live in apartments. Those who are well off enough to have lawns take meticulous care of them and appear to have no compunctions about it. When I was over there I had friends who were very proud of their personal little plot. Heh, looks like your friends and I will get along well. I suggest they raise orchids since you can simply hang them on walls when you are deprived of space. Same thing in Japan. They have a special type of grass - Zoysia, which is a wonderful grass. It grows very tightly and in slowly so need very little care and not much water. A Japanese manicured garden is a beautiful thing. Do I love lawns? Not particularly, but a well kept one is nice to see. I do know that putting in landscaping is expensive, easily upwards of$100k around these parts, and grass is one of the cheapest options.
I like well-kept gardens. It's the monochromatic lawns that is an eyesore. I prefer having bougainvillea's pink or hibiscus' red here and there rather than looking at a sea of green.
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#### EyeSeeCold
##### lust for life
It's crazy to me that even if you wanted to do something about it that you could be stopped by a HOA agreement. Our state passed a protection bill but it isn't absolute.
Personally I think desert xeriscaping can have aesthetic appeal, plus you can probably hide peyote in there somewhere.
#### Pyropyro
##### Magos Biologis
It's crazy to me that even if you wanted to do something about it that you could be stopped by a HOA agreement. Our state passed a protection bill but it isn't absolute.
Personally I think desert xeriscaping can have aesthetic appeal, plus you can probably hide peyote in there somewhere.
You gonna go Carlos Castaneda all over us ESC?
#### redbaron
##### irony based lifeform
Architect said:
Consider Germany. Over there having a personal gardening space or a loan is a rare commodity. So much that they have community gardens where there are waiting lists to get in. Most people live in apartments. Those who are well off enough to have lawns take meticulous care of them and appear to have no compunctions about it.
Yeah except they actually grow things other than a useless patch of grass that does nothing but promote monoculture, while using further damaging pesticides in the process. They actually take care of their gardens.
The reason they "accept" what little greenery they have is because they completely destroyed all of their natural habitat in the first place. Germans are more frequently spending their holidays in the places in Europe where they can be in natural forest. There's recently been a huge influx of Baltic tourists to areas of Macedonia and its bordering countries, precisely because they can offer more nature than a patch of garden. They also visit Scandinavia for much the same reason.
If anything the situation in Germany is entirely an argument against the points you're trying to make.
#### Architect
##### Professional INTP
Yeah except they actually grow things other than a useless patch of grass that does nothing but promote monoculture, while using further damaging pesticides in the process. They actually take care of their gardens.
Were you there? I saw a lot of unkempt plots too.
The reason they "accept" what little greenery they have is because they completely destroyed all of their natural habitat in the first place. Germans are more frequently spending their holidays in the places in Europe where they can be in natural forest. There's recently been a huge influx of Baltic tourists to areas of Macedonia and its bordering countries, precisely because they can offer more nature than a patch of garden. They also visit Scandinavia for much the same reason.
So, Germans who have no property like to garden, and that's because they destroyed their land? Where did you get that ... Germany was destroyed by the war mostly, they're still digging up bombs (dug up an unexploded one at the train station when I was last there). Besides which where's the destroyed land? I spent my time in Southern Germany, it's probably more industrialized in the north but I was never far from a forest. From the air it was farmland and forest. Your point is lost.
And I have a friend who spends his summer in Italy. It has better weather than Germany, I understand. Surprise, he likes to go there. I understand Americans like to travel out of their state too for vacation, must be a deep shame of California which causes that.
You're talking about things you don't really understand. The situation in Germany is entirely an argument against the points you're trying to make.
Whatever, you're just deciding to be a jerk again.
#### Cherry Cola
##### Banned
Actually that's worth checking. Do you know how much food is wasted? I can't remember the percentage but it's enormous, something like half of all edible food (in the US at least) is thrown out. You can see it at the local grocery stores. Stuff expires, gets a little bruised or whatever, gone. Restaurants produce an enormous amount of waste, only a fraction makes it into customers stomachs.
My point is that you have to be extremely cautious about making generalizations about waste, and look at hard numbers. The visible forms of waste are usually far outnumbered by the not visible. I would suspect that lawns are a small piece of the pie.
I never thought it was a huge waste compared to the stuff you list, but it's still a huge waste. Two wrongs don't make a right.
Besides lawns are symbolic of everything that is wrong with SJ's which makes them all the more important to combat.
#### Perfectly Normal Beast
##### the storm is here
IMHO which should slowly phase out most carnivores, they cause a lot of unnecessary suffering, that they are cool and that it's just nature are not valid arguments against the fact that they should be exterminated
if we're going to start phasing out species on the basis of how much unnecessary suffering they cause then fucking humanity is going to be first in line. good, let the genocide commence.
Lawns kill wildlife? Then why do I get gophers and deer all over it. Anyhow 99.99% of all species on earth have gone extinct so that's not new.
ugh, i can't be bothered wasting my time untangling your webs of nonsense.
#### redbaron
##### irony based lifeform
Just going to bring this thread back to biodiversity and its importance since that's what it really was intended to be about.
Seeing a deer in a garden means nothing. Large mammals are not bio-indicators. They're too far along in the cycle to the point that effects on their behaviour and physiology as a result of pollutants in the ecosystem they live in are not apparent until the process has already become close to irreversible. It's important that people have some understanding of what a bio-indicator is.
http://en.wikipedia.org/wiki/Bioindicator
Failing to see the importance of biodiversity is an incredibly common and horribly misinformed mindset. Exhaustive farming and exploiting native ecosystems actually leads to irreversible processes that increase the salinity of soil, to the point that it's completely infertile and can no longer be used for crops. It's already become a huge problem in Australia.
On soil salinity.
The thing is that the term "lawns" in this context is really a euphemism for "monoculture".
Creating a monoculture inherently attracts opportunistic mono-species. The presence of competitive and opportunistic mono-species destroys the potential for biodiversity. With no biodiversity you lose the potential for healthy competition. With no competition, you lose genetic diversity that typically results from inter-species competition. Without that the entire area of monoculture and mono-species become susceptible to diseases of all kinds, be it fungal, bacterial or viral.
So you combine this with the fact that humans are exploiting land to the point that salinity levels rise exponentially until finally the land is dead. The topsoil is too saline for anything to grow and it just becomes a patch of dirt. Which leaves it susceptible to erosion since there's no roots growing to hold it together. The topsoil then blows away and leaves nothing but a wasteland and you're left with a narrow range of species all susceptible to diseases and living with few resources (if they even live at all at this point).
Biodiversity is as much about humans as it is other species. Sadly though it's not surprising when people don't realise its importance because like deer - we're large, opportunistic mammals. In an ecological context we're near the very end of the cycle, where effects don't become noticeable until the irreversible process has already taken place. In our day to day lives there's not much indicator that our ecosystem has been irreparably damaged until the effects have really started to take place.
So in spite of the overwhelming amount of scientific evidence for the importance of biodiversity to the future existence of every living species on the face of the planet, it's all too easy to just ignore it because one sees wildlife in the garden.
#### The Gopher
##### President
Lawns kill wildlife? Then why do I get gophers and deer all over it. Anyhow 99.99% of all species on earth have gone extinct so that's not new.
Because I am monitoring your actions.
#### Cæilon
##### Searching for Ràilona
I don't have a lawn anymore and I miss lying on the grass on a hot summer's day, staring at the clouds in a moment of pure bliss.
#### Fukyo
##### blurb blurb
Biology isn't a "real" science, young'n.
#### redbaron
##### irony based lifeform
I know you're joking but it's actually more to do with geology and chemistry than anything else.
Besides I don't listen to phones
#### Cognisant
##### Prolific Member
Step 1: We should all live underground with hydroponic skyscrapers above us that do nothing but recycle our waste and grow more food than we could ever possibly eat, then when the world's population explodes from an abundance of food we dig deeper and build higher.
Step 2: Classified.
Step 3: Profit.
#### OrLevitate
##### Banned
Personally I find architect's assertions to be the undisputed truth, but good luck informing you all of it.
#### somebodiesfool
##### Member
sounds like a definite need for some high quality h2o
|
{}
|
# [FOM] Pratt on categorical foundations
Tue Feb 21 15:24:53 EST 2012
Dear all,
(this post is deliberately written in a lighthearted style - it is not
how I usually address this list or this topic)
On 20 February 2012 23:31, Harvey Friedman <friedman at math.ohio-state.edu> wrote:
> How would you compare the
> simplicity of categorical foundations versus set theoretic foundations?
this is the nub of the matter. I believe proponents of both sides use
different criteria, and it is difficult to see the benefits of a set
of axioms without working with them.
But I would like not to add fuel to the fire, but some facts to the
discussion. And, if I may be so bold, un-ask Friedman's question, or
at least ask it in a different form.
"How would you compare the simplicity of structural foundations versus
material foundations?"
or
"How would you compare the simplicity of structural set theory versus
material set theory?"
'Structural' and 'material' are more useful distinctions than 'set
theoretic' and 'categorical', most importantly because ETCS is, like
it or not, a theory of sets, and so are other category-based
foundations. Also, because there is a structural set theory which is
not categorical in nature, but which shares some essential features
which might endear it to those who like ETCS. But we shall return to
that in a moment.
But what do 'structural' and 'material' mean? I hear you clamouring.
The distinction is largely metamathematical, and like the judge said,
I know it when I see it.
Material set theories include ZF(C), NBG, MK and so on. They are
roughly characterised by the fact elements of sets have an independent
existence, or to put it another way, the existence of the global
membership predicate. (It is this global membership predicate than
makes structural set theories qua foundations attractive to me because
this is something that mathematics outside of traditional set theory
does not use - but I digress.) The strength of material set theories
is evident, so I don't need to explain them here. Take it as given I
appreciate material set theory (and the more so since I started
teaching myself forcing).
Structural set theories have the contrasting property that elements of
sets are only determined by the sets that contain them and what
functions there are. It is harder to pin down what precisely makes a
set theory structural, but as the name implies, it is akin to
Bourbaki's structuralism, where properties of structures should be
isomorphism invariant. In this case, since we are using sets,
properties that can hold of a set should be preserved by bijections (
for example the statement a \in B is not preserved by a bijection B
\cong C). ETCS is a structural set theory, as is Algebraic Set Theory,
which axiomatises a category of classes and 'small' maps-those with
all fibres sets. The third example I know of is what I want to present
here, and is due to Michael Shulman.
This theory is called SEAR (Sets, Elements And Relations), and is
equiconsistent with ZF. It has a natural extension called SEAR-C which
is equivalent to ZFC (in the sense that a model of one is a model of
the other).
The theory has three sorts as is evident from the name (as opposed to
ZF(C) which has one), and uses the language of dependent type theory.
The details are here (http://ncatlab.org/nlab/show/SEAR), but can be
summarised as follows - my exposition may well not do the theory
justice.
==Preliminaries
Elements are members of a set, and we can only quantify over the
elements belonging to a given set.
Relations are between a pair of sets, and we can only quantify over
relations between a given pair of sets.
We can say when a relation holds of a pair of elements, one from each
of the two sets
We can't compare things of different sorts (so we can't assert x = A
for x an element and A a set, and so on)
(Note: we can quantify over all sets)
Functions are relations which are functional in the usual sense.
the category theory rises independently from them - such comments are
not part of the development)
0. There exists a set with an element
1. Axiom scheme of relational comprehension
2. Relations R between sets A and B correspond to sets 'R' equipped
with functions 'R' --> A and 'R' --> B such that certain expected
properties hold (when we define products, the resulting 'R' --> A x B
is injection)
3. Power set
4. Infinity
5. Collection
6. Choice - every total relation 'contains' a function
==
>From 0-2 we can define the category Set, and it is a well-pointed
Heyting category, while from 0-3 it follows that the category Set is a
well-pointed topos.
SEAR uses 0-5, while SEAR-C adds 6. Nothing in these axioms depends on
category theory.
I hope this contributes light to the discussion, and not heat.
Cordially,
David Roberts
PS Once someone asked for a fully formal definition of the axioms of
ETCS - they can be found here
http://ncatlab.org/nlab/show/fully+formal+ETCS
|
{}
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# Charts in RPE Documents – the Excel way
Updated on 2014.08.20, 20:00 EEST
RPE does not have native support for drawing charts so you need an external tool to generate the chart. Google Chart Tools: Image Charts have been used successfully in the past but it has been deprecated by Google in 2012 and it is unknown how it will work past 2015.
There are other online providers or applications that can be installed in LAN to provide a REST API for generating image charts. But these solutions may present security/confidentiality risks or additional effort in installing and maintaining them.
An alternative to this is using Microsoft Excel to create charts as Excel can be fully automated through Visual Basic Script which in turn can be invoked from RPE.
This solution assumes Excel is installed which is not a trivial prerequisite. Also you need to be able to run Windows scripts on your machine. To verify your machine can run the example and to better understand how the VB Script work see the last section in this article
The example template and VB Script are available on the RPE devWorks wiki: https://www.ibm.com/developerworks/community/wikis/home?lang=en#!/wiki/Rational%20Publishing%20Engine/page/Examples
NOTE: the VB Script is taken from http://automationlab09.wordpress.com/2010/04/29/how-to-draw-a-chart-in-excel-using-vbscript/ and modified it to fit the process. I do not own the copyright and all the credit goes to the original author.
## Solution flow
With the prerequisites in place the high level flow of the solution is rather simple:
1. deploy the VB Script with the RPE template
2. add an image element in the RPE template
3. calculate the data labels and values
4. for the image content use a script that calls the VB Script template with the necessary arguments, one of them being the path where the image is to be generated
5. use the path from 3 as the source of the image
The VB Script generates Pie Charts but you can create new scripts to generate other formats too.
NOTE: the JavaScript assumes that the VB script is in d:\\tmp. You need to manually modify the path to where your script is located.
NOTE: the JavaScript script I use combines steps 3 and 4 in a single place as the data is static. A side effect of this is that an image is generated every time you modify and save the image JavaScript.
NOTE: the only information you will receive in RPE when you run the VB Script is the exit code. You cannot see error details or log messages generated by the command.
## excelPieChart.vbs
The script is designed to take as input 4 arguments. All arguments are strings and are mandatory
1. the title of the chart
2. a “|” separated string with the data labels. Ex: “High|Medium|Low”
3. a “|” separated string with the data value. Ex: “20|50|30”
4. the path of the exported image. The path must have the png extension and should not exist otherwise the script will prompt the user to overwrite the file
To verify that the script can produce chart images successfully on your machine you can run the following command from a Windows command prompt. If everything is in place you should see the Excel window briefly showing on screen and more importantly, the png image in the specified path.
cscript "d:\tmp\excelPieChart.vbs" "Test chart" "High|Medium|Low" "20|50|30" "d:\tmp\testChart.png"
|
{}
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# Caché
126
Sorting: By Date
Period: 2018
### For and If with one line: to brace or not to brace
Hi Community!
Coding guidelines discussion. Consider you have For with one command in the cycle. Here are the options:
One
For i=1:1:1000 set ^Test(i)=""
Two
For i=1:1:1000 {
set ^Test(i)=""
}
Same for the "If":
if a set b=a
or
if a {
set b=a
}
Your choice? Or maybe even other options?
Last comment 23 October 2019
+ 2 1 17
1049
views
+ 2
rating
### Replacing ZEN - Part 2 - Strategic Issues
Index to Articles
Published 2018-05-11 Last edit -
Hi All
I this article I detail some strategic issues that a new development UI will need to address - these are the ones that I can think of now - others may come to light during this journey.
See the webinar by Eduard Lebedyuk here from the last Global Summit describing modern web development and Caché
#### And, as always, if I have missed something please comment....
Last comment 9 October 2019
+ 13 2 7
842
views
+ 13
rating
### How to Open Terminal In Caché Mac OS
HI,
I am a newbie so excuse my basic questions.
I have installed Caché on Mac Os High Sierra 10.13.6 and have started the ObjectScript tutorial but I cannot open Terminal in Caché.
The instructions provided on the tutorial don't appear to be for Mac OS as there is no cube icon:
Last answer 21 September 2018 Last comment 3 October 2019
0 0 5
381
views
0
rating
### How to Publish an Application on InterSystems Open Exchange?
Hi Community!
As you know we launched the InterSystems Open Exchange — the marketplace for solutions and tools on InterSystems Data Platforms!
But how to publish your application on OE?
Before we start, let me answer the few basic questions.
Last comment 2 October 2019
+ 4 2 3
336
views
+ 4
rating
### GraphQL for InterSystems Data Platforms
GraphQL is a standard for declaring data structures and methods of data access that serves as a middleware layer between the client and the server. If you’ve never heard about GraphQL, here is a couple of useful online resources: here, here and here.
In this article, I will tell you how you can use GraphQL in your projects based on InterSystems technologies.
Last comment 1 October 2019
+ 14 9 6
1135
views
+ 14
rating
### Caché eXTreme for .NET - direct access to globals from C#
InterSystems states that Caché supports at least three data models – relational, object and hierarchical (globals). On can work with data presented in relational model in a program written on C# the same way one works with any other relational DB. To work with data presented by object model in C# one needs to use .NET Managed Provider or some kind or ORM. And starting with version 2012.2 one can work directly with globals (or use direct access to hierarchical data) via Caché eXTreme for .NET
Last comment 20 September 2019
+ 4 2 6
765
views
+ 4
rating
If you’ve ever wondered whether there is a way to regulate access to resources in Caché, wonder no more. In version 2014.2 special classes were added that allow developers to work with semaphores.
Last comment 13 September 2019
+ 2 1 3
488
views
+ 2
rating
### Is there a function similar to Oracle's CDC in the cache database?
After enabling archiving log functions, Oracle can get real-time change data through CDC.
Can Cache database realize such functions?
My requirement is to take incremental data from the cache database regularly every day and synchronize it to other relational databases.
Incremental data can be text files.
+ 3 0 6
412
views
+ 3
rating
### How to get rid of JRNREST annoying questions?
I am still working on a generic task where I need to apply journal file records to another database. Initially I didn't want to use Journal.Restore class methods as I need to perform some data transformation, and it seemed that the clearest way to achieve it was to read journal file record by record using %SYS.Journal.Record API.
Last answer 16 June 2018 Last comment 28 August 2019
+ 2 0 3
209
views
+ 2
rating
HI,
I have been using evaluation version of Cache 2017.2, it was working fine and I was using Cache studio, SMP & Cache Terminal/console till yesterday.
Today, cache was in shutdown status, then I restarted. But, Cache terminal is not working and showing as Access Denied while otherthings like studio and SMP is working as expected. I checked all security level services on SMP, all are fine and enabled.
Can anyone help me to diagnose the problem and make it working.
Thanks.
Last answer 26 August 2019 Last comment 1 November 2018
0 0 6
562
views
0
rating
Good day,
Is there a way to change the theme in management portal? or at least the color of the header.
Issue is, some users have access to Development and Testing and Production environments. I would like a way to color-differentiate the environments to reduce the errors.
Last answer 1 August 2019 Last comment 1 August 2019
0 0 4
336
views
0
rating
### Cache Studio 2017.2
Hi all,
I hope this is the right forum to ask this type of question, but I'm running out of ideas.
For reasons beyond my control, we run a version of Intersystems Caché (2013.1) that is not supported by Atelier. As such, I use Caché Studio to do my development.
The issue I have is, I don't run Windows or MAC, but Linux (Ubuntu 18.04 in my case). I've successfully managed to get Studio working using Wine and pretty much everything is usable.
Last answer 4 June 2018 Last comment 26 July 2019
0 0 4
718
views
0
rating
### Get the complete exec statement for store procedure executed with SQL.OutboundAdapter
I am looking to get the exec statement when we call the SP with ..Adapter.ExecuteProcedure.
Set tSQLQuery="exec pSPName ? ? ?"
Last answer 11 July 2019 Last comment 17 May 2018
+ 1 0 2
189
views
+ 1
rating
### Has anyone used .NET Core EF with Caché?
What would a sample DbContext look like and how would you register the DbContext in the Startup.cs ConfigureServices method?
Last answer 10 July 2019 Last comment 10 July 2019
+ 1 0 5
333
views
+ 1
rating
### Caché-Python Binding doesn't work
Hello,
I'm trying to set Caché-Python Binding on Mac, but there is a problem.
I performed installation and configuration of Caché-Python binding module based on the manual (URL)
including setting of PATH and LD_LIBRARY_PATH in "bash_profile",
and they seems to be done successfully (there was no error in the process).
Last answer 30 August 2018 Last comment 25 January 2019
0 0 2
336
views
0
rating
### Terminal can not be connected.
■Setting up CACHÉ preferred connection server.
server name:localhost
port:1972
Telnetport:23
web server port:57772
CSP server instance:
comment:
■hosts
localhost 127.0.0.1
■os
windows10 (virtual box)
Last answer 25 September 2018 Last comment 23 January 2019
0 0 3
403
views
0
rating
### 2018.1 field test release notes
Can someone please correct this or direct me where the release notes could be found
Last answer 8 August 2018 Last comment 11 April 2019
0 0 3
224
views
0
rating
### Continuous Delivery of your InterSystems solution using GitLab - Part IV: CD configuration
In this series of articles, I'd like to present and discuss several possible approaches toward software development with InterSystems technologies and GitLab. I will cover such topics as:
Last comment 22 May 2019
+ 2 1 6
952
views
+ 2
rating
### Determine programmatically if unit tests failed
I needed to know programmatically if last ran failed or not.
After some exploring, here's the code:
ClassMethod isLastTestOk() As %Boolean
{
set in = ##class(%UnitTest.Result.TestInstance).%OpenId(^UnitTest.Result)
for i=1:1:in.TestSuites.Count() {
#dim suite As %UnitTest.Result.TestSuite
set suite = in.TestSuites.GetAt(i)
return:suite.Status=0 $$NO } quit$$\$YES
}
Last comment 13 April 2019
+ 1 1 4
298
views
+ 1
rating
### Replacing ZEN - Part 3 - Progress to date 01
Index to Articles
Hi All
It's been 6 weeks since my original article
- - - - -but I have been busy on this project
I have been looking at/thinking about a replacement for ZEN for around 12 months but only really started in depth 4 months ago.
Also been in IT for long enough that I can "get a feel" for a product/technology and make decisions accordingly without going into great detail.
Any new technology has a learning curve and I don't want to waste time and effort on something that won't fly.
And, as always, I am looking to minimise the learning curve as I want to concentrate on delivering business benefit.
Last comment 11 April 2019
+ 15 0 4
530
views
+ 15
rating
### Replacing ZEN - Index to articles
Hi All
This is the index to a series of articles I hope to create over the coming months.
ZEN and ZEN Mojo are no longer being actively developed by Intesystems - this is a great shame as it is a fine product that works so well for business applications.
However ZEN is a 15 year old product and I need a path forward to replace the ZEN UI with a supported development framework.
This article is an index of the other articles I have, or plan to write. - the articles will be subject to change as I develop my thoughts and climb the learning curve.
Last comment 5 April 2019
+ 12 0 7
795
views
+ 12
rating
### InterSystems Cache with Laravel (Eloquent) using ODBC
Hi Community
I have created a simple package that allows the use of Cache with the Laravel Framework.
From my initial testing everything seems to be operating smoothly but I would like to appeal to the PHP users in the community to help me improve this package.
For those of you out there who have time and would be interested in this, please visit the repo at https://github.com/jeandormehl/laracache
Last comment 25 March 2019
+ 4 3 3
306
views
+ 4
rating
### Querying ODBC SQL Server
Hi I've got a service setup to query a sql server via ODBC.
I've got all the parameters etc setup and everything is ok
My Query is
Last comment 22 March 2019
0 1 3
0
666
views
0
rating
### How to mimic selenium in cache object Script
Is it possible to mimic what selenium does like navigating to a site and logging in and filling out a form then logout in COS.I am trying to do that in COS using %Net.HttpRequest class or should I be using a different class the idea is to be able to call a web app login into it and fill out form and log out
Last answer 18 March 2019 Last comment 11 December 2018
0 0 3
238
views
0
rating
### %UnitTest.TestCase
I need to start doing unit testing for some of my code.
Why does it delete the unit testing class from Cache when I run the test?
Is there a way to turn this off?
Last answer 16 August 2018 Last comment 12 March 2019
0 0 6
346
views
0
rating
### Minimum Monitoring and Alerting Solution
InterSystems Data Platform includes utilities and tools for system monitoring and alerting, however System Administrators new to solutions built on the InterSystems Data Platform (a.k.a Caché) need to know where to start and what to configure.
This guide shows the path to a minimum monitoring and alerting solution using references from online documentation and developer community posts to show you how to enable and configure the following;
1. Caché Monitor: Scans the console log and sends emails alerts.
2. System Monitor: Monitors system status and resources, generating notifications (alerts and warnings) based on fixed parameters and also tracks overall system health.
3. Health Monitor: Samples key system and user-defined metrics and compares them to user-configurable parameters and established normal values, generating notifications when samples exceed applicable or learned thresholds.
4. History Monitor: Maintains a historical database of performance and system usage metrics.
5. pButtons: Operating system and Caché metrics collection scheduled daily.
Remember this guide is a minimum configuration, the included tools are flexible and extensible so more functionality is available when needed. This guide skips through the documentation to get you up and going. You will need to dive deeper into the documentation to get the most out of the monitoring tools, in the meantime, think of this as a set of cheat sheets to get up and running.
Last comment 11 March 2019
+ 10 5 4
831
views
+ 10
rating
### Continuous Delivery of your InterSystems solution using GitLab - Part II: GitLab workflow
In this series of articles, I'd like to present and discuss several possible approaches toward software development with InterSystems technologies and GitLab. I will cover such topics as:
• Git 101
• Git flow (development process)
• GitLab installation
• GitLab Workflow
• Continuous Delivery
• GitLab installation and configuration
• GitLab CI/CD
In the previous article, we covered Git basics, why a high-level understanding of Git concepts is important for modern software development, and how Git can be used to develop software. Still, our focus was on the implementation part of software development, but this part presents:
• GitLab Workflow - a complete software life cycle process - from idea to user feedback
• Continuous Delivery - software engineering approach in which teams produce software in short cycles, ensuring that the software can be reliably released at any time. It aims at building, testing, and releasing software faster and more frequently.
Last comment 1 March 2019
+ 5 0 4
1363
views
+ 5
rating
### Copy csv data into a global object
Hi, I have a CSV file with a list of 5000 records in the following format
Name, Acc, division
Eric, 1234, 567
John, 1235, 987
Peter, 3214, 879
I just want to copy the Acc, division to a global so eventually the global would be like the following:
^People("Customers", "Acc.division")
Can you advice on how I can perform this from the terminal? This is a one time task. I want to read all the values from the csv file and insert them into the global
Regards,
Eric
Last answer 26 February 2019 Last comment 19 November 2018
0 0 6
334
views
0
rating
### Rest return 500 error
I have an application which is distributed across maybe 5 servers since it has over a thousand users at a time we had an upgrade to the application last week and I had an integration build that uses the REST service ( ##class(%Net.HttpResponse) but since the upgrade the integration has not be able to communicate with the application tried testing my URL through Postman and all seems ok but if I test direct I get a 500 error anything that I need to check on please or any advice on how to check what's going on.
Last answer 3 December 2018 Last comment 18 February 2019
0 0 2
140
views
0
rating
### csession with ##class command on a Windows machine
Hi community.
I'm trying to create a "setup" method to be called on a batch script but i'm getting the error <INVALID ARGUMENT> when I pass a string as an argument to this method.
The idea is to call the method with a folder as the parameter, for example:
##class(test.MyClass).MyMethod("D:\path\to\my\file.json")
My class (just for example)
Class test.MyClass
Last answer 31 October 2018 Last comment 14 February 2019
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# Inconsistent integration results using expressions and unexplained imaginary numbers
Consider the following code (Mathematica 8):
mu1 = -1.0; mu2 = 1.0; ss1 = 1; ss2 = 4; cov = 1;
bivModel =
MultinormalDistribution[{mu1, mu2}, {{ss1, cov}, {cov, ss2}}]
myFun[x_, y_] := PDF[bivModel, {x, y}];
a = -2.7; b = 1.6;
yVec = D[myFun[x, y], y];
xVec = D[myFun[x, y], x]
m = (mu2 - b)/(mu1 - a)
c = mu2 - m*mu1
expr3[z_] := (-xVec //. {x -> z, y -> (m*z + c)})/(yVec //. {x -> z,
y -> (m*z + c)})*(x - z) + m*z + c
Using the straight line defined by expr, I want to evaluate a double integral which I do in two steps under Method 1:
Part1F[x_Real, z_Real] :=
Integrate[PDF[bivModel, {x, y}], {y, expr3[z], Infinity}]
Part2F[z_Real] := NIntegrate[Part1F[x, z], {x, -Infinity, Infinity}]
So for example when I type in
Part2F[1.0]
I get a series of error messages and a result of 0.805675 - 1.96891*10^-18 I.
The errors are:
NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>
NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections in x near {x} = {-1.69485}. NIntegrate obtained 0.805675 -1.96891*10^-18 I
and 0.0005750462582540412 for the integral and error estimates. >>
But under Method 2 when I type in:
Part1K[x_Real, z_Real] :=
Integrate[
PDF[bivModel, {x, y}], {y,
11/17 - (6 z)/17 -
1/(2/3 (6/17 + (6 z)/17) + (2 (1 + z))/3) E^(
1/2 (-(1/3 (-1 - z) + 1/3 (-(6/17) - (6 z)/17)) (-(6/17) - (6 z)/
17) - (1 + z) (1/3 (6/17 + (6 z)/17) + (4 (1 + z))/3)) +
1/2 ((1/3 (-1 - z) + 1/3 (-(6/17) - (6 z)/17)) (-(6/17) - (6 z)/
17) + (1 + z) (1/3 (6/17 + (6 z)/17) + (4 (1 + z))/
3))) (x - z) (2/3 (-(6/17) - (6 z)/17) - (8 (1 + z))/3),
Infinity}]
(obtained by pasting in the expansion of exp3[z] into the expression for Part1F) and
Part2K[z_Real] := NIntegrate[Part1K[x, z], {x, -Infinity, Infinity}]
Part2K[1.0]
I get no errors and a result of 0.994423 - 8.13629*10^-21 I.
If under Method 3 I simply start off with a value of z of 1.0 and use the following code:
Part1H[x_Real] :=
Integrate[
PDF[bivModel, {x, y}], {y,
0.29411764705882343 + 3.2173913043478257 (-1. + x), Infinity}]NIntegrate[Part1H[x], {x, -Infinity, Infinity}]
I get:
0.994423 - 8.13629*10^-21 I
Questions:
1. Why am I getting different results between the first method and the second and third?
2. I want to be able to vary the value of z and indeed the value of m. Is there a way of keeping this functionality? The formulae for Part1F and Part2F are the closest I can get to this but I have more confidence in the results from Part1G and Part2G and Part 1H and its integral.
3. I am calculating an integral of the bivariate Normal distribution. Why on earth am I getting imaginary numbers (albeit very small)?
• The small imaginary part in your results come from using machine arithmetic in your computations. Look up Chop in documentation to see how eliminate them. Or rework your computations to use exact or arbitrary precision arithmetic. Dec 4 '18 at 22:38
• Thanks, will give that a go! Dec 5 '18 at 9:29
\$Version
(* "11.3.0 for Mac OS X x86 (64-bit) (March 7, 2018)" *)
Clear["Global*"]
To avoid imaginary artifacts resulting from calculating with machine precision, use exact numbers when possible and Simplify intermediate results. (EDIT: Unless told otherwise, Mathematica operates in the complex plane. Calculations which would cancel the imaginary components if done exactly, can result in imaginary artifacts when done with machine precision.)
mu1 = -1; mu2 = 1; ss1 = 1; ss2 = 4; cov = 1;
bivModel = MultinormalDistribution[{mu1, mu2}, {{ss1, cov}, {cov, ss2}}];
myFun[x_, y_] := Evaluate@Simplify@PDF[bivModel, {x, y}]
a = -27/10; b = 8/5;
{xVec, yVec} = D[myFun[x, y], {{x, y}}] // Simplify;
m = (mu2 - b)/(mu1 - a);
c = mu2 - m*mu1;
expr3[z_] :=
Evaluate@Simplify[(-xVec /. {x -> z, y -> (m*z + c)})/(yVec /. {x -> z,
y -> (m*z + c)})*(x - z) + m*z + c]
Note the simplified form of expr3
expr3[z]
(* 1/391 (253 + 1258 x - 1396 z) *)
Since you are using SetDelayed in defining Part1F, use Evaluate so that the integration is only done once rather than for each evaluation of Part1F
Part1F[x_, z_] :=
Evaluate@Integrate[PDF[bivModel, {x, y}], {y, expr3[z], Infinity}]
Part1F[x, z]
(* (E^(-(1/2) (1 + x)^2) (1 +
Erf[(529 - 867 x + 1396 z)/(391 Sqrt[6])]))/(2 Sqrt[2 π]) *)
Part2F[z_Real] := NIntegrate[Part1F[x, z], {x, -Infinity, Infinity}]
sol1 = Part2F[1.0]
(* 0.994423 *)
Part1K[x_, z_] :=
Evaluate@Integrate[
PDF[bivModel, {x, y}], {y,
11/17 - (6 z)/17 -
1/(2/3 (6/17 + (6 z)/17) + (2 (1 + z))/
3) E^(1/2 (-(1/3 (-1 - z) +
1/3 (-(6/17) - (6 z)/17)) (-(6/17) - (6 z)/17) - (1 +
z) (1/3 (6/17 + (6 z)/17) + (4 (1 + z))/3)) +
1/2 ((1/3 (-1 - z) +
1/3 (-(6/17) - (6 z)/17)) (-(6/17) - (6 z)/17) + (1 +
z) (1/3 (6/17 + (6 z)/17) + (4 (1 + z))/3))) (x -
z) (2/3 (-(6/17) - (6 z)/17) - (8 (1 + z))/3), Infinity}]
The integrals are identical
Part1K[x, z] === Part1F[x, z]
(* True *)
Part2K[z_Real] := NIntegrate[Part1K[x, z], {x, -Infinity, Infinity}]
sol2 = Part2K[1.0]
(* 0.994423 *)
The results are identical
sol1 === sol2
(* True *)
`
• Thank you - this is extremely useful. Dec 10 '18 at 20:58
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真力 40 周年，感谢有你下一个 40 年，也愿与你相伴
It starts with an idea.
And then grows from here.
他们对真力说
来自福州的谢先生：“你的声音令我活在真实中
让灵感的火花，带你一路前行。
It starts with an idea, and then grows from here.
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# AGICLOVIR®800
Composition: Each tablet contains:<br/>
Aciclovir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 800 mg<br/>
Presentation: Box of 2 blisters x 10 tablets.<br/>
Indications:<br/>
Treatment of Varicella zoster virus infection (chickenpox) and Herpes zoster virus (shingles) (excluding neonatal HSV and severe HSV infections in immunocompromised children).<br/>
Agiclovir 800 is recommended for use only in children over 6 years of age.
error: Không được phép!
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## Credits & Info
Aug 16, 2014 | 5:48 PM EDT
File Info
Song
21.6 MB
9 min 27 sec
Score
4.87 / 5.00
## Licensing Terms
Please contact me if you would like to use this in a project. We can discuss the details.
Score:
Rated 4.87 / 5 stars
Genres:
Electronic - Video Game
Tags:
chiptune
buttz
chip-butties
defoyomamma
Blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah
## Reviews
#### EDM364
##### Rated 3.5 / 5 stars2017-02-03 03:47:21
Pretty good song. Mixing and panning is where it falls flat, as well as perc and overall leveling. The highs and pads are totally overpowering your atmosphere and drowning out the bass, taking a 4.5 star song down to a 3.5 for me.
Your writing is good, but a lot of your song is buildup, and repeated phrases. You could use a lot more velocity meddling on adjacent notes as well. I see lots of FX and pitch bending, but these should really be afterthoughts once you handle your arrangement. As is, it's a lot of repeated phrases that feel like they go nowhere fast and it feels quite samey. You've got some very imaginative melodies but it takes FOREVER and a day to hear them.
Anyway, minus that, good song, and I enjoyed it. You've got some talent, but remember -- melody comes first. FX comes second. Mixing comes finally.
capsule69 responds:
Thanks so much for such a detailed and critical review.
It's rare that people will give you an honest opinion in fear of hurting feelings along the way.
I feel like I've made progress with my mixes, which is definitely something I've been aware of for sometime.; but I'll look into melody work too.
Cheers
#### ap0kalyps3
##### Rated 5 / 5 stars2015-03-05 02:44:53
Hey dude, heard your song and it's amazing.
Also I used it for the endcard of my Shadow Warrior Let's Play because I thought it fits.
Check it out, I hope you like it :)
capsule69 responds:
Awesome!
Glad you like the song and thanks for the kind words.
you guys are crazy.
O.o - extreme
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# A box with an initial speed of 2 m/s is moving up a ramp. The ramp has a kinetic friction coefficient of 3/4 and an incline of (5 pi )/8 . How far along the ramp will the box go?
Jul 11, 2017
The distance travelled is $\frac{1}{3} m$
#### Explanation:
We have to find first the retardation of rhe object.
We have already got the retardation of the object.
Hence we have to put the formula
${v}^{2} = {u}^{2} - 2 a s$ where v,u,a & s are respectively final velocity, initial velocity, retardation and displacement.
Here,$u = 2 , v = 0 , a = 6 m {s}^{-} 2$
So,
2^2=2×6×s
$s = \frac{1}{3}$
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# A note on fractional supersolutions
created by palatucci on 29 Oct 2016
[BibTeX]
Published Paper
Inserted: 29 oct 2016
Last Updated: 29 oct 2016
Journal: Electron. J. Differential Equations
Volume: 2016
Number: 263
Pages: 1-9
Year: 2016
We study a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order $s \in (0,1)$ and summability growth $p>1$ whose model is the fractional $p$-Laplacian with measurable coeffcients. We prove that the minimum of the corresponding weak supersolutions is a weak supersolution as well.
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Math Help - Quadrilateral
Here's the picture(I know I suck at paint):
Any help would be appreciated.
Originally Posted by RuyHayabusa
Here's the picture(I know I suck at paint):
Any help would be appreciated.
Hello
1. I've modified your sketch a little bit (see attachment): I refer to the labels of my sketch.
2. Use Pythagorian theorem and Cosine rule: You'll get 4 equations:
• $d^2=7^2+y^2$
• $d^2=x^2+4^2-2\cdot 4 \cdot x \cdot \cos(60^\circ)$
• $s^2=4^2+y^2-2 \cdot 4 \cdot y \cdot \cos(150^\circ)$
• $s^2=x^2+7^2-2 \cdot 7 \cdot x \cdot \cos(60^\circ)$
3. With $\cos(60^\circ)=\frac12$ and $\cos(150^\circ)=-\frac12 \cdot \sqrt{3}$ you'll get rid of the trigonometric functions.
4. The calculations are really ugly und you'll get many opportunities to make mistakes. For conformation only:
$(x,y,d,s)=(10,3\sqrt{3},2\sqrt{19},\sqrt{79})$
Originally Posted by earboth
Hello
1. I've modified your sketch a little bit (see attachment): I refer to the labels of my sketch.
2. Use Pythagorian theorem and Cosine rule: You'll get 4 equations:
• $d^2=7^2+y^2$
• $d^2=x^2+4^2-2\cdot 4 \cdot x \cdot \cos(60^\circ)$
• $s^2=4^2+y^2-2 \cdot 4 \cdot y \cdot \cos(150^\circ)$
• $s^2=x^2+7^2-2 \cdot 7 \cdot x \cdot \cos(60^\circ)$
3. With $\cos(60^\circ)=\frac12$ and $\cos(150^\circ)=-\frac12 \cdot \sqrt{3}$ you'll get rid of the trigonometric functions.
4. The calculations are really ugly und you'll get many opportunities to make mistakes. For conformation only:
$(x,y,d,s)=(10,3\sqrt{3},2\sqrt{19},\sqrt{79})$
Thanks,but I can't go anywhere from d^2=y^2+49=x^2-4x+16 , s^2=x^2-7x+49 = y^2+4*sqrt(3)*y
A few pointers please?
Originally Posted by RuyHayabusa
Thanks,but I can't go anywhere from d^2=y^2+49=x^2-4x+16 , s^2=x^2-7x+49 = y^2+4*sqrt(3)*y
A few pointers please?
This quadrilateral is a truncated equilateral triangle and a geometric solution leads to x =10 .Truncated section has two parts. A 30-60 -90 triangle and a regular trapozoid
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# Is this transformation problem doable?
1. Feb 8, 2012
### mimsy57
We've been talking about Mobius transformations and I feel like I get it, but we just got a homework problem that isn't making sense to me.
It says: find the Mobius transformation taking the circle |z|=1 to |z+2|=1 such that T(-1)=-3 and T(i)=-1.
My problem with this is that all Mobius trans. are the composition of translations, rotations, dilations and inversions. But this SEEMS like it is doing something else because, unless I am screwing up the graphing, it is taking a quarter circle to a half circle.
Both the circle and its image have radius 1, with the first centered at the origin and the second at -2. The additional points we are given mappings for are -1 and i, which are the endpoints to an arc of a quarter circle. These are mapping to -3 and -1 which are the bounds for the half circle. This implies the mapping is going around twice for once around the circle being mapped, which would imply it is not a bijection, and Mobius transformations are bijections.
It would be great if someone could point out where I am doing something wrong in my reasoning! I don't think I need any help with the calculation part once I figure this out.
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How do you find a real-life situation that you could represent with the inequality -2<x<8?
It is now the middle of winter and today's temperature (let's call it $x$) is not going to reach 8 degrees today and may approach a low of -2 degrees.
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# Citing a published book that does not appear on MathSciNet
I want to cite some theorems in Several complex variables. VII by H. Grauert, Th. Peternell, and R. Remmert (eds.). It is a book published in 1994. However, I searched the publication lists of all of the three authors on MathSciNet, this book is not there.
Instead, certain chapters (but not all!) of the book do appear on MathSciNet authored independently, for example,
$$\bullet$$ Dethloff, G.; Grauert, H. Seminormal complex spaces. Several complex variables, VII, 183–220, Ency-clopaedia Math. Sci., 74, Springer, Berlin, 1994. (note a different author appear)
$$\bullet$$ Remmert, R. Local theory of complex spaces. Several complex variables, VII, 7–96, Encyclopaedia Math.Sci., 74, Springer, Berlin, 1994.
I'm wondering should I cite these chapters or the original book even if it does not appear on MathSciNet, or maybe both?
• I don't understand the question: it's of course appropriate to cite things that don't appear in MathSciNet (which is broad but not exhaustive). – Sam Hopkins 2 days ago
• In general if a book is really a collection of different articles by different authors, you should cite the particular article you are referencing. In BibTex I'm pretty sure the right citation type is "incollection." – Sam Hopkins 2 days ago
• In fact for the book you want, it's online here: link.springer.com/book/10.1007/978-3-662-09873-8. And if you click any particular article in it, there's a little button at the top which says "Cite as" that tells you exactly how to cite it. – Sam Hopkins 2 days ago
• By the way you could check ZBmath too. – YCor 2 days ago
• If you click on the MR entry for either of the two chapters you list you will see the text "{For the collection containing this paper see MR1326617.}", and the MR number is actually a link that takes you to the entry for the book (the one listed in Francois's answer. – Andrés E. Caicedo 2 days ago
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Determining whether sets of matrices in a vectorspace are linearly independent?
1. Jul 22, 2011
n00bot
Given matrices in a vectorspace, how do you go about determining if they are independent or not?
Since elements in a given vectorspace (like matrices) are vector elements of the space, I think we'd solve this the same way as we've solved for vectors in R1 -- c1u1 + c2u2 + c3u3 = 0. But I'm not sure I'm setting it up right. I assume that three 2x2 matrices in r2, for example: (a,b;c,d), (e,f; g,h), (i,j;k,l) where a semi-colon denotes a new line, would be set up like this:
a e i
b f j
c g k
d h l
Am I understanding this correctly?
2. Jul 22, 2011
tiny-tim
hi n00bot!
yes, that's correct
checking independence only involves scalar multiplication,
so the matrix structure is irrelevant, and you can treat the matrix components as if they were just vector components
3. Jul 22, 2011
n00bot
OK, great! Thanks very much for the explanation :)
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# Pitfalls and limitations¶
As the OGGM project is gaining visibility and momentum, we also see an increase of potential misuse or misunderstandings about what OGGM can and cannot do. Refer to our FAQ and Troubleshooting for a general introduction. Here, we discuss specific pitfalls in more details.
## The default ice dynamics parameter “Glen A” is roughly calibrated¶
Out-of-the box, non-preprocessed OGGM will use fixed values for the creep parameter $$A$$ and the sliding parameter $$f_s$$:
In [1]: from oggm import cfg
In [2]: cfg.initialize()
In [3]: cfg.PARAMS['glen_a']
Out[3]: 2.4e-24
In [4]: cfg.PARAMS['fs']
Out[4]: 0.0
That is, $$A$$ is set to the standard value for temperate ice as given in [Cuffey_Paterson_2010], and sliding is set to zero. While these values are reasonable, they are unlikely to be the ones yielding the best results at the global scale, and even more unlikely at regional or local scales. In particular, in the absence of sliding parameter, it is recommended to set $$A$$ to a higher value to compensate for this missing process (effectively making ice “less stiff”).
New in version 1.4!
Since v1.4, OGGM can now calibrate $$A$$ based on the consensus from [Farinotti_etal_2019] on any number of glaciers. We recommend to use a large number of glaciers: OGGM’s default glacier directories are calibrated at the RGI region level. This value is then also used by the forward dynamical model for consistency, according to the parameter use_inversion_params_for_run.
The pre-processed directories at level 3 to 5 are already calibrated to the consensus estimate at the RGI region level, i.e. unless specified otherwise, OGGM will use the pre-calibrated $$A$$ value for these glaciers.
There is a way to calibrate $$A$$ for the ice thickness inversion procedure based on observations of ice thickness (see this blog post about g2ti for an example). At the global scale, a value in the range of [1.1-1.5] times the default value gives volume estimates close to [Farinotti_etal_2019]. At regional scale, these values can differ, with a value closer to a factor 3, for example for the Alps. Note that this depends on other variables as well, such as our estimates of solid precipitation amounts (i.e mass turnover). This makes things complicated, as regions with overestimated solid precipitation can be compensated by a higher $$A$$, and the other way around.
Finally, note that a change in $$A$$ has a very strong influence for values close to the default value, but this influence reduces to the power of 1/5 for large values of A (in other words, there is a big difference between values of 1 to 1.3 times the default $$A$$, but a comparatively small difference for values between 3 to 5 times the default $$A$$). This is best shown by this figure from [Maussion_etal_2019]:
Global volume estimated as a function of the multiplication factor applied to the ice creep parameter A, with five different setups: defaults, with sliding velocity, with lateral drag, and with rectangular and parabolic bed shapes only (instead of the default mixed parabolic/rectangular). In addition, we plotted the estimates from standard volume–area scaling (VAS, $$V = 0.034 S^{1.375}$$), Huss and Farinotti (2012) (HF2012) and Grinsted (2013) (G2013). The latter two estimates are provided for indication only as they are based on a different glacier inventory
Now, what you are probably asking yourself: how to choose the “best A” for my application?
Sorry, but we don’t know yet. We are working on it though! At the moment, what we recommend to do is to calibrate $$A$$ so that the regional (or even local) estimates match the volume consensus of Farinotti et al. (2019) using the workflow.calibrate_inversion_from_consensus() global task. This is what we do for the default pre-processed directories at the RGI region level, so that you don’t have to worry about it.
## The numerical model in OGGM is numerically unstable in some conditions¶
OGGM uses a CFL criterion to decide on the timestep to use during the ice dynamics model iteration. The numerical scheme of OGGM is fast and flexible (e.g. it allows to compute the ice flow on multiple flowlines), but it is not following textbook recommendations on numerical stability.
See this github issue for a discussion pointing this out, and this example.
As of OGGM v1.2, we have fixed the most pressing issues. This blog post explains it in detail, but for a summary:
• the old algorithm was flawed, but did not result in significant errors at large scales
• the new algorithm is faster and more likely to be stable
• we don’t guarantee statibility in 100% of the cases, but when the model becomes unstable it will raise an error.
We test OGGM for mass-conservation in several use cases. What might happen, however, is that the calculated velocities display “wobbles” or artifacts, which are a sign of instability. If this occurs, set the global parameter cfg.PARAMS['cfl_number'] to a lower value (0.01 or 0.005 are worth a try).
## References¶
Farinotti_etal_2019(1,2)
Farinotti, D., Huss, M., Fürst, J. J., Landmann, J., Machguth, H., Maussion, F. and Pandit, A.: A consensus estimate for the ice thickness distribution of all glaciers on Earth, Nat. Geosci., 12(3), 168–173, doi:10.1038/s41561-019-0300-3, 2019.
Maussion_etal_2019
Maussion, F., Butenko, A., Champollion, N., Dusch, M., Eis, J., Fourteau, K., Gregor, P., Jarosch, A. H., Landmann, J., Oesterle, F., Recinos, B., Rothenpieler, T., Vlug, A., Wild, C. T. and Marzeion, B.: The Open Global Glacier Model (OGGM) v1.1, Geosci. Model Dev., 12(3), 909–931, doi:10.5194/gmd-12-909-2019, 2019.
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Documentation
Project Setup
# Creating or Integrating ArrayFire into Your Projects
The goal of ArrayFire is to not only work well with your code, but be extremely easy to integrate into your projects. This page lists the steps required to create a project for ArrayFire from scratch. User can also refer to this page to see how to integrate ArrayFire into an existing project by looking at the include directories and libraries sections.
For further configuration settings, you can refer to the examples.
# On Windows using Visual Studio
## Setting up Environment Variables
• Before beginning, check that the AF_PATH and CUDA_PATH variables are defined in environment variables and point to the correct directories.
• Also ensure that AF_PATH/lib64 and CUDA_PATH/bin are a part the PATH variable.
## Creating the Project and Configuring for 64-bit
1. Open Visual Studio and click File -> New -> Project.
2. You can create either a C/C++ project or a CUDA project. The CUDA project gives the option to have custom CUDA code in the project. If you are using OpenCL, create a regular C/C++ project.
3. Enter the project name and location of your preference.
4. ArrayFire works only with 64-bit. To set this as active, go to Build -> Configuration Manager.
5. In the Configuration Manager, click the "Active Solution Platforms" drop down and choose "x64".
1. Right click the project and open "Properties". Here, you may want to select the active platform and configurations from the drop downs or select all configurations.
2. If you are using a regular C/C++ project (or using OpenCL), go to Configuration Properties -> C/C++ -> General. If you are using a CUDA project, go to Configuration Properties -> CUDA C/C++ -> Common
• In "Additional Include Directories" enter:
• For CUDA : "$(AF_PATH)\include;$(CUDA_PATH)\include;"
• For OpenCL: "$(AF_PATH)\include;" 3. If you are using a CUDA C/C++ project, you may want to set the compute version of your GPU (optional). • Go to Configuration Properties -> CUDA C/C++ -> Device. Enter your compute version in "Code Generation". You may find out more about the compute version of you card at: https://developer.nvidia.com/cuda-gpus ## Adding Libraries 1. Right click the project and open "Properties". Here, you may want to select the active platform and configurations from the drop downs or select all configurations. 2. Go to Configuration Properties -> Linker. • Go to the General tab. In "Additional Library Directories" enter: • For CUDA : "$(AF_PATH)\lib64;$(CUDA_PATH)\lib\x64;" • For OpenCL: "$(AF_PATH)\lib64;"
• Go to the Input tab. In "Additional Dependencies" enter
• For CUDA : "cuda.lib;cudart.lib;libafcu.lib;"
• For OpenCL: "libafcl.lib;clBLAS.lib;clFFT.lib;OpenCL.lib;"
cuda_libs.png
## Preprocessor Definitions
1. This step is only for OpenCL. Go to Configuration Properties -> C/C++ -> Preprocessor. Add "AFCL;" to Preprocessor Definitions.
# On Linux
## Setting up Environment Variables
• ArrayFire requires that AF_PATH environment variable be set prior to compilation. The easiest way to set up these is using a script file like a bashrc.
• If using ArrayFire CUDA version, ArrayFire also requires CUDA_PATH environment variable to be set up. This should point to the location of the CUDA installation.
• It is also required to set up the LD_LIBRARY_PATH variable.
An example set up of these variable is as below. The actual directories may differ.
export AF_PATH=/opt/arrayfire-2.0
export CUDA_PATH=/usr/local/cuda
export LD_LIBRARY_PATH=$CUDA_PATH/lib/:$LD_LIBRARY_PATH
export LD_LIBRARY_PATH=$CUDA_PATH/lib64/:$LD_LIBRARY_PATH
export LD_LIBRARY_PATH=$AF_PATH/lib64/:$LD_LIBRARY_PATH
## Choosing the Compiler and Configuring for 64-bit
• If you are using ArrayFire with just C/C++ or using ArrayFire OpenCL, use the gcc/g++ compiler. If you are using ArrayFire with custom CUDA code, use the nvcc compiler. NVCC is required only for files using CUDA. GCC/G++ may be used for other files.
• Use the -m64 option to compile 64-bit if using ArrayFire 64-bit.
• If using CUDA, add the flags : "-I$AF_PATH/include -I$CUDA_PATH/include"
• If using OpenCL, add the flags: "-I$AF_PATH/include" ## Adding Libraries • Add the flags: "-L$AF_PATH/lib64"
• If using CUDA, add the flags : "-lafcu -L\$CUDA_PATH/lib64 -lcuda -lcudart"
• If using OpenCL, add the flags: "-lafcl"
• If using gcc, add the flags : "-lstdc++"
## Preprocessor Definitions
• This step is only for OpenCL. Add the "-DAFCL" flag to the compiler command.
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# Quiz
#### TopicsQuantitative AptitudePipes and Cisterns
Question:
1. There is a leak in the bottom of a cistern. Before the leak, it could be filled in $$3\frac{1}{2}$$ hours, it now takes $$\frac{1}{2}$$ hour longer. If the cistern is full, the time taken to empty the cistern would be
Options:
A. 24 hr. B. 28 hr. C. 32 hr. D. 34 hr.
Earn Reward Points by submitting Detailed Explaination for this Question
### More Questions on This Topic :
Question 1.
1. If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
Options:
1. 10 hr.
2. 15 hr.
3. 15 hr.
4. 20 hr.
Question 2.
1. A tap can fill a cistern in 6 hours, but due to a leakage at the bottom of the cistern, it takes 1 hours more to fill it. If the cistern is full and the tap is turned off, in what time will the leakage empty the cistern?
Options:
1. 30 hr.
2. 32 hr.
3. 34 hr.
4. 36 hr.
Question 3.
A pipe can fill a cistern in 12 minutes and another pipe can till it in 15 minutes. But a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 minutes in the beginning and then the third pipe is also opened. In what time is the cistern emptied?
Options:
1. 35 min.
2. 40 min.
3. 45 min.
4. 50 min.
Question 4.
1. A filler pipe can fill $$\frac{1}{6}^{th}$$ of a cistem in 10 minutes. In how many minutes, can it fill $$\frac{5}{8}^{th}$$ of the cistern?
Options:
1. 37 min.
2. 37.5 min
3. 38 min
4. 38.5 min.
Question 5.
1. An outlet pipe can empty $$\frac{2}{3}^{rd}$$ of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
Options:
1. $$\frac{2}{3}$$
2. $$\frac{3}{2}$$
3. $$\frac{4}{9}$$
4. $$\frac{9}{4}$$
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## Joint density of two random variables
Hello everyone,
I have this problem I can't quite figure out. I am considering the sample space $\displaystyle S$ being the unit circle without the boundary for $\displaystyle x > 0$.
The usual measure $\displaystyle \mu(\: \cdot \: )$ and $\displaystyle \sigma-algebra$ F. Probability is defined as being proportional the area of $\displaystyle A \in F$.
I am then to find the joint CDF for $\displaystyle R_1(x,y) = x \leq c_1$ and $\displaystyle R_2(x,y) = y \leq c_2$ for $\displaystyle c_1 \in (0,1)$ and $\displaystyle b \in (-1,1)$
This leads me to the following:
$\displaystyle P(R_1 \leq c_1 \land R_2 \leq b) = F_{R_1 R_2} (c_1,c_2)= \frac{\mu(A_{R_1 R_2})}{\mu(S)} = \frac{2}{\pi} \begin{cases} \int \limits_{-1}^{-\sqrt{1-c_1^2}} \int \limits_{0}^{\sqrt{1-y^2}} 1 dxdy + \int \limits_{0}^{c_1} \int \limits_{-\sqrt{1-c_1^2}}^{c_2} 1 dydx & c_2 > - \sqrt{1- {c_1}^2} \\ \frac{1}{2} + \frac{c_2 \sqrt{1-c_2^2}}{\pi} + \frac{\sin^{-1}(c_2)}{\pi}& otherwise \end{cases}$
However, I am not sure how to very I find the correct distribution. And it seems odd that the area are give by such messy expressions.
Kind Regards
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# ellipse 2
• November 15th 2010, 07:41 AM
prasum
ellipse 2
if a quadrilateral formed by tangents to the ellipse (x^2/9)+(y^2/4)=1 is a square then area of the quadrilateral is
• November 15th 2010, 11:41 AM
Opalg
Hint: draw a picture of the ellipse. It should be clear from the picture that the tangents should make angles $\pi/4$ with the axes, and that the vertices of the square will lie on the coordinate axes.
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# Differential Amplifier Common-mode Output Resistance
1. Jun 4, 2013
### hisotaso
1. The problem statement, all variables and given/known data
I am learning about differential amplifiers, and am having trouble determining the common-mode output resistance. In the text, we have the two sections "Differential-mode gain and input and output resistances" and "Common-mode gain and input resistance." Notice the lack of common mode output resistance.
The only place I can find reference to common-mode output resistance is in the section "Two-port model for differential pairs", and it is given by Roc =~ 2*μf*Ree (in this section, no derivations are shown). At the end of this section is an "Exercise", and it asks for Rod and Roc. Rod = 3.2MΩ and Roc = 4.8GΩ. In other words, Roc is much bigger.
Now, in the homework problem I am working on, VA is given as infinite, which means ro =~ VA/Ic is infinite, which means μf = gm*ro is infinite. However, in the solutions (authors solution manual) given my prof., Roc is given as Rc/2 which is much less than Rod (in this problem Rod =~ 2*Rc = 94kΩ, and and the given solution to Roc = Rc/2 = 13.5kΩ).
So my question is: what is Roc? I have googled around a bit and have not been able to find any reference to it. I would be happy with a link to a derivation (preferable actually) as opposed to just an expression, though at this point any help would be appreciated.
2. Relevant equations
3. The attempt at a solution
2. Jun 4, 2013
### hisotaso
Ok well I have a line or reasoning that I think works out, please correct me if this is invalid.
Roc=$\frac{voc}{ic1+ic2}$
ic1=ic2=ic
=$\frac{\frac{vc1+vc2}{2}}{2ic}$
=$\frac{\frac{ic*Rc1+ic*Rc2}{2}}{2ic}$
Rc1=Rc2=Rc
=$\frac{ic*Rc+ic*Rc}{2*2ic}$
=$\frac{2Rc}{4}$
=$\frac{Rc}{2}$
Last edited: Jun 4, 2013
3. Jun 4, 2013
### hisotaso
Don't know why itex isn't working, at least on my end...
4. Jun 4, 2013
### The Electrician
Don't use itex; it's just tex. And, don't use the SUB /SUB construct within tex (but you can use it in the non-tex ordinary part of your post); use the underline prefix instead. For example your first tex expression should be like this:
Roc=$$\frac{v_{oc}}{i_{c1}+i_{c2}}$$
That didn't work out as intended. It looks like you get an extra carriage return when following the non-tex part with some tex. Maybe you should put everything inside tex:
$$R_{oc}=\frac{v_{oc}}{i_{c1}+i_{c2}}$$
5. Jun 4, 2013
### The Electrician
Maybe you should ask your instructor what the definition of common mode output impedance is.
If you put an AC short (a big capacitor) between the differential outputs and calculate the impedance from that point to ground, I think you get the result you quote for Roc.
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# plot_projections¶
gala.dynamics.plot_projections(x, relative_to=None, autolim=True, axes=None, subplots_kwargs={}, labels=None, plot_function=None, **kwargs)[source]
Given N-dimensional quantity, x, make a figure containing 2D projections of all combinations of the axes.
Parameters: x : array_like Array of values. axis=0 is assumed to be the dimensionality, axis=1 is the time axis. See Array shapes for more information. relative_to : bool (optional) Plot the values relative to this value or values. autolim : bool (optional) Automatically set the plot limits to be something sensible. axes : array_like (optional) Array of matplotlib Axes objects. subplots_kwargs : dict (optional) Dictionary of kwargs passed to subplots(). labels : iterable (optional) List or iterable of axis labels as strings. They should correspond to the dimensions of the input orbit. plot_function : callable (optional) The matplotlib plot function to use. By default, this is scatter(), but can also be, e.g., plot(). **kwargs All other keyword arguments are passed to the plot_function. You can pass in any of the usual style kwargs like color=..., marker=..., etc. fig : Figure
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## Latex Error Option Clash For Package Xcolor Rmd
저 간격을 조절하고 싶습니다. Note that loading of a4wide is deprecated (and also dubious, as the nips package sets the page geometry), while subfigure is obsolete. See full list on overleaf. titlesec과 titletoc로 헤더와 toc를 꾸며서 사용하려고 하는데 뜻대로 안되는 게 있습니다. tex % % memman. 79k Hypertext links for LaTeX ifxetex. info, Node: Additional packages, Next: Class and package construction, Prev: Document class options, Up: Document classes 3. } % Thirdly, two \BibTeX\ style files are included. Package xcolor Info: Model Gray' substituted by gray' on input line 1370. Q: Latex error: option clash for package XXX (mostly xcolor) A:xcolor is incompatible with tikz, graphicx, etc. 12 * New features: - opagecolor command as introduced in color' v1. The first two warning messages may disappear upon completing the compilation of the input file as discussed in § 14. Time for action – listing LaTeX packages We shall create a list of packages that we got to know in the previous chapter: 1. I am writing a chinese report. Please see package vignette for more information. Or name \end illegal. Information on these, ifyou want it, is obtained from reading the LaTeX source itself and the TeXbook, and perhapsone of the free TeX manuals such as TeX for the Impatient [AHK90] or TeX by Topic [Eij92]. A typical place according to the TEX Directory Structure (TDS) would be the directory texmf/tex/latex/xcolor, where texmfdenotes the main 2 2. Poore % ----- % This work may be distributed and/or modified under the % conditions of the LaTeX. These options are discussed in the following sections The 68 standard colors known to dvips. sty 2009/11/27 v6. The booktabs package is useful for easily providing this professionalism in LaTeX tables, and the documentation also provides guidelines on what constitutes a "good" table. This can cause an options clash when the user's document later loads the same \trouble[options clash]{memoir=\pkg{memoir}>options clash} \trouble{options>clash with \pkg{memoir}} packages with options. 【 详情描述 】 引入xltxtra宏包 (并加载fontspec, xunicode 并定义了 \xetex 短命令) 同时又加载了 graphicx宏包. + Fix typo in fix for notes in tables (#2378, zeeMonkeez). Ask Question Asked 3 years, 7 months ago. Minor Features. This post explains how to configure your. muse file extension. It uses Gnuplot as back-end. 解法：用PS打开并另存为jpg，然后就可以了 解决方案，先停止运行，然后删除AUX文件，如果知道存在的问题，修改后再重新编译。. 8 Hooks at the very end of document (HO) Package: atbegshi 2011/10/05 v1. % % \iffalse meta-comment % % Copyright 2016-2020 Brian Dunn % % This work may be distributed and/or modified under the % conditions of the LaTeX Project Public. LaTeX Error: Option clash for package xcolor. \RequirePackage[option list]{package name}[release date] \RequirePackageWithOptions{package name}[release date] Load a package, like the command \usepackage (see Additional packages). Others are provided separately. The following options define the way length values are processed by the provided macros. cfg qui accompagne ma classe, j'appelle xcolor avec des options puis Tikz mais dans mes packages j'appelle encore tikz et lui appelle xcolor sans option. %#% extstart input preamble. 1a (example added to xcolor3. 6 -Added Biobase, GEOquery, and preprocessCore to package suggests -Minor revisions in the package vignette Changes in version 2-13-16: -Package version changed to 0. 3 This command is executed automatically if the package option hyperref is used. produces the error; even if option b is an alias for option a — LaTeX doesn't "look inside" the package to check anything like that. % \iffalse % *internal> \iffalse % %*readme> _____ The bidi package v18. 07/20/2020. MiKTeX has the ability to install missing packages automatically, i. I am trying to compile the PDF version of Efficient R Programming using RStudio on my Windows 7 machine. 另外,正如我之前所说,在当前的开发版本中,您可以使用函数kableExtra_latex_packages()调出列表. How to use the LaTeX tables generator? Set the desired size of the table using Table / Set size menu option. Note that to make it happen, LaTeX package xcolor is required to be loaded. However, sometimes we may need to a lot of objects in a package, and it will be cumbersome to type package:: again and again. Just don't load the color package twice. Suppose you want to provide a highlight color or background color for text in a LaTeX document. I assume you are familiar with RStudio and knitr/Sweave. For example, when you request that the xcolor package be loaded, you might specify the table option and the dvipsname option, 1 The table option forces the colortbl package to be loaded for coloring rows, columns, and/or cells of tables. Enumeración usando el paquete TikZ. Là tu as raison \PassOptionsToPackage{usesnames}{xcolor} \usepackage{xcolor} permet de se sortir du mauvais pas. LaTeX使用color&xcolor宏包的改变字体颜色 Boen-Zhao 2018-01-16 15:12:08 23544 收藏 9 分类专栏： 论文写作. Please see package vignette or visit the w3schools' Bootstrap Page for more information. Some packages come with the LaTeX base distribution. wrap only matters if width is set. ! Emergency stop. % \iffalse meta-comment % % Copyright (C) 2016-2019 by Geoffrey M. LaTeX output: A single LaTeX file is created, on standard output. =95 [caption name own line] As the name suggests, this options puts the =20= caption name (like =93Figure=94) on its own line. 99996 (TeX Live 2016) (preloaded format=xelatex) restricted \write18 enabled. 0 Major Change: Now when you load kableExtra package, it will automatically set format for kable() based on the working environment: only if you are using rmarkdown/r sweave to render PDFs, the default format will be set to “latex”. The package contains % the parts of the bundle which are appropriate for use with other % document classes. First of all, put the le xcolor. PSTricks graphics, PSfrag replacements, EPS graphics) inside a pdfLaTeX processed document. They should all be stored in subdirectories of texmf/tex/latex named after each package. Some packages come with the LaTeX base distribution. cls change RequirePackagespotcolor to RequirePackagexspotcolor. Package xcolor Info: Model wave' substituted by hsb' on input line 1360. Information on these, ifyou want it, is obtained from reading the LaTeX source itself and the TeXbook, and perhapsone of the free TeX manuals such as TeX for the Impatient [AHK90] or TeX by Topic [Eij92]. 16 (TeX Live 2015) (preloaded format=pdflatex 2015. MiKTeX has the ability to install missing packages automatically, i. In brief, the package uses \toprule for the uppermost rule (or line), \midrule for the rules appearing in the middle of the table (such as under the header), and \bottomrule. Package xcolor Info: Model HSB' substituted by hsb' on input line 1369. 日本の写真家少女愛存命人物 少女ヌード写真家児童買春、児童ポルノに係る行為等の処罰及び児童の保護等に関する法律施行絶版成人女性ヌード作品制作少女モデル撮影力武靖写真事務所スタジオr代表取締役ラックマーク最高経営責任者福岡県1982年1990年代ロリータ少女秘宝館わいせつ図画頒布. GermValue - Updated with option to consider time from start of test in addition to time from onset of germination. 83m Heiko Oberdiek * 6. DVI and PostScript can be produced directly with the options -dvi and -ps. =item C[]> specifies a list of options (in the 'package options' sense) to be passed (possibly in addition to any provided by the calling class or package). | \Description Ein anderes \LaTeX-Paket hat \thispackage\ bereits geladen, Sie können es daher nicht noch einmal mit anderen Optionen laden. We can also refer to specific lines of code in code listings. This is the best practice for checking packages because it makes sure the check starts with a clean slate: because a package bundle doesn’t contain any of the temporary files that can accumulate in your source package, e. Enough flexibility is provided to make local changes to a single reference. artifacts like. 4 Interaction with LATEX 2 and other packages This section documents some areas of adjustment that fontspec makes to improve default behaviour with LATEX 2 and third-party packages. 79k Hyperref: PDFDocEncoding definition (HO). Ask Question Asked 3 years, 7 months ago. LaTeX symbols have either names (denoted by backslash) or special characters. See the LaTeX manual or LaTeX Companion for explanation. 4, consisting of 1296 software packages, 309 experiment data packages, and 933 up-to-date annotation packages. 5 -Added option to specify FDR cutoff when using the Adaptive GMM method in the number_probes function. When I knit the below code as-is, I get: "LaTeX Error: Option clash for package xcolor. It means that the package 〈name〉 is loaded with a set of options, S1 , and that the package is loaded again with options, S2 , where S2 contains an option that is not contained in S1. Try and find the other > place you're loading it and delete that line. In brief, the package uses \toprule for the uppermost rule (or line), \midrule for the rules appearing in the middle of the table (such as under the header), and \bottomrule. Package xcolor Info: Model hsb' substituted by rgb' on input line 1341. In this video, i will show you how to install missing packages into miktex distribution. The eect of this option is altered with the package option prependcaption or the prepend / noprepend option for the todo command. 3 of this license or (at your option) any later version. The second part is the \LaTeX\ package. 另外,正如我之前所说,在当前的开发版本中,您可以使用函数kableExtra_latex_packages()调出列表. Título, contenido, secciones y bibliografía Indice alfabético. A good example is when you want to highlight the background yellow, so it looks like it was highlighted with a marker, to catch a reader's attention. sty' not found. Option clash for package hyperref Option clash for package Google Groups Option Clash Errors LaTeX. which gives the error: ! LaTeX Error: Option clash for package xcolor. Package xcolor Info: Model wave' substituted by hsb' on input line 1371. LaTeX Error: Option clash for package graphicx. It means that the package 〈name〉 is loaded with a set of options, S1 , and that the package is loaded again with options, S2 , where S2 contains an option that is not contained in S1. sty 2009/10/02 xcolor patch pd1enc. The booktabs package is useful for easily providing this professionalism in LaTeX tables, and the documentation also provides guidelines on what constitutes a "good" table. Others are provided separately. 8 is compatible with R 3. 2 This package provides a convenient interface for typesetting bidirectional texts in Plain TeX and LaTeX, using XeTeX engine. We are pleased to announce Bioconductor 3. 9 Manual — miktex-pdftex. VIGNETTE: Fixed LATEX xcolor options clash issue in vignette. No, with usepackage[breaklinks=true]{hyperref} i get: Option clash for package hyperref, and sloppy doesn't work. Installing Extra Packages Add-on features for LaTeX are known as packages. tex % % memman. Forum francophone relatif aux mathématiques avec support MathJax, LaTeX et Asymptote. Paketkonflikt: LaTeX Error: Command already defined. Latex: Error: ! LaTeX Error: Too many unprocessed ROOT: error: Bool_t' does not name a type; Linux: /tmp cleanup frequency; Latex: change row color of table; Linux: how to get cpu and memory information September 2008 (4) October 2008 (4) November 2008 (4) December 2008 (1) 2009 (9). save_kable does not work after installing R v4. Die Option T1 existiert zwar in url tatsächlich, die existiert aber wohl nur aus Kompatibilitätsgründen zu irgendwelchen früheren Versionen. Petr Sojka, Ph. Author: Vít Novotný Field of study: Typesetting Brno, Fall 2015 Annotation Fithesis3 is a LATEX document class, which streamlines the typesetting of the mandatory parts of theses, so that the author can focus at content alone. As a result, one can insert quite a bit of \LaTeX\ code and it will often be successfully post-processed in the last stage of document compilation. Is there a way to get this styling in tufte_handout class without the clash? If I hide this option in header-includes the styling doesn't work. * replace call to luatex85 package by new luatex back end option * Catalan autoref translation contributed in issue #4 2016-05-05 6. Uwe Kern ∗ v2. Ask Question Asked 1 year, 6 months ago. Time for action – listing LaTeX packages We shall create a list of packages that we got to know in the previous chapter: 1. [behavior changes] * --ascii is now implemented in the writers, not in Text. LaTeX Error: Option clash for package hyperref. mark thompson st louis cardinals resumo da nova novela das seis globo mt washington cog railway base station rd bretton woods nh 03575 ben 10 divided we stand part 1. LaTeX Error: Option clash for package xcolor. The second part is the \LaTeX\ package. LaTeX output: A single LaTeX file is created, on standard output. todonotes - Free download as PDF File (. The package eso-pic loads xcolor (without any option); in turn it's nips12submit_e that loads eso-pic, so you have to say \usepackage[table]{xcolor} before \usepackage{nips12submit_e}. Possible Duplicate: Option clash for package xcolor これをやろうとしている間：\\usepackage [ table ]{ xcolor }私はこのエラーを取得する： LaTeX Error: Option clash for package xcolor. cls comment RequirePackagecolor. 文章目录原因 解决 方案结果上传论文到arxiv，在线编译时， 出现 以下 错误 提示：! LaTeX Error: Option clash for package hyperref. tex LaTeX2e <2016/03/31> Babel <3. 저 간격을 조절하고 싶습니다. Note that to make it happen, LaTeX package xcolor is required to be loaded. txt) or read online for free. As a result, one can insert quite a bit of \LaTeX\ code and it will often be successfully post-processed in the last stage of document compilation. 0的package vignette年初添加了一个关于这个问题的新章节. A package allowing to write Hakyll blog posts in Rmd (bsd3, deprecated, library, web) 2015-07-12: CorentinDupont: hakyll-agda: 206: 0. web; books; video; audio; software; images; Toggle navigation. The LaTeX package ps4pdf' provides a new way to use Postscript commands (e. One could say that TikZ is to picture as LaTeX is to TeX. To do so it installs the current package into a temporary library tree, but any dependent packages need to be. Here you can specify further options, e. Package xcolor Info: Model HTML' substituted by rgb' on input line 1355. »option clash«-Fehler vermeiden. sty versions do load xcolor, whereas pstcol is no longer needed. 83n * Load luatex85 package for luatex compatibility 2012-11-06 6. entering extended mode (. The color package implicitly invokes 1 Section 2. 【 详情描述 】 引入xltxtra宏包 (并加载fontspec, xunicode 并定义了 \xetex 短命令) 同时又加载了 graphicx宏包. R の統合開発環境 RStudio を使っていて「RMarkdownなる便利なものがあるのか！」ということで環境構築をしたら手強かったので備忘録＆共有をかねて記事化しますた。 環境 macOS Mojave 10. The eect of this option is altered with the package option prependcaption or the prepend / noprepend option for the todo command. Easily share your publications and get them in front of Issuu’s. 5 -Added option to specify FDR cutoff when using the Adaptive GMM method in the number_probes function. Extending LATEX’s color facilities: the xcolor. 0, and is supported on Linux, 32- and 64-bit Windows, and Mac OS X. Option clash for package MyPackage. すべてのパッケージ \documentclass{article}. Package xcolor Info: Model wave' substituted by hsb' on input line 1371. Knitr hook to add code before \\documentclass line in tex file to avoid options clash with xcolor; Scala, problem with a jar file; phpmailer noname attachment; 1970-01-01 is getting inserted to database when no date is selected; program doesn't contain a static 'main' method suitable for an entry point. 22 milestone Mar 7, 2019. Die Option T1 existiert zwar in url tatsächlich, die existiert aber wohl nur aus Kompatibilitätsgründen zu irgendwelchen früheren Versionen. Refer to the external references at the end of this article for more information. Thus there is a design decision to make: which keys are real package options that cannot be changed, which keys are setup options that can be used, for convenience, with the same syntax as package options but in fact are not part of the "package options" (in the sense of LaTeX) but are part of the "package setup" - or more precisely of the. % \iffalse % *internal> \iffalse % %*readme> _____ The bidi package v18. One way is to make xcolor global as in the following example:. Skip to content. Local options have been specified for this partic-ular package in the options argument of \PassOptionsToPackage{options}, \usepackage[options], or \RequirePackage[options]. Use this =20= option only if your audience has a printed handout or printed lecture notes that follow the same =20 numbering. Option clash for package MyPackage. Package xcolor Info: Model tHsb' substituted by hsb' on input line 1368. Permission is also granted to distribute and/or modify both the documentation and the code under the conditions of the LaTeX Project Public License, either version 1. A typical place according to the TEX Directory Structure (TDS) would be the directory texmf/tex/latex/xcolor, where texmfdenotes the main 2 2. tufte-latex) that uses hyperref settings different from those in the template. in ieeeaccess. LaTeX Error: Option clash for package xcolor. 08/12/2020. Uwe Kern ∗ v2. The package eso-pic loads xcolor (without any option); in turn it's nips12submit_e that loads eso-pic, so you have to say \usepackage[table]{xcolor} before \usepackage{nips12submit_e}. There are 101 new software packages, and many updates and improvements to existing packages; Bioconductor 3. 9\tex\latex\base\fontenc. They are passed to the \adjcalcsetmacro of the adjcalcpackage and load any required packages. Package xcolor' by Dr. Wear gloves when working with the plant or harvesting the fruit. PSTricks graphics, PSfrag replacements, EPS graphics) inside a pdfLaTeX processed document. Viewed 1k times 0. Information on these, ifyou want it, is obtained from reading the LaTeX source itself and the TeXbook, and perhapsone of the free TeX manuals such as TeX for the Impatient [AHK90] or TeX by Topic [Eij92]. It's recommended to use it if your LaTeX distribution. Enhancement: when stars is NULL in huxreg, don't print a note by default. Package xcolor Info: Model wave' substituted by hsb' on input line 1360. Wie kriege ich eine Beschriftung? Package babel Error: You haven't loaded the option ngerman yet. def 2009/11/27 v6. This works for any input format. library(raster);library(ggplot2). I have found solutions on the LaTex pages, here and here, but I do not know LaTex and I have not figured out how to apply these solutions in the rmarkdown arena. Note that the package has been adopted as part of the L a T e X distribution ; the reference here is to the original package, which is now little used (if at all). tufte-latex) that uses hyperref settings different from those in the template. to your documentclass declaration may fix this. It uses Gnuplot as back-end. Problems & Solutions beta; Log in; Upload Ask Computers & electronics; Software; LaTeX lwarp package. 0的package vignette年初添加了一个关于这个问题的新章节. See the reference guide for a complete list of possible colours. 1 Latin letters and Arabic numerals 1. 147 \usepackage {titlesec} The package xcolor has already been loaded with options: [] There has now been an attempt to load it with options [svgnames] Adding the global options: ,svgnames. • Run latex on pack. =item C[]> specifies a list of options (in the 'package options' sense) to be passed (possibly in addition to any provided by the calling class or package). The booktabs package is useful for easily providing this professionalism in LaTeX tables, and the documentation also provides guidelines on what constitutes a "good" table. > > This means you're loading the package twice. Este é o guia de usuário do Beamer. 1 Package installation First of all, put xcolor. Option clash for package MyPackage. The general rule is: the first load of a package defines a set of options; if a further \usepackage or \RequirePackage also calls for the package, the options on that call may not extend the set on the. There has now been an attempt to load it with no options. PSTricks graphics, PSfrag replacements, EPS graphics) inside a pdfLaTeX processed document. ! Emergency stop. Rnw file to automatically generate the bibliography using the biblatex package in a single run from within RStudio. + Added beamer titlegraphic and logo variables (Thomas Hodgson). wrap only matters if width is set. dtx % % Installation: % TDS:tex/latex/mh/empheq. Jedenfalls tut die Option nichts. Many LaTeX packages allow for options to be specified when the package is loaded. 另外,正如我之前所说,在当前的开发版本中,您可以使用函数kableExtra_latex_packages()调出列表. LaTeX 2014 by A. ERROR: LaTeX Error: Option clash for package xcolor. Viewed 713 times. For extended documentation, see epslatex. log le cluttered up. 22 milestone Mar 7, 2019. 0+),kable_styling willloadit. 6 of the beamer user guide Tom's approach can be simplified a bit. LaTeX Error: Option clash for package xcolor. LaTeX Error: Option clash for package - wie beheben? [closed] Option Clash (xcolor) ich fand trotz Hilfe keine Lösung. Here you can specify further options, e. pstricks package leads to either 'option clash for package xcolor' or 'Command \clipbox already defined' #34. すべてのパッケージ \\documentclass{article}. 【 详情描述 】 引入xltxtra宏包 (并加载fontspec, xunicode 并定义了 \xetex 短命令) 同时又加载了 graphicx宏包. Package xcolor Info: Model wave' substituted by hsb' on input line 1360. Package xcolor Info: Model Gray' substituted by gray' on input line 1359. See the LaTeX manual or LaTeX Companion for explanation. memoir extends this by also providing a. Problems & Solutions beta; Log in; Upload Ask Computers & electronics; Software; LaTeX lwarp package. Note that the package has been adopted as part of the L a T e X distribution ; the reference here is to the original package, which is now little used (if at all). 16 (TeX Live 2015) (preloaded format=pdflatex 2015. * Add --strip-empty-paragraphs option. huxtable 4. The table is shown below. We are pleased to announce Bioconductor 3. 또 하나는 toc의 section을 한 줄로 나오게 하고 싶습니다. > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >. The eect of this option is altered with the package option prependcaption or the prepend / noprepend option for the todo command. \Message |Option clash for package caption. LaTeX Error: Option clash for package color. dtx % makeindex -s gind. 21 The package xcolor has already been loaded with options: [] There has now been an attempt to load it with options [dvipsnames,table,xcdraw] Adding the global options: ,dvipsnames,table,xcdraw to. info, Node: Additional packages, Next: Class and package construction, Prev: Document class options, Up: Document classes 3. Option clash for package textcomp. A popular car finance option for employees. 07/20/2020. Package xcolor Info: Model Gray' substituted by gray' on input line 1359. A community for all things R and RStudio. % \iffalse % *internal> \iffalse % %*readme> _____ The bidi package v18. I am writing a chinese report by a R package of articles, there some errors occered, my code is as following: LaTeX Error: Option clash for package color. LaTeX Error: Option clash for package xcolor. We will help you to choose option clash for package xcolor the best iata online schulung Binary Option Robot in the market. Paketkonflikt: LaTeX Error: Command already defined. Poore % ----- % This work may be distributed and/or modified under the % conditions of the LaTeX. aravind-j changed the title xcolor option clash with fancyvrb v 3. These options are discussed in the following sections The 68 standard colors known to dvips. چطور بعضی از سلولهای جدول را رنگ کنم که خطای LaTeX Error: Option clash for package xcolor ندهد; چگونه میتوان برخی از خطوط را در جدول حذف کرد؟. One way is to make xcolor global as in the following example:. The package contains % the parts of the bundle which are appropriate for use with other % document classes. 또 하나는 toc의 section을 한 줄로 나오게 하고 싶습니다. + Fix hyperref options clash (Andrew Dunning, #3847) Avoids an options clash when loading a package (e. Active 3 years, 7 months ago. Here you can specify further options, e. I assume you are familiar with RStudio and knitr/Sweave. すべてのパッケージ \\documentclass{article}. org Option Clash for Package in Presentation LaTeX. ) ("D:\Programme\MiKTeX 2. LaTeX Error: Option clash for package graphicx. * replace call to luatex85 package by new luatex back end option * Catalan autoref translation contributed in issue #4 2016-05-05 6. * Support beamer \alert in LaTeX reader. info, Node: Additional packages, Next: Class and package construction, Prev: Document class options, Up: Document classes 3. Package: letltxmacro 2010/09/02 v1. This works for any input format. Location: CTAN Packages xcolor xcolor – Driver-independent color extensions for L a T e X and pdf L a T e X The package starts from the basic facilities of the color package, and provides easy driver-independent access to several kinds of color tints, shades, tones, and mixes of arbitrary colors. def 2009/11/27 v6. LaTeX Error: Option clash for package color. I've seen in the menukeys documentation that the xcolor options could be passed at the \documentclass and, indeed, that works that way. Otherwise, cell wrapping. Package xcolor Info: Model tHsb' substituted by hsb' on input line 1368. I would like to use some of the predefined colors within the dvipsnames option of xcolor for hyperref but I keep getting "LaTeX Error: Option clash for package Xcolor" from this \usepackage[dvipsnames]{xcolor} \definecolor{linkcolor}{Emerald} \definecolor{ColorForCite}{Blue} \definecolor{URLLinkColor}{Mulberry} \ifpdf% \usepackage[debug=false. The dvipsnames option makes available. If you comment out the uncomment the tufte::tufte_handout output and replace with pdf_document, it works. It's recommended to use it if your LaTeX distribution. + Added beamer titlegraphic and logo variables (Thomas Hodgson). 25/03/16 - Ho controllato il tutto e l'unico errore riscontrato nella compilazione è stato: LaTeX Error: Option clash for package xcolor. A community for all things R and RStudio. Package xcolor Info: Model wave' substituted by hsb' on input line 1371. txt) or read online for free. First, the command to import the xcolor package has an additional parameter:. Ich verwende TikZ und lade jetzt zusätzlich xcolor mit der table-Option und erhalte eine Fehlermeldung. xcolor option clash with fancyvrb v 3. The general rule is: the first load of a package defines a set of options; if a further \usepackage or \RequirePackage also calls for the package, the options on that call may not extend the set on the. 日本の写真家少女愛存命人物 少女ヌード写真家児童買春、児童ポルノに係る行為等の処罰及び児童の保護等に関する法律施行絶版成人女性ヌード作品制作少女モデル撮影力武靖写真事務所スタジオr代表取締役ラックマーク最高経営責任者福岡県1982年1990年代ロリータ少女秘宝館わいせつ図画頒布. % use A4 as paper format: % \PassOptionsToClass{a4paper}{article} % % Programm calls to get the documentation (example): % pdflatex mathtools. Unless R CMD build is invoked with the --no-build-vignettes option (or the package’s DESCRIPTION contains ‘BuildVignettes: no’ or similar), it will attempt to (re)build the vignettes (see Writing package vignettes) in the package. =95 [caption name own line] As the name suggests, this options puts the =20= caption name (like =93Figure=94) on its own line. Baby & children Computers & electronics Entertainment & hobby. Minor Features. 08/12/2020. sty nicht gefunden [closed] Von Unicode nach pdflatex - wie geht das?. While the previous systems (picture, epic, pstricks or metapost) focus on the how to draw, TikZ focuses more on the what to draw. Note that to make it happen, LaTeX package xcolor is required to be loaded. nbconvert failed: PDF creating failed, captured latex output: This is XeTeX, Version 3. 0+),kable_styling willloadit. Paketkonflikt: LaTeX Error: Command already defined. No, with usepackage[breaklinks=true]{hyperref} i get: Option clash for package hyperref, and sloppy doesn't work. artifacts like. + Fix hyperref options clash (Andrew Dunning, #3847) Avoids an options clash when loading a package (e. Suppose you want to provide a highlight color or background color for text in a LaTeX document. Package ‘kableExtra’ August 27, 2020 Type Package Title Construct Complex Table with 'kable' and Pipe Syntax Version 1. The package eso-pic loads xcolor (without any option); in turn it's nips12submit_e that loads eso-pic, so you have to say \usepackage[table]{xcolor} before \usepackage{nips12submit_e}. 原因\usepackage[hidelinks]{ hyperref } 跟其他package 出现 冲突 解决 方案去掉该 包 %\usepackage[hidelinks]{ hyperref. This is pdfTeX, Version 3. 9 Manual — miktex-pdftex. A popular car finance option for employees. Package xcolor Info: Model tHsb' substituted by hsb' on input line 1368. And perhaps you should think about using the more sophisticated xcolor package instead. } % Thirdly, two \BibTeX\ style files are included. sty 2009/10/02 v1. Poore % ----- % This work may be distributed and/or modified under the % conditions of the LaTeX. 저 간격을 조절하고 싶습니다. The package supports the Text Companion fonts, which provide many text symbols (such as baht, bullet, copyright, musicalnote, onequarter, section, and yen), in the TS1 encoding. Das tikz xcolor ebenfalls (aber ohne Option) lädt, musst du natürlich xcolor in dem Fall vor tikz laden. 18 - Red Bank Register Archive. 2 Wrapper for package hooks (HO) Package: xcolor-patch 2011/01/30 xcolor patch Package: atveryend 2011/06/30 v1. CLASS OPTIONSThe standard classes provide point options of 10, 11, or 12 points for the main body font. Fehler: Failed to compile Test. Latex排版论文的过程中遇到的一些编译问题及解决方案. See the LaTeX manual or LaTeX Companion for explanation. 79k Hyperref: PDFDocEncoding definition (HO). info, Node: Additional packages, Next: Class and package construction, Prev: Document class options, Up: Document classes 3. It is based on the standard % \pkg{article} class, but makes various changes to facilitate ease % of use. There are 101 new software packages, and many updates and improvements to existing packages; Bioconductor 3. For example, when you request that the xcolor package be loaded, you might specify the table option and the dvipsname option, 1 The table option forces the colortbl package to be loaded for coloring rows, columns, and/or cells of tables. LaTeX Error: File xcolor. save_kable does not work after installing R v4. Type H for immediate help. > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >. 10) 25 JUL 2015 13:13 entering extended mode restricted \write18 enabled. I am trying to compile the PDF version of Efficient R Programming using RStudio on my Windows 7 machine. Rmd: Idem * vignettes/Rcpp-modules. Este é o guia de usuário do Beamer. Ich verwende TikZ und lade jetzt zusätzlich xcolor mit der table-Option und erhalte eine Fehlermeldung. 1 Latin letters and Arabic numerals 1. ) ("D:\Programme\MiKTeX 2. 解法：用PS打开并另存为jpg，然后就可以了 解决方案，先停止运行，然后删除AUX文件，如果知道存在的问题，修改后再重新编译。. sty' not found. The second option makes sense if you are the administrator of a multi-user system. styfile but there may be others depending on the particular package). Upload Computers & electronics; Software; The beamer class Manual for version 3. Please see package vignette for more information. LaTeX Error: Option clash for package xcolor. pstricks package leads to either 'option clash for package xcolor' or 'Command \clipbox already defined' #34. See the LaTeX manual or LaTeX Companion for. titlesec과 titletoc로 헤더와 toc를 꾸며서 사용하려고 하는데 뜻대로 안되는 게 있습니다. 또 하나는 toc의 section을 한 줄로 나오게 하고 싶습니다. kableExtra 0. LaTeX manual of todonotes style. LaTeX Error: Option clash for package graphicx. As a result, one can insert quite a bit of \LaTeX\ code and it will often be successfully post-processed in the last stage of document compilation. LaTeX Error: Option clash for package - wie beheben? 23 Sep '14, 18:45 cgnieder 20. 3, and is supported on Linux, 32- and 64-bit Windows, and. Baby & children Computers & electronics Entertainment & hobby. A package allowing to write Hakyll blog posts in Rmd (bsd3, deprecated, library, web) 2015-07-12: CorentinDupont: hakyll-agda: 206: 0. 3 of this license or (at your option) any later version. 0, and is supported on Linux, 32- and 64-bit Windows, and Mac OS X. Dans mon fichier. LaTeX files given on the command line are copied ‘as is’ in the final document. \footnote{For example, when writing a thesis. Easily share your publications and get them in front of Issuu’s. #2331: Fix code-blocks are filled by block in dvi; remove xcdraw option from xcolor package Fix the confval type checker emits warnings if unicode is given to confvals which expects string value #2360: Fix numref in LaTeX output is broken. Create Awesome HTML Table with knitr::kable and kableExtra. Here is what I had to do to get tikz working with the IEEE Access template: in ieeeaccess. Rmd: Idem * vignettes/Rcpp-modules. Thus, the generalcommand is \usepackage[hoptionsi]{xcolor}in the document preamble. Au point où j'en suis je vais virer tikz et xcolor de mes packages et demander aux utilisateurs de les appeler eux-mêmes. Basic packages can be structured into the following groups: LaTeX Markup : The Hmisc, xtable and tables packages contain functions to write R objects into. 9 Manual — miktex-pdftex. The second part is the \LaTeX\ package. Here you can specify further options, e. aravind-j changed the title xcolor option clash with fancyvrb v 3. If you are using tikz or pstricks package you must declare the xcolor package before that, otherwise it will not work. Package ‘kableExtra’ August 27, 2020 Type Package Title Construct Complex Table with 'kable' and Pipe Syntax Version 1. CLASS OPTIONSThe standard classes provide point options of 10, 11, or 12 points for the main body font. Package: letltxmacro 2010/09/02 v1. 83m Heiko Oberdiek * 6. These options can also be used as local keys on \adjustbox. latex pagestyle empty funktioniert nicht calivita wit. The package contains % the parts of the bundle which are appropriate for use with other % document classes. Also kann man sie auch weglassen und damit ggf. I've seen in the menukeys documentation that the xcolor options could be passed at the \documentclass and, indeed, that works that way. yml: idem * vignettes/Rcpp-quickref. Information on these, ifyou want it, is obtained from reading the LaTeX source itself and the TeXbook, and perhapsone of the free TeX manuals such as TeX for the Impatient [AHK90] or TeX by Topic [Eij92]. % use A4 as paper format: % \PassOptionsToClass{a4paper}{article} % % Programm calls to get the documentation (example): % pdflatex empheq. which gives the error: ! LaTeX Error: Option clash for package xcolor. 0的package vignette年初添加了一个关于这个问题的新章节. + Fix hyperref options clash (Andrew Dunning, #3847) Avoids an options clash when loading a package (e. 6 of the beamer user guide Tom's approach can be simplified a bit. \Message |Option clash for package caption. I have found solutions on the LaTex pages, here and here, but I do not know LaTex and I have not figured out how to apply these solutions in the rmarkdown arena. See the LaTeX manual or LaTeX Companion for explanation. * Support beamer \alert in LaTeX reader. ERROR: LaTeX Error: Option clash for package xcolor. cls comment RequirePackagecolor. Some packages come with the LaTeX base distribution. #2331: Fix code-blocks are filled by block in dvi; remove xcdraw option from xcolor package Fix the confval type checker emits warnings if unicode is given to confvals which expects string value #2360: Fix numref in LaTeX output is broken. sty 2009/01/23 v0. The booktabs package is useful for easily providing this professionalism in LaTeX tables, and the documentation also provides guidelines on what constitutes a "good" table. I would like to use some of the predefined colors within the dvipsnames option of xcolor for hyperref but I keep getting "LaTeX Error: Option clash for package Xcolor" from this \usepackage[dvipsnames]{xcolor} \definecolor{linkcolor}{Emerald} \definecolor{ColorForCite}{Blue} \definecolor{URLLinkColor}{Mulberry} \ifpdf% \usepackage[debug=false. LaTeX Error: Option clash for package color. Accéder au contenu. , this installer is suitable for computers connected to the Internet. up vote 45 down vote favorite 25. sty" Package: fontenc 2005/09/27 v1. 10) 25 JUL 2015 13:13 entering extended mode restricted \write18 enabled. Enumeración usando el paquete TikZ. »option clash«-Fehler vermeiden. LaTeX manual of todonotes style. Unless R CMD build is invoked with the --no-build-vignettes option (or the package’s DESCRIPTION contains ‘BuildVignettes: no’ or similar), it will attempt to (re)build the vignettes (see Writing package vignettes) in the package. Others are provided separately. Note that loading of a4wide is deprecated (and also dubious, as the nips package sets the page geometry), while subfigure is obsolete. produces the error; even if option b is an alias for option a — LaTeX doesn't "look inside" the package to check anything like that. 25/03/16 - Ho controllato il tutto e l'unico errore riscontrato nella compilazione è stato: LaTeX Error: Option clash for package xcolor. huxtable-options: Package options; huxtable-package: Quick introduction to huxtable; insert_column: Insert a row or column; jams: Prices of 3 jams; knit_print. 21 The package xcolor has already been loaded with options: [] There has now been an attempt to load it with options [dvipsnames,table,xcdraw] Adding the global options: ,dvipsnames,table,xcdraw to. I have found solutions on the LaTex pages, here and here, but I do not know LaTex and I have not figured out how to apply these solutions in the rmarkdown arena. These options can also be used as local keys on \adjustbox. Borbón y W. tex Memoir class user manual (Part II only) last updated 2009/09/07 % Author: Peter Wilson % Copyright 2001, 2002, 2003. Uwe Kern (xcolor at ukern dot de) History ===== 2016/05/11 v2. Otherwise, cell wrapping. See the LaTeX manual or LaTeX Companion for explanation. Stereo Madness is the first level in Geometry Dash, a rhythm based platformer. A character vector for bootstrap table options. Note that to make it happen, LaTeX package xcolor is required to be loaded. Forum francophone relatif aux mathématiques avec support MathJax, LaTeX et Asymptote. Thus there is a design decision to make: which keys are real package options that cannot be changed, which keys are setup options that can be used, for convenience, with the same syntax as package options but in fact are not part of the "package options" (in the sense of LaTeX) but are part of the "package setup" - or more precisely of the. perl561delta - what's new for perl v5. It is based on the standard % \pkg{article} class, but makes various changes to facilitate ease % of use. 5 -Added option to specify FDR cutoff when using the Adaptive GMM method in the number_probes function. A community for all things R and RStudio. 9\tex\latex\base\fontenc. Masaryk University Faculty of Medicine A fithesis3 user guide for the Faculty of Medicine Bachelor’s Thesis Advisor: Doc. Celeste is small, purplish-bronze in color, and is ripe from mid-July to mid-August a good choice because it has a. The second option makes sense if you are the administrator of a multi-user system. 28) 28 AUG 2009 15:07 entering extended mode **D:/haw/vorlesungen/masteraw2. Problems & Solutions beta; Log in; Upload Ask Computers & electronics; Software; LaTeX lwarp package. sty versions do load xcolor, whereas pstcol is no longer needed. \footnote{For example, when writing a thesis. teknisk skole esbjerg fronter workers fail compilation 2020 sr viper accessories xvo time breaker haircut short sides long back anumex gdl jal. Closes #4091. to your documentclass declaration may fix this. Stereo Madness is the first level in Geometry Dash, a rhythm based platformer. Inanenvironmentlikermarkdown::pdf_document(rmarkdown1. There has now been an attempt to load it with no options. 0+),kable_styling willloadit. deffiles to some place where (pdf)LATEX finds them. * Support --webtex for gfm output. sty" Package: fontenc 2005/09/27 v1. Package xcolor Info: Model Gray' substituted by gray' on input line 1359. The second option makes sense if you are the administrator of a multi-user system. up vote 45 down vote favorite 25. There are 101 new software packages, and many updates and improvements to existing packages; Bioconductor 3. -Package version pushed to 0. Dans mon fichier. Viewed 1k times 0. The eect of this option is altered with the package option prependcaption or the prepend / noprepend option for the todo command. =95 [caption name own line] As the name suggests, this options puts the =20= caption name (like =93Figure=94) on its own line. ERROR: LaTeX Error: Option clash for package xcolor. ! Emergency stop. ===== If this worked and helped you Do no. 저 간격을 조절하고 싶습니다. 4) [new features] * New input format man (Yan Pashkovsky, John MacFarlane). Before you run the installer, you should check the prerequisites. Some packages come with the LaTeX base distribution. \footnote{For example, when writing a thesis. + Fix hyperref options clash (Andrew Dunning, #3847) Avoids an options clash when loading a package (e. 14 \begin{document} The package 'color' has already been loaded with options: [pdftex]. It means that the package 〈name〉 is loaded with a set of options, S1 , and that the package is loaded again with options, S2 , where S2 contains an option that is not contained in S1. web; books; video; audio; software; images; Toggle navigation. 79k Hyperref: PDFDocEncoding definition (HO). GermValue - Updated with option to consider time from start of test in addition to time from onset of germination. 08/12/2020. 9r> and hyphenation patterns for 22 language(s) loaded. We can also refer to specific lines of code in code listings. If width is set, it is “tabularx”. CLASS OPTIONSThe standard classes provide point options of 10, 11, or 12 points for the main body font. todonotes - Free download as PDF File (. 1 Description Build complex HTML or 'LaTeX' tables using 'kable()' from 'knitr' and the piping syntax from 'magrittr'. titlesec과 titletoc로 헤더와 toc를 꾸며서 사용하려고 하는데 뜻대로 안되는 게 있습니다. dtx % % Installation: % TDS:tex/latex/mh/empheq. Celeste is small, purplish-bronze in color, and is ripe from mid-July to mid-August a good choice because it has a. tex LaTeX2e <2016/03/31> Babel <3. In sostanza un doppio caricamento della proprietà table per xcolor (ho dovuto quindi aggiungere una opzione globale su documentclass). 2 Additional packages ===== Load a package PKG, with the package options given in the comma-separated list OPTIONS, as here. Inanenvironmentlikermarkdown::pdf_document(rmarkdown1. 3 on page 11 explains how this setting can be overridden at any point in a document. knitr::opts_chunk. They are passed to the \adjcalcsetmacro of the adjcalcpackage and load any required packages. Note that to make it happen, LaTeX package xcolor is required to be loaded. nbconvert failed: PDF creating failed, captured latex output: This is XeTeX, Version 3. Possible Duplicate: Option clash for package xcolor Tout en essayant de le faire: \usepackage [ table ]{ xcolor } je reçois cette erreur: LaTeX Error: Option clash for package xcolor. 2 Additional packages ===== Load a package PKG, with the package options given in the comma-separated list OPTIONS, as here. tex LaTeX2e <2016/03/31> Babel <3. sty 2009/01/23 v0. It can be redirected to a file using the option -o. Type H for immediate help. LaTeX manual of todonotes style. To avoid this,. LaTeX Error: Option clash for package xcolor. Q: Latex error: option clash for package XXX (mostly xcolor) A:xcolor is incompatible with tikz, graphicx, etc. Some packages come with the LaTeX base distribution. It is primarily intended for use with docx and odt documents where empty paragraphs have been used for inter-paragraph spaces. If you only need to use a small number of objects in a package occasionally, you are recommended to use the :: operator, e. %#% extstart input preamble. • Run latex on pack. Wear gloves when working with the plant or harvesting the fruit. Q: Latex error: option clash for package XXX (mostly xcolor) A:xcolor is incompatible with tikz, graphicx, etc. \usepackage der von \fancybox kommt. I can't generate the PDF with TexMaker-Latex. Jedenfalls tut die Option nichts. A popular car finance option for employees. Time for action – listing LaTeX packages We shall create a list of packages that we got to know in the previous chapter: 1. tufte-latex) that uses hyperref settings different from those in the template. 0 Major Change: Now when you load kableExtra package, it will automatically set format for kable() based on the working environment: only if you are using rmarkdown/r sweave to render PDFs, the default format will be set to “latex”. The general rule is: the first load of a package defines a set of options; if a further \usepackage or \RequirePackage also calls for the package, the options on that call may not extend the set on the. Loading menukeys at the end throws the error:! LaTeX Error: Command \c lipbox already defined. چطور بعضی از سلولهای جدول را رنگ کنم که خطای LaTeX Error: Option clash for package xcolor ندهد; option clash for package hyperref; تغییر رنگ یک سطر از جدول در xepersian; آیا بسته xecolor بدون فراخوانی بسته xepersian نباید عمل کند؟ خطای Package. sty" Package: fontenc 2005/09/27 v1. 22 milestone Mar 7, 2019. No, with usepackage[breaklinks=true]{hyperref} i get: Option clash for package hyperref, and sloppy doesn't work. Dans mon fichier. save_kable does not work after installing R v4. 83m Heiko Oberdiek * 6. % use A4 as paper format: % \PassOptionsToClass{a4paper}{article} % % Programm calls to get the documentation (example): % pdflatex empheq. \RequirePackage[option list]{package name}[release date] \RequirePackageWithOptions{package name}[release date] Load a package, like the command \usepackage (see Additional packages). This post explains how to configure your. LaTeX Error: File xcolor. I am trying to compile the PDF version of Efficient R Programming using RStudio on my Windows 7 machine. LaTeX Error: Option clash for package xcolor. Type H for immediate help. Dieses Minimalbeispiel \documentclass{article} \usepackage{tikz} \usepackage[table]{xcolor} \begin{document} text \end{document} gibt! LaTeX Error: Option clash for package xcolor. Package xcolor Info: Model Gray' substituted by gray' on input line 1359. 저 간격을 조절하고 싶습니다. Type H for immediate help l. The order of files on the command line is kept in the final document. Creating headers and footers in Latex can be done by using the package “fancyhdr”. Ask Question Asked 1 year, 6 months ago. See the LaTeX manual or LaTeX Companion for explanation. Nov 14, 2018 yihui added this to the v1. \Message |Option clash for package caption. I am writing a chinese report. 83m * Option pdflang': Default is \relax' that suppresses the entry in the PDF catalogue. Rnw file to automatically generate the bibliography using the biblatex package in a single run from within RStudio. | \Or[aber manchmal auch] |Missing \begin{document}. Note that loading of a4wide is deprecated (and also dubious, as the nips package sets the page geometry), while subfigure is obsolete. latex插入伪代码，看了这个Latex写算法的伪代码排版然后编译报错了，LaTeX Error: Option clash for package geometry. VIGNETTE: Fixed LATEX xcolor options clash issue in vignette. kableExtra 0. 文章目录原因 解决 方案结果上传论文到arxiv，在线编译时， 出现 以下 错误 提示：! LaTeX Error: Option clash for package hyperref. Dieses Minimalbeispiel \documentclass{article} \usepackage{tikz} \usepackage[table]{xcolor} \begin{document} text \end{document} gibt! LaTeX Error: Option clash for package xcolor. These options can also be used as local keys on \adjustbox. up vote 45 down vote favorite 25. tex % % memman. See the LaTeX manual or LaTeX Companion for explanation. Inanenvironmentlikermarkdown::pdf_document(rmarkdown1. Note that to make it happen, LaTeX package xcolor is required to be loaded. Recall that documents in R markdown are converted from Rmd to md by the knitting process, and then into \LaTeX\ by pandoc, and then into PDF by a \LaTeX\ compiler (pdflatex, xetex or similar). sty versions do load xcolor, whereas pstcol is no longer needed. dtx % makeindex -s gind. We can also refer to specific lines of code in code listings. * Support --webtex for gfm` output. Also kann man sie auch weglassen und damit ggf. Package grffile was updated several days ago, on 2019-11-08. Knitr hook to add code before \\documentclass line in tex file to avoid options clash with xcolor; Scala, problem with a jar file; phpmailer noname attachment; 1970-01-01 is getting inserted to database when no date is selected; program doesn't contain a static 'main' method suitable for an entry point. I have found solutions on the LaTex pages, here and here, but I do not know LaTex and I have not figured out how to apply these solutions in the rmarkdown arena. Masaryk University Faculty of Medicine A fithesis3 user guide for the Faculty of Medicine Bachelor’s Thesis Advisor: Doc.
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## The Basics of Strings
Our introduction would not be complete without discussing how to work with text and character data. In this section, you will learn about the string data type and assigning a variable of type "str". String data is text or character data. To assign a variable of type str, the text string must be placed in quotes:
string_example='This is the text string'
To see that this variable assignment has taken place, type the command:
print(string_example)
and you should see the text string echoed to the screen. To assign a variable of type str, you can use either single or double quotes, but single quotes are often the convention of choice. As we dive deeper into the course, many interesting operations and computations using the string data type will be presented. Read this page to learn more about the string variable type. Use the Repl.it IDE to practice some of the string commands.
### Strings
• String basics
• String formatting
string is a sequence of characters
We can store it and associate a name/variable with it.
To strings like "hi" or 'broom', we refer to as a string literal in a Python program.
#### What can I do with strings in Python?
>>> firstPart = "abra"
>>> secondPart = "kadabra"
>>> firstPart[2]
'r'
>>> secondPart[0]
'k'
>>> secondPart[2:]
'dabra'
>>> secondPart[1:4]
'ada'
>>> firstPart + secondPart
'abrakadabra'
>>> len(firstPart)
4
>>> firstPart+"cloud"
'abracloud'
>>> firstPart+'/'+secondPart
'abra/kadabra'
>>> firstPart*3
'abraabraabra'
>>> firstPart
'abra'
### String formatting
Program output commonly includes the value of variables as a part of the text.
Example: for the following code:
num = 18
tum = 9.8
print("I have a number",num,"and a number",tum)
will produce:
I have a number 18 and a number 9.8
Note that we have to keep track of those double quotes (") and commas in the print statement.
Compare the following two print statements:
num = 18,tum = 9.8
print("I have a number",num,"and a number",tum)
print("I have a number %d and a number %f" % (num,tum))
The first one produced:
I have a number 18 and a number 9.8
The second one produced:
I have a number 18 and a number 9.800000
A string formatting expression allows a programmer to create a string with placeholders that are replaced by the value of variables.
Such a placeholder is called a conversion specifier. Different conversion specifiers are used to perform a conversion of the given variable value to a different type when creating the string.
Example:
num = 5.5
print("The integer part is %d" % num)
will yield:
The integer part is 5
Example: Consider the following code fragment
price = 119 # in dollars
discount = 30 # in percent %
print("A $%d jacket at %d%% discount is now priced at %f" % (price,discount,price*0.7)) Produces the output: A$119 jacket at 30% discount is now priced at 83.300000
Example: Consider the following code fragment:
name1 = "Chris"
name2 = "John"
print("%s and %s are heading to the movies tonight" % (name1,name2))
Produces the output:
Chris and John are heading to the movies tonight
Source: City University of New York, https://academicworks.cuny.edu/bx_oers/29/
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Influence of Solvent Molecules on the Stereochemical Code of Glycyl Residues in Proteins
Eswar, Narayanan and Nagarajaram, HA and Ramakrishnan, C and Srinivasan, N (2002) Influence of Solvent Molecules on the Stereochemical Code of Glycyl Residues in Proteins. In: Proteins: Structure, Function, and Genetics, 49 (3). pp. 326-334.
PDF page200.pdf Restricted to Registered users only Download (3383Kb) | Request a copy
Abstract
The Ramachandranstericmap and energy diagrams of the glycyl residue are symmetric. A plot of (\phi,\psi) angles of glycyl residues in 250 nonhomologous and high-resolution protein structures is also largely symmetric. However, there is a clear aberration in the symmetry. Although there is a cluster of points corresponding to the righthanded helical region, the "equivalent" cluster is clearly shifted to in and around the (\phi,\psi) values of $(90^o, 0^o)$ instead of being centered at the left-handed-helical region of $(60^o, 40^o)$. This lack of symmetry exists eveninthe (\phi,\psi) distributionof residues from non- \alpha -helical regions in proteins. Here we provide an explanation for this observation. An analysis of glycyl conformations in small peptide structures and in "coil" proteins, which are largely devoid of helical andsheet regions, shows that glycyl residues prefer to adopt conformations around $(\pm 90^o, 0^o)$ instead of right- and left-handed \alpha helical regions. By using theoretical calculations, such conformations are shown to have highest solvent accessibility in a system of two-linked peptide units with glycyl residue at the central $C^\alpha$ atom. This finding is consistent with the observations from 250 nonhomologous protein structures where glycyl residues with conformations close to $(\pm 90^o, 0^o)$ are seen to have high solvent accessibility. Analysis of a subset of nonhomologous structures with very high resolution (1.5 $\AA$ or better) shows that water molecules are indeed present at distances suitable for hydrogen bond interaction with glycyl residues possessing conformations close to $(\pm 90^o, 0^o)$. It is suggested that water molecules play a key role in determining and stabilizing these conformations of glycyl residues and explain the aberration in the symmetry of glycyl conformations inproteins.
Item Type: Journal Article The copyright belongs to Wiley-Liss, Inc. glycyl residues;protein structures;ramachandran map;solvation Division of Biological Sciences > Molecular Biophysics Unit 31 Dec 2007 19 Sep 2010 04:23 http://eprints.iisc.ernet.in/id/eprint/5599
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by alfredblase
Tags: asap, dipole, fieldplease, inhomogeneous, magnetic
Quote by Meir Achuz The energy difference between the two states is $$\Delta E=2B\cdot\mu$$. The spin can only be flipped by an oscillating magnetic field of frequency $$\hbar\omega=\Delta E$$
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# Calculating the age of the universe
Is the calculated age of the universe that of the visible universe or the entire universe? I dont know how the age is calculated but if it is believed that all we see visibly IS the entire universe then that means it is finite. If it is not finite then the light from the really far astronomcical objects has not reached us yet so there is a possibility it is infinite. Can the method used to calculate the universe age since the Big Bang guarantee that it has an age or is it possible that it existed infinitely?
It is a common point of confusion, but an infinite universe can still have been at a unique singularity in space-time at a finite time in the past.
This singularity is not a "point in space", since every point in the universe participated in the big-bang. It is merely a time at which the scale factor, which multiplies the separation between all spatial points in the universe, was zero.
So in cosmology governed by the Friedmann equation, the age of the universe thus calculated is the same whether you are talking about the "visible" universe or an infinite universe. The light travel time really doesn't come into this, because different parts of even a very large universe can be causally separated yet still have originated at the same singularity.
The simplest assumption about the global properties of the Universe is that it looks the same outside the part that is observable to us, as it does inside. That is, we see a finite part of a Universe that is (probably) infinite in extend. If so, then the calculated age — which is finite — applies to all of the Universe, not just the observable part.
The age is calculated on the basis of the observed expansion rate, and the observed densities of the constituents of the Universe. It is possible to imagine a universe with the right mixture of constituents that has existed forever$^{\dagger}$, but for our particular Universe, this just doesn't seem to be the case; it is ruled out by observations.
As a first-order approximation, you can simply take the age $t_\mathrm{Uni}$ to be the reciprocal of the expansion rate $H_0 = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1} = 2\times10^{-18}$ s. That is,
$$t_\mathrm{Uni} \sim \frac{1}{H_0} = 14\,\mathrm{billion\,years}.$$
However, this assumes that the Universe has been expanding at the same rate throughout its entire history, which is hasn't. More generally, the age is calculated from integrating (numerically except for simplified approximations) the Friedmann equation, yielding 13.819 billion years.
I should say that the calculated age is the time from the Big Bang till now. I guess the safest thing to say is that we don't know what happened the first tiny fraction of a second or so after creation, and in principle it could have existed before this instant, collapsed, and then re-expanded. But no observations I know of suggest this.
$^\dagger$An example of a temporally infinite universe is one containing energy only in the form of a cosmological constant. In this case, the Friedmann equation reduces to $da/dt=aH_0$, with $a$ the scale factor ("size") of the universe, the solution of which is an exponential function with zero size only at $t = -\infty$.
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# A hole is made in a convex lens. Then :(A) a hole appears in the image(B) image size decreases(C) image intensity decreases(D) No change Please give the correct option .
Dear Student
Image intensity decreases.
When an object is placed in front of the convex lens such that the corresponding image is produced after refraction through the lens.
Then there are infinite number of light rays originating from the object which will undergo refraction and converge to produce the corresponding image.
As a result of the hole, a few light rays will not be able to undergo the required refraction.
Hence, the light intensity of the image will decrease. The image will now look a little dull.
But image characteristics (i.e. position and size) will remain unchanged.
Regards
• 1
What are you looking for?
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D. Sum
time limit per test
1.5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output
You are given $n$ non-decreasing arrays of non-negative numbers.
Vasya repeats the following operation $k$ times:
• Selects a non-empty array.
• Puts the first element of the selected array in his pocket.
• Removes the first element from the selected array.
Vasya wants to maximize the sum of the elements in his pocket.
Input
The first line contains two integers $n$ and $k$ ($1 \le n, k \le 3\,000$): the number of arrays and operations.
Each of the next $n$ lines contain an array. The first integer in each line is $t_i$ ($1 \le t_i \le 10^6$): the size of the $i$-th array. The following $t_i$ integers $a_{i, j}$ ($0 \le a_{i, 1} \le \ldots \le a_{i, t_i} \le 10^8$) are the elements of the $i$-th array.
It is guaranteed that $k \le \sum\limits_{i=1}^n t_i \le 10^6$.
Output
Print one integer: the maximum possible sum of all elements in Vasya's pocket after $k$ operations.
Example
Input
3 3
2 5 10
3 1 2 3
2 1 20
Output
26
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## Anas.P one year ago fourier transform question first question please as soon as possible.
1. anas.p
@dan815
2. anas.p
Find the fourier Transform of $e^{-a^{2}x^{2}} ,a>0$Given $\int\limits_{-\infty}^{\infty} e^{-t} dt = \sqrt{\pi}$
3. anas.p
@SolomonZelman
4. anonymous
I think you meant $$e^{-\color{red}{t^2}}$$ in that last integral?
5. anonymous
\large\begin{align*}\mathcal{F}\{e^{-a^2x^2}\}&=\frac{1}{2\pi}\int_{-\infty}^\infty e^{-a^2x^2}e^{-i\xi x}\,dx\\[2ex] &=\frac{1}{2\pi}\int_{-\infty}^\infty e^{-a^2\left(x^2+\frac{i\xi}{a^2}x\right)}\,dx \end{align*} Complete the square: \begin{align*}-a^2\left(x^2+\frac{i\xi}{a^2}x\right)&=-a^2\left(x^2+\frac{i\xi}{a^2}x+\left(\frac{i\xi}{2a^2}\right)^2-\left(\frac{i\xi}{2a^2}\right)^2\right)\\[2ex] &=-a^2\left(\left(x+\frac{i\xi}{2a^2}\right)^2+\frac{\xi^2}{4a^4}\right)\\[2ex] &=-\left(ax+\frac{i\xi}{2a}\right)^2-\frac{\xi^2}{4a^2}\end{align*} A substitution will do the rest: $$y=ax+\dfrac{i\xi}{2a}$$ with $$dy=a\,dx$$.\large\begin{align*}\mathcal{F}\{e^{-a^2x^2}\}&=\frac{1}{2a\pi}\int_{-\infty}^\infty e^{-y^2-\frac{\xi^2}{4a^2}}\,dy \end{align*}
6. anas.p
yes it was $e^{t^{-2}}$ isn't it $\frac{ 1 }{ \sqrt{2\pi} }$ instead of $\frac{ 1 }{ {2\pi} }$ otherwise thank you very much... it had been bugging me for days...
7. anonymous
I've seen a few variations of the transform's definition, things like $$\dfrac{1}{2\pi}\int e^{-i\xi x}\,dx$$ and $$\int e^{-2\pi i\xi x}\,dx$$ (which are identical) as well as $$\dfrac{1}{\sqrt{2\pi}}$$ in place of $$\dfrac{1}{2\pi}$$. (see here: http://mathworld.wolfram.com/FourierTransform.html ) I'm not sure myself about the details of the advantage to using one definition over another, but I think it has something to do with symmetry. As long as you're consistent, either way is fine.
8. anas.p
cool..... thanks again
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Coming Seminars
Our regular seminar program covers a broad range of topics from applied mathematics, pure mathematics and statistics. All welcome, especially students. A complete list of past seminars can be accessed via the left-hand menu.
Thomas Britz
The popular course MATH3411 Information, Codes, and Ciphers was this previous term given a light Digital Uplift. In this talk, I will describe what this actually means, what the processes were, and what the outcomes were (and are). I will also...
Daniel Altman
Szemer\'edi's theorem says that subsets of the integers with positive density contain $k$-term arithmetic progressions ($k$APs). We investigate the probability threshold for which $k$APs are guaranteed when the set of allowed common differences in...
Tim Trudgian
… turn to square-free numbers! These include the primes as well as other numbers that are ‘not too composite’. If the primes are giving us grief, then we can content ourselves with solving questions on square-free numbers. This is a longer, more...
Simos Meintanis
There exist a number of tests for assessing the nonparametric heteroskedastic location-scale assumption. Here we consider a goodness-of-fit test for the more general hypothesis of the validity of this model under a parametric functional...
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# A combinatorial model for the decomposition of multivariate polynomials rings as an $S_n$-module
Orellana Rosa
Abstract:
We consider the symmetric group $S_n$ module of the polynomial ring with $m$ sets of $n$ commuting variables and $m'$ sets of $n$ anti-commuting variables and calculate that the multiplicity of an irreducible indexed by the partition $\lambda$ (a partition of $n$) is the number of multiset tableaux of shape $\lambda$ satisfying certain ...More
Code:
Data:
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# What's the Q of a pole at the origin of the s-plane?
I'm writing a simple function in Python to return the Q of a circuit, given its poles.
The Q of a system with pole p, can be found using $Q=-\frac{\left|p\right|}{2*Re(p)}$. Obviously, in a natural system, such a pole must come as part of a pair, and both would yield the same result.
For coincident poles on the real axis, this gives a Q of 1/2 (critically damped). For poles on the imaginary axis, that gives a Q of $\infty$ (undamped).
Writing the function left me with the question, as a matter of completeness, of what to do if the pole is at the origin. Is there a customary value to assign to poles at the origin?
Background material:
For anyone interested in where the equation relating pole location to Q comes from, It derives from the 2nd order transfer function:
Graphically described here:
A decent discussion of Q and damping in 2nd order systems can also be found here:
which gives an excellent review of how the pole placement corresponds to various damping characteristics.
• have a look to the properties here: en.wikipedia.org/wiki/Pole_and_polar – Behind The Sciences Mar 21 '16 at 8:14
• @BehindTheSciences: Would you be able to answer the question after having read the article you linked to? – Matt L. Mar 21 '16 at 8:45
Note that the formula given in your question is valid for a system with a complex-conjugate pole pair $p$ and $p^*$ with $\text{Re}(p)\neq 0$. As you've correctly pointed out, if for $|p|>0$ the real part $\text{Re}(p)$ approaches zero, the $Q$ factor approaches infinity. This is the case for a pole pair on the $j\omega$-axis with $|p|>0$, i.e. not at $s=0$.
Also note that you can't use that formula for two distinct real-valued poles. That situation corresponds to an overdamped system with $Q<\frac12$.
The problem with a double pole at $s=0$ is that there is no reasonable way to evaluate the formula given in your question. The corresponding limit does not exist.
Having said that, we can think of a reasonable definition of $Q$ for the case of a double pole at $s=0$. For $p=p^*=0$ the transfer function of the corresponding system is (assuming no finite zeros)
$$H(s)=\frac{A}{s^2}\tag{1}$$
with some constant $A$. The impulse response is
$$h(t)=\mathcal{L}^{-1}\{H(s)\}=A\,t\,u(t)\tag{2}$$
We have to ask ourselves what we mean by $Q$ in this case. Since the damping is zero, you could say that $Q=\infty$. I haven't come across a definition of $Q$ in the case of a double real pole at $s=0$, and I think that for this degenerate case there cannot be any useful definition. If I had to decide on a value, I'd say $Q=\infty$, in analogy with all other pole pairs on the $j\omega$-axis.
• @MattL.: Thanks for taking the time to show the inverse Laplace transform that supports your opinion-- I should have thought to try that. I think it's pretty clearly not critically damped when you look at it that way. – Omegaman Mar 22 '16 at 18:37
My research is involving some aspect underdampness lower dampness and almost nodampness the root locus diagram of a planet by its spin forming Q reonance as the pole moves along jw axis a circle above a plus code.Even this oscillate between plus and minus underdamped lower damped with middle zero damped in understanding diffeten Q factors of panetary emissions promoting the Q factor of planets of our solar system playing the role of genetic hologram espeially that of Jupiter takes up the second quadrant and strangely Saturn takes up the fourth Quadrant perhaps forming a helical resonance also is attached with it. Sankaravelayudhan Nandakumar.
New contributor
sankaravelayudhan Nandakumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
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1. ## Gaussian distribution
Hi!
I'm having a hard time solving this problem:
I hope somebody can give me a little help. I've been strugling with this for quite a while now.
/Iljtitj
2. You want to find,
$\displaystyle \int_{-\infty}^{\infty} \frac{1}{\sigma \sqrt{2\pi}}x^2\exp \left( - \frac{(x-\mu)^2}{2\sigma^2} \right) dx$
Let us use the hint,
$\displaystyle u=\frac{x-\mu}{\sqrt{2} \sigma}$
Also,
$\displaystyle u'=\frac{1}{\sigma \sqrt{2}}$
Thus,
$\displaystyle \frac{1}{\sqrt{\pi}}\int_{-\infty}^{\infty} x^2 \exp (-u^2) u' dx$
Since,
$\displaystyle x=\sqrt{2} \sigma u+\mu$
Thus, by substitution rule,
$\displaystyle \frac{1}{\sqrt{\pi}}\int_{-\infty}^{\infty} (\sqrt{2} \sigma u+\mu)^2 \exp (-u^2) du$
Thus, open,
$\displaystyle \frac{1}{\sqrt{\pi}} \int_{-\infty}^{\infty} (2\sigma^2u^2 +u\sqrt{2} \sigma \mu+\mu^2) \exp(-u^2)du$
But that is the idea.
Also note that,
$\displaystyle \int_{-\infty}^{\infty} e^{-x^2}dx=\sqrt{\pi}$
This is why $\displaystyle \pi$ will cancel out in the end.
Hope that helps.
3. ## Thanks
Thanks alot, I'll give it another try with this.
4. Originally Posted by iljitj
Hi!
I'm having a hard time solving this problem:
I hope somebody can give me a little help. I've been strugling with this for quite a while now.
/Iljtitj
$\displaystyle I=\frac{1}{\sigma \sqrt{2 \pi}} \int_{-\infty}^{\infty} x^2 \exp \left( -\frac{(x-\mu)^2}{2\sigma ^2}\right) dx$
Now let $\displaystyle u=\frac{x-\mu}{\sqrt{2}\sigma}$, so $\displaystyle x=\sqrt{2}\sigma u+\mu$. Hence:
$\displaystyle I=\frac{1}{ \sqrt{ \pi}} \int_{-\infty}^{\infty} (\sqrt{2}\sigma u+\mu)^2 \exp (-u^2) du=$$\displaystyle \frac{1}{\sqrt{ \pi}} \int_{-\infty}^{\infty} [2\sigma^2 u^2+2 \sqrt{2}\sigma u \mu+\mu^2] \exp (-u^2) du$
as the middle term in the integral is odd it integrates up to $\displaystyle 0$ so:
$\displaystyle I=\frac{1}{\sqrt{ \pi}} \int_{-\infty}^{\infty} [2\sigma^2 u^2+\mu^2] \exp (-u^2) du$
The last term integrates up to $\displaystyle \mu^2$ as
$\displaystyle \frac{1}{ \sqrt{ \pi}} \int_{-\infty}^{\infty} \exp(-u^2) du=1$
and the first term integrates up to $\displaystyle \sigma^2$ as:
$\displaystyle \frac{1}{ \sqrt{2 \pi}} \int_{-\infty}^{\infty}x^2 \exp(-x^2/2) dx=1$
so:
$\displaystyle I=\sigma^2+\mu^2$
RonL
5. ## Cool, thanks..
Many thanks. I see now It's very much appreciated.
/Iljitj
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# Change is just change
Plus ça change, plus c’est la même chose
In the midst of the COVID-19 pandemic, we should all be getting a lot of time for introspection and examination. This was going to be a post about the changes I needed to make to git-flow so that we can support the changes that github decided on around default branch naming in git. It veered off on a tangent pretty quickly because I didn’t need to do anything with git-flow. The original script writer decided that master, production, and main were all valid trunk branch names for the default behaviour, so now we have git-flow enabled with main+develop and older repositories with master+develop. I suspect this isn’t by coincidence.
The whole naming thing got me to thinking about the the reasons for the change and whether we should consider it something that people will just label political correctness gone mad. It should be apparent now that the bulk of civilization is built on top of the indenture of the other and the exploitation of the other for the beneft of those who are inside. Change only comes when people have a reason to change, this seldom comes from those that want things to stay the same. The people who are most determined to make those changes aren’t going to be the insiders. For me the status quo works so this means I have no fundamental desire to change it, but this just means I should be supportive of change when it comes.
To have some historical context to my own personal situation; I’m a first generation immigrant from Hong Kong (SAR) to the UK a long time ago. I got casual abuse and racism when I was young, I was the only Chinese lad in my school for probably about 10 years (all of primary, 1/2 of secondary). Weakness or otherness in general is going to picked up by children and torn apart and I’ve had plenty of experience of being the other. However, I’ve never been stopped and searched because of the colour of my skin, or been locked up because I got a bit shouty and angry down the pub. That’s left me with a relatively unscathed journey through life, so I’m pretty ambivalent about it all.
My own culture and upbringing feeds in as well when examining my ambivalence. There’s plenty of things that my parents say that are racist; my dad complained about people on the bus chattering away on the bus in a foreign language, I tried to arch an eyebrow at him, failed, but mentioned that he never speaks English to my mum on the bus. They have a phrase they use at dinner time to hurry us along: The Japanese are coming1; they say it to their grandchildren when they’re being particularly tardy at the dinner table. This harks back to a time before theirs (they were born in the 1940s) but is a phrase that has seeped into their consciousness, into mine, and into their grandchildren. Is it a racist turn of phrase? almost certainly. They didn’t experience it, but they are certainly parroting a truth that was relevant to them in living memory. It isn’t relevant to me, but I’m still parroting it as though it were a truism that shouldn’t be questioned.
There are those that are going to go all ragey and quote Niemoller and say it’s the thin end of the wedge, or the start of a slippery slope. Language evolves and changes; its meaning derives from consensus and no amount of railing against the dying of the light is going to change that. Language purists have already lost the fight about literally, fewer/less, use of the semi-colon and the greengrocer’s apostrophe. They’re going to lose the fight about master, especially outside of its meaning of expertise. This isn’t the hill that I’d choose to die on; if I needed to patch git-flow to make things work seamlessly with our internal notion of repository correctness, then I would have. We certainly wouldn’t have insisted on retaining the master+develop naming convention.
1. No, not in the influx of technology way. ↩︎
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Article
# Long-range dependence - Ten years of Internet traffic modeling
Department of Computer Science and Engineering, University of California, Riverside, Riverside, California, United States
(Impact Factor: 2). 10/2004; 8(5):57- 64. DOI: 10.1109/MIC.2004.46
Source: IEEE Xplore
ABSTRACT Self-similarity and scaling phenomena have dominated Internet traffic analysis for the past decade. With the identification of long-range dependence (LRD) in network traffic, the research community has undergone a mental shift from Poisson and memory-less processes to LRD and bursty processes. Despite its widespread use, though, LRD analysis is hindered by the difficulty of actually identifying dependence and estimating its parameters unambiguously. The authors outline LRD findings in network traffic and explore the current lack of accuracy and robustness in LRD estimation. In addition, they present recent evidence that packet arrivals appear to be in agreement with the Poisson assumption in the Internet core.
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##### Conference Paper: Complementary Problems for Subset-Sum and Change Making Problems
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ABSTRACT: In this study, Change Making Problem (CMP) and Subset-Sum Problem (SSP), which can arise, in practice, in some classes of one dimensional cargo loading and cutting stock problems, are researched. These problems are often used in computer science, as well. CMP and SSP are NP-hard problems and these problems can be seen as types of the knapsack problem in some ways. The complementary problems for the change making problem and the subset-sum problem are defined in this study, and it is aimed to examine the CMP and SSP by means of the complementary problems.
Third International Conference on Computational Science, Engineering and Information Technology, Konya Turkey; 06/2013
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##### Article: Marcinkiewicz Law of Large Numbers for Outer-products of Heavy-tailed, Long-range Dependent Data
[Hide abstract]
ABSTRACT: The Marcinkiewicz Strong Law, lim n→∞ 1 n 1 p n ∑ k=1 (D k − D) = 0 a.s. with p ∈ (1, 2), is studied for outer products D k = X k X T k , where {X k }, {X k } are both two-sided (multivariate) linear processes (with coefficient matrices (C l), (C l) and i.i.d. zero-mean innovations {Ξ}, {Ξ}). Matrix sequences C l and C l can decay slowly enough (as |l| → ∞) that {X k , X k } have long-range dependence while {D k } can have heavy tails. In particular, the heavy-tail and long-range-dependence phenomena for {D k } are handled simultaneously and a new decoupling property is proved that shows the convergence rate is determined by the worst of the heavy-tails or the long-range dependence, but not the combination. The main result is applied to obtain Marcinkiewicz Strong Law of Large Numbers for stochastic approximation, non-linear functions forms and autocovariances.
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##### Article: Convergence Rates and Decoupling in Linear Stochastic Approximation Algorithms
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ABSTRACT: Almost sure convergence rates for linear algorithms $h_{k+1} = h_k +\frac{1}{k^\chi} (b_k-A_kh_k)$ are studied, where $\chi\in(0,1)$, $\{A_{k}\}_{k=1}^\infty$ are symmetric, positive semidefinite random matrices and $\{b_{k}\}_{k=1}^\infty$ are random vectors. It is shown that $|h_n- A^{-1}b|=o(n^{-\gamma})$ a.s. for the $\gamma\in[0,\chi)$, positive definite $A$ and vector $b$ such that $\frac{1}{n^{\chi-\gamma}}\sum\limits_{k=1}^n (A_{k}- A)\to 0$ and $\frac{1}{n^{\chi-\gamma}}\sum\limits_{k=1}^n (b_k-b)\to 0$ a.s. When $\chi-\gamma\in\left(\frac12,1\right)$, these assumptions are implied by the Marcinkiewicz strong law of large numbers, which allows the $\{A_k\}$ and $\{b_k\}$ to have heavy-tails, long-range dependence or both. Finally, corroborating experimental outcomes and decreasing-gain design considerations are provided.
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# How to Append to a File With PHP
Data is usually stored in a database when people are creating their website. However, sometimes we need to store data in files to make it easier for people to read or modify at a later time.
PHP comes with a lot of functions to read and write data to a file. We can also use a few of them to append data to a file. In this tutorial, you'll learn two different ways of appending data to a file with PHP.
## Understanding the file_put_contents() Function
The file_put_contents() function is one of the easiest ways to write data to a file with PHP. It accepts four different parameters that determine its behavior. These parameters are:
• filename: the path to the location of the file to which we want to write our data.
• data: specifies the data that you want to write to the file. It is usually a string, but you can also specify an array or a stream resource. The function will automatically implode the contents of a single dimensional array with implode() in order to write the data to a file.
• flags: controls the behavior of file_put_contents(). There are three different flags that you can set here, either by themselves or in combination with other flags. Different flags can be combined using the | operator.
• context: useful only in providing additional data to PHP when you are reading or accessing content from a stream.
## Using file_put_contents() to Append Data to a File With PHP
The default behavior of the file_put_contents() function is to overwrite the contents of a given file with any new data you provide. This is not desirable when you want to preserve the old data and add some new data. In such cases, you can use the FILE_APPEND flag to let PHP know that it should append data at the end of content originally present in the file.
Under some special circumstances, you might be appending data to a file from multiple scripts at the same time. In these situations, it is advisable to get an exclusive lock on the file using the LOCK_EX flag. This can help prevent data corruption or some other unexpected behavior. When you use this flag, other scripts will wait for the current process to complete writing to the file before they append their own data.
Here is an example in which some text is appended to an existing file using file_put_contents().
In the above example, we wrote some strings to a file called canada.txt which contains information about Canada. Both the string were appended at the end of the file one after the other.
Keep in mind that this function will create a file if one doesn't already exist. However, it won't create a non-existent directory. So it might be a good idea to check if a file exists before you start writing to it.
## Using fwrite() to Write Data to a File With PHP
Using the file_put_contents() function to write data to a file with PHP is similar to calling fopen(), fwrite(), and fclose() in that order. This means that doing multiple write operations on the same file can be inefficient because we are constantly opening and closing the file again and again.
One way to overcome this issue is to call these functions yourself. Just begin by calling fopen() at the start of the write operation. After that, write content to the file as many times as you like with the fwrite() function. In the end, you can simply call fclose() to close the file handle. Let's discuss each of these steps in detail now.
The fopen() function accepts four different parameters that you can use to tell PHP how it should open a file.
• filename: the name of the file that you want to open.
• mode: the mode for opening a file can be specified using either one or two characters. We want to open the file and then append some text to it. To append, set the mode with the character a or a+. This will place the file pointer at the end of the file. PHP will also try to create the file if it doesn't already exist. When files are opened with the a+ mode, you can also read the contents of the file.
• use_include_path: instructs PHP to look for files inside the specified include path as well. Defaults to false.
• context: useful only in providing additional data to PHP when you are reading or accessing content from a stream.
Now that the file is open, we can use the fwrite() function to add information to the file. fwrite() takes three parameters:
• resource: this is the resource handle we created earlier with fopen().
• string: the text that you want to append to your file.
• length: is optional and it is used to set the maximum number of bytes that should be written to the file.
You can close the file handle by using the fclose() function once you have completed all your write operations.
Here is an example that shows you how to use fopen(), fwrite(), and fclose() to append data to a file.
Contents of square.txt
In this case, we are writing the square of the numbers 1 to 10 in a file called square.txt. We opened it using the fopen() function in a+ mode, which means we can also read content from the file as well as appending our own content. A new line with the current value of \$i and its square is appended to our file with each iteration of the for loop.
There are a few functions like fread() and fgets() that you could use to read whatever is written inside the file. However, you will usually need to use fseek() to place the file pointer at the desired position to read the data as expected. After the loop, we go to the beginning of the file and read its first line with fgets().
Finally, we close the handle to our file by calling the function fclose().
## Final Thoughts
In this tutorial, we learned two different methods of appending data to a file with PHP. Using the file_put_contents() function is more convenient for writing data to a file. However, using fwrite() can be more efficient when you have to do multiple write operations on a file. Opening a file with fopen() to append the data also gives you the option to read its contents by moving the file pointer to the desired location.
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# Base 10 arithmetic
The characters in the ascii codes have a decimal equivalent: http://www.asciitable.com/. Let's assume the decimal value of each ascii code requires to be 3 digits. So the NUL character is 000. The lower case d character is 100. And so forth. Below is an arithmetic solution to find what the middle digit will be.
(x - (100 * (x / 100))) / 10
For example, if the decimal code is 010, then the formula will work because it gives us 1, which is the middle digit:
(10 - (100 * (10 / 100))) / 10 = 1
Same thing if we plug in another decimal like 100, whose middle digit is 0:
(100 - (100 * (100 / 100))) / 10 = 0
I can easily solve for the solution, but my question is how does the arithmetic work so effectively here in getting us that middle digit? I am quite familiar with the base-10 decimal system, and I can see why we divide by 10 since the middle digit is in the 10's place, but other than that, I'm not sure how this works so effectively.
• What do you think dividing by 100 does? (Note that you are implicitly using C-style division here: 10 / 100 == 0 for your middle statement to actually work out.) – tabstop Feb 10 '14 at 23:56
• The $i$'th digit from the right in base $d$ can also be extracted with $\frac{n}{d^{i-1}}\pmod d$, if you can use the modulo ($\%$) operator. – Ragnar Feb 10 '14 at 23:57
• @tabstop yes that is true, it ignores the remainder and decimal and just keeps the quotient. – JohnMerlino Feb 10 '14 at 23:57
Your division signs are integer divisions, so $x/100$ is the hundreds digit of $x$. If $x$ could be larger than $999$, this expression would have all the digits of $x$ except the lowest two. When you do $(x-(100*(x/100))$ you are subtracting off $100$ times the hundreds digit, which leaves you with just the tens and ones digit. Another way to express this is to use $x \pmod {100}$, which is expressed in many computer languages as $x \% 100$ Now, given that you just have the lowest two digits of $x$, dividing by $10$ will get you the higher of those.
A more general approach for extracting digits is to start from the ones digit and use the modulo operator. The ones digit of $x$ is $x\%10$ The tens digit of $x$ is $(x/10)\%10$ The hundreds digit is $(x/100)\%10$ and so on.
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## Algebraic & Geometric Topology
### The coarse geometry of the Kakimizu complex
#### Abstract
We show that the Kakimizu complex of minimal genus Seifert surfaces for a knot in the $3$–sphere is quasi-isometric to a Euclidean integer lattice $ℤn$ for some $n≥0$.
#### Article information
Source
Algebr. Geom. Topol., Volume 14, Number 5 (2014), 2549-2560.
Dates
Revised: 31 January 2014
Accepted: 7 February 2014
First available in Project Euclid: 19 December 2017
https://projecteuclid.org/euclid.agt/1513715995
Digital Object Identifier
doi:10.2140/agt.2014.14.2549
Mathematical Reviews number (MathSciNet)
MR3276840
Zentralblatt MATH identifier
1302.57022
#### Citation
Johnson, Jesse; Pelayo, Roberto; Wilson, Robin. The coarse geometry of the Kakimizu complex. Algebr. Geom. Topol. 14 (2014), no. 5, 2549--2560. doi:10.2140/agt.2014.14.2549. https://projecteuclid.org/euclid.agt/1513715995
#### References
• J E Banks, On links with locally infinite Kakimizu complexes, Algebr. Geom. Topol. 11 (2011) 1445–1454
• J E Banks, The Kakimizu complex of a connected sum of links, Trans. Amer. Math. Soc. 365 (2013) 6017–6036
• R Budney, JSJ-decompositions of knot and link complements in $S\sp 3$, Enseign. Math. 52 (2006) 319–359
• P de la Harpe, Topics in geometric group theory, University of Chicago Press, Chicago, IL (2000)
• A Hatcher, Notes on basic $3$–manifold topology (2007) Available at \setbox0\makeatletter\@url http://www.math.cornell.edu/~hatcher/3M/3Mfds.pdf {\unhbox0
• O Kakimizu, Finding disjoint incompressible spanning surfaces for a link, Hiroshima Math. J. 22 (1992) 225–236
• O Kakimizu, Classification of the incompressible spanning surfaces for prime knots of 10 or less crossings, Hiroshima Math. J. 35 (2005) 47–92
• R C Pelayo, Diameter bounds on the complex of minimal genus seifert surfaces for hyperbolic knots, PhD thesis, California Institute of Technology (2007) Available at \setbox0\makeatletter\@url http://search.proquest.com/docview/1039265228 {\unhbox0
• P Przytycki, J Schultens, Contractibility of the Kakimizu complex and symmetric Seifert surfaces, Trans. Amer. Math. Soc. 364 (2012) 1489–1508
• M Sakuma, Minimal genus Seifert surfaces for special arborescent links, Osaka J. Math. 31 (1994) 861–905
• M Sakuma, K J Shackleton, On the distance between two Seifert surfaces of a knot, Osaka J. Math. 46 (2009) 203–221
• M Scharlemann, A Thompson, Finding disjoint Seifert surfaces, Bull. London Math. Soc. 20 (1988) 61–64
• R T Wilson, Knots with infinitely many incompressible Seifert surfaces, J. Knot Theory Ramifications 17 (2008) 537–551
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# Examples of Mathematics in Court
In court trials, natural sciences such as physics and biology routinely make an appearance, e.g. when estimating the speed of a vehicle based on impact damage or trying to deduce from the condition of a corpse how long ago the person died.
Pure mathematics is found in courtrooms much more rarely (perhaps because of the difficulty of convincing a judge – or worse, a jury – with mathematical arguments). I am currently aware of the following two broad categories of mathematics being invoked in a trial:
1. Probability and conditional probability, especially the misunderstanding thereof. One instance of this is known as the Prosecutor's fallacy and basically involves a confusion of prior and posterior in Bayesian inference. The Wikipedia page mentions the infamous "Sally Clark case" as a possible example of this fallacy resulting in a wrongful conviction. BBC News also has an article according to which mathematical reasoning about test results played a role in the Knox/Sollecito murder trial.
2. Benford's First-Digit Law which predicts the approximate frequency distribution of digits in real-life data, is not only used as a heuristic for the detection of possible fraud, but shockingly even accepted as evidence of the same by some jurisdictions.
Are there examples of other branches of mathematics that have played a role (for the better or worse) in the courtroom?
As a side note, is is interesting that much of the key courtroom vocabulary like "trial", "case", "law" etc. is also part of standard mathematics lingo, which makes meaningful web searches for such material quite challenging.
• matheducators.stackexchange.com/questions/5676/… – JP McCarthy Nov 14 '14 at 12:10
• There's a section in Salvadori's Why Buildings Fall Down in which he describes testifying as an expert witness in a case involving a building collapse, explaining to the jury the equations that govern the maximum loading of a dome, and being cross-examined about that. – MJD Nov 14 '14 at 14:28
• The infamous Indiana pi Bill comes to mind. :) – David H Nov 21 '14 at 10:23
• "Objection, your honor! The counselor is assuming the continuum hypothesis, which is clearly unprovable from the axioms of $\sf ZFC$ as shown by Goedel and Cohen!!!" $\tag*{}$ "Sustained." – Asaf Karagila Nov 23 '14 at 23:54
• "The paper was awarded a special prize of $400 that the author did not have to pay to the state of California." :) – user139000 Nov 14 '14 at 11:31 The book Math on Trial: How Numbers Get Used and Abused in the Courtroom by Leila Schneps and Coralie Colmez has many examples. B. Grofman and H. Scarrow, ‘Iannucci and Its Aftermath: The Application of the Banzhaf Index to Weighted Voting in the State of New York’, in Steven Brams, Andrew Schotter and Gerhard Schwodiauer (Eds.), Applied Game Theory, Physica-Verlag, Vienna,$1979$,$168$-$183\$, discusses the use and misuse of the Banzhaf power index by the courts; a PDF is available here.
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PERTURBO is an open source software to compute from first principles the scattering processes between charge carriers (electrons and holes) and phonons, defects, and photons in solid state materials, including metals, semiconductors, oxides, and insulators. In the current version, PERTURBO mainly computes electron-phonon (e-ph) interactions and phonon limited transport properties in the framework of the Boltzmann transport equation (BTE). These include the carrier mobility, electrical conductivity, and Seebeck coefficient. PERTURBO can also compute the ultrafast carrier dynamics (for now, with fixed phonon occupations) by explicitly time-stepping the time-dependent BTE. We will include additional electron interactions, transport and ultrafast dynamics calculations in future releases.
PERTURBO is written in Fortran95 with hybrid parallelization (MPI and OpenMP). The main output format is HDF5, which is easily portable from one machine to another and is convenient for postprocessing using high-level languauges (e.g., Python). PERTURBO has a core software, called perturbo.x, for electron dynamics calculations and an interface software, called qe2pert.x, to read output files of Quantum Espresso (QE, version 6.4.1) and Wannier90 (W90, version 3.0.0 and higher). The qe2pert.x interface software generates an HDF5 file, which is then read from the core perturbo.x software. In principle, any other third-party density functional theory (DFT) codes (e.g., VASP) can use PERTURBO as long as the interface of the DFT codes can prepare an HDF5 output format for PERTURBO to read.
For more details on the code structure of PERTURBO, we refer the users to the manuscript accompying the source code:
• Jin-Jian Zhou, Jinsoo Park, I-Te Lu, Ivan Maliyov, Xiao Tong, Marco Bernardi, “Perturbo: a software package for ab initio electron-phonon interactions, charge transport and ultrafast dynamics”. Preprint: arxiv 2002.02045
We gratefully acknowledge the National Science Foundation for supporting the development of PERTURBO.
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# For which values is $x^3$ less than or equal to $3x$?
The title says it all. The answers say:
$x\le -\sqrt{3}$ and $0\le x\le \sqrt{3}$
(can someone edit this so all the $<$ have an 'or equal to' sign. Edit the roots as well please.
I'm not sure how to attempt this question. When I simplify, I get $x^2\le 3$, so $x\le \pm\sqrt{3}$.
Thanks!
• For $\le$ you want \le; the plus-or-minus sign is \pm, and the square root is \sqrt{3}. – Brian M. Scott May 23 '13 at 9:13
The equality can be solved very easily.
$$x^3< 3x\iff x(x^2-3)< 0$$
If $x<0, x^2-3>0$
As $x^2-3>0\implies$ either $x>\sqrt3$ or $x<-\sqrt3$
and as $x<0$ the required region will be $x<-\sqrt3$
Similarly, if $x>0, x^2-3<0\implies -\sqrt3<x<\sqrt3$
and as $x>0$ the required region will be $0<x<\sqrt3$
Alternatively,
HINT:
$$x^3< 3x\iff x(x-\sqrt3)(x+\sqrt3)< 0$$
This will hold true if odd number (one or three) of factors $< 0$
Now check for the ranges $(-\infty,-\sqrt3);[-\sqrt3,0);[0,\sqrt3);[\sqrt3, \infty)$
• I got: $x \le 0$, $x \le -\sqrt {3}$, $x \le \sqrt {3}$ What did I do wrong? – missiledragon May 23 '13 at 9:16
• @missiledragon, how have you simplified ? Please find the edited answer – lab bhattacharjee May 23 '13 at 9:22
• Alright, if there was a similar question, but it had an $x^2$ instead of $x^3$ would you need to test for both greater than or less than $0$? – missiledragon May 23 '13 at 9:27
• @missiledragon, $a\cdot b<0\implies$ either $(a>0$ and $b<0)$ or $(b>0$ and $a<0)$ So, try to prove $(x-a)(x-b)<0$ where $a<b\implies a<x<b$ – lab bhattacharjee May 23 '13 at 9:28
• There seems to be a mistake in the first explanation. If $x<-\sqrt{3}$ or $x>\sqrt{3}$, and it's known that $x<0$, then $x<-\sqrt{3}$, not $-\sqrt{3}<x<0$. – Glen O May 23 '13 at 9:35
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# Trying to Understand Encrypting INI data
## Recommended Posts
So to use the _StringEncrypt function I have to have the value I'm encrypting in the function. Then once I want to decrypt I have to have that value in the function too? That is what I do not understand. For example I used the following code to add two encrypted values to an INI file:
#include <String.au3>
#include <file.au3>
#include <INet.au3>
$iniFile = "dir"$s_EncryptText1 = "username"
$s_EncryptText2 = "password"$s_EncryptPassword = "random characters"
IniWrite ( $iniFile, "Settings", 6, _StringEncrypt ( 1,$s_EncryptText1, $s_EncryptPassword, 1 ) ) IniWrite ($iniFile, "Settings", 7, _StringEncrypt ( 1, $s_EncryptText2,$s_EncryptPassword, 1 ) )
So those two variables, $s_EncryptText1 and 2, would they be necessary to be able to decrypt the values in the INI files? That to me doesn't make much sense and would seem to defeat the purpose of encrypting in the first place. Or am I missing something? If not, is there a way I could safely encrypt the strings without having to type the username and password in the script in clear text. BTW, this is part of an automated script so it would not help me to have a popup box or something that asks for input. #### Share this post ##### Link to post ##### Share on other sites It doesn't work the way you think, hopefully. Here is how it really works: Local$plaintext = "Assume that you can read this sentence."
Local $password = "s0Me 95% SékiuRe p@ß_wörd" ;; encryption Local$cyphertext = _StringEncrypt(1, $plaintext,$password)
ConsoleWrite($cyphertext & @LF) ; .../... ;; in some other part of code or another program Local$recoveredPlaintext = _StringEncrypt(0, $cyphertext,$password)
I guess what I'm trying to explain is that I'm okay with having a clear text password for encryption in the script. But I just do not understand what the value "$s_EncryptText" is used for? Would this be my username, and then I would need a whole new line for the password with a second value? Edited by Webs #### Share this post ##### Link to post ##### Share on other sites This should make sense to you I hope. You're waaaay overcomplicating this: #NoTrayIcon #include <String.au3> #cs Ini File: [Settings] user=50980AD72A6D1F0F997015124C4B3583 pass=509D0DD52B6B1F0E980015674D443582 Generate those values: ConsoleWrite(_StringEncrypt(1, "username",$sEncPass) & @CRLF)
ConsoleWrite(_StringEncrypt(1, "password", $sEncPass) & @CRLF) #ce$iniFile = "C:\some\path\to\inifile.ini"
$sEncPass = "secret"$sUser = _StringEncrypt(0, IniRead($iniFile, "Settings", "user", ""),$sEncPass)
$sPass = _StringEncrypt(0, IniRead($iniFile, "Settings", "pass", ""), $sEncPass) ConsoleWrite($sUser & " : " & \$sPass & @CRLF)
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Put simply: the same function call that encrypted your plain text can also be used to decrypt the encrypted version. So you pass the plain text and password in the first time, then you call the same functon but this time you pass in the encrypted text and the password, and you get back the unencrypted text.
The simplest form of symmetric encryption is "ROT13", which means "Rotate 13 characters". If you write down the 26-character alphabet on the outside of a circle, and rotate by 13 characters on the circle for each character of your input, a user name of "phibbs" would become "cuvoof". If you then take "cuvoof" and pass it through the same encryption process, you get "phibbs" back again. _StringEncrypt() is like that, but uses a password to make it a bit less obvious than ROT13.
Edited by PhilHibbs
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Thanks wraithdu, I wasn't think about it correctly. Having the INIRead function inside the stringencrypt is what I was missing. For someone my brain didn't latch onto that concept.
Thanks for the explanation of the encryption Phil, that makes sense. I think it should be secure enough for what I'm doing.
## Create an account
Register a new account
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# Ubuntu – Can the “Starred” folder in the left pane of Files (nautilus) be removed
nautilus
On Ubuntu 19.10, I disable tracker because I do not like how my computer is overheating for several minutes after startup, and because I prefer full text search not be enabled in the file manager by default. The "Star" feature relies on Tracker and therefore does not work when tracker is disabled.
No option to disable the "Starred" folder is exposed in the Nautilus preferences, nor is a dconf setting available. The file user-dirs-dir determines the "special user folders" displayed in the left pane, but not the "Recent" or "Starred" items.
The question is: can the "Starred" item in the left pane (bookmark pane) of Files (nautilus) be removed?
There are a couple of not that trivial ways to remove the "Starred" item in the left bar of nautilus. The second option involves editing source code and recompiling. I will only cover the first way here.
1 - Create a folder to store the override
mkdir ~/.config/nautilus/ui
2 - Extract the resource description of the main window:
gresource extract /bin/nautilus \
/org/gnome/nautilus/ui/nautilus-window.ui \
> ~/.config/nautilus/ui/nautilus-window.ui
3 - Edit the properties of the GtkPlacesSidebar object: open the file you created in the previous step:
gedit ~/.config/nautilus/ui/nautilus-window.ui
and change the property show-starred-location to false as in following code snippet:
<object class="GtkPlacesSidebar" id="places_sidebar">
...
<property name="show-recent">False</property>
<property name="show-starred-location">False</property>
...
</object>
4 - Set the environment variable to make GLib use this override:
export G_RESOURCE_OVERLAYS="/org/gnome/nautilus/ui=\$HOME/.config/nautilus/ui"
5 - You also need to set this via ~/.pam_environment, because Nautilus is started via D-Bus:
gedit ~/.pam_environment
G_RESOURCE_OVERLAYS DEFAULT="/org/gnome/nautilus/ui=/home/confetti/.config/nautilus/ui"
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Problem when generating hg38 genome indexes using STAR
0
0
Entering edit mode
13 months ago
Sara ▴ 220
I am trying to generate index files for hg38 genome using STAR using this command:
STAR --runThreadN 24 --runMode genomeGenerate --genomeDir /data/star_38/star --genomeFastaFiles hg38.fasta
the process while running seems to be normal as it is shown here:
STAR --runThreadN 24 --runMode genomeGenerate --genomeDir /data/star_38/star --genomeFastaFiles hg38.fasta
STAR version: 2.7.9a compiled: 2021-05-04T09:43:56-0400 vega:/home/dobin/data/STAR/STARcode/STAR.master/source
Dec 28 11:23:53 ..... started STAR run
!!!!! WARNING: Could not move Log.out file from ./Log.out into /data/star_38/star/Log.out. Will keep ./Log.out
Dec 28 11:23:53 ... starting to generate Genome files
Dec 28 11:25:23 ... starting to sort Suffix Array. This may take a long time...
Dec 28 11:25:50 ... sorting Suffix Array chunks and saving them to disk...
Killed
I tried different locations to make sure it's not due to memory but got the same error. do you know what the problem could be?
STAR • 771 views
0
Entering edit mode
I tried different locations to make sure it's not due to memory
This statement makes little sense. Disk location (is that what you mean?) has nothing to do with memory. What is on the machine the output of free -hm?
0
Entering edit mode
ATpoint here is the output:
total used free shared buff/cache available
Mem: 125G 11G 15G 510M 98G 112G
Swap: 8.0G 2.7G 5.3G
0
Entering edit mode
can you try this along with other parameters: --limitGenomeGenerateRAM 100000000000 (100 gb) . Make sure that you have write permissions to the index folder and enough HDD space.
0
Entering edit mode
@cpad0112, I got the same error!
0
Entering edit mode
Could not move Log.out file from ./Log.out into /data/star_38/star/Log.out.
This indicates that you are not able to write to /data/star_38 using the account this job is running under. That is the location you have chosen to put the index in.
0
Entering edit mode
Hi Sara try furnishing gtf file for your reference build and retry the command.(--sjdbGTFfile <input.gtf>)
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# zbMATH — the first resource for mathematics
Perfectly competitive markets as the limits of Cournot markets. (English) Zbl 0553.90023
A perfectly competitive, partial equilibrium market for a single homogeneous good with a (bounded) continuum of infinitesimal firms is considered. Cost functions are essentially unrestricted and are allowed to vary smoothly across firms. A sequence (net) of Cournot markets (each with a finite number of firms) which converge smoothly to the perfectly competitive limit in terms of both the inverse demand functions and the distribution of firm technologies is introduced and it is shown that all markets sufficiently far along the sequence have a Cournot equilibrium and all the Cournot equilibria converge to the perfectly competitive equilibrium of the limit market.
##### MSC:
91B50 General equilibrium theory
Full Text:
##### References:
[1] \scR. Bamon and J. Fraysse, Existence of Cournot equilibrium in large markets, Econometrica, in press. · Zbl 0573.90014 [2] Dasgupta, P.S; Ushio, Y, On the rate of convergence of oligopoly equilibria in large markets: an example, Econom. lett., 8, 13-17, (1981) [3] Fraysse, J; Moreaux, M, Cournot equilibrium in large markets under increasing returns, Econom. lett., 8, 217-220, (1981) [4] Hart, O, Monopolistic competition in a large economy with differentiated commodities, Rev. econom stud., 46, 1-30, (1979) · Zbl 0413.90014 [5] Mas-Colell, A, Walrasian equilibria as limits of noncooperative equilibria. I. mixed strategies, J. econom. theory, 30, 153-170, (1983) · Zbl 0512.90025 [6] Novshek, W, Cournot equilibrium with free entry, Rev. econom. stud., 47, 473-486, (1980) · Zbl 0433.90007 [7] Novshek, W, On the existence of Cournot equilibrium, Rev. econom. stud., 52, (1985) · Zbl 0547.90011 [8] Novshek, W; Sonnenschein, H, Cournot and Walras equilibrium, J. econom. theory, 19, 223-266, (1978) · Zbl 0399.90012 [9] Novshek, W; Sonnenschein, H, Walrasian equilibria as limits of noncooperative equilibria. II. pure strategies, J. econom. theory, 30, 171-187, (1983) · Zbl 0524.90018 [10] Ushio, Y, Cournot equilibrium with free entry: the case of decreasing average cost functions, Rev. econom. stud., 50, 347-354, (1983) · Zbl 0508.90014 [11] Ushio, Y, On the approximate efficiency of Cournot equilibria in large markets, (1983), mimeo
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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# 3+(3)/(2)x+4=4x-(5)/(2)x
## Simple and best practice solution for 3+(3)/(2)x+4=4x-(5)/(2)x equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so dont hesitate to use it as a solution of your homework.
If it's not what You are looking for type in the equation solver your own equation and let us solve it.
## Solution for 3+(3)/(2)x+4=4x-(5)/(2)x equation:
3+(3)/(2)x+4=4x-(5)/(2)x
We move all terms to the left:
3+(3)/(2)x+4-(4x-(5)/(2)x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
3/2x-(+4x-5/2x)+3+4=0
We add all the numbers together, and all the variables
3/2x-(+4x-5/2x)+7=0
We get rid of parentheses
3/2x-4x+5/2x+7=0
We multiply all the terms by the denominator
-4x*2x+7*2x+3+5=0
We add all the numbers together, and all the variables
-4x*2x+7*2x+8=0
Wy multiply elements
-8x^2+14x+8=0
a = -8; b = 14; c = +8;Δ = b2-4acΔ = 142-4·(-8)·8Δ = 452The delta value is higher than zero, so the equation has two solutionsWe use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$The end solution:
$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{113}}{2*-8}=\frac{-14-2\sqrt{113}}{-16}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{113}}{2*-8}=\frac{-14+2\sqrt{113}}{-16}$
`
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×
# Infinite Differentiability
Hey Brilliant users,
I haven't been on here in a while, I've been really busy with school lately. I have, however, found time to write a few original proofs in the past few weeks. At some point I'll put the better/more interesting ones up here. However, I'm having a somewhat annoying problem with one of my proofs. I probably won't post the proof on here for many reasons, one being the proof's actual length and the other being the originality of it. My problem is, the entirety of the proof rests on the fact that the function I'm considering is infinitely differentiable. Assuming this is true, the remainder of the proof is complex but manageable. For some reason, I'm having trouble proving that this function is infinitely differentiable. I know that it is, it wouldn't make sense for it not to be, but I'm having trouble applying full rigor to the problem. I don't want a direct answer, as I'd rather prove it myself, but I would like some advice if anyone can offer it. In short, my question is: How do you prove that a function is infinitely differentiable?
Note by Ethan Robinett
2 years, 3 months ago
Sort by:
The problem is to prove that the function given by y=0,x≤ 0 and y=$$e^{-1/x}$$ , x>0 is C∞
When x is less than 0, there's no problem as obviously the function is infinitely differentiable. Similarly, when x is greater than zero the function is infinitely differentiable, by the properties of the exponential function. As I see it, the difficulty arises in what happens right at 0. For the function to be differentiable there, the function needs to be continuous at 0, and for that to happen both the right hand and left hand limits need to equal 0. So for the function to be infinitely differentiable, one would need to show that in the limit the function $$e^{-1/x}$$ , and all its derivatives, go to zero as x goes to 0.
Am I on the right track? Thanks for any advice. · 2 years, 3 months ago
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Now showing items 1-2 of 2
• #### Evolution of electronic and magnetic properties in the topological semimetal SmSbxTe2-x
(American Physical Society, 2022-04-21)
The ZrSiS-Type materials have attracted intensive attention due to the existence of various topological fermions. The magnetic version of the ZrSiS-Type materials, LnSbTe (Ln=lanthanides), is an ideal candidate to explore ...
• #### Evolution of structure and transport properties of the Ba$_8$Cu$_{16}$P$_{30}$ clathrate-I framework with the introduction of Ga
(American Institute of Physics Inc., 2022-05-09)
Two type-I clathrates were synthesized by introducing Ga into the framework of the Ba$_8$Cu$_{16}$P$_{30}$ type-I clathrate. The introduction of minute amounts of Ga, 1.9% Ga/Mtotal (where $M_{total}$ = Cu + Ga), resulted ...
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Perfect Rainbow Polygons for Colored Point Sets in the Plane
EasyChair Preprint no. 2980
4 pagesDate: March 17, 2020
Abstract
Given a planar $n$-colored point set $S= S_1 \cup \ldots \cup S_n$ in general position, a simple polygon $P$ is called a \emph{perfect rainbow} polygon if it contains exactly one point of each color. The \emph{rainbow index} $r_n$ is the minimum integer $m$ such that every $n$-colored point set $S$ has a perfect rainbow polygon with at most $m$ vertices. We determine the values of $r_n$ for $n \leq 7$, and prove that in general $\frac{20n-28}{19} \leq r_n \leq \frac{10n}{7} + 11$.
Keyphrases: colored point sets, covering, polygon
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# Simon game / Four tiles game
When I read the community challange, I couldn't wait. So here I go with the very first Four tiles game:
import pygame as pg
import sys
import random
import time
import tkMessageBox
if sys.version_info.major == 3:
import tkinter as tk
else:
import Tkinter as tk
from pygame.locals import *
def game(LENGHT):
pg.init()
pg.display.set_caption("Four tiles game")
WIDTH = 600
HEIGHT = 400
DISPLAY = pg.display.set_mode((WIDTH, HEIGHT), 0, 32)
WHITE = (255, 255, 255)
RED = (255, 0, 0)
green = (0, 255, 0)
blue = (0, 0, 255)
yellow = (255, 255, 0)
COLORS = [RED, blue, green, yellow]
WAITING_TIME = 500
def generate_correct_sequence(length):
return [random.randint(1, 4) for _ in range(length)]
def draw_button(n, color):
if n == 1:
pg.draw.rect(DISPLAY, color, (0, 0, WIDTH / 2, HEIGHT / 2))
if n == 2:
pg.draw.rect(DISPLAY,color,
(WIDTH / 2, 0, WIDTH / 2, HEIGHT / 2))
if n == 3:
pg.draw.rect(DISPLAY,color,
(0, HEIGHT / 2, WIDTH / 2, HEIGHT / 2))
if n == 4:
pg.draw.rect(DISPLAY,color,
(WIDTH / 2, HEIGHT / 2, WIDTH / 2, HEIGHT / 2))
def draw_buttons():
for i in range(1, 5):
draw_button(i, COLORS[i - 1])
def what_button_is_clicked(mouse_pos):
"""
The buttons are numbered in the following way
1 | 2
_____
3 | 4
"""
if mouse_pos[0] < WIDTH / 2 and mouse_pos[1] < HEIGHT / 2:
return 1
if mouse_pos[0] > WIDTH / 2 and mouse_pos[1] < HEIGHT / 2:
return 2
if mouse_pos[0] < WIDTH / 2 and mouse_pos[1] > HEIGHT / 2:
return 3
elif mouse_pos[0] > WIDTH / 2 and mouse_pos[1] > HEIGHT / 2:
return 4
def flash(button_number, waiting_time):
draw_button(button_number, WHITE)
pg.display.update()
pg.time.wait(waiting_time)
draw_button(button_number, COLORS[button_number - 1])
pg.display.update()
def inform_user(correct_sequence, delay):
for button in correct_sequence:
flash(button, delay)
draw_buttons()
correct_sequence = generate_correct_sequence(LENGHT)
inform_user(correct_sequence, WAITING_TIME)
while True:
for event in pg.event.get():
if event.type == QUIT:
pg.quit()
if event.type == pg.MOUSEBUTTONUP:
mouse_pos = pg.mouse.get_pos()
if what_button_is_clicked(mouse_pos) == correct_sequence[0]:
correct_sequence.pop(0)
else:
tkMessageBox.showinfo("LOSE", "You are the loser...")
pg.quit()
if correct_sequence == []:
tkMessageBox.showinfo("WIN", "You are the winner!!!")
pg.quit()
if __name__ == "__main__":
root = tk.Tk()
root.wm_title("Four tiles game")
def play():
game(w.get())
INTRODUCTION = tk.StringVar()
INTRODUCTION.set("""Welcome to the four tiles game.
You will see some tiles light up one after the other.
Afterwards, you must click them in the same order they lit up before.""")
tk.Message(root, textvariable=INTRODUCTION, width=500, font=30).pack()
tk.Label(root, text="Select the lenght down here", font=30).pack()
w = tk.Scale(root, from_=1, to=15, orient=tk.HORIZONTAL, length=400)
w.pack()
EDIT: If you want to look at the game with added functionalaties and features and with nicer style go to this GitHub repo.
• Holy code, you're fast! +1 for being first! – Simon Forsberg Dec 4 '14 at 21:33
• +1! I did notice you have a slight typo, def game(LENGHT): should be LENGTH I do that all the time! – Phrancis Dec 4 '14 at 21:39
• is this Python 3 or Python 2.7? – Malachi Dec 4 '14 at 21:49
• @Malachi if sys.version_info.major == 3: should tell you. – 200_success Dec 4 '14 at 21:54
• I might have to try it in 3, because I can't get it to run in 2.7, but I could just be doing something wrong.... – Malachi Dec 4 '14 at 21:57
## 1 Answer
### Missing the specs
You're missing a very important rule of the game:
The pattern gets longer each time the player completes the pattern. If the player presses a wrong button, the game ends.
You implemented only a one-shot round, which is not so interesting.
### Mutually exclusive conditions
These conditions are mutually exclusive:
if n == 1:
# ...
if n == 2:
# ...
if n == 3:
# ...
So you should use elif for the 2nd and later conditions.
### Use consistent names
It's odd to name some constants with all caps, and others with all lowercase like this:
WHITE = (255, 255, 255)
RED = (255, 0, 0)
green = (0, 255, 0)
blue = (0, 0, 255)
yellow = (255, 255, 0)
Be consistent, name all of them all caps!
### Avoid hard-coding
This function relies on having 4 buttons:
def generate_correct_sequence(length):
return [random.randint(1, 4) for _ in range(length)]
It would be better to avoid hardcoding the number 4. You could for example use len(COLORS) instead. Even better would be to use a dedicated constant, and derive both the elements of colors from it, and use it everywhere else where it's relevant, as in this function.
### Use local variables to explain logic
In this code:
if mouse_pos[0] < WIDTH / 2 and mouse_pos[1] < HEIGHT / 2:
return 1
if mouse_pos[0] > WIDTH / 2 and mouse_pos[1] < HEIGHT / 2:
return 2
# ...
mouse_pos[0] and mouse_pos[1] are repeated many times, which is tedious, and not as clear as it can be. I don't actually have tkinter now, but I'm guessing these stand for x and y coordinates.
I would either change the method to take parameters named x and y, or introduce the local variables x and y early in the method:
x = mouse_pos[0]
y = mouse_pos[1]
The rest of the code would become shorter, and clearer.
### Why not use 0-base indexing everywhere?
This method is slightly more complex than it needs to be due to the 1-based indexing:
def draw_buttons():
for i in range(1, 5):
draw_button(i, COLORS[i - 1])
I bet you could change to this simpler implementation, and adjust the rest of the code to work with it without sacrificing anything:
def draw_buttons():
for i in range(4):
draw_button(i, COLORS[i])
Notice the hardcoded number 4 again. This highlights again the importance to avoid hardcoding. The range(1, 5) came from the fact of the hard limit 4, and if you decided to change 4 at some point, searching in the code for "4" you would never find range(1, 5).
So, really, replace the number 4 with a constant. len(COLORS) may look tempting, but as I explained above, I suggest to use something else as the single authoritative point of control.
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# Chapter 9 - Quadratic Functions and Equations - 9-8 Systems of Linear and Quadratic Equations - Lesson Check - Page 585: 5
$(-3, -3)$, $(-1.5,-1.5)$ Graphing is easier than completing the square.
#### Work Step by Step
Please see the graph. The orange line is $y=x$, and the green line is $y=2x^2+10x+9$. $2x^2+10x+9=x$ $2x^2+10x+9-x=x-x$ $2x^2+9x+9=0$ $(2x^2+9x+9)/2=0/2$ $x^2+4.5x+4.5=0$ $x^2+4.5x+(4.5/2)^2+4.5=0+(4.5/2)^2$ $x^2+4.5x+5.0625+4.5=5.0625$ $x^2+4.5x+5.0625+4.5-4.5=5.0625-4.5$ $(x+2.25)^2 = 9/16$ $\sqrt {(x+2.25)^2} = \sqrt {9/16}$ $x+2.25 = ±.75$ $x+2.25=.75$ $x+2.25-2.25=.75-2.25$ $x=-1.5$ $x+2.25=-.75$ $x+2.25-2.25=-.75-2.25$ $x = -3$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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# You're Here Right Now!
More Riley Riddles coming your way!
RIDDLE :
My prefix is whole
I mean, literally whole
My infix has something to do with money
It comes as a %
My suffix can help many people
But it can also be for fun
And you are all here right now!
NOTES :
The last line is about the whole word
Will add more hints in the future
Super Small Hint :
Perhaps the answer is very near to you?
What am I?
• You've clued the prefix, infix, and suffix, but what about a clue for the whole word? The best riddles have self-confirming answers, i.e. when you find the right word, everything fits together and matches neatly. – Rand al'Thor Oct 10 '18 at 13:55
• @Randal'Thor Ah yes, I forgot about that. Haven't made a riley riddle in a while XD – Kevin L Oct 11 '18 at 2:21
Here is my take on this
Internet
My prefix is whole
Integer (Int) is a whole number
My infix has something to do with money
TER (Total Expense Ratio) is a financial indicator used in measuring fund performance
It comes as a %
It is a percentage indicator of Total Fund Costs/Total Fund Assets, typically well below 100% before it goes bust :p
My suffix can help many people
Nets are a means of living for fishermen
But it can also be fun
Some people fish for leisure with a net. Or as per TS. a net is often used in ball games.
And you are all here right now!
Well the Internet is the _net_work via which we got on this site
Lets see if this works for this riddle
• Indeed, it is the correct answer. Can you answer some extra parts like line 4 and also the hint :D – Kevin L Oct 11 '18 at 5:36
• Opps, didnt notice the additional lines. Must have left the browser on too long prior to answering :p – Kryesec Oct 11 '18 at 5:59
• It's OK. Well, I'll accept your answer tomorrow :D – Kevin L Oct 11 '18 at 6:01
• BTW, what I meant about the suffix being fun is that it can be used in a basketball game as a net – Kevin L Oct 11 '18 at 8:04
Well of course, you're
stackexchange.com
My prefix is whole
stack can refer to an entire collection of objects (esp. in programming)
My infix has something to do with money
Exchange as in stock exchange
My suffix can help many people
com stands for company which helps people through either the company you keep or by selling goods
But it can also be fun
this site is pretty fun (this one especially). Plus it fits the title "You're Here Right Now!"
• Very good answer but not the intended one :D – Kevin L Oct 11 '18 at 2:21
• I might give this a $+50$ rep bounty :P – Mr Pie Oct 12 '18 at 11:40
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# How many different-sized circles with positive integer radii have area
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28 Nov 2017, 20:02
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### HideShow timer Statistics
How many different-sized circles with positive integer radii have areas less than 100?
(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen
[Reveal] Spoiler: OA
_________________
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Re: How many different-sized circles with positive integer radii have area [#permalink]
### Show Tags
28 Nov 2017, 20:29
B
For radius=6 the area is 113.09>100. Hence only upto 5
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### Show Tags
29 Nov 2017, 15:13
Bunuel wrote:
How many different-sized circles with positive integer radii have areas less than 100?
(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen
I can see potential trouble with area = 100.
Area of circle is $$πr^2$$.
So it must be $$r^2 * 3.14 < 100$$, where r is an integer.
Radii 1, 2, 3, 4, and 5 (25 * 3.14 = approx 78) work.
Radius 6 does not: 36 * 3 = 108, so with 3.14 it would be higher.
Five values satisfy the conditions.
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Re: How many different-sized circles with positive integer radii have area [#permalink]
### Show Tags
01 Dec 2017, 06:54
Bunuel wrote:
How many different-sized circles with positive integer radii have areas less than 100?
(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen
If r = 1, then the area of the circle is π(1)^2 = π.
If r = 2, then the area is π(2)^2 = 4π.
If r = 3, then the area is π(3)^2 = 9π.
If r = 4, then the area is π(4)^2 = 16π.
If r = 5, then the area is π(5)^2 = 25π.
Since π < 4, the area of any of the circles above will be less than 100. However, if r = 6, then the area of the circle will be π(6)^2 = 36π. However, since π > 3, 36π will be greater than 100. Thus, there are five different-sized circles with positive integer radii with area less than 100.
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Re: How many different-sized circles with positive integer radii have area [#permalink] 01 Dec 2017, 06:54
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# How many different-sized circles with positive integer radii have area
Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.
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Outlook: Titan Medical Inc. is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Sell
Time series to forecast n: 07 Mar 2023 for (n+6 month)
Methodology : Supervised Machine Learning (ML)
## Abstract
Titan Medical Inc. prediction model is evaluated with Supervised Machine Learning (ML) and Multiple Regression1,2,3,4 and it is concluded that the TMD:TSX stock is predictable in the short/long term. According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Sell
## Key Points
1. Stock Forecast Based On a Predictive Algorithm
2. Is it better to buy and sell or hold?
3. Is Target price a good indicator?
## TMD:TSX Target Price Prediction Modeling Methodology
We consider Titan Medical Inc. Decision Process with Supervised Machine Learning (ML) where A is the set of discrete actions of TMD:TSX stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4
F(Multiple Regression)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Supervised Machine Learning (ML)) X S(n):→ (n+6 month) $∑ i = 1 n r i$
n:Time series to forecast
p:Price signals of TMD:TSX stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
## TMD:TSX Stock Forecast (Buy or Sell) for (n+6 month)
Sample Set: Neural Network
Stock/Index: TMD:TSX Titan Medical Inc.
Time series to forecast n: 07 Mar 2023 for (n+6 month)
According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Sell
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
## IFRS Reconciliation Adjustments for Titan Medical Inc.
1. A firm commitment to acquire a business in a business combination cannot be a hedged item, except for foreign currency risk, because the other risks being hedged cannot be specifically identified and measured. Those other risks are general business risks.
2. IFRS 16, issued in January 2016, amended paragraphs 2.1, 5.5.15, B4.3.8, B5.5.34 and B5.5.46. An entity shall apply those amendments when it applies IFRS 16.
3. For the purpose of recognising foreign exchange gains and losses under IAS 21, a financial asset measured at fair value through other comprehensive income in accordance with paragraph 4.1.2A is treated as a monetary item. Accordingly, such a financial asset is treated as an asset measured at amortised cost in the foreign currency. Exchange differences on the amortised cost are recognised in profit or loss and other changes in the carrying amount are recognised in accordance with paragraph 5.7.10.
4. A hedge of a firm commitment (for example, a hedge of the change in fuel price relating to an unrecognised contractual commitment by an electric utility to purchase fuel at a fixed price) is a hedge of an exposure to a change in fair value. Accordingly, such a hedge is a fair value hedge. However, in accordance with paragraph 6.5.4, a hedge of the foreign currency risk of a firm commitment could alternatively be accounted for as a cash flow hedge.
*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.
## Conclusions
Titan Medical Inc. is assigned short-term Ba1 & long-term Ba1 estimated rating. Titan Medical Inc. prediction model is evaluated with Supervised Machine Learning (ML) and Multiple Regression1,2,3,4 and it is concluded that the TMD:TSX stock is predictable in the short/long term. According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Sell
### TMD:TSX Titan Medical Inc. Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementBaa2C
Balance SheetCBa1
Leverage RatiosCB3
Cash FlowCBa2
Rates of Return and ProfitabilityBaa2Baa2
*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?
### Prediction Confidence Score
Trust metric by Neural Network: 81 out of 100 with 457 signals.
## References
1. uyer, S. Whiteson, B. Bakker, and N. A. Vlassis. Multiagent reinforcement learning for urban traffic control using coordination graphs. In Machine Learning and Knowledge Discovery in Databases, European Conference, ECML/PKDD 2008, Antwerp, Belgium, September 15-19, 2008, Proceedings, Part I, pages 656–671, 2008.
2. Morris CN. 1983. Parametric empirical Bayes inference: theory and applications. J. Am. Stat. Assoc. 78:47–55
3. E. Collins. Using Markov decision processes to optimize a nonlinear functional of the final distribution, with manufacturing applications. In Stochastic Modelling in Innovative Manufacturing, pages 30–45. Springer, 1997
4. Holland PW. 1986. Statistics and causal inference. J. Am. Stat. Assoc. 81:945–60
5. Morris CN. 1983. Parametric empirical Bayes inference: theory and applications. J. Am. Stat. Assoc. 78:47–55
6. Cheung, Y. M.D. Chinn (1997), "Further investigation of the uncertain unit root in GNP," Journal of Business and Economic Statistics, 15, 68–73.
7. Dimakopoulou M, Athey S, Imbens G. 2017. Estimation considerations in contextual bandits. arXiv:1711.07077 [stat.ML]
Frequently Asked QuestionsQ: What is the prediction methodology for TMD:TSX stock?
A: TMD:TSX stock prediction methodology: We evaluate the prediction models Supervised Machine Learning (ML) and Multiple Regression
Q: Is TMD:TSX stock a buy or sell?
A: The dominant strategy among neural network is to Sell TMD:TSX Stock.
Q: Is Titan Medical Inc. stock a good investment?
A: The consensus rating for Titan Medical Inc. is Sell and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of TMD:TSX stock?
A: The consensus rating for TMD:TSX is Sell.
Q: What is the prediction period for TMD:TSX stock?
A: The prediction period for TMD:TSX is (n+6 month)
## People also ask
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# Test Sentences, 52
Continuing with Gary’s list:
1. Near the mouth of the river, its course turns sharply towards the East.
Hmm. This is a description of the river’s path. Which means we get to use some neato path words, one of which we’ve already seen: edatta “entrance, beginning of a path”. For this sentence we will use mɛddatta “end of a path” and hɨddatta “turn in a path”.
74. tanan dantɨŋi daka nokiɬi mɛddatta tɨŋi hɨddatta aŋana notɨŋi sandɨŋi dɛstɛ.
tanan
river.MTsg
dan-
along
tɨŋi
tɨŋi.IMP
daka
path
no-
towards
kiɬi
kiɬi.IMP
mɛddatta
end of path
tɨŋi
tɨŋi.IMP
hɨddatta
turn
aŋana
sharp
no-
towards
tɨŋi
tɨŋi.IMP
sandɨŋi
east
dɛstɛ
I’m told
The river goes along its path and goes towards its end and goes to a sharp turn and goes towards the east. We could probably omit dantɨŋi daka.
In Kēlen:
74. ñi jatāna rā jatōrren nō rānnie ānen anāŋŋena;
ñi
NI
jatāna
river
to
jatōrren
end
towards
rānnie
to east
ānen
with
anāŋŋena
sharpness
Questions?
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Main Content
# Two-Dimensional CWT of Noisy Pattern
This example shows how to detect a pattern in a noisy image using the 2-D continuous wavelet transform (CWT). The example uses both isotropic (non-directional) and anisotropic (directional) wavelets. The isotropic wavelet is not sensitive to the orientation of the feature, while the directional wavelet is.
Use the isotropic (non-directional) Mexican hat wavelet, also known as the Ricker wavelet, and the anisotropic (directional) Morlet wavelet. Demonstrate that the real-valued Mexican hat wavelet does not depend on the angle.
Y = zeros(32,32);
Y(16,16) = 1;
cwtmexh = cwtft2(Y,'wavelet','mexh','scales',1,...
'angles',[0 pi/2]);
surf(real(cwtmexh.cfs(:,:,1,1,1)));
shading interp; title('Angle = 0 Radians');
Extract the wavelet corresponding to an angle of $\pi$/2 radians. The wavelet is isotropic and therefore does not differentiate oriented features in data.
surf(real(cwtmexh.cfs(:,:,1,1,2)));
shading interp; title('Angle = pi/2 Radians');
Repeat the preceding steps for the complex-valued Morlet wavelet. The Morlet wavelet has a larger spatial support than the Mexican hat wavelet, therefore this example uses a larger matrix. The wavelet is complex-valued, so the modulus is plotted.
Y = zeros(64,64);
Y(32,32) = 1;
cwtmorl = cwtft2(Y,'wavelet','morl','scales',1,...
'angles',[0 pi/2]);
surf(abs(cwtmorl.cfs(:,:,1,1,1)));
shading interp; title('Angle = 0 Radians');
Extract the wavelet corresponding to an angle of $\pi$/2 radians. Unlike the Mexican hat wavelet, the Morlet wavelet is not isotropic and therefore is sensitive to the direction of features in the data.
surf(abs(cwtmorl.cfs(:,:,1,1,2)));
shading interp; title('Angle = pi/2 Radians');
Apply the Mexican hat and Morlet wavelets to the detection of a pattern in noise. Create a pattern consisting of line segments joined at a 90-degree angle. The amplitude of the pattern is 3 and it occurs in additive N(0,1) white Gaussian noise.
X = zeros(256,256);
X(100:200,100:102) = 3;
X(200:202,100:125) = 3;
X = X+randn(size(X));
imagesc(X); axis xy;
Obtain the 2-D CWT at scales 3 to 8 in 0.5 increments with the Mexican hat wavelet. Visualize the magnitude-squared 2-D wavelet coefficients at scale 3.
cwtmexh = cwtft2(X,'wavelet','mexh','scales',3:0.5:8);
surf(abs(cwtmexh.cfs(:,:,1,3,1)).^2);
view(0,90); shading interp; axis tight;
Use a directional Morlet wavelet to extract the vertical and horizontal line segments separately. The vertical line segment is extracted by one angle. The horizontal line segment is extracted by another angle.
cwtmorl = cwtft2(X,'wavelet','morl','scales',3:0.5:8,...
'angles',[0 pi/2]);
surf(abs(cwtmorl.cfs(:,:,1,4,1)).^2);
view(0,90); shading interp; axis tight;
figure;
surf(abs(cwtmorl.cfs(:,:,1,4,2)).^2);
view(0,90); shading interp; axis tight;
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# Higher moments (skewness and kurtosis)¶
gsl_stats_skew(data)
This function computes the skewness of data, a dataset of length n. The skewness is defined as,
$skew = {1 \over N} \sum {\left( x_i - {\hat{\mu}} \over {\hat{\sigma}} \right)}^3$
where $$x_i$$ are the elements of the dataset data. The skewness measures the asymmetry of the tails of a distribution.
The function computes the mean and estimated standard deviation of data via calls to gsl_stats_mean() and gsl_stats_sd().
gsl_stats_skew_m_sd(data, mean, sd)
This function computes the skewness of the dataset data using the given values of the mean mean and standard deviation sd,
$skew = {1 \over N} \sum {\left( x_i - mean \over sd \right)}^3$
where $$x_i$$ are the elements of the dataset data. The skewness measures the asymmetry of the tails of a distribution.
These functions are useful if you have already computed the mean and standard deviation of data and want to avoid recomputing them.
gsl_stats_kurtosis(data)
This function computes the kurtosis of data. The kurtosis is defined as,
$kurtosis = {1 \over N} \left( \sum {\left(x_i - {\hat{\mu}} \over {\hat{\sigma}} \right)}^4 \right) - 3$
The kurtosis measures how sharply peaked a distribution is, relative to its width. The kurtosis is normalized to zero for a Gaussian distribution.
gsl_stats_kurtosis_m_sd(data, mean, sd)
This function computes the kurtosis of the dataset data using the given values of the mean mean and standard deviation sd,
$kurtosis = {1 \over N} \left( \sum {\left(x_i - mean \over sd \right)}^4 \right) - 3$
This function is useful if you have already computed the mean and standard deviation of data and want to avoid recomputing them.
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# Can an asteroid have a molten core?
Most natural satellites in our Solar System are expected to contain fission furnaces at their cores, and some of these moons do have a striking resemblance to an asteroid. I'm wondering if we could establish a colony on an asteroid and harvest the "aster-thermal" energy (if there is a proper term for it) or rather create a space tourism hotspot for people to enjoy a relaxing bath in the hot spring. Is it possible for an asteroid to contain a molten core or do I need to look elsewhere to locate my "colony"?
• Haha.. Seriously? Hot spring bath in nearly zero G? – user931 Mar 26 '15 at 6:20
• what happens why did the migration took place automatically and unauthoris-tically? I learnt a moment ago that these two genres/categories are at two extreme end of the spectrum! Anyway please keep the answers coming as they are good scientifically, theoretically and logically speaking. – user6760 Mar 26 '15 at 6:22
• This question is suitable for Physics.SE, I think.. – user931 Mar 26 '15 at 6:23
Yeah, entirely possible.
There are a couple of examples of asteroids that we've identified which may have, or recently had, molten cores. 21 Lutetia is a notable example. Vesta is another.
The main issue is that because of their size, the ratio of surface area to volume is higher than the average planet. This means it cools much faster. So while some may have molten cores, they won't stay that way for as long as a planet might. Additionally, most aren't very near large gravity wells like a moon might be, so they don't have the same tidal forces adding energy to their interiors.
All this makes it less likely to find an asteroid with a molten core, but it's not impossible.
• @PiminKonstantinKefaloukos Note that the surface area of a sphere is given by $4\pi r^2$ while the volume is given by ${4\over 3} \pi r^3$. The volume grows much faster than the surface area for an increasing radius. Thus for a smaller radius the surface area to volume ratio is higher than for a larger radius. – Samuel Mar 26 '15 at 15:47
• @JDługosz ha ha, what was I thinking. Thank you for referencing the principle that was stated by Galileo Galilei. Nice to learn something cultural. – Pimin Konstantin Kefaloukos Mar 27 '15 at 22:14
Ceres is the largest asteroid (or smallest dwarf planet, whatever); the core isn't molten based on best current data and modeling, but new data is forthcoming soon, in the sense of Earth, Io; but it may be warm enough to have liquid water. Note that Mars also doesn't have a molten core and that Io and the Moon, etc. have molten cores due not to nuclear decay or to primordial heat but gravitational energy primarily.
• Suggest you wait a few months before making blanket statements about Ceres :-) – jamesqf Mar 26 '15 at 18:15
• true, we should have more information on it in the near future. – John_H Mar 26 '15 at 18:17
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# Rosser sentence
Given a theory (say $T$) which satisfies the hypotheses of the Godel- Rosser theorem. How to show whether a Rosser sentence $R$ for $T$ is true for the standard interpretation ($\Bbb N$) or not?.
(I know it is true but how we can prove this claim!)
-
Isn't Rosser's sentence: "If this sentence is provable then its negation is provable with a proof of smaller Gödel number than this one's"? If so, if arithmetic is consistent then if $R$ was provable then its negation would be provable. This is impossible. Thus it's not provable therefore it's true. – Apostolos Mar 6 '11 at 14:44
Rosser's sentence: "If this sentence is provable then its negation is provable with a proof of smaller Gödel number than this one's"! yes it is. – user7863 Mar 6 '11 at 15:07
Now you reason in the metatheory as Apostolos did in a comment: if the sentence was provable in $T$, then its negation would also be provable in $T$, which is impossible because $T$ was assumed to be consistent. So the sentence is not provable. The sentence itself is an implication whose hypothesis is "if this sentence is provable". Since it isn't provable, the hypothesis is false, which makes the entire implication vacuously true. That's how you prove the Rosser sentence is true in the standard interpretation.
One thing that can be confusing about this is that when we prove the sentence is true in the standard interpretation, we don't just work in $T$. We know the sentence is not provable in $T$, so we can't do that anyway: we have to add extra metatheoretic assumptions about a particular model if we want to show the sentence is true in that model.
The way we make those assumptions here is by working with a particular model of $T$ in which the formal provability predicate "Pvbl" corresponds to actual provability. That is the only special property of the standard model that we need in our proof. So the proof that the Rosser sentence is true in the standard model can be viewed equally well as a proof that the Rosser sentence is true in any model whose formal provability predicate agrees with the standard one for standard sentences.
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## Properties of a Circular Area
This tool calculates the basic geometric properties of a circular area. Enter the shape dimensions R or D below. The calculated results will have the same units as your input. Please use consistent units for any input.
R = ...or D = Geometric properties: Radius = Diameter = Area = Perimeter =
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## Definitions
### Geometry
The circle is a curved, closed, planar shape, every point of which has equal distance from a constant point, called centre. The points (x,y) of the circumference, satisfy the equation:
where x0, y0the coordinates of the centre of the circle and R its radius.
### Properties
The area A and the perimeter P of a circular area, with radius R, can be found with these formulas:
### The π number
Looking at the area formula, a physical definition of the π number can be given, as the times we should scale a square area R×R in order to get an equivalent circular area (problem of squaring a circle). Also, taking the circumference formula, an alternative physical definition is the times we should scale the diameter 2R of the circle in order to get its circumference. There is no way to precisely solve any of these problems either algebraically or geometrically, in a finite number of steps. The π number, that is involved in the equations, is an irrational number, which means that not only its decimal digits never end, but also they never reach a repeatable pattern (in other words, π can't be represented by a fraction). Approximations of π nowadays have reached to trillionth's of digits, however for most practical problems only a few digits are needed.
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Total shareholders’ equity $77,228$ 75,716 Leverage ratio (2) 12.4 x 12.4 x Adjusted leverage ratio (3) 8.9 x 9.1 x Common shareholders’ equity $71,028$ 69,516 Tangible common shareholders’ equity (4) 66,345 64,417 Book value per common share (5) $148.41$ 144.67 Tangible book value per common share (4) (5) 138.62 134.06 In most cases, investors who place equity funds into a business expect to earn a financial return. Return on tangible equity Tangible equity is equity or net assets less intangible assets such as goodwill. 1 Return on Average Tangible Common Shareholders’ Equity (ROTCE) and ROTCE Excluding the Impact of the Series G Preferred Stock Dividend ROTCE is computed by dividing net earnings applicable to common shareholders by average monthly tangible common shareholders' equity. Return on equity is the gain, business net income, or percentage earnings yield on invested capital. You can learn more about the standards we follow in producing accurate, unbiased content in our. One of the lessons that the financial crisis of the last few years has taught us is that financial institutions’ capability to generate capital based only on the risk they assume is not sufficient condition for their survival. In the absence of debt, shareholder equity and the company's total assets will be equal. Return on assets is net income divided by the total value of a company’s assets, and return on equity is net income divided by the total value of the company’s equity. The basic concept is similar to that of ROE - i.e. Return on tangible equity can be defined as the amount of net income returned as a percentage of shareholders equity, after subtracting intangible assets, goodwill and preferred equity. Investopedia uses cookies to provide you with a great user experience. A company with $11 million in assets and$1 million in liabilities has $10 million in shareholders' equity. But, which ratio is the most reliable to measure a bank’s profitability? If, for example, you spend$100,000 to open a laundromat and make a net profit of $15,000 in one year, your annual ROI equals$15,000 / $100,000 x … The second group of ratios differs from the first one in that it excludes intangible elements from the capital, such as goodwill, convertible issuances or preferred stocks. Return on Equity is an accounting valuation method which calculates the amount of profit a company earned in comparison to the total amount of shareholder's equity found on the balance sheet. it is net earnings as a proportion of shareholders equity. Return on equity for Jefferies Group was 7.1% and return on tangible equity was 10.2%." Analysts look at the trend over time and compare the company’s ratio to the industry average to determine the profitability of … Current and historical return on tangible equity values for McDonald's (MCD) over the last 10 years. Result is shown as a percentage. You need to provide the two inputs i.e Net Income and Shareholder’s Equity. Graph and download economic data for Return on Average Equity for all U.S. Banks (USROE) from Q1 1984 to Q3 2020 about ROE, banks, depository institutions, and USA. DuPont analysis is a useful technique used to decompose the different drivers of return on equity (ROE). Return on equity (ROE) Indicator of profitability. Like all calculations designed to assess a company’s financial health, return on tangible equity … The second half of the equation is called financial leverage, which is also known as the equity multiplier. In fact, to prove their solvency, the regulator requires financial institutions to keep a percentage of capital with respect to its risk-weighted assets. Return on Equity is an accounting valuation method which calculates the amount of profit a company earned in comparison to the total amount of shareholder's equity found on the balance sheet. Intangible assets are non-physical assets that still carry value. How to Use the DuPont Analysis to Assess a Company's ROE, Bank of America Corporation 2013 Annual Report. The investment dollars differ in that it only accounts for common shareholders. Return-on-Tangible-Equity is calculated as Net Income attributable to Common Stockholders divided by its average total shareholder tangible equity. ROE is a useful tool in comparing … Return on equity may also be calculated by dividing net income by the average shareholders' equity; it is more accurate to calculate the ratio this w… Return on equity is the gain, business net income, or percentage earnings yield on invested capital. The horizontal axis is the volatility or risk as measured by the standard deviation. 12%). One of the best – because it is a truer measure of actual financial strength – is the tangible common equity ratio (TCE). Cost of Equity vs Return on Equity . Dividing the profit by invested equity produces a 10-percent return on equity. Calculate the ROE or return on common stockholders’ equity. Our valuation model uses many indicators to compare DUSIT THANI value to that of its competitors to determine the firm's financial worth. For some reason, bank investors have lately come to view a single, once-obscure number, tangible-common equity to tangible assets, as indispensable in judging a bank’s balance sheet. The measure is calculated by subtracting preferred equity and intangible assets from total book value. Together, these initiatives should allow us to deliver on our medium-term ambition of a (return on tangible equity) of 10per cent to 12per cent in a … ROE and ROA are important components in banking for measuring corporate performance. It also distorts the spread between ROE and IDCFP's COE. Tangible common equity (TCE) is the subset of shareholders' equity that is not preferred equity and not intangible assets.. TCE is an uncommonly used measure of a company's financial strength. There is a sea of acronyms to measure profitability. Another factor that is being taken more and more into consideration when calculating an institution’s profitability is risk. This is important because of the nature of equity which is something when gives a right to a share of the residual net assets of a company upon liquidation. It seems logical that, in order to determine the profitability of a product, portfolio or institution, it should be calculated taking into account the risk that is being assumed. It is in this context that the leverage ratio concept arises, a complementary measure that reinforces the capital requirements regardless of the risk assumed, which can be calculated easily and whose homogeneity allows to compare institutions better. Jul 24 Back To Home Return on Common Equity (ROCE) Return on Common Equity (ROCE) Definition. Definition: Return on Equity (ROE) is one of the Financial Ratios that use to measure and assess the entity’s profitability based on the relationship between net profits over its averaged equity. ROE vs COE - Measuring Return on Equity and Cost of Equity. The max risk, min risk, max return and min return for each asset class is plotted. Return on equity (ROE) and return on assets (ROA) are two of the most important measures for the effectiveness of management at a company. Two brothers, Abe and Zac, both inheritedRead More Profitability ratios are financial metrics used to assess a business's ability to generate profit relative to items such as its revenue or assets. It has no preferred stock.However,$4 million of Company XYZ's assets are intangible assets -- mostly goodwill from previous acquisitions and trademarks. Return-on-Tangible-Equity measures the rate of return on the ownership interest (shareholder's tangible equity) of the common stock owners. It's a popular formula that's another way of looking at ROE. Asset turnover ratio measures the value of a company's sales or revenues generated relative to the value of its assets. The bank last year set an ambition for a return on tangible equity (RoTE) ambition of approximately 10% for 2020, with an aim to reach an RoTE above 12% in the medium term. Accessed Sept. 30, 2020. Return on tangible equity (rendimento del patrimonio netto tangibile, ROTE) è un indicatore che misura il tasso di rendimento sul patrimonio netto tangibile.. Il ROTE è calcolato dividendo l'utile netto per il patrimonio tangibile (il patrimonio da cui sono esclusi gli attivi intangibili come l'avviamento). Tangible equity is equity or net assets less intangible assets such as goodwill. Prior to the financial crisis of 2008-09, Bank of America reported ROE levels closer to 13% and ROA levels closer to 1%.. Its common equity is $40 million -$25 million = $15 million. The offers that appear in this table are from partnerships from which Investopedia receives compensation. Because shareholders' equity is equal to a company’s assets minus its debt, ROE could be thought of as the return on net assets. The debt-to-equity (D/E) ratio indicates how much debt a company is using to finance its assets relative to the value of shareholders’ equity. 1 Return on Average Tangible Common Shareholders’ Equity (ROTCE) and ROTCE Excluding the Impact of the Series G Preferred Stock Dividend ROTCE is computed by dividing net earnings applicable to common shareholders by average monthly tangible common shareholders' equity. Tangible equity is also known as “tangible common equity” and “tangible common shareholders’ equity”, and refers to the amount shareholders have invested in common stock. Current and historical return on tangible equity values for Barclays (BCS) over the last 10 … A TCE of 5% results, say, when a … Return on Equity indicates how well a company is doing with the money it has now, whereas Return on Capital indicates how well it will do with further Capital. ROE is a useful tool in … Using both equated to a ROE of 4.8%, which is a pretty low level. And, as we also discussed in said article, not all banking assets have the same risk. Let’s go over each one of them to understand their meaning and apply the most appropriate one in each case. Return-on-Tangible-Equity is calculated as Net Income attributable to Common Stockholders divided by its average total shareholder tangible equity. Return on equity (ROE) helps investors gauge how their investments are generating income, while return on assets (ROA) helps investors measure how management is using its assets or resources to generate more income. Definition: Return on Equity (ROE) is one of the Financial Ratios that use to measure and assess the entity’s profitability based on the relationship between net profits over its averaged equity. In this case, we are talking about very general ratios that do not include elements such as the risk or the invested capital, elements that provide a more adjusted measure of the actual profitability of an institution. Return on equity (ROE) is a measure of financial performance calculated by dividing net income by shareholders' equity. In the first equity group, a series of standard ratios such as the ROE (Return on Equity) or the ROTE (Return on Tangible Equity) are used extensively. The DuPont analysis is a framework for analyzing fundamental performance popularized by the DuPont Corporation. The key difference is the 'tangible common' bit. It is essential to have a magnitude that measures the quality of said capital and its actual capacity to absorb losses. Sustainable Growth Rate (SGR) A company’s return on equity can be used to predict its growth rate (also known as the sustainable growth rate).. SGR is the realistic pace at which a business can grow with internally-generated net income or profit – without having to finance growth with borrowed money or seek more equity from shareholders. But if that company takes on financial leverage, its ROE would rise above its ROA. We also reference original research from other reputable publishers where appropriate. The highly regulated financial sector has to meet a series of requirements. This is how three ratios arise, which are the most commonly used by financial institutions. Return on equity is an easy-to-calculate valuation and growth metric for a publicly traded company. In 2013, banking giant Bank of America Corp (BAC) reported a ROA of 0.53%. Its financial leverage was 9.60. However, the more r’s they have, the more complicated things get (RORWA, RAROC, RORAC, RARORAC). Current and historical return on tangible equity values for CocaCola (KO) over the last 10 years. ROE combines the income statement and the balance sheet as the net income or profit is compared to the shareholders’ equity. For a simple example, a business is started with$50,000 of paid-in owner or shareholder capital, and ends up the year with a $5,000 profit. Determined by dividing net income for the past 12 months by common stockholder equity (adjusted for stock splits). It measures a firm's efficiency at generating profits from every unit of shareholders' tangible equity (shareholders equity minus intangibles). Return on Equity vs. This article analyzes the question of whether return on equity (ROE) or return on capital (ROC) is the better guide to performance of an investment. Depending on the company, one may be more relevant than the other—that's why it's important to consider ROE and ROA in context with other financial performance metrics. Calculating premium rates An insurer can also use the ROE to calculate premiums. Return on equity for Jefferies Group was 7.1% and return on tangible equity was 10.2%." You can easily calculate the Return on Equity … Return on Equity Formula in Excel (With Excel Template) Here we will do the same example of the Return on Equity formula in Excel. Comparative valuation techniques use various fundamental indicators to help in determining DUSIT THANI's current stock value. ROE vs ROCContents1 ROE vs ROC2 Return on Capital versus Return on Equity Example3 ROC and ROE Formulas We’ll start with an example. The vertical axis the return. Return on equity was calculated by dividing net profit by average equity (the value of assets after all liabilities are paid) for the period, and in general, a higher number is better. DUSIT THANI FREEHOLD Return On Equity vs. Shares Outstanding Fundamental Analysis. ROE is one of the most important financial ratios and profitability metrics. Return on Equity (ROE) is a measure of a company’s profitability that takes a company’s annual return (net income) divided by the value of its total shareholders' equity (i.e. Return on Tangible Equity: The amount of net income returned as a percentage of shareholders equity, after subtracting intangible assets, goodwill and preferred equity. For banks to cover their cost of capital, ROE levels should be closer to 10%. Equity returns consist mainly of capital gains when you sell, although some companies pay cash dividends as well. The DuPont identity explains the relationship between both ROE and ROA as measures of management effectiveness. For a simple example, a business is started with$50,000 of paid-in owner or shareholder capital, and ends up the year with a $5,000 profit. Sustainable Growth Rate (SGR) A company’s return on equity can be used to predict its growth rate (also known as the sustainable growth rate).. SGR is the realistic pace at which a business can grow with internally-generated net income or profit – without having to finance growth with borrowed money or seek more equity from shareholders. Return on investment is the financial benefit that results from making an investment or spending money on something. Return on equity can be calculated by taking a company's net income and dividing it by shareholders' equity. This article analyzes the question of whether return on equity (ROE) or return on capital (ROC) is the better guide to performance of an investment. Thus, the decision regarding the activity that is to be pursued becomes of key importance. Here we will be looking at a series of ratios that make it easier to adopt said decisions, while providing more accurate information about the returns they yield, taking into account elements such as the risk they assume or the capital they invest. So for gold these four data points represent the four corners of the yellow rectangle. Equity is the external funds a company uses for major business operations. Return on Equity indicates how well a company is doing with the money it has now, whereas Return on Capital indicates how well it will do with further Capital. Credit Suisse Reiterates 10%-12% Return on Tangible Equity Ambition By Reuters , Wire Service Content Dec. 15, 2020 By Reuters , Wire Service Content Dec. 15, 2020, at 1:16 a.m. Total shareholder tangible equity equals to Total Stockholders Equity minus Intangible Assets. Return on equity and return on assets (ROA) are distinct ratios for measuring the performance of companies. How Does the Tangible Common Equity Ratio Work? Tangible common equity (TCE) is the subset of shareholders' equity that is not preferred equity and not intangible assets.. TCE is an uncommonly used measure of a company's financial strength. The ratio of the return on capital investments to equity will be referred to as return on capital (ROC). These include white papers, government data, original reporting, and interviews with industry experts. The second group of ratios differs from the first one in that it excludes intangible elements from the capital, such as goodwill, convertible issuances or preferred stocks. In other words, when debt increases, equity shrinks, and since shareholder equity is the ROE's denominator, its ROE, in turn, gets a boost. The RAROC method allows institutions to adjust the ROE’s numerator and denominator based on risk. Return on tangible equity (ROTE) (also return on average tangible common shareholders' equity (ROTCE)) measures the rate of return on the tangible common equity. Tangible equity or tangible common equity is a measure used to evaluate the strength of a financial institution. The first half of the equation (net income divided by total assets) is actually the definition of ROA, which measures how efficiently management is using its total assets (as reported on the balance sheet) to generate profits (as measured by net income on the income statement). Return on tangible equity or ROTE is the net profit (after interest and tax) as a percentage of the (average) tangible equity or shareholders' funds. Bank of America. Return-on-Tangible-Equity measures the rate of return on the ownership interest (shareholder's tangible equity) of the common stock owners. It is considered a conservative measure of total company value. This is a disclosure of BBVA’s ratios calculated at the end of March 2016. ... As an example, banks generally believe returns should be measured on tangible equity, excluding goodwill, and other intangible assets. Cost of capital refers to the cost incurred in obtaining either equity capital (the cost incurred in issuing shares) or debt capital (interest cost). Whereas ROE helps investors understand the growth they get from an equity … It is very easy and simple. Capital maybe obtained using many methods such as issuing shares, bonds, loans, owner’s contributions, etc. This is often beneficial because it allows companies and investors alike to see what sort of return the voting shareholders are getting if preferred and other types of shares are not counted. Recall that the denominator of the return on equity formula is shareholder equity, the comparison of a firm's assets to its liabilities. If the company has earned$1 million in a year, its return on equity for that year is $1 divided by$10, or 10 percent. Return on Equity Disadvantages. But since shareholder equity equals assets minus total debt, a company decreases its equity by increasing debt. It has no preferred stock, but it does have a $3,000,000 line item for goodwill and$2,000,000 worth of trademarks. Gold vs Equity: risk vs reward charts 3 years. It reveals how much profit a company earned in comparison to the total amount of shareholder equity found on the balance sheet. This is where the RAROC (Risk-adjusted Return on Capital) comes in, a method intended to help efficiently allocate capital and that was developed by Bankers Trust in the 1970s. Some are more widely known in the industry, such as ROE, ROTE or ROA. Logically, their ROE and ROA would also be the same. Return on tangible equity can be defined as the amount of net income returned as a percentage of shareholders equity, after subtracting intangible assets, goodwill and preferred equity. ROE is a measure of a company’s profitability. It can be a powerful weapon in your investing arsenal as … Total shareholders’ equity $77,228$ 75,716 Leverage ratio (2) 12.4 x 12.4 x Adjusted leverage ratio (3) 8.9 x 9.1 x Common shareholders’ equity $71,028$ 69,516 Tangible common shareholders’ equity (4) 66,345 64,417 Book value per common share (5) $148.41$ 144.67 Tangible book value per common share (4) (5) 138.62 134.06 Thanks to this method, financial institutions are capable of calculating the actual profitability of each one of the activities they develop, by comparing them against the consumption of capital they entail. Current and historical return on tangible equity values for FTAC Olympus Acquisition (FTOC) over the last 10 years. Calculate profit margin or ROS for 2015. ROE vs ROCContents1 ROE vs ROC2 Return on Capital versus Return on Equity Example3 ROC and ROE Formulas We’ll start with an example. Return on Total Capital (ROTC) is a return on investment ratio that quantifies how much return a company has generated through the use of its capital structure Capital Structure Capital structure refers to the amount of debt and/or equity employed by a firm to fund its operations and finance its assets. Return on equity is calculated by taking a year’s worth of earnings and dividing them by the average shareholder equity for that year, and is expressed as a percentage: ROE = Net income after tax / Shareholder's equity Instead of net income, comprehensive income can be used in the formula's numerator (see statement of comprehensive income). Since equity includes invested funds and borrowed funds, a company could have too much debt to remain profitable in the long term. © Banco Bilbao Vizcaya Argentaria, S.A. 2019, Customer service profiles on social media, Photos Directors / Executive Leadership Team, Shareholders and Investors Communication and Contact Policy, Corporate Governance and Remuneration Policy, Information Circular 2/2016 of Bank of Spain, Internal Standards of Conduct in the Securities Markets, Information related to integration transactions, The bank leverage ratio: Quality is just as important as quantity. Total shareholder tangible equity equals to Total Stockholders Equity minus Intangible Assets. Answers and explanations. Return on Equity Disadvantages. Calculated as: Income from Continuing Operations / Tangible Shareholders Equity. Bank of America. The DuPont Identity divides ROE into three core components: ROE=Profit Margin×Asset Turnover×SEwhere:SE=Shareholder equityProfit Margin=Net IncomeRevenueAsset Turnover=RevenueTotal AssetsFinancial Leverage=Total AssetsSE\begin{aligned} &\text{ROE} = \text{Profit Margin} \times \text{Asset Turnover} \times \text{SE} \\ &\textbf{where:}\\ &\text{SE} = \text{Shareholder equity} \\ &\text{Profit Margin} = \frac{ \text{Net Income} }{ \text{Revenue} } \\ &\text{Asset Turnover} = \frac{ \text{Revenue} }{ \text{Total Assets} } \\ &\text{Financial Leverage} = \frac{ \text{Total Assets} }{ \text{SE} } \\ \end{aligned}ROE=Profit Margin×Asset Turnover×SEwhere:SE=Shareholder equityProfit Margin=RevenueNet IncomeAsset Turnover=Total AssetsRevenueFinancial Leverage=SETotal Assets. Shareholders equity minus intangibles ) the returns generated based on the risk assumed ( and return on tangible equity vs return on equity! Roa discussed above requires writers to use primary sources to support their.. 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You need to provide the two can not be calculated or used in any analysis SE ) is measure! Which are the most important financial ratios and profitability metrics complicated things get ( RORWA, RAROC,,!
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Chin. Phys. Lett. 2017, Vol. 34 Issue (9): 090401 DOI: 10.1088/0256-307X/34/9/090401
GENERAL |
Effects of Homogeneous Plasma on Strong Gravitational Lensing of Kerr Black Holes
Chang-Qing Liu1**, Chi-Kun Ding1, Ji-Liang Jing2
1Department of Physics, Hunan University of Humanities Science and Technology, Loudi 417000
2Department of Physics, and Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081
Download: PDF(694KB) PDF(mobile)(685KB) HTML Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract Considering the Kerr black hole surrounded by a homogeneous unmagnetized plasma medium, we study the strong gravitational lensing on the equatorial plane of the Kerr black hole. It is found that the presence of the uniform plasma can increase the photon-sphere radius $r_{\rm ps}$, the coefficients $\bar{a}$ and $\bar{b}$, the angular position of the relativistic images ($\theta_{\infty}$), the deflection angle $\alpha(\theta)$ and the angular separation $s$. However, the relative magnitude $r_{\rm m}$ decreases in the presence of the uniform plasma medium. It is also shown that the impact of the uniform plasma on the effect of strong gravitational lensing becomes smaller as the spin of the Kerr black hole increases in the prograde orbit ($a>0$). In particular, for the extreme black hole ($a=0.5$), the effect of strong gravitational lensing in the homogeneous plasma medium is the same as the case in vacuum for the prograde orbit.
Received: 15 June 2017 Published: 15 August 2017
PACS: 04.70.Dy (Quantum aspects of black holes, evaporation, thermodynamics) 98.62.Sb (Gravitational lenses and luminous arcs) 95.30.Sf (Relativity and gravitation) 97.60.Lf (Black holes)
Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11447168 and 11247013, and the Hunan Provincial Natural Science Foundation under Grant Nos 12JJ4007 and 2015JJ2085.
TRENDMD: Cite this article: Chang-Qing Liu, Chi-Kun Ding, Ji-Liang Jing 2017 Chin. Phys. Lett. 34 090401 URL: http://cpl.iphy.ac.cn/10.1088/0256-307X/34/9/090401 OR http://cpl.iphy.ac.cn/Y2017/V34/I9/090401
[1] Chi-Kun Ding. Gravitational Perturbations in Einstein Aether Black Hole Spacetime[J]. Chin. Phys. Lett., 2018, 35(10): 090401 [2] Mahamat Saleh, Bouetou Bouetou Thomas, Timoleon Crepin Kofane. Energy and Thermodynamics of the Quantum-Corrected Schwarzschild Black Hole[J]. Chin. Phys. Lett., 2017, 34(8): 090401 [3] Jun Liang. The $P$–$v$ Criticality of a Noncommutative Geometry-Inspired Schwarzschild-AdS Black Hole[J]. Chin. Phys. Lett., 2017, 34(8): 090401 [4] M. Azam, A. Aslam. Accretion onto the Magnetically Charged Regular Black Hole[J]. Chin. Phys. Lett., 2017, 34(7): 090401 [5] Xiao-Xiong Zeng, Xin-Yun Hu, Li-Fang Li. Effect of Phantom Dark Energy on Holographic Thermalization[J]. Chin. Phys. Lett., 2017, 34(1): 090401 [6] Jun-Jin Peng, Wen-Chang Xiang, Shao-Hong Cai. Abbott–Deser–Tekin Charge of Dilaton Black Holes with Squashed Horizons[J]. Chin. Phys. Lett., 2016, 33(08): 090401 [7] Belhaj A., Chabab M., El Moumni H., Masmar K., Sedra M. B.. On Hawking Radiation of 3D Rotating Hairy Black Holes[J]. Chin. Phys. Lett., 2015, 32(10): 090401 [8] MA Meng-Sen, ZHAO Ren. Notes on Phase Transition of Nonsingular Black Hole[J]. Chin. Phys. Lett., 2015, 32(03): 090401 [9] ZHANG Ming, YUE Rui-Hong, YANG Zhan-Ying. Critical Behavior of Black Holes in an Einstein–Maxwell Gravity with a Conformal Anomaly[J]. Chin. Phys. Lett., 2015, 32(02): 090401 [10] LAI Chu-Yu, CHEN Ju-Hua, WANG Yong-Jiu. The Motion of Spinning Particles in the Spacetime of a Black Hole with a Cosmic String Topological Defect[J]. Chin. Phys. Lett., 2014, 31(09): 090401 [11] HE Tang-Mei, YANG Jin-Bo, ZHANG Jing-Yi. Corrected Stefan–Boltzmann Law and Lifespan of a Black Hole[J]. Chin. Phys. Lett., 2014, 31(08): 090401 [12] Ahmad Sheykhi. Quasi-Topological Cosmology from Emergence of Cosmic Space[J]. Chin. Phys. Lett., 2014, 31(2): 090401 [13] FANG Heng-Zhong, ZHOU Kai-Hu. Emission of Phonons from a Rotating Sonic Black Hole[J]. Chin. Phys. Lett., 2014, 31(1): 090401 [14] G. Abbas, R. M. Ramzan. Thermodynamics of Phantom Energy Accreting onto a Black Hole in Einstein–Power–Maxwell Gravity[J]. Chin. Phys. Lett., 2013, 30(10): 090401 [15] Kourosh Nozari, A. Yazdani. The Energy Distribution of a Noncommutative Reissner–Nordström Black Hole[J]. Chin. Phys. Lett., 2013, 30(9): 090401
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Math Help - rational expontent problem
1. rational expontent problem
the problem is as follows:
write the expression in simplest form
2/(81^(1/6))
can you explain step by step how to do this?
the answer is supposed to be:
2(3^(1/3)) / 3
i posted this somwhere else too but i wasnt getting a reply quickly enough sorry
2. Originally Posted by talhaguy
the problem is as follows:
write the expression in simplest form
2/(81^(1/6))
can you explain step by step how to do this?
the answer is supposed to be:
2(3^(1/3)) / 3
i posted this somwhere else too but i wasnt getting a reply quickly enough sorry
2 / [81^(1/6)]
= 2 / [(3^4)^(1/6)]
= 2 / [3^(4/6)]
= 2 / [3^(2/3)]
Now rationalize the denominator,
Multiply both numerator and denominatoe by 3^(1/3),
= [2 *3^(1/3)] / [3^(2/3) *3^(1/3)]
= [2 *3^(1/3)] / [3^(2/3 +1/3)]
= [2 *3^(1/3)] / [3^(3/3)]
= [2 *3^(1/3)] / [3^(1)]
= [2 *3^(1/3)] / 3 ------------answer
or,
3. Don't make double posts it wastes moderators and helpers time, and
confuses everybody.
RonL
4. Hello, talhaguy!
Write the expression in simplest form: . $\frac{2}{81^{\frac{1}{6}}}$
The answer is: . $\frac{2\cdot3^{\frac{1}{3}}}{3}$
This is identical to ticbol's solution . . . written in LaTeX.
. . $\frac{2}{81^{16}} \;=\;\frac{2}{\left(3^4\right)^{\frac{1}{6}}} \;=\;\frac{2}{3^{\frac{4}{6}}} \;=\;\frac{2}{3^{\frac{2}{3}}}$
Rationalize: . $\frac{2}{3^{\frac{2}{3}}}\cdot\frac{3^{\frac{1}{3} }} {3^{\frac{1}{3}}} \;=\;\boxed{\frac{2\cdot3^{\frac{1}{3}}}{3}}$
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# Tag Info
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You have to use the i option. This is in the help page: i In-word expansion - By default a snippet is expanded only if the tab trigger is the first word on the line or is preceded by one or more whitespace characters. A snippet with this option is expanded regardless of the preceding character. In other words, the snippet can ...
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Main Ideas There are 3 cases to consider (reworded slightly from the original question): a) If not in an itemize environment, create one, and place the cursor after the first \item. b) If in an itemize environment and if the list item is not empty, create a new \item. c) If in an itemize environment and if the list item is empty, delete the line and jump out ...
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:UltiSnipsEdit will automatically open ultisnips for current filetype. From there you can see that it's supposed to be python.snippets.
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The problem is that you have updated your plugins in the transition Linux to Mac. This also brings a major update of Vimtex, in which the syntax plugin has been included as part of Vimtex. Part of the syntax script changes are to simplify the math zones. The exact issue you raise is discussed here, and this comment should provide the required change, ...
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Change the entire format to Google's... It's not documented, but the Python snippets file from vim-snippets does allow you to specify docstring style. Simply add let g:ultisnips_python_style = 'google' to your configuration, and the snippet will behave accordingly. When adding exception in a forward trigger, the docstring will add a "Raises" section (...
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It seems that when you copied the snippet you forgot to add the indentation spaces in the python snippet conditional code as shown in the error message: Executed snippet code: 1 2 if t[2] and t[2][0] not in [',', '.', '?', '-', ' ']: 3 snip.rv = ' ' 4 else: 5 snip.rv = '' 6 Try to change it to: snippet im "create an inline ...
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From this video: UltiSnips evaluates each text object that might have a dependency on some types of text multiple times, to make sure that all dependencies are properly updated. To prevent the date from being updated several times, you could switch to a python interpolation, and use the guard if not snip.c. For example, you could replace this: ** ...
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Put the check in a function so it’s not a mess: function react#add_snips() abort if search('styled-components', 'nw') != 0 UltiSnipsAddFiletypes css endif endfunction (This can go in ~/.vim/autoload/react.vim) And then call the function: augroup react autocmd! autocmd Filetype javascript,typescript call react#add_snips augroup END Alternatively,...
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UltiSnips uses a strategy similar to how Vim detects :h ftplugins. That is, it will look for the filenames that match the following pattern in your UltiSnips directory: ft.snippets, ft_*.snippets, or ft/*, where ft is replaced with your Vim filetype (python, c, etc.) and * matches any string including the empty string. A table from :h UltiSnips-how-snippets-...
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You need to use the vimrc file (~/.vimrc or ~/.vim/vimrc on MacOS, Linux/Unix) to configure most of initialization, in particular plug-ins. The gvimrc file is mostly reserved for additional settings that are only to be used to configure GUI-specific settings, such as which font to use in GUI versions of Vim such as MacVim. See :help initialization, which ...
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The following snippet worked out for me: snippet pder(\w*) "Description" rw \\frac{\\partial^{!p snip.rv=findSum(match.group(1))}}{!p snip.rv=printd("\\partial",match.group(1))} $0 endsnippet with global !p def findSum(str1): # A temporary str1ing temp = 0 # holds sum of all numbers # present in the str1ing ... 2 I got it to work: global !p def mycontext(char): x = vim.current.window.buffer y = vim.current.window.cursor[0] z = vim.current.window.cursor[1] try: return x[y-1][z-1] + x[y-1][z] != char except: return True endglobal context "mycontext('()')" snippet ( &... 1 Yes, it's possible to use parts of the snippet trigger in the output, but it's not as simple as using a matching character class on each side. To correctly configure this, you need to use an r flag to use a regular expression in the trigger, use a capturing group inside parens for the character class (the trigger needs to be inside quotes as well.) And then ... 1 Simply extend the snippet to (\d)pder(\w*) and handle the second submatch appropriately. 1 Because of Jake Grossman's comment, I eventually realized the$ in the regex trigger should be escaped: (Also had to use python interpolation) snippet "\$(.+)\$" "whatever" r $$!p snip.rv = match.group(1)$$ $0 endsnippet The trigger right after snippet will match anything between$ and capture it in a group (with the ()) In the ...
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What about writing your own mapping for TAB that analyses its context? if it detect ^\s*\\item\s*$on the current line, it clears the line then jumps over the end of the current itemize/enumerate/... environment otherwise it runs the default mapping. In lh-brackets, I have a function that may help to override existing mappings: lh#bracket#enrich_imap() &... 1 global !p def insert_before_unique(name): vim.command('/unique_text') snip.expand_anon(name + '\n\n\n') endglobal post_jump "if snip.tabstop == 0: insert_before_unique(snip.tabstops[1].current_text)" snippet trigger "tricky stuff"$1 endsnippet This seems to do the trick. Or close to it. If you type trigger and hit tab you'll be ...
1
The error you are getting is happening because your Vim doesn't include support for Python, which is required by UltiSnips, as that plug-in is implemented in Python for the most part. My recommendation is that you should get a Vim binary from your distribution. You mentioned using Linux Mint, so make sure you are not using a vim-tiny package, since that ...
1
You should only set a default value on the first occurrence of the placeholder, that way it works. From :help UltiSnips-mirrors: [...] A mirrored tabstop can have a default value defined. Only the first instance of the tabstop need have a default value. Mirrored tabstop will take on the default value automatically. While the help says "need", it only ...
1
Nevermind, I figured out how to implement it as a custom context snippet: snippet { "braces" "snip.column == len(snip.buffer[snip.line]) - 1" e { \$0 } endsnippet
1
This works for markdown files with the vimwiki filetype. The only change needed is the addition ["VimwikiMath", "VimwikiEqIn"] to texMathZones. texMathZones = ['texMathZone' + x for x in ['A', 'AS', 'B', 'BS', 'C', 'CS', 'D', 'DS', 'E', 'ES', 'F', 'FS', 'G', 'GS', 'H', 'HS', 'I', 'IS', 'J', 'JS', 'K', 'KS', 'L', 'LS', 'DS', 'V', 'W', 'X', 'Y', 'Z', 'AmsA', '...
1
Like statox said, you should really write you own snippets. But I understand it is nice to have a set to look at, see what others are doing. One post I thought was really helpful was "How I'm able to take notes in mathematics lectures using LaTeX and Vim" From there, you can also find his github, with all his snippets. I find it a bit too complex, ...
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# Analysis of some neutral delay differential equations
## Abstract
The paper is devoted to the study of the neutral differential equation with delay $$\backslash(x^{\prime})t=f(t,x\left( t\right) ,(\theta \left(t\right) ),x^{\prime}(\theta \left( t\right) )).$$ Our analysis is concerned with existence, uniqueness and monotone iterative approximation of the nondecreasing global solutions of the initial-value problem. We use fixed point theorems (Schauder, Krasnoselskii, Leray-Schauder) and monotone iterative tehniques.
## Authors
Babeş-Bolyai University, Cluj-Napoca, Romania
## Paper coordinates
R. Precup, Analysis of some neutral delay differential equations, Studia Univ. Babes-Bolyai Math. 44, no.3 (1999), 67-84
## PDF
##### Journal
Studia Universitatis Babeş-Bolyai Mathematica
##### Publisher Name
Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca
##### Print ISSN
Not available yet.
##### Online ISSN
Not available yet.
## References
[1] D.D. Blecher, V.I. Paulsen, Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262-292.
[2] I. Golhberg, M. Krein, Introduction on the theory of the linear, non-adjoint operators on Hilbert space, Nauka, Moscow, 1965, (in Russian(.
[3] V.I. Paulsen, Completely bounded maps and dilations, Pitman Research Notes in Mathematics, Longmans, London, 1986.
[4] V.I. Paulsen, Representation of function algebras, abstract operator spaces and Banach space geometry, J. Funct. anal. 109 (1992), 113-129.
[5] G. Pisier,. Operator spaces and similarity problems, Documenta Math. (I.C.M. 1998) I-429-452.
[6] N. Salinas, Symmetric norm ideals and relative conjucate ideals, Trans. A.M.S. 188 (1974), 213-240.
[7] R. Schatten, Norm ideals of completely continuousoperatros, Berlin-Gottingen-Heidelberg,1960.
[8] N. Tita, Operators of σ_{p}-class on non-Hilbert spaces, Studii Cercet. Mat. 23 (1971), 467-487 (in Romanian).
[9] N. Tita, On a class of l_{?,p}operators, Collect.Math.32(1981),257-279.
[10] N. Tita, Some inequalities for the approximation numbers of tensor product operators, Anal.St.Univ.”Al. I. Cuza” Iași 40 (1994), 329-331.
[11] N. Tita, S-numbers operator ideals, Ed. Univ. Transilvania, Brașov.
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