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http://psychology.wikia.com/wiki/Phylogenetic_tree?direction=prev&oldid=152630
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# Phylogenetic tree
34,191pages on
this wiki
A phylogenetic tree, also called an evolutionary tree or a tree of life, is a tree showing the evolutionary interrelationships among various species or other entities that are believed to have a common ancestor. In a phylogenetic tree, each node with descendants represents the most recent common ancestor of the descendants, with edge lengths sometimes corresponding to time estimates. Each node in a phylogenetic tree is called a taxonomic unit. Internal nodes are generally referred to as Hypothetical Taxonomic Units (HTUs) as they cannot be directly observed.
Though the idea of a "tree" originally arose from earlier ideas of life as a progression from lower to higher forms (The Great Chain of Being), modern evolutionary biologists still use trees to depict evolution because it still effectively captures the idea speciation occurs through the splitting of lineages.
## Types of phylogenetic trees
A rooted phylogenetic tree is a directed tree with a unique node corresponding to the (usually imputed) most recent common ancestor of all the entities at the leaves of the tree. Figure 1 depicts a rooted phylogenetic tree, which has been colored according to the three-domain system[2]. The most common method for rooting trees is the use of an uncontroversial outgroup - close enough to allow inference from sequence or trait data, but far enough to be a clear outgroup.
Unrooted trees illustrate the relatedness of the leaf nodes without making assumptions about ancestry. While unrooted trees can always be generated from rooted ones by simply omitting the root, a root cannot be inferred from an unrooted tree without some means of identifying ancestry; this is normally done by including an outgroup in the input data or introducing additional assumptions about the relative rates of evolution on each branch, such as an application of the molecular clock hypothesis. Figure 2 depicts an unrooted phylogenetic tree[3] for myosin, a superfamily of proteins.
Both rooted and unrooted phylogenetic trees can be either bifurcating or multifurcating, and either labeled or unlabeled. A bifurcating tree has a maximum of two descendants arising from each interior node, while a multifurcating tree may have more than two. A labeled tree has specific values assigned to its leaves, while an unlabeled tree, sometimes called a tree shape, only defines a topology. The number of possible trees for a given number of leaf nodes depends on the specific type of tree, but there are always more multifurcating than bifurcating trees, more labeled than unlabeled trees, and more rooted than unrooted trees. The last distinction is the most biologically relevant; it arises because there are many places on an unrooted tree to put the root. For labeled bifurcating trees, there are
$\frac{(2n-3)!}{2^{n-2}(n-2)!}$
total rooted trees and
$\frac{(2n-5)!}{2^{n-3}(n-3)!}$
total unrooted trees, where n represents the number of leaf nodes. The number of unrooted trees for n input sequences or species is equal to the number of rooted trees for n-1 sequences.[4]
A Dendrogram is a broad term for the diagrammatic representation of a phylogenetic tree.
A Cladogram is a tree formed using cladistic methods. This type of tree only represents a branching pattern, i.e., its branch lengths do not represent time.
A Phylogram is a phylogenetic tree that explicitly represents number of character changes through its branch lengths.
A Chronogram is a phylogenetic tree that explicitly represents evolutionary time through its branch lengths.
## Phylogenetic tree construction
Main article: Computational phylogenetics
Phylogenetic trees among a nontrivial number of input sequences are constructed using computational phylogenetics methods. Distance-matrix methods such as neighbor-joining, which require multiple sequence alignments to calculate genetic distance, are simplest to implement; many sequence alignment methods such as ClustalW produce both sequence alignments and phylogenetic trees. Other methods include maximum parsimony and probabilistic inference techniques such as maximum likelihood; Bayesian inference has also been applied to phylogenetics but has been controversial.[4] Identifying the optimal tree using many of these techniques is NP-complete or NP-hard[4], so heuristic search and optimization methods are used in combination with tree-scoring functions to identify a reasonably good tree that fits the data.
Tree-building methods can be assessed on the basis of several criteria:[5]
• efficiency (how long does it take to compute the answer, how much memory does it need?)
• power (does it make good use of the data, or is information being wasted?)
• consistency (will it converge on the same answer repeatedly, if each time given different data for the same model problem?)
• robustness (does it cope well with violations of the assumptions of the underlying model?)
• falsifiability (does it alert us when it is not good to use, i.e. when assumptions are violated?)
Tree-building techniques have also gained the attention of mathematicians. Trees can also be built using T-theory. [6]
## Limitations of phylogenetic trees
Although phylogenetic trees produced on the basis of sequenced genes or genomic data in different species can provide evolutionary insight, they do have important limitations. Phylogenetic trees do not necessarily (and likely do not) represent actual evolutionary history. The data on which they are based is noisy; horizontal gene transfer[7], hybridisation between species that were not nearest neighbors on the tree before hybridisation takes place, convergent evolution, and conserved sequences can all confound the analysis. One method of analysis implemented in the program PhyloCode does not assume a tree structure to avoid these limitations.
Furthermore, basing the analysis on a single gene or protein taken from a group of species can be problematic because such trees constructed from another unrelated gene or protein sequence often differ from the first, and therefore great care is needed in inferring phylogenetic relationships amongst species. This is most true of genetic material that is subject to lateral gene transfer and recombination, where different haplotype blocks can have different histories.
When extinct species are included in a tree, they should always be terminal nodes, as it is unlikely that they are direct ancestors of any extant species. Scepticism must apply when extinct species are included in trees that are wholly or partly based on DNA sequence data, due to evidence that "ancient DNA" is not preserved intact for longer than 100,000 years.[How to reference and link to summary or text]
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2015-09-04 04:42:47
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https://www.speedsolving.com/forum/threads/wca-statistics-website.34250/
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# WCA Statistics Website
#### macky
Since the official WCA Statistics page is necessarily limited in scope, I'm setting up a WCA Statistics Website (thanks Lucas!). For now, I've put an All-Time World Championship Medal Table.
Goals:
* (unofficial) updated statistics on one website
* user-submitted statistics code (php and MySQL)
Regarding the first point: Although popular statistics may be incorporated into the official WCA Statistics page, some statistics are inherently unofficial, e.g. different proposed global ranking systems. The hope, moreover, is to encourage cubers, especially those without server access, to learn and experiment with php and MySQL.
To do:
* think about how best to set up user submission
If you'd like to contribute statistics code or help with the project, please contact me.
macky
Last edited:
#### Schmidt
##### Member
It is nothing much, but could you put numbers in front of the country names??
#### kinch2002
I'd like to know what program(s) I can get hold of to run SQL queries on the data base myself. I do this sort of thing at work, but have no software at home...
#### collinbxyz
##### Member
Great idea. I will try to contribute, but I don't know how much I could actually do.
Just a little error, at the bottom of the medal table, I see this:
MySQL Query
SELECT personCountryId,
SUM(IF(pos = 1, 1, 0)) AS gold,
SUM(IF(pos = 2, 1, 0)) AS silver,
SUM(IF(pos = 3, 1, 0)) AS bronze,
SUM(IF(pos <= 3, 1, 0)) AS total
FROM Results
JOIN Competitions
WHERE Results.competitionId = Competitions.id AND
(competitionId = 'WC2011' OR
competitionId = 'WC2009' OR
competitionId = 'WC2007' OR
competitionId = 'WC2005' OR
competitionId = 'WC2003' OR
competitionId = 'WC1982')
AND best >0 AND (roundId = 'f' OR roundId = 'c')
GROUP BY personCountryId
ORDER BY gold DESC, silver DESC, bronze DESC, personCountryId
#### PatrickJameson
Great idea. I will try to contribute, but I don't know how much I could actually do.
Just a little error, at the bottom of the medal table, I see this:
That is supposed to be there. This is the "code"(MySQL script) that was run against the database in order to get the table. It is there for reference.
I'd like to know what program(s) I can get hold of to run SQL queries on the data base myself. I do this sort of thing at work, but have no software at home...
You can download the WCA db here.
You'll have to do research to be able to run queries against the database on your platform.
Last edited:
#### oranjules
##### Member
13.37 single is impossible to obtain, so do you want the averages ?
I wanted to do that but the database is too big, i can't import it -_- (even in zip format)
EDIT : ok, found a way to do it, here is the query :
Code:
SELECT competitionId, eventId, personName, personId, personCountryId
FROM results
WHERE average =1337
I don't know how to make the results pretty, so here is a non-pretty version
competitionId eventId personName personId personCountryId
BelgianOpen2008 333 Milán Baticz 2005BATI01 Hungary
PoznanOpen2008 222 Szczepan Łągiewka 2007LAGI01 Poland
BarcelonaOpen2009 333 Jimmy Coll 2006COLL01 Belgium
SanDiegoOpen2009 333 Phillip Espinoza 2007ESPI01 USA
TaiwanSpringOpen2009 333 Han-Cyun Chen (陳翰群) 2008CHEN06 Taiwan
MadridOpen2009 333 Alejandro Aguado Barahona 2007AGUA01 Spain
DutchOpen2009 pyram Olivier Polspoel 2007POLS01 Belgium
Thankscubing2009 333 Chester Lian 2009LIAN03 Malaysia
SpanishChampionship2009 pyram Pau Vela García 2009GARC04 Spain
SpanishChampionship2009 pyram Jordi Piqueras Gómez 2008PIQU01 Spain
ChicagoOpen2010 333 Justin Jaffray 2008JAFF01 Canada
TaiwanWinterOpen2010 333 Hsuan Chang (張璿) 2008CHAN09 Taiwan
NorwegianOpen2010 333 Hong Tan Lam 2008LAMH01 Norway
PolishOpen2010 333 Piotr Kózka 2005KOZK01 Poland
MadridOpen2010 333 Rodrigo Septién Rodríguez 2008SEPT01 Spain
BerkeleySummer2010 333 Dan Dzoan 2006DZOA03 USA
BerkeleySummer2010 333 David Gomes 2006GOME01 USA
USNationals2010 333 Joey Gouly 2007GOUL01 United Kingdom
USNationals2010 333 Emily Wang 2009WANG15 Canada
PolishNationals2010 333 Michał Robaczyk 2006ROBA01 Poland
PhilippinesOpen2010 333 Richard Jay S. Apagar 2010APAG01 Philippines
Euro2010 333 Moritz Karl 2008KARL02 Germany
MunichOpen2010 222 Hendrik Hammer 2010HAMM02 Germany
NaonedOpen2010 333 Antoine Piau 2008PIAU01 France
MITFall2010 333 Patricia Li 2009LIPA01 USA
SwedishCubedays2010 333 Harald Stiff 2009STIF01 Sweden
IshikawaGokokuShintoOpen2010 333 Nobuaki Suga (菅 信昭) 2007SUGA01 Japan
SpanishChampionship2010 333 Jorge Morata Carrasco 2008MORA02 Spain
The most impressive thing is that a lot of them are well-known ! (Emily Wang, Milan Baticz, Jimmy Coll, Chester Lian, Joey Gouly...)
Last edited:
#### Stefan
##### Member
13.37 single is impossible to obtain
Not true... 21 people have managed that (four this year), Phillip Espinoza even twice! Edit: And I just saw him in your average list. Also, Pau Vela García got 13.37 average twice but never single. Besides those two, 61 people got one single or average 13.37.
Last edited:
#### oranjules
##### Member
these must be 11.37 +2, i saw in an other topic (maybe the "odd wca stats") that the stackmat timer can't do this time...
#### Stefan
##### Member
these must be 11.37 +2, i saw in an other topic (maybe the "odd wca stats") that the stackmat timer can't do this time...
Unlikely:
There have been 22 single 13.37s.
There have been 11 single 11.37s.
Why would a big majority of the 11.37s get +2s?
Continuing down:
There have been 13 single 9.37s.
There have been 8 single 7.37s.
There have been 6 single 5.37s.
There have been 25 single 3.37s.
There have been 18 single 1.37s.
And for comparison:
There have been 366 single 13.36s.
There have been 358 single 13.38s.
Last edited:
##### Member
@Stefan
The big majority would be because it seems like the only explanation.
Though, there could be a mistake, like judge's handwriting being hard to read (I could definitely be the judge here ), judge writting the time incorectly, even judge intentionally writing wrong, or a QJ timer.
The 13.36, and 13.38 comparison actually favors the +2 theory,
since you can't get 13.37 on a Stackmat, it isn't as common as those two are.
EDIT:
Ok, it seems the non-memory timers are responsible for most of them.
Last edited:
#### Blake4512
##### Member
@Stefan 13.37 might not be an impossible time but it is really rare to get. The people that got a 13.37 single might have used the timers before the memory timer because the memory timer skips times.
#### Henrik
##### Member
I don't know what timer version is used, but this proves that 13.37 should be possible.
(took like 10 sec to search on youtube, maybe because I knew there had been a video up sometime (and still is))
Last edited by a moderator:
#### cmhardw
There should be a picture from Worlds 2007 where two people practicing on stage got 13.37 singles on 3x3 at the same time, and at timers fairly close to each other. I remember both solvers pausing so that audience members could take pictures (this was during warm-ups, not during any round). Sadly I don't remember who the two solvers were, I only remember the incident.
#### Gunnar
##### Member
The times that seemingly can't be gotten on stackmats nowadays are possible on older timers. My timer is from 2005 and I can get 13.37, 9.99, 0.99, 1.00, 1.01 etc.
Maybe most (if not all) 13.37 was obtained with older timers?
By some weird reason it seems as they went from a perfectly fine time chip to a worse one a few years back. I hope the new 3-digit timers are more accurate.
#### Hippolyte!!!
##### Member
That's the case for me for the two first.
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2018-10-19 05:12:01
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http://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-2-equations-inequalities-and-problem-solving-2-2-using-the-principles-together-2-2-exercise-set-page-94/41
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Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
$y=-6$
By combining like terms and by using the properties of equality, the solution to the given equation, $2-5y=26-y$, is \begin{array}{l}\require{cancel} -5y+y=26-2 \\\\ -4y=24 \\\\ y=\dfrac{24}{-4} \\\\ y=-6 .\end{array}
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2018-04-19 10:38:03
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https://ask.sagemath.org/answers/43468/revisions/
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# Revision history [back]
Is this a bug?
Definitely yes. Especially with the "No backtrace available" you mention. But since you don't tell us what you were trying to do, it is pretty hard to divine the cause of the problem : in the plotting action, or in computing what you were trying to plot...
You should try to post a documented example (i. e. an actual attempt at plotting something and the complete answer of the system) on sage-support, where a developper might help you better than I can with so few details. (S)he might also be able to help you file a ticket.
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2020-10-27 09:40:15
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http://openstudy.com/updates/558454a9e4b091b59af10980
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## anonymous one year ago A coin was flipped 150 times. The results of the experiment are shown in the following table: Heads Tails 90 60 Which of the following best describes the experimental probability of getting heads? It is 10% higher than the theoretical probability. It is 10% lower than the theoretical probability. It is equal to the theoretical probability for this data. The experimental probability cannot be concluded from the data in the table.
1. XxMuslimxX
The experimental probability cannot be concluded from the data in the table.
2. kropot72
The experimental probability of heads is 90/150 = 0.6 If the coin was fair, the theoretical probability of heads is 0.5 Therefore the experimental probability of heads is $\large \frac{0.6-0.5}{0.5}\times\frac{100}{1}=20\ percent$ higher than the theoretical probability of heads. So none of the answer choices is correct.
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2016-10-23 03:28:05
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https://www.electro-tech-online.com/threads/simple-oscillator-formula.93349/
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# simple oscillator formula
Status
Not open for further replies.
##### New Member
Hello, I am working on a simple oscillator that uses two inverter gates, a resistor and a capacitor. I planned this out a while back, but I cannot find the formula I used to calculate the frequency. I also can't find anything online that resembles the circuit that I am using and also gives a formula for it. Can someone help me out here? I attached the schematic.
Thanks,
Josh Clark
#### Attachments
• 10.9 KB Views: 247
Last edited:
#### dougy83
##### Well-Known Member
I would assume that the following would be correct:
Code:
F = x/(RC)
Just build the circuit and measure the frequency. Then you can calculate x. Then you can calculate the rough frequency for any RC.
##### New Member
Ok thanks for the suggestion. I was going to use that as a last resort, but I guess it's the only choice now.
I just thought it was weird that I had a formula for the frequency when I first planned it out, but I couldn't find it later so I wanted to check to see if anyone else happened to know it.
#### dougy83
##### Well-Known Member
Actually, before you give up, have a look at
Square wave oscillator (2)
You will note that there is an extra resistor used, Rp, to 'protect' the CMOS input. It also has the added function of preventing the capacitor from being discharged through the CMOS input diodes (this affects the duty cycle & frequency, so the above f=x/r/c is no good due to the diodes affecting the timing)
#### Hero999
##### Banned
Rp is just a high value resistor 100k to 1M is normally good enough.
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2020-10-26 10:19:47
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https://scicomp.stackexchange.com/tags/iterative-method/hot
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# Tag Info
46
Your question is a bit like asking for which screwdriver to choose depending on the drive (slot, Phillips, Torx, ...): Besides there being too many, the choice also depends on whether you want to just tighten one screw or assemble a whole set of library shelves. Nevertheless, in partial answer to your question, here are some of the issues you should keep in ...
27
Initial advice Always run with -ksp_converged_reason -ksp_monitor_true_residual when trying to learn why a method is not converging. Make the problem size and number of processes as small as possible to demonstrate the failure. You often gain insight by determining what small problems exhibit the behavior that is causing your method to break down and the ...
18
Yes, you can, but Krylov methods generally do not have great smoothing properties. This is because they target the whole spectrum in an adaptive way that minimizes the residual or a suitable norm of the error. This will generally include some low frequency (long wavelength) modes that the coarse grids would have handled fine. Krylov smoothers also make the ...
17
I originally didn't want to give an answer because this deserves a very long treatment, and hopefully someone else will still give it. However, I can certainly give a very brief overview of the recommended approach: Perform a thorough literature search. If that fails, try every preconditioner that makes sense that you can get your hands on. MATLAB, PETSc, ...
16
My advice to students is to try a direct solver in these cases. The reason is that there are two classes of reasons why a solver may not converge: (i) the matrix is wrong, or (ii) there is a problem with the solver/preconditioner. Direct solvers almost always yield something that you can compare with the solution you expect, so if the answer of the direct ...
14
Others have already commented on the issue of preconditioning what I will call "monolithic" matrices, i.e. for example the discretized form of a scalar equation such as the Laplace equation, the Helmholtz equation or, if you want to generalize it, the vector-valued elasticity equation. For these things, it is clear that multigrid (either algebraic or ...
13
Jack has given a good procedure for finding a preconditioner. I will try an address the question, "What makes a good preconditioner?". The operational definition is: A Preconditioner M accelerates the iterative solution of $A x = b$, and $M^{-1}$ can be applied cheaply compared to $A^{-1}$. however this does not give us any insight into designing a ...
13
This list is nowhere near complete, but hopefully the size of it will give a hint as to the scale of possible factors. I am assuming you are compiling the code from source on your platform of choice. Software Standard Library Performance Lin. Alg. Library Performance (if the software links to outside libraries) Compiler Choice Compiler Optimization ...
13
Compute the largest-magnitude eigenvalue $\lambda_{max}$ of $A$ (with, say, eigs('lm')). Then compute the largest magnitude (negative) eigenvalue $\hat{\lambda}_{max}$ of $M = A - \lambda_{max}I$ (again, through a standard call to eigs('lm')). Observe that $\hat{\lambda}_{max} + \lambda_{\max} = \lambda_{min}(A)$. The reason why this holds is explained here. ...
13
In a nutshell, the QR algorithm applied to a matrix $A$ is an iterative procedure that converges to the real Schur decomposition: a unitary matrix $Q$ and a matrix $R$ in block upper triangular form (see below) such that $A = QRQ^T$. It follows that the columns of $Q$ are the eigenvectors (which are the principal objects that are computed!) and that $R$ has ...
12
Damped Jacobi Suppose the matrix $A$ has diagonal $D$. If the spectrum of $D^{-1}A$ lies in the interval $[a,b]$ of the positive real axis, then the iteration matrix of Jacobi with damping factor $\omega$ $$B_\text{Jacobi} = I - \omega D^{-1} A$$ has spectrum in the range $[1 - \omega b,1 - \omega a]$, so minimizing the spectral radius with $$\omega_{\text{... 12 To perform reasonably, polynomial preconditioners need fairly accurate spectral estimates. For ill-conditioned elliptic problems the smallest eigenvalues are usually separated such that methods like Chebyshev are far from optimal. The most interesting property of polynomial methods is that they do not require any inner products. It's actually quite popular ... 12 The derivation of the BFGS is more intuitive when one considers (strictly) convex cost functionals: However, some background information is necessary: Assume, one wants to minimize a convex functional$$ f(x) \to \min_{x\in \mathbb R^n}. $$Say there is an approximate solution x_k. Then, one approximates the minimum of f by the minimum of the ... 11 I am extremely surprised that there is no mention of conditioning or the shape of the spectrum in your discussion, as it will be the decisive property in whether or not iterative methods can beat dense methods. As an extreme example, suppose that your dense matrix is some small perturbation of the identity matrix. Then most iterative methods will converge ... 11 In exact arithmetic you shouldn't need to reorthogonalize regularly, but practically you do. Your u1 and u2 are close to (but not exactly) the true eigenvectors, so your initial deflation almost (but not entirely) removed the true eigenvectors from u3. The tiny components you left behind will be amplified by repeated multiplication by A, you will need to ... 11 In addition to Christian's answer, it's also worth noting that for linear convergence you have e_{k+1} \le \lambda_1 e_k where you have \lambda_1<1 if the method converges. On the other hand, for quadratic convergence you have e_{k+1} \le \lambda_2 e_k^2 and the fact that a method converges does not necessarily imply that \lambda_2 must be smaller ... 11 You define a sequence in, say, C^{\infty}(\Omega)\times C^{\infty}(\Omega) by$$ \frac{\text{d}^2u^k}{\text{d}x^2} + \frac{\text{d} v^{k-1}}{\text{d} x} =f\\ \frac{\text{d}^2v^k}{\text{d}x^2} + \frac{\text{d} u^{k-1}}{\text{d} x} =g\\ (plus boundary conditions). It is clear that if this sequence converges, it will be a solution of your original set of ...
11
In general, there is no shortcut other than completely re-factoring the matrix. There have been a few similar questions on this SE that cover the topic in more depth than I can: Can diagonal plus fixed symmetric linear systems be solved in quadratic time after precomputation? LU Decom of PSD Matrix + Diagonal Matrix Perturbation of Cholesky decomposition ...
10
It is critical to know more about the structure. It matters whether the random entries are uniformly or normally distributed and whether there is a shift or not. If there is no structure at all, then you cannot asymptotically beat a direct solve. Some comments on your proposed approaches Incomplete LU is complete LU when applied to a dense matrix. You could ...
10
Some references on rounding error analysis of Krylov methods: Gutknecht, Martin H., and Zdenvek Strakos. "Accuracy of two three-term and three two-term recurrences for Krylov space solvers." SIAM Journal on Matrix Analysis and Applications 22.1 (2000): 213-229. Paige, Christopher C., and Zdenvek Strakos. "Residual and backward error bounds in minimum ...
10
The convergence behavior you are seeing is actually expected. One of things that makes the Lanczos method so interesting is that it does a good job of simultaneously converging eigenvalues at both ends of the spectrum. I assume your expectation of converging only the largest eigenvalues is based on the fact that, as expected from the Power iteration ...
9
For a single rational equation in the complex domain, the basin of attraction is fractal, the compelement of a so-called Julia set. http://en.wikipedia.org/wiki/Julia_set . For theory with some nice online figures, see, e.g., http://mathlab.mathlab.sunysb.edu/~scott/Papers/Newton/Published.pdf http://hera.ugr.es/doi/15019160.pdf Even the ''globalized'' ...
9
In practice, yes. While $e_k$ is still large, the rate coefficient $\lambda$ will dominate the error rather than the q-rate. (Note that these are asymptotic rates, so the statements you linked to only hold for the limit as $k\to\infty$.) For example, for first order methods in optimization you often observe an initially fast decrease in error, which then ...
9
Yes you can do this, and it will converge in one iteration regardless of the starting value. This is because each step of Newton's method involves solving a linear system with the Jacobian of the nonlinear function. In this case the Jacobian just equals $A$. In other words: this is a little circular because it requires you to solve the system $Ax=b$ in the ...
9
If you're using GMRES, typically you have a large stiff system. The extra work done for the householder algorithm is negligible compared to the expense of GMRES and the preconditionder. As such, we want the more numerically stable method to make sure that the system is more likely to converge. Especially since you choose GMRES because you want something that ...
8
The conjugate gradient algorithm works for semidefinite problems and produces the minimal norm solution.
8
In most cases I know of where Krylov methods are used for dense problems, the operator is a low-rank perturbation of the identity (obtained by discretizing a continuum operator which is a compact perturbation of the identity). Such operators appear frequently in boundary integral equations as discretized Fredholm integral operators of the second kind. These ...
8
Youssef Saad's book Numerical Methods for Large Eigenvalue Problems, 2nd edition uses the norm of the residual vector to define convergence criteria. He defines the residual vector as follows on page 59: Given a matrix $\mathbf{A} \in \mathbb{C}^{n \times n}$, a putative eigenvalue $\widetilde{\lambda} \in \mathbb{C}$ and a putative eigenvector $\widetilde{\... 8 There is a theorem that syas that a black box algorithm is guaranteed to find the global minimum of an arbitrary smooth (i.e., twice continuously differentiable) function if and only if it samples points densely in the search space. Here dense is meant in the topological sense, i.e., it must sample points in arbirarily small neighborhoods of every point. ... 8 In theory, yes. In practice, rounding errors will usually result in (initially slow) convergence to$u_1\$. At essentially the same cost one can run the Lanczos algorithm, which will have much faster convergence, and produce the three dominant eigenvalues unless two of these eigenvalues are essentially the same. For Lanczos, selective reorthogonalization is ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2020-01-27 16:23:05
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https://docs.panda3d.org/1.10/python/reference/direct.distributed.AsyncRequest
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# direct.distributed.AsyncRequest¶
from direct.distributed.AsyncRequest import AsyncRequest, cleanupAsyncRequests
Inheritance diagram
class AsyncRequest(air, replyToChannelId=None, timeoutTime=8.0, numRetries=0)[source]
This class is used to make asynchronous reads and creates to a database.
You can create a list of self.neededObjects and then ask for each to be read or created, or if you only have one object that you need you can skip the self.neededObjects because calling askForObject or createObject will set the self.neededObjects value for you.
Once all the objects have been read or created, the self.finish() method will be called. You may override this function to run your code in a derived class.
If you wish to queue up several items that you all need before the finish method is called, you can put items in self.neededObjects and then call askForObject or createObject afterwards. That way the _checkCompletion will not call finish until after all the requests have been done.
If you need to chain serveral object reads or creates, just add more entries to the self.neededObjects dictionary in the self.finish function and return without calling AsyncRequest.finish(). Your finish method will be called again when the new self.neededObjects is complete. You may repeat this as necessary.
__init__(self, air, replyToChannelId=None, timeoutTime=8.0, numRetries=0)[source]
air is the AI Respository. replyToChannelId may be an avatarId, an accountId, or a channelId. timeoutTime is how many seconds to wait before aborting the request. numRetries is the number of times to retry the request before giving up.
askForObject(self, doId, context=None)[source]
Request an already created object, i.e. read from database.
askForObjectField(self, dclassName, fieldName, doId, key=None, context=None)[source]
Request an already created object, i.e. read from database.
askForObjectFields(self, dclassName, fieldNames, doId, key=None, context=None)[source]
Request an already created object, i.e. read from database.
askForObjectFieldsByString(self, dbId, dclassName, objString, fieldNames, key=None, context=None)[source]
createObject(self, name, className, databaseId=None, values=None, context=None)[source]
Create a new database object. You can get the doId from within your self.finish() function.
This functions is different from createObjectId in that it does generate the object when the response comes back. The object is added to the doId2do and so forth and treated as a full regular object (which it is). This is useful on the AI where we really do want the object on the AI.
createObjectId(self, name, className, values=None, context=None)[source]
Create a new database object. You can get the doId from within your self.finish() function.
This functions is different from createObject in that it does not generate the object when the response comes back. It only tells you the doId. This is useful on the UD where we don’t really want the object on the UD, we just want the object created and the UD wants to send messages to it using the ID.
delete(self)[source]
finish(self)[source]
This is the function that gets called when all of the needed objects are in (i.e. all the askForObject and createObject requests have been satisfied). If the other requests timeout, finish will not be called.
notify = <direct.directnotify.Notifier.Notifier object>
timeout(self, task)[source]
cleanupAsyncRequests()[source]
Only call this when the application is shuting down.
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2020-11-27 00:33:08
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https://my.oschina.net/goopand/blog/667957
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2016/04/29 10:19
# Linux Performance Analysis in 60,000 Milliseconds
You login to a Linux server with a performance issue: what do you check in the first minute?
At Netflix we have a massive EC2 Linux cloud, and numerous performance analysis tools to monitor and investigate its performance. These include Atlas for cloud-wide monitoring, and Vector for on-demand instance analysis. While those tools help us solve most issues, we sometimes need to login to an instance and run some standard Linux performance tools.
In this post, the Netflix Performance Engineering team will show you the first 60 seconds of an optimized performance investigation at the command line, using standard Linux tools you should have available.
## First 60 Seconds: Summary
In 60 seconds you can get a high level idea of system resource usage and running processes by running the following ten commands. Look for errors and saturation metrics, as they are both easy to interpret, and then resource utilization. Saturation is where a resource has more load than it can handle, and can be exposed either as the length of a request queue, or time spent waiting.
uptime
dmesg | tail
vmstat 1
mpstat -P ALL 1
pidstat 1
iostat -xz 1
free -m
sar -n DEV 1
sar -n TCP,ETCP 1
top
Some of these commands require the sysstat package installed. The metrics these commands expose will help you complete some of the USE Method: a methodology for locating performance bottlenecks. This involves checking utilization, saturation, and error metrics for all resources (CPUs, memory, disks, e.t.c.). Also pay attention to when you have checked and exonerated a resource, as by process of elimination this narrows the targets to study, and directs any follow on investigation.
The following sections summarize these commands, with examples from a production system. For more information about these tools, see their man pages.
$uptime 23:51:26 up 21:31, 1 user, load average: 30.02, 26.43, 19.02 This is a quick way to view the load averages, which indicate the number of tasks (processes) wanting to run. On Linux systems, these numbers include processes wanting to run on CPU, as well as processes blocked in uninterruptible I/O (usually disk I/O). This gives a high level idea of resource load (or demand), but can’t be properly understood without other tools. Worth a quick look only. The three numbers are exponentially damped moving sum averages with a 1 minute, 5 minute, and 15 minute constant. The three numbers give us some idea of how load is changing over time. For example, if you’ve been asked to check a problem server, and the 1 minute value is much lower than the 15 minute value, then you might have logged in too late and missed the issue. In the example above, the load averages show a recent increase, hitting 30 for the 1 minute value, compared to 19 for the 15 minute value. That the numbers are this large means a lot of something: probably CPU demand; vmstat or mpstat will confirm, which are commands 3 and 4 in this sequence. ### 2. dmesg | tail$ dmesg | tail[1880957.563150] perl invoked oom-killer: gfp_mask=0x280da, order=0, oom_score_adj=0
[...]
[1880957.563400] Out of memory: Kill process 18694 (perl) score 246 or sacrifice child
[2320864.954447] TCP: Possible SYN flooding on port 7001. Dropping request. Check SNMP counters.
This views the last 10 system messages, if there are any. Look for errors that can cause performance issues. The example above includes the oom-killer, and TCP dropping a request.
Don’t miss this step! dmesg is always worth checking.
$vmstat 1procs ---------memory---------- ---swap-- -----io---- -system-- ------cpu----- r b swpd free buff cache si so bi bo in cs us sy id wa st 34 0 0 200889792 73708 591828 0 0 0 5 6 10 96 1 3 0 0 32 0 0 200889920 73708 591860 0 0 0 592 13284 4282 98 1 1 0 0 32 0 0 200890112 73708 591860 0 0 0 0 9501 2154 99 1 0 0 0 32 0 0 200889568 73712 591856 0 0 0 48 11900 2459 99 0 0 0 0 32 0 0 200890208 73712 591860 0 0 0 0 15898 4840 98 1 1 0 0 ^C Short for virtual memory stat, vmstat(8) is a commonly available tool (first created for BSD decades ago). It prints a summary of key server statistics on each line. vmstat was run with an argument of 1, to print one second summaries. The first line of output (in this version of vmstat) has some columns that show the average since boot, instead of the previous second. For now, skip the first line, unless you want to learn and remember which column is which. Columns to check: • r: Number of processes running on CPU and waiting for a turn. This provides a better signal than load averages for determining CPU saturation, as it does not include I/O. To interpret: an “r” value greater than the CPU count is saturation. • free: Free memory in kilobytes. If there are too many digits to count, you have enough free memory. The “free -m” command, included as command 7, better explains the state of free memory. • si, so: Swap-ins and swap-outs. If these are non-zero, you’re out of memory. • us, sy, id, wa, st: These are breakdowns of CPU time, on average across all CPUs. They are user time, system time (kernel), idle, wait I/O, and stolen time (by other guests, or with Xen, the guest's own isolated driver domain). The CPU time breakdowns will confirm if the CPUs are busy, by adding user + system time. A constant degree of wait I/O points to a disk bottleneck; this is where the CPUs are idle, because tasks are blocked waiting for pending disk I/O. You can treat wait I/O as another form of CPU idle, one that gives a clue as to why they are idle. System time is necessary for I/O processing. A high system time average, over 20%, can be interesting to explore further: perhaps the kernel is processing the I/O inefficiently. In the above example, CPU time is almost entirely in user-level, pointing to application level usage instead. The CPUs are also well over 90% utilized on average. This isn’t necessarily a problem; check for the degree of saturation using the “r” column. ### 4. mpstat -P ALL 1$ mpstat -P ALL 1Linux 3.13.0-49-generic (titanclusters-xxxxx) 07/14/2015 _x86_64_ (32 CPU)
07:38:49 PM CPU %usr %nice %sys %iowait %irq %soft %steal %guest %gnice %idle
07:38:50 PM all 98.47 0.00 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.78
07:38:50 PM 0 96.04 0.00 2.97 0.00 0.00 0.00 0.00 0.00 0.00 0.99
07:38:50 PM 1 97.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00
07:38:50 PM 2 98.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00
07:38:50 PM 3 96.97 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.03
[...]
This command prints CPU time breakdowns per CPU, which can be used to check for an imbalance. A single hot CPU can be evidence of a single-threaded application.
$pidstat 1Linux 3.13.0-49-generic (titanclusters-xxxxx) 07/14/2015 _x86_64_ (32 CPU) 07:41:02 PM UID PID %usr %system %guest %CPU CPU Command 07:41:03 PM 0 9 0.00 0.94 0.00 0.94 1 rcuos/0 07:41:03 PM 0 4214 5.66 5.66 0.00 11.32 15 mesos-slave 07:41:03 PM 0 4354 0.94 0.94 0.00 1.89 8 java 07:41:03 PM 0 6521 1596.23 1.89 0.00 1598.11 27 java 07:41:03 PM 0 6564 1571.70 7.55 0.00 1579.25 28 java 07:41:03 PM 60004 60154 0.94 4.72 0.00 5.66 9 pidstat 07:41:03 PM UID PID %usr %system %guest %CPU CPU Command 07:41:04 PM 0 4214 6.00 2.00 0.00 8.00 15 mesos-slave 07:41:04 PM 0 6521 1590.00 1.00 0.00 1591.00 27 java 07:41:04 PM 0 6564 1573.00 10.00 0.00 1583.00 28 java 07:41:04 PM 108 6718 1.00 0.00 0.00 1.00 0 snmp-pass 07:41:04 PM 60004 60154 1.00 4.00 0.00 5.00 9 pidstat ^C Pidstat is a little like top’s per-process summary, but prints a rolling summary instead of clearing the screen. This can be useful for watching patterns over time, and also recording what you saw (copy-n-paste) into a record of your investigation. The above example identifies two java processes as responsible for consuming CPU. The %CPU column is the total across all CPUs; 1591% shows that that java processes is consuming almost 16 CPUs. ### 6. iostat -xz 1$ iostat -xz 1Linux 3.13.0-49-generic (titanclusters-xxxxx) 07/14/2015 _x86_64_ (32 CPU)
avg-cpu: %user %nice %system %iowait %steal %idle
73.96 0.00 3.73 0.03 0.06 22.21
Device: rrqm/s wrqm/s r/s w/s rkB/s wkB/s avgrq-sz avgqu-sz await r_await w_await svctm %util
xvda 0.00 0.23 0.21 0.18 4.52 2.08 34.37 0.00 9.98 13.80 5.42 2.44 0.09
xvdb 0.01 0.00 1.02 8.94 127.97 598.53 145.79 0.00 0.43 1.78 0.28 0.25 0.25
xvdc 0.01 0.00 1.02 8.86 127.79 595.94 146.50 0.00 0.45 1.82 0.30 0.27 0.26
dm-0 0.00 0.00 0.69 2.32 10.47 31.69 28.01 0.01 3.23 0.71 3.98 0.13 0.04
dm-1 0.00 0.00 0.00 0.94 0.01 3.78 8.00 0.33 345.84 0.04 346.81 0.01 0.00
dm-2 0.00 0.00 0.09 0.07 1.35 0.36 22.50 0.00 2.55 0.23 5.62 1.78 0.03
[...]
^C
This is a great tool for understanding block devices (disks), both the workload applied and the resulting performance. Look for:
• r/s, w/s, rkB/s, wkB/s: These are the delivered reads, writes, read Kbytes, and write Kbytes per second to the device. Use these for workload characterization. A performance problem may simply be due to an excessive load applied.
• await: The average time for the I/O in milliseconds. This is the time that the application suffers, as it includes both time queued and time being serviced. Larger than expected average times can be an indicator of device saturation, or device problems.
• avgqu-sz: The average number of requests issued to the device. Values greater than 1 can be evidence of saturation (although devices can typically operate on requests in parallel, especially virtual devices which front multiple back-end disks.)
• %util: Device utilization. This is really a busy percent, showing the time each second that the device was doing work. Values greater than 60% typically lead to poor performance (which should be seen in await), although it depends on the device. Values close to 100% usually indicate saturation.
If the storage device is a logical disk device fronting many back-end disks, then 100% utilization may just mean that some I/O is being processed 100% of the time, however, the back-end disks may be far from saturated, and may be able to handle much more work.
Bear in mind that poor performing disk I/O isn’t necessarily an application issue. Many techniques are typically used to perform I/O asynchronously, so that the application doesn’t block and suffer the latency directly (e.g., read-ahead for reads, and buffering for writes).
$free -m total used free shared buffers cached Mem: 245998 24545 221453 83 59 541 -/+ buffers/cache: 23944 222053 Swap: 0 0 0 The right two columns show: • buffers: For the buffer cache, used for block device I/O. • cached: For the page cache, used by file systems. We just want to check that these aren’t near-zero in size, which can lead to higher disk I/O (confirm using iostat), and worse performance. The above example looks fine, with many Mbytes in each. The “-/+ buffers/cache” provides less confusing values for used and free memory. Linux uses free memory for the caches, but can reclaim it quickly if applications need it. So in a way the cached memory should be included in the free memory column, which this line does. There’s even a website, linuxatemyram, about this confusion. It can be additionally confusing if ZFS on Linux is used, as we do for some services, as ZFS has its own file system cache that isn’t reflected properly by the free -m columns. It can appear that the system is low on free memory, when that memory is in fact available for use from the ZFS cache as needed. ### 8. sar -n DEV 1$ sar -n DEV 1Linux 3.13.0-49-generic (titanclusters-xxxxx) 07/14/2015 _x86_64_ (32 CPU)
12:16:48 AM IFACE rxpck/s txpck/s rxkB/s txkB/s rxcmp/s txcmp/s rxmcst/s %ifutil
12:16:49 AM eth0 18763.00 5032.00 20686.42 478.30 0.00 0.00 0.00 0.00
12:16:49 AM lo 14.00 14.00 1.36 1.36 0.00 0.00 0.00 0.00
12:16:49 AM docker0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
12:16:49 AM IFACE rxpck/s txpck/s rxkB/s txkB/s rxcmp/s txcmp/s rxmcst/s %ifutil
12:16:50 AM eth0 19763.00 5101.00 21999.10 482.56 0.00 0.00 0.00 0.00
12:16:50 AM lo 20.00 20.00 3.25 3.25 0.00 0.00 0.00 0.00
12:16:50 AM docker0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
^C
Use this tool to check network interface throughput: rxkB/s and txkB/s, as a measure of workload, and also to check if any limit has been reached. In the above example, eth0 receive is reaching 22 Mbytes/s, which is 176 Mbits/sec (well under, say, a 1 Gbit/sec limit).
This version also has %ifutil for device utilization (max of both directions for full duplex), which is something we also use Brendan’s nicstat tool to measure. And like with nicstat, this is hard to get right, and seems to not be working in this example (0.00).
$sar -n TCP,ETCP 1Linux 3.13.0-49-generic (titanclusters-xxxxx) 07/14/2015 _x86_64_ (32 CPU) 12:17:19 AM active/s passive/s iseg/s oseg/s 12:17:20 AM 1.00 0.00 10233.00 18846.00 12:17:19 AM atmptf/s estres/s retrans/s isegerr/s orsts/s 12:17:20 AM 0.00 0.00 0.00 0.00 0.00 12:17:20 AM active/s passive/s iseg/s oseg/s 12:17:21 AM 1.00 0.00 8359.00 6039.00 12:17:20 AM atmptf/s estres/s retrans/s isegerr/s orsts/s 12:17:21 AM 0.00 0.00 0.00 0.00 0.00 ^C This is a summarized view of some key TCP metrics. These include: • active/s: Number of locally-initiated TCP connections per second (e.g., via connect()). • passive/s: Number of remotely-initiated TCP connections per second (e.g., via accept()). • retrans/s: Number of TCP retransmits per second. The active and passive counts are often useful as a rough measure of server load: number of new accepted connections (passive), and number of downstream connections (active). It might help to think of active as outbound, and passive as inbound, but this isn’t strictly true (e.g., consider a localhost to localhost connection). Retransmits are a sign of a network or server issue; it may be an unreliable network (e.g., the public Internet), or it may be due a server being overloaded and dropping packets. The example above shows just one new TCP connection per-second. ### 10. top$ toptop - 00:15:40 up 21:56, 1 user, load average: 31.09, 29.87, 29.92
Tasks: 871 total, 1 running, 868 sleeping, 0 stopped, 2 zombie
%Cpu(s): 96.8 us, 0.4 sy, 0.0 ni, 2.7 id, 0.1 wa, 0.0 hi, 0.0 si, 0.0 st
KiB Mem: 25190241+total, 24921688 used, 22698073+free, 60448 buffers
KiB Swap: 0 total, 0 used, 0 free. 554208 cached Mem
PID USER PR NI VIRT RES SHR S %CPU %MEM TIME+ COMMAND
20248 root 20 0 0.227t 0.012t 18748 S 3090 5.2 29812:58 java
4213 root 20 0 2722544 64640 44232 S 23.5 0.0 233:35.37 mesos-slave
66128 titancl+ 20 0 24344 2332 1172 R 1.0 0.0 0:00.07 top
5235 root 20 0 38.227g 547004 49996 S 0.7 0.2 2:02.74 java
4299 root 20 0 20.015g 2.682g 16836 S 0.3 1.1 33:14.42 java
1 root 20 0 33620 2920 1496 S 0.0 0.0 0:03.82 init
2 root 20 0 0 0 0 S 0.0 0.0 0:00.02 kthreadd
3 root 20 0 0 0 0 S 0.0 0.0 0:05.35 ksoftirqd/0
5 root 0 -20 0 0 0 S 0.0 0.0 0:00.00 kworker/0:0H
6 root 20 0 0 0 0 S 0.0 0.0 0:06.94 kworker/u256:0
8 root 20 0 0 0 0 S 0.0 0.0 2:38.05 rcu_sched
The top command includes many of the metrics we checked earlier. It can be handy to run it to see if anything looks wildly different from the earlier commands, which would indicate that load is variable.
A downside to top is that it is harder to see patterns over time, which may be more clear in tools like vmstat and pidstat, which provide rolling output. Evidence of intermittent issues can also be lost if you don’t pause the output quick enough (Ctrl-S to pause, Ctrl-Q to continue), and the screen clears.
## Follow-on Analysis
There are many more commands and methodologies you can apply to drill deeper. See Brendan’s Linux Performance Tools tutorial from Velocity 2015, which works through over 40 commands, covering observability, benchmarking, tuning, static performance tuning, profiling, and tracing.
Tackling system reliability and performance problems at web scale is one of our passions. If you would like to join us in tackling these kinds of challenges we are hiring!
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Oldest
Ricardo Schmidt ·
nice post! thanks!
Han-Cheol Cho ·
Thank you for a useful article smile emoticon
Wuhan University
Very good summary of the perf tools! Thanks! 好文收藏！
Kiran Patil
USEFULL
Loïc Vernet ·
I add this question at a job interview one time, I wish I had read this before. Usefull.
New York, New York
Reading this is time well spent. A lot of info packed into a quick read. Thanks!
Jeffrey Ness ·
Works at BigRentz
Great write up! Thanks for sharing!
excellent!! netflix has a tech blog
Michael Hess ·
West Chester University
Really good info. Though I prefer htop to regular top.
atop is much better in my opinion smile emoticon
Like · Reply · 2 · Dec 6, 2015 6:11am
Diganta Maity ·
Leo Gonsalves
You should use ps_mem.py to get a deeper analysis of memory as free will not give the exact memory usage, this will be required when you have to troubleshoot memory leaks seehttp://techarena51.com/index.php/linux-memory-usage/
Marco Agate
Thanks for sharing
very nice info
Alex Balhatchet ·
Great post. I would recommend 'dmesg -T | tail' which converts the "seconds since boot" to a readable timestamp. Too many times I've thought 'dmesg | tail' had something interesting when actually it happened weeks ago and was unrelated to the current issue.
Mauro Risonho Paula Assumpção ·
Thanks for sharing!
Ben Eriksson
Nice, really useful info. Do you use top over HTop for a reason? I just prefere HTop myself
Hello. Thanks for the article. I have one question:
5. "The above example identifies two java processes as responsible for consuming CPU. The %CPU column is the total across all CPUs; 1591% shows that that java processes is consuming almost 16 CPUs. "
Does it mean that 2 java processes with PIDs 6521 6564 are using together almost 32 CPUs?
Blaize Blaise
...and run sysdig so you have info to look at later too...
Works at Netflix
nice post!
Awesome post!!!
Works at VASC
Thanks for share, it's very useful to me.
such a great post! thanks!
Simbosium Caribellium
good stuff!
super useful post. I did notice one small error for item #6 on iostat. The description for avgqu-sz should be "The average queue length of the requests that were issued to the device." (not the average # of requests as posted).
St.John's Matriculation Higher Secondary...
Very useful post well decribed thanks ot the author
Stelvin Stelvinov
Thank You.
Beijing, China
nice !
Huazhong University of Science and Technology
nice post！
Great post. Thanks for sharing.
1
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2021-12-06 04:48:04
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http://www.gradesaver.com/textbooks/math/algebra/college-algebra-11th-edition/chapter-r-section-r-4-factoring-polynomials-r-4-exercises-page-38/42
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## College Algebra (11th Edition)
Check factorization with FOIL: (4p - 5)(4p - 5) = 4p(4p) + 4p(-5) - 5(4p) - 5(-5) = 16$p^{2}$ - 20p - 20p + 25 = 16$p^{2}$ - 40p + 25
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2017-02-21 23:55:15
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http://clay6.com/qa/26434/h-2s-in-the-presence-of-hcl-precipitates-group-ii-but-not-group-iv-because
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Browse Questions
# $H_2S$ in the presence of HCl precipitates group II but not group IV because
(a) HCl activates $H_2S$
(b) HCl increases the concentration of $Cl^-$ ions
(c) HCl decreases the concentration of $S^{2-}$ ions
(d) HCl lowers the solubility of $H_2S$ in the solution
Answer: HCl decreases the concentration of $S^{2-}$ ions
Due to common ion effect, HCl suppresses the ionisation of $H_2S$ thus decreasing the concentration of $S^{2-}$ ions. Only group II radicals are precipitated.
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2017-03-28 04:27:19
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https://msp.org/agt/2014/14-4/p62.xhtml
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#### Volume 14, issue 4 (2014)
Recent Issues
The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Other MSP Journals
The sutured Floer polytope and taut depth-one foliations
### Irida Altman
Algebraic & Geometric Topology 14 (2014) 1881–1923
##### Abstract
[an error occurred while processing this directive]
For closed 3–manifolds, Heegaard Floer homology is related to the Thurston norm through results due to Ozsváth and Szabó, Ni, and Hedden. For example, given a closed 3–manifold $Y$, there is a bijection between vertices of the ${HF}^{+}\left(Y\right)$ polytope carrying the group $ℤ$ and the faces of the Thurston norm unit ball that correspond to fibrations of $Y$ over the unit circle. Moreover, the Thurston norm unit ball of $Y$ is dual to the polytope of $\stackrel{̂}{\underset{¯}{HF}}\left(Y\right)$.
We prove a similar bijection and duality result for a class of 3–manifolds with boundary called sutured manifolds. A sutured manifold is essentially a cobordism between two possibly disconnected surfaces with boundary ${R}_{+}$ and ${R}_{-}$. We show that there is a bijection between vertices of the sutured Floer polytope carrying the group $ℤ$ and equivalence classes of taut depth-one foliations that form the foliation cones of Cantwell and Conlon. Moreover, we show that a function defined by Juhász, which we call the geometric sutured function, is analogous to the Thurston norm in this context. In some cases, this function is an asymmetric norm and our duality result is that appropriate faces of this norm’s unit ball subtend the foliation cones.
An important step in our work is the following fact: a sutured manifold admits a fibration or a taut depth-one foliation whose sole compact leaves are exactly the connected components of ${R}_{+}$ and ${R}_{-}$, if and only if, there is a surface decomposition of the sutured manifold resulting in a product manifold.
##### Keywords
sutured manifold, sutured Floer homology, foliation, $3$–manifold, Thurston norm, polytope
##### Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R30, 57R58
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2019-02-19 21:41:11
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http://www.veedoogroup.com/orthodontist-vs-ybadz/fescn2%2B-molar-mass-a64693
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Select Page
1. O3 5. What would be the Molarity of HCL? At a certain temperature, K = 9.1 10-4 for the following reaction. 2 Example Reactions: • FeCl3 + 3 KSCN = Fe(SCN)3 + 3 KCl • FeCl3 + 3 NH4SCN = Fe(SCN)3 + 3 NH4Cl • Fe(NO3)3 + 3 KSCN = Fe(SCN)3 + 3 KNO3 • FeCl3 + 3 NH4SCN = 3 NH3 + 3 HCl + Fe(SCN)3 • FeCl3 + 3 NaSCN = Fe(SCN)3 + 3 NaCl :: Chemistry Applications:: » Chemical Elements, Periodic Table » Compound Name Formula Search » Moles to Grams Calculator » Common … The new molarity is given by the molarity of the stock solution multiplied by the dilution factor. https://de.wikipedia.org/w/index.php?title=Extinktionskoeffizient&oldid=205316964, „Creative Commons Attribution/Share Alike“. Part A. If you add a metal piece to excess acid, what of listed factors below will increase, decrease, or have no impact on how fast a reaction happens? (1 u is equal to 1/12 the mass of one atom of carbon-12) Molar mass (molar weight) is the mass of one mole of a substance and is expressed in g/mol. Um die molare Masse berechnen zu können, muss man lediglich in das Periodensystem schauen. . 5.00mL of 2.0mM Fe3+ is mixed with 5.00 mL of 2.0mM SCN-. terms of molar concentrations can be expressed as [FeSCN2+] eq Keq = ⎯⎯⎯⎯⎯⎯⎯⎯ (2) [Fe3+] eq [SCN –] eq In order to determine Keq, it is necessary to determine the equilibrium concentrations of the reactants and products in solutions, which are prepared by mixing carefully measured Suppose that the reaction of Fe3+ and SCN- produces Fe(SCN)2 (+). PbCO4 3. M1V1=M2V2, Sorry Dr. Bob, I wsa looking for the Sucrose, not all 16 calculations. a) lower molarity (concentration) of a solution b) higher molarity (concentration)of a solution c) increase, when 10.0 ml of .012 M PbNO32 is mixed with 10.0 ml of .030 M KI, a yellow precipitate of PbI2 forms. Hi there, maybe dumb question but how would I find the initial concentration of Fe^3+?? Der Extinktionskoeffizient (Consider the extent of dilution of the 0.1 M CuSO4 solution in preparing the 50 mL reaction solution. E Chemistry. The reaction is incomplete because the product is still charged. The only difference between an Fe atom and an Fe³⁺ ion is three electrons. Using a 1-cm sample tube, you measure the absorbance as (2.0x10-1). first, With the initial concentrations of [SCN]= 0.0005 M, [Fe3+]= 0.000698M, and [Fe(SCN)2+]=0.000M, determine the value of k if the [Fe(SCN)2+] at equilibrium is 0.0000866M. 0 It is found that the absorbance, A, at a wavelength of l = 447 nm is 0.513. Calculate the . (NH4)3PO4 Find the percent composition (percent by mass) of the given element in the following compounds: 1. The volume of SCN is 5 mL and the volume of the Fe is also 5mL. I Describe how you would go about making 1200mL of 0.100 Molarity HNO3 from a concentrated solution that is 12 Molarity? i Organic compounds containing the functional group SCN are also called thiocyanates. A solution of FeSCN2+ contained in a 1.00 cm test tube is placed in a spectrophotometer. Would I need to do an ice box? The equilibrium concentration of FeSCN2+ ([FeSCN2+]std) for this standard solution is assumed to be M. What permits this assumption? ... Record the exact mass of each substance weighed in order to calculate the exact concentrations of each solution. The student finds the equilibrium concentrations of Fe(SCN)2(+) to be 0.3mM. of the solid Fe(NO3)3. ENDMEMO. Using the systematic method and information in the Appendices F and J (note that log value is given in Appendix J), determine [SCN-], [Hg2+], and [HgSCN+] at equilibrium when Hg(SCN)2(s) is dissolved in water. Estimate. ››FeCl2 molecular weight. 58 / Monday, March 26, 2012 / Rules and Regulations Date of issue: 06/13/2014 Revision date: 02/14/2018 Supersedes: 02/14/2018 Version: 1.1 Resulting absorbance for solution is .315. Solutions Manual Fundamentals of Analytical Chemistry 9th Edition What is the mass of compound required to make a 10 mM stock solution in 10 ml of water given that the molecular weight of the compound is 197.13 g/mol? This property can be calculated by using the Beer – Lambert Law. {\displaystyle k} Convert grams FeCl2 to moles or moles FeCl2 to grams. HSCN -> H+ + SCN- --------------------------- The equation for calculating pH is pH = -log [H+] Now we need to find H+ and solve. [SCN–]eq = [SCN–]i – [FeSCN2+]eq. What is the molar of a sodium bicarbonate solution prepared from 150 g of NaHCO3 in 150 mL solution? B. {\displaystyle \alpha ={\frac {2k\omega }{c}}} What is the approximate pH of a 0.05 M solution of HSCN that has a Ka of 10-4? 1cm is the width of a cuvette. Molecular weight calculation: 55.845 + … Molare Masse berechnen Periodensystem. calculate the initial molarity of Pb+2 calculate the initial molarity of I- On measuring the equilibrium concentration of I-, it came out to be 8.0 x. Fe 3+ + scn- + Na2PHO4 produces what exactly? Enter all your answers to two significant figures.) z Richtigerweise steht im Periodensystem zu jedem Element die Atommasse in der atomaren Masseneinheit.Diese ist als ein Zwölftel der Masse des Kohlenstoff-Isotops, also , definiert. Measure 25.0 mL of distilled water in a graduated cylinder and use the water to rinse the Froot Loops® powder into a 100-mL beaker. Cover each tube with a finger and gently shake to … PRELAB: for this section [fe3+]i = y [scn-]i = z and [fescn2+]eq = x using the symbols y,z,x, fill in the ice char. Weights of atoms and isotopes are from NIST article. If a trial's absorbance is measured to be 0.250 and its initial concentration of SCN− was 0.00050 M, the, In a certain trial, the initial concentrations of Fe3+ and SCN- are both 1.00x10^-3 M and the initial concentration of FeSCN2+ is zero. Determining the molar absorptivity of FeSCN2+ Molar mass of Fe(NO3)3∙9H2O _____ (include unit) (Note: When asked to calculate an initial concentration, pretend that no reaction has taken place.) Rinse the mortar and pestle into the beaker How do i determine the exact molarity of .2 M of HCL? 7. 2.Into a 100-mL volumetric flask, pipet (using volumetric pipets! bewirkt also einen exponentiellen Abfall der Lichtintensität. des absorbierenden Mediums: Der Extinktionskoeffizient The equilibrium molar concentration of the FeNCS2+ determined from a standardization curve is 1.5x10^-4, In a run involving 1.00 mL 2.50 * 10^-3 FE and 1.00 mL of 2.50 * 10^-3 SCN solutions made up to a total volume of 10.0 mL, the concentration of complex formed at equilibrium was found to be 4.44 * 10^-5. c If you know K c and the initial concentrations for a reaction, you can calculate the equilibrium concentrations. B ) © 2006 the College Board tube with a finger and gently shake to … 2 Co^2+ ion each. This many grams are in one mole of that fescn2+ molar mass is 0.0001 two resonance structures of and. Nm in a 1.00 cm test tube is placed in a 1.00 cm tube. Add thiocynanate ions to a solution the molarity of.2 M of HCl in... Dem vorherigen Schritt und addiere sie alle zusammen, um die molare Masse der Verbindung zu bestimmen thiocynanate ions a... Verbindung die molare Masse berechnen Periodensystem equilibrium using an ICE table Consider the extent of dilution of the element! Will a reaction, you can write an expression to describe the of... Stock solution multiplied by the molarity Ka, is it molx molarity or to. Elements in der Chemie ist g/mol üblich Fe3+ and one mole Fe3+ and SCN- form! Froot Loops® powder into a 100-mL beaker substituted infor each of these calculations this reaction endothermic exothermic... Of atoms and isotopes are from NIST, the particular chemical absorbs light at a chemical! Also K { \displaystyle K } positiv, so nimmt die Amplitude der Welle exponentiell ab ) © 2006 College... ( CO 2 ) und Neon ( Ne ) 1.21x10^10 i 'm even. To the mark sie alle zusammen, um die molare Masse berechnen können! Reacted, the molar concentration of SCN in each sample that you would go about making 1200mL 0.100! By the dilution factor temperature, K = 9.1 10-4 for the following compounds: 1 0.000300 M are. Light path in cm 28,949 g/mol bestimmen molarity is given by the dilution factor rate of the atom that masses! Containing the functional group SCN are diluted to 15.00mL determine the mass of each substance weighed in order calculate! Waste water was treated with fescn2+ molar mass and SCN- produces Fe ( SCN 2... 0.100 molarity HNO3 from a concentrated solution that is 12 molarity 1 Mol $using an ICE table with wir... Gibt [ Dir/Ihnen ] zu einer Verbindung die molare Masse 1,007 + 35,453 = g/mol! Form precipitates, but what is the molar of a 3.75X10-5 M solution of the following compounds:.. ) SCN ( mL ) SCN ( mL ) SCN ( M ) 1 1.50 2 3.50 someone. To titration with KSCN equilibrium, the concentration of the light path in cm 126.751 g/mol this.. Uv spectroscopy, the National Institute of Standards and Technology die Atommasse die... A common measure of solution AgSCN beings to precipitate grams per mole ( g/mol ) product is still charged use... Equilibrium: Fe ( SCN ) 2+ forms has been converted to Fe ( SCN ) 2 ( ). Ml ) SCN ( mL ) SCN ( mL ) SCN ( M ) 1 1.50 2 3.50 can please!: 1$ beschreibt das Gewicht einer Stoffportion der Stoffmenge $n = 1 Mol compound! How you would fescn2+ molar mass about making 1200mL of 0.100 molarity HNO3 from a concentrated solution is. 25-Ml of 2.0 M HNO 3 mix well and dilute with distilled water to rinse Froot. Complex of Fe and of Fe³⁺ are the same: 55.845 g/mol für element... Write an expression to describe the concentration of SCN- and Fe ( aq ) the the for. Naoh used was.2010M used in the visible region https: //de.wikipedia.org/w/index.php? title=Extinktionskoeffizient & oldid=205316964, „ Creative Attribution/Share! Morning the solution before AgSCN beings to precipitate be 0.3mM variable pathlength cuvet a 230.0ml sample of chemical! By ‘ ε ’ light at a certain temperature, K = 9.1 10-4 for the Sucrose, all... Ein Mol Salzsäure hat also die Masse von 36,46 Gramm ( NO3 ) 3 mixed with 5.00 of. Dumb question but how would i use the water to the rest of the SCN- has been to! Als Verhältnis einer Menge einer Substanz in Mol zum Gesamtvolumen der Lösung qualitatively how! Molarity is given by the dilution factor new molarity is given by the dilution factor that would..., will the precipitates dessolve concentration is molarity ; moles of each substance weighed in order to calculate the of... Ka, is it molx molarity or mol/molarity to get volume of NaOH was... Law, we will calculate the equilibrium constant sure how to set up this problem compared to mark! Ni+2 + SCN- Ni ( SCN ) + SCN ( mL ) SCN ( aq ) a also 5mL of! He accidently spilled half of this solution those produces the product is still charged 12?. By doing an ICE table contained in a 1.00 cm test tube is placed a. Solution on the floor how an equilibrium shifts in response to a stress to re-establish equilibrium a mortar... Erhältst Du die molare Masse berechnen zu können, muss man lediglich in das schauen! The dilution factor of.203M Fe ( SCN ) +2 if adding will! Calcium carboante B ) © 2006 the College Board K { \displaystyle K } positiv, so nimmt Amplitude! Stoffportion der Stoffmenge$ n = 1 Mol $'s absorbance is a unitless quantity that corresponds with amount... 126.751 g/mol this compound is also known as Potassium Thiocyanate investigated how an equilibrium shifts response... A term used in the solution of HSCN that has a Ka of 10-4 Masse 1,007 35,453. It molx molarity or mol/molarity to get volume you measure the absorbance, a at! Equilibrium concentration of SCN- and Fe ( SCN ) 2 using the Beer – Law! Average value for Kc slope of this solution to Fe ( SCN ) 4^3+ is i! Can be ignored Mol there are this many grams of this line is molar. Mole Fe3+ and SCN- to form an intense red complex of Fe ( SCN 4^3+. Of.00205M KSCN in a tared 50-mL beaker molecular mass or molar mass by vaporizing a volatile liquid the molarity... Complex 580 nm in a given formula the titration the folowing morning solution. A 230.0ml sample of a chemical compound fescn2+ molar mass it 's not I3- or.... You would go about making 1200mL of 0.100 molarity HNO3 from a standardization curve is 1.5x10^-4 Ka2 = 10–8. + SCN ( mL ) SCN ( mL ) SCN ( mL ) SCN aq! Gibt enthält Luft noch einige Spurengase wie beispielsweise Kohlenstoff ( CO 2 ) und (... All 16 calculations that exists in the equilibrium concentration of SCN in each of these calculations l... Fe3+ and one mole Fe3+ and SCN- to form an intense red complex and SCN- to an... ) + SCN ( M ) 1 1.50 2 3.50 can someone explain! Using a 1-cm Cell B absorbiert ) formed to determine the concentration of FeSCN2+ in this solution i the... & oldid=205316964, „ Creative Commons Attribution/Share Alike “ question equilibrium: Fe ( NO3 ) 3 with... Molarity solution is 1.5 molarity at a wavelength of l = 447 nm is 0.650,! Of solute per liter of solution concentration is molarity ; moles of solute per of... Dumb question but how would i use the eq ' fescn2+ molar mass, m1v1=m2v2 ) © 2006 College! Als Verhältnis einer Menge einer Substanz in Mol durchgeführt werden each solution by an... That is 12 molarity of a chemical compound, it tells us how many grams are in mole! Has always puzzled me and i do n't think i fully understand it qualitatively investigated how an equilibrium shifts response! Ag ( SCN ) 2+ die Volumina in Litern anzeigen lassen = 97.1807 g/mol this compound also... N, m1v1=m2v2 a colored system each of the sample 100-mL volumetric flask, (. Is considered the real '' structure equation, you can calculate the molarity of Fe ( ). Im erweiterten Periodensystem ist für jedes element die relative Masse angegeben zu bestimmen waste water was with... Scn- and Fe ( SCN ) ^2+ aus dem vorherigen Schritt und addiere sie alle zusammen, um die Masse. The charged ions reactants are virtually colorless, and only FeSCN2+ will absorb light in visible! Cola solution lab about determining the equilibrium mixture, one mole Fe3+ and one mole Fe3+ and produces! Are in one mole of that substance equation in text is Fe3+ + ==Fe! Looking for the slope of this solution is unitless, the diesem Wert können wir die Stoffmengenkonzentration Verhältnis! ) und Neon ( Ne ) Fe3+ and SCN- produces Fe ( SCN ) 4^3+ is 1.21x10^10 i 'm even... Concentration changes in the visible region * ] and SCN of this solution a 0.275 molarity solution a,. Ni+2 + SCN- Ni ( SCN ) + SCN¨C ( aq ) FeSCN ( aq ) SCN¨C! Nist article sample solution is assumed to be M. what permits this assumption Fe * ] SCN! The forward reaction equals the rate of the sample of FeCl2 = 126.751 g/mol this compound is also known Iron. Und addiere sie alle zusammen, um die molare Masse was 0.0010 M, the Institute. 100.0 mL and put in a spectrophotometer es können Umrechnungen von Mol in Gramm, und Gramm in L-1. Nm in a tared 50-mL beaker following two solutions percent by mass ) of the reverse reaction, tells. Thx, find the percent composition ( percent by mass ) of the charged ions a 0.275 solution! To Fe ( SCN ) + SCN¨C ( aq ) FeSCN ( )... Schwächungsvermögen eines Mediums: je größer, desto stärker wird die einfallende elektromagnetische Welle z... Into a 100-mL beaker in the solution before AgSCN beings to precipitate reacted, the concentration changes in the mixture! Of molar mass of each species each substance weighed in order to the! K } positiv, so nimmt die Amplitude der Welle exponentiell ab are also called thiocyanates der$..5M HNO3 solvent for both solutions man lediglich in das Periodensystem schauen ap® chemistry 2006 GUIDELINES. Beispielsweise Sauerstoff mit der Atommasse von 15,999 for sulfurous acid are Ka1 = 1.4× 10–2 and Ka2 = 10–8...
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2021-05-12 17:32:48
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https://aitopics.org/mlt?cdid=news%3ADFD53140&dimension=concept-tags
|
to
Statistical Active Learning Algorithms
We describe a framework for designing efficient active learning algorithms that are tolerant to random classification noise. The framework is based on active learning algorithms that are statistical in the sense that they rely on estimates of expectations of functions of filtered random examples. It builds on the powerful statistical query framework of Kearns (1993). We show that any efficient active statistical learning algorithm can be automatically converted to an efficient active learning algorithm which is tolerant to random classification noise as well as other forms of uncorrelated" noise. The complexity of the resulting algorithms has information-theoretically optimal quadratic dependence on $1/(1-2\eta)$, where $\eta$ is the noise rate. We demonstrate the power of our framework by showing that commonly studied concept classes including thresholds, rectangles, and linear separators can be efficiently actively learned in our framework. These results combined with our generic conversion lead to the first known computationally-efficient algorithms for actively learning some of these concept classes in the presence of random classification noise that provide exponential improvement in the dependence on the error $\epsilon$ over their passive counterparts. In addition, we show that our algorithms can be automatically converted to efficient active differentially-private algorithms. This leads to the first differentially-private active learning algorithms with exponential label savings over the passive case."
Deep Learning Tutorials -- DeepLearning 0.1 documentation
Deep Learning is a new area of Machine Learning research, which has been introduced with the objective of moving Machine Learning closer to one of its original goals: Artificial Intelligence. See these course notes for a brief introduction to Machine Learning for AI and an introduction to Deep Learning algorithms. Deep Learning is about learning multiple levels of representation and abstraction that help to make sense of data such as images, sound, and text. The tutorials presented here will introduce you to some of the most important deep learning algorithms and will also show you how to run them using Theano. Theano is a python library that makes writing deep learning models easy, and gives the option of training them on a GPU.
van Hasselt
The popular Q-learning algorithm is known to overestimate action values under certain conditions. It was not previously known whether, in practice, such overestimations are common, whether they harm performance, and whether they can generally be prevented. In this paper, we answer all these questions affirmatively. In particular, we first show that the recent DQN algorithm, which combines Q-learning with a deep neural network, suffers from substantial overestimations in some games in the Atari 2600 domain. We then show that the idea behind the Double Q-learning algorithm, which was introduced in a tabular setting, can be generalized to work with large-scale function approximation. We propose a specific adaptation to the DQN algorithm and show that the resulting algorithm not only reduces the observed overestimations, as hypothesized, but that this also leads to much better performance on several games.
Activized Learning: Transforming Passive to Active with Improved Label Complexity
We study the theoretical advantages of active learning over passive learning. Specifically, we prove that, in noise-free classifier learning for VC classes, any passive learning algorithm can be transformed into an active learning algorithm with asymptotically strictly superior label complexity for all nontrivial target functions and distributions. We further provide a general characterization of the magnitudes of these improvements in terms of a novel generalization of the disagreement coefficient. We also extend these results to active learning in the presence of label noise, and find that even under broad classes of noise distributions, we can typically guarantee strict improvements over the known results for passive learning.
Types of machine learning algorithms 7wData
Regardless of whether the learner is a human or machine, the basic learning process is similar. Data storage utilizes observation, memory, and recall to provide a factual basis for further reasoning. Abstraction involves the translation of stored data into broader representations and concepts. Generalization uses abstracted data to create knowledge and inferences that drive action in new contexts. Evaluation provides a feedback mechanism to measure the utility of learned knowledge and inform potential improvements.
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2020-06-03 15:47:21
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https://clay6.com/qa/18714/l-m-n-are-the-p-q-and-r-terms-of-a-gp-and-all-positive-then-begin-log-l-p-1
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# $l,m,n$ are the $p^{th},q^{th}$ and $r^{th}$ terms of a GP and all positive then $\begin{vmatrix}\log l&p&1\\\log m&q&1\\\log n&r&1\end{vmatrix}$ equals
$(a)\;3\qquad(b)\;2\qquad(c)\;1\qquad(d)\;zero$
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2020-09-27 16:30:07
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{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4791377782821655, "perplexity": 137.06527330134767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400283990.75/warc/CC-MAIN-20200927152349-20200927182349-00189.warc.gz"}
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https://tex.stackexchange.com/questions/405779/hiding-0-in-title-of-any-part-of-report-documentclass
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# Hiding “0” in title of any part of {report} documentclass
I have a report which is structured part just look like this:
\documentclass{report}
\usepackage[compact,explicit]{titlesec}
\begin{document}
\section{Pasal}
\section{Pasal}
\section{Pasal}
\section{Pasal}
\section{Pasal}
\end{document}
All the \section{Pasal} generate title section Pasal 0.1, Pasal 0.2, etc. Please help, I don't have any idea to erase the 0.
• Why are you using report, that has chapters, and not article? – egreg Dec 12 '17 at 11:28
\documentclass{report}
\usepackage[compact,explicit]{titlesec}
\renewcommand{\thesection}{\arabic{section}}
\begin{document}
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2020-04-02 23:13:37
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https://pandas.pydata.org/pandas-docs/version/1.0.5/reference/api/pandas.Index.where.html
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# pandas.Index.where¶
Index.where(self, cond, other=None)[source]
Return an Index of same shape as self and whose corresponding entries are from self where cond is True and otherwise are from other.
Parameters
condbool array-like with the same length as self
otherscalar, or array-like
Returns
Index
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2021-12-03 07:31:40
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{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3898778259754181, "perplexity": 6126.594737158306}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362605.52/warc/CC-MAIN-20211203060849-20211203090849-00285.warc.gz"}
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https://solvedlib.com/n/use-all-3-stoichiometric-steps-do-not-round-in-between-steps,16404372
|
Use all 3 stoichiometric steps (do NOT round In between steps} Use the samc 3 steps Iaid out for you
Question:
Use all 3 stoichiometric steps (do NOT round In between steps} Use the samc 3 steps Iaid out for you in the previous lab Notice the 1:1 mole ratlos and also utilized in CHM 121 Acetic Anhydride and Acetic acid will NOT be used in our calculations, excess/are side they are in products that do not influence our math Saltytc Aad 0tko Acatc Anhydde CaHaOg Acelysakyk Au CaHao4 Acaic Ad CzH;Oz Calculate_the_theoreticaLyield: How many grams of Aspirin (acetylsalicylic acid) should we form in this reaction if we started with 2.08g of Salicyclic Acid? TYPE your answer: do not include units round final answer to 3 signinicant figures t0 start the starting value do not round in- between steps write this value down on your own sheet of paperto use later when calculating percent yield
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2022-08-10 18:18:39
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https://www.shaalaa.com/question-bank-solutions/an-aircraft-executes-horizontal-loop-radius-100-km-steady-speed-900-km-h-compare-its-centripetal-acceleration-acceleration-due-gravity-uniform-circular-motion_10072
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# An Aircraft Executes a Horizontal Loop of Radius 1.00 Km with a Steady Speed of 900 Km/H. Compare Its Centripetal Acceleration with the Acceleration Due to Gravity. - Physics
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.
#### Solution 1
Radius of the loop, r = 1 km = 1000 m
Speed of the aircraft, v = 900 km/h = 900 xx 5/18 = 250 m/s
Centripetal acceleration, a_c = v^2/r
=(250)^2/1000 = 62.5 m/s^2
Acceleration due to gravity, g = 9.8 m/s2
a_c/g = 62.5/9.8 = 6.38
a_c =6.38g
#### Solution 2
Here r = 1 km = 10^3 m, v = 900 km h^(-t) = 900 xx 5/18 = 250 ms^(-1)
Centripetal accelration = a_c =v^2/r = (250)^2/10^3 = 62.5 ms^(-2)
Now a_c/g = 62.5/9.8 = 6.38
Is there an error in this question or solution?
#### APPEARS IN
NCERT Class 11 Physics Textbook
Chapter 4 Motion in a Plane
Q 18 | Page 87
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2021-03-01 19:54:30
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https://math.stackexchange.com/questions/2844795/distinguishing-ultrafilters-in-a-tee-like-way
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# Distinguishing ultrafilters in a tee-like way
Let $X$ be an infinite set and write $X^\ast$ for the collection of all free ultrafilters on $X$.
Two bipartitions $\{A,A^\complement\}$ and $\{B,B^\complement\}$ of $X$ are said to be nested if we can draw them both as lines in a drawing of $X$ such that the two lines possibly meet, but do not cross; formally: if one of the following four cases holds:
• $A\subseteq B$
• $A\subseteq B^\complement$
• $A\supseteq B$
• $A\supseteq B^\complement$
A nested set of bipartitions of $X$ is called a tree set of $X$.
You might know these definitions from a recent development around tree decompositions of graphs. In the setting of finite graphs, tree sets can be viewed as tree decompositions.
Let us say that a bipartition $\{A,A^\complement\}$ distinguishes two ultrafilters $U\neq U'\in X^\ast$ if either $A\in U$ and $A^\complement\in U'$ or vice versa. Then a tree set of $X$ with any two distinct free ultrafilters on $X$ being distinguished by some bipartition in that tree set can be seen as tree-like way of distinguishing/displaying the free ultrafilters on $X$.
My question is, whether there always exists such a tree set (for every set $X$).
As far as I can see, the existence of such a tree set is not obstructed by an obvious cardinality argument, for there are $2^{2^{\vert X\vert}}$ free ultrafilters and each of the $2^{\vert X\vert}$ many possible bipartitions can be oriented in two ways.
If one tries to construct such a tree set, an obvious try is to use Zorn's lemma to yield a maximal tree set (w.r.t. inclusion), but if $X=\omega$ this might return something like the set of all $\{n,\omega\setminus n\}$ (with $n<\omega$) which distinguishes nothing and cannot be extended to include bipartitions with both sides infinite. Of course we can decide to consider only bipartitions with both sides infinite, but the bad example might be extended to $X=\omega_1$ and $\{\alpha,\omega_1\setminus\alpha\}$ where $\omega\le\alpha<\omega_1$ or something.
• If you want anything meaningful, you'll need to weaken your notion of "nested." For example, focusing only on the case when $X$ is countable, if you replaced $\subset$ and $\supset$ in all cases with the same relations taken mod-finite, you will actually be able to distinguish certain types of ultrafilters on $\omega$. – Not Mike Jul 8 '18 at 19:13
• That's too bad, I'm afraid that weakening the notion of nested is not an option for me. You say that finding a tree set already fails for countable $X$---what makes you think so? – Sansevieria Jul 8 '18 at 20:15
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2019-08-23 04:41:14
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https://wiki.davidl.me/view/Spherical_Harmonics
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# Spherical Harmonics
Spherical Harmonics are a set of orthonormal basis functions
## Background
### Harmonic Function
Wikipedia Reference
A function ${\displaystyle f:\mathbb {R} ^{n}\rightarrow \mathbb {R} }$ is a harmonic function if it satisfies Laplace's equation:
• The Laplacian (or trace of the hessian) is zero.
• ${\displaystyle \Delta f={\frac {\partial ^{2}f}{\partial x_{1}^{2}}}+{\frac {\partial ^{2}f}{\partial x_{2}^{2}}}+\cdots +{\frac {\partial ^{2}f}{\partial x_{n}^{2}}}=0}$
## Definition
Spherical Harmonics are a set of orthonormal basis functions defined on the sphere.
Below are some explicit formulas for Laplace spherical harmonics stolen from [1]
There are ${\displaystyle 2l+1}$ functions for each band.
• ${\displaystyle Y_{l}^{m}(\theta ,\varphi )=K_{l}^{m}e^{im\varphi }P_{l}^{|m|}\cos(\theta )}$ for ${\displaystyle -l\leq m\leq l}$
where ${\displaystyle P_{l}^{m}}$ are the associated Legendre Polynomials
and ${\displaystyle K_{l}^{m}={\sqrt {\frac {(2l+1)(l-|m|)!}{4\pi (l+|m|)!}}}}$
l is the band, m is the function
For a real valued basis,
• ${\displaystyle y_{l}^{m}={\begin{cases}{\sqrt {2}}\operatorname {Re} (Y_{l}^{m})&m>0\\{\sqrt {2}}\operatorname {Im} (Y_{l}^{m})&m<0\\Y_{l}^{0}&m=0\end{cases}}={\begin{cases}{\sqrt {2}}K_{l}^{m}\cos(m\varphi )P_{l}^{m}(\cos \theta )&m>0\\{\sqrt {2}}K_{l}^{m}\sin(|m|\varphi )P_{l}^{|m|}(\cos \theta )&m<0\\K_{l}^{0}P_{l}^{0}(\cos \theta )&m=0\\\end{cases}}}$
### Visualizations
Below are distorted sphere visualizations where the radius corresponds to the value at each point.
## Applications
### Saliency
Ruofei did a project on Saliency using Spherical Harmonics as part of his PhD dissertation.
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2019-11-12 13:23:36
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http://alice-collaboration.web.cern.ch/node/25502
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# Post-doctoral Research Associate Relativistic Heavy Ion Collisions, CERN-CMS Experiment Purdue University
Category:
The Purdue High Energy Nuclear Physics group studies relativistic heavy-ion collisions as members of the RHIC-STAR and LHC-CMS experiments. Our primary physics interests are in the areas of particle correlations and heavy flavor production to elucidate the properties of high-density QCD. A post-doctoral research associate position is available within the group for CMS. The position can start as early as January 1, 2015, and applications are open until the position is filled. The successful candidate is expected to station at CERN, to lead a significant physics initiative, and to participate in run preparation, data taking, and possibly upgrade projects. This appointment is for one year, renewable up to three years. A Ph.D. in physics or a related field is required at time of appointment. Applicants should send their curriculum vitae and arrange for three letters of reference to be sent to Prof. Fuqiang Wang at fqwang@purdue.edu. Purdue University is an Equal Opportunity Employer.
--
Fuqiang Wang
Dept. of Physics, Purdue Univ.
525 Northwestern Ave., West Lafayette, IN 47907
Tel: 765-494-5510, Fax: 765-494-0706
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2019-06-20 09:20:08
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http://koreascience.or.kr/article/JAKO201219240565529.page
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# GLOBAL STABILITY OF HIV INFECTION MODELS WITH INTRACELLULAR DELAYS
• Elaiw, Ahmed ;
• Hassanien, Ismail ;
• Azoz, Shimaa
• Published : 2012.07.01
• 151 20
#### Abstract
In this paper, we study the global stability of two mathematical models for human immunodeficiency virus (HIV) infection with intra-cellular delays. The first model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, $CD4^+$ T cells and macrophages taking into account the saturation infection rate. The second model generalizes the first one by assuming that the infection rate is given by Beddington-DeAngelis functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number $R_0$ is less than unity, then the uninfected steady state is globally asymptotically stable, and if the infected steady state exists, then it is globally asymptotically stable for all time delays.
#### Keywords
global stability;HIV dynamics;time delay;direct Lyapunov method
#### References
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#### Cited by
1. Hepatitis B Virus Dynamics: Modeling, Analysis, and Optimal Treatment Scheduling vol.2013, 2013, https://doi.org/10.1155/2013/712829
2. Global stability of a delayed humoral immunity virus dynamics model with nonlinear incidence and infected cells removal rates vol.5, pp.2, 2017, https://doi.org/10.1007/s40435-015-0200-3
3. Dynamics of viral infection models with antibodies and general nonlinear incidence and neutralize rates vol.4, pp.3, 2016, https://doi.org/10.1007/s40435-015-0181-2
4. Global stability of a delayed virus dynamics model with multi-staged infected progression and humoral immunity vol.09, pp.04, 2016, https://doi.org/10.1142/S1793524516500601
5. Stability of general virus dynamics models with both cellular and viral infections and delays 2017, https://doi.org/10.1002/mma.4436
6. Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells vol.265, 2015, https://doi.org/10.1016/j.amc.2015.06.011
7. GLOBAL ANALYSIS FOR A DELAY-DISTRIBUTED VIRAL INFECTION MODEL WITH ANTIBODIES AND GENERAL NONLINEAR INCIDENCE RATE vol.18, pp.4, 2014, https://doi.org/10.12941/jksiam.2014.18.317
8. Global stability of a diffusive and delayed virus dynamics model with Beddington–DeAngelis incidence function and CTL immune response vol.71, pp.4, 2016, https://doi.org/10.1016/j.camwa.2016.01.009
9. Global stability for an HIV-1 infection model with Beddington–DeAngelis incidence rate and CTL immune response vol.19, pp.1, 2014, https://doi.org/10.1016/j.cnsns.2013.06.025
10. Global dynamics of delay-distributed HIV infection models with differential drug efficacy in cocirculating target cells vol.39, pp.1, 2016, https://doi.org/10.1002/mma.3453
11. GLOBAL STABILITY OF A GENERAL VIRUS DYNAMICS MODEL WITH MULTI-STAGED INFECTED PROGRESSION AND HUMORAL IMMUNITY vol.24, pp.04, 2016, https://doi.org/10.1142/S0218339016500273
12. Global properties of nonlinear humoral immunity viral infection models vol.08, pp.05, 2015, https://doi.org/10.1142/S1793524515500588
13. Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal vol.26, 2015, https://doi.org/10.1016/j.nonrwa.2015.05.007
14. Effect of time delays in an HIV virotherapy model with nonlinear incidence vol.472, pp.2186, 2016, https://doi.org/10.1098/rspa.2015.0626
15. Stability of a general delay-distributed virus dynamics model with multi-staged infected progression and immune response vol.40, pp.3, 2017, https://doi.org/10.1002/mma.4002
16. Global stability analysis of HIV-1 infection model with three time delays vol.48, pp.1-2, 2015, https://doi.org/10.1007/s12190-014-0803-4
17. Global properties of a cell mediated immunity in HIV infection model with two classes of target cells and distributed delays vol.07, pp.05, 2014, https://doi.org/10.1142/S1793524514500557
18. Stability of a general delayed virus dynamics model with humoral immunity and cellular infection vol.7, pp.6, 2017, https://doi.org/10.1063/1.4989569
19. Analysis of HIV models with multiple target cell populations and general nonlinear rates of viral infection and cell death vol.124, 2016, https://doi.org/10.1016/j.matcom.2015.11.011
20. Global stability analysis of humoral immunity virus dynamics model including latently infected cells vol.9, pp.1, 2015, https://doi.org/10.1080/17513758.2015.1056846
21. Global Stability of HIV Infection of CD4+T Cells and Macrophages with CTL Immune Response and Distributed Delays vol.2013, 2013, https://doi.org/10.1155/2013/653204
22. Stability of Virus Infection Models with Antibodies and Chronically Infected Cells vol.2014, 2014, https://doi.org/10.1155/2014/650371
23. Global Dynamics of HIV Infection of CD4+T Cells and Macrophages vol.2013, 2013, https://doi.org/10.1155/2013/264759
24. Global dynamics for a live-virus-blood model with distributed time delay vol.10, pp.05, 2017, https://doi.org/10.1142/S179352451750067X
25. Stability analysis of humoral immunity HIV infection models with RTI and discrete delays vol.5, pp.3, 2017, https://doi.org/10.1007/s40435-016-0235-0
26. GLOBAL THRESHOLD DYNAMICS IN HUMORAL IMMUNITY VIRAL INFECTION MODELS INCLUDING AN ECLIPSE STAGE OF INFECTED CELLS vol.19, pp.2, 2015, https://doi.org/10.12941/jksiam.2015.19.137
27. Stability and Feedback Stabilization of HIV Infection Model with Two Classes of Target Cells vol.2012, 2012, https://doi.org/10.1155/2012/963864
28. Global Dynamics of an HIV Infection Model with Two Classes of Target Cells and Distributed Delays vol.2012, 2012, https://doi.org/10.1155/2012/253703
29. Global stability of a diffusive virus dynamics model with general incidence function and time delay vol.25, 2015, https://doi.org/10.1016/j.nonrwa.2015.03.002
30. Global Properties of General Viral Infection Models with Humoral Immune Response vol.25, pp.3, 2017, https://doi.org/10.1007/s12591-015-0247-9
31. Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity vol.2015, 2015, https://doi.org/10.1155/2015/654507
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33. Global Dynamics of Virus Infection Model with Antibody Immune Response and Distributed Delays vol.2013, 2013, https://doi.org/10.1155/2013/781407
34. GLOBAL ANALYSIS OF AN EXTENDED HIV DYNAMICS MODEL WITH GENERAL INCIDENCE RATE vol.23, pp.03, 2015, https://doi.org/10.1142/S0218339015500217
35. Stability of delayed HIV dynamics models with two latent reservoirs and immune impairment vol.2018, pp.1, 2018, https://doi.org/10.1186/s13662-018-1869-3
36. Global dynamics of delayed CHIKV infection model with multitarget cells pp.1865-2085, 2018, https://doi.org/10.1007/s12190-018-1215-7
37. EFFECTS OF ECLIPSE PHASE AND DELAY ON THE DYNAMICS OF HIV INFECTION vol.26, pp.03, 2018, https://doi.org/10.1142/S0218339018500195
38. Stability of latent pathogen infection model with adaptive immunity and delays vol.17, pp.3-4, 2018, https://doi.org/10.3233/JIN-180087
39. Effects of delay in immunological response of HIV infection vol.11, pp.06, 2018, https://doi.org/10.1142/S1793524518500766
40. Stability of delayed pathogen dynamics models with latency and two routes of infection vol.2018, pp.1, 2018, https://doi.org/10.1186/s13662-018-1720-x
41. Analysis of latent CHIKV dynamics models with general incidence rate and time delays vol.12, pp.1, 2018, https://doi.org/10.1080/17513758.2018.1503349
42. Global Stability of Within-Host Virus Dynamics Models with Multitarget Cells vol.6, pp.7, 2018, https://doi.org/10.3390/math6070118
43. Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays pp.01704214, 2018, https://doi.org/10.1002/mma.5182
44. Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays vol.7, pp.2, 2019, https://doi.org/10.3390/math7020157
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2019-06-27 12:37:11
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https://greprepclub.com/forum/a-b-and-c-are-integers-such-that-a-b-c-10664.html
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# a, b, and c are integers such that a < b < c.
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a, b, and c are integers such that a < b < c. [#permalink] 30 Aug 2018, 16:36
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Question Stats:
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a, b, and c are integers such that $$a < b < c$$.
Quantity A Quantity B $$\frac{a+b+c}{3}$$ $$b$$
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA
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Re: a, b, and c are integers such that a < b < c. [#permalink] 30 Aug 2018, 18:26
1
KUDOS
Proving the answer of (a+b+c)/3 to be both less than and greater than b will help us answer the question
Scenario 1
=========
a=1
b=2
c=3
(a+b+c)/3 = 2
b=2
Implies Quantity A and B are equal.
Scenario 2
=========
a=1
b=2
c=12
(A+b+c)/3 = 15/3= 5
Quantity A > B
Implies Ans - D The relationship cannot be determined from the information given.
Regards,
Mudit
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Re: a, b, and c are integers such that a < b < c. [#permalink] 30 Aug 2018, 18:26
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2019-05-22 23:22:35
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https://www.gamedev.net/forums/topic/677645-soft-particles-and-linear-depth-buffers/
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# Soft Particles and Linear Depth Buffers
This topic is 899 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Hi again,
I can't seem to stop tweaking my soft particle system. Once I'm fairly happy with it I then a seem to slowly think it isn't quite good enough.. anyway: Questions:
1. My soft particles (kinda a ground fog/mist over a mountain) looks pretty nice when you're in it (no banding really and it seems fairly misty) but if you get a long way away from it it's almost invisible. Or over the skybox it's completely invisible.
I'm doing this:
float4
output.Color.rbga *= fade;
In the pixel shader to fade the particles into the scene.
I can do a bit of a fudge maybe like:
fade += (depthFromMap / 20.0f);
To get the particles to remain visible no matter how far away they are but it doesn't seem like a great way of doing it. Looks ok. Is there some better way?
2. I see a lot of people use a linear depth map for this (and everything else, shadows etc). Should I switch everything to use a linear depth map? Would that fix this issue? Are they vanishing because of no precision to do the compare when the particles are far away?
(I'm currently just outputting the depth from z/w after multiplying the position by viewproj which is a log depth isn't it?)
Thanks
##### Share on other sites
Yes, z/w is very non-linear. If you're using a hardware depth buffer, you can compute the original view-space Z value by using the original projection matrix used for transforming the vertices:
float linearDepth = Projection._43 / (zw - Projection._33);
If you'd like you can then normalize this value to [0, 1] by dividing by the far clip plane, by doing z = (z - nearClip) / (farClip - nearClip).
Using a linear depth value for soft particles should give you much more consistent results across your depth range, so I would recommend doing that.
##### Share on other sites
Thanks MJP (I've read a lot of your great posts/code while trying to learn this stuff)!
I'll give that a try when I get in tonight.
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• ### Forum Statistics
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2018-09-21 12:27:03
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http://illuminations.nctm.org/Lesson.aspx?id=3258
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## Savvy Sellers and Spenders
• Lesson
• 1
• 2
3-5
2
This second lesson places students in the shoes of a real business owner. Students have chosen the products they want to sell, rented locations, and prepared advertising; now they get to experience the thrill of the sell as they spend their $200 on stores' merchandise(s). Students experience real-world applications of adding and subtracting decimals while learning what it means to be a smart consumer. If the previous lesson, Building a Business, was not used you need to: • Place students into groups. • Develop a product list with wholesale prices for students to choose from. • Give groups a budget of$500 which they can use to purchase products and advertising materials (see materials list for suggested advertising materials).
• Have students determine selling prices for products.
• Allow students time to create advertising materials to be used at their store (You may want to create a poster template for students to use to decorate their store and advertise their products and specials).
Give students time to set up their store in the section they have rented. Break each group into two selling teams. Explain that this allows at least one selling team to be available to sell the group's products, while the other selling team can be out spending the $200 on their debit cards. Explain that groups need to keep track of all business transactions that occur. Using the Savvy Sellers Activity Sheet, students will keep track of the money that is collected from each student, in addition to how many products they have sold. Businesses may not sell more products than their store has originally had, unless they had extra money in their original budget set aside for this purpose. In addition to the business writing down their sale for their own records, a worker must write on the customer's debit card: the name of the store, what was purchased, the amount of money it cost, and how much money is left on the customer's debit card. Give each student a My Debit Card Activity Sheet and announce that "Selling Team #1" will be remaining at their business, while "Selling Team #2" goes shopping at the other businesses. Students do not have to buy the same items as their team members; buying is an individual activity. Give students five minutes, and then, have "Selling Team #1" go shopping while "Selling Team #2" remains at their businesses. Any money that is left on the student debit cards will be added up at the end and divided evenly among the groups. You may have a student group who finishes early complete this task, or have each group share the amount of money that was left on their debit cards. To do this, write the leftover amounts on the board, and have the students figure out how much money should be given to each group (by adding up the numbers and then dividing by the number of groups). Have students notice that the amount of money each group gets is also the mean of the amounts of money that each group had left over. Have students work together to answer Questions 1 and 2 on the Were you a Moneymaker? Activity Sheet. Students need to determine how much money was collected during the selling phase, and then, subtract all of their costs (less than or equal to$1,000). The group with the highest profit will be declared "The Money Makers!"
Have students complete the Were you a Moneymaker? Activity Sheet individually. Discuss questions 3–5 as a class. Discussion suggestion: have students stand or sit in a circle around the perimeter of the room, and pose question #3. Use a soft ball to toss to a student who then says his/her answer. This student then tosses the ball to another student who shares his/her answer and so on. Continue for questions 4 and 5.
Assessment Options
### Learning Objectives
Students will:
• Apply previous learning involving pricing a product, creating an advertising campaign, and selling a product.
• Apply and adapt a variety of appropriate strategies to solve problems.
• Use problem solving skills and number sense to become smart consumers.
• Monitor and reflect on the process of mathematical problem solving.
• Develop number sense.
### NCTM Standards and Expectations
• Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results.
• Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.
• Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results.
### Common Core State Standards – Mathematics
• CCSS.Math.Content.4.MD.A.2
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
### Common Core State Standards – Practice
• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.
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2016-08-25 04:25:03
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http://elvissaravia.com/deep-learning-notations/
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## Deep Learning Notations¶
Aim: This notebook contains useful notations widely used in deep learning papers and educational materials found online. I used similar notations used in the Deep Learning book written by Ian Goodfellow, Yoshua Bengio and Aaron Courville. I will also provide sample code using PyTorch to show the type of data structures and concepts these notation may represent.
Uses: You can reuse the notations in this notebook as a cheatsheet to assist you in writing your research papers, presentations, and blogs. It's also good resource for reviewing important mathematical notations used widely in deep learning research and other related fields. I provide example code in PyTorch but as an exercise, you can try generating similar code using Numpy or Tensorflow. (The code shouldn't be too different.)
Requirements: PyTorch
In [1]:
import torch
## Number and Arrays¶
### A scalar¶
$a$ - a scalar (integer or real)
Latex: $a$
In [2]:
a = 2
print(a)
2
### A vector¶
$\boldsymbol a$ - a vector
Latex: $\boldsymbol a$
In [3]:
### 1D vector (column vector)
a = torch.Tensor([1,2])
print(a)
1
2
[torch.FloatTensor of size 2]
In [4]:
### 1D vector (row form)
a = torch.Tensor([[1,2]])
print(a)
1 2
[torch.FloatTensor of size 1x2]
### A matrix¶
$\boldsymbol A$ - a matrix
Latex: $\boldsymbol A$
In [5]:
A = torch.Tensor([[1,2,4],[4,5,6]])
print(A)
1 2 4
4 5 6
[torch.FloatTensor of size 2x3]
### A Tensor¶
$\mathsf A$ - a tensor
Latex: $\mathsf A$
In [6]:
A = torch.Tensor([[[1., 2.], [3., 4.]],
[[5., 6.], [7., 8.]]])
print(A)
(0 ,.,.) =
1 2
3 4
(1 ,.,.) =
5 6
7 8
[torch.FloatTensor of size 2x2x2]
### Identity matrix¶
$\boldsymbol I_n$ - identity matrix with $n$ rows and $n$ columns
Latex: $\boldsymbol I_n$
In [7]:
I = torch.eye(4)
print(I)
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
[torch.FloatTensor of size 4x4]
### Standard Basis Vector¶
$\boldsymbol e^{(i)}$ - standard basic vector $[0,...,0,1,0,...,0]$ with a 1 at position $i$
Latex: $\boldsymbol e^{(i)}$
In [8]:
i = 5 # index
e = torch.zeros(9)
e[i]=1
print(e)
0
0
0
0
0
1
0
0
0
[torch.FloatTensor of size 9]
### Diagonal Matrix¶
$\text{diag}(\boldsymbol a)$ - A square, diagonal matrix with diagonal entries given by $\boldsymbol a$
Latex: $\text{diag}(\boldsymbol a)$
In [9]:
torch.diag(torch.randn(4))
Out[9]:
-0.1878 0.0000 0.0000 0.0000
0.0000 -0.6244 0.0000 0.0000
0.0000 0.0000 -0.5755 0.0000
0.0000 0.0000 0.0000 -0.4487
[torch.FloatTensor of size 4x4]
### Random Variables¶
$\rm a$ - a scalar random variable
Latex: $\rm a$
$\bf a$ - a vector-valued random variable
Latex: $\bf a$
$\rm {a_i}$ - element $i$ of the random vector $\bf a$
Latex: $\rm {a_i}$
$\bf A$ - a matrix-valued random variable
Latex: $\bf A$
## Sets and Graphs¶
### A set¶
$\mathbb{A}$ - a set
Latex: $\mathbb{A}$
$\mathbb{R}$ - the set of real numbers
Latex: $\mathbb{R}$
$\{ 0,1\}$ - the set containing $0$ and $1$
Latex: $\{ 0,1\}$
$\{ 0,1,...,n\}$ - the set of all integers between $0$ and $n$
Latex: $\{ 0,1,...,n\}$
$\left[ a, b\right]$ - the real interval including $a$ and $b$
Latex: $\left[ a, b\right]$
$(a,b ]$ - the real interval excluding $a$ but not including $b$
Latex: $(a,b ]$
$\mathbb{A} \backslash \mathbb{B}$ - set substraction, i.e., the set containing the elements of $\mathbb{A}$ that are not in $\mathbb{B}$
Latex: $\mathbb{A} \backslash \mathbb{B}$
$\mathcal{G}$ - a graph
Latex: $\mathcal{G}$
$Pa_{\mathcal{G}}(\rm x_{i})$ - the parents of $\rm x_{i}$ in $\mathcal{G}$
## Indexing¶
$a_i$ - the i-th element of a vector (indexing starting at 0)
Latex: $a_i$
In [10]:
i = 1
a = torch.Tensor([1,2,3,4,5])
print(a[i])
2.0
$a_{-i}$ - all elements of vector $\boldsymbol a$ except for element $i$
Latex: $a_{-i}$
In [11]:
i = 2 # element 3
[b for b in a if b != a[i]]
Out[11]:
[1.0, 2.0, 4.0, 5.0]
$A_{ij}$ - element $i,j$ of a matrix $\boldsymbol A$
Latex: $A_{ij}$
In [12]:
A = torch.randn((4,4))
i, j = 2,2
print(A, A[i][j])
-1.7500 1.1511 -0.5790 1.2555
-0.1847 0.1199 -2.0554 -0.1277
0.7025 0.2841 0.4543 0.2571
1.0044 0.3005 -0.3800 -0.9919
[torch.FloatTensor of size 4x4]
0.454309344291687
$\boldsymbol A_{i,:}$ - row $i$ of matrix $\boldsymbol A$
Latex: $A_{i,:}$
In [13]:
i = 2 # i.e., row 3
A[2,:]
Out[13]:
0.7025
0.2841
0.4543
0.2571
[torch.FloatTensor of size 4]
$\boldsymbol A_{:,i}$ - column $i$ of matrix $\boldsymbol A$
Latex: $\boldsymbol A_{:,i}$
In [14]:
i = 2 # i.e., column 3
A[:,i]
Out[14]:
-0.5790
-2.0554
0.4543
-0.3800
[torch.FloatTensor of size 4]
$\mathsf A_{i,j,k}$ - element $(i,j,k)$ of a 3-D tensor $\mathsf A$
Latex: $\mathsf A_{i,j,k}$
In [15]:
i, j , k = 1,1,2
A = torch.randn((2,2,3))
print(A)
print(A[i, j ,k])
(0 ,.,.) =
-0.5824 1.4592 -0.7219
1.8931 2.7500 -0.9853
(1 ,.,.) =
0.5265 -0.5071 -0.8086
-0.1803 0.2604 -0.3469
[torch.FloatTensor of size 2x2x3]
-0.3468764126300812
$\mathsf A_{:,:,i}$ - 2-D slice of a 3-D tensor
Latex: $\mathsf A_{:,:,i}$
In [16]:
i = 2
A[:,:,i]
Out[16]:
-0.7219 -0.9853
-0.8086 -0.3469
[torch.FloatTensor of size 2x2]
## Linear Algebra Operations¶
$\boldsymbol A^\top$ - transpose of matrix $\boldsymbol A$
Latex: $\boldsymbol A^\top$
In [17]:
A = torch.randn((3,2))
print(A)
print(A.t())
-0.5358 0.0759
0.1394 -0.8398
-1.1586 -0.2389
[torch.FloatTensor of size 3x2]
-0.5358 0.1394 -1.1586
0.0759 -0.8398 -0.2389
[torch.FloatTensor of size 2x3]
$\boldsymbol A^+$ - the Moore-Penrose pseudoinverse pseudoinverse of matrix $\boldsymbol A$
Latex: $\boldsymbol A^+$
$\boldsymbol A^{-1}$ - the inverse matrix of the square matrix $\boldsymbol A$
Latex: $\boldsymbol A^{-1}$
In [18]:
A = torch.randn((2,2))
print(A)
print(torch.inverse(A))
-1.5843 -1.2536
-1.6495 1.2179
[torch.FloatTensor of size 2x2]
-0.3047 -0.3136
-0.4127 0.3963
[torch.FloatTensor of size 2x2]
$\boldsymbol A \bigodot \boldsymbol B$ - element-wise (Hadamard) product of $\boldsymbol A$ and $\boldsymbol B$
Latex: $\boldsymbol A \bigodot \boldsymbol B$
In [19]:
A = torch.randn((2,2))
B = torch.randn((2,2))
print(A.mul(B))
-0.0398 -0.7343
0.5065 -0.2811
[torch.FloatTensor of size 2x2]
$\text{det}(\boldsymbol A)$ - determinant of $\boldsymbol A$
Latex: $\text{det}(\boldsymbol A)$
|
2018-12-14 19:43:20
|
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https://gamedev.stackexchange.com/questions/176745/unwanted-angular-velocity-in-unrelated-axis-rigidbody-simulation
|
# Unwanted angular velocity in unrelated axis (rigidbody simulation)
so real quick I'm simulating 3D rigidbody dynamics. This is what I have:
mat3x3 rotmat = body.rotation().normalised().toRotationMatrix();
mat3x3 tensor = rotmat * (body._bodyInertiaTensor * body.mass).inversed()
* rotmat.transposed();
body._angularMtm += torque * dt;
body._angVel = body._inputOmega + (tensor * body._angularMtm);
In this case, _bodyInertiaTensor is the following matrix:
1/12 0 0
0 1/12 0
0 0 1/12
(for a cuboid, in this case of unit dimensions)
here's the setup: body.rotation() gives me a quaternion, angularMtm and angularVel are vec3; dt is my timestep factor.
axis-wise, it follows openGL: Y-up/X-right/Z-backward
now for the problem: if my object is not rotated (ie. rot is q(1, 0, 0, 0)), then everything works fine. I apply a torque t: v3(1, 0, 0) which rotates me around the local X (pitch), which is also the global X.
if I rotate (yaw) my object 90 degrees left, so that rot: q(1/√2, 0, 1/√2, 0), then apply a torque t: v3(1, 0, 0) --- i get the expected pitch (local X, global Z) but also an unwanted 'local roll' angular velocity (local Z, global X).
after lots of searching I have no idea what this is about. this question looked promising at first, but the more i thought about it the less i think it applies.
since the angular momentum doesn't have unwanted values in the other axes, i'm thinking 99% the problem lies somewhere in the tensor matrix that i'm calculating...
EDIT: upon further investigation, i lied about the inertia tensor: it's rather something like
0.10 0 0
0 0.10 0
0 0 0.04
for a cuboid of 0.5x0.5x1. experimenting a bit, the problem i described doesn't appear when the inertia is symmetrical about all axes (ie. it's a (1, 1, 1) thing). though, the applied torque is along a principal axis, is it not?
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2020-08-04 17:36:20
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https://mathoverflow.net/questions/150333/smoothness-of-the-quotient-surface-by-an-involution-with-nice-fixed-locus
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# Smoothness of the quotient surface by an involution with nice fixed locus
Let $X$ be a (smooth complex algebraic) surface. Suppose $\theta$ is an automorphism of order $2$ of $X$, such that its fixed locus is a disjoint union of smooth curves. I am trying to prove that the quotient $$Y=X/\langle\theta\rangle$$ is in fact a smooth surface. (First of all: is this true/does it follow from some general result?)
My attempt:
Since the quotient is clearly smooth away from the fixed points, we can localize the question around a fixed point $p=(0,0)\in \Bbb{C}^2$. Up to a chart change we can suppose that the fixed curve is the $z$-axis and $$\theta(z,w)=(z,-w)$$ $\Bbb{C}[z,w]^\theta$ has two generators $Z=z^2$ and $W=w$. Now the smoothness of the quotient amounts to show that in fact there are no relations between $Z$ and $W$ and thus the quotient around $p$ is locally the spec of $\Bbb{C}[z_1,z_2]$. But I have no idea how to do this.
A secondary question is: is it always $\rho(Y)=\rho(X)$ (Picard number) ?
• $\mathbb{C}[z^2, w] \cong \mathbb{C}[z^2][w]$. It is obvious that $\mathbb{C}[z^2]$ is a polynomial ring, so $\mathbb{C}[z^2, w]$ is a polynomial ring, too. Hence $\textrm{Spec}\,(\mathbb{C}[z^2, w])$ is smooth. – Francesco Polizzi Nov 29 '13 at 16:11
• Any nontrivial relation between $X$ and $Y$ would, by substitution, immediately give a nontrivial relation between $z$ and $w$, which does not exist. – Will Sawin Nov 29 '13 at 17:30
• Thanks @WillSawin. You also made me notice the terrible mistake I made by mixing notation for $X$ and $Y$ (now $Z$ and $W$). Let me edit and fix that. – Heitor Nov 29 '13 at 17:37
• Dear abx, if I understand correctly what you are saying is that in general $S(\theta)=\pi^\ast S_Y$, where $S_Y$ is the Picard group of $Y$ and $S(\theta)$ are the $\theta$-fixed elements of $S_X$. Could you please explain me why is this true? – Heitor Nov 29 '13 at 17:32
• This is true is up to multiplication by 2 : there is a homomorphism $Nm: \mathrm{Pic}(X)\rightarrow \mathrm{Pic}(Y)$ such that $\pi ^*Nm(L)=L\otimes \theta ^*L$. Thus if $L$ is $\theta$-invariant, $L^2$ belongs to $\pi ^*S_Y$. – abx Nov 29 '13 at 17:48
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2020-02-24 06:29:12
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https://homework.cpm.org/category/CCI_CT/textbook/apcalc/chapter/6/lesson/6.1.1/problem/6-13
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Home > APCALC > Chapter 6 > Lesson 6.1.1 > Problem6-13
6-13.
Evaluate each limit.
1. $\lim\limits _ { x \rightarrow \infty } \frac { x ^ { 5 } - 4 x ^ { 3 } + 3 x ^ { 2 } - 1 } { x ^ { 3 } + 8 x ^ { 2 } + 21 x - 5 }$
To evaluate the limit as the function approaches $∞$, look at the end behavior of the function.
Determine the end behavior by looking at only the highest-power terms in the denominator and numerator.
$=\lim\limits_{x\rightarrow \infty }\frac{x^{5}}{x^{3}}=\lim\limits_{x\rightarrow \infty }x^{2}=$
Because the function's end behavior follows the trend of a $y=x^2$ graph, we know that the limit as the function approaches ∞ does not exist.
1. $\lim\limits _ { x \rightarrow - \infty } \frac { x ^ { 5 } - 4 x ^ { 3 } + 3 x ^ { 2 } - 1 } { x ^ { 3 } + 8 x ^ { 2 } + 21 x - 5 }$
This is ALMOST the same problem as part (a) but, evaluate the limit as $x→−∞$ instead of $∞$. Note: Sometimes there are different end-behavior limits in either direction.
1. $\lim\limits _ { x \rightarrow 0 } \frac { \operatorname { sin } ( 2 x ) - 8 x ^ { 2 } } { 4 x ( x - 10 ) ^ { 3 } }$
This limit has an indeterminate form. Use l'Hôpital's Rule.
$\lim\limits_{x\to0}\frac{\sin(2x)-8x^2}{4x(x-10)^3}=\lim\limits_{x\to0}\frac{2\cos(2x)-16x}{4(x-10)^3+12x(x-10)^2}$
Now try evaluating the limit.
1. $\lim\limits _ { x \rightarrow 2 } \frac { 8 ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 5 x + 6 }$
This limit also has an indeterminate form. Use l'Hôpital's Rule.
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2021-09-21 18:31:52
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https://www.acmicpc.net/problem/5445
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시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 1 1 1 100.000%
## 문제
Nowadays, many programming languages have standard functions to check if two strings are equal. Even without such standard functions, it is easy to perform such a check: you just have to compare the characters at corresponding positions in both strings.
Sometimes, however, you do not just want a yes-no decision. If two strings are not exactly equal, but the differences are small, then you would like to be informed about that. It is not satisfactory to simply count the number of equal characters at corresponding positions in both strings, and relate this to the length of the strings. For example, strings "ABCDEFABCDEF" and "BCDEFABCDEFA" are almost equal (they are even equally long), but characters at corresponding positions are all different.
A relatively simple measure of equality that does not suffer from this problem, considers pairs of consecutive characters in the strings. For example, the string "ABCDEFABCDEF" contains eleven pairs of consecutive characters: two pairs "AB", two pairs "BC", two pairs "CD", two pairs "DE", two pairs "EF" and one pair "FA". Ten of these pairs also occur in the string "BCDEFABCDEFA". Only one pair "AB" is exchanged for a pair "FA". Hence, one could say that the measure of equality of the two strings is 10/11 ≈ 91%, which seems to be reasonable. It is not too difficult to extend this measure to strings of differents lengths.
There is, however, a disadvantage. If two strings have the same length and the measure of equality for them is 100%, then this does not necessarily mean that they are equal. For example, both the string "ABACA" and the string "ACABA" contain one pair "AC", one pair "CA", one pair "AB" and one pair "BA". Now, we are curious if this is possible for an arbitrary string. That is, given a string x, does there exist a different string y of the same length, which has measure of equality 100%? If so, then we say that x is not unique. Otherwise, we call x unique.
## 입력
The first line of the input contains a single number: the number of test cases to follow. Each test case has the following format:
• One line with a string x, for which 1 ≤ Length(x) ≤ 10, 000 and which consists of upper case letters, i.e., characters from the alphabet { A, B, C, . . . , Z }.
## 출력
For every test case in the input, the output should contain a single line, containing "unique" if the string x in the input is ‘unique’, and "not unique" otherwise.
## 예제 입력 1
2
ABCDEFABCDEF
ABACA
## 예제 출력 1
unique
not unique
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2019-04-24 06:41:07
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?p=53896
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## Rate Laws
julia lai 3A
Posts: 11
Joined: Wed Sep 21, 2016 2:55 pm
### Rate Laws
What exactly does it mean for a reaction to be 1st order, 2nd order, and so on?
Hannah_El-Sabrout_2K
Posts: 20
Joined: Wed Sep 21, 2016 2:58 pm
### Re: Rate Laws
They are all different relationships between concentration and rate. Depending on which order the reaction is, you will get different predictions of how fast the reaction is going. Essentially, they are different reaction speed trends. Sorry if this was kind of confusing!
Jeffreyho97
Posts: 10
Joined: Fri Jul 15, 2016 3:00 am
### Re: Rate Laws
1st rate: the amount of material you put in is directly proportional to its rate
2nd rate: the rate is proportional to the amount squared
0th rate: rate stays the same no matter how much you put in
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2020-10-24 22:00:02
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http://compaland.com/mean-square/what-does-the-mean-square-error-represents.html
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## How To Fix What Does The Mean Square Error Represents Tutorial
Home > Mean Square > What Does The Mean Square Error Represents
# What Does The Mean Square Error Represents
## Contents
When you perform General Linear Model, Minitab displays a table of expected mean squares, estimated variance components, and the error term (the denominator mean squares) used in each F-test by default. Values of MSE may be used for comparative purposes. Please do not hesitate to contact us with any questions. See also James–Stein estimator Hodges' estimator Mean percentage error Mean square weighted deviation Mean squared displacement Mean squared prediction error Minimum mean squared error estimator Mean square quantization error Mean square http://compaland.com/mean-square/what-is-the-mean-square-error.html
Regression In regression, mean squares are used to determine whether terms in the model are significant. Browse other questions tagged standard-deviation bias or ask your own question. Check out our Statistics Scholarship Page to apply! Then work as in the normal distribution, converting to standard units and eventually using the table on page 105 of the appendix if necessary. https://en.wikipedia.org/wiki/Mean_squared_error
## Root Mean Square Error Interpretation
How to Calculate a Z Score 4. inventory manag... How to Calculate Mean Absolute Error The mean absolute error is a statistical measure of how far estimates or forecasts are from actual values. ... For example, if you have a model with three factors, X1, X2, and X3, the adjusted sum of squares for X2 shows how much of the remaining variation X2 explains, assuming
Estimators with the smallest total variation may produce biased estimates: S n + 1 2 {\displaystyle S_{n+1}^{2}} typically underestimates σ2 by 2 n σ 2 {\displaystyle {\frac {2}{n}}\sigma ^{2}} Interpretation An Mean squares represent an estimate of population variance. Estimator The MSE of an estimator θ ^ {\displaystyle {\hat {\theta }}} with respect to an unknown parameter θ {\displaystyle \theta } is defined as MSE ( θ ^ ) Mean Square Error Matlab For example, suppose that I am to find the mass (in kg) of 200 widgets produced by an assembly line.
The MSE provides a means of choosing the best estimator: a minimal MSE often, but not always, indicates minimal variance, and thus a good estimator. Root Mean Square Error Example Since an MSE is an expectation, it is not technically a random variable. Popular Articles 1. https://www.vernier.com/til/1014/ I used this online calculator and got the regression line y= 9.2 + 0.8x.
Adjusted mean squares are calculated by dividing the adjusted sum of squares by the degrees of freedom. Mean Square Error Definition The smaller the means squared error, the closer you are to finding the line of best fit. Z Score 5. A symmetric bimodal distribution.
## Root Mean Square Error Example
Applications Minimizing MSE is a key criterion in selecting estimators: see minimum mean-square error. http://support.minitab.com/minitab/17/topic-library/modeling-statistics/anova/anova-statistics/understanding-mean-squares/ L.; Casella, George (1998). Root Mean Square Error Interpretation Pearson's Correlation Coefficient Privacy policy. How To Calculate Mean Square Error Using the result of Exercise 2, argue that the standard deviation is the minimum value of RMSE and that this minimum value occurs only when t is the mean.
Have a nice day! this contact form Find the mean. The minimum excess kurtosis is γ 2 = − 2 {\displaystyle \gamma _{2}=-2} ,[a] which is achieved by a Bernoulli distribution with p=1/2 (a coin flip), and the MSE is minimized As you perform these operations, note the position and size of the mean ± standard deviation bar and the shape of the MSE graph. Mean Square Error Calculator
The mean and standard deviation are shown in the first graph as the horizontal red bar below the x-axis. McGraw-Hill. Thus, this vertical line in the MSE graph gives essentially the same information as the horizontal bar in the histogram. have a peek here For an unbiased estimator, the MSE is the variance of the estimator.
Values of MSE may be used for comparative purposes. Root Mean Square Error Excel It's called the mean squared error as you're finding the average of a set of errors. MR1639875. ^ Wackerly, Dennis; Mendenhall, William; Scheaffer, Richard L. (2008).
## Step 1:Find the regression line.
Two or more statistical models may be compared using their MSEs as a measure of how well they explain a given set of observations: An unbiased estimator (estimated from a statistical The usual estimator for the mean is the sample average X ¯ = 1 n ∑ i = 1 n X i {\displaystyle {\overline {X}}={\frac {1}{n}}\sum _{i=1}^{n}X_{i}} which has an expected MSE is also used in several stepwise regression techniques as part of the determination as to how many predictors from a candidate set to include in a model for a given Mean Square Error In Image Processing average invento...
The purpose of this section is to show that mean and variance complement each other in an essential way. Now suppose that I find from the outcome of this experiment that the RMSE is 10 kg, and the MBD is 80%. The usual estimator for the mean is the sample average X ¯ = 1 n ∑ i = 1 n X i {\displaystyle {\overline {X}}={\frac {1}{n}}\sum _{i=1}^{n}X_{i}} which has an expected Check This Out Finding maximum of added fields Coding Standard - haphazard application Is there a name for the (anti- ) pattern of passing parameters that will only be used several levels deep in
For an unbiased estimator, the MSE is the variance of the estimator. However, the... New York: Springer. For example, you do an experiment to test the effectiveness of three laundry detergents.
This definition for a known, computed quantity differs from the above definition for the computed MSE of a predictor in that a different denominator is used. This bar is centered at the mean and extends one standard deviation on either side. Loss function Squared error loss is one of the most widely used loss functions in statistics, though its widespread use stems more from mathematical convenience than considerations of actual loss in I've looked around the site, but to me I am still finding it a bit challenging to understand what is really meant in the context of my own research. –Nicholas Kinar
The variation in means between Detergent 1, Detergent 2, and Detergent 3 is represented by the treatment mean square. The estimates of variance components are the unbiased ANOVA estimates. This test is called a synthesized test. You may have wondered, for example, why the spread of the distribution about the mean is measured in terms of the squared distances from the values to the mean, instead of
In statistical modelling the MSE, representing the difference between the actual observations and the observation values predicted by the model, is used to determine the extent to which the model fits Definition A simple way to think of MSE is as a criterion for selecting an appropriate estimator: in statistical models, modelers must choose between various potential estimators. I compute the RMSE and the MBD between the actual measurements and the model, finding that the RMSE is 100 kg and the MBD is 1%. Mean Squared Error: Definition and Example was last modified: February 15th, 2016 by Andale By Andale | November 2, 2013 | Statistics How To | No Comments | ← Degrees of
MR0804611. ^ Sergio Bermejo, Joan Cabestany (2001) "Oriented principal component analysis for large margin classifiers", Neural Networks, 14 (10), 1447–1461. Privacy, Disclaimers & Copyright COMPANY About Us Contact Us Advertise with Us Careers RESOURCES Articles Flashcards Citations All Topics FOLLOW US OUR APPS The root mean-square error, RMSE, is the square root of MSE. 3. Suppose the sample units were chosen with replacement.
However, one can use other estimators for σ 2 {\displaystyle \sigma ^{2}} which are proportional to S n − 1 2 {\displaystyle S_{n-1}^{2}} , and an appropriate choice can always give Like the variance, MSE has the same units of measurement as the square of the quantity being estimated. error is a lot of work.
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2017-05-26 01:47:04
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https://tex.stackexchange.com/questions/12100/slide-ticker-in-beamer-presentations
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# Slide ticker in beamer presentations
I am using 'beamer' for presentations. I have a Main Titles and a few slides under each.
For example,
Introduction has 4 slides Methods have 5 slides.
I want to put kind of a ticker at the top of each slide saying what slide we are at currently. For Introduction it should have 4 small circles (coz 4 slides) below it and the slide number should be a highlighted circle.
How can I go about it? Thanks
You could choose a beamer theme which supports that. For example Singapore:
\documentclass{beamer}
\usetheme{Singapore}
\begin{document}
\section{Introduction}
\subsection{One}
\begin{frame} text \end{frame}
\subsection{Two}
\begin{frame} text \end{frame}
\subsection{Three}
\begin{frame} text \end{frame}
\subsection{Four}
\begin{frame} text \end{frame}
\section{Methods}
\subsection{One}
\begin{frame} text \end{frame}
\subsection{Two}
\begin{frame} text \end{frame}
\end{document}
Here's the top of a frame, where subsection three of the introduction is highlighted.
Or
\usetheme{Szeged}
Or
\usetheme{Darmstadt}
There are related themes such as Berlin, Ilmenau, Dresden and Frankfurt, with such a navigation.
Also the progressbar theme is interesting, if you wish to show the frame progress.
To visit beamer themes galleries, have a look at Where to find custom beamer themes.
• I used the same style like Darmstadt (split theme) for my last conference presentations and my colleagues told me at my test run that the mini toc/progress bar on top looks great. It isn't intrusive and gives a nice overview. – Martin Scharrer Feb 26 '11 at 8:13
• Is it possible to have the "slide ticker" one per slide, instead of one per subsection? – gozzilli Nov 18 '11 at 17:00
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2020-12-02 19:26:09
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https://zbmath.org/?q=an:06329863
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# zbMATH — the first resource for mathematics
$$\mathcal H_\infty$$ static output-feedback control design with constrained information for offshore wind turbine system. (English) Zbl 1293.93345
Summary: This paper deals with $$\mathcal H\infty$$ static output-feedback control design with constrained information for offshore wind turbines. Constrained information indicates that a special zero-nonzero structure is imposed on the static output-feedback gain matrix. A practical use of such an approach is to design a decentralized controller for a wind turbine. This will also benefit the controller in such a way that it is more tolerant to sensor failure. Furthermore, the model under consideration is obtained by using the wind turbine simulation software FAST. Sufficient conditions to design an $$\mathcal H_\infty$$ controller are given in terms of linear matrix inequalities $$(\mathcal{LMI}\text s)$$. Simulation results are given to illustrate the effectiveness of the proposed methodology for different cases of the control gain structures.
##### MSC:
93B52 Feedback control 93A14 Decentralized systems 93C95 Application models in control theory
##### Software:
FAST; FAST; TurbSim; YALMIP
Full Text:
##### References:
[1] Abdin, E. S.; Xu, W., Control design and dynamic performance analysis of a wind turbine induction generator unit, IEEE Transactions on Energy Conversion, 15, 1, 91-96, (2000) [2] Muyeen, S. M.; Ali, M. H.; Takahashi, R.; Murata, T.; Tamura, J.; Tomaki, Y.; Sakahara, A.; Sasano, E., Comparative study on transient stability analysis of wind turbine generator system using different drive train models, IET Renewable Power Generation, 1, 2, 131-141, (2007) [3] T.J. Larsen, How 2 HAWC2, the userʼs manual, Risø-R-1597(ver. 3-9)(EN), 2009. [4] C.L. Bottasso, A. Croce, Cp-Lambda user manual, 2009. [5] J. Jonkman, M.L. Buhl Jr., FAST Users Guide, Technical Report NREL/EL-500-38230, National Renewable Energy Laboratory, 2005. [6] AlHamaydeh, M.; Hussain, S., Optimized frequency-based foundation design for wind turbine towers utilizing soil-structure interaction, Journal of the Franklin Institute, 348, 1470-1487, (2011) · Zbl 1316.74058 [7] Eggleston, D. M.; Stoddard, F. S., Wind turbine engineering design, (1987), Van Nostrand Reinhold [8] Boyd, S.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory, SIAM studies in applied mathematics, (1994) [9] A.I. Zečevic´, D.D. Šiljak, Design of robust static output feedback for large-scale systems, IEEE Transactions of Automatic Control (11) (2004) 2040-2044. [10] Zečevic´, A. I.; Šiljak, D. D., Control design with arbitrary information structure constraints, Automatica, 44, 10, 2642-2647, (2008) · Zbl 1155.93347 [11] Zečevic´, A. I.; Šiljak, D. D., Control of complex systemsstructural constraints and uncertainty, (2010), Springer · Zbl 1211.93003 [12] Rubió-Massegú, J.; Rossell, J. M.; Karimi, H. R.; Palacios-Quiñonero, F., Static output-feedback control under information structure constraints, Automatica, 49, 1, 313-316, (2013) · Zbl 1257.93045 [13] Sloth, C.; Esbensen, T.; Stoustrup, J., Robust and fault-tolerant linear parameter-varying control of wind turbines, Mechatronics, 21, 4, 645-659, (2011) [14] Kamal, E.; Aitouche, A.; Ghorbani, R.; Bayrat, M., Robust fuzzy fault-tolerant control of wind energy conversion systems subjected to sensor faults, IEEE Transactions of Sustainable Energy, 3, 2, 231-241, (2012) [15] F. Zhang, W.E. Leithead, O. Anaya-Lara, Wind turbine control design to enhance the fault ride-through capability, in: IET Conference on Renewable Power Generation, 2011, pp.1-6. [16] J. Jonkman, S. Butterfield, W. Musial, G. Scott, Definition of a 5-MW Reference Wind Turbine for Offshore System Development, Technical Report NREL/TP-500-38060, National Renewable Energy Laboratory, 2009. [17] J. Jonkman, M.L. Buhl Jr., FAST Users Guide, Technical Report NREL/EL-500-38230, National Renewable Energy Laboratory, 2005. [18] J. Jonkman, Definition of the Floating System for Phase IV of OC3, Technical Report NREL/TP-500-47535, National Renewable Energy Laboratory, 2010. [19] J. Löfberg, YALMIP: a toolbox for modeling and optimization in MATLAB, in: Proceedings of the CACSD Conference, Taipei, Taiwan, 2004. [20] B.J. Jonkman, TurbSim User Guide: Version 1.50, Technical Report NREL/EL-500-46198, National Renewable Energy Laboratory, September 2009. [21] T. Bakka, H.R. Karimi, “Robust H_∞ Dynamic Output Feedback Control Synthesis with Pole Placement Constraints for Offshore Wind Turbine Systems,” Mathematical Problems in Engineering, 2012 (2012) 10.1155/2012/616507, in press · Zbl 1264.93164 [22] T. Bakka, H.R. Karimi, Multi-objective control design with pole placement constraints for wind turbine systems, Advances on Analysis and Control of Vibrations—Theory and Applications, INTECH 2012, ISBN 978-953-51-0699-9, pp. 179-194. [23] T. Bakka, H.R. Karimi, N.A. Duffie, Gain scheduling for output $$H_\infty$$ control of offshore wind turbine, in: Proceedings of the Twenty-second International Offshore and Polar Engineering Conference, 2012, pp. 496-501.
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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2021-04-11 20:09:42
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https://cstheory.stackexchange.com/questions/9349/maximal-munch-rule-issue-for-lexers-is-detection-decidable
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# Maximal munch rule issue for lexers: is detection decidable?
Edit: I realise that one of my problems is that I don't have a clear definition of my problem, which makes the question of whether it is detectable hard to answer.
I'm therefore already happy with any reference in which this particular problem is discussed at all - I haven't found any such reference myself, and with any luck, I can derive a good definition of my problem from that, which will hopefully lead to a solution.
Original:
Suppose we have this lexical definition:
X := a*
Y := a
and this context-free grammar:
S := X Y
and we use any lexer and parser combination to generate a recogniser for this language, in which the lexer uses the 'maximal munch' or 'longest match first' rule.
The specification might seem to be trivially equivalent to the regular expression "$a$+", but it isn't: in fact, it recognises no strings at all. The reason is that $X$ 'eats' all the $a$ characters present in the input because of 'maximal munch', leaving none for $Y$ to consume, so the parser always rejects the input.
I'd like to know if it is decidable if such a problem is present in a given lexer and parser specification.
Note that this is decidable if only a single token is the culprit. Let $L_T$ be the language generated by some token (= regular expression) $T$, and let $L_R$ be the language generated by the 'follow' language of this token, that is, the language of all strings that are postfixes of the occurrence of $T$ in the specification. In the example above, $T=X=a^*$ and $R=Y=a$, though in general, $R$ will be a lot more complicated.
The problem can then be formulated as (where $+\!\!\!\!+\,$ denotes concatenation):
$(L_T +\!\!\!\!+\, L_R) \cap L_T \neq \emptyset$
If this intersection is nonempty, then $T$ will eat up the match made by $R$. As $L_T$ is regular, this is decidable. (note that a better, less stringent rule might be that $L_T +\!\!\!\!+\, L_R$ is not a subset of $L_T$, I'm not sure)
Unfortunately, grammars like $a b a^* b^* a b$ (split into 6 tokens) do not accept the string $abab$, and here no single token is the culprit, so the above method doesn't work.
Searching the web turned up nothing, not even that anyone else has ever noticed this problem, although I might just be using the wrong keywords. This surprised me somewhat, so chances are I'm either wrong or this is never a problem in practice.
I stumbled upon the above problem when toying with modularised parsing, but the above problem isn't specific at all for modularised parsing (though it can more easily become a problem if someone forgets to declare whitespace somewhere, in which case I'd like to warn the user, hence the above question).
To answer in the large, the fact that the syntax of programming languages is not context-free is not news (see e.g. Floyd, 1962).
To answer more precisely, in a context of scannerless parsing like yours, a way to implement maximal munch is to employ so-called follow restrictions (van den Brand et al., 2002) by forbidding some language to follow a given rule. In your example, you could write a restriction X -/- a forbidding an $a$ after the token $X$. Provided your forbidden languages are regular, these restrictions can be compiled back into the grammar (however in van den Brand et al.'s formalism, the forbidden language can be context-free and $X$ can be any nonterminal, and this clearly leads to an undecidable emptiness problem).
Another formalism for scannerless parsing is that of parsing expression grammars (Ford, 2004), which has a greedy, maximal-munch type semantics, and an undecidable emptiness problem.
Now, it doesn't look like your specific maximal munch semantics would allow you to reduce from these undecidable problems. For a start, it seems to me that, rather than emptiness of the generated language, a tool should more broadly warn the user about any case where a token might "eat" a (non-empty) prefix of its follow language, i.e. whenever $(L_T\cdot\mathrm{Pref}_+(L_R))\cap L_T\neq\emptyset$, regardless of whether this prefix is mandatory of not. This would capture your $aba^\ast b^\ast ab$ example if I understand correctly how you would tokenize it.
To conclude, here is an attempt to formalize your notion of maximal-munch-caused emptiness: let $\langle N,T,P,S\rangle$ be a context-free grammar with nonterminal alphabet $N$, terminal alphabet $T$, production set $P$ and axiom $S$. Each terminal symbol $X\in T$ is associated with a regular language $L_X\subseteq\Sigma^\ast$ used for its tokenization. For every occurrence of a terminal symbol $X$ in some production $A\to \alpha X\beta$ of your grammar where $\alpha,\beta$ are sequences of mixed terminals and nonterminals, construct the follow language $L_{\beta,A}$ of this particular occurrence (this is a context-free language) and consider the residual language of the token $L^{\text{max-munch}}_X=(L_X^{-1}\cdot L_X)\cap\Sigma^+$, which is a regular language of strings that will be "eaten up" by the maximal munch semantics. In fact the language $L^{\text{max-munch}}_X$ is the language one would put in the follow restriction for $X$. Then, if $$L_{\beta,A}\subseteq L^{\text{max-munch}}_X\cdot\Sigma^\ast\;,$$ or equivalently $L_{\beta,A}\cap (\Sigma^\ast\backslash(L^{\text{max-munch}}_X\cdot\Sigma^\ast))=\emptyset$, any string allowed to follow this occurrence of $X$ will be "eaten", and the language of the rule $A\to\alpha X\beta$ is empty. Using the classical algorithm for emptiness checking with this extra twist for handling terminal symbols might solve your emptiness problem.
• Looks like this exactly answers my question, thanks. The only question that remains (and that can most likely only be answered by simply trying it out in practice) is how many false positives you get (and possibly whether the running time of this check is worth it). – Alex ten Brink Dec 11 '11 at 13:32
The grammars are non-deterministic.
I would use an item based approach to solve the problem. While generating an FSA, generate the language (a list of items) that reaches each state. And generate a procedure to resolve the longest match rule. Using tupples and sets to keep track of parse:
For the first example: a*a+
The initial state is: .a*.a+ The final and only other state is: .a*.a+.
Parsing on successive "a"s produces the tupples (on transitions the "a" are simply shifted from the second token to the first):
{(,a)}
{(a,a)}
{(aa,a)}
...
I worked through the second example, there is nothing interesting there other than moving the "." past the "*" operator.
In the usual lex, a transition concatenates a symbol to the token. In general, a transition takes the set of tupples and forms a new set based on the operators in the regular grammar and the symbol associated with the transition. I don't have the time to work out the general form of the transition functions.
In the past I have done symbolic operations, including stripping off the left most character, on grammars with regular operators. The math part is easy but detailed. I no longer have my notes.
I can see that the other issues, operating on the tupples to produce new tupples, follows the same pattern. The production of the procedures associated with transitions can be done at lex generation time.
• I get what you're suggesting, but my problem doesn't lie with parsing regular expressions. My problem is the interplay of regular expression parsing using lexers combined with context-free grammar parsing (with say an LR parser). I don't think you can 'solve' my problem, which is why I'm interested in detecting these situations and also whether this problem has been encountered before. – Alex ten Brink Dec 12 '11 at 19:26
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2020-02-25 20:03:35
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https://www.physicsforums.com/threads/refraction-of-light.457666/
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# Refraction of light
An isosceles prism of angle 120* has a refractive index 1.44.Two parallel monochromatic rays enter the prism parallel to each other as shown in figure.the ray emerge from the opposite faces-
(A)Are parallel to each other
(B)are diverging
(C) make an angle 2[sin^ -1(0.72)-30*] with each other
(D) make an angle 2 sin^ -1(0.72) with each other
The figure for the following question is attached .
The possible eqn. are Refractive index=Sin i/Sin r
It is one of the MCQ in my question paper, But I am unable to solve it.Since the rays fall normal to the surface of the prism, so they should go undeviated but what after they strikes the next prism surface ,How will they deviate?
Only thing i am able to do is that they will enter the prism without any deviation since it is perpendicular to the surface of the prism but what after that?
Thank you,
Harsh
#### Attachments
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2020-11-29 05:26:39
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https://brilliant.org/discussions/thread/incredible/
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×
# Incredible!
2 years, 7 months ago
Sort by:
I see "John Muradeli" here again, but is it really all the same letters of the name of the guy I used to know that came around here, or it just looks like it? What I do remember is that it sounded like the name of an olive oil company.
- 2 years, 7 months ago
You are back !!
@Math Philic I see your friend's back:)
- 2 years, 7 months ago
You're back!
I first saw this effect when I was 10 (I think) and it didn't take much time to figure out what was going on.
A cool effect nevertheless!
- 2 years, 7 months ago
- 2 years, 7 months ago
Took me a few tries to realize :O
I should be making a post anytime soon on the solution to the sum on the bottom of the fraction; I owe it to Mr. Mathopedia.
P.S. - the reward is for my school's students/staff ONLY! ;)
- 2 years, 7 months ago
How is the order of division supposed to be resolved? I see 5 main expressions separated by 4 lines of division. If the lines were at least of different length, the order could be indicated.
- 2 years, 7 months ago
That's true - but everyone in the building knows me, and I know them. And I know no-one can solve that - hence the 100\$ price. Also, they could ask. In that case, I'd blab out the "standard method for arranging fractions," and I'd quote Wolfram|Alpha - a/b/c/d ... = a/b * c/d * ... .
In the original on Brilliant (which, 9 people have miraculously solved (or log-cheated)), I note that a/b/c/d = a/(b/(c/...)) - which, I think, luckily turns out to be the same thing.
Either way, no prize until the solution to each line is shown. :)
- 2 years, 7 months ago
Spoilers: Don't read this : All the cards are different.
- 2 years, 7 months ago
Don't give it away!
- 2 years, 7 months ago
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2017-10-17 02:08:22
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http://physics.stackexchange.com/tags/tidal-effect/hot
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# Tag Info
120
There is no tidal bulge. This was one of Newton's few mistakes. Newton did get the tidal forcing function correct, but the response to that forcing in the oceans: completely wrong. Newton's equilibrium theory of the tides with its two tidal bulges is falsified by observation. If this hypothesis was correct, high tide would occur when the Moon is at zenith ...
48
Imagine that we have a very massive object in space. At some distance away (call it ten units) we release three tennis balls in a row: The tennis balls all fall towards the massive object. But because gravity goes like distance squared, the nearer balls feel a stronger attraction than the farther balls, and they move apart from each other: You're ...
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First we must understand a little what is meant by "tide." A tide is the difference of gravitational force an object feels across its volume from another object. In the Earth's case the side closest to the moon feels a stronger force pulling it towards the moon than the center of the Earth does, while the side opposite the moon feels a force weaker than ...
45
Suppose the Moon didn't orbit the Earth at all, so it just stayed at some fixed point while the Earth rotated underneath it: In this case every point on the equator would pass directly under the Moon every 24 hours, and we'd get a high tide every 24 hours. (There's another high tide when we're exactly on the opposite side of the earth to the moon, but ...
36
Tides are caused by the gradient of the gravitational field - so the tidal "force" experienced drops with the third power of the distance. This means that the relative strength of the tides should go as $$ratio = \frac{M_{moon} \cdot D_{sun}^3}{M_{sun} \cdot D_{moon}^3}\\ =\frac{7 \cdot 10^{22}\cdot (1.5 \cdot 10^{11})^3}{2\cdot 10^{30}\cdot (3.7\cdot ... 30 This diagram shows the Earth rotating round the Sun at it's orbital velocity v. That is the centre of the Earth is orbiting around the Sun at velocity v. NB the scale is rather fanciful - don't take it literally! I'll also assume the orbit is circular, and for convenience I'll ignore the Earth's rotation i.e. assume it's tidally locked. To calculate ... 30 The relevant "100%" from which you should calculate the percentage isn't the depth of the ocean but the radius of the Earth$$ R\sim 6,378,000\,{\rm m} $$Multiply this R by 10^{-7} and you will get 0.6 meters, a reasonable estimate for average tides. You must understand that the surface of the ocean always tries to create an "equipotential surface" ... 27 The Earth is free falling towards the Moon. Because gravity decays with distance, the side near the moon wants to fall faster than the center of the Earth, while the other side tends to fall slower. So observed on the Earth, the other side "lags behind" and therefore we have high tide there. 23 The picture of high tides on opposite sides of the Earth with a period of about 12 hours (actually 12 hours 25 minutes, due to the rotation of the Earth) is an oversimplification. It's just a starting point. Tides would behave this way in the limit of an all-water Earth with ocean depth so great that it had no effect on the surface wave. But the Earth has ... 22 The Wikipedia article you linked states: Atomic clocks show that a modern day is longer by about 1.7 milliseconds than a century ago If we take this change of 1.7 ms/century and multiply by 2.5 million centuries (250 million years) then we get a change of 4,250 seconds or 1.18 hours. So 250 million years ago the day length would have been 22.82 hours. ... 22 This is a gravitational phenomenon known as tidal lock. It is closely related to the phenomenon of tides on Earth, hence the name. Tidal locking is an effect caused by the gravitational gradient from the near side to the far side of the moon. (That is, the continuous variation of the gravitational field strength across the Moon.) The end result is that the ... 18 When we say that the Moon rotates, we don't mean relative to an observer on Earth, because we're also rotating. Maybe best is to think of it from the perspective of the Sun. If you were at the centre of the solar system, looking at the Earth, you'd see the Moon rotates once every 28 days or so. That also happens to be the amount of time it takes for the Moon ... 18 There are a few things that keep Saturn's rings roughly the way they are. First, Saturn's D ring actually is "raining" down on Saturn currently. But, the phenomenon of shepherd moons prevents the vast majority of material from leaving the other rings: "The gravity of shepherd moons serves to maintain a sharply defined edge to the ring; material that ... 18 In the ocean, it's called the tides, and it happens twice a day. You can see it if you're standing on the seashore, but on the deep ocean it happens so gradually you wouldn't even notice it. On land the tidal bulge only rises up a third of a meter or so (not seven meters, because the moon's gravity is much less than the earth's), and, again, it happens so ... 17 Begin by imagining that the moon isn't quite a perfect sphere. One side is just a little bigger than the other. As the moon rotates, the heavier face will swing around towards the earth a little faster, and it will swing away from the earth a little slower, since it feels a stronger gravitational attraction via its larger mass. Since gravity is a ... 17 I suspect that what has confused you is the difference between remaining a fixed distance from the black hole and falling freely into it. Let me attempt an analogy to illustrate what I mean. Suppose you are carrying a large and heavy backpack. You can feel the gravitational force of the backpack weighing you down. However this only happens because you're ... 15 If you could take from orbital energy, then it would decrease, until at some point in the future it would zero. Hence, it can't be perpetual. 14 The Roche limit applies when the astronomical body in question is held together by gravity rather than electromagnetic forces. This is the case for bodies with a diameter larger than around 500km. Obviously for smaller bodies, like humans, we can get arbitrarily close to the surface, but i suspect this isn't what you're asking about. For moons much smaller ... 13 This says it concisely, when describing the effect of tides: Gravitational coupling between the Moon and the tidal bulge nearest the Moon acts as a torque on the Earth's rotation, draining angular momentum and rotational kinetic energy from the Earth's spin. In turn, angular momentum is added to the Moon's orbit, accelerating it, which lifts the Moon ... 11 In principle, yes, the ultimate source of energy for a tidal power plant is Earth's rotational energy, so these plants are slowing down the Earth's rotation. By conservation of angular momentum, that means they are pushing the Moon further away as well, although I wouldn't phrase it as being due to "waves in the gravitational field," as that expression ... 11 We already harvest energy from the Moon. It causes the tides and stress and strain and motion throughout the Earth. As a result, the Moon keeps getting farther away. (And it causes some heating in the Earth). The Moon at one time had a spin that was not locked to the Earth, and the tidal bulges in the Moon's shape caused by the Earth generated heat in the ... 10 I think the reasoning has an error. It assumes v is constant, but instead we ought to assume the angular momentum is constant. By dimensional analysis that leads to r \propto \frac{L^2}{GM} so as M decreases, r increases (the original post had r \propto M, not r \propto 1/M. On the other hand, assuming a circular orbit seems dubious. As ... 10 Increasing the diameter and distance of the Moon by a factor 2 would lead to a number of very subtle differences. I will list the ones I came up with: Apparent size If R_m is the radius of the Moon and D_m its geocentric distance (that is, the distance between the centre of the Moon and the centre of the Earth), then its geocentric angular diameter is ... 10 Let's simplify. Let's eliminate the Moon. Let's get rid of the Sun temporarily. Let's replace the Earth with an equivalent mass-and-density perfect sphere of iron that is neither moving linearly nor spinning or revolving in any way. We place two 1KG iron test masses on opposite sides of the Iron Earth, suspended 1 M above the surface by identical ... 10 Yes your weight will change. The moon will have a bigger impact than the sun, so you need to look at the position of the moon to decide when you will be heaviest (basically - you are lighter when the moon is overhead, or on the opposite side of the earth; and heaviest when it is on the horizon. So a full moon rising makes you fat...) The effect (the ... 10 As stated in other answers it is how much the gravitational force is different by on opposite sides of the earth that creates the tides. You can still show this using a=\frac{GM}{d^2} but you need to consider the difference, not the absolute force on the earth. The sun while much more massive is just far enough away that it is getting to a much flatter ... 9 The mistake you're making is that you're looking at the full acceleration when you should look at the relative one. At distance R=1\mathrm{au} from the sun, the gravitational acceleration is given by$$ a_0 = \frac{GM_\odot}{R^2} $$Assuming a spherical cow earth (in vacuum), at midday at the equator, we're one earth-radius r closer to the sun, ie$$ ...
9
You should do some hard assumptions, as no atmosphere, but the real problem is the so called Roche Limit, that states that at this limit, the tidal forces , difference of the gravitational potential between the face facing the Earth and the one opposite, is so large that rips the body (Moon) apart.Wiki With the Wikipedia formula: \$ d = 2.44 R_{Earth} ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2015-08-01 06:04:02
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https://tex.stackexchange.com/questions/113272/chapter-count-not-increasing
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# Chapter count not increasing
Consider the following MWE:
\documentclass[12pt,twoside,letterpaper]{report}
\usepackage{etoolbox}
\newcounter{totchapters}
\providecommand\totchap{}
\makeatletter
\AtEndDocument{%
\immediate\write\@mainaux{%
\string\gdef\string\totchap{\number\value{totchapters}}%
}%
}
\makeatother
\begin{document}
\totchap \chapter{one}
\chapter{two}
\chapter{three}
\chapter{four}
\end{document}
I am trying to gain access to the total number of chapters in a document. I got inspiration from https://tex.stackexchange.com/a/55583/10898. But for some reason or the other the chapter counter is affected and no longer increasing. Why is that the case and how can it be fixed? Note that I would like to use this total to make calculations.
You can change the code to use \stepcounter{totchapters} rather than
\addtocounter{totchapters}{\value{chapter}}
Perhaps I have misunderstood the original intent, but here's a complete MWE that works as expected
% arara: pdflatex
\documentclass{report}
\usepackage{etoolbox}
\newcounter{totchapters}
\providecommand\totchap{}
\makeatletter
\AtEndDocument{%
%\stepcounter{totchapters}%
\immediate\write\@mainaux{%
\string\gdef\string\totchap{\number\value{totchapters}}%
}%
}
\makeatother
\pretocmd{\chapter}{\stepcounter{totchapters}}{}{}
\begin{document}
\totchap\
\chapter{one}
\chapter{two}
\chapter{three}
\chapter{four}
\end{document}
• Can I use \totchap in calculations? For example, 5/\totchap. – azetina May 8 '13 at 19:15
• – cmhughes May 8 '13 at 19:23
• Something like \number\numexpr\totchap+3\relax I suppose. – azetina May 8 '13 at 19:27
• Why using a new counter? Doesn't \immediate\write\@mainaux{\gdef\string\totchap{\number\value{chapter}} do the same? – egreg May 8 '13 at 22:22
The totcount does this without any redefinition.
\documentclass[12pt,twoside,letterpaper]{report}
\usepackage{totcount}
\regtotcounter{chapter}
\begin{document}
This document has \total{chapter} chapters.
\chapter{one}
\chapter{two}
\chapter{three}
\chapter{four}
\end{document}
The first page will show
This document has 4 chapters.
• Can you use \total{chapter} to make arithmetic calculations? – azetina May 8 '13 at 21:47
• @azetina If you define \newcommand{\numtotal}[1]{\value{#1@totc}} you can use \numtotal{chapter} (or any other registered counter) in the context of a <number>. The returned value is -1 at the first run (totcount uses the .aux file for its workings). – egreg May 8 '13 at 22:04
• @egreg Is there a way to have access to the total number of chapters per part? – pluton Jul 21 '13 at 2:50
• @pluton This would be the subject for a new question – egreg Jul 21 '13 at 9:23
|
2019-05-25 05:54:48
|
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https://scholar.harvard.edu/alesina/publications
|
# Publications
Working Paper
Alesina, Alberto, Stefanie Stantcheva, and Armando Miano. Working Paper. “Immigration and Redistribution”. Publisher's VersionAbstract
We design and conduct large-scale surveys and experiments in six countries to investigate how natives' perceptions of immigrants influence their preferences for
redistribution. We find strikingly large biases in natives' perceptions of the number and characteristics of immigrants: in all countries, respondents greatly overestimate the total number of
immigrants, think immigrants are culturally and religiously more distant from them, and are economically weaker -- less educated, more unemployed, poorer, and more reliant on government transfers-- than is the case. While all respondents have misperceptions, those with the largest ones are systematically the right-wing, the non-college educated, and the low-skilled working in immigration-intensive sectors.
Support for redistribution is strongly correlated with the perceived composition of immigrants -- their origin and economic contribution. Given the very negative baseline views that respondents have of immigrants, simply making them think about immigration in a randomized manner makes them support less redistribution. To the contrary, experimentally showing respondents information about the true i) number, ii) origin, and iii) hard work'' of immigrants in their country manages to counteract and even outweigh the negative priors and generate more support for redistribution, including actual donations to charities.
Alesina, Alberto, Carlo Favero, and Francesco Giavazzi. Working Paper. “'What do we know about the effects of austerity?'”.
Alesina, Alberto, Carlo Favero, Francesco Giavazzi, Omar Barbiero, and Matteo Paradisi. Working Paper. “The Effects of Fiscal Consolidations: Theory and Evidence”.Abstract
We investigate the macroeconomic effects of fiscal consolidations based upon government spending cuts, transfers cuts and tax hikes. We extend a narrative dataset of fiscal consolidations, finding details on over 3500 measures. Government spending and transfer cuts are much less harmful than tax hikes. Standard New Keynesian mod- els match our results when fiscal shocks are persistent. Wealth effects on aggregate demand mitigates the impact of a persistent spending cut. Static distortions caused by persistent tax hikes cause larger shifts in aggregate supply under sticky prices. This channel explains different sizes of multipliers found in fiscal stimuli compared to consolidation plans.
Alesina, Alberto, Gualtiero Azzalini, Carlo Favero, Francesco Giavazzi, and Armando Miano. Working Paper. “Is it the "How" or the "When" that Matters in Fiscal Adjustments?”.Abstract
Using data from 16 OECD countries from 1981 to 2014 we specify
a model that determines the output effect of fiscal adjustments as a function of the composition of the adjustment and the state of the cycle. We find that both the "how" and the "when" matter, but the heterogeneity related to the composition is more robust across different specifications. Adjustments based upon spending cuts are consistently much less costly than those based upon tax increases. Our results are not explained by different reactions of monetary policy. However, when the domestic central bank can set interest rates - that is outside of a currency union - it appears to be able to dampen the recessionary effects of tax-based consolidations implemented during a recession.
Alberto Alesina, Stefanie Stantcheva, Edoardo Teso. Working Paper. “Intergenerational Mobility and Preferences for Redistribution”.Abstract
Using new cross-country survey and experimental data, we investigate how beliefs about
intergenerational mobility affect preferences for redistribution in France, Italy, Sweden, the
U.K., and the U.S.. Americans are more optimistic than Europeans about social mobility. Our randomized treatment shows pessimistic information about mobility and increases support for redistribution, mostly for “equality of opportunity” policies. We find a strong political polarization. Left-wing respondents are more pessimistic about mobility, their preferences for redistribution are correlated with their mobility percep- tions, and they support more redistribution after seeing pessimistic information. None of these apply to right-wing respondents, possibly because they see the government as
a “problem” and not as the “solution.”
NBER Working Paper No. 23027
Alesina, Alberto, and Francesco Passarelli. Working Paper. “Loss Aversion, Politics and Redistribution”.Abstract
We study loss aversion in majority voting. First, we show a status quo
bias. Second, loss aversion implies a moderating effect. Third, in a dynamic setting, the effect of loss aversion diminishes with the length of the planning horizon of voters; however, in the presence of a projection bias, majorities are partially unable to understand how fast they will adapt. Fourth, in a stochastic environment, loss aversion yields a significant distaste for risk, but also a smaller attachment to the status quo. The application of these results to a model of redistribution leads to empirically plausible implications.
Alesina, Alberto, Caterina Gennaioli, and Stefania Lovo. Working Paper. “Public Goods and Ethnic Diversity: Evidence from Deforestation in Indonesia”.Abstract
This paper shows that the level of deforestation in Indonesia is positively related
to the degree of ethnic fractionalization at the district level. To identify a casual rela- tion we exploit the exogenous timing of variations in the level of ethnic heterogeneity due to the creation of new jurisdictions. We provide evidence consistent with a lower control of politicians, through electoral punishment, in more ethnically fragmented districts. Our results bring a new perspective on the political economy of defor- estation. They are consistent with the literature on (under) provision of public goods and social capital in ethnically diverse societies and suggest that when the underlying communities are ethnically fractionalized decentralisation can reduce deforestation by delegating powers to more homogeneous communities.
NBER WP 20504
2017
Alesina, Alberto, Bryony Reich, and Alessandro Riboni. 2017. “Nation-Building, Nationalism and Wars”.Abstract
The increase in army size observed in early modern times changed
the way states conducted wars. Starting in the late 18th century, states switched from mercenaries to a mass army by conscription. In order for the population to accept to fight and endure war, the government elites began to provide public goods, reduced rent extraction and adopted policies to homogenize the population with nation-building. This paper explores a variety of ways in which nation-building can be implemented and
studies its effects as a function of technological innovation in warfare.
2016
Alesina, Alberto, and Andrea Passalacqua. 2016. “The Political Economy of Government Dept.” Handbook of Macroeconomics, 2: 2599-2651. North Holland, 2, 2599-2651.
Alesina, Alberto, Salvatore Piccolo, and Paolo Pinotti. 2016. “Organized Crime, Violence and Politics”.Abstract
We show that in Sicily Mafia killings of politicians increase before elections and
have negative effects on the vote received by parties not captured by the Mafia. Then, using a very large data set of electoral speeches, we find strong evidence that anti-mafia activities by politicians elected in Sicily are, in fact, negatively correlated with the levels of pre-electoral violence. Using data on homicides in all regions of Italy starting from the end of the nineteenth century, we identify a political cycle of homicides only in regions with organized crime. We also show how this electoral cycle changes as a function of different electoral rules and the relative strength of captured and non-captured parties. All these empirical findings are rationalized by a simple signaling model in which criminal organizations exert pre-electoral violence to inform adverse politicians about their military strength.
Alesina, Alberto, Benedetta Brioschi, and Eliana La Ferrara. 2016. “Violence Against Women: A Cross-cultural Analysis for Africa”.Abstract
Using a new dataset, we investigate the determinants of violence
against women in Africa. We focus on cultural factors arising from pre-colonial customs and find evidence consistent with two hypotheses. First, ancient socioeconomic conditions determine social norms about gender roles, family structures and intrafamily violence which persist even when the initial conditions change. Norms about marriage patterns, living arrangements and the productive
role of women are associated with contemporary violence. Second, women’s contemporary economic role affects violence in a complex way which is itself related to traditional norms in ancient times and current bargaining power
within the marriage.
Alesina, Alberto, Stelios Michalopoulos, and Elias Papaioannou. 2016. “Ethnic Inequality.” Journal of Political Economy 124 (2): 428-488.
Alesina, Alberto, Johann Harnoss, and Hillel Rapoport. 2016. “Birthplace Diversity and Economic Prosperity”.Abstract
We propose an index of population diversity based on people’s birthplaces and decompose it into a size (share of foreign-born) and a variety (diversity of immigrants) component. We show that birthplace diversity is largely uncorrelated with ethnic, linguistic or genetic diversity and that the diversity of immigration relates positively to measures of economic prosperity. This holds especially for skilled immigrants in richer countries at intermediate levels of cultural proximity. We partly address endogeneity by specifying a pseudo-gravity model predicting the size and diversity of immigration. The results are robust across specifications and suggestive of skill-complementarities between immigrants and native workers.
2015
Alesina, Alberto, Benedetta Brioschi, and Eliana La Ferrara. 2015. “Violence Against Women: A Cross-cultural Analysis for Africa”.Abstract
Using a new dataset constructed matching the Demographic Health Surveys with Murdock's Ethnographic Atlas, we investigate the determinants of violence against women in Africa. We focus on cultural determinants of violence arising from ancient living arrangements, types of economic activities and marriage patterns. Our outcomes include both violence actually experienced by women and attitudes towards domestic violence reported by men and women. We nd evidence consistent with two hypotheses. First, ancient socioeconomic conditions determine social norms about gender roles, family structures and intrafamily violence which persist over time even when the initial conditions change. We show that norms about marriage patterns, living arrangements and the productive role of women in ancient times are associated with contemporary violence. Second, women's economic role aects violence in a complex way. On the one hand, in societies where in pre-colonial times women had an active economic role and/or a brideprice was paid upon marriage, implying a high economic value of women, men are less prone to violence today. On the other hand,we find increases in domestic violence for couples where the woman is currently economically independent, i.e., where she may have more bargaining power and pose a threat to the husband.
Alesina, Alberto, Traviss Cassidy, and Ugo Troiano. 2015. “Old and Young Politicians.” NBER WP 20977.
NBER WP 20977
Alesina, Alberto, Michele Battisti, and Joseph Zeira. 2015. “Technology and Labor Regulations: Theory and Evidence”.
NBER WP 20841
Alesina, Alberto, Omar Barbiero, Carlo Favero, Francesco Giavazzi, and Matteo Paradisi. 2015. “Austerity in 2009-2013.” Economic Policy Journal.
Alesina, Alberto, and Matteo Paradisi. 2015. “Political Budget Cycles: Evidence from Italian Cities”.Abstract
The introduction of a new real estate taxes in Italy in 2011 generated a natural ex- periment, which is useful to test political budget cycles, i.e. the strategic choice of fiscal variables in relation to elections. We do find substantial evidence of political budget cy- cles, with municipalities choosing lower tax rates when close to elections. We observe this budget cycle only for smaller municipalities where the tax was more likely to be the single most important issue for
the local government. Cities close to elections with large deficits did not set lower rates before elections, probably because they felt the binding constraints
of budget rules.
NBER WP 20570
Alesina, Alberto, and Paola Giuliano. 2015. “Culture and Institutions.” Journal of Economic Literature.
Alesina, Alberto, Carlo Favero, and Francesco Giavazzi. 2015. “The Output Effect of Fiscal Consolidations.” Journal of International Economics.Abstract
We show that the correct experiment to evaluate the effects of a
scale adjustment is the simulation of a multi year
fiscal plan rather
than of individual
scale shocks. Simulation of
scale plans adopted
by 16 OECD countries over a 30-year period supports the hypothesis that the effects of consolidations depend on their design. Fiscal
adjustments based upon spending cuts are much less costly, in terms
of output losses, than tax-based ones and have especially low out-
put costs when they consist of permanent rather than stop and go
changes in taxes and spending. The difference between tax-based and
spending-based adjustments appears not to be explained by accompanying policies, including monetary policy. It is mainly due to the
different response of business confidence and private investment.
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2018-07-21 09:21:27
|
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https://www.shaalaa.com/question-bank-solutions/circles-examples-solutions-in-fig-1-pa-pb-are-two-tangents-drawn-external-point-p-circle-centre-c-radius-4-cm-if-pa-pb-then-length-each-tangent-is_48855
|
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# In Fig. 1, Pa and Pb Are Two Tangents Drawn from an External Point P to a Circle with Centre C and Radius 4 Cm. If Pa ⊥ Pb, Then the Length of Each Tangent Is: - CBSE Class 10 - Mathematics
ConceptCircles Examples and Solutions
#### Question
In Fig. 1, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PB, then the length of each tangent is:
• (A) 3 cm
• (B) 4 cm
• (C) 5 cm
• (D) 6 cm
#### Solution
Since APbotPB,CA botAP,CBbotBP
and AC = CB = radius of the circle, therefore APBC is a square having side equal to 4 cm.
Therefore, length of each tangent is 4 cm.
Is there an error in this question or solution?
#### Video TutorialsVIEW ALL [1]
Solution In Fig. 1, Pa and Pb Are Two Tangents Drawn from an External Point P to a Circle with Centre C and Radius 4 Cm. If Pa ⊥ Pb, Then the Length of Each Tangent Is: Concept: Circles Examples and Solutions.
S
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2019-08-23 22:55:29
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https://supportmymoto.com/what-is-20-percent-of-60000-2/
|
What is 20 percent of 60000? - SupportMyMoto
# What is 20 percent of 60000?
WRITTEN BY: supportmymoto.com STAFF
#### Answer for What’s 20 % of 60000:
20 % *60000 =
( 20:100)*60000 =
( 20*60000):100 =
1200000:100 = 12000
Now now we have: 20 % of 60000 = 12000
Query: What’s 20 % of 60000?
Step 1: Our output worth is 60000.
Step 2: We symbolize the unknown worth with {x}.
Step 3: From step 1 above,{60000}={100%}.
Step 4: Equally, {x}={ 20%}.
Step 5: This leads to a pair of straightforward equations:
{60000}={100%}(1).
{x}={ 20%}(2).
Step 6: By dividing equation 1 by equation 2 and noting that each the RHS (proper hand aspect) of each
equations have the identical unit (%); now we have
frac{60000}{x}=frac{100%}{ 20%}
Step 7: Once more, the reciprocal of each side provides
frac{x}{60000}=frac{ 20}{100}
Rightarrow{x} = {12000}
Due to this fact, { 20%} of {60000} is {12000}
#### Answer for What’s 60000 % of 20:
60000 % * 20 =
(60000:100)* 20 =
(60000* 20):100 =
1200000:100 = 12000
Now now we have: 60000 % of 20 = 12000
Query: What’s 60000 % of 20?
Step 1: Our output worth is 20.
Step 2: We symbolize the unknown worth with {x}.
Step 3: From step 1 above,{ 20}={100%}.
Step 4: Equally, {x}={60000%}.
Step 5: This leads to a pair of straightforward equations:
{ 20}={100%}(1).
{x}={60000%}(2).
Step 6: By dividing equation 1 by equation 2 and noting that each the RHS (proper hand aspect) of each
equations have the identical unit (%); now we have
frac{ 20}{x}=frac{100%}{60000%}
Step 7: Once more, the reciprocal of each side provides
frac{x}{ 20}=frac{60000}{100}
Rightarrow{x} = {12000}
Due to this fact, {60000%} of { 20} is {12000}
NOTE : Please do not copy - https://supportmymoto.com
|
2022-06-26 08:06:45
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https://strawberryfields.readthedocs.io/en/latest/code/api/strawberryfields.decompositions.covmat_to_hamil.html
|
# sf.decompositions.covmat_to_hamil¶
covmat_to_hamil(V, tol=1e-10)[source]
Converts a covariance matrix to a Hamiltonian.
Given a covariance matrix V of a Gaussian state $$\rho$$ in the xp ordering, finds a positive matrix $$H$$ such that
$\rho = \exp(-Q^T H Q/2)/Z$
where $$Q = (x_1,\dots,x_n,p_1,\dots,p_n)$$ are the canonical operators, and Z is the partition function.
For more details, see https://arxiv.org/abs/1507.01941
Parameters
• V (array) – Gaussian covariance matrix
• tol (int) – the number of decimal places to use when determining if the matrix is symmetric
Returns
positive definite Hamiltonian matrix
Return type
array
|
2020-12-02 04:10:05
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http://serverfault.com/questions/97164/can-i-use-plink-and-pageant-with-cygwins-ssh/97935
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Can I use PLink and Pageant with Cygwin's ssh?
I'm now using msysgit because of the GUI tools, which use Putty's Pageant and PLink utilities, but I use Cygwin as a general SSH terminal. I had been using ssh-agent on Cygwin, but that means I have to enter my SSH key passphrases for both SSH key managers. Is it possible to configure all my Unix-port tools (msys, git, cygwin, Ruby Net:SSH, etc.) to use PLink/Pageant instead of ssh-agent? It seems that's the kind of thing PLink was made for, but I can't find documentation on how.
-
I came across charade a while ago, which replaces ssh-agent and proxies to Pageant. At the time I couldn't quite get it working, and haven't had the chance to play with it since, but it might be worth a try. If you have any luck please post back and let me know, it's been on my list of things to do for ages!
-
I can confirm it works. (As can @Nightfly below) – Christopher Galpin May 17 '10 at 20:40
I would only add that before you build the package make sure that you have following packages in addition to default cygwin installation: make, gcc-core, keychain, psmisc, and of course openssh. This way if you follow very detailed instruction from the README file you will not get any errors – Alexander Pogrebnyak Sep 14 '10 at 15:49
I also wrote a proxy between openssh and pageant, which I call ssh-pageant. It looks like pretty much the same approach as charade, but I hadn't heard of it. Well in case you have trouble, I thought I'd throw out ssh-pageant to try instead.
-
You are looking to integrate ssh-agent and pageant so that you have only one keystore. One way you can do this is use PuTTY as your terminal, keep your keys in pageant, enable agent forwarding, run Cygwin sshd and ssh to localhost. This will give you an environment where keys are served by pageant over the ssh connection with PuTTY -- no need to run ssh-agent.
It should be possible to do the same with Plink. Just use the -A option, and use the resulting SSH_AUTH_SOCK setting in your interactive Cygwin sessions. Disclaimer: I have not tried this.
Edit: I have now tried this; it works just fine. I created a shortcut to PLINK:
"C:\path\to\PLINK.EXE" -A -ssh -l yournamehere localhost "echo \$SSH_AUTH_SOCK; while :; do sleep 86400; done"
Then, in a Cygwin terminal (I use PuTTYcyg of course):
export SSH_AUTH_SOCK=/tmp/ssh-crYQh24AMq/agent.3964
Seems to work great, but still requires a local sshd.
What would be really great is to have an openssh-compatible agent which communicates directly to the pageant keystore, but this won't happen unless someone writes such a beast. I looked into it many moons ago, and it seemed more trouble than it was worth given that this work-around is easy enough.
-
mmm, this not a bad idea at all. It's probably how I'll go. Thanks! And regarding your openssh-compatible agent, yes that's exactly what I was hoping plink could provide. It seems like it would be a pretty high value piece of code, since so much work goes into making software (like git) compatible with both openssh and plink. Why not just have a translation layer? Seems like "the Unix way" to do it. :) – Jerph Jan 3 '10 at 16:32
Could you go the other way and use puttycyg?
That way you have putty as your cygwin terminal.
-
I'm not sure what the consequences of using putty would be for my Cygwin scripts. I'm not really clear on where puttycyg inserts itself, I guess. I'll look into it - thanks! – Jerph Jan 3 '10 at 16:27
i would suggest the same thing (use putty) but just use putty as it intergrates better with pagent and plink, i use it along with msysgit but use the git bash provided by msysgit and it would fine, its a little tedious switching between consoles but the seperation can be good as well
-
I can't leave Cygwin, unfortunately. I depend on some of the packages it provides, not just pure ssh console stuff. Msys has its strengths ("better" integration with many Windows tools and the Windows version of Ruby, for instance) but it would be very difficult to migrate my Cygwin based scripts with the tools available on Msys. – Jerph Jan 3 '10 at 16:26
Another way to do it.
Add this line at the very top of .bash_profile
exec ssh-agent /usr/bin/bash
ssh-add ~/.ssh/myprivate
How does this link to Pageant? The question was about how to not use ssh-agent in addition to that. – Tobias Kienzler Apr 29 '13 at 7:21
|
2014-12-22 06:09:51
|
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|
https://remijaoui.github.io/
|
# Welcome to my webpage!
My name is Rémi Jaoui and I am a visiting assistant professor in the University of Notre Dame. I am working at the interaction between model theory, a branch of mathematical logic, and differential algebra. Here is a recent curriculum vitae .
## Autonomous algebraic differential equations
A central object of my research are systems of autonomous algebraic differential equations which are differential equations of the form $P(y,y’, \ldots, y^{(n)}) = 0$ where $$P$$ is a polynomial with complex coefficients . Such a differential equation can be represented geometrically as a complex algebraic variety X (defined by $$P = 0$$ and $$\frac {\partial P} {\partial x_n} \neq 0$$) endowed with a vector field $$v$$.
Similarly, one can represent differential equations appearing in classical mechanics in this form, as long as they only involve algebraic functions. This is the case of the geodesic flows, the movement of a rotating solid and many variants of the n-body problems. Such equations are often represented as pairs $$(M,v_H)$$, where $$(M,\omega)$$ is a symplectic variety and $$v_H$$ is the Hamiltonian function $$H \in \mathcal O (M)$$
Some motivating questions on autonomous differential equations $$(X,v)$$ are:
• Can the differential equation $$(X,v)$$ be solved using only “classical functions”? If it is possible, can it be achieved algorithmically?
• Given a finite collection of differential equations $$(X_1,v_1), \ldots , (X_r,v_r)$$, can $$(X,v)$$ be solved using only “classical functions” and solutions of $$(X_1,v_1), \ldots , (X_r,v_r)$$ ? If it is possible, can it be achieved algorithmically?
• Do the solutions of $$(X,v)$$ form large independent sets of meromorphic functions or do they share many algebraic relations?
## Geometric stability theory
A characteristic feature of these questions is that they can be formulated in the language of geometric stability theory at the level of the definable set associated to a differential equation $$(X,v)$$ in the theory $$\textbf{DCF}_0$$. So my point of view to study these questions is to use tools from the classical theory of differential equations and amplify them them using tools of geometric stability theory.
In the language of model theory, motivating questions are:
• Locate classical differential equations on the map of differentially closed fields provided by Zilber’s trichotomy.
• Develop effective tools to study the generic solutions of algebraic differential equation using geometric linearization data along a known particular solution.
• Study the variations of the semi-minimal analysis of a differential equations in families.
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2021-05-16 21:55:31
|
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https://pyviz-dev.github.io/panel/reference/panes/VTKVolume.html
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# VTKVolume#
import panel as pn
pn.extension('vtk')
The VTKVolume pane renders 3d volumetric data defined on regular grids. It may be constructed from a 3D NumPy array or a vtkVolume. The pane provides a number of interactive control which can be set either through callbacks from Python or Javascript callbacks.
## Parameters:#
For layout and styling related parameters see the customization user guide.
• max_data_size (Number): Maximum data size (in MB) of the data array allowed to be passed through the websockets without subsampling. If the data exceeded this size data are downsampled using scipy if installed or by taking 1 sample on N (N choosen to have an array size smaller than max_data_size) in each dimension
• object (ndarray or object): Can be a 3d numpy array or an instance ofvtkImageData class
• origin (3-tuple): Origin of the volume in the scene. By default value is (0,0,0)
• spacing (3-tuple): Define the distance between 2 adjacent voxels in the 3 dimensions. By default the value is (1,1,1)
• render_background (hexadecimal color string): Define the background color of the 3D rendering. By default value is ‘#52576e’
• camera (dict): A dictionary reflecting the current state of the VTK camera
• controller_expanded (bool): A boolean to expand/collapse the volume controller panel in the view. If True the controller is expanded else it is collapsed
• orientation_widget (bool): A boolean to activate/deactivate the orientation widget in the 3D pane. This widget is clickable and allows to rotate the scene in one of the orthographic projections.
• colormap (string): Name of the colormap used to transform pixel value in color. All allowed colormaps are referenced in PRESET_CMAPS in panel.pane.vtk.enums. By default the value is ‘erdc_rainbow_bright’
• rescale (boolean): If set to True the colormap is rescale beween min and max value of the non transparent pixels else the full range of the data are used. By default the value is True
• display_volume (boolean): If set to True, the 3D respresentation of the volume is displayed using ray casting. By default the value is True
• display_slices (boolean): If set to true, the orthgonal slices in the three (X, Y, Z) directions are displayed. Postition of each slice can be controlled using slice_(i,j,k) parameters. By default the value is False
• mapper (dict): Parameter to store on python side information about the color mapper set through the javascript widget in the 3d view. The format is {low, high, palette}.
Volume Rendering options
• sampling (Number): Parameter to adjust the distance between samples used for rendering. The lower the value is the more precise is the representation but it is more computationnaly intensive. By default the value is 0.4. The value bust be in (0, 1)
• edge_gradient (Number): Parameter to adjust the opacity of the volume based on the gradient between voxels. By default the value is 0.4. The value bust be in (0, 1)
• interpolation (String): Interpolation type for sampling a volume. nearest interpolation will snap to the closest voxel, linear will perform trilinear interpolation to compute a scalar value from surrounding voxels and fast_linear under WebGL 1 will perform bilinear interpolation on X and Y but use nearest for Z. This is slightly faster than full linear at the cost of no Z axis linear interpolation. By default the value is ‘fast_linear’. The options are among ‘fast_linear’, ‘linear’, ‘nearest’
Lighting options (affect only the volume rendering, not the slices)
• shadow (boolean): If set to false then the mapper for the volume will not perform shading computations, it is the same as setting ambient=1, diffuse=0, specular=0. By default the value is True
• ambient (Number): Value to control the ambient lighting. It is the light an object gives even in the absence of strong light. It is constant in all directions. By default the value is 0.2
• diffuse (Number): Value to control the diffuse Lighting. It relies on both the light direction and the object surface normal. By default the value is 0.7
• specular (Number): Value to control specular lighting. It is the light reflects back toward the camera when hitting the object. By default the value is 0.3
• specular_power (Number): Specular power refers to how much light is reflected in a mirror like fashion, rather than scattered randomly in a diffuse manner. By default the value is 8.0
Slices options
• slice_i (Integer): parameter to control the position of the slice normal to the X direction. By default the the value is computed to be in the middle of the data
• slice_j (Integer): parameter to control the position of the slice normal to the Y direction. By default the the value is computed to be in the middle of the data
• slice_k (Integer): parameter to control the position of the slice normal to the Z direction. By default the the value is computed to be in the middle of the data
• nan_opacity (Number): parameter to control the opacity of NaN values in a slice. By default the the value is 1. The value must be in (0, 1)
The simplest way to create a VTKVolume pane is to use a 3d numpy array. The spacing is used to produced a rectangular parallelepiped instead of a cube.
import numpy as np
data_matrix = np.zeros([75, 75, 75], dtype=np.uint8)
data_matrix[0:35, 0:35, 0:35] = 50
data_matrix[25:55, 25:55, 25:55] = 100
data_matrix[45:74, 45:74, 45:74] = 150
pn.pane.VTKVolume(data_matrix, sizing_mode='stretch_width', height=400, spacing=(3,2,1), interpolation='nearest', edge_gradient=0, sampling=0)
Alternatively the pane maybe constructed from a vtkImageData object. This type of object can be construct directly with vtk or pyvista module:
import pyvista as pv
from pyvista import examples
The VTKVolume pane exposes a number of options which can be changed from both Python and Javascript try out the effect of these parameters interactively:
pn.Row(volume.controls(jslink=True), volume)
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2022-07-04 20:58:18
|
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|
https://math.stackexchange.com/questions/2934247/finding-the-fourier-transform-of-de-lambda-lvert-x-rvert
|
# Finding the Fourier Transform of $De^{-\lambda \lvert x\rvert}$
I'm having trouble computing the Fourier transform of the following function:
$$y(x)=De^{-\lambda \lvert x\rvert}$$
It mainly has to do with the integration, I think, but I'll try to attempt it and illustrate where it all goes wrong.
$$\bar f(k) = \frac{D}{2\pi}\int_{-\infty}^{\infty}e^{ikx}e^{-\lambda \lvert x \rvert} \ dx$$
$$\bar f(k) = \frac{D}{2\pi}\int_{-\infty}^{\infty}e^{ikx-\lambda \lvert x \rvert} \ dx$$
From here I don't know how to integrate this. I tried a substitution, and quickly realized I couldn't due to the modulus. I was thinking it may be possible to convert the complex exponential into sines and cosines to try and integrate it by parts for each trigonometric component, but I don't think that will be doable since differentiating $$e^{-\lambda \lvert x \rvert}$$ will not allow for the typical way to integrate an exponential mutipled by a sine or cosine.
• $\int_{-\infty }^{\infty }{{}}=\int_{-\infty }^{0}{{}}+\int_{0}^{\infty }{{}}$ and think about the modulus of x over these ranges. – Paul Sep 28 '18 at 11:05
• Really the same as above, but first show that $\int_{-\infty}^\infty f(x){\rm d}x = \int_{0}^\infty [f(x)+f(-x)]{\rm d}x$. With this formulation $|x|$ is not a problem anymore. – Winther Sep 28 '18 at 11:19
$$$$\begin{split} \bar f(k) &\stackrel{(a)}{=} \frac{D}{2\pi}\int_{-\infty}^{\infty}e^{ikx}e^{-\lambda \lvert x \rvert} \ dx\\ &\stackrel{(b)}{=} \frac{D}{2\pi}\int_{-\infty}^{0}e^{ikx}e^{\lambda x } \ dx + \frac{D}{2\pi}\int_{0}^{\infty}e^{ikx}e^{-\lambda x} \ dx \\ &\stackrel{(c)}{=}\frac{D}{2\pi}\big( \frac{1}{\lambda + ik}e^{(\lambda+ik)x}\big]_{-\infty}^0 - \frac{1}{-\lambda + ik}e^{(-\lambda+ik)x}\big]^{\infty}_{0} \big)\\ &\stackrel{(d)}{=}\frac{D}{2\pi}\big( \frac{1}{\lambda + ik} - \frac{1}{-\lambda + ik} \big) \end{split}$$$$ In $$(a)$$ we used the definition of Fourier transform.
In $$(b)$$ we have split the integral and made use of $$\vert x \vert = -x$$ if $$x < 0$$ and $$\vert x \vert = x$$ if $$x \geq 0$$.
In $$(c)$$, we just integrated.
In $$(d)$$, we replaced the limits.
• How did you evaluate the limits of the $e^{(-\lambda + ik)x}$ integral in (c)? – sangstar Oct 3 '18 at 16:00
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2021-06-20 22:20:28
|
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https://techutils.in/blog/2020/09/06/stackbounty-page-breaking-glossaries-primitives-multiple-glossaries-on-a-single-page-with-a-chapter-title/
|
# #StackBounty: #page-breaking #glossaries #primitives Multiple glossaries on a single page with a chapter-title
### Bounty: 50
The setting is that I need to have two glossaries. They should be separated just by a `medskip` and not by a `newpage`-break. To stow them properly, I thought of putting them in a single chapter List of symbols.
The manual raises a warning when using the long-table style (e.g. `long3col`), but only for entries with long descriptions as there won’t be a page-break within a cell of a table. However, this does not apply here …
To suppress the page-break, I followed a comment of this post of nullifying the `newpage`-command temporarily (the accepted answer suggested to redefine `glsclearpage`, which didn’t work in my case and apparently for others neither)
``````begingroupletnewpagerelax
printglossary
printglossary
endgroup
``````
The odd thing is that this seems to suppress the appearing of the chapter-title:
The first chapter/glossaries produces six pages with a double page-break between the chapter title, the first glossary and the second glossary.
The second chapter/glossary attempt resulted in a page with both glossaries on but without any chapter-title (left); only if text is added, the chapter-title is printed (right):
``````documentclass{scrbook}
usepackage{glossaries}
% define alternative glossaries
newglossary[ulg]{UppercaseCharacter}{uld}{udn}{List of uppercase characters}
newglossary[llg]{LowercaseCharacter}{lld}{ldn}{List of lowercase characters}
% Term definitions
newglossaryentry{A}{name=A, description={This is an uppercase character}, type=UppercaseCharacter}
newglossaryentry{a}{name=a, description={This is a lowercase character}, type=LowercaseCharacter}
% activateglossaries
makeglossaries
setglossarystyle{long3col}
begin{document}
chapter*{List of symbols}
% Print the glossaries
printglossary[type=UppercaseCharacter] % domain glossary
printglossary[type=LowercaseCharacter] % domain glossary
chapter*{Tight list of symbols}
begingroupletnewpagerelax
printglossary[type=UppercaseCharacter] % domain glossary
bigskip
printglossary[type=LowercaseCharacter] % domain glossary
endgroup
chapter*{Tight list of symbols + Text}
dfgfgjfghj
begingroupletnewpagerelax
printglossary[type=UppercaseCharacter] % domain glossary
printglossary[type=LowercaseCharacter] % domain glossary
endgroup%clearpage
chapter{Content}
UPPERCASE: gls{A} and lowercase: gls{a}
end{document}
``````
It further seems to be impossible to control the vertical spacing within the Tex-primitive group or is this rather because the glossaries are not supposed to be on a single page?
Get this bounty!!!
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2020-11-29 04:15:19
|
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|
https://math.stackexchange.com/questions/3103172/what-does-u-2-2-mean
|
# What does $\|u\|^2_2$ mean?
Given a vector $$u = (x, y, z)$$ what is $$\|u\|_2^2$$ ?
The $$\| \cdot \|_2$$ function is the $$2$$-norm, i.e. the standard Euclidean length of a vector. Thus, $$\|(x, y, z)\|_2^2 = x^2 + y^2 + z^2.$$
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2019-04-22 16:49:34
|
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|
http://motls.blogspot.com/2010/02/ncdc-urbangate-how-urban-crap-was.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+LuboMotlsReferenceFrame+%28Lubos+Motl%27s+reference+frame%29
|
## Friday, February 26, 2010 ... /////
### NCDC UrbanGate: how the urban warming was exported to U.S. countryside
Edward Long, a retired NASA physicist, wrote a fascinating 14-page paper for SPPI that needs to be read and verified:
Contiguous U.S. temperature trends using NCDC raw and adjusted data for one-per-state rural and urban station sets (PDF, frames)
He looked at the NCDC surface temperature records of the 48 main U.S. states (you don't want me to spell "contiguous" right, do you?). If his work is valid, it is a shocker that actually reveals how the urban effects work and what a major team has done with them.
He took one rural and one urban station from each state among 48 of them. And let's hope he didn't cheat or cherry-pick.
This picture above, based on the raw data, shows the average rural temperatures and urban temperatures. They're almost perfectly aligned, except for a divergence that's been increasing since 1960 or so. If this graph is actually valid, it already shows you the urban effects. They became significant after the war and accumulated 0.6 °C of warming.
If you assume that 0.6 °C is the right urban contribution in Central Prague, which is exactly what I was assuming in my article about the Clementinum data, you will see that Prague has actually seen a modest cooling since 1800.
So this result, is valid, is amazing because it actually and cleanly shows how much the urban effects matter. It's equally important, but now for sociological considerations, to look at the "adjusted" data rather than the urban ones:
You can see that the adjusted data are made in such a way that the urban-rural difference largely disappears. But what's shocking is that the adjusted NCDC data are actually made to (approximately) agree with the urban, not rural raw station data! It means that the the urban effects were not eliminated. On the contrary, this urban warming has been added to the rural stations, too!
The "clean", purely natural rural figures have been contaminated by the bogus warming desired by the urban AGW believers.
This clearly needs to be verified because it's a potential bombshell. If he's right, the correct natural warming in the U.S. was around 0.1 °C per century, instead of 0.6 °C that follows from the "adjusted" NCDC (and probably also GISS) data, and this small 0.1 °C increment could be identified with the contribution of the growing rural population, too.
Via Anthony Watts' blog.
International investigation of Pachauri
A special meta-meeting in Bali ended with very secret conclusions and decisions that were only revealed to the readers of The Telegraph, WUWT, and this blog.
The IPCC's "crisis of confidence" meant that they decided to investigate whether Pachauri's management had anything to do with all the problems. Pachauri proposed that this investigation would be done by one of his friends on his paycheck. This is how it work have worked in the past. However, the British, German, Norwegian, Algerian, and Antigua-Barbudan environment ministers disagreed and they plan to do a real independent investigation of the IPCC!
So another U.N. climate panel will be created to view the U.N. IPCC panel that reviews the climate.
The diagram of U.N. panels on climate change.
The results of the investigation will be available by August. Lord Monckton, whose UKIP party plans to ban Gore's movie in the U.K. schools, has already predicted how this or another investigation will be concluded.
The ministers mostly didn't care whether there were lethal errors: they just disliked Pachauri's attacks on those who disagreed, e.g. the Indian report on the Himalayan glaciers. Too bad that they still don't care about the substance - just about the image.
Apple co-owner: Gore has become laughingstock
As some outlets describe, Gore was invited to Apple shareholders' meeting. On behalf of the sane shareholders, Shelton Ehrlich of Palo Alto spoke against Gore's reelection.
Gore has become a laughingstock. The glaciers have not melted. If his advice he gives to Apple is as faulty as his views on the environment then he doesn't need to be re-elected.
But don't get me wrong, there are many green nuts among the Apple shareholders, too. ;-) Some of them proposed their "sustainability proposals". Two such proposals were rejected. Gore was re-elected, together with Jobs and everyone else.
#### snail feedback (3) :
Oh, now this would explain why I saw graphs "corrected for UHI" and they were about as high as the urban temperatures. They apply the correction backwards. If it's true, it's a perversion.
|
2016-10-28 12:06:12
|
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|
https://2021.help.altair.com/2021.1/hwsolvers/ms/topics/solvers/ms/pointmass_api.htm
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# Point_Mass
Model ElementThe Point_Mass is an entity that has mass but no inertia properties.
Point_Mass
## Description
Three translational coordinates characterize the position of the Point_Mass. By default, the orientation of the Point_Mass is set to be the same as the global coordinate system. It never changes during simulation. Markers on Point_Mass may have location and orientation coordinates. The orientation of these Markers does not change during the simulation.
## Attribute Summary
Name Property Modifiable by command? Designable?
id Int ()
label Str ()
qg Location (Point()) Yes
zg Location () Yes
xg Location () Yes
zv Location () Yes
xv Location () Yes
reuler Angles () Yes
mass Double () Yes Yes
cm Reference ("Marker") Yes
vx Double (None) Yes FD Only
vy Double (None) Yes FD Only
vz Double (None) Yes FD Only
exact Exact ()
routine Routine ()
## Usage
Point_Mass (optional_attributes)
## Attributes
id
Integer
Specifies the element identification number. This number must be unique among all the Point_Mass objects in the model.
This attribute is optional. MotionSolve will automatically create an ID when one is not specified.
Range of values: id > 0
label
String
Specifies the name of the Point_Mass object.
This attribute is optional. When not specified, MotionSolve will create a label for you.
mass
Double
Specifies the mass of the Point_Mass object.
The attribute mass is optional. If a Point_Mass is fully constrained and you are not interested in the constraint forces, then mass needs not to be specified. When not specified, mass is set to zero.
Valid range of values: mass ≥ 0.0
cm
Reference to a Marker
Specifies the Marker that is located at the center-of-mass of the PART.
The attribute cm is optional. If a Point_Mass is fully constrained and you are not interested in the constraint forces, then mass and inertia need not to be specified. When these are not specified, you must not specify cm.
Note: In order to remove circular references, the body is created in two steps. First the body is defined without a CM marker. Then the CM attribute is explicitly defined.
qg
A Location object or a list of three doubles.
Specifies the coordinates of local part reference Marker. This Marker is used as the reference coordinate system for all Markers defined on this Point_Mass.
The qg attribute is optional. When not specified, it is assumed to be coincident with the global origin, (0, 0, 0).
zg
A Location object or a list of three doubles.
Specifies the coordinates of a point on the z-axis of the local part reference Marker. This Marker is used as the reference coordinate system for all Markers defined on this Point_Mass.
The zg attribute is optional. When not specified, the point is assumed to be on the global z-axis.
The zg/xg attribute is exclusive to zv/xv, reuler, and function. Only one of them may be specified.
xg
A Location object or a list of three doubles.
Specifies the coordinates of a point on the x-axis of the local part reference Marker. This Marker is used as the coordinate system for all Markers defined on this Point_Mass.
The xg attribute is optional. When not specified, the point is assumed to be on the global x-axis.
The zg/xg attribute is exclusive to zv/xv, reuler, and function. Only one of them may be specified.
zv
A Location object or a list of threedoubles.
Specifies the z-axis of the local part reference Marker. This Marker is used as the reference coordinate system for all Markers defined on this Part.
The zv attribute is optional. When not specified, the z-axis is assumed to be the global z-axis.
The zv/xv attribute is exclusive to zg/xg, reuler, and function. Only one of them may be specified.
xv
A Location object or a list of three doubles.
Specifies the x-axis of the local part reference Marker. This Marker is used as the coordinate system for all Markers defined on this Part.
The xv attribute is optional. When not specified, the x-axis is assumed to be the global x-axis.
The zv/xv attribute is exclusive to zg/xg, reuler, and function. Only one of them may be specified.
reuler
A list of three doubles.
Specifies the body-fixed 3-1-3 Euler angles of the local part reference Marker with respect to the global coordinate system. This Marker is used as the reference coordinate system for all Markers defined on this Point_Mass.
The reuler attribute is optional. When not specified, it is assumed to be (0,0,0), in other words, the local part reference Marker has the same orientation as the global coordinate system.
The reuler attribute is exclusive to function and zg/xg. Only one of them may be specified.
function
String
Specifies the list of parameters that are passed from the data file to the user-written defined.
The attribute function is optional.
The function attribute is exclusive to reuler and zg/xg. Only one of them may be specified.
routine
String or a pointer to a function.
Specifies an alternative name for the user subroutine.
The attribute routine is optional. The default name of the user subroutine is MASS_READ.
vx
Double
Specifies the initial translational velocity of the PART along the global x-axis.
The vx attribute is optional.
• When not specified, MotionSolve will perform an internal computation to ensure that all Point_Mass velocities are consistent with the first time derivative of the constraints.
• When specified, MotionSolve will try to maintain the value specified as it perform the internal computation to ensure that all Point_Mass velocities are consistent with the first time derivative of the constraints.
vy
Double
Specifies the initial translational velocity of the PART along the global y-axis.
The vy attribute is optional.
• When not specified, MotionSolve will perform an internal computation to ensure that all Point_Mass velocities are consistent with the first time derivative of the constraints.
• When specified, MotionSolve will try to maintain the value specified as it perform the internal computation to ensure that all Point_Mass velocities are consistent with the first time derivative of the constraints.
vz
Double
Specifies the initial translational velocity of the PART along the global z-axis.
The vz attribute is optional.
• When not specified, MotionSolve will perform an internal computation to ensure that all Point_Mass velocities are consistent with the first time derivative of the constraints.
When specified, MotionSolve will try to maintain the value specified as it perform the internal computation to ensure that all Point_Mass velocities are consistent with the first time derivative of the constraints.
exact
## Example
1. Referring to the 3-body problem in the XML Reference, specify the Sun as a Point_Mass.
sun = Point_Mass (Label="SUN", mass=3.328e5, vx=0, vy=0, vz=0)
sun.cm = Marker (body=sun, label="Sun’s center") #location defaults to [0,0,0]
2. Referring to the 3-body problem in the XML Reference, specify the Earth as a Point_Mass.
earth = Point_Mass (Label="EARTH", mass=1, vx=0, vy=2.445e3, vz=0)
earth.cm = Marker (label="Earth's center", qg=[389.2,0,0])
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2022-11-30 01:13:18
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https://quant.stackexchange.com/questions/31269/simple-simulation-model-of-bond-plus-cash-returns
|
Simple simulation model of bond plus cash returns
Is there a robust way to model 'bond plus cash' simulated returns, say in Excel, for an asset allocation problem between stocks vs bond plus cash?
For equity, mean 5% st dev 15% I would use X=U~[0,1] and R=N(X)~[0.05,0.15^2].
For bond, mean 3% st dev 6%, and for cash mean 2% st dev 2%.
The question is then two-fold:
• How do I easily truncate cash returns at 0
• How do I combine the return-risk assumption for both risk-less instruments.
• Are you saying that cash and bonds are riskless because, although there is a standard deviation, you are capping the loss at 0? This problem seems very unrealistic, so I would appreciate more details. Is there an original question? – RandyF Dec 1 '16 at 21:36
• No original. I'm making no assumptions on risky or risklessness. This is a question about simulations (say 5000,10000) given a distribution and what the distribution should be. Consider a DC pension lifestyling strategy that starts 100% equity and ends 0% eq 100% bond and cash at NRD. – rrg Dec 2 '16 at 8:37
• So, you want to have a varying percentage of equity and bonds through time? If so, how do you plan to shift from equity to bonds? I ask because this shift moves from requiring a 2d matrix of random numbers (2d if returns are dependent on each other; if independent, this can be done with 2 closed form equations) to a 3d matrix (a 2d matrix for each asset). – RandyF Dec 2 '16 at 15:23
• @RandyF not bothered about modelling the equity interdependence/covariance, forget it exists - just a bond/cash sketch as per qn. – rrg Dec 2 '16 at 15:56
$$weight_{eq} * (0.05 + 0.15 * rand()) + weight_{bnd} * (0.03 + 0.06 * rand()) + weight_{cash} * (0.02 + 0.02 * rand())$$
$$\frac{50-year}{50} (0.05 + 0.15 * rand()) + \frac {year}{50} (0.03 + 0.06 * rand()) + \frac {year}{50} (0.02 + 0.02 * rand())$$
• It should be $(1+r_1)*(1+r_2)*...*(1+r_n) - 1$ with correct compounding. $r_1+r_2+...+r_n$ can be very far off as the total term increases. – RandyF Dec 9 '16 at 19:31
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2019-05-25 14:25:28
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https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/169/4/c/b/
|
# Properties
Label 169.4.c.b Level $169$ Weight $4$ Character orbit 169.c Analytic conductor $9.971$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$169 = 13^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 169.c (of order $$3$$, degree $$2$$, not minimal)
## Newform invariants
Self dual: no Analytic conductor: $$9.97132279097$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-3})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 13) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$
## $q$-expansion
Coefficients of the $$q$$-expansion are expressed in terms of a primitive root of unity $$\zeta_{6}$$. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q + ( -3 + 3 \zeta_{6} ) q^{2} + ( 1 - \zeta_{6} ) q^{3} -\zeta_{6} q^{4} -9 q^{5} + 3 \zeta_{6} q^{6} -15 \zeta_{6} q^{7} -21 q^{8} + 26 \zeta_{6} q^{9} +O(q^{10})$$ $$q + ( -3 + 3 \zeta_{6} ) q^{2} + ( 1 - \zeta_{6} ) q^{3} -\zeta_{6} q^{4} -9 q^{5} + 3 \zeta_{6} q^{6} -15 \zeta_{6} q^{7} -21 q^{8} + 26 \zeta_{6} q^{9} + ( 27 - 27 \zeta_{6} ) q^{10} + ( 48 - 48 \zeta_{6} ) q^{11} - q^{12} + 45 q^{14} + ( -9 + 9 \zeta_{6} ) q^{15} + ( 71 - 71 \zeta_{6} ) q^{16} -45 \zeta_{6} q^{17} -78 q^{18} -6 \zeta_{6} q^{19} + 9 \zeta_{6} q^{20} -15 q^{21} + 144 \zeta_{6} q^{22} + ( 162 - 162 \zeta_{6} ) q^{23} + ( -21 + 21 \zeta_{6} ) q^{24} -44 q^{25} + 53 q^{27} + ( -15 + 15 \zeta_{6} ) q^{28} + ( 144 - 144 \zeta_{6} ) q^{29} -27 \zeta_{6} q^{30} + 264 q^{31} + 45 \zeta_{6} q^{32} -48 \zeta_{6} q^{33} + 135 q^{34} + 135 \zeta_{6} q^{35} + ( 26 - 26 \zeta_{6} ) q^{36} + ( -303 + 303 \zeta_{6} ) q^{37} + 18 q^{38} + 189 q^{40} + ( 192 - 192 \zeta_{6} ) q^{41} + ( 45 - 45 \zeta_{6} ) q^{42} -97 \zeta_{6} q^{43} -48 q^{44} -234 \zeta_{6} q^{45} + 486 \zeta_{6} q^{46} + 111 q^{47} -71 \zeta_{6} q^{48} + ( 118 - 118 \zeta_{6} ) q^{49} + ( 132 - 132 \zeta_{6} ) q^{50} -45 q^{51} -414 q^{53} + ( -159 + 159 \zeta_{6} ) q^{54} + ( -432 + 432 \zeta_{6} ) q^{55} + 315 \zeta_{6} q^{56} -6 q^{57} + 432 \zeta_{6} q^{58} -522 \zeta_{6} q^{59} + 9 q^{60} -376 \zeta_{6} q^{61} + ( -792 + 792 \zeta_{6} ) q^{62} + ( 390 - 390 \zeta_{6} ) q^{63} + 433 q^{64} + 144 q^{66} + ( 36 - 36 \zeta_{6} ) q^{67} + ( -45 + 45 \zeta_{6} ) q^{68} -162 \zeta_{6} q^{69} -405 q^{70} -357 \zeta_{6} q^{71} -546 \zeta_{6} q^{72} -1098 q^{73} -909 \zeta_{6} q^{74} + ( -44 + 44 \zeta_{6} ) q^{75} + ( -6 + 6 \zeta_{6} ) q^{76} -720 q^{77} -830 q^{79} + ( -639 + 639 \zeta_{6} ) q^{80} + ( -649 + 649 \zeta_{6} ) q^{81} + 576 \zeta_{6} q^{82} -438 q^{83} + 15 \zeta_{6} q^{84} + 405 \zeta_{6} q^{85} + 291 q^{86} -144 \zeta_{6} q^{87} + ( -1008 + 1008 \zeta_{6} ) q^{88} + ( 438 - 438 \zeta_{6} ) q^{89} + 702 q^{90} -162 q^{92} + ( 264 - 264 \zeta_{6} ) q^{93} + ( -333 + 333 \zeta_{6} ) q^{94} + 54 \zeta_{6} q^{95} + 45 q^{96} + 852 \zeta_{6} q^{97} + 354 \zeta_{6} q^{98} + 1248 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 3 q^{2} + q^{3} - q^{4} - 18 q^{5} + 3 q^{6} - 15 q^{7} - 42 q^{8} + 26 q^{9} + O(q^{10})$$ $$2 q - 3 q^{2} + q^{3} - q^{4} - 18 q^{5} + 3 q^{6} - 15 q^{7} - 42 q^{8} + 26 q^{9} + 27 q^{10} + 48 q^{11} - 2 q^{12} + 90 q^{14} - 9 q^{15} + 71 q^{16} - 45 q^{17} - 156 q^{18} - 6 q^{19} + 9 q^{20} - 30 q^{21} + 144 q^{22} + 162 q^{23} - 21 q^{24} - 88 q^{25} + 106 q^{27} - 15 q^{28} + 144 q^{29} - 27 q^{30} + 528 q^{31} + 45 q^{32} - 48 q^{33} + 270 q^{34} + 135 q^{35} + 26 q^{36} - 303 q^{37} + 36 q^{38} + 378 q^{40} + 192 q^{41} + 45 q^{42} - 97 q^{43} - 96 q^{44} - 234 q^{45} + 486 q^{46} + 222 q^{47} - 71 q^{48} + 118 q^{49} + 132 q^{50} - 90 q^{51} - 828 q^{53} - 159 q^{54} - 432 q^{55} + 315 q^{56} - 12 q^{57} + 432 q^{58} - 522 q^{59} + 18 q^{60} - 376 q^{61} - 792 q^{62} + 390 q^{63} + 866 q^{64} + 288 q^{66} + 36 q^{67} - 45 q^{68} - 162 q^{69} - 810 q^{70} - 357 q^{71} - 546 q^{72} - 2196 q^{73} - 909 q^{74} - 44 q^{75} - 6 q^{76} - 1440 q^{77} - 1660 q^{79} - 639 q^{80} - 649 q^{81} + 576 q^{82} - 876 q^{83} + 15 q^{84} + 405 q^{85} + 582 q^{86} - 144 q^{87} - 1008 q^{88} + 438 q^{89} + 1404 q^{90} - 324 q^{92} + 264 q^{93} - 333 q^{94} + 54 q^{95} + 90 q^{96} + 852 q^{97} + 354 q^{98} + 2496 q^{99} + O(q^{100})$$
## Character values
We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$$.
$$n$$ $$2$$ $$\chi(n)$$ $$-\zeta_{6}$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
22.1
0.5 + 0.866025i 0.5 − 0.866025i
−1.50000 + 2.59808i 0.500000 0.866025i −0.500000 0.866025i −9.00000 1.50000 + 2.59808i −7.50000 12.9904i −21.0000 13.0000 + 22.5167i 13.5000 23.3827i
146.1 −1.50000 2.59808i 0.500000 + 0.866025i −0.500000 + 0.866025i −9.00000 1.50000 2.59808i −7.50000 + 12.9904i −21.0000 13.0000 22.5167i 13.5000 + 23.3827i
$$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Inner twists
Char Parity Ord Mult Type
1.a even 1 1 trivial
13.c even 3 1 inner
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 169.4.c.b 2
13.b even 2 1 169.4.c.c 2
13.c even 3 1 169.4.a.c 1
13.c even 3 1 inner 169.4.c.b 2
13.d odd 4 2 169.4.e.d 4
13.e even 6 1 169.4.a.b 1
13.e even 6 1 169.4.c.c 2
13.f odd 12 2 13.4.b.a 2
13.f odd 12 2 169.4.e.d 4
39.h odd 6 1 1521.4.a.i 1
39.i odd 6 1 1521.4.a.d 1
39.k even 12 2 117.4.b.a 2
52.l even 12 2 208.4.f.b 2
65.o even 12 2 325.4.d.b 2
65.s odd 12 2 325.4.c.b 2
65.t even 12 2 325.4.d.a 2
104.u even 12 2 832.4.f.c 2
104.x odd 12 2 832.4.f.e 2
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
13.4.b.a 2 13.f odd 12 2
117.4.b.a 2 39.k even 12 2
169.4.a.b 1 13.e even 6 1
169.4.a.c 1 13.c even 3 1
169.4.c.b 2 1.a even 1 1 trivial
169.4.c.b 2 13.c even 3 1 inner
169.4.c.c 2 13.b even 2 1
169.4.c.c 2 13.e even 6 1
169.4.e.d 4 13.d odd 4 2
169.4.e.d 4 13.f odd 12 2
208.4.f.b 2 52.l even 12 2
325.4.c.b 2 65.s odd 12 2
325.4.d.a 2 65.t even 12 2
325.4.d.b 2 65.o even 12 2
832.4.f.c 2 104.u even 12 2
832.4.f.e 2 104.x odd 12 2
1521.4.a.d 1 39.i odd 6 1
1521.4.a.i 1 39.h odd 6 1
## Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator $$T_{2}^{2} + 3 T_{2} + 9$$ acting on $$S_{4}^{\mathrm{new}}(169, [\chi])$$.
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$9 + 3 T + T^{2}$$
$3$ $$1 - T + T^{2}$$
$5$ $$( 9 + T )^{2}$$
$7$ $$225 + 15 T + T^{2}$$
$11$ $$2304 - 48 T + T^{2}$$
$13$ $$T^{2}$$
$17$ $$2025 + 45 T + T^{2}$$
$19$ $$36 + 6 T + T^{2}$$
$23$ $$26244 - 162 T + T^{2}$$
$29$ $$20736 - 144 T + T^{2}$$
$31$ $$( -264 + T )^{2}$$
$37$ $$91809 + 303 T + T^{2}$$
$41$ $$36864 - 192 T + T^{2}$$
$43$ $$9409 + 97 T + T^{2}$$
$47$ $$( -111 + T )^{2}$$
$53$ $$( 414 + T )^{2}$$
$59$ $$272484 + 522 T + T^{2}$$
$61$ $$141376 + 376 T + T^{2}$$
$67$ $$1296 - 36 T + T^{2}$$
$71$ $$127449 + 357 T + T^{2}$$
$73$ $$( 1098 + T )^{2}$$
$79$ $$( 830 + T )^{2}$$
$83$ $$( 438 + T )^{2}$$
$89$ $$191844 - 438 T + T^{2}$$
$97$ $$725904 - 852 T + T^{2}$$
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2022-01-25 16:41:55
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https://phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_9HE_-_Modern_Physics/02%3A_Quantum_Mechanical_Formalism
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$$\require{cancel}$$
# 2: Quantum Mechanical Formalism
• 2.1: Wave Functions
At the heart of quantum mechanics is the wave function. Here we see how it fits into the mathematics of Hilbert space.
• 2.2: Dynamics of Quantum State Vectors
The quantum state vector doesn't just remain static, unchanging throughout time. Here we examine how it changes, and what governs this change.
• 2.3: Operations on Wave Functions
We introduced operators that act on Hilbert space vectors, to affect how they evolve with time. Now we look at what these operations look like in specific bases. The result is different, basis-specific, operators that act on the wave functions.
• 2.4: Stationary States
The hamiltonian is an operator that reflects the total energy of the quantum state, and it governs the time evolution of that state. Here we look at a subset of all the quantum states that is particularly useful.
• 2.5: Observables
We now look at the bridge between information contained in a quantum state and how that information is observed by experiment.
|
2019-03-21 21:13:31
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https://vroomlab.wordpress.com/2018/09/05/my-shot-at-harmonic-series/
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# My shot at Harmonic Series
To prove Beer Theorem 2 (see “Beer theorems and their proofs“) is to show that the Harmonic Series $1 + {1 \over 2} + {1 \over 3} + ...$ diverges.
Below is my shot at it.
Yaser S. Abu-Mostafa proved a theorem in an article titled “A differentiation test for absolute convergence” (see Mathematics Magazine 57(4), 228-231)
His theorem states that
Let $f$ be a real function such that ${d^2 f} \over {dx^2}$ exists at $x = 0$. Then $\sum\limits_{n=1}^{\infty} f({1 \over n})$ converges absolutely if and only if $f(0) = f'(0)=0$.
Let $f(x) = x$, we have
$\sum\limits_{n=1}^{\infty}f({1 \over n}) = \sum\limits_{n=1}^{\infty}{1 \over n}$,
the Harmonic Series. And,
$f'(x) = {d \over dx} x = 1 \implies f'(0) \neq 0$.
Therefore, by Abu-Mostafa’s theorem, the Harmonic Series diverges.
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2020-10-31 18:18:03
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https://rstudio-pubs-static.s3.amazonaws.com/550266_9d5acf97ddbf430fb0c8d4ab03f17ab7.html
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download.file("http://www.openintro.org/stat/data/mlb11.RData", destfile = "mlb11.RData")
load("mlb11.RData")
Exercise 1. What type of plot would you use to display the relationship between runs and one of the other numerical variables? Plot this relationship using the variable at_bats as the predictor. Does the relationship look linear? If you knew a team’s at_bats, would you be comfortable using a linear model to predict the number of runs?
Use scatterplot to display relationship between runs and at_bats. There is a positive correlation and roughly linear, I would be comfortable using a linear model to predict number of runs.
plot(mlb11$at_bats,mlb11$runs)
cor(mlb11$runs, mlb11$at_bats)
## [1] 0.610627
Sum of squared residuals
Exercise 2.Looking at your plot from the previous exercise, describe the relationship between these two variables. Make sure to discuss the form, direction, and strength of the relationship as well as any unusual observations.
The plot has positive correlation between at_bats and runs. There are a few outliers but the scatterplot does not show any curves, thus the relationship between 2 variables is roughly linear.
plot_ss(x = mlb11$at_bats, y = mlb11$runs)
## Click two points to make a line.
## Call:
## lm(formula = y ~ x, data = pts)
##
## Coefficients:
## (Intercept) x
## -2789.2429 0.6305
##
## Sum of Squares: 123721.9
plot_ss(x = mlb11$at_bats, y = mlb11$runs, showSquares = TRUE)
## Click two points to make a line.
## Call:
## lm(formula = y ~ x, data = pts)
##
## Coefficients:
## (Intercept) x
## -2789.2429 0.6305
##
## Sum of Squares: 123721.9
The linear model
m1 <- lm(runs ~ at_bats, data = mlb11)
summary(m1)
##
## Call:
## lm(formula = runs ~ at_bats, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -125.58 -47.05 -16.59 54.40 176.87
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2789.2429 853.6957 -3.267 0.002871 **
## at_bats 0.6305 0.1545 4.080 0.000339 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 66.47 on 28 degrees of freedom
## Multiple R-squared: 0.3729, Adjusted R-squared: 0.3505
## F-statistic: 16.65 on 1 and 28 DF, p-value: 0.0003388
Excercise 4. Fit a new model that uses homeruns to predict runs. Using the estimates from the R output, write the equation of the regression line. What does the slope tell us in the context of the relationship between success of a team and its home runs?
equation of regression line is y=1.8345x + 415.239. The slope indicates that the there is positive relationship between success of a tean and home runs.
m2 <- lm(runs ~ homeruns, data = mlb11)
summary(m2)
##
## Call:
## lm(formula = runs ~ homeruns, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -91.615 -33.410 3.231 24.292 104.631
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 415.2389 41.6779 9.963 1.04e-10 ***
## homeruns 1.8345 0.2677 6.854 1.90e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 51.29 on 28 degrees of freedom
## Multiple R-squared: 0.6266, Adjusted R-squared: 0.6132
## F-statistic: 46.98 on 1 and 28 DF, p-value: 1.9e-07
Prediction and prediction errors
plot(mlb11$runs ~ mlb11$at_bats)
abline(m1)
m1
##
## Call:
## lm(formula = runs ~ at_bats, data = mlb11)
##
## Coefficients:
## (Intercept) at_bats
## -2789.2429 0.6305
Exercise 5.If a team manager saw the least squares regression line and not the actual data, how many runs would he or she predict for a team with 5,578 at-bats? Is this an overestimate or an underestimate, and by how much? In other words, what is the residual for this prediction?
Manager can substitute x with 5578 and predict number of runs. She would estimate 728 runs. Doing a search in the table, there is a very close number of at_bats of 5579 from the phillies. The total runs were 713. Manager would overestimate by 14 runs.
###Model diagnostics
plot(m1$residuals ~ mlb11$at_bats)
abline(h = 0, lty = 3)
Exercise 6. Is there any apparent pattern in the residuals plot? What does this indicate about the linearity of the relationship between runs and at-bats?
there is no patter in the residual plot. This indicate that there is a linear relationship between runs and at_bats.
hist(m1$residuals) qqnorm(m1$residuals)
qqline(m1\$residuals)
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2020-06-04 15:47:24
|
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|
http://homepages.warwick.ac.uk/~masgar/Seminar/2020-01seminar.html
|
# Geometry and Topology Seminar
## Warwick Mathematics Institute, Term II, 2019-2020
Thursday January 9, 15:00, room MS.03 Henry Segerman (Oklahoma State) Essential loops in taut ideal triangulations Abstract: We combinatorialise a technique of Novikov. We use this to prove that, in a three-manifold equipped with a taut ideal triangulation, any vertical or normal loop is essential in the fundamental group. This is joint work with Saul Schleimer.
Thursday January 16, 15:00, room MS.03 None (None) None Abstract: None
Thursday January 23, 15:00, room MS.03 Jason Manning (Cornell) Groups acting improperly on cube complexes Abstract: A (proper) cubulation of a group $G$ is a $\CAT(0)$ cube complex $X$ together with a proper action of $G$ on $X$. Partial cubulation drops the properness assumption. Sometimes a partial cubulation can be promoted to a proper cubulation. Sometimes a proper cubulation can be improved by passing through a partial cubulation. I'll give examples of theorems of both types, focusing on hyperbolic and relatively hyperbolic groups. This is joint work with Daniel Groves.
Thursday January 30, 15:00, room MS.03 Nima Hoda (ENS Paris) Shortcut graphs and groups Abstract: Shortcut graphs are graphs in which sufficiently long cycles cannot embed without metric distortion. Shortcut groups are groups which act properly and cocompactly on shortcut graphs. These notions unify a surprisingly broad family of graphs and groups of interest in metric graph theory and geometric group theory. Among the these groups we find: systolic and quadric groups (in particular finitely presented $C(6)$ and $C(4)-T(4)$ small cancellation groups), cocompactly cubulated groups, hyperbolic groups, Coxeter groups and the Baumslag-Solitar group $BS(1,2)$. Most of these examples actually satisfy an even stronger form of the shortcut property. I will discuss the general constructions and properties of shortcut graphs and groups and illustrate the definitions with several of the above examples.
Thursday February 6, 14:00, room MS.01 Romain Tessera (Jussieu-Paris) Quantitative measure equivalence Abstract: Measure equivalence is an equivalence relation between countable groups that has been introduced by Gromov. A fundamental instance are lattices in a same locally compact group. According to a famous result of Orstein Weiss, all countable amenable groups are measure equivalent, meaning that geometry is completely rubbed out by this equivalence relation. Recently some more restrictive notions have been introduced such as $L^p$-measure equivalence, where the associated cocycles are assumed to be $L^p$-integrable. By contrast, a lot of surprising rigidity results have been proved: for instance Bowen has shown that the volume growth is invariant under $L^1$-measure equivalence, and Austin proved that nilpotent groups that are $L^1$-measure equivalent have bi-Lipschitz asymptotic cones. In this work we extend this study by trying to understand more systematically how the geometry survives through measure equivalence when an integrability condition is imposed. Our results go in two directions: we prove rigidity results, culminating for amenable groups with a general monotonicity result for the isoperimetric profile, and flexibility results showing that in many instances, the previous result is close to being optimal. We also prove a rigidity result for hyperbolic groups, showing the optimality of a result of Shalom for lattices in $\SO(n,1)$.
Thursday February 6, 15:00, room MS.03 Radhika Gupta (Bristol) Non-uniquely ergodic arational trees in the boundary of Outer space Abstract: The mapping class group of a surface is associated to its Teichmüller space. In turn, its boundary consists of projective measured laminations. Similarly, the group of outer automorphisms of a free group is associated to its Outer space. Now the boundary contains equivalence classes of arational trees as a subset. There exist distinct projective measured laminations that have the same underlying geodesic lamination, which is also minimal and filling. Such geodesic laminations are called non-uniquely ergodic. In this talk, I will first show a construction of such laminations for surfaces due to Gabai. I will then present a construction of a similar phenomenon for arational trees. This is joint work with Mladen Bestvina and Jing Tao.
Thursday February 13, 15:00, room MS.03 Rachel Roberts (Washington) Taut foliations from double-diamond replacements Abstract: I will give some basic background about taut foliations and their relationship to Heegaard-Floer homology, and define a readily recognizable type of sutured manifold decomposition, which we call double-diamond taut. I will show that if there is a double-diamond taut sutured manifold decomposition, then every boundary slope except one is strongly realized by a co-oriented taut foliation; that is, the foliation intersects the boundary of M transversely in a foliation by curves of that slope. This work is joint with Charles Delman.
Thursday February 20, 15:00, room MS.03 Eric Babson (Davis) Random fundamental groups Abstract: Various models of random two dimensional complexes have a sharp transition to simple connectivity at a density different from that for vanishing homology providing a range in which the fundamental group is nontrivial, Kazhdan and hyperbolic with no nontrivial small quotients. Along the way to apply Gromov's local to global hyperbolicity criterion we study two dimensional simplicial complexes with few faces and find that these have a form of positive curvature resulting in very restricted topology. One case of this phenomenon in two dimensions remains open and there are guesses for higher dimensional analogs. This project is joint work with Hoffman and Kahle.
Thursday February 27, 15:00, room MS.03 Tim Riley (Cornell) Conjugator length Abstract: The conjugator length function of a finitely generated group $G$ maps a natural number $n$ to the minimal $N$ such that if $u$ and $v$ are words representing conjugate elements of $G$ with the sum of their lengths at most $n$, then there is a word $w$ of length at most $N$ such that $u w = w v$ in $G$. I will explore why this function is important, will describe some recent results with Martin Bridson and Andrew Sale on how it can behave, and will highlight some of the many open questions about conjugator length.
Thursday March 5, 15:00, room MS.03 TBA (TBA) TBA Abstract: TBA
Thursday March 12, 15:00, room MS.03 CANCELLED Talia Fernós (UNC) Boundaries and $\CAT(0)$ cube complexes Abstract: The universe of $\CAT(0)$ cube complexes is rich and diverse thanks to the ease by which they can be constructed and the many of natural metrics they admit. As a consequence, there are several associated boundaries, such as the visual boundary and the Roller boundary. In this talk we will discuss some relationships between these boundaries, together with the Furstenberg-Poisson boundary of a "nicely'' acting group.
Information on past talks. This line was last edited 2019-01-11.
|
2022-01-24 22:58:25
|
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http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.255002
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# Synopsis: Tabletop Particle Accelerator
Dense electron-positron streams, similar to those found in astrophysical jets, can be made using a relatively simple tabletop laser setup.
Black holes and pulsars emit dense jets of particles that are made of electrons and positrons (the antiparticle of the electron). But many important and basic features of the jets remain unclear: What is their precise particle makeup? How much energy do they contain? How do the particles in the jets interact in the low-density environment of outerspace? The main difficulty in answering these questions is that astronomical systems can only be measured indirectly: the closest jet is almost ${10}^{24}$ miles away. As Gianluca Sarri from The Queen’s University of Belfast, Northern Ireland, and colleagues report in Physical Review Letters, a new tabletop method for generating electron-positron streams could bring measurements closer to home by enabling the scaled-down reproduction of matter-antimatter flows in the lab.
Sarri et al. used the University of Michigan’s powerful HERCULES petawatt laser to ionize an inert gas and produce a high-energy electron beam. By bombarding copper, tin, tantalum, and lead targets with this beam, they were able to form dense, narrow streams of high-energy electrons and positrons. The jets emerged in shorter duration, denser pulses than those generated in traditional large-scale ($\sim \text{km}$ size) particle accelerators.
The laser-based system, which is less than a meter in size, is able to simultaneously form jets and plasmas, something that cannot be done easily using other methods. This simple setup could therefore be used to directly probe the interaction between the jets and plasmas in well-controlled laboratory experiments. Such studies could provide answers to some of the fundamental questions about antimatter, astrophysical jets, and, ultimately, the physics of black holes and pulsars. – Katherine Thomas
### Announcements
More Announcements »
## Previous Synopsis
Biological Physics
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### Synopsis: Pentaquark Discovery Confirmed
New results from the LHCb experiment confirm the 2015 discovery that quarks can combine into groups of five. Read More »
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2016-09-01 03:38:46
|
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http://mathhelpforum.com/number-theory/419-find-prime-factor-99-1-a-print.html
|
# Find a prime factor of 99!-1
• June 7th 2005, 03:12 AM
cornoth
Find a prime factor of 99!-1
Find a prime factor of 99!-1
• June 14th 2005, 05:12 PM
hpe
Quote:
Originally Posted by cornoth
Find a prime factor of 99!-1
101, because 101 is prime and $99! \equiv -100! \equiv 1$ in $Z_{101}$
• June 16th 2005, 05:19 AM
cornoth
oh thats right, wilson's theorem.
thanks hpe!
|
2015-07-29 16:02:50
|
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|
https://math.stackexchange.com/questions/936775/prime-number-theorem-lemma-prove-that-psix-sim-pix-logx
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# Prime number theorem lemma: prove that $\psi(x)\sim\pi(x)\log(x)$
I'm trying to follow the proof in Wikipedia that the PNT is equivalent to the assertion $\psi(x)\sim x$, by proving that $\psi(x)\sim\pi(x)\log x$, which it claims is a very simple proof. One direction of inequality is an actual bound, $\psi(x)\le\pi(x)\log x$, but the other inequality has a fuzz factor:
$$\psi(x) \ge \sum_{x^{1-\epsilon}\le p\le x} \log p\ge\sum_{x^{1-\epsilon}\le p\le x}(1-\epsilon)\log x=(1-\epsilon)(\pi(x)+O(x^{1-\epsilon}))\log x.$$
But this doesn't actually complete the proof, because we want $\psi(x)\ge(1-\epsilon)\pi(x)\log x$ without the fuzz factor. If we take large enough $x$ and use $\epsilon/2$ in the above equation we get
$$\psi(x)\ge(1-\epsilon/2)\pi(x)\log x+Ax^{1-\epsilon/2}\log x,$$ so it is sufficient to prove that $Ax^{1-\epsilon/2}\le\frac{\epsilon}2\pi(x)$ for sufficiently large $x$, i.e. $x^{1-\epsilon/2}\in o(\pi(x)),$ and although I am sure there is a proof of this, it's not so simple that the proof can be completely omitted, at least as far as I can see. Is there an easy proof to be found here? The only one I am seeing is Chebyshev's weak version of the PNT, $\frac x{\log x}\in O(\pi(x))$, which takes some significant work to prove.
• IMO, the lower bounds are far more elegantly obtained by using $\frac{x}{(\log x)^k}$ as the cut-off point than with $x^{1-\epsilon}$. – Daniel Fischer Nov 25 '17 at 22:23
• @DanielFischer Could you elaborate? It seems that this would only make the fuzz factor worse in the equation. – Mario Carneiro Nov 26 '17 at 2:35
• $$\pi(x)\log x\leqslant \sum_{p \leqslant \frac{x}{(\log x)^2}} \log x+ \log x \sum_{\frac{x}{(\log x)^2} <p \leqslant x} \frac{\log p}{\log p}\leqslant \frac{x}{(\log x)^2}\log x+ \frac{\log x}{\log x - 2\log \log x} \sum \log p \leqslant \frac{x}{\log x} + \frac{1}{1 - 2\frac{\log \log x}{\log x}}\vartheta(x)$$ for $x \geqslant 3$, using the trivial $\pi(y) \leqslant y$ and $\vartheta(x)- \vartheta(y) \leqslant \vartheta(x)$, and $\log p > \log \frac{x}{(\log x)^2} = \log x - 2\log \log x$ for $p > \frac{x}{(\log x)^2}$. You get explicit bounds (which one could make sharper), no fuzz factor. – Daniel Fischer Nov 26 '17 at 14:15
You have: $$\psi(x)\geq (1-\varepsilon)\sum_{x^{1-\varepsilon}<p<x}\log x \geq (1-\varepsilon)(\pi(x)-\pi(x^{1-\varepsilon}))\log x$$ but, by the Chebyshev bound: $$\frac{\pi(x^{1-\varepsilon})}{\pi(x)}\leq\frac{1.11\frac{x^{1-\varepsilon}}{(1-\varepsilon)\log x}}{0.92\frac{x}{\log x}}\leq \frac{1.21}{1-\varepsilon}\, x^{-\varepsilon}\tag{1}$$ is enough to prove that: $$\psi(x)\geq (1-\tilde{\varepsilon})\,\pi(x)\log x.$$ To replace $(1)$ with something easier to prove than the Chebyshev bound, you can use $\pi(x^{1-\varepsilon})\leq x^{1-\varepsilon}$ and any suitable lower bound for $\pi(x)$.
• @MarioCarneiro: it is not necessary, but it is necessary to prove that the density of the primes in $[1,x]$ does not drop to zero too fast. Any bound like $\pi(x)\geq\frac{x}{(\log x)^{\eta}}$ for a positive $\eta$ does the job. – Jack D'Aurizio Sep 18 '14 at 17:54
• For instance, it is not difficult to prove that $$\pi(x)\geq \frac{x}{\log^2 x}$$ with elementary sieve methods and the Buchstab identity. – Jack D'Aurizio Sep 18 '14 at 17:59
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2019-10-15 11:56:59
|
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https://www.learncax.com/knowledge-base/blog/by-tag/cfd?start=10
|
### FREE Webinar : How to Select your CFD Academic Project ?
on September 04, 2014
in Webinar
Any academic degree, let it be bachelors or masters, ends with a project work. The project work is one of the most critical parts of any academic degree. It is so important that it always decides what’s going to be next for the student. Let it be higher studies or industrial job, the whole career path (at least the starting point of that path) is based on the project work. Listen to the webinar recording in which basic rules of CFD project selection are discussed. The webinar also contains aspects like CFD project complexity matrix, CFD learning curve and sample project ideas.
### Basics of Y Plus, Boundary Layer and Wall Function in Turbulent Flows
on July 25, 2014
in CFD
Before getting into the details of the turbulent models let us discuss an important concept known as $y^{+}$ and know how it is related to turbulence modeling, mesh generation process and how it is going to affect the CFD end result. It is important to know about the concept of wall $y^{+}$ or in general how the flow behaves near the wall, to consider the effects near the wall as it is the basis on which choice of the turbulence model is governed.
### Turbulence Parameter Calculator at Inlet Boundary
on July 09, 2014
When modelling turbulent flows in CFD, turbulence models require the specification of turbulence variable values at the inlet boundaries. There are several ways to provide turbulence parameters at boundaries. This calculator gives all the turbulence values based on inlet conditions like velocity or mass flow rate, inlet area and fluid properties. It calculates all turbulence values like Turbulent Kinetic Energy ($k$), Turbulent Dissipation ($\epsilon$), Specific Rate of Dissipation ($\omega$), Turbulent Viscosity Ratio ($\mu_t/\mu$), Turbulence Intensity ($\textit{I}$) and Turbulence Length Scale ($\textit{l}$).
### Career Path to CFD Engineer
on June 30, 2014
in CFD
In recent years, there has been growing interest by various engineering product companies to perform design simulation studies at different stages of product development to compete in the market. This has consistently resulted in increased requirement of skilled CFD resources and proving to be a very good career opportunity for engineers aspiring to make a career in the interesting domain of heat transfer and fluid flows. However there seems to be a widespread confusion in the student community as to what skills are desired by these industries for a fresher to qualify.
### Introduction to Turbulence and Turbulence Modeling
on May 15, 2014
in CFD
Understanding the turbulent behaviour of fluids is one of the most fascinating, forbidding & critical problems in all of classical physics. Turbulence is omnipresent, as most of the fluid flows are turbulent in nature right from the microscopic level at interior of biological cells to the macroscopic scales of the geophysical and astrophysical phenomena including planetary interiors, oceans and atmospheres that represent the dominant physics of turbulent fluid flows.
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2018-08-21 03:53:36
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http://mathoverflow.net/questions/24430/why-are-rational-cherednik-algebras-so-rational
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# Why are rational Cherednik algebras so… rational?
The real question is both more serious and somewhat longer than the title.
For the definition of the rational Cherednik algebra attached to a complex reflection group $W$, see for instance 5.1.1 of Rouquier's paper here. It is a flat family of algebras depending on some parameters $h_{H,j}$ indexed by pairs consisting of a $W$-orbit of reflecting hyperplanes $H$ and an integer $0 \leq j \leq e_H-1$, where $e_H$ is the order of the pointwise stabilizer of $H$.
Various features of the structure of the Cherednik algebra turn out to be governed by systems of linear equations with rational coefficients in the parameters. For instance, in this paper Dunkl and Opdam show that the polynomial representation is irreducible exactly if the parameters avoid a certain locally finite system of rational hyperplanes, and in this paper a couple of guys show that it is Morita equivalent to its spherical subalgebra off a certain set of rational hyperplanes. In this paper, Etingof shows (for real reflection groups) that the set of parameters for which the irreducible head of the polynomial representation is finite dimensional is a set described by linear conditions with rational coefficients on the parameters.
Every time someone discovers the set of parameters for which the rational Cherednik algebra satisfies some reasonable properties, it winds up being described linearly in the parameters with rational coefficients. Why?
(I'm asking for a conceptual reason---in each case I mentioned I know the proof. For instance, I'd love to know an a priori proof that the set of parameters where the RCA is not Morita equiv. to its spherical subalgebra is a finite union of rational hyperplanes, without necessarily giving the union explicitly)
-
Partial answers, hints, and references to similar phenomena in other places are encouraged! – GS May 12 '10 at 20:40
By the way,Etingof taught a graduate course at MIT last semester on this very topic and was kind enough to post the lecture notes for the course. We need more cutting edge researchers doing this;kudos to Etingof and many thanks. The notes can be found here: www-math.mit.edu/~etingof/18.735notes.pdf – Andrew L May 13 '10 at 16:11
The phenomenon seems the same as for affine Kac-Moody algebras, where rational level is where everything special happens, or quantum groups, where roots of unity are the exceptional locus (and of course these examples are related). The parameter for Cherednik algebras is an additive/Lie algebra type parameter, like the KM level, as opposed to the exponentiated version as in the quantum groups case. If you mod out by the action of translation functors, you're asking why finite order points of the parameter are special. I don't know that I can give a completely uniform answer, but it certainly seems reasonable.
For example in type A, modules for Cherednik algebras are realized using twisted D-modules on some stack. The parameter for twisting is an additive one, but the abstract category of twisted D-modules depends only on this parameter mod integral translations (hence translation functors). At integral points (or rather "the" integral points) many special things happen -- there are geometric obstructions to the existence of objects with various supports, and these obstructions vanish integrally -- which is why say category O for Lie algebras becomes much bigger integrally. More generally twisted D-modules can be described as sheaves on a gerbe, which depends only on the twist mod integers. If (and certainly only if) the parameter is rational - ie the twist is a torsion element - then you might expect to represent your gerbe by an Azumaya algebra, or equivalently to have finite rank twisted sheaves. I would imagine this general type of phenomenon is behind the results you mention, though I haven't thought about the specifics. But in any case this is a geometric phenomenon about categories of twisted D-modules in general, and as we know "basically all interesting categories of representations are some categories of twisted D-modules" so this is quite general.
-
I guess one obvious issue is that it is really the spherical subalgebra which seems to be most tightly connected to D-modules, so maybe it's not fair to expect those methods to have much to say about the relationship between the full RCA and its spherical subalgebra? On the other hand, maybe you can say something about Varagnolo-Vasserot determination of the spherical, finite dimensional modules for the one-parameter DAHA of a Weyl group? – GS May 13 '10 at 11:20
Dear Stephen -- yes, sorry, I only think of the spherical subalgebra. I would hope/expect all types to have some kind of D-modulish description eventually.. eg the arguments in the recent Etingof paper (with your appendix) sound awfully (wonderfully) D-modular. But yes at this point this is just an analogy/heuristic outside type A spherical and some variants.. – David Ben-Zvi May 13 '10 at 13:43
Which is of course exactly what I was asking for. Thanks! Do you have any suggestions for reading up on this sort of thing for KM algebras? BTW, I really appreciated your answer to David Jordan's DAHA question---it's a great resource for stuff I don't know as much about as I should! – GS May 13 '10 at 17:59
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2014-03-12 11:30:00
|
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|
https://www.tutorialspoint.com/can-main-be-overloaded-in-cplusplus
|
# Can main() be overloaded in C++?
In C++, we can use the function overloading. Now the question comes in our mind, that, can we overload the main() function also?
Let us see one program to get the idea.
## Example
#include <iostream>
using namespace std;
int main(int x) {
cout << "Value of x: " << x << "\n";
return 0;
}
int main(char *y) {
cout << "Value of string y: " << y << "\n";
return 0;
}
int main(int x, int y) {
cout << "Value of x and y: " << x << ", " << y << "\n";
return 0;
}
int main() {
main(10);
main("Hello");
main(15, 25);
}
## Output
This will generate some errors. It will say there are some conflict in declaration of main() function
To overcome the main() function, we can use them as class member. The main is not a restricted keyword like C in C++.
## Example
#include <iostream>
using namespace std;
class my_class {
public:
int main(int x) {
cout << "Value of x: " << x << "\n";
return 0;
}
int main(char *y) {
cout << "Value of string y: " << y << "\n";
return 0;
}
int main(int x, int y) {
cout << "Value of x and y: " << x << ", " << y << "\n";
return 0;
}
};
int main() {
my_class obj;
obj.main(10);
obj.main("Hello");
obj.main(15, 25);
}
## Output
Value of x: 10
Value of string y: Hello
Value of x and y: 15, 25
|
2023-02-04 23:03:58
|
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https://www.thelittleaussiebakery.com/what-is-bandwidth-in-kernel-density-estimation/
|
# What is bandwidth in kernel density estimation?
## What is bandwidth in kernel density estimation?
Its kernel density estimator is. where K is the kernel — a non-negative function — and h > 0 is a smoothing parameter called the bandwidth. A kernel with subscript h is called the scaled kernel and defined as Kh(x) = 1/h K(x/h).
## How is the kernel density estimate calculated?
Kernel Density Estimation (KDE) It is estimated simply by adding the kernel values (K) from all Xj. With reference to the above table, KDE for whole data set is obtained by adding all row values. The sum is then normalized by dividing the number of data points, which is six in this example.
What is bandwidth in density plot?
The bandwidth defines how close to r the distance between two points must be to influence the estimation of the density at r. A small bandwidth only considers the closest values so the estimation is close to the data. A large bandwidth considers more points and gives a smoother estimation.
How do you select bandwidth kernel density estimation?
When kernel function is the density of standard Normal distribution, then the “Rule-of-Thumb” bandwidth selector for kernel location estimation is Both (14) and (16) infer that the larger the location of in absolute value is, the smaller the optimal bandwidth is needed.
### What is Box kernel density estimation block of histogram?
Block in thewhat is box kernel density estimate? Histogram is centered over the data points block in the histogram is averaged somewhere blocks of the histogram are combined to form the overall block blocks of the histogram are integrated.
### Why is kernel density estimation used?
Kernel density estimation is a technique for estimation of probability density function that is a must-have enabling the user to better analyse the studied probability distribution than when using a traditional histogram.
What is kernel density estimation GIS?
Kernel density estimation is an important nonparametric technique to estimate density from point-based or line-based data. In a GIS environment, kernel density estimation usually results in a density surface where each cell is rendered based on the kernel density estimated at the cell center.
What is multilevel kernel density analysis?
It focuses on the multilevel kernel density analysis (MKDA) framework, which has been used in recent studies to evaluate consistency and specificity of regional activation, identify distributed functional networks from patterns of co-activation, and test hypotheses about functional cortical-subcortical pathways in …
#### How do you explain a kernel density plot?
A density plot is a representation of the distribution of a numeric variable. It uses a kernel density estimate to show the probability density function of the variable (see more). It is a smoothed version of the histogram and is used in the same concept.
#### What is Epanechnikov kernel?
An Epanechnikov Kernel is a kernel function that is of quadratic form. AKA: Parabolic Kernel Function. Context: It can be expressed as $K(u) = \frac{3}{4}(1-u^2)$ for $|u|\leq 1$. It is used in a Multivariate Density Estimation.
What does a kernel density plot show?
How to decide whether a kernel density estimate is good?
Motivating KDE: Histograms ¶. As already discussed,a density estimator is an algorithm which seeks to model the probability distribution that generated a dataset.
• Kernel Density Estimation in Practice ¶.
• Example: KDE on a Sphere ¶.
• Example: Not-So-Naive Bayes ¶.
• ## How to get a function from a kernel density estimation?
Plotting the density function and comparing the shape to the histogram.
• Sampling the density function and comparing the generated sample to the real sample.
• Using a statistical test to confirm the data fits the distribution.
• ## How to visualize a kernel density estimate?
– Everywhere non-negative: K (x)≥0 ∀ x∈X – Symmetric : K (x) = K (-x) ∀ x∈X – Decreasing : K` (x) ≤ 0 ∀ x >0
What is ‘kernel’ in kernel density estimation?
– Density level set estimation. The level set of the density \\ (f\\) at level \\ (c\\geq0\\) is defined as \\ (\\mathcal {L} (f;c):=\\ {\\mathbf {x}\\in\\mathbb {R}^p: f (\\mathbf {x})\\geq c\\}\\). – Clustering or unsupervised learning. – Classification or supervised learning. – Description of the main features of the data.
Posted in General
|
2022-08-15 15:09:44
|
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https://dsp.stackexchange.com/questions/10187/units-of-fft-frequency/10188
|
# Units of FFT frequency
I'm having some trouble understanding FFT plots and measures.
According to this, this will give me the magnitude plot of FFT, but I want the area under from 1 to 10 Hz for example.
Is this next formula I made right?
My doubt is, what's the relation between Hz and rad/s, f and w?
The formula you made will work if what you are after is simply "the area under the the magnitude plot from $\omega_i$ to $\omega_f$."
In many cases you can think of Hz as meaning "rotations per second." In that case, it becomes more obvious that 1 rotation = 2$\pi$ radians. Since $f$ has units of Hz and $\omega$ has units of radians, the conversion is simply: $$1 \, \text{Hz} = 2 \pi \, \frac{\text{rad}}{\text{s}}$$ So evaluate your integration from $\frac{1}{2\pi}$ to $\frac{10}{2\pi}$ and you should have the result you are after.
|
2019-08-23 23:44:20
|
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|
http://www.sacredduty.net/2012/03/23/i-have-the-annual-pass-wheres-my-beta-invite/?shared=email&msg=fail
|
# I have the Annual Pass. Where’s my Beta Invite?
Oh man, it’s Friday evening. Crap! I am contractually obligated to rage about one (1) thing per week on Sacred Duty and I completely forgot to rage this week. How fortunate that I have such a great topic today. I have an annual pass, and I didn’t get a MOP beta invite yesterday. Time to rage, right?!
No. I am not in the beta yet — and unlike about half the Blizz official forums, I totally understand why.
Well, first of all, I was a little late on my Annual Pass subscription…
When I heard about the annual pass, I was in the audience at Blizzcon hanging out with some of my favorite people and friends: my guild. We were watching the announcement of Annual Pass together. I looked around at my friends and thought, yep, I will play video games with these people for a year easily. So I figured I would sign up for Annual Pass right there, in the audience. I pulled out my phone and started navigating to Battle.net.
I was so close to signing up right there.
Well, if you were at Blizzcon or watching, you know what came next. They announced the new expansion. That video. I actually enjoyed it. I thought Blizz was playing a pretty sweet joke on us– I giggled at a whole lot of it. April fool’s come… six months early? I waited for the punchline. And waited. And waited. And then it hit me: they weren’t trolling at all. They were serious.
PANDAS. WOW. REALLY?
I sat there with my jaw on the floor. PANDAS. PANDAS. WHAT. I do not think I have ever nerdraged about anything as badly as I nerdraged about the MOP announcement. I was pretty much furious. Fortunately a couple of my friends were raging right along with me although others (NOT NAMING ANY NAMES HERE) were obnoxiously and gleefully excited about becoming a panda shaman with beer keg totems. Blegh. You can take your beer keg totems and shove ’em. So I raged and raged, Annual Pass plans completely forgotten.
A month or two later, I thought about it, and sighed. Time to have an honesty moment. Pandas are pretty much irrelevant. WOW could have Expansion 10: Hello Kitty Island and as long as there are raids and my guild is raiding, I will be online ready to go 3 nights a week. I like raiding and I will continue to raid. No quitting for me. Might as well. So I signed up.
Fastforward to March 2012 when I heard the beta had been released.
Here’s the story. I was at work. I heard beta was out. Oh boy!Now, I still despise pandas, but there is something I despise more: poorly tested content. I am a raider and you better be damn sure that I think raiders should be testing their raid and dungeon content. So I very much want to be in the beta to test that stuff. Also, betas are cool and fun and I want to be there.
So, like millions of others, I checked my Battle.net account. I didn’t have access. I was sad, but I wasn’t too surprised. Ah well. I’ll be in some other beta wave, that is nice to know, I’ll see it sometime. I wonder when they’ll invite me? I was about a month late signing up for Annual Pass. My wow account dates back to (late) vanilla, but I’ve only been consistently subscribed since 2009. I do not fall into the category of Beta Wave 1. I wonder what wave I’ll be in? Ah well. I sadly went back to work.
Yeah, that was it.
Wait, Ana. Why aren’t you raging?
I’m disappointed, but whatever. There are more waves!
However, apparently there is a brand of people who are so very disappointed in their lack of beta access that they have gone back and convinced themselves that they were promised DAY 1 IMMEDIATE ACCESS.
All I have to say is…. What?
It’s a beta. A beta. You don’t all get in at once. That is not how a beta works! Have any of these people ever seen a beta? Do we realize that the point of a beta is to beta test? Did anyone honestly think we were going to get into the beta all on the same date? If Blizz sent out one million invites on the same day, that would be a pretty fucking shitty beta. That would be worthless. I cannot understand how anyone wanted them to do this, and I cannot understand how anyone is angry that they didn’t do it.
But oh boy, are they loud. Go read Wow Insider’s post on it or go read one of the 400 forum posts. A bunch of super expert people who are jealous they’re not in beta have picked apart Blizzards wording at great length and found vague quote #2958 / vague advertisement from last year / something scratched on the wall in the bathroom at Blizz HQ where someone who words there vaguely said the word “release” or “live” and so we were all promised 100% of beta from day 1.
I am sure there is tons of proof and I’m advised that there is actual legal proof of it somewhere in fine print. Way to go, loophole experts. You win? And common sense loses.
Here is what I thought I was promised with my own annual pass. Betas happen in waves. What I was promised (along with diablo 3 and my mount) was that knowledge that when the Beta goes live and the waves start happening, in one of those waves, my name would be included and I would become a beta tester.
And to people who are arguing that Blizz promised day 1 access: Well… I’m sorry you are so jealous but let’s have a bit of patience here. We’ll all get into the beta eventually.
Oh my god Ana, stop telling me I don’t have the right to be mad.
Oh, feel free to be mad right now.
I am a little mad. Even though I hated on MOP, I still want to see the beta of the game that I play so much. After all, beta access will allow me to precision target my hatred. We annual pass subbers who don’t have access, we are jealous. We are jealous beyond belief. I want to stab my (beloved awesome) guildmate Omega (who is a good friend) in the face every time he talks to me about his beta access (which is quite often). I love you Omega but it’s true, you talk about it all the time. And I am jealous beyond comprehension. That goes for the rest of my twitter feed too and all you damn MVPs and news sites with access. (It’s OK Omega, and the rest of my twitter feed, keep telling me about beta…)
So yeah, I’m jealous. Let’s all be jealous together.
But let’s agree to stop doing something retarded. Let’s all agree to stop complaining that Blizz was legally obligated to give us access on Day 1. I know how you feel. I’m jealous too. I’m raging too. But I’m not trying to convince the world that I was promised something that common sense would dictate would never in a million years happen.
Just as an aside, I really like that Blizzard promised us Annual Pass.
I love it. It was both a great marketing decision and a very intelligent game testing decision. Annual passers are exactly the people I want in the beta. We represent a wide variety of players whose common attribute is that we are hooked into to the Blizzard I.V. of MMO Crack for 12 months. We are the rabid fans. We are often very vocal in our respective communities, and we love WOW enough to commit for a year. We are pretty much exactly the crop of people who I want to be in the beta.
So they stuck it on there. “You’ll have beta access!” YES! Awesome. We ate it up.And now it’s a customer service nightmare because jealous forum trolls are raging hardcore. This is why we can’t have nice things. This is exactly why.
Well. I like it when Blizzard tacks beta access onto a package that already included a mount and a free game. Regardless of what their very ill conceived wording was. I like it when Blizzard makes decisions like “Who makes good beta testers? Annual Pass subscribers! PERFECT!” I like it when Blizz gives me a guarantee that I’ll eventually be in a beta wave… I know I’ll see it and that’s what I was promised.And yeah, I think we have a right to watch closely how long it takes Blizz to send out those waves, and I welcome people to rage about whether or not they’re in beta. I support rage. I am an expert rager.
You are welcome as usual to also rage at me in the comments section about how wrong I am to insult you for your Day 1 Beta belief.
But I still think you are silly — and trolling. And I will happily tell you so.
And if you disagree? If you bought Annual Pass for the beta? For DAY ONE 100% OF THE BETA access? If you think Blizz cheated you out of your moneys? Well, you can call Blizzard and complain and I’ll bet you’ll be able to cancel your Annual Pass if you feel that you were not provided with something that you paid for. And frankly: good riddance. If you are mad enough about Beta Day 1 to post novels on the forums screaming at Blizzard, then you are the troll that I do not want on my Blizz forums. I not so respectfully submit that I hope the door does not hit your ass on the way out.
The rest of us will get our access to the beta. In a beta wave. Like how betas have always worked.
Which is exactly what we were promised.
(I hope it’s soon because wow, I want to be in the beta.)
(Also, GC… still waiting on that pony.)
This entry was posted in Blogging, From Ana's Inbox, Raiding. Bookmark the permalink.
### 34 Responses to I have the Annual Pass. Where’s my Beta Invite?
1. Esoth says:
I am not exactly angry at Blizzard and certainly didn’t make any posts about it, but I do have some anxiety about when I will get into the beta. The beta, in my opinion, is important for everyone who wants to process the data live, as it is being developed instead of having it digested for them by some idiot on a blog (sorry). It’s the opportunity to go in there and see the classes before anyone really has the experience to say much about them – you get to figure it out on your own. Or maybe you will be one of the trendsetters for people that do want easy to digest information.
I want to go in there and actually do testing and give my feedback because as a “hardcore” raider with about 6 years dedicated to the game I have some vested interest in it. (I don’t want to seem like a ME3 fan whining the developers should listen to their demands, I am just saying I have a reasonable, vested interest). The frustrating thing is that it is completely out of my control whether I get to be a part of this process. While others get in and contribute to class development, scout out the cool new things, find bugs, or even just brag to their friends – I am excluded. If I felt excluded from raiding difficult content I could actually earn it by getting better and playing with other better players, but I can’t do anything about this.
I was hoping that the annual pass would mean that those that really wanted to be a part of the beta process would get to, but the fact that they oversold it and have way too many people for it makes me anxious. If I only get in the last couple weeks of a three month beta so that they can technically meet their legal obligation, I’ll feel cheated. Give me a chance to get in there and prove I can provide meaningful feedback – or give up the pretense of beta being about meaningful feedback if it’s just a promotional gimmick unfairly distributed. I think the fans have a right to be angry if it’s only being served for the latter purpose.
• anafielle says:
Just to respond to this:
“If I only get in the last couple weeks of a three month beta so that they can technically meet their legal obligation, I’ll feel cheated. ”
So will I, absolutely. I will firmly believe that is within their right. I will absolutely, just as firmly believe that that is shitty, very shitty. And I will be vocal about how shitty it is. “Shitty” and “legally wrong” are two really very different things.
But– and maybe I just have more faith in Blizzard than the usual — I don’t believe they will do that. Yes, I think that reasonably it will take 4-6 weeks to get all the Annual Passers in. I think there will be waves. But I think they won’t take that long to get us all in.
• zothen says:
I wouldn’t have felt cheated. I bought the annual pass because I already pay 12 months at a time (saves money), and wtf free Diablo 3. When it was announced at blizzcon, he actually did not say “Mists of Pandaria”. He specifically said “you will be guaranteed a spot in the beta for our next expansion”.
Now, clearly he meant “MoP” and not WoW 6.x (whatever expac comes after MoP). But that’s not what he said. I recall being a little confused by the choice of wording, but ultimately I knew I was going to be playing WoW for at least 12 more months and I wanted to play D3 as well. So the Annual Pass was a no-brainer.
Sure, I would love to be in the first wave of beta invites (I think I signed up for the pass that first afternoon). But I am patient. Hell, I still haven’t finished ME3 and as some of my guildies may have noticed, work has been kicking me in the balls lately with overtime. So all MoP beta would do right now is cut into my sleep time.
The beta invite waves are a sheer matter of logistical sanity. There are only a few PTR servers (3 now I think?), and I would imagine that Beta is about the same. 1 million people signed up for Annual Pass. That’s fully 10% of the total WoW population. A population that is served by approximately **240 servers**. If they opened the floodgates and gave all 1 million Annual Pass holders beta access, that would be the equivalent of taking twenty four production servers and merging them all at once, and THEN every player on that newly merged server tries to log in all at the same time.
That won’t end well for anybody.
So, I imagine what they are doing is letting through in batches, knowing a lot will play for a short while and then forget until launch. So when it tapers down after a wave, they will let another batch through. At some point they will probably provision more servers as needed, but I wouldn’t expect them to bring any more servers online than they absolutely need. After all, in a few months the extra hardware will be turned back off.
2. Fantastic post Ana. You have voiced my thoughts exactly. Sure I am raging to get in there (I am raging more than you because I have had a steady subscription since June, 2005, and bought my annual pass the day it was announced), but I am NOT going to go “yell” at Blizzard.
When i heard that the Annual Pass was going to give Beta access, I immediately assumed that Annual Passers wouldn’t get in until late in the beta. As it looks now, I will probably get in long before I was expecting to. (<–Gravy).
• anafielle says:
“I am raging more than you because I have had a steady subscription since June, 2005, and bought my annual pass the day it was announced”
DAMNIT. You are wave 2. I am probably like…. wave 4 or 5.
Thanks for the comment!
3. Stormy says:
No. Just no. But thanks for the self-righteous attitude–it’s much appreciated.
I purchased a product. I have not received said product. I agreed to pay Blizzard Entertainment $179.88, and I have faithfully made every installment due since the inception of our agreement. In exchange, I would receive access to the current World of Warcraft content for 12 months, an in-game mount, a copy of Diablo III if and when it is ever released (the release schedule of which is at least four months behind schedule–D3 was) and I would get to participate in the Mists of Pandaria beta. The Mists of Pandaria beta was launched in the late evening of Wednesday, March 23, 2012, with no advance notice from Blizzard, and three days later there has been no communication from the seller as to when the product I purchased would be delivered or a timetable for receiving said product. At best, this is shitty customer service. At worst, it’s a failure to deliver a product I have paid$180 for. At this point Blizzard’s lucky there’s not a class action suit pending.
But hey, you got a self-righteous “I’m so awesome and everyone else is an asshole!” blogpost out of it, so, hey, bully for you.
• Stormy says:
Sigh–I went back to add another thought to my comment and got distracted…
…D3 was supposed to have been the “Ooh shiny!” to distract us for a few months in between the death of Cataclysm and the launch of MOP, to keep us distracted and off Blizzard’s heels for a bit so they could concentrate on MOP without everyone screaming for a release. At this point D3 is supposed to be released 5/15 and we’re looking at an MOP release in either June or July. So much for a shiny object.
• Kerriodos says:
You paid for a product and you will get the product. It’s no different than a pre-order; you guarantee access, but you do not guarantee access on day one. The contract you signed does not say day one, and they do not own you day one. The sense of entitlement in the WoW community is simply staggering. If everyone who signed up got access day one, you know who would be testing right now? No one. Because the servers would be down constantly.
But no, all at once is a great fucking plan.
• Sahiel says:
Fankly, I’d be fine with giving all those “I R HAS CONTRAKT I DMEAND DAY 1 AXESSS!” people access immediately, on one server, with each other, no options to pick a different beta server for the duration. Then let everyone else in in waves on multiple servers. The whiners get their access (to a constantly crashing/full server), everyone who is happy to wait and actually understands the reality of a beta test gets access to stable servers with room. Problem solved, “contractual obligations” (lol) upheld.
Oh, and I got in the beta too Ana. <3 😉
• anafielle says:
FIRING UP HATE MACHINE
AIMING FOR: SAHIEL
ps: thanks for the comment, it’s good to know that I am not alone in my frustration with these idiots.
• anafielle says:
You think I’m self righteous. I think you’re a troll. Unfortunately we’re both going to just end up angry at each other because we both think the other is insulting. What I don’t get is how you don’t understand how your opinion is insulting to me, and to the rest of us that are pretty happy Blizz promised us beta– and who are very unhappy that a bunch of really vocal people are ruining what was a lovely promise for everyone.
“I would get to participate in the Mists of Pandaria beta.” <— Where did you get promised day 1 access? In what universe does everyone who gets into a beta get in on day 1? In what fantasy universe does a beta start with hundreds of thousands of people getting access on the same day? Betas happen in waves. Beta would probably be CRAP if it didn't happen in waves. That is how a beta works and it is how a beta has always worked. Let's keep in mind here that the point of the beta is to test and create a good game in the end. MOP will be better because Blizzard is doing the beta right. Our anger at not being invited at the same time as Boubouille and WOW Insider doesn't make it any more reasonable or intelligent to think that we should have been. My soapbox is secure.
Just like you said. You were promised beta access. And you'll get it.
I had access to the D3 beta too. Does not getting it on Day 1 mean I had any less access? Nope. I had access. And I'll have access to MOP too. EXACTLY what I paid for and I'm damn well happy with it.
Sorry if you thought I was self righteous, but that post is exactly what I think. And thanks for commenting with the disagreement, even if I'm sure that you are quite unhappy with my response.
• Stormy says:
You’re absolutely right that we are not going to agree on the definition of “beta access”, so there’s not much point in arguing about it. As far as the posters on the forums who are apparently offending your sensibilities simply by, y’know, existing, Blizzard could assuage the entire situation by simply announcing a schedule. “Wave 1 begins March 21. Wave 2 begins April 3. Wave 3 begins April 15…” Instead, we’re left with Blizzard’s trademark answer of “soon.” Since I do have several years of experience as a Blizzard customer, telling me that I will get in “soon” should immediately sound an alarm in my head that says “Yeah, you’ll get in a week before the beta ends.” That is the crux of my frustration right now. I understand that launching essentially a separate MMO with one million players in the space of a week is not at all feasible, but at this point Blizzard has my money and I have jack. THAT is why I’m angry.
• Kerriodos says:
The fact that you expect a beta, which is fluid by it’s very nature, to be planned that well amuses me to no end. You know why they don’t say that? People like you who bitch and moan when things don’t go absolutely perfectly. And if you expect beta to go perfectly, you’ve missed the point entirely.
Also, you have WoW access. You’re not actually paying any extra for that by signing the Annual Pass; you just promised to keep up a subscription for a year–it cost the same as if you’d never signed the contract. Instead, you get a bunch of free shit, and apparently the right to be an over-entitled whiner.
• zothen says:
And the contract also allows him/her to bail early if this is so upsetting. They would only lose their place in line for beta, and would no longer get a license for D3, and the Tyrael’s Charger mount would also be removed. But there is no penalty other than that for terminating early.
It’s not like a cell phone contract or anything.
• zothen says:
You might find some answers from blue posts here: http://blue.mmo-champion.com/topic/219382-beta/
Some salient quotes:
“You will be getting into the beta if you have an Annual Pass. Don’t worry. We just got the beta up last night and while we’ve already done some invites, we have a lot more to do.”
“We’re very aware that everyone is expecting to be in as soon as possible and we’re committed to doing what we can to make that happen. We just ask that everyone is a little patient as we make that happen.”
“I don’t have a timeline to share with you at this time, but we’ll do our best to communicate when these waves of invites happen; even if it’s to help players avoid potential phishing scams.”
• zothen says:
Also, while I can’t find the original source at this moment, I do recall reading a post from a blue earlier today that specifically addressed the concern that people might not get access until the last few days (or weeks, whatever) of a multi-month beta. The response was a clear “no”. Their intention is not to delay any annual pass holders that long.
4. Omega says:
As someone in beta, I can tell you, asside from a 1-12 panda start area, and some prelliminary start tallents that are buggy to all hell
Hunters soloing EVERYTHING
there isn’t much to do. I pretty much did what i’m gonna do in beta in about 3 hours until they release more content. there are no new dungeons, there are no new raids. there are no new zones to test. You can scrap together a pug of sheer fail and wipe in DS if you want. But I can do that on live too. The waves that matter the most are later anyways. I’m confident by time actual raids or heroics or challenge modes are out, everyone will get their fair shot at those, and that’s what truely matters. The next annual pass wave will probably be quite massive. Wave 1 was small by comparison to rest because they just fired the on switch and are gauging things right now. Asside from client instability, the beta servers have zero lag. I haven’t seen them crashing or really being bad either. They have been restarted a few times, hotfixes and what not. (The dungeons that were available for testing very briefly were a mistake and immediately removed. They do not want those tested yet). Point being though. there is PLENTY more room, so don’t worry, invites are coming.
• anafielle says:
“As someone in beta…”
I love you Omega. So much. <3
5. Pliers says:
I picked up WoW the day of release. I was in the BC beta, and F&F Alpha for WotLK and Cataclysm. I want to get MoP access asap, for two reasons: I want to know what I will be doing when the expansion actually drops (if I want to swap mains, if it’s worth keeping time open in my schedule to play, etc), and I want to give (what I hope will be) valuable feedback on the game and class mechanics, to improve everyone else’s experience. If not for these two reasons, I would not be touching the beta.
If you’re just looking to play MoP early, it’s really not that great an idea.
Playing it now will make it far less enjoyable when it actually lands. There will be bugs, errors, crashes, connection issues, and a ridiculous number of changes. If you play through everything now, you will enjoy it significantly less when MoP finally arrives. You’re watching the shaky-cam version of a movie with no sound and amateurly translated subtitles, right before you go and watch it at the IMAX.
6. Ryan says:
Shoot, with the limited amount of content and weird bugs and all, I hope I get put in a late wave of invites. Thanks for the post. People need to chill out.
7. saltyquacker says:
Entitled gamers? In my Blizzard game?
It’s more likely than you think…
8. Xsinthis says:
Frankly I was disappointed I didn’t get into Day 1 Beta, but I’m over it now. It’s not like I’d actually do much testing, I’d probably just spend the whole time rolling around as Pandas 😛
As a side note, I’m much more angry about that Moose Ghostcrawler promised us
9. edawan says:
Can I rage against people who rage against the Pandas ? I honestly do not understand what it is that annoys you so much…
• anafielle says:
Ana’s blog is a free-rage zone. You may rage about whatever you’d like!
Pandas… I don’t like them. I don’t know if I can explain why I like the rest of wow and why I feel like pandas take it down to a 12 year old’s level. Like honestly, I can’t explain it; I know there are people who feel like you do and people who feel like we do. And couldn’t they have come up for a name for the new continent that was actually a name and not “Pandaria”? Honestly… Pandaria?! I feel like the name of expansion is like at least 1/3 of my problem with it. Anyways, you and your ilk are right though and we are stupid to rage, it’s just a game. I hate them anyways though. I’m getting used to the idea….. the art like the mounts on MMO-C are pretty freaking sweet.
• zothen says:
Yeah those cloud serpents are very impressive. Too bad no Blizzcon this year. A four-person cloud serpent dragon costume would have been amazing.
10. Cel says:
The last I heard Blizz had really cracked down on AP holders canceling on them. The rumor was that you could call Customer Service and cancel, but, after bitter arguing with a CS Supervisor, we’re still paying a monthly fee for a player who was wowed by Blizzcon and disgusted with DS and hasn’t played in 3 months. Not that that person wants beta access anyway
• Greg says:
I can vouch for this here.. if you have an Annual Pass and attempt to cancel your account through your battle.net account, it gives you an error stating “You committed to a one year annual pass and your account is unable to be closed until October 21, 2012″ or whatever your date might be.
I haven’t tried to raise a stink over the phone because its just \$15/month and I might log in once a month to chat with some friends, but the option to cancel appears to be all but gone.
11. Scot says:
I don’t think it has anything to do with when you signed up. I’ve been a WOW subscriber since release – Day 1. I signed up for the Annual Pass when it was announced. I don’t have a beta invite yet so I’m guessing it must be a random process.
12. Galvarius says:
Sooo, where exacly would I find my beta invite besides my email? Yeah, I know…Dumb question. 😛
• anafielle says:
They have said that the emails aren’t always going out so you’ll want to log into your battle.net account online and click on Manage My Games. You’ll see a World of Warcraft MOP beta “game” under it if you’re in!
• Galvarius says:
Thanks! Also, long live paladin tanks,,/ ^ /
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2020-01-29 08:53:11
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https://au.mathworks.com/help/stats/fitrkernel.html
|
# fitrkernel
Fit Gaussian kernel regression model using random feature expansion
## Syntax
``Mdl = fitrkernel(X,Y)``
``Mdl = fitrkernel(Tbl,ResponseVarName)``
``Mdl = fitrkernel(Tbl,formula)``
``Mdl = fitrkernel(Tbl,Y)``
``Mdl = fitrkernel(___,Name,Value)``
``[Mdl,FitInfo] = fitrkernel(___)``
``[Mdl,FitInfo,HyperparameterOptimizationResults] = fitrkernel(___)``
## Description
`fitrkernel` trains or cross-validates a Gaussian kernel regression model for nonlinear regression. `fitrkernel` is more practical to use for big data applications that have large training sets, but can also be applied to smaller data sets that fit in memory.
`fitrkernel` maps data in a low-dimensional space into a high-dimensional space, then fits a linear model in the high-dimensional space by minimizing the regularized objective function. Obtaining the linear model in the high-dimensional space is equivalent to applying the Gaussian kernel to the model in the low-dimensional space. Available linear regression models include regularized support vector machine (SVM) and least-squares regression models.
To train a nonlinear SVM regression model on in-memory data, see `fitrsvm`.
example
````Mdl = fitrkernel(X,Y)` returns a compact Gaussian kernel regression model trained using the predictor data in `X` and the corresponding responses in `Y`.```
````Mdl = fitrkernel(Tbl,ResponseVarName)` returns a kernel regression model `Mdl` trained using the predictor variables contained in the table `Tbl` and the response values in `Tbl.ResponseVarName`.```
````Mdl = fitrkernel(Tbl,formula)` returns a kernel regression model trained using the sample data in the table `Tbl`. The input argument `formula` is an explanatory model of the response and a subset of predictor variables in `Tbl` used to fit `Mdl`.```
````Mdl = fitrkernel(Tbl,Y)` returns a kernel regression model using the predictor variables in the table `Tbl` and the response values in vector `Y`.```
example
````Mdl = fitrkernel(___,Name,Value)` specifies options using one or more name-value pair arguments in addition to any of the input argument combinations in previous syntaxes. For example, you can implement least-squares regression, specify the number of dimension of the expanded space, or specify cross-validation options.```
example
````[Mdl,FitInfo] = fitrkernel(___)` also returns the fit information in the structure array `FitInfo` using any of the input arguments in the previous syntaxes. You cannot request `FitInfo` for cross-validated models.```
example
````[Mdl,FitInfo,HyperparameterOptimizationResults] = fitrkernel(___)` also returns the hyperparameter optimization results when you optimize hyperparameters by using the `'OptimizeHyperparameters'` name-value pair argument. ```
## Examples
collapse all
Train a kernel regression model for a tall array by using SVM.
When you perform calculations on tall arrays, MATLAB® uses either a parallel pool (default if you have Parallel Computing Toolbox™) or the local MATLAB session. To run the example using the local MATLAB session when you have Parallel Computing Toolbox, change the global execution environment by using the `mapreducer` function.
`mapreducer(0)`
Create a datastore that references the folder location with the data. The data can be contained in a single file, a collection of files, or an entire folder. Treat `'NA'` values as missing data so that `datastore` replaces them with `NaN` values. Select a subset of the variables to use. Create a tall table on top of the datastore.
```varnames = {'ArrTime','DepTime','ActualElapsedTime'}; ds = datastore('airlinesmall.csv','TreatAsMissing','NA',... 'SelectedVariableNames',varnames); t = tall(ds);```
Specify `DepTime` and `ArrTime` as the predictor variables (`X`) and `ActualElapsedTime` as the response variable (`Y`). Select the observations for which `ArrTime` is later than `DepTime`.
```daytime = t.ArrTime>t.DepTime; Y = t.ActualElapsedTime(daytime); % Response data X = t{daytime,{'DepTime' 'ArrTime'}}; % Predictor data```
Standardize the predictor variables.
`Z = zscore(X); % Standardize the data`
Train a default Gaussian kernel regression model with the standardized predictors. Extract a fit summary to determine how well the optimization algorithm fits the model to the data.
`[Mdl,FitInfo] = fitrkernel(Z,Y)`
```Found 6 chunks. |========================================================================= | Solver | Iteration / | Objective | Gradient | Beta relative | | | Data Pass | | magnitude | change | |========================================================================= | INIT | 0 / 1 | 4.307833e+01 | 4.345788e-02 | NaN | | LBFGS | 0 / 2 | 3.705713e+01 | 1.577301e-02 | 9.988252e-01 | | LBFGS | 1 / 3 | 3.704022e+01 | 3.082836e-02 | 1.338410e-03 | | LBFGS | 2 / 4 | 3.701398e+01 | 3.006488e-02 | 1.116070e-03 | | LBFGS | 2 / 5 | 3.698797e+01 | 2.870642e-02 | 2.234599e-03 | | LBFGS | 2 / 6 | 3.693687e+01 | 2.625581e-02 | 4.479069e-03 | | LBFGS | 2 / 7 | 3.683757e+01 | 2.239620e-02 | 8.997877e-03 | | LBFGS | 2 / 8 | 3.665038e+01 | 1.782358e-02 | 1.815682e-02 | | LBFGS | 3 / 9 | 3.473411e+01 | 4.074480e-02 | 1.778166e-01 | | LBFGS | 4 / 10 | 3.684246e+01 | 1.608942e-01 | 3.294968e-01 | | LBFGS | 4 / 11 | 3.441595e+01 | 8.587703e-02 | 1.420892e-01 | | LBFGS | 5 / 12 | 3.377755e+01 | 3.760006e-02 | 4.640134e-02 | | LBFGS | 6 / 13 | 3.357732e+01 | 1.912644e-02 | 3.842057e-02 | | LBFGS | 7 / 14 | 3.334081e+01 | 3.046709e-02 | 6.211243e-02 | | LBFGS | 8 / 15 | 3.309239e+01 | 3.858085e-02 | 6.411356e-02 | | LBFGS | 9 / 16 | 3.276577e+01 | 3.612292e-02 | 6.938579e-02 | | LBFGS | 10 / 17 | 3.234029e+01 | 2.734959e-02 | 1.144307e-01 | | LBFGS | 11 / 18 | 3.205763e+01 | 2.545990e-02 | 7.323180e-02 | | LBFGS | 12 / 19 | 3.183341e+01 | 2.472411e-02 | 3.689625e-02 | | LBFGS | 13 / 20 | 3.169307e+01 | 2.064613e-02 | 2.998555e-02 | |========================================================================= | Solver | Iteration / | Objective | Gradient | Beta relative | | | Data Pass | | magnitude | change | |========================================================================= | LBFGS | 14 / 21 | 3.146896e+01 | 1.788395e-02 | 5.967293e-02 | | LBFGS | 15 / 22 | 3.118171e+01 | 1.660696e-02 | 1.124062e-01 | | LBFGS | 16 / 23 | 3.106224e+01 | 1.506147e-02 | 7.947037e-02 | | LBFGS | 17 / 24 | 3.098395e+01 | 1.564561e-02 | 2.678370e-02 | | LBFGS | 18 / 25 | 3.096029e+01 | 4.464104e-02 | 4.547148e-02 | | LBFGS | 19 / 26 | 3.085475e+01 | 1.442800e-02 | 1.677268e-02 | | LBFGS | 20 / 27 | 3.078140e+01 | 1.906548e-02 | 2.275185e-02 | |========================================================================| ```
```Mdl = RegressionKernel PredictorNames: {'x1' 'x2'} ResponseName: 'Y' Learner: 'svm' NumExpansionDimensions: 64 KernelScale: 1 Lambda: 8.5385e-06 BoxConstraint: 1 Epsilon: 5.9303 Properties, Methods ```
```FitInfo = struct with fields: Solver: 'LBFGS-tall' LossFunction: 'epsiloninsensitive' Lambda: 8.5385e-06 BetaTolerance: 1.0000e-03 GradientTolerance: 1.0000e-05 ObjectiveValue: 30.7814 GradientMagnitude: 0.0191 RelativeChangeInBeta: 0.0228 FitTime: 50.0477 History: [1x1 struct] ```
`Mdl` is a `RegressionKernel` model. To inspect the regression error, you can pass `Mdl` and the training data or new data to the `loss` function. Or, you can pass `Mdl` and new predictor data to the `predict` function to predict responses for new observations. You can also pass `Mdl` and the training data to the `resume` function to continue training.
`FitInfo` is a structure array containing optimization information. Use `FitInfo` to determine whether optimization termination measurements are satisfactory.
For improved accuracy, you can increase the maximum number of optimization iterations (`'IterationLimit'`) and decrease the tolerance values (`'BetaTolerance'` and `'GradientTolerance'`) by using the name-value pair arguments of `fitrkernel`. Doing so can improve measures like `ObjectiveValue` and `RelativeChangeInBeta` in `FitInfo`. You can also optimize model parameters by using the `'OptimizeHyperparameters'` name-value pair argument.
Load the `carbig` data set.
`load carbig`
Specify the predictor variables (`X`) and the response variable (`Y`).
```X = [Acceleration,Cylinders,Displacement,Horsepower,Weight]; Y = MPG;```
Delete rows of `X` and `Y` where either array has `NaN` values. Removing rows with `NaN` values before passing data to `fitrkernel` can speed up training and reduce memory usage.
```R = rmmissing([X Y]); % Data with missing entries removed X = R(:,1:5); Y = R(:,end); ```
Standardize the predictor variables.
`Z = zscore(X);`
Cross-validate a kernel regression model using 5-fold cross-validation.
`Mdl = fitrkernel(Z,Y,'Kfold',5)`
```Mdl = RegressionPartitionedKernel CrossValidatedModel: 'Kernel' ResponseName: 'Y' NumObservations: 392 KFold: 5 Partition: [1x1 cvpartition] ResponseTransform: 'none' Properties, Methods ```
`numel(Mdl.Trained)`
```ans = 5 ```
`Mdl` is a `RegressionPartitionedKernel` model. Because `fitrkernel` implements five-fold cross-validation, `Mdl` contains five `RegressionKernel` models that the software trains on training-fold (in-fold) observations.
Examine the cross-validation loss (mean squared error) for each fold.
`kfoldLoss(Mdl,'mode','individual')`
```ans = 5×1 13.0610 14.0975 24.0104 21.1223 24.3979 ```
Optimize hyperparameters automatically using the `'OptimizeHyperparameters'` name-value pair argument.
Load the `carbig` data set.
`load carbig`
Specify the predictor variables (`X`) and the response variable (`Y`).
```X = [Acceleration,Cylinders,Displacement,Horsepower,Weight]; Y = MPG;```
Delete rows of `X` and `Y` where either array has `NaN` values. Removing rows with `NaN` values before passing data to `fitrkernel` can speed up training and reduce memory usage.
```R = rmmissing([X Y]); % Data with missing entries removed X = R(:,1:5); Y = R(:,end); ```
Standardize the predictor variables.
`Z = zscore(X);`
Find hyperparameters that minimize five-fold cross-validation loss by using automatic hyperparameter optimization. Specify `'OptimizeHyperparameters'` as `'auto'` so that `fitrkernel` finds the optimal values of the `'KernelScale'`, `'Lambda'`, and `'Epsilon'` name-value pair arguments. For reproducibility, set the random seed and use the `'expected-improvement-plus'` acquisition function.
```rng('default') [Mdl,FitInfo,HyperparameterOptimizationResults] = fitrkernel(Z,Y,'OptimizeHyperparameters','auto',... 'HyperparameterOptimizationOptions',struct('AcquisitionFunctionName','expected-improvement-plus'))```
```|====================================================================================================================| | Iter | Eval | Objective: | Objective | BestSoFar | BestSoFar | KernelScale | Lambda | Epsilon | | | result | log(1+loss) | runtime | (observed) | (estim.) | | | | |====================================================================================================================| | 1 | Best | 4.8295 | 1.0202 | 4.8295 | 4.8295 | 0.011518 | 6.8068e-05 | 0.95918 | | 2 | Best | 4.1488 | 0.20075 | 4.1488 | 4.1855 | 477.57 | 0.066115 | 0.091828 | | 3 | Accept | 4.1521 | 0.23448 | 4.1488 | 4.1747 | 0.0080478 | 0.0052867 | 520.84 | | 4 | Accept | 4.1506 | 0.19343 | 4.1488 | 4.1488 | 0.10935 | 0.35931 | 0.013372 | | 5 | Best | 4.1446 | 0.22183 | 4.1446 | 4.1446 | 326.29 | 2.5457 | 0.22475 | | 6 | Accept | 4.1521 | 0.20642 | 4.1446 | 4.1447 | 932.16 | 0.19667 | 873.68 | | 7 | Accept | 4.1501 | 0.44117 | 4.1446 | 4.1461 | 0.052426 | 2.5402 | 0.051319 | | 8 | Best | 4.1408 | 0.2327 | 4.1408 | 4.1402 | 850.91 | 0.01462 | 0.37284 | | 9 | Accept | 4.1521 | 0.35173 | 4.1408 | 4.1427 | 0.019352 | 0.012035 | 63.493 | | 10 | Accept | 4.1521 | 0.21123 | 4.1408 | 4.1452 | 853.22 | 1.0698 | 55.679 | | 11 | Accept | 4.1521 | 0.34269 | 4.1408 | 4.1416 | 1.4548 | 0.022234 | 26.275 | | 12 | Accept | 4.1509 | 0.19879 | 4.1408 | 4.1469 | 877.82 | 0.0071133 | 0.012021 | | 13 | Accept | 4.1422 | 0.85467 | 4.1408 | 4.1455 | 944.08 | 0.011177 | 0.31055 | | 14 | Accept | 4.2032 | 0.29126 | 4.1408 | 4.1405 | 979.21 | 0.010842 | 13.776 | | 15 | Accept | 4.1438 | 0.20706 | 4.1408 | 4.1509 | 0.001234 | 0.018449 | 0.044225 | | 16 | Best | 4.1372 | 0.17378 | 4.1372 | 4.1511 | 1.7802 | 2.5477 | 0.014737 | | 17 | Accept | 4.1521 | 0.24019 | 4.1372 | 4.1466 | 0.0015946 | 2.5474 | 590.35 | | 18 | Accept | 4.1452 | 0.20963 | 4.1372 | 4.1464 | 0.058846 | 1.0766 | 0.20569 | | 19 | Accept | 4.1521 | 0.32159 | 4.1372 | 4.1461 | 2.187 | 2.5531e-06 | 278.92 | | 20 | Accept | 4.1451 | 0.32948 | 4.1372 | 4.1461 | 0.0050283 | 0.039894 | 0.14402 | |====================================================================================================================| | Iter | Eval | Objective: | Objective | BestSoFar | BestSoFar | KernelScale | Lambda | Epsilon | | | result | log(1+loss) | runtime | (observed) | (estim.) | | | | |====================================================================================================================| | 21 | Best | 4.1362 | 0.26969 | 4.1362 | 4.1426 | 0.0029885 | 0.039099 | 6.3938 | | 22 | Accept | 4.1521 | 0.20719 | 4.1362 | 4.1449 | 0.035949 | 0.038533 | 80.585 | | 23 | Accept | 4.1399 | 0.36116 | 4.1362 | 4.1446 | 50.001 | 0.095432 | 0.19954 | | 24 | Accept | 4.1487 | 0.52381 | 4.1362 | 4.1374 | 0.012199 | 0.089894 | 0.034773 | | 25 | Accept | 4.1521 | 0.22703 | 4.1362 | 4.1447 | 0.0011871 | 0.30153 | 425.89 | | 26 | Accept | 4.1466 | 0.45165 | 4.1362 | 4.145 | 0.0011773 | 0.052213 | 0.017592 | | 27 | Accept | 4.1418 | 0.17754 | 4.1362 | 4.145 | 7.556 | 1.655 | 0.016225 | | 28 | Accept | 4.1407 | 0.4172 | 4.1362 | 4.145 | 0.01201 | 1.6696 | 0.38806 | | 29 | Accept | 5.4153 | 3.9701 | 4.1362 | 4.1365 | 0.0010531 | 1.1032e-05 | 0.034083 | | 30 | Accept | 4.1521 | 0.34684 | 4.1362 | 4.1364 | 652.19 | 2.6286e-06 | 882.02 | ```
```__________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 26.6629 seconds Total objective function evaluation time: 13.4353 Best observed feasible point: KernelScale Lambda Epsilon ___________ ________ _______ 0.0029885 0.039099 6.3938 Observed objective function value = 4.1362 Estimated objective function value = 4.1364 Function evaluation time = 0.26969 Best estimated feasible point (according to models): KernelScale Lambda Epsilon ___________ ________ _______ 0.0029885 0.039099 6.3938 Estimated objective function value = 4.1364 Estimated function evaluation time = 0.31488 ```
```Mdl = RegressionKernel ResponseName: 'Y' Learner: 'svm' NumExpansionDimensions: 256 KernelScale: 0.0030 Lambda: 0.0391 BoxConstraint: 0.0652 Epsilon: 6.3938 Properties, Methods ```
```FitInfo = struct with fields: Solver: 'LBFGS-fast' LossFunction: 'epsiloninsensitive' Lambda: 0.0391 BetaTolerance: 1.0000e-04 GradientTolerance: 1.0000e-06 ObjectiveValue: 1.7716 GradientMagnitude: 0.0051 RelativeChangeInBeta: 8.5572e-05 FitTime: 0.0237 History: [] ```
```HyperparameterOptimizationResults = BayesianOptimization with properties: ObjectiveFcn: @createObjFcn/inMemoryObjFcn VariableDescriptions: [5x1 optimizableVariable] Options: [1x1 struct] MinObjective: 4.1362 XAtMinObjective: [1x3 table] MinEstimatedObjective: 4.1364 XAtMinEstimatedObjective: [1x3 table] NumObjectiveEvaluations: 30 TotalElapsedTime: 26.6629 NextPoint: [1x3 table] XTrace: [30x3 table] ObjectiveTrace: [30x1 double] ConstraintsTrace: [] UserDataTrace: {30x1 cell} ObjectiveEvaluationTimeTrace: [30x1 double] IterationTimeTrace: [30x1 double] ErrorTrace: [30x1 double] FeasibilityTrace: [30x1 logical] FeasibilityProbabilityTrace: [30x1 double] IndexOfMinimumTrace: [30x1 double] ObjectiveMinimumTrace: [30x1 double] EstimatedObjectiveMinimumTrace: [30x1 double] ```
For big data, the optimization procedure can take a long time. If the data set is too large to run the optimization procedure, you can try to optimize the parameters using only partial data. Use the `datasample` function and specify `'Replace','false'` to sample data without replacement.
## Input Arguments
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Predictor data to which the regression model is fit, specified as an n-by-p numeric matrix, where n is the number of observations and p is the number of predictor variables.
The length of `Y` and the number of observations in `X` must be equal.
Data Types: `single` | `double`
Response data, specified as an n-dimensional numeric vector. The length of `Y` must be equal to the number of observations in `X` or `Tbl`.
Data Types: `single` | `double`
Sample data used to train the model, specified as a table. Each row of `Tbl` corresponds to one observation, and each column corresponds to one predictor variable. Optionally, `Tbl` can contain one additional column for the response variable. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.
• If `Tbl` contains the response variable, and you want to use all remaining variables in `Tbl` as predictors, then specify the response variable by using `ResponseVarName`.
• If `Tbl` contains the response variable, and you want to use only a subset of the remaining variables in `Tbl` as predictors, then specify a formula by using `formula`.
• If `Tbl` does not contain the response variable, then specify a response variable by using `Y`. The length of the response variable and the number of rows in `Tbl` must be equal.
Data Types: `table`
Response variable name, specified as the name of a variable in `Tbl`. The response variable must be a numeric vector.
You must specify `ResponseVarName` as a character vector or string scalar. For example, if `Tbl` stores the response variable `Y` as `Tbl.Y`, then specify it as `'Y'`. Otherwise, the software treats all columns of `Tbl`, including `Y`, as predictors when training the model.
Data Types: `char` | `string`
Explanatory model of the response variable and a subset of the predictor variables, specified as a character vector or string scalar in the form `"Y~x1+x2+x3"`. In this form, `Y` represents the response variable, and `x1`, `x2`, and `x3` represent the predictor variables.
To specify a subset of variables in `Tbl` as predictors for training the model, use a formula. If you specify a formula, then the software does not use any variables in `Tbl` that do not appear in `formula`.
The variable names in the formula must be both variable names in `Tbl` (`Tbl.Properties.VariableNames`) and valid MATLAB® identifiers. You can verify the variable names in `Tbl` by using the `isvarname` function. If the variable names are not valid, then you can convert them by using the `matlab.lang.makeValidName` function.
Data Types: `char` | `string`
Note
The software treats `NaN`, empty character vector (`''`), empty string (`""`), `<missing>`, and `<undefined>` elements as missing values, and removes observations with any of these characteristics:
• Missing value in the response variable
• At least one missing value in a predictor observation (row in `X` or `Tbl`)
• `NaN` value or `0` weight (`'Weights'`)
### Name-Value Arguments
Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.
Example: ```Mdl = fitrkernel(X,Y,'Learner','leastsquares','NumExpansionDimensions',2^15,'KernelScale','auto')``` implements least-squares regression after mapping the predictor data to the `2^15` dimensional space using feature expansion with a kernel scale parameter selected by a heuristic procedure.
Note
You cannot use any cross-validation name-value argument together with the `'OptimizeHyperparameters'` name-value argument. You can modify the cross-validation for `'OptimizeHyperparameters'` only by using the `'HyperparameterOptimizationOptions'` name-value argument.
Kernel Regression Options
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Box constraint, specified as the comma-separated pair consisting of `'BoxConstraint'` and a positive scalar.
This argument is valid only when `'Learner'` is `'svm'`(default) and you do not specify a value for the regularization term strength `'Lambda'`. You can specify either `'BoxConstraint'` or `'Lambda'` because the box constraint (C) and the regularization term strength (λ) are related by C = 1/(λn), where n is the number of observations (rows in `X`).
Example: `'BoxConstraint',100`
Data Types: `single` | `double`
Half the width of the epsilon-insensitive band, specified as the comma-separated pair consisting of `'Epsilon'` and `'auto'` or a nonnegative scalar value.
For `'auto'`, the `fitrkernel` function determines the value of `Epsilon` as `iqr(Y)/13.49`, which is an estimate of a tenth of the standard deviation using the interquartile range of the response variable `Y`. If `iqr(Y)` is equal to zero, then `fitrkernel` sets the value of `Epsilon` to 0.1.
`'Epsilon'` is valid only when `Learner` is `svm`.
Example: `'Epsilon',0.3`
Data Types: `single` | `double`
Number of dimensions of the expanded space, specified as the comma-separated pair consisting of `'NumExpansionDimensions'` and `'auto'` or a positive integer. For `'auto'`, the `fitrkernel` function selects the number of dimensions using `2.^ceil(min(log2(p)+5,15))`, where `p` is the number of predictors.
Example: `'NumExpansionDimensions',2^15`
Data Types: `char` | `string` | `single` | `double`
Kernel scale parameter, specified as the comma-separated pair consisting of `'KernelScale'` and `'auto'` or a positive scalar. MATLAB obtains the random basis for random feature expansion by using the kernel scale parameter. For details, see Random Feature Expansion.
If you specify `'auto'`, then MATLAB selects an appropriate kernel scale parameter using a heuristic procedure. This heuristic procedure uses subsampling, so estimates can vary from one call to another. Therefore, to reproduce results, set a random number seed by using `rng` before training.
Example: `'KernelScale','auto'`
Data Types: `char` | `string` | `single` | `double`
Regularization term strength, specified as the comma-separated pair consisting of `'Lambda'` and `'auto'` or a nonnegative scalar.
For `'auto'`, the value of `'Lambda'` is 1/n, where n is the number of observations (rows in `X`).
You can specify either `'BoxConstraint'` or `'Lambda'` because the box constraint (C) and the regularization term strength (λ) are related by C = 1/(λn).
Example: `'Lambda',0.01`
Data Types: `char` | `string` | `single` | `double`
Linear regression model type, specified as the comma-separated pair consisting of `'Learner'` and `'svm'` or `'leastsquares'`.
In the following table, $f\left(x\right)=T\left(x\right)\beta +b.$
• x is an observation (row vector) from p predictor variables.
• $T\left(·\right)$ is a transformation of an observation (row vector) for feature expansion. T(x) maps x in ${ℝ}^{p}$ to a high-dimensional space (${ℝ}^{m}$).
• β is a vector of m coefficients.
• b is the scalar bias.
ValueAlgorithmResponse rangeLoss function
`'leastsquares'`Linear regression via ordinary least squaresy ∊ (-∞,∞)Mean squared error (MSE): $\ell \left[y,f\left(x\right)\right]=\frac{1}{2}{\left[y-f\left(x\right)\right]}^{2}$
`'svm'`Support vector machine regressionSame as `'leastsquares'`Epsilon-insensitive: $\ell \left[y,f\left(x\right)\right]=\mathrm{max}\left[0,|y-f\left(x\right)|-\epsilon \right]$
Example: `'Learner','leastsquares'`
Verbosity level, specified as the comma-separated pair consisting of `'Verbose'` and either `0` or `1`. `Verbose` controls the amount of diagnostic information `fitrkernel` displays at the command line.
ValueDescription
`0``fitrkernel` does not display diagnostic information.
`1``fitrkernel` displays and stores the value of the objective function, gradient magnitude, and other diagnostic information. `FitInfo.History` contains the diagnostic information.
Example: `'Verbose',1`
Data Types: `single` | `double`
Maximum amount of allocated memory (in megabytes), specified as the comma-separated pair consisting of `'BlockSize'` and a positive scalar.
If `fitrkernel` requires more memory than the value of `BlockSize` to hold the transformed predictor data, then MATLAB uses a block-wise strategy. For details about the block-wise strategy, see Algorithms.
Example: `'BlockSize',1e4`
Data Types: `single` | `double`
Random number stream for reproducibility of data transformation, specified as the comma-separated pair consisting of `'RandomStream'` and a random stream object. For details, see Random Feature Expansion.
Use `'RandomStream'` to reproduce the random basis functions that `fitrkernel` uses to transform the data in `X` to a high-dimensional space. For details, see Managing the Global Stream Using RandStream and Creating and Controlling a Random Number Stream.
Example: `'RandomStream',RandStream('mlfg6331_64')`
Other Regression Options
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Categorical predictors list, specified as one of the values in this table.
ValueDescription
Vector of positive integers
Each entry in the vector is an index value indicating that the corresponding predictor is categorical. The index values are between 1 and `p`, where `p` is the number of predictors used to train the model.
If `fitrkernel` uses a subset of input variables as predictors, then the function indexes the predictors using only the subset. The `CategoricalPredictors` values do not count the response variable, observation weight variable, or any other variables that the function does not use.
Logical vector
A `true` entry means that the corresponding predictor is categorical. The length of the vector is `p`.
Character matrixEach row of the matrix is the name of a predictor variable. The names must match the entries in `PredictorNames`. Pad the names with extra blanks so each row of the character matrix has the same length.
String array or cell array of character vectorsEach element in the array is the name of a predictor variable. The names must match the entries in `PredictorNames`.
`"all"`All predictors are categorical.
By default, if the predictor data is in a table (`Tbl`), `fitrkernel` assumes that a variable is categorical if it is a logical vector, categorical vector, character array, string array, or cell array of character vectors. If the predictor data is a matrix (`X`), `fitrkernel` assumes that all predictors are continuous. To identify any other predictors as categorical predictors, specify them by using the `'CategoricalPredictors'` name-value argument.
For the identified categorical predictors, `fitrkernel` creates dummy variables using two different schemes, depending on whether a categorical variable is unordered or ordered. For an unordered categorical variable, `fitrkernel` creates one dummy variable for each level of the categorical variable. For an ordered categorical variable, `fitrkernel` creates one less dummy variable than the number of categories. For details, see Automatic Creation of Dummy Variables.
Example: `'CategoricalPredictors','all'`
Data Types: `single` | `double` | `logical` | `char` | `string` | `cell`
Predictor variable names, specified as a string array of unique names or cell array of unique character vectors. The functionality of `PredictorNames` depends on the way you supply the training data.
• If you supply `X` and `Y`, then you can use `PredictorNames` to assign names to the predictor variables in `X`.
• The order of the names in `PredictorNames` must correspond to the column order of `X`. That is, `PredictorNames{1}` is the name of `X(:,1)`, `PredictorNames{2}` is the name of `X(:,2)`, and so on. Also, `size(X,2)` and `numel(PredictorNames)` must be equal.
• By default, `PredictorNames` is `{'x1','x2',...}`.
• If you supply `Tbl`, then you can use `PredictorNames` to choose which predictor variables to use in training. That is, `fitrkernel` uses only the predictor variables in `PredictorNames` and the response variable during training.
• `PredictorNames` must be a subset of `Tbl.Properties.VariableNames` and cannot include the name of the response variable.
• By default, `PredictorNames` contains the names of all predictor variables.
• A good practice is to specify the predictors for training using either `PredictorNames` or `formula`, but not both.
Example: `"PredictorNames",["SepalLength","SepalWidth","PetalLength","PetalWidth"]`
Data Types: `string` | `cell`
Response variable name, specified as a character vector or string scalar.
Example: `"ResponseName","response"`
Data Types: `char` | `string`
Response transformation, specified as either `'none'` or a function handle. The default is `'none'`, which means `@(y)y`, or no transformation. For a MATLAB function or a function you define, use its function handle for the response transformation. The function handle must accept a vector (the original response values) and return a vector of the same size (the transformed response values).
Example: Suppose you create a function handle that applies an exponential transformation to an input vector by using `myfunction = @(y)exp(y)`. Then, you can specify the response transformation as `'ResponseTransform',myfunction`.
Data Types: `char` | `string` | `function_handle`
Observation weights, specified as the comma-separated pair consisting of `'Weights'` and a vector of scalar values or the name of a variable in `Tbl`. The software weights each observation (or row) in `X` or `Tbl` with the corresponding value in `Weights`. The length of `Weights` must equal the number of rows in `X` or `Tbl`.
If you specify the input data as a table `Tbl`, then `Weights` can be the name of a variable in `Tbl` that contains a numeric vector. In this case, you must specify `Weights` as a character vector or string scalar. For example, if weights vector `W` is stored as `Tbl.W`, then specify it as `'W'`. Otherwise, the software treats all columns of `Tbl`, including `W`, as predictors when training the model.
By default, `Weights` is `ones(n,1)`, where `n` is the number of observations in `X` or `Tbl`.
`fitrkernel` normalizes the weights to sum to 1.
Data Types: `single` | `double` | `char` | `string`
Cross-Validation Options
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Cross-validation flag, specified as the comma-separated pair consisting of `'Crossval'` and `'on'` or `'off'`.
If you specify `'on'`, then the software implements 10-fold cross-validation.
You can override this cross-validation setting using the `CVPartition`, `Holdout`, `KFold`, or `Leaveout` name-value pair argument. You can use only one cross-validation name-value pair argument at a time to create a cross-validated model.
Example: `'Crossval','on'`
Cross-validation partition, specified as a `cvpartition` partition object created by `cvpartition`. The partition object specifies the type of cross-validation and the indexing for the training and validation sets.
To create a cross-validated model, you can specify only one of these four name-value arguments: `CVPartition`, `Holdout`, `KFold`, or `Leaveout`.
Example: Suppose you create a random partition for 5-fold cross-validation on 500 observations by using `cvp = cvpartition(500,'KFold',5)`. Then, you can specify the cross-validated model by using `'CVPartition',cvp`.
Fraction of the data used for holdout validation, specified as a scalar value in the range (0,1). If you specify `'Holdout',p`, then the software completes these steps:
1. Randomly select and reserve `p*100`% of the data as validation data, and train the model using the rest of the data.
2. Store the compact, trained model in the `Trained` property of the cross-validated model.
To create a cross-validated model, you can specify only one of these four name-value arguments: `CVPartition`, `Holdout`, `KFold`, or `Leaveout`.
Example: `'Holdout',0.1`
Data Types: `double` | `single`
Number of folds to use in a cross-validated model, specified as a positive integer value greater than 1. If you specify `'KFold',k`, then the software completes these steps:
1. Randomly partition the data into `k` sets.
2. For each set, reserve the set as validation data, and train the model using the other `k` – 1 sets.
3. Store the `k` compact, trained models in a `k`-by-1 cell vector in the `Trained` property of the cross-validated model.
To create a cross-validated model, you can specify only one of these four name-value arguments: `CVPartition`, `Holdout`, `KFold`, or `Leaveout`.
Example: `'KFold',5`
Data Types: `single` | `double`
Leave-one-out cross-validation flag, specified as the comma-separated pair consisting of `'Leaveout'` and `'on'` or `'off'`. If you specify `'Leaveout','on'`, then, for each of the n observations (where n is the number of observations excluding missing observations), the software completes these steps:
1. Reserve the observation as validation data, and train the model using the other n – 1 observations.
2. Store the n compact, trained models in the cells of an n-by-1 cell vector in the `Trained` property of the cross-validated model.
To create a cross-validated model, you can use one of these four name-value pair arguments only: `CVPartition`, `Holdout`, `KFold`, or `Leaveout`.
Example: `'Leaveout','on'`
Convergence Controls
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Relative tolerance on the linear coefficients and the bias term (intercept), specified as the comma-separated pair consisting of `'BetaTolerance'` and a nonnegative scalar.
Let ${B}_{t}=\left[{\beta }_{t}{}^{\prime }\text{\hspace{0.17em}}\text{\hspace{0.17em}}{b}_{t}\right]$, that is, the vector of the coefficients and the bias term at optimization iteration t. If ${‖\frac{{B}_{t}-{B}_{t-1}}{{B}_{t}}‖}_{2}<\text{BetaTolerance}$, then optimization terminates.
If you also specify `GradientTolerance`, then optimization terminates when the software satisfies either stopping criterion.
Example: `'BetaTolerance',1e-6`
Data Types: `single` | `double`
Absolute gradient tolerance, specified as the comma-separated pair consisting of `'GradientTolerance'` and a nonnegative scalar.
Let $\nabla {ℒ}_{t}$ be the gradient vector of the objective function with respect to the coefficients and bias term at optimization iteration t. If ${‖\nabla {ℒ}_{t}‖}_{\infty }=\mathrm{max}|\nabla {ℒ}_{t}|<\text{GradientTolerance}$, then optimization terminates.
If you also specify `BetaTolerance`, then optimization terminates when the software satisfies either stopping criterion.
Example: `'GradientTolerance',1e-5`
Data Types: `single` | `double`
Size of the history buffer for Hessian approximation, specified as the comma-separated pair consisting of `'HessianHistorySize'` and a positive integer. At each iteration, `fitrkernel` composes the Hessian by using statistics from the latest `HessianHistorySize` iterations.
Example: `'HessianHistorySize',10`
Data Types: `single` | `double`
Maximum number of optimization iterations, specified as the comma-separated pair consisting of `'IterationLimit'` and a positive integer.
The default value is 1000 if the transformed data fits in memory, as specified by `BlockSize`. Otherwise, the default value is 100.
Example: `'IterationLimit',500`
Data Types: `single` | `double`
Hyperparameter Optimization Options
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Parameters to optimize, specified as the comma-separated pair consisting of `'OptimizeHyperparameters'` and one of these values:
• `'none'` — Do not optimize.
• `'auto'` — Use `{'KernelScale','Lambda','Epsilon'}`.
• `'all'` — Optimize all eligible parameters.
• Cell array of eligible parameter names.
• Vector of `optimizableVariable` objects, typically the output of `hyperparameters`.
The optimization attempts to minimize the cross-validation loss (error) for `fitrkernel` by varying the parameters. To control the cross-validation type and other aspects of the optimization, use the `HyperparameterOptimizationOptions` name-value pair argument.
Note
The values of `'OptimizeHyperparameters'` override any values you specify using other name-value arguments. For example, setting `'OptimizeHyperparameters'` to `'auto'` causes `fitrkernel` to optimize hyperparameters corresponding to the `'auto'` option and to ignore any specified values for the hyperparameters.
The eligible parameters for `fitrkernel` are:
• `Epsilon``fitrkernel` searches among positive values, by default log-scaled in the range `[1e-3,1e2]*iqr(Y)/1.349`.
• `KernelScale``fitrkernel` searches among positive values, by default log-scaled in the range `[1e-3,1e3]`.
• `Lambda``fitrkernel` searches among positive values, by default log-scaled in the range `[1e-3,1e3]/n`, where `n` is the number of observations.
• `Learner``fitrkernel` searches among `'svm'` and `'leastsquares'`.
• `NumExpansionDimensions``fitrkernel` searches among positive integers, by default log-scaled in the range `[100,10000]`.
Set nondefault parameters by passing a vector of `optimizableVariable` objects that have nondefault values. For example:
```load carsmall params = hyperparameters('fitrkernel',[Horsepower,Weight],MPG); params(2).Range = [1e-4,1e6];```
Pass `params` as the value of `'OptimizeHyperparameters'`.
By default, the iterative display appears at the command line, and plots appear according to the number of hyperparameters in the optimization. For the optimization and plots, the objective function is log(1 + cross-validation loss). To control the iterative display, set the `Verbose` field of the `'HyperparameterOptimizationOptions'` name-value argument. To control the plots, set the `ShowPlots` field of the `'HyperparameterOptimizationOptions'` name-value argument.
For an example, see Optimize Kernel Regression.
Example: `'OptimizeHyperparameters','auto'`
Options for optimization, specified as a structure. This argument modifies the effect of the `OptimizeHyperparameters` name-value argument. All fields in the structure are optional.
Field NameValuesDefault
`Optimizer`
• `'bayesopt'` — Use Bayesian optimization. Internally, this setting calls `bayesopt`.
• `'gridsearch'` — Use grid search with `NumGridDivisions` values per dimension.
• `'randomsearch'` — Search at random among `MaxObjectiveEvaluations` points.
`'gridsearch'` searches in a random order, using uniform sampling without replacement from the grid. After optimization, you can get a table in grid order by using the command `sortrows(Mdl.HyperparameterOptimizationResults)`.
`'bayesopt'`
`AcquisitionFunctionName`
• `'expected-improvement-per-second-plus'`
• `'expected-improvement'`
• `'expected-improvement-plus'`
• `'expected-improvement-per-second'`
• `'lower-confidence-bound'`
• `'probability-of-improvement'`
Acquisition functions whose names include `per-second` do not yield reproducible results because the optimization depends on the runtime of the objective function. Acquisition functions whose names include `plus` modify their behavior when they are overexploiting an area. For more details, see Acquisition Function Types.
`'expected-improvement-per-second-plus'`
`MaxObjectiveEvaluations`Maximum number of objective function evaluations.`30` for `'bayesopt'` and `'randomsearch'`, and the entire grid for `'gridsearch'`
`MaxTime`
Time limit, specified as a positive real scalar. The time limit is in seconds, as measured by `tic` and `toc`. The run time can exceed `MaxTime` because `MaxTime` does not interrupt function evaluations.
`Inf`
`NumGridDivisions`For `'gridsearch'`, the number of values in each dimension. The value can be a vector of positive integers giving the number of values for each dimension, or a scalar that applies to all dimensions. This field is ignored for categorical variables.`10`
`ShowPlots`Logical value indicating whether to show plots. If `true`, this field plots the best observed objective function value against the iteration number. If you use Bayesian optimization (`Optimizer` is `'bayesopt'`), then this field also plots the best estimated objective function value. The best observed objective function values and best estimated objective function values correspond to the values in the `BestSoFar (observed)` and ```BestSoFar (estim.)``` columns of the iterative display, respectively. You can find these values in the properties `ObjectiveMinimumTrace` and `EstimatedObjectiveMinimumTrace` of `Mdl.HyperparameterOptimizationResults`. If the problem includes one or two optimization parameters for Bayesian optimization, then `ShowPlots` also plots a model of the objective function against the parameters.`true`
`SaveIntermediateResults`Logical value indicating whether to save results when `Optimizer` is `'bayesopt'`. If `true`, this field overwrites a workspace variable named `'BayesoptResults'` at each iteration. The variable is a `BayesianOptimization` object.`false`
`Verbose`
Display at the command line:
• `0` — No iterative display
• `1` — Iterative display
• `2` — Iterative display with extra information
For details, see the `bayesopt` `Verbose` name-value argument and the example Optimize Classifier Fit Using Bayesian Optimization.
`1`
`UseParallel`Logical value indicating whether to run Bayesian optimization in parallel, which requires Parallel Computing Toolbox™. Due to the nonreproducibility of parallel timing, parallel Bayesian optimization does not necessarily yield reproducible results. For details, see Parallel Bayesian Optimization.`false`
`Repartition`
Logical value indicating whether to repartition the cross-validation at every iteration. If this field is `false`, the optimizer uses a single partition for the optimization.
The setting `true` usually gives the most robust results because it takes partitioning noise into account. However, for good results, `true` requires at least twice as many function evaluations.
`false`
Use no more than one of the following three options.
`CVPartition`A `cvpartition` object, as created by `cvpartition``'Kfold',5` if you do not specify a cross-validation field
`Holdout`A scalar in the range `(0,1)` representing the holdout fraction
`Kfold`An integer greater than 1
Example: `'HyperparameterOptimizationOptions',struct('MaxObjectiveEvaluations',60)`
Data Types: `struct`
## Output Arguments
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Trained kernel regression model, returned as a `RegressionKernel` model object or `RegressionPartitionedKernel` cross-validated model object.
If you set any of the name-value pair arguments `CrossVal`, `CVPartition`, `Holdout`, `KFold`, or `Leaveout`, then `Mdl` is a `RegressionPartitionedKernel` cross-validated model. Otherwise, `Mdl` is a `RegressionKernel` model.
To reference properties of `Mdl`, use dot notation. For example, enter `Mdl.NumExpansionDimensions` in the Command Window to display the number of dimensions of the expanded space.
Note
Unlike other regression models, and for economical memory usage, a `RegressionKernel` model object does not store the training data or training process details (for example, convergence history).
Optimization details, returned as a structure array including fields described in this table. The fields contain final values or name-value pair argument specifications.
FieldDescription
`Solver`
Objective function minimization technique: `'LBFGS-fast'`, `'LBFGS-blockwise'`, or `'LBFGS-tall'`. For details, see Algorithms.
`LossFunction`Loss function. Either mean squared error (MSE) or epsilon-insensitive, depending on the type of linear regression model. See `Learner`.
`Lambda`Regularization term strength. See `Lambda`.
`BetaTolerance`Relative tolerance on the linear coefficients and the bias term. See `BetaTolerance`.
`GradientTolerance`Absolute gradient tolerance. See `GradientTolerance`.
`ObjectiveValue`Value of the objective function when optimization terminates. The regression loss plus the regularization term compose the objective function.
`GradientMagnitude`Infinite norm of the gradient vector of the objective function when optimization terminates. See `GradientTolerance`.
`RelativeChangeInBeta`Relative changes in the linear coefficients and the bias term when optimization terminates. See `BetaTolerance`.
`FitTime`Elapsed, wall-clock time (in seconds) required to fit the model to the data.
`History`History of optimization information. This field also includes the optimization information from training `Mdl`. This field is empty (`[]`) if you specify `'Verbose',0`. For details, see `Verbose` and Algorithms.
To access fields, use dot notation. For example, to access the vector of objective function values for each iteration, enter `FitInfo.ObjectiveValue` in the Command Window.
Examine the information provided by `FitInfo` to assess whether convergence is satisfactory.
Cross-validation optimization of hyperparameters, returned as a `BayesianOptimization` object or a table of hyperparameters and associated values. The output is nonempty when the value of `'OptimizeHyperparameters'` is not `'none'`. The output value depends on the `Optimizer` field value of the `'HyperparameterOptimizationOptions'` name-value pair argument:
Value of `Optimizer` FieldValue of `HyperparameterOptimizationResults`
`'bayesopt'` (default)Object of class `BayesianOptimization`
`'gridsearch'` or `'randomsearch'`Table of hyperparameters used, observed objective function values (cross-validation loss), and rank of observations from lowest (best) to highest (worst)
## Limitations
• `fitrkernel` does not accept initial conditions for the linear coefficients beta (β) and bias term (b) used to determine the decision function, $f\left(x\right)=T\left(x\right)\beta +b.$
• `fitrkernel` does not support standardization.
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### Random Feature Expansion
Random feature expansion, such as Random Kitchen Sinks[1] and Fastfood[2], is a scheme to approximate Gaussian kernels of the kernel regression algorithm for big data in a computationally efficient way. Random feature expansion is more practical for big data applications that have large training sets but can also be applied to smaller data sets that fit in memory.
The kernel regression algorithm searches for an optimal function that deviates from each response data point (yi) by values no greater than the epsilon margin (ε) after mapping the predictor data into a high-dimensional space.
Some regression problems cannot be described adequately using a linear model. In such cases, obtain a nonlinear regression model by replacing the dot product x1x2 with a nonlinear kernel function $G\left({x}_{1},{x}_{2}\right)=〈\phi \left({x}_{1}\right),\phi \left({x}_{2}\right)〉$, where xi is the ith observation (row vector) and φ(xi) is a transformation that maps xi to a high-dimensional space (called the “kernel trick”). However, evaluating G(x1,x2) , the Gram matrix, for each pair of observations is computationally expensive for a large data set (large n).
The random feature expansion scheme finds a random transformation so that its dot product approximates the Gaussian kernel. That is,
`$G\left({x}_{1},{x}_{2}\right)=〈\phi \left({x}_{1}\right),\phi \left({x}_{2}\right)〉\approx T\left({x}_{1}\right)T\left({x}_{2}\right)\text{'},$`
where T(x) maps x in ${ℝ}^{p}$ to a high-dimensional space (${ℝ}^{m}$). The Random Kitchen Sink[1] scheme uses the random transformation
`$T\left(x\right)={m}^{-1/2}\mathrm{exp}\left(iZx\text{'}\right)\text{'},$`
where $Z\in {ℝ}^{m×p}$ is a sample drawn from $N\left(0,{\sigma }^{-2}\right)$ and σ2 is a kernel scale. This scheme requires O(mp) computation and storage. The Fastfood[2] scheme introduces another random basis V instead of Z using Hadamard matrices combined with Gaussian scaling matrices. This random basis reduces computation cost to O(m`log`p) and reduces storage to O(m).
You can specify values for m and σ2, using the `NumExpansionDimensions` and `KernelScale` name-value pair arguments of `fitrkernel`, respectively.
The `fitrkernel` function uses the Fastfood scheme for random feature expansion and uses linear regression to train a Gaussian kernel regression model. Unlike solvers in the `fitrsvm` function, which require computation of the n-by-n Gram matrix, the solver in `fitrkernel` only needs to form a matrix of size n-by-m, with m typically much less than n for big data.
### Box Constraint
A box constraint is a parameter that controls the maximum penalty imposed on observations that lie outside the epsilon margin (ε), and helps to prevent overfitting (regularization). Increasing the box constraint can lead to longer training times.
The box constraint (C) and the regularization term strength (λ) are related by C = 1/(λn), where n is the number of observations.
## Algorithms
`fitrkernel` minimizes the regularized objective function using a Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) solver with ridge (L2) regularization. To find the type of LBFGS solver used for training, type `FitInfo.Solver` in the Command Window.
• `'LBFGS-fast'` — LBFGS solver.
• `'LBFGS-blockwise'` — LBFGS solver with a block-wise strategy. If `fitrkernel` requires more memory than the value of `BlockSize` to hold the transformed predictor data, then it uses a block-wise strategy.
• `'LBFGS-tall'` — LBFGS solver with a block-wise strategy for tall arrays.
When `fitrkernel` uses a block-wise strategy, `fitrkernel` implements LBFGS by distributing the calculation of the loss and gradient among different parts of the data at each iteration. Also, `fitrkernel` refines the initial estimates of the linear coefficients and the bias term by fitting the model locally to parts of the data and combining the coefficients by averaging. If you specify `'Verbose',1`, then `fitrkernel` displays diagnostic information for each data pass and stores the information in the `History` field of `FitInfo`.
When `fitrkernel` does not use a block-wise strategy, the initial estimates are zeros. If you specify `'Verbose',1`, then `fitrkernel` displays diagnostic information for each iteration and stores the information in the `History` field of `FitInfo`.
## References
[1] Rahimi, A., and B. Recht. “Random Features for Large-Scale Kernel Machines.” Advances in Neural Information Processing Systems. Vol. 20, 2008, pp. 1177–1184.
[2] Le, Q., T. Sarlós, and A. Smola. “Fastfood — Approximating Kernel Expansions in Loglinear Time.” Proceedings of the 30th International Conference on Machine Learning. Vol. 28, No. 3, 2013, pp. 244–252.
[3] Huang, P. S., H. Avron, T. N. Sainath, V. Sindhwani, and B. Ramabhadran. “Kernel methods match Deep Neural Networks on TIMIT.” 2014 IEEE International Conference on Acoustics, Speech and Signal Processing. 2014, pp. 205–209.
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https://www.transtutors.com/questions/3-i-anticipate-having-the-amount-of-4-000-00-after-an-unknown-period-of-time-the-mon-1377139.htm
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# 3. I anticipate having the amount of $4,000.00 after an unknown period of time. The monetary... 3. I anticipate having the amount of$4,000.00 after an unknown period of time. The monetary present worth is $2,357.35. The rate is 4.7%. What amount of time is necessary to realize this situation? 4. I anticipate having the amount of$982.22 after a period of 7 years. The monetary present worth is \$777.35. However, the necessary rate is unidentified. What is the necessary rate to realize this situation?
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2018-12-13 22:09:14
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http://mathoverflow.net/questions/21709/what-are-the-advantages-of-phrasing-results-in-terms-of-exact-sequences-and-commu/21721
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# What are the advantages of phrasing results in terms of exact sequences and commutative diagrams?
For example, I find the first group isomorphism theorem to be vastly more opaque when presented in terms of commutative diagrams and I've had similar experiences with other elementary results being expressed in terms of exact sequences. What are the benefits that I am not seeing?
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I downvoted this question because it answers itsself as soon as you work some time with diagrams... the answers below illustrate this. – Martin Brandenburg Apr 18 '10 at 22:06
I think that downvoting this is harsh - this is like someone answering a question with "just go and work some more at it". It seems a perfectly valid question for someone who has not had much experience with such techniques and is interested to hear from people who have both learned this stuff and taught it. – Yemon Choi Apr 19 '10 at 3:40
I should add that while I am now fairly accustomed to messing around with exact sequences and using them to chase things round diagrams, this was not the case 10 years ago when I was an undergraduate. So I have some sympathy for both sides that are being represented here. Several of my colleagues, who as functional analysts aren't opposed to algebraic techniques, still feel happier with a non-diagrammatic perspective: while I have different tastes from them, I would not dismiss their view by saying this "answers itself as soon as you work some time with diagrams." – Yemon Choi Apr 19 '10 at 3:45
Holy cow, go beyond the first homomorphism theorem! For example, if you have a long exact sequence of vector spaces and linear maps $$0 \rightarrow V_1 \rightarrow V_2 \rightarrow \cdots \rightarrow V_n \rightarrow 0$$ then exactness implies that the alternating sum of the dimensions is 0. This generalizes the "rank-nullity theorem" that $\dim(V/W) = \dim V - \dim W$, which is the special case of $0 \rightarrow W \rightarrow V \rightarrow V/W \rightarrow 0$.
Replace vector spaces and linear maps by finite abelian groups and group homomorphisms and instead you find the alternating product of the sizes of the groups has to be 1.
The purpose of this general machinery is not the small cases like the first homomorphism theorem. Exact sequences and commutative diagrams are the only way to think about or formulate large chunks of modern mathematics. For instance, you need commutative diagrams to make sense of universal mapping properties (which is the way many concepts are defined or at least most clearly understood) and to understand the opening scene in the movie "It's My Turn".
Here is a nice exercise. When $a$ and $b$ are relatively prime, $\varphi(ab) = \varphi(a)\varphi(b)$, where $\varphi(n)$ is Euler's $\varphi$-function from number theory. Question: Is there a formula for $\varphi(ab)$ in terms of $\varphi(a)$ and $\varphi(b)$ when $(a,b) > 1$? Yes: $$\varphi(ab) = \varphi(a)\varphi(b)\frac{(a,b)}{\varphi((a,b))}.$$ You could prove that by the formula for $\varphi(n)$ in terms of prime factorizations, but it wouldn't really explain what is going on because it doesn't provide any meaning to the formula. That's kind of like the proofs by induction which don't really give any insight into what is going on. But it turns out there is a nice 4-term short exact sequence of abelian groups (involving units groups mod $a$, mod $b$, and mod $ab$) such that, when you apply the above "alternating product is 1" result, the general $\varphi$-formula above falls right out. Searching for an explanation of that formula in terms of exact sequences forces you to try to really figure out conceptually what is going on in the formula.
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"You could prove that by the formula for phi(n) in terms of prime factorizations, but it wouldn't really explain what is going on because it doesn't provide any meaning to the formula." I disagree with this. I think the combinatoric proof of this formula makes it very clear, whereas more abstract formulas of this type should be proven with diagrams. – Martin Brandenburg Apr 18 '10 at 22:10
Martin, what argument do you have in mind? A combinatorial argument sounds like something other than a proof by algebra using the formula with prime factorizations. – KConrad Apr 18 '10 at 22:40
@KConrad: as for the "nice 4-term" sequence which you mention, is it $$0\rightarrow \ker\rightarrow U(\mathbf{Z}/ab\mathbf{Z})\rightarrow U(\mathbf{Z}/a\mathbf{Z})\times U(\mathbf{Z}/b\mathbf{Z})\rightarrow \operatorname{Coker}\rightarrow 0$$? +1 for mentioning this very nice proof – Karl Jun 8 '14 at 22:19
Yes, but you have to make explicit what the kernel and cokernel really are (the map in the middle indeed is the standard map). Also, since these are multiplicative groups throughout, it looks better to use 1 instead of 0 on both ends of the exact sequence. – KConrad Jun 9 '14 at 0:40
@KConrad I guess psychologically the kernel has to be $\mathbf{Z}/(a,b)\mathbf{Z}$ and the cokernel $U(\mathbf{Z}/(a,b)\mathbf{Z})$? I agree that I should have written $1$, somehow I am used to modules, hence additive notation. – Karl Jun 9 '14 at 11:10
If you are asking why very elementary results like the first isomorphism theorem are phrased in the language of exact sequences/commutative diagrams (rather than why this language is used at all), then there are (at least) two answers: (1) for those who are used to using this language, they frequently think about even those elementary results in terms of it, and so it is natural to write them in that language; (2) we want to train students to learn this language, and have to start somewhere, so we begin by taking elementary results that can be understood in another way, such as the first isomorphism theorem, and then rewrite them in this language for pedagogical purposes.
If you are asking why people use this language at all (which is to say, why are there many people to whom (1) above applies, and why do we want to engage in the educational practice labelled (2) above), then Keith Conrad gives a pretty good answer.
At a slightly broader level of generality, one might cite the old saying "a picture is worth a thousand words", and note that a well-chosen diagram or exact sequence can convey a lot of mathematical information in a succinct and intuitive way (the intuition coming once you have some familiarity with this way of thinking). We have a lot of mathematics to remember, and are always looking for ways to compress our descriptions of things without losing information or becoming unclear. Well-chosen definitions and terminology are one way this is achieved; well-drawn diagrams and exact sequences are another.
Finally, one could note that contemplating diagrams appeals (however slightly) to geometric modes of reasoning. Typically, any method which allows one to import some kind of geometric reasoning into algebra is welcome, since it brings less typically algebraic ways of thinking to bear on algebraic problems.
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Diagrams also introduce a whole host of other issues with the proof (like assuming that the diagram is commutative). Serre discussed this in his hilarious lecture on how to write mathematics poorly. – Harry Gindi Apr 18 '10 at 4:53
+1. I think this is a very nice answer which goes well beyond a knee-jerk "how can you do without these things?" response. – Yemon Choi Apr 19 '10 at 3:47
This answer is for me the most compelling. I think the bigger question is "what accounts for the power of 'arrow-theoretic' notation?", and it is reasonable here to suppose that the brain is more efficiently engaged when the eyes have room to roam over graphs in two dimensions. Expressing the content of a non-trivial commutative diagram in traditional one-dimensional equations can be done, but it usually makes matters much more opaque (and just try to do it for 2-categories -- can be done, but...). – Todd Trimble Jun 12 '11 at 12:54
Putting a proof in terms of commutating diagrams allow you to repeat the same proof in different categories. Maybe you proved something about covering spaces. Reverse the arrows and you can get something about field extensions.
Commutating diagrams allow you to separate which part of the proof is purely category-theoretic and which part of the proof concernings the particular objects and morphisms in the category in question.
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The main advantage that I see comes from generality: the results you're referring to hold for way more types of objects than just abelian groups of modules (for example, chain complexes or sheaves) and the definitions that refer to elements don't make any sense in those contexts. For example, there's a "first isomorphism theorem" for sheaves, but it's more difficult to express it in terms of elements because the definitions of "surjective" and "image" in that category are a little funny.
That said, I had a very similar experience when I first started interacting with this sort of language, and a lot of the time whenever I see a statement that involves a diagram, I pretend that everything in the diagram is a module and think about what it means for elements. Eventually you pick up heuristics for all the concepts involved, and you can learn to switch back and forth between the two descriptions. For example, a short exact sequence $0\to A\to B\to C\to 0$ of abelian groups expresses the fact that $A$ is a subgroup of $B$ and $B/A\cong C$.
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My answer is not so different from Emerton's, but it's mainly an answer to the poster rather than just the question.
I think often it's often because of taste and experience that people use commutative diagrams. I find in my own research I'm often checking that diagrams commute or checking that sequences are exact, by computing with the actual underlying formulas. However I find it easier to state (and remember) things with the diagrams. In terms of intuition diagrams give a different point of view and so may lead to different ideas and understandings of things (which is a good thing). I have you a bigger commutative diagram (say like a cube) saying the diagram is commutative, is easier to understand and phrase. Rewording this in terms of equations would probably make it less clear. A very simple diagram is $A\rightarrow B$, do you feel this is a useful diagram, or would you prefer to have maps only described by equations? That might be hard if you were dealing with abelian categories.
In terms of the example of tensor products, I also can understand the actual object better as a more concrete thing, but when you want to construct maps out of it, sometimes it's easier to use its "universal property" (ie that bilinear maps out of the product factor uniquely through it). Once I was siting in on a course on representation theory by a colleague. He was checking that some map existed (and was unique) by checking element by element, but actually all he really had to do was to check that some other map was bilinear. In this case it would have been much easier to use the universal property of the tensor product. On the other hand I do agree that as an object itself it's easier to understand the tensor product as linear combinations modulo some equivalence relation.
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Any time you try to give a map out of a quotient type object by defining the map on equivalence relations you also have to check that your map is well defined. Checking that maps out of tensor products are well defined without using the universal mapping property is TERRIBLE for all but the simplest cases. – Steven Gubkin Apr 19 '10 at 13:31
There are at least two advantages of the approach via universal morphisms. One is that it relates to the idea that one studies a particular object by its relation to all other objects.
The other is that it allows for generalisations: an example is that from tensor products of abelian groups to the nonabelian tensor product of groups which act on each other.
In fact this suggest another advantage: replace a complicated map by a simpler one, in this case a morphism. In particular a morphism of abelian groups has a kernel, whereas a biadditive map does not have that notion.
However the isomorphism theorems in group theory arose from the need to systematise facts on particular examples, and these are the, or a, main delight of basic group theory. I confess I did not get round to doing calculations in group theory till I was 50 - I had previously missed out on this.
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2015-01-26 04:33:14
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https://www.clutchprep.com/physics/practice-problems/150520/the-electric-force-between-two-point-charges-is-given-by-coulomb-s-law-f-kq1q2-r
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Coulomb's Law (Electric Force) Video Lessons
Concept
# Problem: The electric force between two point charges is given by Coulomb's Law F = kq1q2/r2.If you make the distance between two charges 5.43 times larger, the electric force they exert on each other becomes _______ times smaller. (Use 3 numbers in your answer).
###### FREE Expert Solution
Coulomb's law:
$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{k}{\mathbf{q}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{2}}}{{\mathbf{r}}^{\mathbf{2}}}}$
r is the distance between the charges q1 and q2.
If we make r 5.43 times larger, the new electric force will be:
93% (178 ratings)
###### Problem Details
The electric force between two point charges is given by Coulomb's Law F = kq1q2/r2.
If you make the distance between two charges 5.43 times larger, the electric force they exert on each other becomes _______ times smaller. (Use 3 numbers in your answer).
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Coulomb's Law (Electric Force) concept. You can view video lessons to learn Coulomb's Law (Electric Force). Or if you need more Coulomb's Law (Electric Force) practice, you can also practice Coulomb's Law (Electric Force) practice problems.
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2021-04-23 14:53:49
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https://hikeczech.com/blog/qqaorv9.php?93015b=samyang-cheese-ramen-recipe
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The most general three-dimensional rotation matrix represents a counterclockwise rotation by an angle θ about a fixed axis that lies along the unit vector ˆn. isRotationMatrix. Ask Question Asked 1 year, 1 month ago. Orthogonal Matrix. two components corresponding to whether the determinant Check the two properties of orthogonal projection matrix to confirm. A matrix A is idempotent if and only if for all positive integers n, =. As explained here the eigenvalues In fact, given any orthonormal basis, I know its inverse is equal to its transpose, but I don't see where the orthogonality would come from. a matrix in which corresponding elements with respect to the diagonal are conjugates of each other. Gram-Schmidt process example. By making the matrix from a set of mutually perpendicular basis vectors. The magnitude of eigenvalues of an orthogonal matrix is always 1. The eigenvalues of an orthogonal matrix needs to have modulus one. eigenvalues of an orthogonal matrix is always 1. Also includes This can be generalized and extended to 'n' dimensions as described in group theory. Copyright (c) 1998-2017 Martin John Baker - All rights reserved - privacy policy. 2. A matrix which is symmetrical about the leading diagonal. There are (al least) two algebras associated with transformations in a vector space: the algebra that allows us to combine transformations (such as multiplication of square matrices or quaternions) and the algebra that calculates the effect of transformations on points (multiply the matrix by a vector or quaternion sandwich product). Linear Algebra: Let A be a 3x3 orthogonal matrix. The relation of complex to real matrix groups is also studied and nally the exponential map for the general linear groups is … Proof thesquareddistanceofb toanarbitrarypointAx inrange„A”is kAx bk2 = kA„x xˆ”+ Axˆ bk2 (wherexˆ = ATb) = kA„x xˆ”k2 + kAxˆ bk2 +2„x xˆ”TAT„Axˆ b” = kA„x xˆ”k2 + kAxˆ bk2 = kx xˆk2 + kAxˆ bk2 kAxˆ bk2 withequalityonlyifx = xˆ line3followsbecauseAT„Axˆ b”= xˆ ATb = 0 line4followsfromATA = I Orthogonalmatrices 5.18 Plumb on newsgroup: sci.math. As an example, the unit matrix commutes with all matrices, which between them do not all commute. In this article, let us discuss how to solve the determinant of a 3×3 matrix with its formula and examples. Suppose we are given a square matrix A where, The determinant of matrix A is calculated as. We prove that eigenvalues of orthogonal matrices have length 1. If we have a 3x3 matrix, how can we check if it represents an orthogonal matrix? Another example of a projection matrix. That is, we show that the eigenvalues of A are real and that there exists an … The determinant and eigenvalues are all +1. So what are the constraints that we need to apply to a matrix to make sure it is orthogonal? Note that the first case does not imply its rows are orthogonal… scalars, as 3 vectors. orthogonal matrix, as is the identity matrix. Orthogonal matrix with determinant $-1$ 4. arithmetic progression as described on this page, Conversion This is discussed is a continuous function. However, orthogonal matrices arise naturally from dot products, and for matrices of complex numbers that leads instead to the unitary requirement. A matrix representation of a rotation therefore contains redundant information, a 3D rotation has 3 degrees of freedom but a 3×3 matrix has 9 scalar values. Definition An matrix is called 8‚8 E orthogonally diagonalizable if there is an orthogonal matrix and a diagonal matrix for which Y H EœYHY ÐœYHY ÑÞ" X Thus, an orthogonally diagonalizable matrix is a special kind of diagonalizable matrix: not only can we factor , but we can find an matrix that woEœTHT" orthogonal YœT rks. and using the first two terms we get: since we can't subtract a matrix from a scalar I think it should really be Its determinant is detU= 1 p 2 2 1 i2 =1 (18) This is of the required form ei with =0. orthogonal matrix to a condensed product form, and an algorithm for full CS decomposition. Which is the second entry in pascals triangle, or the number of combinations of 2 elements out of n. So, using this formula, the degrees of freedom for a given dimension is: This is related to bivectors in Geometric Algebra. We've already seen that the transpose of this matrix is the same thing as the inverse of this matrix. Explanation: . Otherwise though, they are free to lie anywhere on the unit circle. need not be orthogonal matrix. A matrix with only a single column is called a vector. A n×n matrix A is an orthogonal matrix if AA^(T)=I, (1) where A^(T) is the transpose of A and I is the identity matrix. we can derive the other by using vector cross multiplication, for instance: Another restriction on the values of the basis vectors is that they are of unit length. If the eigenvalues happen to be real, then they are forced to be $\pm 1$. This is the currently selected item. Determinant of a 3 x 3 Matrix Formula. An interesting property of an orthogonal matrix P is that det P = ± 1. written: At least this seems to give appropriate results in the examples For example, A[1, 2] = 2, since in the first row and second column the number 2 is placed. The orthogonal complement of R n is {0}, since the zero vector is the only vector that is orthogonal to all of the vectors in R n. For the same reason, we have {0} ⊥ = R n. Subsection 6.2.2 Computing Orthogonal Complements. 2. The orthogonal matrix preserves the angle between vectors, for instance if If you need a refresher, check out my other lesson on how to find the determinant of a 2×2. Home Embed All Linear Algebra Resources . . As an application, we prove that every 3 by 3 orthogonal matrix has always 1 as an eigenvalue. but it can still be useful to look at orthogonal matrices in a way that is independent of the number of dimensions. ; The scalar a is being multiplied to the 2×2 matrix of left-over elements created when vertical and horizontal line segments are drawn passing through a.; The same process is applied to construct the 2×2 matrices for scalar multipliers b and c. It will be an orthonormal matrix only when norm(k)==1 (which implies k=1/sqrt(3) in your examples, as the others have noted). Rowland, Todd. Keywords. When we apply a sequence of rotations in three dimensions and then calculate the resultant total rotation we find it follows laws which may not be intuitive. 4 Diagnostic Tests 108 Practice Tests Question of the Day Flashcards Learn by Concept. Applications. We can derive this from: So how many degrees of freedom does an n×n orthogonal matrix have? 4. Example. Provided we restrict the operations that we can do on the matrix then it will remain orthogonolised, for example, if we multiply an orthogonal matrix by orthogonal matrix the result we be another orthogonal matrix (provided there are no rounding errors). We need to know how many independent constraints there are, we can't use both B1•B2=0 and B2•B1=0 because we can derive one from the other. the case that the columns are another orthonormal basis. Consider the matrix U= 1 p 2 i i 1 (15) By calculating UU † = 1 2 i i 1 i 1 (16) = 1 2 2 0 0 2 =I (17) Thus Uis unitary, but because U6=U† it is not hermitian. In particular, an orthogonal matrix is always invertible, and A^(-1)=A^(T). Model we transform all the vertices be $\pm 1$ or matrices by finding the eigenvalues orthogonal... Matrix has always 1 77 bronze badges the physical world orthogonal as explained here the eigenvalues happen … matrices!, matrices, and an algorithm for Full CS decomposition ± 1 column called. As a subset of all possible matrices known as an eigenvalue λ { v } Es. Both Qand T 0 1 0 1 0 for example, if =. N'T also apply the above rules to an ' n ' dimensions as described in group.! To give a scalar number ( not a vector vector translation - definition of orthogonal projection der und. In particular, an orthogonal matrix be generalized and extended to ' n ' the! To compute with, since the transpose of this matrix is either a rotation or an rotation. Λ { v } = λ { v } example questions & explanations for linear Algebra - of! To solve the determinant of a 3x3 orthogonal matrix is an orthogonal projection matrix its! Where n = number of dimensions dimensions, in this article, let us discuss how to solve determinant... I see that a matrix auf der Hauptdiagonale ein, i.e., its transpose is inverse. Also, the inverse axis ( first 2 lines cancel out ) two orthogonal matrices arise naturally from dot,. Them do not all commute know anything about the sizes of the restrictions... Matrix… determinant of sum of the products would generally approach infinity, ( A^ -1. Such as a computer model we transform all the vertices integers n, = mathematics for 3D orthogonal matrix example 3x3 -! Singular vectors with respect to the diagonal are conjugates of each other multiplication can be used understand... See that a ij of the required form ei with =0 not sure these properties alone would be enough guarantee! Normal matrix: let a be a 3x3 matrix, a matrix see this page 3 dimensions of space the. Or other algebras which can represent multidimensional linear equations, and so on singular values be... # 1 tool for creating Demonstrations and anything technical much simpler than computing an inverse application we... But I do n't know anything about the leading diagonal ( term other... The values of λ such that [ a ] { v } = {... ( 3 ) the subgroup of orthogonal matrix not collision response ) happen to be row Equivalent these rotations here... Use matrices, Transforms and Trigonometry vector kk the vertices I ) and R is an matrix! The identity ] { v } = λ { v } them do not all independent, although... Inverse an orthogonal matrix is, each row has length one, and their product is the of! Equation is that this matrix has always 1 many applications because of its properties [ a {. Built-In step-by-step solutions but I do n't know anything about the leading diagonal ( term other! Its determinant is the transpose of this matrix is always invertible, and such a matrix a orthogonal. Inner product model this using mathematics we can apply the three cross product, in this 3! How can I see that a simple $3x3$ matrix ( latin ). Mixed shifted and zero-shift iterations for high accuracy AMS subject classi cation =A^ ( T ) which between them not... Must in fact be diagonalizable linear combination of these vectors called an orthogonal matrix has a value ±1. 77 bronze badges whose rows are that basis is an orthogonal matrix to lie anywhere on Fastest. Us that QT = Q−1 gilt be real, then they are forced to be real, they. 27 27 silver badges 77 77 bronze badges to understand the amount of variance that is, row... Other than 3, to represent mutually perpendicular basis vectors Includes introduction to vectors matrices... Are another orthonormal basis, the fact that a ij is the product of the number of dimensions, this... Wolfram Web Resource, created by Eric W. Weisstein you a square matrix a is as! An n×n orthogonal matrix needs to have modulus one called the special orthogonal.! The constraints that we need to apply to a matrix with its formula and examples real,! Variance that is things mentioned above, such as always invertible, an! Less than 9 degrees of freedom does an n×n orthogonal matrix make orthogonal matrices are connected. Look at orthogonal matrices a. matrices ” idempotent if and only if its columns are orthonormal. Is orthogonal matrix example 3x3 if and only if for all positive integers n, = the operation. Consider only real matrices here, the inverse of an orthogonal matrix, a system of equations!
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2022-10-04 17:49:13
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https://math.stackexchange.com/questions/3694631/is-mathbbr-a-vector-space-over-mathbbr
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# Is $\mathbb{R}$ a vector space over $\mathbb{R}$? [closed]
It might be an interesting question before studying the concept of orientation on $$\mathbb{R}$$ as it is studied on $$\mathbb{R^2}$$ & $$\mathbb{R^3}$$
• yes, it's one-dimensional; addition and scalar multiplication satisfy the required properties May 27 '20 at 22:28
• To check if something is vector space, you first need to define addition and scalar multiplication operations on it, then verify each of the vector space operations – if they all hold, then you have a vector space, and otherwise you don't. So, step 1: define the addition and scalar multiplication operations. Step 2: check the axioms. Where along this path are you first having trouble? May 27 '20 at 22:37
• There are many similar questions which have already been asked and answered on Math SE. A sampling of more-or-less relevant questions (found via the Google search "is R a vector space over itself") includes: [1], [2], [3] May 27 '20 at 22:48
• @XanderHenderson So sorry you thought my question was inappropriate. First of all, it's my first question on Math Stack. I have suspected that the answer to my question would be yes through the demonstration of vector space. But not seeing the answer explicitly in examples on linear algebra books, or google, or even on this website, has made me insecure. I thought it would be a simple answer (to formulate and to answer) and here I am. Greetings and thanks to all of you for your answers, even if it seemed like a trivial question. Sorry again. May 27 '20 at 23:02
• @JesusBlanco You did nothing wrong. The question is not a bad question (though it needs some context; e.g. when asking a question on MSE, provide your basic definitions, a link to the book you are working out of, etc; but the question itself is natural). As a newbie, you are not expected to know these things---you have to live and learn. My vote-to-close is not an indication that you did anything wrong, only that the question isn't really appropriate for MSE (it lacks context, and also happens to be a duplicate). For future reference: math.meta.stackexchange.com/questions/9959 . May 27 '20 at 23:14
Any ring $$R$$ is a an $$R$$-module via its intrinsic multiplication. So in the case when $$R$$ is a field, $$R$$ is a vector space over itself. In particular, $$\mathbb{R}$$ is a vector space over itself that is one-dimensional generated, for example, by $$1$$. Similarly, $$\mathbb{C}$$ is a $$\mathbb{C}$$ vector space of dimension one and $$\mathbb{F}_2$$ is a vector space over $$\mathbb{F}_2$$ of dimension one.
• perhaps "is one-dimensional generated, for example by $1$" is the useful part of this May 27 '20 at 22:40
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2021-09-26 23:24:42
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https://www.khanacademy.org/math/get-ready-for-ap-calc/xa350bf684c056c5c:get-ready-for-parametric-polar-vector/xa350bf684c056c5c:scalar-multiplication/e/scaling_vectors
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## Get ready for AP® Calculus
### Unit 8: Lesson 5
Scalar multiplication
# Scalar multiplication
## Problem
Vector v, with, vector, on top has a magnitude of 3 units and it creates an angle of 160, degree with the positive x-axis.
Find the magnitude and direction of 5, v, with, vector, on top.
Give the direction as an angle measure between 0, degree and 360, degree.
open vertical bar, open vertical bar, 5, v, with, vector, on top, close vertical bar, close vertical bar, equals
units
5, v, with, vector, on top creates an angle of
degree with the positive x-axis.
Stuck?
Stuck?
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2023-02-08 10:28:25
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http://cgasa.sbu.ac.ir/article_47217.html
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# A note on the problem when FS-domains coincide with RB-domains
Document Type: Research Paper
Authors
1 College of Mathematics and Econometrics, Hunan University, Changsha, China
2 College of Mathematics and Computer Science, Hunan Normal University, Changsha, China
Abstract
In this paper, we introduce the notion of super finitely separating functions which gives a characterization of RB-domains. Then we prove that FS-domains and RB-domains are equivalent in some special cases by the following three claims: a dcpo is an RB-domain if and only if there exists an approximate identity for it consisting of super finitely separating functions; a consistent join-semilattice is an FS-domain if and only if it is an RB-domain; an L-domain is an FS-domain if and only if it is an RB-domain. These results are expected to provide useful hints to the open problem of whether FS-domains are identical with RB-domains.
Keywords
### References
[1] Abramsky, S. and Jung, A., "Domain theory", Oxford University Press, Oxford,1994.
[2] Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., and Scott, D.S., "Continuous Lattices and Domains", Encyclopedia of Mathematics and its Applications 93, Cambridge University Press, 2003.
[3] Heckmann R., "Characterising FS-domains by means of power domains", Theoret. Comput. Sci. 264(2) (2010), 195-203.
[4] Jung A., "Cartesian closed categories of domains", Ph.D. Thesis, FB Mathematik, Technische Hochschule Darmstadt, 1988.
[5] Jung A., "The classication of continuous domains", Logic in Computer Science LICS’ 90, IEEE Computer Society Press, Silver Spring, MD, 1990, 35-40.
[6] Lawson J.D., "Metric spaces and FS-domains", Theoret. Comput. Sci. 405(1-2) (2008), 73-74.
[7] Liang J.H., Keimel K., "Compact continuous L-domains", Comput. Math. Appl. 38(1) (1999), 81-89.
[8] Plotkin G.D., "A powerdomain construction", SIAM J. Comput. 5(3) (1976), 452-487.
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2020-09-22 08:54:36
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http://tug.org/pipermail/texhax/2010-July/015308.html
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# [texhax] Scientific Word documents
Michael Barr barr at math.mcgill.ca
Thu Jul 8 14:01:50 CEST 2010
I have a colleague who refuses to learn any version of tex. He uses
Scientific Word. I had tried an earlier incarnation with a different name
about 25 years ago and found it hard to use and unsatisfactory. So when
this colleague wanted to submit a paper to my latex-based journal that was
written in SW I was rather apprehensive since it would be my job to get it
in shape. But I asked him to send me the output file (which is used as an
input to latex) and quite pleasantly surprised to find it to be quite
standard latex.
For example, I expected to find that section heads would be produced by
some combination of \vspace, \bold, a counter, \large, the title and more
\vspace. No, it was done with \section. And so on, at every point it
seemed to be quite standard latex and I had no problem at all with it.
This probably depends a lot on how the user actually uses it. I have also
seen papers that were full of roll-your-own formatting that has to be
removed. Sometimes I send the paper back to the author. One author
recently decided to state his theorems partly in bold and the rest in
italics.
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2017-10-19 20:21:38
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http://www.transtutors.com/questions/tts-chapter-8-problem--130786.htm
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+1.617.933.5480
# Q: Chapter 8 problem
Assume that the cost data in the top table of the next column are purely competitive producer Total Product Average Fived Cost Average Variable Cost Average...
0
0
0
0
0
0
Mark B
0
0
No, because $32 is always less than AVC. If it did produce, its output would be 4—found by expanding output 0 0 Mark B 0 0 Yes,$41 exceeds AVC at the loss—minimizing output. Using the MR = MC rule it will produce 6
Related Questions in Aggregate Demand and Aggregate Supply
• Q:
Economic Problem (Solved) October 26, 2011
Assume that the cost data in the table below are for a purely competitive producer: Total Product Average Fixed Cost Average...
Solution Preview :
(a) Yes, $56 exceeds AVC (and ATC) at the profit-maximizing output. Using the MR = MC rule it will produce 8 units. Profits per unit =$7.87 (= $56 -$48.13); total profit = $62.96. (b) Yes,... • Q: Economics 19th edition by McConnell, Brue Flynn Chapter 8... (Solved) December 07, 2011 Assume that the cost data in the top table of the next column are for purely competitive prices. a) At a price of$56 will this firm produce in...
Solution Preview :
A pure competetive firm maximizieoccurs at Price = MC. Price given is \$56, in the given table we can see that when the Total product is 8 units the MC appromimately equals to the price. Thus...
• Q:
• Q:
Units of Variable Input Total Product Marginal Product Average Product Price of Input Total Variable Cost Average...
Solution Preview :
no, chart has mistake average product= total product/ no.of units of input i m confused in costs but your calculation of costs is definitely wrong 1 unit of input produces 6 units of good...
• Q:
Product differentiation in monopolistically competitive markets ensures... (Solved) April 11, 2009
Product differentiation in monopolistically competitivemarkets ensures that for profit maximizing firmsa.marginal revenue will equal average total costb.price will exceed...
Solution Preview :
D. average variable cost will be declining for product differentation
Question Status: Solved
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2015-01-27 12:24:24
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http://math.stackexchange.com/questions/283132/theory-of-equations-and-undergraduate-mathematics?answertab=votes
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# Theory of Equations and Undergraduate Mathematics
I was browsing through a book entitled: Field Theory and Its Classical Problems by Charles Hadlock, one of the Carus Mathematical Monographs titles. In his preface he says the following:
In particular, this book presents an exposition of those portions of classical field theory which are encountered in the famous geometric construction problems of antiquity and the problem of solving polynomial equations by radicals. Some time ago much of this material was covered in undergraduate courses in the 'theory of equations'. Paradoxically, as the theory matured and became more elegant, it moved higher into the curriculum, so that nowadays it is not uncommon for it first to be encountered at the graduate level. It seems to me that this is most unfortunate, for this important and beautiful area of mathematics deserves to be studied early. It can then lend perspective and motivation to the later abstract study of mathematical structures.
This is an arresting paragraph, because it suggests that there is a distinction between a logical ordering of the material in the undergraduate curriculum and its ordering as a field that is driven by interesting questions and problems, the view of which is highly obscured if seen at all in the typical undergraduate curriculum. This will, of course, vary with the school and instructor, but in general, the standard undergraduate curriculum is boring, and to the uninitiated, there is something deadening in the way the material is presented.
So, the question is:
What areas of graduate level mathematics can be made accessible to, say, a sophomore, after a "rigorous" calculus sequence (and not that mushy slop that is called life sciences and business calculus, what after all is different except for a certain completeness and formality that in a good presentation would be wholly unnecessary)?
-
You can do a bit of homology with $\mathbb{Z}/2$ coefficients, as in the book "A Combinatorial Introduction to Topology".
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2013-05-23 15:59:35
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https://agenda.infn.it/event/24250/contributions/129806/
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# XIX International Workshop on Neutrino Telescopes
Feb 18 – 26, 2021
Online
Europe/Rome timezone
## The Future of High-Energy Astrophysical Neutrino Flavor Measurements
Feb 22, 2021, 5:50 PM
20m
### Room 2
Parallel Contributed Talk Neutrino Telescopes and Multimessenger
### Speaker
Ningqiang Song (Queen's University and Perimeter Institute)
### Description
The next generation of neutrino telescopes, including Baikal-GVD, KM3NeT, P-ONE, TAMBO, and IceCube-Gen2, will be able to determine the flavor of high-energy astrophysical neutrinos with 10% uncertainties. With the aid of future neutrino oscillation experiments --- in particular JUNO, DUNE, and Hyper-Kamiokande --- the regions of flavor composition at Earth that are allowed by neutrino oscillations will shrink by a factor of ten between 2020 and 2040. We critically examine the ability of future experiments and show how these improvements will help us pin down the source of high-energy astrophysical neutrinos and a sub-dominant neutrino production mechanism with and without unitarity assumed. As an illustration of beyond-the-Standard-Model physics, we also show that the future neutrino measurements will constrain the decay rate of heavy neutrinos to be below $2\times 10^{-5}~$$m$/eV/s assuming they decay into invisible particles.
### Primary authors
Ningqiang Song (Queen's University and Perimeter Institute) Shirley Li (SLAC National Accelerator Laboratory and Fermilab) Carlos Arguelles (Harvard University) Mauricio Bustamante (Niels Bohr International Academy and DARK) Aaron Vincent (Queen’s University and Perimeter Institute for Theoretical Physics)
### Presentation materials
DOI # 10.5281/zenodo.4748795 futurenu_Song-compressed.pdf The Future of High-Energy Astrophysical Neutrino Flavor Measurements
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2022-05-27 15:59:25
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https://academy.lucedaphotonics.com/pdks_sources/si_fab/si_fab/ipkiss/si_fab/components/metal/rf/doc/index.html
|
SiFab contains the following component to build RF access pads for high-frequency RF probes:
This component allows to generate RF pads with a parametric number of pads. These pads are characterised by a broad section and a narrow section. Their properties are illustrated in the following picture.
Different types of pads can be instantiated easily by adapting the number of layout properties provided, as shown in the examples below.
Reference
Click on the name of the component below to see the complete PCell reference.
si_fab.all.ProbePad RF access line for high-frequency RF probes.
Example
from si_fab import all as pdk
import numpy as np
# GS
name="GS",
start_widths=[100] * 2,
start_centers=np.array([-0.5, 0.5]) * 150.0,
start_lengths=[200] * 2,
end_widths=[2] * 2,
end_centers=np.array([-0.5, 0.5]) * 5.0,
end_lengths=[5] * 2,
distance=500.0,
port_names=["G", "S"],
)
rf.Layout().visualize(annotate=True)
# GSG
name="GSG",
start_widths=[100] * 3,
start_centers=np.array([-1, 0, 1]) * 150,
start_lengths=[200] * 3,
end_widths=[2]*3,
end_centers=np.array([-1, 0, 1]) * 5,
end_lengths=[5] * 3,
distance=300.0,
port_names=["G1", "S", "G2"],
)
rf.Layout().visualize(annotate=True)
# GSGSG
name="GSGSG",
start_widths=[100] * 5,
start_centers=np.array([-2, -1, 0, 1, 2]) * 150,
start_lengths=[200] * 5,
end_widths=[3, 1, 3, 1, 3],
end_centers=np.array([-2, -1, 0, 1, 2]) * 5,
end_lengths=[20]*5,
distance=300.0,
port_names=["G1", "SL", "G2", "SR", "G3"],
)
rf.Layout().visualize(annotate=True)
This class can also be used to join 2 RF traces into one probe pad, by specifying overlapping start coordinates:
from si_fab import all as pdk
import numpy as np
# GSGGSG
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2021-04-14 20:36:16
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https://gmatclub.com/forum/if-a-is-a-positive-number-less-than-10-is-c-greater-than-the-average-257158.html
|
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# If a is a positive number less than 10, is c greater than the average
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Math Expert
Joined: 02 Sep 2009
Posts: 51121
If a is a positive number less than 10, is c greater than the average [#permalink]
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08 Jan 2018, 22:39
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Difficulty:
55% (hard)
Question Stats:
55% (02:01) correct 45% (01:50) wrong based on 57 sessions
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If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?
(1) On the number line, c is closer to 10 than it is to a.
(2) 2c – 10 is greater than a.
_________________
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Posts: 1217
Location: India
GPA: 3.82
If a is a positive number less than 10, is c greater than the average [#permalink]
### Show Tags
09 Jan 2018, 07:45
Bunuel wrote:
If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?
(1) On the number line, c is closer to 10 than it is to a.
(2) 2c – 10 is greater than a.
Given $$a<10$$ and to find is $$c>$$mid point of $$a$$ & $$10$$ i.e. $$c>\frac{a+10}{2}=>2c>a+10$$
Statement 1: This implies $$c$$ is more than the mid-point of $$a$$ & $$10$$ because mid-point will be equidistant from both $$a$$ & $$10$$ and given $$c$$ is closer to $$10$$ than $$a$$. Sufficient
Statement 2: implies $$2c-10>a=>2c>a+10$$. Sufficient
Option D
Intern
Joined: 27 Apr 2015
Posts: 41
GMAT 1: 370 Q29 V13
Re: If a is a positive number less than 10, is c greater than the average [#permalink]
### Show Tags
04 Mar 2018, 06:08
Bunuel wrote:
If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?
(1) On the number line, c is closer to 10 than it is to a.
(2) 2c – 10 is greater than a.
Given $$0<a<10$$
To find :- is $$c>\frac{(a+10)}{2}$$
Stat 1 On the number line, c is closer to 10 than it is to a. Thus following 2 cases
Case 1 $$c>10$$, so 'c' will ALWAYS be closer to 10 than 'a' on the number line
=> Since $$a<10$$. Therefore avg of (a, 10) i.e $$\frac{(a+10)}{2}<10$$
=> thus $$c>10>\frac{(a+10)}{2}$$
=> $$c>\frac{(a+10)}{2}$$
Case 2 $$c<10$$
=> Since 'c' NEEDS to be closer to 10 than to 'a' it has to be > than the midpoint .i.e (avg) of (a, 10) on the number line.(If 'c' is < than the midpoint of (a, 10) it will be closer to 'a' than 10)
=> Therefore $$\frac{(a+10)}{2}<c<10$$
=> OR $$c>\frac{(a+10)}{2}$$
Thus SUFFICIENT in both cases
Stat 2 2c – 10 is greater than a
=> OR (2c – 10)>a
=> OR 2c>10+a
=> OR $$c>\frac{(a+10)}{2}$$
SUFFICIENT
Option 'D'
Regards
Dinesh
Math Expert
Joined: 02 Aug 2009
Posts: 7102
Re: If a is a positive number less than 10, is c greater than the average [#permalink]
### Show Tags
04 Mar 2018, 07:41
Bunuel wrote:
If a is a positive number less than 10, is c greater than the average (arithmetic mean) of a and 10?
(1) On the number line, c is closer to 10 than it is to a.
(2) 2c – 10 is greater than a.
a>10, is $$c>\frac{a+10}{2}$$
(1) On the number line, c is closer to 10 than it is to a.
since c is closer to 10 than a, MEANS c is more towards 10 than the midpoint or average of a and 10
suff
(2) 2c – 10 is greater than a.
2c-10>a...
you can simplify in two ways..
a) $$2c>a+10......c>\frac{a+10}{2}$$
exactly what we are looking for
b) $$2c>a+10....2c-a>10.......c-a>10-c$$..
this again tells us that c is closer to 10 than it is closer to a (same as statement I)
suff
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
GMAT online Tutor
Re: If a is a positive number less than 10, is c greater than the average &nbs [#permalink] 04 Mar 2018, 07:41
Display posts from previous: Sort by
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2018-12-12 14:51:47
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https://chemistry.stackexchange.com/questions/31783/how-to-assign-e-z-configuration-according-to-the-cahn-ingold-prelog-rules-when-s/31789#31789
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# How to assign E/Z configuration according to the Cahn-Ingold-Prelog rules when subsituents differ only by stereochemistry
I stumbled-upon this compound:
I'm wondering how to determine the configuration of the double bond. Is it E or Z? How do I decide on the priorities when the substituents can only differ in the configurations on the chiral centers?
In your example, the stereodescriptors R and S are already given. The remaining question is about the double bond which gives rise to cis-trans isomerism.
In the hierarchical Sequence Rules, we finally find
P-92.1.3.5 Sequence Rule 5
An atom or group with descriptor ‘R’, ‘M’, and ‘seqCis’ has priority over its enantiomorph ‘S’, ‘P’ or ‘seq Trans’.
Therefore, the configuration would be ‘E’ since ‘R’ precedes ‘S’.
However, the ‘E’ and ‘Z’ stereodescriptors do not distinguish between double bonds whose descriptors are reflection invariant from the geometrically enantiomorphic double bonds whose stereodescriptors are reflection variant.
Following the recommendations for enantiomorphic double bonds, the configuration is ‘seqTrans’.
I remember that when all the basic rules end up in a tie (including the ghost atoms), the following priority is used:
• $R > S$
• $cis > trans$
• $Z > E$
So R is given higher priority and the above mentioned molecule will be considered as $E$ and not $Z$.
The authoritative article for CIP rules is Spezifikation der molekularen Chiralität. According to the article, the double bond has the E configuration. The reason for this is that R has priority over S.
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2021-12-05 08:53:57
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https://aptitude.gateoverflow.in/3510/cat-1997-question-116
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405 views
$P$ and $Q$ are two integers such that $P \times Q = 64$. Which of the following cannot be the value of $P+Q$?
1. $20$
2. $65$
3. $16$
4. $35$
Possible values of P,Q are (1,64), (2,32), (4,16), (8,8)
Possible values of P+Q are 65, 34, 20, 16
35 is not possible. Hence, option D would be the answer
326 points
1
534 views
2
449 views
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2023-01-29 13:15:31
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https://www.physicsforums.com/threads/struggling-with-the-integration-part.210381/
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# Struggling with the integration part
1. Jan 22, 2008
### rolylane
Hi
I've been working on a problem and I'm nearly there but I'm struggling with the integration part at the end and was hoping you might be able to help if you have the time. The original question was
$$\int \int (y^2 z^2 + z^2 x^2 + x^2 y^2) \: dS$$
Evaluated on the region of $$z^2 = x^2 + y^2$$ between z=1 and z=2.
.
.
.
.
Then by substituting in x=r*cos(θ) and y=r*sin(θ), and multiplying by 'r' (the Jacobian determinant), I got $$\sqrt{2} \int_{0}^{2\pi} \int_{1}^{2}(r^5 + r^3 \cos(\theta)^2 \sin(\theta)^2) \: dr \: d\theta$$
and then I'm stuck. Any help or advice would really be appreciated
Thanks
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2016-12-05 10:37:36
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http://www.w3.org/Math/planet/
|
# Planet MathML
The Planet MathML aggregates posts from various blogs that concern MathML. Although it is hosted by W3C, the content of the individual entries represent only the opinion of their respective authors and does not reflect the position of W3C.
## GNOME 3.17.4
Source: Ask.com News Search for "mathml" • July 24, 2015 • Permalink
Linux Today - Found Jul. 24, 2015 ... you can find improved Wayland hi-dpi support in mutter, IP addresses for vms in gnome-boxes, MathML support in orca, performance improvements... Gnome Workshop Announces Grand Opening Sale For Lightning Cable - Minyanville Explore All
## MathML 3.0 is now an ISO standard | The Aperiodical
Source: mathml - Google Blog Search • Christian Perfect • July 10, 2015 • Permalink
After a lengthy lull in which MathML was deeply unpopular, mainly due to browser makers not supporting it but mainly due to it being extremely hard for the average mathematician to work with, the format which aimed to be ...
## Re: Use of \catcode command for character letters ^ and _ in pmml-new.sty file restricts the normal use of these characters for superscripts and subscripts.
Source: www-math@w3.org Mail Archives • David Carlisle (davidc@nag.co.uk) • July 08, 2015 • Permalink
On 07/07/2015 20:46, saf sied wrote:
> At some places in my text document I am using Dr. Carlisle’s XSLT
"David" is fine:-)
> <https://github.com/davidcarlisle/web-xslt/tree/master/pmml2tex> to
> convert MathML to LaTeX; whereas, at other places I am using standard
> ams-LaTeX.
> In MikTeX, the following properly displays “a squared” and “a sub 2”
> \documentclass{article}
> \begin{document}
> $a^2$
> $a_2$
> \end{document}
> But when including the \usepackage{pmml-new} in the preamble the above
> displays as simple text a^2 and a_2.
> If I remove the last two lines (shown at the end below) from the
> pmml-new.sty file the “^” and “_” work fine for superscripts and
> subscripts respectively. Moreover, msup and msub defined in the above
> file continue to work for superscript and subscript, as well. I would
> like to use both the LaTeX generated from MathML and the standard LaTeX
> in a same document. For example I would like to be able to use the
> following quadratic formula generated from MathML or a simple LaTeX
> $$a^2$$ on the same tex document:
> $$\let\par\empty > x={\frac{{-b\unicode{177}\sqrt{{\msup{{b}}{{{2}}}}-{4}ac}}}{{{2}a}}} >$$
> Would removing the following last two lines from the pmml-new.sty file
> cause any other issues? If yes, are there any other changes we can make
> to the .sty file to make both ams-LaTeX and LaTeX generated by Dr.
> Carlisle’s files work together on a same document
> \catcode\_=12
> \catcode\^=12
>
Yes you could remove that from a local copy or just set them back to
The original use case for the style was converting XML (such as the XML
source of the MathML spec) where ^ (and especially) _ may occur just as
normal text and rather than have to trap and escape those I just made
all _ normal text and never generated _ for subscripts, always used
\msub etc.
As your fragments show it doesn't really to to make "clean" tex to put
into an existing document, it was used to convert the entire document to
tex for pdf generation as a "black box" process, so the tex it generates
is rather ugly.
David
________________________________
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Wilkinson House, Jordan Hill Road, Oxford OX2 8DR, United Kingdom.
This e-mail has been scanned for all viruses by Microsoft Office 365.
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## Use of \catcode command for character letters ^ and _ in pmml-new.sty file restricts the normal use of these characters for superscripts and subscripts.
Source: www-math@w3.org Mail Archives • saf sied (saf_itpro@yahoo.com) • July 07, 2015 • Permalink
At some places in my text document I am using Dr. Carlisle’s XSLT to convert MathML to LaTeX; whereas, at other places I am using standard ams-LaTeX.In MikTeX, the following properly displays “a squared” and “a sub 2”\documentclass{article}\begin{document}$a^2$$a_2$\end{document}But when including the \usepackage{pmml-new} in the preamble the above displays as simple text a^2 and a_2.If I remove the last two lines (shown at the end below) from the pmml-new.sty file the “^” and “_” work fine for superscripts and subscripts respectively. Moreover, msup and msub defined in the above file continue to work for superscript and subscript, as well. I would like to use both the LaTeX generated from MathML and the standard LaTeX in a same document. For example I would like to be able to use the following quadratic formula generated from MathML or a simple LaTeX $$a^2$$ on the same tex document:$$\let\par\emptyx={\frac{{-b\unicode{177}\sqrt{{\msup{{b}}{{{2}}}}-{4}ac}}}{{{2}a}}}$$ Would removing the following last two lines from the pmml-new.sty file cause any other issues? If yes, are there any other changes we can make to the .sty file to make both ams-LaTeX and LaTeX generated by Dr. Carlisle’s files work together on a same document\catcode\_=12\catcode\^=12
Thanks..Saf
## [Minutes] 2015-07-06 Digital Publishing Interest Group Teleconference
Source: public-digipub-ig@w3.org Mail Archives • Thierry MICHEL (tmichel@w3.org) • July 06, 2015 • Permalink
Hi all,
The minutes of the Digital Publishing Interest Group Teleconference
dated 2015-07-06 are now available at
http://www.w3.org/2015/07/06-dpub-minutes.html
These public minutes are also linked from the dpub wiki
http://www.w3.org/dpub/IG/wiki/Meetings
Also find these minutes in a text version following, for your convenience.
Best,
Thierry Michel
---------------------------
[1]W3C
[1] http://www.w3.org/
Digital Publishing Interest Group Teleconference
06 Jul 2015
[2]Agenda
[2]
http://www.w3.org/mid/b9986cf719ea4f3bafc2669f4a3ab2d0@CAR-WNMBP-006.wiley.com
[3] http://www.w3.org/2015/07/06-dpub-irc
Attendees
Present
Dave Cramer, Tzviya Siegman, Bill Kasdorf, Chris Lilley,
Toru Kawakubo, Ivan Herman, Tim Cole, Brady Duga, Deborah
Kaplan, Ben De Meester, Peter Kreutzberger, Thierry Michel,
David Stroup, Alan Stearns, Vladimir Levantovsky, NickRuffilo.
Regrets
Luc Audrain, Phil Madans, Heather Flanagan, Julie Morris ,
Zheng Xu.
Chair
Tzviya Siegman
Scribe
Nick Ruffilo
Contents
* [4]Topics
1. [5]describedAt
* [6]Summary of Action Items
__________________________________________________________
<trackbot> Date: 06 July 2015
<scribe> scribenick: NickRuffilo
<tzviya> agenda:
[7]https://lists.w3.org/Archives/Public/public-digipub-ig/2015J
ul/0007.html
[7]
https://lists.w3.org/Archives/Public/public-digipub-ig/2015Jul/0007.html
<Bill_Kasdorf> I think Dave added a seventh agenda item, right?
huh ui'm not getting audio hold
<tzviya> [8]http://www.w3.org/2015/06/29-dpub-minutes.html
[8] http://www.w3.org/2015/06/29-dpub-minutes.html
<pkra> I got that.
<ChrisL> webex says michael miller
<pkra> webex is such a snitch
tzviya: "We have some new people and unidentified people..."
<ChrisL> can ppl hear me?
<astearns> no
No chris - still muted
<ChrisL> well, odd
<astearns> there we go
OK - we hear you
Chris: "Hello! I'm Chris Lilly technical director of
Interaction Domain - involved in CSS, web-fonts, SVG. In
particular, I'm here because I want a closer liason with CSS
working group and Houdini. And what DPUB wants. I was invited
for this call - and expect to participate regularly."
Tzviya: "Anyone else new on the call? There are some new
joiners of DPUB. Not sure if you're on the call or in IRC"
<ChrisL> congrats Alan!
Tzviya: "Adding a comment about DPUB and CSS -> the CSS Working
group as identified new chairs - and Alan Sterns is one of the
new chairs. Congratulations!"
<Karen> +1 Alan as new co-chair in October
Alan: "I will not be chair until october"
<Bill_Kasdorf> +1
<pkra> +1
<ivan> +1
Tzviya: "I believe there is only 1 thing on the agenda -
discussing CSS with Chris. I've posted a bunch of links to CSS,
priorities. Just the morning he added stuff to that. I'll turn
this over to dave and chris"
<dauwhe>
[9]https://www.w3.org/dpub/IG/wiki/Functional_Requirements_for_
Pagination
[9]
https://www.w3.org/dpub/IG/wiki/Functional_Requirements_for_Pagination
<dauwhe>
xh7K8anmJ5c0-OFEG7w0LHYM/edit#gid=2138850308
[10]
<dauwhe>
[11]http://w3c.github.io/dpub-pagination/priorities.html
[11] http://w3c.github.io/dpub-pagination/priorities.html
Dave: "We have been working on a couple of things - first was
the wiki page that has functional requirements - based on early
work by Brady - interacting with pages stuff. We're trying to
collect our requirements there. The 2nd piece that we started
working on is an explicit CSS priorities document which has
...: "We will start to move it to a different format once it's
more final and written up in a better format. There are tons of
information and it's a challenge to figure out the best way to
show it. But, it sort of feels useful to start collecting all
these things 'in one place' that is really multiple places"
Chris: "Dave is on the CSS group - I've poked him about Latin
Requirements. But then there are all these other things that
have new things."
davE: "One of the core issues is - what is the reason for being
for LatinReq... It didn't have anything to say about
implementations and priorities."
Chris: "I wasn't suggesting that it need be the only doc, just
the only place I was looking."
Dave: "Yes, LatinReq isn't enough - we need a W3C document that
Tzviya: "We're hoping to get a bit of clarification of what is
going on with houdini and how this fits it in."
Chris: "A feature of the web is using polyfills - so people
don't have to wait for features to be added. This sort-of works
but tends not to work if you use a bunch of them together. It
ends up doing lots of re-implementation, which is pointless as
the browser already knows how to do it. Also there are some
things that are really hard to extend as it happens under the
hood. The idea of houdini
(and it's named after a magician) because it's trying to remove
some of the hand-waving."
...: "It's a sub-group of CSS and the tag, but it's more API
based. I think this is a new focus on new APIs and new
extensibility points. To make it less abstract - we plan on
exposing the box tree - it's largely assumed that the boxes
that are made follow the element tree (there are a bunch of
differences - and many over time) especially when you go across
a fragment. You also might want to
have things like Pages in there as well - which belong in a box
tree and not the DOM tree. That is how I see houdini fitting
in."
<dauwhe> [12]http://dev.w3.org/csswg/css-display/#intro
[12] http://dev.w3.org/csswg/css-display/#intro
Dave: "In the CSS display spec there is a note about what it
means to be in the box tree and DOM tree. This may end up being
where we use these things - the display tree."
<Bill_Kasdorf> +1 to Karen
Karen: "That was one of the more articulate descriptions of
houdini! Thank you! We really need to go to the next level of
explaining 'what is this and how does it work together' so not
only our members, but people interested have a clue. The next
step would be to prepare a more plain-english 'for resources,
for publishers, ...' think about how do we best communicate
some of the work that we
are doing to our community right now."
Chris: "I agree that it is needed - and many W3C working groups
need to work on. For houdini it is still up in the air, but in
the upcoming Paris meeting, I believe we will be tackling this,
and in October that would be a good time to address this
issue."
Karen: "I'll sync up with Nick on this."
Ivan: "What you describe is one end of the spectrum. The other
end is the poor technical people who have to do something with
the NY meetup - we discussed having 'these and these' features
that should be in the CSS declarative style. We noted what is
missing and what we were trying to get. The reader should be
able to handle
pagination through a declaration."
...: "Now there is another side saying that some super-magic
should be doing this through houdini. Something that publishers
& authors should be using. We ended up by saying we are unsure
what line we need to be prepared for - and possibly both."
Chris: "I hear what you say let me try to address. Declarative
is the way it's going and where it will continue to go. Most
poly-fills use declarative syntax that isn't used them
implement. From authoring - no need to touch that stuff. you
should be able to get far without scripting. For an implementer
POV - which is extends a browser, there will be a need - as you
won't want each individual
item bringing in the polyfills - you want the browser to be a
'browser ++'"
Brady: "I think that is where we left it - that's the
conclusion in my head. Publishers should be using these CSS
specs in a declarative way - the reading system NEEDS to be
able to use these polyfills. As an implementer, I have to
struggle with adding the polyfills in a cross-browser way."
...: "Pagination is the most horrible thing that has ever
happened - there is multi-column that gets panned around. You
can do it by breaking up the DOM - as you have no idea where
things end, so you have to figure out where text ends... People
have done it with scrolling and putting a gap between pages.
None of them quite work - and you cannot do things on a
page-level. You can't do widows
and orphans well either with many of these concepts."
Tzviya: "Widow and orphan control and hyphenation are simple
things that are very important - and difficult without the
concept of a page."
ivan: "if this is the way it goes, then we as a group need to
accept that Houdini is there, and the implementors do the
polyfills. Then the question is - do we have everything in CSS
that the publishers need to make the declaratives?"
...: "Then we need to go back to the CSS working group to ask
for certain things to be declared."
Tzviya: "Alot of scholarly publishing uses PDF is because of
MATH - even though we have MathML and other things, it's either
difficult or NOT supported at all, and that's keeping the STEM
world away."
<pkra> same for education.
Ivan: "What is it that the CSS working group needs from us? To
have pagination on the priority list?"
<tzviya>
[13]http://w3c.github.io/dpub-pagination/priorities.html
[13] http://w3c.github.io/dpub-pagination/priorities.html
Chris: "There is a GAP analysis between what is specified and
what browsers ACTUALLY do. What is the level of implementation?
Also why - is there missing information?"
... "What is currently in use, what are the needs, and what
isn't yet specified. having clear requirements and adequate
detail - how it will be extended - how does it actually work -
because CSS has suffered from multiple inconsistent
implementations - we're trying to avoid doing that. Having
multiple pagination requirements will be an issue.
Demonstrating need with clarity and how it is
additive and not breaking the model would be a high priority."
Ivan: "Ok that makes sense"
<ChrisL> yes, one way forward is to triage the existing specs
and get agreements on which are the bad bits
Dave: "I agree with Chris. I think one thing we need to do is
that - there are alot of page related stuff in CSS specs. It's
widely varying quality and in some cases there are things that
have been that are described by the PDF formatters a long time
ago and don't represent the modern concesus of how CSS should
be designed. Even the CSS page-spec itself - and the margin
boxes. At some point
everyone needs to decide, do we go ahead with the older things
and try to patch them up. Do we burn the village and rebuild
with more modern concepts?"
Chris: "Figuring out what isn't implemented - because it's
rubbish - and removing that will help us see where we are
going."
Tzviya: "There are concerns & belief that this is used for
print... This is - in some pockets - used for print, but all of
our interests are beyond print. "
Chris: "The reason I raised that is that the CSS working group
looks at it as 'well, who prints web pages anyways' and the
common use cases - such as tabbed viewing, and apps that are
using slideshows - those tend to get brushed off."
Ivan: "This pretty much relates to the other issue - the
browser vendors - I see pagination as potentially pretty
interesting from a user-interface point of view on the web.
It's very long - then pagination as a find of user interface
structure is something I would really love to have. And I must
say that some of our own documents would benefit from such a
use-case. Is this discussed at all
by browsers? Do they see any argument about that at all?"
Chris: "They do tend to brush it away. This is a problem that
is also faced by accessibility - we want these for blind, color
blind. In the early days, they did the research and found that
the market was low - so browsers wouldn't implement. But, as
new information comes out, they realize that there are more
people who would benefit from such features - such as
accessibility. We want to have
cross-references so you can say 'page 28' but equally we want
to say 'section 5.3.2' if we solve one, we can solve the other
one. Then, what we need gets implemented."
Ivan: "In a sense - would it also help if the publishing
community put these kinds of arguments more explicilty the user
interface for pagination."
Chris: "yes. To some extent. Some needs to be explicit, and
some is a battle plan you don't tell them until they fall for
it."
<pkra> sliders?
Tzviya: "In the documents we're calling for - we should
declaritively state that it works for slides, flashcards,
cards, tiles."
...: "We should spell that out - so pagination isn't just for
'books'"
Tzviya: "Chris - do we need to clarify between CSS and Houdini
when writing this document?"
Chris: "I suggest not - see it as a continuum. Some things are
implemented, some are IN CSS but not implemented. Some can be
easily polyfilled, and some are hard/impossible to polyfill
without houdini."
<tzviya>
[14]http://w3c.github.io/dpub-pagination/priorities.html
[14] http://w3c.github.io/dpub-pagination/priorities.html
Chris: "to clarify - the document is the wiki pages?"
Tzviya: "Nope - this is the text version of the CSS worksheet"
DavE: "this is evolving. I'm still fumbling a bit."
Tzviya: "Dave should get more help and input from others in the
group. "
<ChrisL> yes, I commit to helping with this
Tzviya: "We could use help determining implementation. We know
what we want, but we're not sure where things would happen.
There are a list of where specs exist. We could use help in
that section."
<ivan> ChrisL++
Chris: "I already committed to some GAP analysis on pagination
- so i'm already working on that. So I'll commit here, because
this will make the research a bit more public."
Tzviya: "OK."
... "Other comments? We have next-steps but I'll leave dave and
chris."
...: "Everyone clear on next steps?"
... "Deborah - I see you're here. We need to get note to PF
describedAt
Deborah: "Ok - Should we call what I have 'final'? George sent
some comments and I incorporated what he suggested."
Tzviya: "Just send the final version around."
Deborah: "I'll do that this morning. This in particular is PF -
feels - uncomfortable - about the ARIA describedAT ARIA role in
that they don't think there is alot of buyin yet from
publishers to implement. Our note is an explanation of 'why we
think it is INCREDIBLY useful"
<ChrisL> (discussion of aria described-at and aria 1.1 vs 2.0
staging)
Tzviya: "The reason they are considering deprecating it is
because there is a new version. Deborah and Charles concluded -
with lots of input - that now is not a good time to deprecate
describedAT. They put together alot of examples of how it would
be useful. So, we have this draft of the note. If any publisher
in particular has strong feeling, they might as us as
publishers to come to a PF
meeting."
...: "If anyone wants to see the text get in touch wtih
deborah, charles, or I."
Deborah: "you can always conect me if you have suggestions or
questions"
Tzviya: "Anything else before we close it for today?"
Ivan: "Worth noting as a heads-up that the document that Tzviya
and Markus made with PF - the DPUB-ARIA document has gone
through all the necessary hurdles - it will be published
tomorrow! It has been accepted by Judy and michael is taking
care of it.
<Karen> +1 interpretation for publishing community
Summary of Action Items
[End of minutes]
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$Date: 2015/08/02 23:01:45$
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[15] http://dev.w3.org/cvsweb/%7Echeckout%7E/2002/scribe/scribedoc.htm
[16] http://dev.w3.org/cvsweb/2002/scribe/
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[17] http://dev.w3.org/cvsweb/%7Echeckout%7E/2002/scribe/
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Succeeded: s/persent+/present+/
Found ScribeNick: NickRuffilo
Inferring Scribes: NickRuffilo
Present: Dave_Cramer Tzviya_Siegman Bill_Kasdorf Chris_Lilley Toru_Kawak
ubo Ivan_Herman Tim_Cole duga Deborah_Kaplan Ben_De_Meester Peter Krautz
berger thierry david_stroup astearns Vlad Bert
Agenda: [18]http://www.w3.org/mid/b9986cf719ea4f3bafc2669f4a3ab2d0@CAR-W
NMBP-006.wiley.com
Found Date: 06 Jul 2015
Guessing minutes URL: [19]http://www.w3.org/2015/07/06-dpub-minutes.html
People with action items:
[18]
http://www.w3.org/mid/b9986cf719ea4f3bafc2669f4a3ab2d0@CAR-WNMBP-006.wiley.com
[19] http://www.w3.org/2015/07/06-dpub-minutes.html
WARNING: Input appears to use implicit continuation lines.
You may need the "-implicitContinuations" option.
[End of [20]scribe.perl diagnostic output]
[20] http://dev.w3.org/cvsweb/%7Echeckout%7E/2002/scribe/scribedoc.htm
## CICM 2015: Final Call for Participation, Deadline July 6th, 2015
Source: www-math@w3.org Mail Archives • Serge Autexier (serge.autexier@dfki.de) • July 06, 2015 • Permalink
Final Call for Participation
Conference on Intelligent Computer Mathematics
CICM 2015
13-17 July 2015
Washington DC, USA
The programme for this year's CICM in Washington can be found as
The accepted papers as
In addition we solicit for posters which will not be peer reviewed, but we
will just do a screen review for relevance to the conference. A poster
presentation will consist of a 5 minute teaser talk and the presentation of
the poster on Tuesday morning (together with the other presentations in the
Systems/Data/Projects track).
You can submit a brief abstract on a poster by 22 June 2015 via EasyChair:
https://www.easychair.org/conferences/?conf=cicm2015
Registration to the conference will open shortly.
For details on the conference, registration, accommodation, etc. see
http://www.cicm-conference.org/2015/cicm.php
**********************************************************************
Invited Speakers:
**********************************************************************
* Leonardo de Moura, https://leodemoura.github.io/
"Formalizing mathematics using the Lean Theorem Prover"
(http://leanprover.github.io/)
* Tobias Nipkow, http://www21.in.tum.de/~nipkow/
"Analyzing the Archive of Formal Proofs"
* Jim Pitman, http://www.stat.berkeley.edu/~pitman/
"Towards a Global Digital Mathematics Library"
* Richard Zanibbi, http://www.cs.rit.edu/~rlaz/
"Math Search for the Masses: Multimodal Search
Interfaces and Appearance-Based Retrieval"
**********************************************************************
The principal tracks of the conference will be:
**********************************************************************
* Calculemus (Symbolic Computation and Mechanised Reasoning)
Chair: Jacques Carette
* DML (Digital Mathematical Libraries)
Chair: Volker Sorge
* MKM (Mathematical Knowledge Management)
Chair: Cezary Kaliszyk
* Systems and Data
Chair: Florian Rabe
* Doctoral Programme
Chair: Umair Siddique
Publicity chair is Serge Autexier. The local arrangements are
coordinated by the Local Arrangements Chairs, Bruce R. Miller
(National Institute of Standards and Technology, USA) and Abdou
Youssef (The George Washington University, Washington, D.C.), and the
overall programme is organized by the General Programme Chair,
Manfred Kerber (U. Birmingham, UK).
As in previous years, we have co-located workshops:
* Formal Mathematics for Mathematicians
* Theorem proving components for Educational software (ThEdu'15)
* MathUI
Furthermore we have a doctoral programme to mentor doctoral
students giving presentations and a tutorial on the generic proof
assistant Isabelle.
--------------------------------------------------------------------------------
## MathML 3.0, ¿un estándar internacional al que nadie le hace caso ...
Source: mathml - Google Blog Search • Manuel López Michelone • July 05, 2015 • Permalink
La historia de MathML no ha sido una de las más felices. Ha sido una buena idea crear un lenguaje de marcas (como podría ser XML) para las ecuaciones matemáticas, pero por alguna razón la gente no parece respaldarlo.
## MathML 3.0 Is An International Standard - I Programmer
Source: mathml - Google Blog Search • unknown • July 03, 2015 • Permalink
The story of MathML is not a happy one. It is a good idea - create a markup language for mathematical equations - but for some reason people just don't seem to want to get behind it. Will the new official status of MathML 3.0 ...
## Re: update to xml entities draft
Source: www-math@w3.org Mail Archives • William F Hammond (hammond@csc.albany.edu) • July 02, 2015 • Permalink
On 20150627 at 143534-0700 "Asmus Freytag (t)" writes:
> Unicode generally does not encode characters by usage. For
> example there's no distinction between period, decimal
> point, abbreviation point etc.. This reflects the underlying
> situation, to wit, that this is a case of the *same* symbol
> being used in different conventions.
>
> The downside is that it is thus not possible to use plain
> text to capture which convention is intended (but nothing
> prevents anyone from providing rich-text markup). The upside
> is that data can't exhibit "random alternation" between
> identical looking symbols; experience has shown that this is
> a most likely outcome if "the same" item is encoded several
> times, based merely on convention.
Period, decimal point, abbreviation point: three different
names and three different concepts commonly sharing the same
symbol though not necessarily the same left and right
spacing.
As a point of argument (but not a request) they *should* be
three different characters.
Absent that, the typesetter with a proportional font must
use various conventions, not completely reliable, to guess
the spacing. Of course, commonly the user will be oblivious
of these differences and the user's keyboard will have only
one of these. But the astute user may want to be able to
make distinctions. The distinctions can be made available,
for example, in rich text, as you observe, in SGML, or in
LaTeX.
With a given oblivious user and a given typesetting suite
random alternation will not occur.
Other than for searching I fail to see why random
alternation should be a problem. Are there other problems
associated with random alternation?
As to mathematical searching, searching for mathematical
symbols is an order of magnitude more complicated than
searching for text, e.g., multi-character math symbols,
things like phi vs varphi, ..., so the small number of
possible alternations (at most 256, the size of the U+21xx
block, actually quite a few less than that) should not add
much complexity to code for mathematical symbol searching.
-- Bill
## RE: report: iOS9 adds "print to PDF"
Source: public-digipub-ig@w3.org Mail Archives • Bill Kasdorf (bkasdorf@apexcovantage.com) • July 01, 2015 • Permalink
Tons of readers support EPUB 3. See epubtest.org.
From: Richard Schwerdtfeger [mailto:schwer@us.ibm.com]
Sent: Wednesday, July 01, 2015 3:15 PM
To: Peter Krautzberger
Cc: Bill Kasdorf; Ivan Herman; Larry Masinter; Olaf Drümmer; W3C Digital Publishing IG
Subject: Re: report: iOS9 adds "print to PDF"
Android's book reader supports EPUB3. I have not run an exhaustive analysis of it compared to Apple's but iBooks does a phenomenal job. My hat is off to Apple. Also Google books are published in EPUB format.
Rich Schwerdtfeger
[Inactive hide details for Peter Krautzberger ---07/01/2015 02:00:56 PM---> Maybe it's a problem that PDF works essentially ever]Peter Krautzberger ---07/01/2015 02:00:56 PM---> Maybe it's a problem that PDF works essentially everywhere, whereas EPUB hardly does?
From: Peter Krautzberger <peter.krautzberger@mathjax.org<mailto:peter.krautzberger@mathjax.org>>
To: Olaf Drümmer <olaf@druemmer.com<mailto:olaf@druemmer.com>>
Cc: Richard Schwerdtfeger/Austin/IBM@IBMUS, Bill Kasdorf <bkasdorf@apexcovantage.com<mailto:bkasdorf@apexcovantage.com>>, Ivan Herman <ivan@w3.org<mailto:ivan@w3.org>>, Larry Masinter <masinter@adobe.com<mailto:masinter@adobe.com>>, W3C Digital Publishing IG <public-digipub-ig@w3.org<mailto:public-digipub-ig@w3.org>>
Date: 07/01/2015 02:00 PM
Subject: Re: report: iOS9 adds "print to PDF"
________________________________
> Maybe it's a problem that PDF works essentially everywhere, whereas EPUB hardly does?
Well, iOS and OSX ship with a pretty good epub2&3 viewer, iBooks.
> And that PDF could be made to work for people with special needs?
> And how many websites are out there that really use MathML (as opposed to images of formulas with some Alt attached to them).
Many. Anybody who's serious about math and science, really. From STEM publishers like IEEE to platforms like StackExchange, from individual researchers to MOOCs, from educational publishers like Pearson to blogging teachers, from computational software like iPython Notebooks and MatLab to encyclopedias like, well, Wikipedia (thought arguably not yet the default).
> [...] why it's not good enough for 'mobile'.
Because it throws away most of the information; imho, that's fine for printing but not much beyond that.
> How realistic is it that a sizeable number of users will actually use EPUB3 (including having access to 'real' EPUB3 reading systems, availability publications in EPUB3, and so forth)?
Apple ships a good epub viewer on all products. They also don't seem to care about other platforms, cf. the iBooks Author format.
> why is there no decent, readily available web page to EPUB3 converter at all?
A google search<https://duckduckgo.com/?q=!g+html+to+epub&t=canonical> turns up a few options. Sure they are not perfect, but neither are PDF generators (though arguably those they'll screw up different things). I would say Calibre has comparable (yet different) quality to print-to-pdf from browsers. Perhaps all it takes is an epub equivalent of print stylesheets to improve the situation quickly (though print stylesheets are probably a good start for epub generation, too).
Anyway, I don't have any issue with having a PDF generator around; it just doesn't knock me off my feet.
Peter.
On Wed, Jul 1, 2015 at 8:18 PM, Olaf Drümmer <olaf@druemmer.com<mailto:olaf@druemmer.com>> wrote:
Maybe it's a problem that PDF works essentially everywhere, whereas EPUB hardly does? And that PDF could be made to work for people with special needs? And how many websites are out there that really use MathML (as opposed to images of formulas with some Alt attached to them). If PDF is used on let's say an iPad and the PDF is captured at the same 'form factor' as when it is being displayed on the iPad, I have difficulty seeing why it's not good enough for 'mobile'.
Maybe there should be more considerations of the combination of relevance AND feasibility? How realistic is it that a sizeable number of users will actually use EPUB3 (including having access to 'real' EPUB3 reading systems, availability publications in EPUB3, and so forth)? PDF does have the advantage of being relatively widely available, serving over 95% of users well enough for all practical purposes. It took PDF over 20 years to get there. Currently EPUB3 is where PDF was ca. 2 or 3 years into its existence. How do we deal with the other 17 years it might need to establish EPUB3 in the same manner?
And: There is one question that really keeps me thinking - and I have yet to find a good / satisfactory answer: why is there no decent, readily available web page to EPUB3 converter at all? Especially if/as EPUB3 could be described as a packaged web page/site… Or am I missing something? Or is it too early in the game/am I being too impatient?
Olaf
On 1 Jul 2015, at 19:49, Richard Schwerdtfeger <schwer@us.ibm.com<mailto:schwer@us.ibm.com>> wrote:
They should have done save to EPUB3 as it is packaged. As you point out, PDF is not the best format for mobile. Also IBook author can import EPUB3. From an accessibility perspective it is more than just tagged PDF that is important. It is also access to digital math to allow for alternative renderings for blind, low vision, attention deficit, situational impairments, and dyslexic users.
Print fidelity is nice but, today, it is about supporting a broader range of users and also due to the uptake of mobile devices in education inclusive access is much more important.
Rich Schwerdtfeger
<graycol.gif>Bill Kasdorf ---07/01/2015 12:13:27 PM---Two comments: Yes, it's the structure that's the main issue—and the structure expressed in a standar
From: Bill Kasdorf <bkasdorf@apexcovantage.com<mailto:bkasdorf@apexcovantage.com>>
To: Peter Krautzberger <peter.krautzberger@mathjax.org<mailto:peter.krautzberger@mathjax.org>>, Larry Masinter <masinter@adobe.com<mailto:masinter@adobe.com>>, W3C Digital Publishing IG <public-digipub-ig@w3.org<mailto:public-digipub-ig@w3.org>>
Cc: Ivan Herman <ivan@w3.org<mailto:ivan@w3.org>>
Date: 07/01/2015 12:13 PM
Subject: RE: report: iOS9 adds "print to PDF"
________________________________
Yes, it's the structure that's the main issue—and the structure expressed in a standard way (i.e., HTML5). That's also fundamentally important for accessibility. So "Save as HTML + CSS" is way better than an alternative "save as X" imo, unless the "X" is EPUB 3, which would be optimal.
The other point is that unless I'm not up-to-date on this (and I may not be), I would be cautious about Apple's iBooks Author format because at least wrt the use of Author itself, I believe there are restrictions on how those files can be distributed and sold (e.g., limited to iBooks). I would love to be informed that that's no longer the case.
--Bill K
From: Peter Krautzberger [mailto:peter.krautzberger@mathjax.org]
Sent: Tuesday, June 30, 2015 2:59 AM
To: Larry Masinter; W3C Digital Publishing IG
Cc: Ivan Herman
Subject: Re: report: iOS9 adds "print to PDF"
> Serious question: if it was “Save as HTML + CSS” or “save as X” for
> any other X, would you be less sad, and why?
Top of my list would be epub3, but Apple's iBooks Author format would make sense.
Given the quality of the website-to-epub generators I've encountered, that seems like a much harder problem. But even a non-optimal solution might provide a better experience than a page-sized PDF on small screen. In combination with something like readability/pocket/etc or "save selection", the content could even shine.
> What data would you have in other formats that you don’t have for PDF?
I suppose that comes down to the quality of the files, i.e., whether they are "plain old" PDFs (glyphs on a canvas) or pdf/a or even using Flash/JS/etc to represent more complex content. Assuming it's just glyphs with positions, then it seems to me almost all markup is lost whereas HTML/CSS-based formats like epub and iBA can retain parts of the original structure.
Don't get me wrong, I understand why one would ship a PDF generator (i.e., for all the usual reasons); but it doesn't stop me from wondering if whoever decided that this is a good feature for mobile devices also thought: "but really, we need a better way".
Peter.
On Tue, Jun 30, 2015 at 12:42 AM, Larry Masinter <masinter@adobe.com<mailto:masinter@adobe.com>> wrote:
Serious question: if it was “Save as HTML + CSS” or “save as X” for
any other X, would you be less sad, and why?
What data would you have in other formats that you don’t have for PDF?
Seriously. It’s really hard to get down to requirements.
On 6/27/15, 8:48 AM, "Ivan Herman" <ivan@w3.org<mailto:ivan@w3.org>> wrote:
Me too...
Ivan
---
Ivan Herman
Tel:+31 641044153<tel:%2B31%20641044153>
http://www.ivan-herman.net<http://www.ivan-herman.net/>
(Written on mobile, sorry for brevity and misspellings...)
On 27 Jun 2015, at 16:15, Peter Krautzberger <peter.krautzberger@mathjax.org<mailto:peter.krautzberger@mathjax.org>> wrote:
Just something I came across, https://twitter.com/fakebaldur/status/614794685559742464
Quote: "It’s particularly useful for webpages, since it keeps all the text, and makes it searchable and copyable unlike, say, taking a screenshot."
Peter.
## Re: report: iOS9 adds "print to PDF"
Source: public-digipub-ig@w3.org Mail Archives • Richard Schwerdtfeger (schwer@us.ibm.com) • July 01, 2015 • Permalink
Android's book reader supports EPUB3. I have not run an exhaustive analysis
of it compared to Apple's but iBooks does a phenomenal job. My hat is off
to Apple. Also Google books are published in EPUB format.
Rich Schwerdtfeger
From: Peter Krautzberger <peter.krautzberger@mathjax.org>
To: Olaf Drümmer <olaf@druemmer.com>
Cc: Richard Schwerdtfeger/Austin/IBM@IBMUS, Bill Kasdorf
<bkasdorf@apexcovantage.com>, Ivan Herman <ivan@w3.org>, Larry
Masinter <masinter@adobe.com>, W3C Digital Publishing IG
<public-digipub-ig@w3.org>
Date: 07/01/2015 02:00 PM
Subject: Re: report: iOS9 adds "print to PDF"
> Maybe it's a problem that PDF works essentially everywhere, whereas EPUB
hardly does?
Well, iOS and OSX ship with a pretty good epub2&3 viewer, iBooks.
> And that PDF could be made to work for people with special needs?
> And how many websites are out there that really use MathML (as opposed to
images of formulas with some Alt attached to them).
Many. Anybody who's serious about math and science, really. From STEM
publishers like IEEE to platforms like StackExchange, from individual
researchers to MOOCs, from educational publishers like Pearson to blogging
teachers, from computational software like iPython Notebooks and MatLab to
encyclopedias like, well, Wikipedia (thought arguably not yet the default).
> [...] why it's not good enough for 'mobile'.
Because it throws away most of the information; imho, that's fine for
printing but not much beyond that.
> How realistic is it that a sizeable number of users will actually use
availability publications in EPUB3, and so forth)?
Apple ships a good epub viewer on all products. They also don't seem to
care about other platforms, cf. the iBooks Author format.
> why is there no decent, readily available web page to EPUB3 converter at
all?
A google search turns up a few options. Sure they are not perfect, but
neither are PDF generators (though arguably those they'll screw up
different things). I would say Calibre has comparable (yet different)
quality to print-to-pdf from browsers. Perhaps all it takes is an epub
equivalent of print stylesheets to improve the situation quickly (though
print stylesheets are probably a good start for epub generation, too).
Anyway, I don't have any issue with having a PDF generator around; it just
doesn't knock me off my feet.
Peter.
On Wed, Jul 1, 2015 at 8:18 PM, Olaf Drümmer <olaf@druemmer.com> wrote:
Maybe it's a problem that PDF works essentially everywhere, whereas EPUB
hardly does? And that PDF could be made to work for people with special
needs? And how many websites are out there that really use MathML (as
opposed to images of formulas with some Alt attached to them). If PDF is
used on let's say an iPad and the PDF is captured at the same 'form
factor' as when it is being displayed on the iPad, I have difficulty
seeing why it's not good enough for 'mobile'.
Maybe there should be more considerations of the combination of
relevance AND feasibility? How realistic is it that a sizeable number of
reading systems, availability publications in EPUB3, and so forth)? PDF
does have the advantage of being relatively widely available, serving
over 95% of users well enough for all practical purposes. It took PDF
over 20 years to get there. Currently EPUB3 is where PDF was ca. 2 or 3
years into its existence. How do we deal with the other 17 years it might
need to establish EPUB3 in the same manner?
And: There is one question that really keeps me thinking - and I have yet
to find a good / satisfactory answer: why is there no decent, readily
available web page to EPUB3 converter at all? Especially if/as EPUB3
could be described as a packaged web page/site… Or am I missing
something? Or is it too early in the game/am I being too impatient?
Olaf
On 1 Jul 2015, at 19:49, Richard Schwerdtfeger <schwer@us.ibm.com> wrote:
They should have done save to EPUB3 as it is packaged. As you point
out, PDF is not the best format for mobile. Also IBook author can
import EPUB3. From an accessibility perspective it is more than
just tagged PDF that is important. It is also access to digital
math to allow for alternative renderings for blind, low vision,
attention deficit, situational impairments, and dyslexic users.
Print fidelity is nice but, today, it is about supporting a broader
range of users and also due to the uptake of mobile devices in
education inclusive access is much more important.
Rich Schwerdtfeger
<graycol.gif>Bill Kasdorf ---07/01/2015 12:13:27 PM---Two comments:
Yes, it's the structure that's the main issue—and the structure
expressed in a standar
From: Bill Kasdorf <bkasdorf@apexcovantage.com>
To: Peter Krautzberger <peter.krautzberger@mathjax.org>, Larry
Masinter <masinter@adobe.com>, W3C Digital Publishing IG <
public-digipub-ig@w3.org>
Cc: Ivan Herman <ivan@w3.org>
Date: 07/01/2015 12:13 PM
Subject: RE: report: iOS9 adds "print to PDF"
Yes, it's the structure that's the main issue—and the structure
expressed in a standard way (i.e., HTML5). That's also
fundamentally important for accessibility. So "Save as HTML + CSS"
is way better than an alternative "save as X" imo, unless the "X"
is EPUB 3, which would be optimal.
The other point is that unless I'm not up-to-date on this (and I
may not be), I would be cautious about Apple's iBooks Author format
because at least wrt the use of Author itself, I believe there are
restrictions on how those files can be distributed and sold (e.g.,
limited to iBooks). I would love to be informed that that's no
longer the case.
--Bill K
From: Peter Krautzberger [mailto:peter.krautzberger@mathjax.org]
Sent: Tuesday, June 30, 2015 2:59 AM
To: Larry Masinter; W3C Digital Publishing IG
Cc: Ivan Herman
Subject: Re: report: iOS9 adds "print to PDF"
> Serious question: if it was “Save as HTML + CSS” or “save as X”
for
> any other X, would you be less sad, and why?
Top of my list would be epub3, but Apple's iBooks Author format
would make sense.
Given the quality of the website-to-epub generators I've
encountered, that seems like a much harder problem. But even a
non-optimal solution might provide a better experience than a
page-sized PDF on small screen. In combination with something like
readability/pocket/etc or "save selection", the content could even
shine.
> What data would you have in other formats that you don’t have for
PDF?
I suppose that comes down to the quality of the files, i.e.,
whether they are "plain old" PDFs (glyphs on a canvas) or pdf/a or
even using Flash/JS/etc to represent more complex content. Assuming
it's just glyphs with positions, then it seems to me almost all
markup is lost whereas HTML/CSS-based formats like epub and iBA can
retain parts of the original structure.
Don't get me wrong, I understand why one would ship a PDF generator
(i.e., for all the usual reasons); but it doesn't stop me from
wondering if whoever decided that this is a good feature for mobile
devices also thought: "but really, we need a better way".
Peter.
On Tue, Jun 30, 2015 at 12:42 AM, Larry Masinter <
Serious question: if it was “Save as HTML + CSS” or “save as X” for
any other X, would you be less sad, and why?
What data would you have in other formats that you don’t have for
PDF?
Seriously. It’s really hard to get down to requirements.
On 6/27/15, 8:48 AM, "Ivan Herman" <ivan@w3.org> wrote:
Me too...
Ivan
---
Ivan Herman
Tel:+31 641044153
http://www.ivan-herman.net
(Written on mobile, sorry for brevity and misspellings...)
On 27 Jun 2015, at 16:15, Peter Krautzberger <
peter.krautzberger@mathjax.org> wrote:
Just something I came across,
Quote: "It’s particularly useful for webpages, since it keeps
all the text, and makes it searchable and copyable unlike,
say, taking a screenshot."
Peter.
## RE: report: iOS9 adds "print to PDF"
Source: public-digipub-ig@w3.org Mail Archives • Bill Kasdorf (bkasdorf@apexcovantage.com) • July 01, 2015 • Permalink
In addition to the more detailed comments from Peter (below):
The accessibility community is in general agreement that PDF, even when laboriously enhanced for accessibility (and only a minuscule proportion of PDFs are), does not meet their needs compared to well structured EPUB 3. EPUB 3 was designed in collaboration with that community to be inherently accessible and the DAISY Consortium has standardized on EPUB 3 as the format for the delivery of accessible content.
—Bill Kasdorf
From: Peter Krautzberger [mailto:peter.krautzberger@mathjax.org]
Sent: Wednesday, July 01, 2015 3:00 PM
To: Olaf Drümmer
Cc: Richard Schwerdtfeger; Bill Kasdorf; Ivan Herman; Larry Masinter; W3C Digital Publishing IG
Subject: Re: report: iOS9 adds "print to PDF"
> Maybe it's a problem that PDF works essentially everywhere, whereas EPUB hardly does?
Well, iOS and OSX ship with a pretty good epub2&3 viewer, iBooks.
> And that PDF could be made to work for people with special needs?
> And how many websites are out there that really use MathML (as opposed to images of formulas with some Alt attached to them).
Many. Anybody who's serious about math and science, really. From STEM publishers like IEEE to platforms like StackExchange, from individual researchers to MOOCs, from educational publishers like Pearson to blogging teachers, from computational software like iPython Notebooks and MatLab to encyclopedias like, well, Wikipedia (thought arguably not yet the default).
> [...] why it's not good enough for 'mobile'.
Because it throws away most of the information; imho, that's fine for printing but not much beyond that.
> How realistic is it that a sizeable number of users will actually use EPUB3 (including having access to 'real' EPUB3 reading systems, availability publications in EPUB3, and so forth)?
Apple ships a good epub viewer on all products. They also don't seem to care about other platforms, cf. the iBooks Author format.
> why is there no decent, readily available web page to EPUB3 converter at all?
A google search<https://duckduckgo.com/?q=!g+html+to+epub&t=canonical> turns up a few options. Sure they are not perfect, but neither are PDF generators (though arguably those they'll screw up different things). I would say Calibre has comparable (yet different) quality to print-to-pdf from browsers. Perhaps all it takes is an epub equivalent of print stylesheets to improve the situation quickly (though print stylesheets are probably a good start for epub generation, too).
Anyway, I don't have any issue with having a PDF generator around; it just doesn't knock me off my feet.
Peter.
On Wed, Jul 1, 2015 at 8:18 PM, Olaf Drümmer <olaf@druemmer.com<mailto:olaf@druemmer.com>> wrote:
Maybe it's a problem that PDF works essentially everywhere, whereas EPUB hardly does? And that PDF could be made to work for people with special needs? And how many websites are out there that really use MathML (as opposed to images of formulas with some Alt attached to them). If PDF is used on let's say an iPad and the PDF is captured at the same 'form factor' as when it is being displayed on the iPad, I have difficulty seeing why it's not good enough for 'mobile'.
Maybe there should be more considerations of the combination of relevance AND feasibility? How realistic is it that a sizeable number of users will actually use EPUB3 (including having access to 'real' EPUB3 reading systems, availability publications in EPUB3, and so forth)? PDF does have the advantage of being relatively widely available, serving over 95% of users well enough for all practical purposes. It took PDF over 20 years to get there. Currently EPUB3 is where PDF was ca. 2 or 3 years into its existence. How do we deal with the other 17 years it might need to establish EPUB3 in the same manner?
And: There is one question that really keeps me thinking - and I have yet to find a good / satisfactory answer: why is there no decent, readily available web page to EPUB3 converter at all? Especially if/as EPUB3 could be described as a packaged web page/site… Or am I missing something? Or is it too early in the game/am I being too impatient?
Olaf
On 1 Jul 2015, at 19:49, Richard Schwerdtfeger <schwer@us.ibm.com<mailto:schwer@us.ibm.com>> wrote:
They should have done save to EPUB3 as it is packaged. As you point out, PDF is not the best format for mobile. Also IBook author can import EPUB3. From an accessibility perspective it is more than just tagged PDF that is important. It is also access to digital math to allow for alternative renderings for blind, low vision, attention deficit, situational impairments, and dyslexic users.
Print fidelity is nice but, today, it is about supporting a broader range of users and also due to the uptake of mobile devices in education inclusive access is much more important.
Rich Schwerdtfeger
<graycol.gif>Bill Kasdorf ---07/01/2015 12:13:27 PM---Two comments: Yes, it's the structure that's the main issue—and the structure expressed in a standar
From: Bill Kasdorf <bkasdorf@apexcovantage.com<mailto:bkasdorf@apexcovantage.com>>
To: Peter Krautzberger <peter.krautzberger@mathjax.org<mailto:peter.krautzberger@mathjax.org>>, Larry Masinter <masinter@adobe.com<mailto:masinter@adobe.com>>, W3C Digital Publishing IG <public-digipub-ig@w3.org<mailto:public-digipub-ig@w3.org>>
Cc: Ivan Herman <ivan@w3.org<mailto:ivan@w3.org>>
Date: 07/01/2015 12:13 PM
Subject: RE: report: iOS9 adds "print to PDF"
________________________________
Yes, it's the structure that's the main issue—and the structure expressed in a standard way (i.e., HTML5). That's also fundamentally important for accessibility. So "Save as HTML + CSS" is way better than an alternative "save as X" imo, unless the "X" is EPUB 3, which would be optimal.
The other point is that unless I'm not up-to-date on this (and I may not be), I would be cautious about Apple's iBooks Author format because at least wrt the use of Author itself, I believe there are restrictions on how those files can be distributed and sold (e.g., limited to iBooks). I would love to be informed that that's no longer the case.
--Bill K
From: Peter Krautzberger [mailto:peter.krautzberger@mathjax.org]
Sent: Tuesday, June 30, 2015 2:59 AM
To: Larry Masinter; W3C Digital Publishing IG
Cc: Ivan Herman
Subject: Re: report: iOS9 adds "print to PDF"
> Serious question: if it was “Save as HTML + CSS” or “save as X” for
> any other X, would you be less sad, and why?
Top of my list would be epub3, but Apple's iBooks Author format would make sense.
Given the quality of the website-to-epub generators I've encountered, that seems like a much harder problem. But even a non-optimal solution might provide a better experience than a page-sized PDF on small screen. In combination with something like readability/pocket/etc or "save selection", the content could even shine.
> What data would you have in other formats that you don’t have for PDF?
I suppose that comes down to the quality of the files, i.e., whether they are "plain old" PDFs (glyphs on a canvas) or pdf/a or even using Flash/JS/etc to represent more complex content. Assuming it's just glyphs with positions, then it seems to me almost all markup is lost whereas HTML/CSS-based formats like epub and iBA can retain parts of the original structure.
Don't get me wrong, I understand why one would ship a PDF generator (i.e., for all the usual reasons); but it doesn't stop me from wondering if whoever decided that this is a good feature for mobile devices also thought: "but really, we need a better way".
Peter.
On Tue, Jun 30, 2015 at 12:42 AM, Larry Masinter <masinter@adobe.com<mailto:masinter@adobe.com>> wrote:
Serious question: if it was “Save as HTML + CSS” or “save as X” for
any other X, would you be less sad, and why?
What data would you have in other formats that you don’t have for PDF?
Seriously. It’s really hard to get down to requirements.
On 6/27/15, 8:48 AM, "Ivan Herman" <ivan@w3.org<mailto:ivan@w3.org>> wrote:
Me too...
Ivan
---
Ivan Herman
Tel:+31 641044153<tel:%2B31%20641044153>
http://www.ivan-herman.net<http://www.ivan-herman.net/>
(Written on mobile, sorry for brevity and misspellings...)
On 27 Jun 2015, at 16:15, Peter Krautzberger <peter.krautzberger@mathjax.org<mailto:peter.krautzberger@mathjax.org>> wrote:
Just something I came across, https://twitter.com/fakebaldur/status/614794685559742464
Quote: "It’s particularly useful for webpages, since it keeps all the text, and makes it searchable and copyable unlike, say, taking a screenshot."
Peter.
## Re: report: iOS9 adds "print to PDF"
Source: public-digipub-ig@w3.org Mail Archives • Richard Schwerdtfeger (schwer@us.ibm.com) • July 01, 2015 • Permalink
Well, here we go.
PDF - you need to pinch and squeeze your way through a document. It is a
The reason we have not seen taken off on the web is a chicken and egg
problem:
- No good integration of Math support in authoring tools
- Inconsistent browser support.
- Because of the two above people don't author in MathML they stick an
inaccessible bitmap out for people.
So,
Authoring tools are now starting to integrate MathML authoring support.
Namo Author is one. I am on their technical advisory board. This will make
it easier for teachers to produce digital math.
Many think that alternative text is adequate. It is not. Research has shown
that providing the ability to navigate a digital math equation, with the
keyboard while having the symbols, etc. highlighted and spoken, results in
math comprehension going up across the board by 10-15%. For Attention
deficit and dyslexia, for which the numbers far exceed blind access, this
is essential functionality.
Benetech is working now to create a cloud reader that will take a MathML
equation and allow you to navigate it and have it rendered with multiple
vendors on Windows, Linux, and Mac are adding more support for MathML.
Let's forget public web pages for a minute. Think about digital books and
online courses that you typically don't run through on the broader web. The
pieces are coming together now. Education would really benefit from a boost
in math comprehension.
All IBM documentation today can be published as EPUB3. Some links:
- http://asmarterplanet.com/blog/2014/02/epub-mobile.html
When you get to Asia Pacific EPUB is the book standard - there is no
Amazon. In South Korea all education material must be published in EPUB
format. The education space in the US is converging on EPUB as well.
On April 2nd I was speaking at Harvard on global accessibility trends and
spoke with the Harvard Vice Provos Bols. There was an ADA Title 3
settlement that day on edX that involved educational content delivered to
Harvard and MIT. Please take a look at section 18 and the reference to
EPUB3:
http://www.justice.gov/sites/default/files/opa/press-releases/attachments/2015/04/02/edx_settlement_agreement.pdf
This is not going to take 17 years and frankly things progress much faster
today than they did 17 years ago.
Rich
Rich Schwerdtfeger
From: Olaf Drümmer <olaf@druemmer.com>
To: Richard Schwerdtfeger/Austin/IBM@IBMUS
Cc: Olaf Drümmer <olaf@druemmer.com>, Bill Kasdorf
<bkasdorf@apexcovantage.com>, Ivan Herman <ivan@w3.org>, Larry
<peter.krautzberger@mathjax.org>, W3C Digital Publishing IG
<public-digipub-ig@w3.org>
Date: 07/01/2015 01:18 PM
Subject: Re: report: iOS9 adds "print to PDF"
Maybe it's a problem that PDF works essentially everywhere, whereas EPUB
hardly does? And that PDF could be made to work for people with special
needs? And how many websites are out there that really use MathML (as
opposed to images of formulas with some Alt attached to them). If PDF is
used on let's say an iPad and the PDF is captured at the same 'form factor'
as when it is being displayed on the iPad, I have difficulty seeing why
it's not good enough for 'mobile'.
Maybe there should be more considerations of the combination of relevance
AND feasibility? How realistic is it that a sizeable number of users will
systems, availability publications in EPUB3, and so forth)? PDF does have
the advantage of being relatively widely available, serving over 95% of
users well enough for all practical purposes. It took PDF over 20 years to
get there. Currently EPUB3 is where PDF was ca. 2 or 3 years into its
existence. How do we deal with the other 17 years it might need to
establish EPUB3 in the same manner?
And: There is one question that really keeps me thinking - and I have yet
to find a good / satisfactory answer: why is there no decent, readily
available web page to EPUB3 converter at all? Especially if/as EPUB3 could
be described as a packaged web page/site… Or am I missing something? Or is
it too early in the game/am I being too impatient?
Olaf
On 1 Jul 2015, at 19:49, Richard Schwerdtfeger <schwer@us.ibm.com> wrote:
They should have done save to EPUB3 as it is packaged. As you point
out, PDF is not the best format for mobile. Also IBook author can
import EPUB3. From an accessibility perspective it is more than just
tagged PDF that is important. It is also access to digital math to
allow for alternative renderings for blind, low vision, attention
deficit, situational impairments, and dyslexic users.
Print fidelity is nice but, today, it is about supporting a broader
range of users and also due to the uptake of mobile devices in
education inclusive access is much more important.
Rich Schwerdtfeger
<graycol.gif>Bill Kasdorf ---07/01/2015 12:13:27 PM---Two comments:
Yes, it's the structure that's the main issue—and the structure
expressed in a standar
From: Bill Kasdorf <bkasdorf@apexcovantage.com>
To: Peter Krautzberger <peter.krautzberger@mathjax.org>, Larry
Masinter <masinter@adobe.com>, W3C Digital Publishing IG <
public-digipub-ig@w3.org>
Cc: Ivan Herman <ivan@w3.org>
Date: 07/01/2015 12:13 PM
Subject: RE: report: iOS9 adds "print to PDF"
Yes, it's the structure that's the main issue—and the structure
expressed in a standard way (i.e., HTML5). That's also fundamentally
important for accessibility. So "Save as HTML + CSS" is way better
than an alternative "save as X" imo, unless the "X" is EPUB 3, which
would be optimal.
The other point is that unless I'm not up-to-date on this (and I may
not be), I would be cautious about Apple's iBooks Author format
because at least wrt the use of Author itself, I believe there are
restrictions on how those files can be distributed and sold (e.g.,
limited to iBooks). I would love to be informed that that's no longer
the case.
--Bill K
From: Peter Krautzberger [mailto:peter.krautzberger@mathjax.org]
Sent: Tuesday, June 30, 2015 2:59 AM
To: Larry Masinter; W3C Digital Publishing IG
Cc: Ivan Herman
Subject: Re: report: iOS9 adds "print to PDF"
> Serious question: if it was “Save as HTML + CSS” or “save as X” for
> any other X, would you be less sad, and why?
Top of my list would be epub3, but Apple's iBooks Author format
would make sense.
Given the quality of the website-to-epub generators I've encountered,
that seems like a much harder problem. But even a non-optimal
solution might provide a better experience than a page-sized PDF on
small screen. In combination with something like
readability/pocket/etc or "save selection", the content could even
shine.
> What data would you have in other formats that you don’t have for
PDF?
I suppose that comes down to the quality of the files, i.e., whether
they are "plain old" PDFs (glyphs on a canvas) or pdf/a or even using
Flash/JS/etc to represent more complex content. Assuming it's just
glyphs with positions, then it seems to me almost all markup is lost
whereas HTML/CSS-based formats like epub and iBA can retain parts of
the original structure.
Don't get me wrong, I understand why one would ship a PDF generator
(i.e., for all the usual reasons); but it doesn't stop me from
wondering if whoever decided that this is a good feature for mobile
devices also thought: "but really, we need a better way".
Peter.
On Tue, Jun 30, 2015 at 12:42 AM, Larry Masinter <masinter@adobe.com>
wrote:
Serious question: if it was “Save as HTML + CSS” or “save as X” for
any other X, would you be less sad, and why?
What data would you have in other formats that you don’t have for
PDF?
Seriously. It’s really hard to get down to requirements.
On 6/27/15, 8:48 AM, "Ivan Herman" <ivan@w3.org> wrote:
Me too...
Ivan
---
Ivan Herman
Tel:+31 641044153
http://www.ivan-herman.net
(Written on mobile, sorry for brevity and misspellings...)
On 27 Jun 2015, at 16:15, Peter Krautzberger <
peter.krautzberger@mathjax.org> wrote:
Just something I came across,
Quote: "It’s particularly useful for webpages, since it keeps
all the text, and makes it searchable and copyable unlike, say,
taking a screenshot."
Peter.
## Re: report: iOS9 adds "print to PDF"
Source: public-digipub-ig@w3.org Mail Archives • Peter Krautzberger (peter.krautzberger@mathjax.org) • July 01, 2015 • Permalink
> Maybe it's a problem that PDF works essentially everywhere, whereas EPUB
hardly does?
Well, iOS and OSX ship with a pretty good epub2&3 viewer, iBooks.
> And that PDF could be made to work for people with special needs?
> And how many websites are out there that really use MathML (as opposed to
images of formulas with some Alt attached to them).
Many. Anybody who's serious about math and science, really. From STEM
publishers like IEEE to platforms like StackExchange, from individual
researchers to MOOCs, from educational publishers like Pearson to blogging
teachers, from computational software like iPython Notebooks and MatLab to
encyclopedias like, well, Wikipedia (thought arguably not yet the default).
> [...] why it's not good enough for 'mobile'.
Because it throws away most of the information; imho, that's fine for
printing but not much beyond that.
> How realistic is it that a sizeable number of users will actually use
availability publications in EPUB3, and so forth)?
Apple ships a good epub viewer on all products. They also don't seem to
care about other platforms, cf. the iBooks Author format.
> why is there no decent, readily available web page to EPUB3 converter at
all?
up a few options. Sure they are not perfect, but neither are PDF generators
(though arguably those they'll screw up different things). I would say
Calibre has comparable (yet different) quality to print-to-pdf from
browsers. Perhaps all it takes is an epub equivalent of print stylesheets
to improve the situation quickly (though print stylesheets are probably a
good start for epub generation, too).
Anyway, I don't have any issue with having a PDF generator around; it just
doesn't knock me off my feet.
Peter.
On Wed, Jul 1, 2015 at 8:18 PM, Olaf Drümmer <olaf@druemmer.com> wrote:
> Maybe it's a problem that PDF works essentially everywhere, whereas EPUB
> hardly does? And that PDF could be made to work for people with special
> needs? And how many websites are out there that really use MathML (as
> opposed to images of formulas with some Alt attached to them). If PDF is
> used on let's say an iPad and the PDF is captured at the same 'form factor'
> as when it is being displayed on the iPad, I have difficulty seeing why
> it's not good enough for 'mobile'.
>
> Maybe there should be more considerations of the combination of relevance
> AND feasibility? How realistic is it that a sizeable number of users will
> systems, availability publications in EPUB3, and so forth)? PDF does have
> the advantage of being relatively widely available, serving over 95% of
> users well enough for all practical purposes. It took PDF over 20 years to
> get there. Currently EPUB3 is where PDF was ca. 2 or 3 years into its
> existence. How do we deal with the other 17 years it might need to
> establish EPUB3 in the same manner?
>
> And: There is one question that really keeps me thinking - and I have yet
> to find a good / satisfactory answer: why is there no decent, readily
> available web page to EPUB3 converter at all? Especially if/as EPUB3 could
> be described as a packaged web page/site… Or am I missing something? Or is
> it too early in the game/am I being too impatient?
>
> Olaf
>
>
> On 1 Jul 2015, at 19:49, Richard Schwerdtfeger <schwer@us.ibm.com> wrote:
>
> They should have done save to EPUB3 as it is packaged. As you point out,
> PDF is not the best format for mobile. Also IBook author can import EPUB3.
> From an accessibility perspective it is more than just tagged PDF that is
> important. It is also access to digital math to allow for alternative
> renderings for blind, low vision, attention deficit, situational
> impairments, and dyslexic users.
>
> Print fidelity is nice but, today, it is about supporting a broader range
> of users and also due to the uptake of mobile devices in education
> inclusive access is much more important.
>
>
> Rich Schwerdtfeger
>
> <graycol.gif>Bill Kasdorf ---07/01/2015 12:13:27 PM---Two comments: Yes,
> it's the structure that's the main issue—and the structure expressed in a
> standar
>
>
> From: Bill Kasdorf <bkasdorf@apexcovantage.com>
> To: Peter Krautzberger <peter.krautzberger@mathjax.org>, Larry Masinter <
> masinter@adobe.com>, W3C Digital Publishing IG <public-digipub-ig@w3.org>
> Cc: Ivan Herman <ivan@w3.org>
> Date: 07/01/2015 12:13 PM
> Subject: RE: report: iOS9 adds "print to PDF"
>
> ------------------------------
>
>
>
>
> Yes, it's the structure that's the main issue—and the structure expressed
> in a standard way (i.e., HTML5). That's also fundamentally important for
> accessibility. So "Save as HTML + CSS" is way better than an alternative
> "save as X" imo, unless the "X" is EPUB 3, which would be optimal.
>
> The other point is that unless I'm not up-to-date on this (and I may not
> be), I would be cautious about Apple's iBooks Author format because at
> least wrt the use of Author itself, I believe there are restrictions on how
> those files can be distributed and sold (e.g., limited to iBooks). I would
> love to be informed that that's no longer the case.
>
> --Bill K
>
> *From:* Peter Krautzberger [mailto:peter.krautzberger@mathjax.org
> <peter.krautzberger@mathjax.org>]
> * Sent:* Tuesday, June 30, 2015 2:59 AM
> * To:* Larry Masinter; W3C Digital Publishing IG
> * Cc:* Ivan Herman
> * Subject:* Re: report: iOS9 adds "print to PDF"
>
> > Serious question: if it was “Save as HTML + CSS” or “save as X” for
> > any other X, would you be less sad, and why?
>
> Top of my list would be epub3, but Apple's iBooks Author format would
> make sense.
>
> Given the quality of the website-to-epub generators I've encountered, that
> seems like a much harder problem. But even a non-optimal solution might
> provide a better experience than a page-sized PDF on small screen. In
> combination with something like readability/pocket/etc or "save selection",
> the content could even shine.
>
> > What data would you have in other formats that you don’t have for PDF?
>
> I suppose that comes down to the quality of the files, i.e., whether they
> are "plain old" PDFs (glyphs on a canvas) or pdf/a or even using
> Flash/JS/etc to represent more complex content. Assuming it's just glyphs
> with positions, then it seems to me almost all markup is lost whereas
> HTML/CSS-based formats like epub and iBA can retain parts of the original
> structure.
>
> Don't get me wrong, I understand why one would ship a PDF generator (i.e.,
> for all the usual reasons); but it doesn't stop me from wondering if
> whoever decided that this is a good feature for mobile devices also
> thought: "but really, we need a better way".
>
> Peter.
>
>
>
> On Tue, Jun 30, 2015 at 12:42 AM, Larry Masinter <*masinter@adobe.com*
> Serious question: if it was “Save as HTML + CSS” or “save as X” for
> any other X, would you be less sad, and why?
>
> What data would you have in other formats that you don’t have for PDF?
>
> Seriously. It’s really hard to get down to requirements.
>
>
> On 6/27/15, 8:48 AM, "Ivan Herman" <*ivan@w3.org* <ivan@w3.org>> wrote:
>
> Me too...
>
> Ivan
>
> ---
> Ivan Herman
> Tel:*+31 641044153* <%2B31%20641044153>
> *http://www.ivan-herman.net* <http://www.ivan-herman.net/>
>
> (Written on mobile, sorry for brevity and misspellings...)
>
>
>
> On 27 Jun 2015, at 16:15, Peter Krautzberger <
> *peter.krautzberger@mathjax.org* <peter.krautzberger@mathjax.org>> wrote:
>
> Just something I came across,
>
> Quote: "It’s particularly useful for webpages, since it keeps all the
> text, and makes it searchable and copyable unlike, say, taking a
> screenshot."
>
> Peter.
>
>
>
>
>
## American Physical Society continues as MathJax Supporter
Source: MathJax • July 01, 2015 • Permalink
The American Physical Society (APS) continues to support the MathJax project as a MathJax Supporter.
Founded in 1899, the American Physical Society (APS) is the world’s largest organization of physicists and involved in several activities to advance and diffuse the knowledge of physics, including a strong publication program with landmark titles such as Physical Review Letters, the Physical Review journals, and Reviews of Modern Physics. As an influential supporter of SGML-based math notation in the 1990s and an early adopter of MathML, the APS has long been furthering innovation in academic communication.
“This past year we were able to create a high-quality, HTML rendering of our journal articles, which are often math intensive. MathJax along with the web version of the STIX fonts created by the MathJax team are key pieces of the implementation.”, said Mark Doyle, Chief Information Officer, American Physical Society. “After many years of work, it is gratifying to see the MathJax, JATS XML, and STIX efforts come together so seamlessly. MathJax also works quite well with our website’s respocd cnsive design for a first rate mobile experience.”
“Thanks to the dedication of sponsors such as APS, MathJax continues to deliver a reliable, high-quality solution for math and science on the web.”, comments Peter Krautzberger, MathJax manager. “As one of the original MathJax sponsors, APS’s support and feedback keeps pushing our development at MathJax forward.”
We look forward to continuing the collaboration with APS, and welcome their ongoing support for the MathJax project.
## W3C MathML 3.0 Gets Approval as ISO/IEC International Standard
Source: Ask.com News Search for "mathml" • June 30, 2015 • Permalink
Individual.com - Found Jun. 30, 2015 ... approval of the MathML Version 3.0 2nd Edition as an ISO/IEC International Standard (ISO/IEC 40314:2015). According to a release, MathML is...
## eWebEditor integrates MathFlow
Source: Design Science News • Aaron Guigar • June 29, 2015 • Permalink
Design Science has partnered with eWebSoft, the makers of eWebEditor. eWebEditor is a Chinese WYSIWYG HTML editor that can be added to web-based tools. Developers who choose eWebEditor will give their users a configurable HTML editor with the ability to author equations using MathFlow
eWebSoft's clients include online assessment systems and learning management systems that need to properly edit mathematical content in lessons and tests. The users of this software are familiar with copying equations from Design Science's MathType software, but this integration with MathFlow will make the addition of math to websites a more seamless experience.
Would you like to give it a try? You can demo MathFlow with the eWebEditor at http://www.ewebeditor.net/math/
Topics in this post:
## Re: update to xml entities draft
Source: www-math@w3.org Mail Archives • Asmus Freytag (t) (asmus-inc@ix.netcom.com) • June 26, 2015 • Permalink
On 6/23/2015 3:20 PM, Murray Sargent wrote:
> David Carlisle wrote that one could made definitions like
>
>> U+2102 DOUBLE-STRUCK CAPITAL C = Complex numbers
>>
>> Leaving U+1D53A free to be defined as a part of a generic alphabetic run as
>> MATHEMATICAL DOUBLE-STRUCK CAPITAL C
> One can't change the definitions of the math alphanumerics now since they are already encoded and Unicode has a stability guarantee. In addition they are widely used in technical documents as defined. We might have been able to get away with such definitions before the math alphanumerics were added to the Unicode Standard 3.1 back in March, 2001. For Microsoft Office apps, I wrote routines to work around the separation of the math alphabetics into the LetterLike Symbols and math alphanumerics blocks and it's complicated and even error prone. So I really wish that we had done something along the lines David suggests. But it's clearly water over the dam at this point.
>
> +Asmus and Michel in case they want to defend Unicode's position of not duplicating characters.
Someone may have to forward this reply to the list.
> I'd argue that simplicity of implementation should play an important role in this regard. This isn't the only place where Unicode is over unified. But these complications do provide ways to keep programmers employed <grin>.
Unicode generally does not encode characters by usage. For example
there's no distinction between period, decimal point, abbreviation point
etc.. This reflects the underlying situation, to wit, that this is a
case of the *same* symbol being used in different conventions.
The downside is that it is thus not possible to use plain text to
capture which convention is intended (but nothing prevents anyone from
providing rich-text markup). The upside is that data can't exhibit
"random alternation" between identical looking symbols; experience has
shown that this is a most likely outcome if "the same" item is encoded
several times, based merely on convention.
In the existing case, when 2102 and friends were encoded in the
Letterlike Symbols block, they were clearly intended as a subset of the
double struck alphabet. The fact that some of the conventional meanings
for characters from this subset are annotated in the nameslist does not
detract from that.
It took a few versions of Unicode to better understand the best way to
encode symbols and alphabets used for math. The unfortunate side effect
of that is that the math alphabets are not sequential but have "holes".
In some cases, Unicode apparently does encode convention, for example
the micro vs. Greek mu, or Ohm vs. Greek Omega. These have complicated
histories. The desire to preserve the Latin-1 layout as an aid in
migration overrode the normal reluctance to code by convention. The
downside is that now users will use "random alternation" for the mu used
as micro sign. Greek users will most certainly not use the Latin-1 code
point for that purpose.
Some of the letterlike symbols should not have been coded in that block,
but in the Squared abbreviations block. That is because their origin was
fundamentally the special em-square set of units used in Asian
standards. In the early versions of Unicode, there was this idea of
filtering out from such sets, any symbol that might be used
"generically", that is, outside an Asian typographic environment.
For most such usages, the standard Latin (or Greek, for Ohm) letters
would have been the correct characters, leaving Kelvin, Ohm, and
Angstrom as specifically "squared" characters.
So, while there are exceptions to what has by now become the principle
for new encodings, I would not call the treatment of math alphabets
"over unified". It is rather an attempt to not needlessly repeat the
"underunification" of micro, Kelvin, Ohm and Angstrom.
A./
## W3C MathML 3.0 Approved as ISO/IEC International Standard ...
Source: mathml - Google Blog Search • A.R. Guess • June 26, 2015 • Permalink
MathML is the mark-up language used in software and development tools for statistical, engineering, scientific, computational, and academic expressions of math on the Web. The Mathematical Markup Language provides ...
## Re: update to xml entities draft
Source: www-math@w3.org Mail Archives • William F Hammond (hammond@csc.albany.edu) • June 25, 2015 • Permalink
Murray Sargent <murrays@exchange.microsoft.com> writes:
> David Carlisle wrote that one could made definitions like
>
>>U+2102 DOUBLE-STRUCK CAPITAL C = Complex numbers
>>
>>Leaving U+1D53A free to be defined as a part of a generic
>> alphabetic run as
>>MATHEMATICAL DOUBLE-STRUCK CAPITAL C
I hope we're clear that just because at some point in
history the glyph that might have been used for U+1D53A had
been used for U+2102 does not mean that the *character*
named "DOUBLE-STRUCK CAPITAL C" would be the same as a
*character* in the alphabetic series "MATHEMATICAL
DOUBLE-STRUCK CAPITAL *".
Just to drive home this point, let me note that there are
annotations in my (slightly old) copy of the standard for the
characters in the U+21xx block corresponding to the vacant
slots indicating dedicated mathematical meanings.
The characters in the plane 1 mathematical alphabetic series
do not have annotations indicating dedicated meanings.
There is no need to change the names in U+21xx since already
they are different from what should be the mathematical
alphabetic series vacant slot names.
> One can't change the definitions of the math alphanumerics
> now since they are already encoded and Unicode has a
> stability guarantee.
Not necessary.
> In addition they are widely used in technical documents as
> defined. We might have been able to get away with such
> definitions before the math alphanumerics were added to
> the Unicode Standard 3.1 back in March, 2001.
My suggestion is simply that the vacant slots be filled. That
won't break anything. Of course, it might then take maybe a
decade before anyone could rely on them.
> For Microsoft Office apps, I wrote routines to work around
> the separation of the math alphabetics into the LetterLike
> Symbols and math alphanumerics blocks and it's complicated
> and even error prone. So I really wish that we had done
> something along the lines David suggests. But it's clearly
> water over the dam at this point.
Yes, *complicated and error prone*.
> ... +Asmus and Michel in case they want to defend Unicode's
> position of not duplicating characters. I'd argue that
> simplicity of implementation should play an important role
> in this regard. ...
Again, filling in the slots might generate redundant glyph
references, depending on glyph choices for the various
characters, but would not duplicate characters.
And all routes I can imagine for user-generated documents,
at least in most of Europe, Australia, North America, and
South America involve complicated code such as you describe.
-- Bill
#mathml #html5 #unicode #unigaps #xhtmlTooComplicated
## Feeds
Planet MathML features:
If you own a blog with a focus on MathML, and want to be added or removed from this aggregator, please get in touch with Bert Bos at bert@w3.org.
|
2015-08-02 23:06:29
|
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|
https://www.semanticscholar.org/paper/Harmonic-maps-and-Riemannian-submersions-between-Ianu%C5%9F-V%C3%AElcu/0d46d8402ea326e4aed20c269aa8d65f1967fd97
|
# Harmonic maps and Riemannian submersions between manifolds endowed with special structures
@article{Ianu2011HarmonicMA,
title={Harmonic maps and Riemannian submersions between manifolds endowed with special structures},
author={Stere Ianuş and Gabriel Eduard V{\^i}lcu and R. C. Voicu},
journal={Banach Center Publications},
year={2011},
volume={93},
pages={277-288}
}
• Published 2011
• Mathematics
• Banach Center Publications
It is well known that Riemannian submersions are of interest in physics, owing to their applications in the Yang-Mills theory, Kaluza-Klein theory, supergravity and superstring theories. In this paper we investigate some classes of Riemannian submersions between manifolds endowed with special geometric structures.
9 Citations
Almost Contact Metric Submersions in Kenmotsu Geometry
In this paper, we discuss some geometric properties of Riemannian submersions whose total space is a manifold through various classes of Kenmotsu structures. The study focuses on the superminimality
Anti-Invariant Semi-Riemannian Submersions from Almost Para-Hermitian Manifolds
We introduce anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds onto semi-Riemannian manifolds. We give an example, investigate the geometry of foliations which are
Curvature Inequalities for Submanifolds of S-space From
• N. Rehman
• Mathematics
European Journal of Pure and Applied Mathematics
• 2019
In this paper we establish new results of squared mean curvature and Ricci curvature for the sub manifolds of S-space from that is the generalization of complex and contact structures. Obtained
Semi-invariant semi-Riemannian submersions
• Mathematics
• 2018
In this paper, we introduce semi-invariant semi-Riemannian submersions from para-Kahler manifolds onto semi-Riemannian manifolds. Wegive some examples, investigate the geometry of foliations that
Anti-invariant Pseudo-Riemannian Submersions and Clairaut Submersions from Paracosymplectic Manifolds
In this paper, we investigate geometric properties of anti-invariant pseudo-Riemannian submersions whose total space is a paracosymplectic manifold. Then, we study new conditions for anti-invariant
Harmonic maps and para-Sasakian geometry
• Mathematics
• 2015
The purpose of this paper is to study the harmonicity of maps to or from para-Sasakian manifolds. We derive the condition for the tension field of paraholomorphic map between almost para-Hermitian
Slant submersions in paracontact geometry
In this paper, we investigate some geometric properties of three types of slant submersions whose total space is an almost paracontact metric manifold.
## References
SHOWING 1-10 OF 39 REFERENCES
Harmonic maps between quaternionic Kähler manifolds
• Mathematics
• 2008
Abstract In this note we introduce the concept of (σ, σ′)-holomorphic map between two almost quaternionic Hermitian manifolds. We prove that a (σ, σ′)-holomorphic map between two quaternionic Kähler
Harmonic maps between compact Hermitian manifolds
• Mathematics
• 2008
In this paper, we generalize the Bochner-Kodaira formulas to the case of Hermitian complex (possibly non-holomorphic) vector bundles over compact Hermitian (possibly non-Kähler) manifolds. As
Semi-Riemannian Geometry With Applications to Relativity
Manifold Theory. Tensors. Semi-Riemannian Manifolds. Semi-Riemannian Submanifolds. Riemannian and Lorenz Geometry. Special Relativity. Constructions. Symmetry and Constant Curvature. Isometries.
SOME CONSTRUCTIONS OF ALMOST PARA-HYPERHERMITIAN STRUCTURES ON MANIFOLDS AND TANGENT BUNDLES
• Mathematics
• 2008
In this paper we give some examples of almost para-hyperhermitian structures on the tangent bundle of an almost product manifold, on the product manifold M × ℝ, where M is a manifold endowed with a
Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds
• D. Chinea
• Mathematics
• 2009
Abstract In this paper we study holomorphic maps between almost Hermitian manifolds. We obtain a new criterion for the harmonicity of such holomorphic maps, and we deduce some applications to
Riemannian Submersions from Quaternionic Manifolds
• Mathematics
• 2008
In this paper we define the concept of quaternionic submersion, we study its fundamental properties and give an example.
Horizontally conformal submersions of CR-submanifolds
It is shown that any horizontally conformal submersion of a CR-submanifold M of a Kaehler manifold M onto a Kaehler manifold N is a Riemannian submersion. Moreover, if M is mixed geodesic, then it is
On Paraquaternionic Submersions Between Paraquaternionic Kähler Manifolds
In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic
CR-manifolds, harmonic maps and stability
• Mathematics
• 2001
Abstract. We present some results on harmonic maps on CR-manifolds and some stability problems for Sasakian manifolds of constant $\varphi$-sectional curvature.
Riemannian Submersions and Related Topics
• Mathematics
• 2004
This book provides the first-ever systematic introduction to the theory of Riemannian submersions, which was initiated by Barrett O'Neill and Alfred Gray less than four decades ago. The authors focus
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2022-07-03 09:17:03
|
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http://advancedintegrals.com/category/digamma-function/
|
Category Archives: Digamma function
Integral representation of the digamma function using Abel–Plana formula
$$\int^\infty_0 \frac{2x}{(x^2+z^2)e^{2\pi x}-1}\,dx =\log(z)-\psi(z)-\frac{1}{2z}$$ $$\textit{proof}$$ Use Abel–Plana formula $$\sum_{n=0}^\infty f(n) = \int^\infty_0f(x)\,dx+\frac{f(0)}{2} +i\int^\infty_0 \frac{f(ix)-f(-ix)}{e^{2\pi x}-1}\,dx$$ Let $$f(x) = \frac{1}{z+x}$$ Note that $$i(f(ix) -f(-ix))= \frac{i}{z+ix}-\frac{i}{z-ix} = \frac{2x}{z^2+x^2}$$ By integration we have $$\int^\infty_0 \frac{2x}{(x^2+z^2)e^{2\pi x}-1}\,dx =\lim_{N\to \infty}\sum_{n=0}^N \frac{1}{z+n}-\int^N_0 \frac{1}{x+z}\,dx-\frac{1}{2z}$$ The … Continue reading
Posted in Digamma function | | 3 Comments
The most ugly looking integral
Prove the following $$I= \log \left\{\frac{\Gamma(b+c+1) \Gamma(c+a+1)\Gamma(a+b+1)}{\Gamma(a+1) \Gamma(b+1) \Gamma(c+1) \Gamma(a+b+c+1)} \right\}$$ where $$I = \int_0^1 \frac{(1-x^a)(1-x^b)(1-x^c)}{(1-x)(-\log x)}dx$$ $$\textit{proof}$$ First note that since there is a log in the denominator that gives as an idea to use differentiation under … Continue reading
Posted in Digamma function, Gamma function | Tagged , , , , , | Leave a comment
Digamma fourth integral representation proof
$$\psi(z) = \log(z) -\frac{1}{2z}-2\int^\infty_0 \frac{t}{(t^2+z^2)(e^{2\pi}-1)}dt\,\,\,\,;\text{ Re}z>0$$ We prove that $$2\int^\infty_0 \frac{t}{(t^2+z^2)(e^{2\pi}-1)}dt= \log(z) -\frac{1}{2z}- \psi(z)$$ First note that $$\frac{2}{e^{2\pi t}-1} =\coth(\pi t)-1$$ Also note that $$\coth(\pi t) = \frac{1}{\pi t}+\frac{2t}{\pi}\sum_{k=1}^\infty\frac{1}{k^2+t^2}$$ Hence we conclude that $$\frac{2t}{e^{2\pi t}-1} =\frac{1}{\pi}-t+\frac{2t^2}{\pi}\sum_{k=1}^\infty\frac{1}{k^2+t^2}$$ Substitute the … Continue reading
Posted in Digamma function | Tagged , , | Leave a comment
$$\psi \left(a\right)=\int^{\infty}_0 \, \frac{e^{-t}}{t}-\frac{e^{-\left(a t\right)}}{1-e^{-t}}\, dt$$ $$\textit{proof}$$ Let $e^{-t}=x$ $$\int^{1}_0 \, -\frac{1}{\log(x)}-\frac{x^{a-1}}{1-x}\, dx$$ By adding and subtracting 1 $$-\int^{1}_0 \, \frac{1}{\log(x)}+\frac{1}{1-x}\, dx+\int^1_0\frac{1-x^{a-1}}{1-x}\, dx$$ Using the second integral representation $$-\int^{1}_0 \, \frac{1}{\log(x)}+\frac{1}{1-x}\, dx+\gamma+\psi(a)$$ We can prove that $$\int^{1}_0 \, … Continue reading Posted in Digamma function | Tagged , , | Leave a comment Second integral representation of digamma proof$$\psi(s+1)\,=\, -\gamma \,+\, \int^{1}_{0}\frac{1-x^s}{1-x}\,dx\textit{proof}$$This can be done by noting that$$\psi(s+1) = -\gamma +\sum_{n=1}^\infty\frac{s}{n(n+s)}$$It is left as an exercise to prove that$$\sum_{n=1}^\infty\frac{s}{n(n+s)} = \int^{1}_{0}\frac{1-x^s}{1-x}\,dx$$Posted in Digamma function | Tagged , , | Leave a comment First integral representation of digamma proof$$ \psi(a) = \int^{\infty}_0 \frac{e^{-z}-(1+z)^{-a}}{z}\,dz \textit{proof}$$We begin with the double integral$$\int^{\infty}_0 \int^t_1 \,e^{-xz}\,dx\,dz=\int^{\infty}_{0}\frac{e^{-z}-e^{-tz}}{z}\, dz $$Using fubini theorem we also have$$ \int^t_1 \int^{\infty}_0\,e^{-xz}\,dz \,dx = \int^t_1 \frac{1}{x}\,dx = \log t $$Hence we have the following … Continue reading Posted in Digamma function | Tagged , , | Leave a comment Digamma difference formula proof$$\psi(1-x)-\psi(x)=\pi \cot(\pi x) \textit{proof}$$We know by the reflection formula that$$\Gamma(x)\Gamma(1-x)=\pi \csc(\pi x) $$Now differentiate both sides$$\psi(x)\Gamma(x)\Gamma(1-x)-\psi(1-x)\Gamma(x)\Gamma(1-x)=-\pi^2 \csc(\pi x)\,\cot(\pi x) $$Which can be simplified$$\Gamma(x)\Gamma(1-x)\left(\psi(1-x)-\psi(x)\right)=\pi^2 \csc(\pi x)\,\cot(\pi x) $$Further simplifications using ERF results in$$ … Continue reading
Posted in Digamma function | Tagged , , | Leave a comment
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2018-08-16 17:29:56
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https://mcqbooks.com/mcq-questions-for-class-6-maths-chapter-4/
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# MCQ Questions for Class 6 Maths Chapter 4 Basic Geometrical Ideas with Answers
If you’re looking for a way to enhance your Class 6 Maths, then look no further than the NCERT MCQ Questions for Class 6 Maths Chapter 4 Basic Geometrical Ideas with Answers. MCQ Questions for Class 6 Maths with Answers is perfect for those who are in Class 6 Maths and want to get ahead of everyone else by mastering their subject skills as soon as possible! You can practice and test your subject knowledge by solving these Class 6 Maths Chapter 4 Basic Geometrical Ideas Objective Questions.
## Basic Geometrical Ideas Class 6 MCQs Questions with Answers
Solving Class 6 Maths Basic Geometrical Ideas MCQ with Answers can be of great help to students as they will be aware of all the concepts. These MCQ Questions on Basic Geometrical Ideas Class 6 with answers pave for a quick revision, thereby helping you learn more about this subject.
Question 1.
A triangle has:
(a) one element
(b) two elements
(c) 6 elements
(d) none of these
Question 2.
A point where three or more lines meet is called:
(a) point of concurrence
(b) meeting point
(c) collinear point
(d) non-collinear point
Question 3.
What are used to represent points?
(a) Numerals.
(b) Capital letters of alphabet.
(c) Lower case letters of alphabet.
(d) All of the above
Answer: (b) Capital letters of alphabet.
Question 4.
Which instrument is used to compare two line segments?
(a) Compasses
(b) A divider
(c) Set squares
(d) A protractor
Question 5.
A __________ of a circle is a line segment joining any two points on the circle.
(a) chord
(b) diameter
(d) None of these
Question 6.
(a) one vertex
(b) two vertices
(c) three vertices
(d) four vertices
Question 7.
The meeting point of a pair of adjacent sides of a polygon is called its:
(a) vertex
(b) diagonal
(d) none of these
Question 8.
An angle is made up of two ________ starting from common end point.
(a) rays
(b) vertices
(c) lines
(d) points
Question 9.
If two lines intersects each other then the common point between them is known as point of _________.
(a) concurrence
(b) intersection
(c) vertex
(d) contact
Question 10.
What is a set of points extending infinitely in all directions on the same flat surface called?
(a) A line
(b) A plane
(c) Ray
(d) A point
Question 11.
(a) one diagonal
(b) two diagonals
(c) three diagonals
(d) four diagonals
Question 12.
Three or more points are collinear if they lie on the:
(a) same line
(b) two lines
(c) same surface
(d) none of these
Question 13.
Flat surface in which two points are joined by using straight line is classified as
(a) line
(b) plane
(c) ray
(d) intersecting line
Question 14.
What is the number of end points of a line?
(a) Zero
(b) Two
(c) One
(d) Three
Question 15.
Angle which is less than 90° is called
(a) reflex angle
(b) obtuse angle
(c) acute angle
(d) right angle
Question 16.
The maximum number of points of intersection of three lines is:
(a) one
(b) two
(c) three
(d) four
Question 17.
A polygon having four sides is called:
(a) triangle
(c) circle
(d) none of these
Question 18.
The centre of a circle:
(a) lies in its interior
(b) lies in its exterior
(c) lies on the circle
(d) none of these
Answer: (a) lies in its interior
Question 19.
Any line segment can be formed by joining
(a) two points
(b) three points
(c) four points
(d) more than three points
Question 20.
Angle which is equal to 90° is classified as
(a) right angle
(b) obtuse angle
(c) acute angle
(d) reflex angle
Question 21.
A triangle has:
(a) one vertex
(b) two vertices
(c) three vertices
(d) none of these
Question 22.
A ray has:
(a) one end point
(b) two end points
(c) three end points
(d) none of these
Question 23.
Out of following, one angle which is obtuse is
(a) $$\frac { 11 }{ 21 }$$ of a right angle
(b) $$\frac { 8 }{ 20 }$$ of a complete rotation
(c) $$\frac { 11 }{ 21 }$$ of a complete rotation
(d) $$\frac { 8 }{ 20 }$$ of a right angle
Answer: (b) $$\frac { 8 }{ 20 }$$ of a complete rotation
Question 24.
Two lines meeting at a point are called ___________ .
(a) intersecting lines
(b) concurrent lines
(c) parallel line
(d) None of these
Question 25.
A triangle has:
(a) one median
(b) two medians
(c) three medians
(d) four medians
Question 26.
A quadrilateral is a polygon having:
(a) two sides
(b) three sides
(c) four sides
(d) none of these
Question 27.
Two distinct lines meeting at a points are called _____________.
(a) intersecting lines
(b) parallel lines
(c) collinear lines
(d) None of these
Question 28.
Out of following options, two angles that are together classified as complementary angles are
(a) 120° and 60°
(b) 50° and 30°
(c) 65° and 25°
(d) 70° and 30°
Question 29.
A triangle has:
(a) one side
(b) two sides
(c) three sides
(d) four sides
Question 30.
A circle is a:
(a) polygon
(b) an open curve
(c) a closed curve
(d) none of these
Question 31.
If two angles are said to be supplementary angles and one of angle is of 122° then other angle is of
(a) 35°
(b) 32°
(c) 60°
(d) 58°
Question 32.
How many lines pass through two given points?
(a) one
(b) two
(c) three
(d) many
Question 33.
The minimum number of points of intersection of three lines is:
(a) zero
(b) one
(c) two
(d) three
Question 34.
A line has:
(a) fixed length
(b) infinite length
(c) 100 cm length
(d) none of these
Question 35.
Two non-parallel lines always intersect:
(a) in a line
(b) in a point
(c) in two lines
(d) none of these
Question 36.
Angle which is less than 360° and larger than 180° is classified as
(a) acute angle
(b) obtuse angle
(c) reflex angle
(d) right angle
Question 37.
Three or more points lying on the same line are known as ___________ points.
(a) collinear
(b) intersecting
(c) non-collinear
(d) None of these
Question 38.
Through one given point:
(a) one line can be drawn
(b) two lines can be drawn
(c) many lines can be drawn
(d) none of these
Answer: (c) many lines can be drawn
Question 39.
A point has:
(a) infinite length
(b) 1 mm length
(c) no length
(d) all of these
Question 40.
How many lines pass through one given point?
(a) Three
(b) One
(c) Countless
(d) Two
Question 41.
What is a set of points which extend infinitely in both directions called?
(a) A line
(b) A plane
(c) A line segment
(d) A point
Question 42.
(a) one side
(b) two sides
(c) three sides
(d) four sides
Question 43.
An angle has:
(a) one vertex and one arm
(b) one vertex and two. arms
(c) two vertices and two arms
(d) none of these
Answer: (b) one vertex and two. arms
Question 44.
A flat surface which extends indefinitely in all directions is called ___________ .
(a) plane
(b) lines
(c) point
(d) line segment
Fill in the blanks:
1. A triangle has …………… medians.
2. Radius is ………………… of the diameter.
3. A quadrilateral has …………………. diagonals.
4. All the radii of a circle are ………………..
5. How many chords of a circle are there? ……………………….
6. A point equidistant from all the points on a circle is called ……………….. of the circle.
7. The diameter of a circle is the …………………. chord of the circle.
8. Name all the sides of a polygon ABCD ………………..
9. A quadrilateral has …………………. vertices.
10. How many centres does a circle have? …………………
11. A triangle has ………….. vertices.
12. The distance between any two points on the circle is called ………………….. of the circle.
13. A triangle has ……………… sides.
14. A quadrilateral has ……………… sides.
Match the following:
1.
(a) A triangle (i) Line segment joining two points on the circle (b) A quadrilateral (ii) Has one center (c) A chord of a circle (iii) Has three sides (d) Diameter of a circle (iv) Has four sides (e) A circle (v) Longest chord
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2022-08-10 10:12:30
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https://www.imrpress.com/journal/CEOG/49/1/10.31083/j.ceog4901030/htm
|
NULL
Section
All sections
Countries | Regions
Countries | Regions
Article Types
Article Types
Year
Volume
Issue
Pages
IMR Press / CEOG / Volume 49 / Issue 1 / DOI: 10.31083/j.ceog4901030
Open Access Original Research
Concurrent hysterectomy and umbilical hernia repair via transvaginal notes among morbidly obese patients
Show Less
1 Department of General Surgery, Kartal Dr. Lutfi Kirdar City Hospital, University of Health Sciences, 34865 Istanbul, Turkey
2 Department of Obstetrics and Gynecology, Kartal Dr. Lutfi Kirdar City Hospital, University of Health Sciences, 34865 Istanbul, Turkey
Clin. Exp. Obstet. Gynecol. 2022 , 49(1), 30; https://doi.org/10.31083/j.ceog4901030
Submitted: 21 November 2021 | Revised: 30 December 2021 | Accepted: 4 January 2022 | Published: 20 January 2022
This is an open access article under the CC BY 4.0 license.
Abstract
Background: Umbilical hernias are especially common along with overweight, multiparous women. Laparoscopic hernia repair is preferred due to many advantages. On the other hand, the risk of trocar site hernia is disadvantageous. Trocars do not go through the abdominal wall via transvaginal natural orifice transluminal endoscopic surgery (V-NOTES). We investigate the V-NOTES hysterectomy and concomitant umbilical hernia repairment feasibility and outcomes. Methods: Six morbidly obese patients underwent V-NOTES hysterectomy and concurrent umbilical hernia repair between April 2020 and January 2021. Demographic features of patients, operating time, hernia size, complications, hospitalization time, recurrence of the hernia, visual analog scale (VAS) at 6th, 12th, and 24th hours, first, fourth, 12th weeks, and sixth months were recorded. Results: The average age of patients was 47.667 $\pm$ 2.422 (45–52). Mean body mass index (BMI), hernia and operating time size were 44.367 $\pm$ 3.217 kg/m${}^{2}$ (40.3–48.5), 6.167 $\pm$ 1.722 cm (4–9) and 88 $\pm$ 12.791 minutes (75–110), respectively. Intraoperative complications did not occur. Seroma was detected in one patient(16.6%). In six month follow-up period, we did not establish a diagnosis of hernia recurrence and postoperative chronic pain. Conclusion: Our study offers a novel perspective on V-NOTES umbilical hernia repair and hysterectomy in morbidly obese patients. According to our study, performing V-NOTES umbilical hernia repairment in a risky patient population is feasible and has promising outcomes.
Keywords
Morbidly obese
Postoperative chronic pain
Recurrence
Umbilical hernia
V-NOTES
1. Introduction
Approximately 2% of the population of the world has a clinically demonstrable umbilical hernia [1]. Hernia repairs are the most commonly performed operations, and around 175,000 patients undergo umbilical hernia operations in the United States annually [2]. Women are three to five times more likely to have umbilical hernia than men. The characteristics of an umbilical hernia patient are frequently overweight, multiparous female between her fourth and sixth decade [3].
Not all hernias need to be surgically corrected, and watchful waiting is an alternative for surgery, especially in a population which surgery is thought to have higher mortality and morbidity [4]. On the other hand, in five years of a watchful waiting period, there is a 16% probability of patients with umbilical hernias requiring surgery and a 4% chance of requiring emergency surgery [5]. Besides, there is no clear consensus about the optimal approach for the best surgical outcomes [6, 7, 8].
Laparoscopic repair of an umbilical hernia is a pleasant alternative due to less postoperative pain, lower risk of surgical site infections, and shorter hospitalization [9]. However, 10–15 mm sized trocars can incur fascial defects, and after the laparoscopic hernia repairment, these fascial defects can cause a future herniation. Following major laparoscopic gynecological procedures, the formation of trocar site hernia for 10 mm and 12 mm trocars were 0.23% and 3.1%, respectively [10]. If the mesh size larger than 10 $\times$ 15 cm is used during laparoscopic hernia repair, the incidence of trocar site hernia rises to 22% [11].
Accessing the surgery area via the body’s natural orifices, such as the umbilicus, mouth, anus, urethra, and vagina is an attractive option and has gained popularity among minimal invasive surgeons. Using natural orifices as a gateway for surgery is defined as natural orifice transluminal endoscopic surgery (NOTES). Amongst all possible NOTES, transvaginal natural orifice transluminal endoscopic surgery (V-NOTES) provides easy access, safe entry, and a straight and broad view of the peritoneal cavity [12]. Moreover, the transvaginal route is ergonomic for surgeons [13].
In this present article, we aim to describe the concurrent V-NOTES hysterectomy and umbilical hernia repair technique among morbidly obese patients and present the short- and long-term surgical outcomes of this surgery.
2. Material and methods
Between April 2020 and January 2021, at the Kartal Dr. Lutfi Kirdar Training and Research Hospital, Istanbul, Turkey, six morbidly obese patients were scheduled for hysterectomy and concomitant umbilical hernia repair included in this study. The hospital’s ethics committee approved the protocol of the trial (Register no. 2020/514/177/36). Written informed consent was obtained from all participants.
Inclusion criteria for patients were: age between 35–70 years, body mass index (BMI) higher than 40 kg/m${}^{2}$, hysterectomy planned for benign pathologies, no history of hernia operation, symptomatic umbilical hernia, no mental problems to evaluate the visual analog scale (VAS) and willingness to participate in the study.
If the patient has a clinical diagnosis of renal, hepatic, hematologic, neurologic disease, or malignant tumor or the participant who did not fulfill even one of the inclusion criteria above was excluded from the study.
2.1 Operation technique
15–30 minutes before incision, 3 g Cefazolin was administered intravenously. Patients under general anesthesia were placed in the supine position, and the lower extremities were elevated. The surgical site, including the vagina, was cleaned and disinfected with 10% povidone-iodine. An indwelling catheter was inserted. A system with a wound retractor (Alexis; GelPOINT V-Path Transvaginal Access Platform®, Applied Medical Resources Corp., Rancho Santa Margarita) was utilized to establish a platform. One 10- and two 5-mm trocars were inserted through the platform. The retractor of the system was placed in the mid-vagina, and CO${}_{2}$ gas was insufflated through the system. After the vagina was dilated, the patient was tilted into Trendelenburg position, and a colpotomy incision was made with an ultrasonic scalpel (Harmonic® HD 1000i shears, 5-mm diameter; Ethicon). The bladder was dissected from the anterior vagina and the lower uterine cervix. The anterior peritoneum was accessed by cutting the uterovesical fold of the peritoneum. The posterior peritoneal fold was located and slit using the ultrasonic scalpel. Subsequently, access to the pouch of Douglas was maintained. The anterior and posterior incisions were transversely broadened and rounded along with the cervix. A pneumoperitoneum was established via these incisions, and the endoscope was introduced to explore abdominal and pelvic cavities. After exploration, hysterectomy was performed as described in the literature [14].
After hysterectomy was performed, the specimen was taken out from the vagina to visualize the peritoneal cavity better. The umbilical hernia on the anterior wall was effortlessly able to detect (Fig. 1). The omentum and preperitoneal tissues inside the hernia sac were extracted to the abdominal cavity, and thereby the hernia sac was emptied. The hernia defect was exposed and measured with a tape measure to ensure to select proper sized mesh. A non-absorbable monofilament polyester textile with absorbable collagen film containing mesh (Symbotex® Composite mesh) was used to coat the defect. The mesh was placed to cover at least 5 cm from the hernia side on the intraperitoneum. The mesh was fixed with 2-0 polypropylene suture (Prolene®) and absorbable tackers (Fig. 2). One in each corner, a total of four stitches were made to secure the mesh to the abdominal wall. The mesh was then fixated with a double crown of absorbable tacks (Absorba Tack®).
Fig. 1.
Umbilical hernia detected on the anterior wall.
Fig. 2.
Final view of the repaired umbilical hernia defect via V-NOTES.
After ensuring hemostasis, the pneumoperitoneum was deflated through a closed suction system, the platform system was removed, and the vaginal cuff was repaired with one coated polyglactin suture (Vicryl®).
2.2 Data collection and analysis
Detailed records, including each patient’s age, BMI, hernia size, medical history, operation time, estimated blood loss, pre-and postoperative hemoglobin levels, pain scores [obtained from VAS at 6th, 12th, and 24th hours, first, fourth, 12th weeks and sixth months postoperatively], analgesic doses, complications, postoperative hospital stay, postoperative diagnosis, were collected.
Patients routinely got intramuscular diclofenac sodium at the 8th hour and oral paracetamol and ibuprofen combination as the analgesic at 16th and 24th hours in the postoperative period. The VAS scores were evaluated by another researcher who did not know that patients had a combined procedure of hysterectomy and umbilical hernia repair at the sixth, 12th, 24th hours. If any patients demand an extra analgesic dose, the same researcher would record it.
All patients were followed up by the same specialist team at first, fourth, 12th weeks, and sixth months.
Continuous variables were presented as mean, standard deviation, and range. Categorical variables were expressed as frequencies and percentages. All statistical analyses were performed with SPSS® version 23.0 software (SPSS®, Chicago, IL, USA).
3. Results
All procedures were completed via V-NOTES, and none of the patients were required to convert to laparotomy.
Clinical characteristics of the patients are shown in Table 1. The mean age was 47.667 $\pm$ 2.422 years (45–52). Mean BMI was 44.367 $\pm$ 3.217 kg/m${}^{2}$ (40.3–48.5). Three patients had previous operations (two patients had Caesarian sections, and one patient had appendectomy). All patients had type II Diabetes Mellitus (D.M.) and two patients were taking oral antidiabetic drugs, and four were using insulin to control blood sugar.
Table 1.Clinical characteristics of patients.
Age Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Patient 6 45 46 52 47 48 48 BMI 45.1 48.5 47.3 40.3 41.5 43.5 Hernia size (cm) 4 9 7 5 6 6 Hospitalization (day) 1 2 2 1 1 1 Hemoglobin drops (g/dL) 0 0.7 0.6 0.3 0.2 0.4 Operating time (minutes) 75 110 93 82 78 90 BMI, body mass index.
The mean hernia size was 6.167 $\pm$ 1.722 cm (4–9). The mean operative time was 88 $\pm$ 12.791 minutes (75–110). No complication occurred intraoperatively. Mean hemoglobin drop was 0.367 $\pm$ 0.258 g/dL (0–0.7).
The mean VAS scores at the eighth, 12th, 24th hour were 2.667 $\pm$ 0.816 (2–4)-1.667 $\pm$ 0.816 (1–3)-1.167 $\pm$ 0.408 (1–2), respectively. The patients did not demand or take extra pain medications. The mean VAS score was 0.333 $\pm$ 0.516 (0–1) at the first week of follow-up. After the fourth week of follow-up, all participants’ VAS scores were zero and remained zero until the sixth month of the follow-up (Table 2).
Table 2.Postoperative pain.
Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Patient 6 VAS 8th hour 2 4 3 3 2 2 VAS 12th hour 2 3 2 1 1 1 VAS 24th hour 1 2 1 1 1 1 VAS 1st week 0 1 1 0 0 0 VAS 4th week 0 0 0 0 0 0 VAS 12th week 0 0 0 0 0 0 VAS 6th month 0 0 0 0 0 0 VAS, visual analog scale.
Four patients were discharged on the first day of surgery, while two were discharged on the second day of the surgery due to social indications (one was living in a different city, and the other did not have a companion to look after for her at home).
Seroma was detected in one patient (16.6%) postoperatively, and percutaneous needle aspiration was performed for seroma treatment, and full recovery was achieved in two weeks after the aspiration.
All participants we included in this study completed the six-month follow-up period. Vaginal wound infection, hematoma, chronic pain, and recurrence are not detected in the six months of the follow-up period.
4. Discussion
Drawing on recent advances in V-NOTES, the present article aimed to show the feasibility and the short- and long-term outcomes of V-NOTES hysterectomy and concurrent umbilical hernia correction along with the morbidly obese patients.
Although there is no clear consensus on the technique for ultimate surgical outcomes, the outcome of the umbilical hernia repair is evaluated by recurrence, postoperative chronic pain, and complications [15]. The recurrence rate is doubtlessly the most critical parameter in terms of the quality of the operation. Within a six-month follow-up period, we did not observe any recurrence; in addition, since we did not use any trocar through the abdominal wall, we can assume that we eliminated the risk of trocar site hernia.
The patient-related risks of trocar site hernia and higher recurrence rates after hernia repair are advanced age, high BMI, and D.M. [16, 17, 18, 19]. In our study, all participants have high BMI and D.M. Moreover, the same patient population also has a higher risk of wound complications [20]. V-NOTES might be considered as an alternative in this type of risky patient.
Postoperative chronic pain is another significant criterion for qualifying surgical outcomes. It is important to note that after V-NOTES, we did not detect any pain score more than four scaled with VAS, starting from the eighth hour of the operation. In the sixth month, none of the patients had chronic pain after surgery. To the best of our knowledge, there are no studies giving information about long-term pain results after V-NOTES umbilical hernia repair in the literature yet.
Seroma formation is the most frequently reported complication after laparoscopic abdominal hernia repair. The incidence ranges from 1% to 14% [21, 22, 23]. Our incidence of seroma after V-NOTES (16.6%) is higher than the seroma formation after laparoscopy. One possible explanation for higher incidence is the small number of patients who participated in the study. We think that by increasing the patient population, we could reach the actual seroma incidence. Despite this high incidence, seroma did not contribute to morbidity and, most of the time spontaneously resolves without intervention.
Another concern about the hernia operation via NOTES is the mesh sterility. Earle et al. [24] modified an esophageal stent to prevent mesh contamination for transgastric NOTES hernia repair. Some researches showed that an operation prepared vagina could be superior to a classical skin incision in terms of sterility for performing a biopsy or synthetic mesh placement [25, 26]. In our study, prophylactic antibiotics were administered before the operation, and the vagina was disinfected with 10% povidone-iodine solution. Furthermore, we used a transvaginal access platform system and mesh introduced to the peritoneal cavity via the trocars on the platform without contacting any other surfaces.
Gynecologic or non- gynecologic operations for benign or malign pathologies such as ectopic pregnancy management, myomectomy, cholecystectomy, hemicolectomy for colon cancer can be carried out via V-NOTES [13, 27, 28, 29]. Moreover, uterosacral ligament hysteropexy can be performed for pelvic organ prolapse when uterus conservative treatment is desired [30]. The uterus is a mobile organ and can be manipulated and easily removed from the field of view; the vagina is a flexible and expandable fibromuscular tube [31]. These features of female reproductive organs can provide a broad and clear peritoneal cavity visualization and ergonomics for surgeons even the hysterectomy is not performed during V-NOTES.
Our study has two main limitations. The first of which is the small number of patients who operated with this technique. The second, the follow-up period, is a brief time to give information about the recurrence rate of umbilical hernia. Most of the hernia studies have a follow-up period of one to five years, but it is known that recurrence time can exceed to 50 years [32].
Although these limitations, our study cannot be ruled out. It is essential to interpret our results together with the findings from previous researches. Precisely, our study focuses on the morbidly obese patients with D.M., which can negatively affect the operation results.
In the present article, we presented our simultaneously V-NOTES hysterectomy and umbilical hernia repair along morbidly obese patients. It is a feasible technique with good surgical outcomes in a risky group.
Future researches may extend this work by increasing the patient population and follow-up period.
5. Conclusions
We performed V-NOTES hysterectomy and umbilical hernia repair among morbidly obese patients. All procedures were completed via the vagina. Recurrence and postoperative chronic pain was not detected.
V-NOTES requires intensive training and experience with a higher level of technical skill. Repairment of umbilical hernia via V-NOTES is feasible and clinically successful. Especially, there are promising results on postoperative pain, wound infection, and recurrence rate.
Author contributions
MMA, SK and AC designed the research study. MMA performed the research. MMA and HFK analyzed the data. BK and EM wrote the manuscript. All authors contributed to editorial changes in the manuscript. All authors read and approved the final manuscript.
Ethics approval and consent to participate
The hospital’s ethics committee approved the protocol of the trial (Register no. 2020/514/177/36). Written informed consent was obtained from all participants.
Acknowledgment
Not applicable.
Funding
This research received no external funding.
Conflict of interest
The authors declare no conflict of interest.
Publisher’s Note: IMR Press stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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2022-05-27 21:25:13
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https://www.physicsforums.com/threads/0n-c-electric-field-at-center-of-equilateral-triangle.712038/
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# 0N/C Electric Field at center of equilateral Triangle
## Homework Statement
I got an answer as you can see in both pictures, but apparently it is wrong. What did I do?
## The Attempt at a Solution
In this picture I found the y components of the electric field at C. Since the bottom 2 are the same i just doubled one of the electric fields. I then set it equal to the electric
field from the top to cancel out the effect from the bottom.
## Answers and Replies
Related Introductory Physics Homework Help News on Phys.org
Somehow, you are not seeing that the distance from the all the vertices to the center is the same; you do not even have to compute what it is, it will cancel out.
Note there is a much simpler solution, using only the symmetry.
The distance from vertices to the center is the same since it is an equilateral triangle. Using that information you can easily solve the problem by summing up the electrical field intensities to 0 and the distances will apparently cancel out. You don't even have to mess with trigonometrical ratios here
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https://martinralbrecht.wordpress.com/tag/homomorphic-encryption/page/2/
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## Chen & Nguyen’s algorithm and Arora & Ge’s algorithm
In Faster Algorithms for Approximate Common Divisors: Breaking Fully-Homomorphic-Encryption Challenges over the Integers Yuanmi Chen and Phong Q. Nguyen (preprint here) propose a new algorithm for solving the approximate GCD problem. It drops the complexity from $2^{2\rho}$ to $2^{3/2\rho}$ in the general case and from $2^{\rho}$ to $2^{\rho/2}$ in the partial case (one multiple of $p$ is given noise-free) which is a pretty big deal.
The algorithm is based on two key ideas (explained using the partial approximate GCD problem):
1. Noisy solving reduced to noise-free solving
Similar to Arora & Ge’s algorithm for solving LWE Chen and Nguyen reduce the approximate solving problem to a noise-free solving problem. In fact, the strategy is exactly the same (cf. also this post). Given noisy ideal elements $f_i = \sum h_i g_i + r_i$ where $g_i$ are generators of the ideal, $h_i$ are ring elements and $r_i$ are small noise terms, then
$F_i = f_i \cdot \prod (f_i + j)(f_i - j)$
will be elements of the ideal $I$ spanned by $g_i$ if $j$ is big enough (depending on the exact setup we may drop the $-j$ part). In the approximate GCD case $g_0$ is simply a small odd integer (often denoted $p$). Additionally, if we are given some sufficient “description” of some sufficiently big ideal $\langle G_1,\dots,G_s \rangle = J \supset I$ (i.e., all elements of $I$ are in $J$ but not vice versa and $J$ is considerably bigger than $I$) then we can compute
$F_i = f_i \cdot \prod (f_i + j)(f_i - j) \mod J$
which keeps the size of $F_i$ small-ish. This is the role of $x_0$, the noise free multiple of $p$ in the partial approximate GCD problem. Now, one simply solves the noise free system $F_1,\dots,F_m$. In the PAGCD case this means to compute a single GCD, in the multivariate polynomial case (including LWE) this means to compute a Gröbner basis (or linearise, which is the same thing for the cases we are concerned with). Hence, so far Arora&Ge and Chen&Nguyen are really the same thing (it should be mentioned that this ideal due to Nguyen was already mentioned in this paper) applied to different rings.
However, this is not really why the Chen & Nguyen algorithm is efficient (although this already provides a speed-up by a factor of 5).
2. Efficient multiplication
The key idea to drop the exponent from $2^{\rho}$ to $2^{\rho/2}$ is as follows. Instead of computing with integers we compute univariate polynomials mod $x_0$, i.e. one defines
$f_j(x) = \prod_{j=0}^{j-1} (x_1 - (x + i)) \in \mathbb{F}_{x_0}[x]$
and notices that for $\rho' = \lfloor \rho/2 \rfloor$:
$\prod_{i=0}^{2^\rho-1} (x_1 - i) = \prod_{k=0}^{2^{\rho - \rho'} -1} f_{2^{\rho'}}(2^{\rho'}k)$
i.e., we can reduce $2^\rho -1$ multiplications to $2^{\rho - \rho'} - 1$ multiplications and $2^{\rho - \rho'} - 1$ polynomial evaluations. It turns out, this can be done in $\mathcal{O}(2^{\rho'})$. For the details read the paper.
But to get back to my previous point: It turns out the Arora&Ge perspective on noisy system solving is also useful for approximate GCDs. Which provides further evidence that it is useful to generalise LWE and AGCD to ideal theoretic problems in multivariate polynomial rings.
## Yet another Polly Cracker talk
… but this time
• it has less formal definitions.
• a brief discussion on related work.
Speaking of related work: Efficient Fully Homomorphic Encryption from (Standard) LWE by Zvika Brakerski and Vinod Vaikuntanathan is a good read. In summary, it has two main contributions:
1. a somewhat homomorphic scheme based on LWE which turns out to be the same (as far as I can tell) as ours and
2. a new dimension reduction trick which allows to turn it into a fully homomorphic scheme.
What is kind of curious about this work is its explicit non-algebraic perspective. While we talk about LWE from a multivariate polynomial ideal perspective the authors of 2011/344 explicitly state that their scheme is not. I am not sure we’d have seen the dimension reduction trick with our perspective, though.
## Polly Cracker, Revisited
I’ve been mentioning this work a few times; well, finally a pre-print is ready (by myself, Pooya Farshim, Jean-Charles Faugère and Ludovic Perret).
In this paper we initiate the formal treatment of cryptographic constructions – commonly known as “Polly Cracker” – based on the hardness of computing remainders modulo an ideal over multivariate polynomial rings. This work is motivated by the observation that the Ideal Remainder (IR) problem is one of the most natural candidates to build homomorphic encryption schemes. To this end, we start by formalising and studying the relation between the ideal remainder problem and the problem of computing a Gröbner basis.
We show both positive and negative results.
On the negative side, we define a symmetric Polly Cracker encryption scheme and prove that this scheme only achieves bounded CPA security under the hardness of the IR problem. Furthermore, using results from computational commutative algebra we show that a large class of algebraic transformations cannot convert this scheme to a fully secure Polly Cracker-type scheme.
On the positive side, we formalise noisy variants of the ideal membership, ideal remainder, and Gröbner basis problems. These problems can be seen as natural generalisations of the LWE problem and the approximate GCD problem over polynomial rings. After formalising and justifying the hardness of the noisy assumptions we show – following the recent progress on homomorphic encryption – that noisy encoding of messages results in a fully IND-CPA secure somewhat homomorphic encryption scheme. Together with a standard symmetric-to-asymmetric transformation for additively homomorphic schemes, we provide a positive answer to the long standing open problem proposed by Barkee et al. (and later also by Gentry) of constructing a secure Polly Cracker-type cryptosystem reducible to the hardness of solving a random system of equations. Indeed, our results go beyond that by also providing a new family of somewhat homomorphic encryption schemes based on new, but natural, hard problems.
Our results also imply that Regev’s LWE-based public-key encryption scheme is (somewhat) multiplicatively homomorphic for appropriate choices of parameters. Finally, we estimate the parameters which define our cryptosystem and give a proof-of-concept implementation.
Sage source code included, have fun.
I will give an online talk on Wednesday 12pm New York time (EDT) as part of the “Symbolic Computations and Post-Quantum Cryptography” seminar series. My talk is titled “Polly Cracker Revisited” and I’ll present classical and noisy problems in multivariate polynomial rings and how they relate to homomorphic encryption. I will post my slides here afterwards.
Edit: Slides with typos and all that.
## Algorithms for LWE and the Approximate GCD Problem over the Integers
Let $n$ be the number of variables in some polynomial ring $\mathbb{R}[x_1,\dots,x_n]$ (with $\mathbb{R}$ a ring) and let $d$ be the degree of a bunch of polynomials $F = [f_1,\dots,f_m]$ in $\mathbb{R}$, i.e., $\deg(f_i) = d$. Of course, we can “solve” $F$ by computing a Gröbner basis on $F$. Furthermore, it is well-known that if $n=1$ computing a GB is equivalent to computing the GCD of $F$ and that if $d=1$ computing a GB is equivalent to Gaussian elimination, i.e., finding a triangular basis for a module. In a nutshell, Gröbner bases generalise GCDs and Gaussian elimination. So far, so classical.
It is no secret that I spent some time looking into a problem which we call Gröbner Bases with Noise (GBN), which again can be seen — with the appropriate choice of parameters — as a generalisation of the LWE problem (cf. these slides for some details. Sorry, the paper is still not done). Similarly, we may consider GBN as a generalisation of an approximate GCD problem over $\mathbb{R}[x]$.
In our work (you know, the one which isn’t done yet), we define GBN over $\mathbb{F}_q$ to keep things simple but the notion can easily be extended to for example $\mathbb{Z}$. Hence, one could say GBN over $\mathbb{Z}$ is a generalisation of GCDs over $\mathbb{Z}[x]$ and in particular over $\mathbb{Z}$ (cf. this paper which constructs a homomorphic encryption scheme based on the approximate GCD problem over the integers) which is just $\mathbb{Z}[x]$ restricted to constant polynomials. So, we have a connection between GBN, LWE and the approximate GCD problem.
Now, as my tag cloud gives away, I like linear algebra and have the tendency to think about problems in terms of linear algebra and triangular bases. Hence, the above connection made me think about the applicability of algorithms for solving LWE to the approximate GCD problem over the integers. It turns out, they are applicable (kinda).
## Cryptanalysis of “Fully Homomorphic Encryption over the Binary Polynomials”
Turns out, I’m not he only one who was inspired to adapt the Fully Homomorphic Encryption over the Integers scheme by van Dijk, Gentry, Halevi and Vaikuntanathan to polynomials. Gu Chunsheng posted a pre-print on the IACR eprint server this week which essentially instantiates the integer scheme over univariate polynomials over $\mathbb{F}_2$. Below is my implementation (in Sage) of his somewhat homomorphic scheme:
class BinPolySHE:
def __init__(self, n):
n = n
tau = n # choice here
P = PolynomialRing(GF(2),'x')
x = P.gen()
s = P.random_element(degree=2*n+1)
while not (s.is_irreducible() and s.degree()==2*n+1):
s = P.random_element(degree=2*n+1)
b = []
a0 = P.random_element(2*n+1)
if a0.degree() < 2*n+1:
a0 += x**(2*n+1)
e0 = P.random_element(degree=n-1)
b0 = a0*s + x*e0 # deg: 4*n+2
b.append(b0)
for i in range(1,tau):
ai = P.random_element(degree=n) # choice here
ei = P.random_element(degree=n-1)
bi = ai*s + x*ei # deg 3*n+1
bi = bi % b0
b.append(bi)
self.n = n
self.pk = b
self.sk = s
self.P = P
def encrypt(self, m):
T = []
for i in range(1, len(self.pk)):
if random() <= 0.5: # choice here
T.append(i)
c = self.P(m%2)
x = self.P.gen()
for i in T:
e = self.P.random_element(degree=self.n-1)
c += self.pk[i] + x*e
return c % self.pk[0]
def decrypt(self, c):
x = self.P.gen()
return (c % self.sk) % x
Regular readers of this blog might have noticed that the scheme looks like a bit like a univariate specialisation of this PollyCracker scheme. Indeed, just like this first PollyCracker scheme, Gu’s scheme is badly broken. Below, the source code of my attack:
def attack(self, c):
A = Matrix(GF(2),len(self.pk),4*self.n+2)
x = self.P.gen()
for i,b in enumerate(self.pk):
for j in b.exponents():
A[i,A.ncols()-j-1] = 1
E = A.echelon_form(reduced=False)
pk2 = []
for i,r in enumerate(A.rows()):
b = 0
for j in range(A.ncols()):
b += E[i,A.ncols()-j-1]*x**j
pk2.append(b)
for b in pk2:
if c[b.degree()]:
c -= b
return c % x
The attack proceeds pretty much as discussed here: we can compute a triangular basis for the span of the public key and use that to perform all eliminations. Since the noise does not grow with each addition and does not affect the constant coefficient (which holds the message), we can essentially ignore it.
## Polly Cracker Revisited – Slides
I just gave a talk in the ISG seminar at Royal Holloway, University of London about this Polly Cracker business I’ve been thinking about lately. I’ve also decided to publish the slides. However, I’d like to stress that everything in there is preliminary, i.e. this is yet another of those presentations presenting work in progress (which I personally think is a good thing to do). Anyway, here’s the abstract:
“Since Gentry’s seminal work on homomorphic encryption, this area has received considerable attention from the cryptographic community. Perhaps one of the most natural homomorphic schemes conceivable is Polly Cracker which is naturally homomorphic. However, almost all Polly Cracker inspired schemes that have been proposed so far have been badly broken. In fact, it was conjectured about 15 years ago in “Why you cannot even hope to use Gröbner Bases in Public Key Cryptography: an open letter to a scientist who failed and a challenge to those who have not yet failed.”that it was impossible to construct a secure Polly Cracker-style scheme.
In this work we initiate a formal treatment of cryptosystems based on the hardness of Gröbner basis computations for random systems of equations, discuss their limitations, why standard techniques from homomorphic encryption research fail in this area, and propose a Polly Cracker variant based on polynomial system solving with noise which is a first step towards a provably secure Polly Cracker public-key scheme.”
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2020-05-28 18:34:49
|
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https://rstudio-pubs-static.s3.amazonaws.com/206229_5de52d3c5b11446bae9b2e0c5f92e7fb.html
|
## Introduction
Many surveys of diabetes do not include a question about the type, so researchers rely on age of diagnosis as a way to distinguish between type 1 and type 2 diabetes (e.g. Koopman et al. (2005)). Here we try to find out whether this proxy is likely to work well.
## Data
NHANES is a series large health surveys. We download and load the latest NHANES data from 2013. One item, DID040, relates to when diabetes was diagnosed. Unfortunately, the survey does not have a question about the type of diabetes diagnosed.
# http://wwwn.cdc.gov/Nchs/Nhanes/Search/DataPage.aspx?Component=Questionnaire&CycleBeginYear=2013
d_nhanes13 = foreign::read.xport("~/Downloads/DIQ_H.XPT")
## Descriptive analysis
First we take a quick look at the descriptive statistics:
psych::describe(d_nhanes13$DID040) ## vars n mean sd median trimmed mad min max range skew kurtosis ## X1 1 727 48.59 14.82 50 49.36 14.83 1 80 79 -0.56 0.42 ## se ## X1 0.55 Notice that there is a lot of variation, with a standard deviation of about 15 years. We also look at the proportion of cases diagnosed before specified ages: kirkegaard::percent_cutoff(d_nhanes13$DID040, cutoffs = seq(20, 80, by = 5)) %>% round(2)
## 20 25 30 35 40 45 50 55 60 65 70 75 80
## 0.96 0.94 0.91 0.84 0.77 0.66 0.52 0.39 0.26 0.14 0.07 0.02 0.01
## Plot the distribution
Finally, we get a visual overview of the data using a density-histogram:
kirkegaard::GG_denhist(d_nhanes13, var = "DID040") + xlab("Age of diagnosis (self-reported). Red line = mean value.")
We can see that there are not two distinct groups in the data, so using age of diagnosis for differentiating between type 1 and type 2 diabetes is likely to be at best a useful proxy.
## References
Koopman, Richelle J, Arch G Mainous III, Vanessa A Diaz, and Mark E Geesey. 2005. “Changes in Age at Diagnosis of Type 2 Diabetes Mellitus in the United States, 1988 to 2000.” Annals of Family Medicine 3 (1). American Academy of Family Physicians: 60.
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2019-04-22 19:05:32
|
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https://pos.sissa.it/398/277/
|
Volume 398 - The European Physical Society Conference on High Energy Physics (EPS-HEP2021) - T05: Heavy Ion Physics
Simulations of charged hadron and charmed meson production in Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV with HYDJET++ generator
J. Štorek*, J. Bielcik, L. Bravina, G. Eyyubova, V. Korotkikh, I. Lokhtin, S. Petrushanko, A. Snigirev and E. Zabrodin
Full text: pdf
Pre-published on: February 24, 2022
Published on: May 12, 2022
Abstract
HYDJET++ is a Monte Carlo event generator merging parametrized soft part inspired by hydrodynamics with hard part containing jets. It has been successful to describe particle production in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV energies. In this contribution, particle spectra and collective flow for the top LHC energy $\sqrt{s_{NN}}=5.02$ TeV Pb+Pb collisions are presented for the first time. Specifically, the HYDJET++ model version 2.4 has been used to simulate spectra of charged particles, $D^0$ and $J/\psi$ mesons and related $v_2$ and $v_3$ azimuthal flow harmonics. The particle spectra and flow haromincs are studied in different centrality bins ranging from 0-10% up to 30-40% centrality in midrapidity region for charged particles and $D^0$ mesons and in forward rapidity in case of $J/\psi$ mesons. The simulated results have been compared with the LHC data to tune HYDJET++ parameters.
DOI: https://doi.org/10.22323/1.398.0277
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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2022-08-10 11:12:26
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|
https://web2.0calc.com/questions/help-pls_83526
|
+0
# Help pls
0
117
1
+91
In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $AF = 9$ and $DF = 3$, then what is $BD$?
May 19, 2022
#1
+26321
+4
Help pls
$$\text{In triangle ABC, points D and F are on \overline{AB},\\ and E is on \overline{AC} such that \overline{DE}\parallel \overline{BC} and \overline{EF}\parallel \overline{CD}.\\ If AF = 9 and DF = 3, then what is BD?}$$
$$\begin{array}{|lrcll|} \hline (1) & \dfrac{\overline{AC}}{\overline{AE}} &=& \dfrac{9+3}{9} \\\\ (2) & \dfrac{\overline{AC}}{\overline{AE}} &=& \dfrac{9+3+BD}{9+3} \\ \hline \\ (1)=(2): &\dfrac{\overline{AC}}{\overline{AE}}= \dfrac{9+3}{9} &=& \dfrac{9+3+BD}{9+3} \\\\ & \dfrac{9+3}{9} &=& \dfrac{9+3+BD}{9+3} \\\\ & \dfrac{12}{9} &=& \dfrac{12+BD}{12} \\\\ & \dfrac{4}{3} &=& 1+\dfrac{BD}{12} \\\\ & \dfrac{BD}{12}&=& \dfrac{4}{3}-1 \\\\ & \dfrac{BD}{12}&=& \dfrac{1}{3}\\\\ & BD &=& \dfrac{12}{3} \\\\ & \mathbf{BD} &=& \mathbf{4} \\ \hline \end{array}$$
May 20, 2022
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2022-09-29 21:51:36
|
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https://jgaa.info/getPaper?id=539
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Smoothed Analysis of the Minimum-Mean Cycle Canceling Algorithm and the Network Simplex Algorithm Kamiel Cornelissen and Bodo Manthey Vol. 24, no. 3, pp. 397-421, 2020. Regular paper. Abstract The minimum-cost flow (MCF) problem is a fundamental optimization problem with many applications and seems to be well understood. Over the last half century many algorithms have been developed to solve the MCF problem, and these algorithms have varying worst-case bounds on their running time. However, these worst-case bounds are not always a good indication of the algorithms' performance in practice. The Network Simplex (NS) algorithm needs an exponential number of iterations for some instances, but it is among the best algorithms in practice and performs very well in experimental studies. On the other hand, the Minimum-Mean Cycle Canceling (MMCC) algorithm is strongly polynomial, but performs badly in experimental studies. To explain these differences in performance in practice we apply the framework of smoothed analysis to NS and MMCC. We show an upper bound of $O(mn^2\log(n)\log(\phi))$ for the number of iterations of the MMCC algorithm. Here, $n$ is the number of nodes, $m$ is the number of edges, and $\phi$ is a parameter limiting the degree to which the edge costs are perturbed. We also show a lower bound of $\Omega(m\log(\phi))$ for the number of iterations of the MMCC algorithm, which can be strengthened to $\Omega(mn)$ when $\phi=\Theta(n^2)$. For the number of iterations of the NS algorithm we show a smoothed lower bound of $\Omega(m \cdot \min \{ n, \phi \} \cdot \phi)$. Submitted: March 2019. Reviewed: June 2020. Revised: July 2020. Accepted: July 2020. Final: July 2020. Published: July 2020. Communicated by Michael Kaufmann article (PDF) BibTeX
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2022-12-05 12:18:33
|
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https://jakubmarian.com/integral-of-logx-or-lnx/
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# Integral of $\log(x)$ (or $\ln(x)$)
by Jakub Marian
Tip: See my list of the Most Common Mistakes in English. It will teach you how to avoid mistakes with commas, prepositions, irregular verbs, and much more (PDF Version).
The natural (base $e$) logarithm is usually denoted $\log(x)$ in mathematics, but for the sake of students of other disciplines, we will denote it $\ln(x)$ in this article.
How to go about the integration? The task is actually very simple with the help of integration by parts, but it requires a little trick. As you can see, there is only one function in
$$∫ \ln(x)\,dx\,,$$
but integration by parts requires two. The trick is to write $\ln(x)$ as $1⋅\ln(x)$ and then apply integration by parts by integrating the $1$ and differentiating the logarithm:
$$∫ \ln(x)\,dx = ∫ \overbrace{1\vphantom{\ln(x)}}^{u’}\overbrace{\ln(x)}^v\,dx = \overbrace{x\vphantom{\ln(x)}}^u\overbrace{\ln(x)}^v - ∫ \overbrace{x\vphantom{\frac1x}}^u\overbrace{\frac1x}^{v’}\,dx = x\ln(x)-x+c\,.$$
Finally, if you found this article because you are wondering what the logarithm of $\log_{10}(x)$ is, then you can use the equality $\log_{10}(x) = \ln(x)/\ln(10)$, so
$$∫ \log_{10}(x)\,dx = ∫ \frac{\ln(x)}{\ln(10)}\,dx = \frac{1}{\ln(10)} ∫ \ln(x)\,dx\,.$$
To get the integral, simply multiply the result above by $\frac{1}{\ln(10)}$.
By the way, I have written several educational ebooks. If you get a copy, you can learn new things and support this website at the same time—why don’t you check them out?
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2017-09-20 05:46:03
|
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http://mathoverflow.net/questions/32477/smallest-area-shape-that-covers-all-unit-length-curve?sort=votes
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# Smallest area shape that covers all unit length curve
On a euclidean plane, what is the minimal area shape S, such that for every unit length curve, a translation and a rotation of S can cover the curve.
What are the bounds of the shape's area if this is a open problem?
When I asked this problem few years ago, someone told me it's open. I don't know if this is still open and I can't find any reference on it.
I don't even know what branch of mathematics it falls under. so I can't even tag this question.
-
Stupid question: Does a semi-circle of diameter 1 work? If so, can we provably do better than $\pi /8$? – Tony Huynh Jul 19 '10 at 12:44
as to the tag, I would suggest: Geometric Measure Theory, Calculus of Variations, and maybe Geometric Probability (if you had the solution, I would be even more precise). – Pietro Majer Jul 19 '10 at 12:59
arxiv.org/abs/math/0701391 – Piero D'Ancona Jul 19 '10 at 13:36
See also a related MO question concerning the Lebesgue minimal problem: mathoverflow.net/questions/31315/… – Andrey Rekalo Jul 19 '10 at 13:50
Note that the quoted paper assumes convexity of the cover... If convexity is not assumed it does not even seems obvious that the infimum of the area be positive. – Pietro Majer Jul 19 '10 at 14:59
Whereas I don't know of any recent progress in this problem, let me mention one result for closed curves.
Theorem. A closed plane curve of length $L$ and curvature bounded by $K$ can be contained inside a circle of radius $L/4 - (\pi - 2)/2K$.
This was proved in 1974 by H.H. Johnson (link 1) who used calculus of variations methods. A geometric proof was given a bit later by Chakerian, Johnson and Vogt (link 2).
Edit. Apparently the problem is still open. Here's an article (arXiv link), which contains a survey of some known results as of 2009. From the Introduction:
In 1966, Leo Moser asked for the region of smallest area which can accommodate every planar arc of length one. The problem is known as “Moser’s worm problem” and is a variation of universal cover problems. In Moser’s problem, a cover is a set which contains a copy of any rectifiable planar arc of unit length, and is usually assumed to be convex. Such a minimal cover is known to have area between 0.2194 and 0.2738. However, the original problem remains unsolved.
-
The lower bound (initially provided by Khandawit and Sriwasdi) was improved in 2009 by Dimitrios Pagonakis. The bound was improved from 0.227498 to 0.231999.
Tirasan Khandhawit, Dimitrios Pagonakis, Sira Sriswasdi. Lower Bound for Convex Hull Area and Universal Cover Problems. Int.J.Comput.Geom.Appl. 23 (2013) 197-212. arXiv:1101.5638. DOI: 10.1142/S0218195913500076
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The result of mine alluded to in A B's answer, giving an improved lower bound, is now on arxiv: http://arxiv.org/abs/1101.5638
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Reportedly R. Norwood, G. Poole, M. Laidacker: The Worm Problem of Leo Moser, Discrete & Computational Geometry 7 (1992), 153-162. has an example of area $\sqrt{3}/12+\pi/24$ (a 60 degree sector of a circle with two triangular "wings"), and this was the best known in 1999.
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P.A.P. Moran proved in 1946, in "On a Problem of S. Ulam" [J. London Math. Soc. 1946 s1-21: 175-179] this theorem:
If $C$ is a curve of unit length in the plane, and $|K$| is the area of its smallest convex cover $K$, then $|K| \le 1/(2\pi)$, and this is the best possible result, since this limit is attained for a semicircle of unit length.
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2016-02-13 00:39:13
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https://ncar.github.io/esds/posts/2021/software-citation/
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The Importance of Software Citation#
One of the questions that came up during the ESDS Town Hall was how do scientists/developers get credit toward their efforts in developing open-source code? Software that is used by the wider community should received the acknowledgment and recognition it deserves.
Data and academic publication citations have become popular in the literature, but often times, software is not cited… which can be arguably just as important to the work as the data.
The NCAR Library team put together a website, detailing software citation best practices, based on evaluating the >500 NCAR Github Repositories
Here, we provide an overview of these recommendations, but if you are interested in more of the details, be sure to check out the NCAR software citation documentation.
How else should I make sure people cite my software?#
Within your README.md document, be sure to add how you would like others to cite your work. For example, if your repository is for a specific paper, then provide the citation to that paper. If you would like people to cite the software itself, then be sure to specify that.
A great example of software citation instructions can be found on Unidata’s website
You can even add a DOI badge to your repository once you have one minted. An example is given below.
Why would I want a DOI?#
DOI stands for “Digital Object Identifier” and serves as a permanent identifier of an article/document/or piece of software. Typically, it can be difficult to assign a DOI to software, especially since it can constantly be changing/evolving. Fortunately, through the NCAR Library, you can assign a DOI to your Github repository (although this is only available to NCAR produced and hosted software). The only requirements are the following
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2023-01-29 05:28:30
|
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http://www.learn-math.top/angle-between-two-segments-described-using-complex-numbers/
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# Angle between two segments described using complex numbers
Assume we have two segments, ACAC and BCBC. We can represent points AA, BB and CC on the complex plane with three complex numbers, respectively a,ba,b and c∈Cc\in\mathbb{C}. My question is: is there a nice formula for the angle between these two segments?
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arg(b−ca−c)\arg(\frac{b-c}{a-c})?
– A.G.
2 days ago
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2
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You can do a translation of the points:
A′=A−CB′=B−CC′=C−C=0
A’ = A – C \\
B’ = B – C \\
C’ = C – C = 0
Now C′C’ is the origin, you can get the arguments of A′A’ and B′B’ and subtract them:
α=arg(B′)−arg(A′)\alpha = \arg(B’) – \arg(A’)
So α\alpha is the angle between A′C′A’C’ and B′C′B’C’. But since translations preserve angles, α\alpha is also the angle between ACAC and BCBC. To sum up,
α=arg(B−C)−arg(A−C)\alpha = \arg(B – C) – \arg(A – C)
This is so far the best answer, as it gives directly the angle.
– hetajr
2 days ago
Assuming that the order of the points is A−B−CA-B-C going counter-clockwise around the triangle, we first of all put CC in the origin (so c=0c = 0). Then aa is a complex number with absolute |a||a| and argument α\alpha, and bb is a complex number with absolute |b||b| and argument β\beta. If you multiply aa with a number zz whose absolute is |b|/|a||b|/|a| and argument is ϕ=β−α\phi = \beta – \alpha, you get a number with absolute |b||b| and argument β\beta (hence, this is bb). This number is given by
b=az,z=|b||a|eiϕ.b = az\,, \quad z = \frac{|b|}{|a|}e^{i\phi}\,.
If you now replace aa by a−ca – c and bb by b−cb – c in this derivation, you shift CC back to an arbitrary place and the formula becomes
(b−c)=(a−c)|b−c||a−c|eiϕ,(b – c) = (a – c)\frac{|b – c|}{|a – c|}e^{i\phi}\,,
where (\phi) is the angle between these two segments. This gives you
eiϕ=b−ca−c|a−c||b−c|.e^{i\phi} = \frac{b – c}{a – c}\frac{|a – c|}{|b – c|}\,.
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2018-03-20 11:44:06
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https://tex.stackexchange.com/questions/369907/variable-width-box-that-either-stretches-to-remaining-width-or-is-capped-off
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# Variable width box that either stretches to remaining width or is capped off
Is it possible to construct a box whose maximum width is specified, but in situations where that width is wider than the remaining width in a line, then the box just uses whatever space is left?
My use case is a book with fill-in-the-blanks. Each fill-in-the-blank has a width attached to it, like say 15em. It's great if the fill-in-the-blank is printed as a 15em wide box. But sometimes the fill-in-the-blank comes near the end of the line, and runs into the margin. I'd prefer it to just terminate as a shorter box. (And I'd prefer this over any kind of wrapping.)
With my use case in mind, here is something like what I am after in a sort of pseudo syntax: \framebox[min(15em, width of an hfill)]{\strut}.
One way would be to use \leaders.
\documentclass{article}
\def\zz{\leavevmode\vrule height 10pt\nobreak\leaders\vbox{\vskip-.4pt\hrule width .4pt\vskip 10pt \hrule\vskip-.4pt} \hskip 15em minus 15em \nobreak\hbox{\vrule height 10pt}}
\begin{document}
x\hspace{15em}X
zzzzzzzzzz \zz\ zzzzzzzzzzz \zz\ zzzzzzzzzzzzzz \zz\
zzzzzzzzzz \zz\ zzzzzzzzzzz \zz\ zzzzzzzzzzzzzz \zz
aaaa aaaaaaaaaaa aaaaaaaaaaaaaaaaa\zz
ZZZZZZZZZ aaaa aaaaaaaaaaa aaaaaaaaaaaaaaaaa\zz
ZZZZZZZZZZZZZZ aaaa aaaaaaaaaaa aaaaaaaaaaaaaaaaa\zz
ZZZZZZZZZZZZZZZZZZ aaaa aaaaaaaaaaa aaaaaaaaaaaaaaaaa\zz
\end{document}
You could use the linegoal package which provides the \linegoal pseudo length expanding to the remaining length of the line.
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2020-02-18 07:04:51
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