text:
# Re-use code like figures and paragraphs in other documents

I was wondering if there is a way in which I can reuse the code, for example one figure, that is written in one file into another file.

I want to use something similar to xr package that allows you to reuse the labels references from one file into another. But I want to use it in the figures code or in entire paragraphs.

To illustrate what I need to do lets assume I have a file A.tex in which I already define a figure. And I have another file B.tex. And now I want to use the same definition of the figure in B. However, I want to "link" to the figure code in A; because if I do some change in A, I don't have to copy and paste everything in B again. Also, I want to do this with paragraphs. It is kind of quoting the previous file.

Is it possible using LaTeX? What do you suggest me to do?

Edit:

I need to do this "copy & paste" to include text and figures from the main document, into a second one. This references should have the same number of figures, and same bibliography reference, etc. That's why I say that I need something similar to xr package.

I tried using \include and \input to see if it was readable. However, I run into another problem. The number of figures and references are not maintained in the second document. The \include creates new numbers for each document. But I need to maintain the same as the original document.

Is there a way to do this "copy & paste" automatically?

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If the two documents are quite similar, i.e. only differ in some paragraphs, the package "versions" may be helpful. –  Christoph Jüngling Aug 31 '11 at 12:34
@Christoph: nice addition! I converted it to a comment, because it's not really an answer. –  Stefan Kottwitz Sep 3 '11 at 12:29

The standalone package is perfectly suited for this kind of task. As mentioned in About \include in LaTeX use the following for the figure:

\documentclass[preview=false]{standalone}

Then, where you need this figure you you \input the figure. A good example is provided here.

This also allows you to fine tune the figure and reuse it as desired. Here is an example. Save the following as Ellipse.tex:

\documentclass{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}

\coordinate (EllipseOrigin) at (0,0);

\draw [blue, thin, ->] (-5,0) -- (5,0) node [right] {$x$};
\draw [blue, thin, ->] (0,-4) -- (0,4) node [above] {$y$};

\draw [red, ultra thick]% Graph Ellipse

\end{tikzpicture}
\end{document}

Then where you want to use this:

\documentclass{article}
\usepackage{standalone}
\usepackage{tikz}

\begin{document}
Here is the graph of an ellipse:

\input{Ellipse}
\end{document}

If you want the exact same content (same Figure numbers) you should consider using pdfpages:

\documentclass{article}
\usepackage{pdfpages}

\begin{document}
\includepdf{Ellipse}
\end{document}

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Hi, thanks for the pointer to the standalone package. I was able to compile the first part of your example. However, the last part, in which you use the pdfpages, does not compile. Is there a special way to compile it? –  adn Sep 2 '11 at 5:38
Also, I tried to add the figure environment into Ellipse.tex to check the figures numbers. But, it stop compiling when I added it. :( –  adn Sep 2 '11 at 6:03
Have corrected the typo in the pdfpages example. Not sure why the Figure did not work for you, but I prefer to have the Figure environment where the Figure is used (ie the main document) instead of the standalone file. –  Peter Grill Sep 2 '11 at 15:52
Actually, what I need is test the ability of standalone to handle the figures numbers when they are alone. Because, if I create, let say, picture 20. Then I need to insert that same picture in the derive.tex document. That image should have again the same image number: 20. However, when I put the figure environment inside the standalone file, it doesn't allow me to compile. I get some errors ! LaTeX Error: Not in outer par mode ! Undefined control sequence. \@xfloat ...@fltovf \fi \global \setbox \@currbox \color@vbox \normalcolor \... –  adn Sep 3 '11 at 5:19
Ok, after some reading I found out that the problem with the "Not in outer par mode" error is because I want to put the figure environment within another environment that will restrict its float-ability. I imagine that the standalone creates some environments in which it places all the content the user defined. So, back to square one. Ideas? –  adn Sep 7 '11 at 8:11

You can move the code that needs to be used in multiple documents to a separate .tex file. Then, in each document write

\input{something.tex}

or just

\input{something}

in the exact place where you would want to include the .tex file. \input will cause TeX to read the file and treat its content as if it was written directly instead of \input. If you know C or C++, then \input is very similar to the #include preprocessor directive.

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Hi, thanks for the quick answer. However, I wanted to avoid this approach because I have several figures and paragraphs that I need to refer to. Then the original document will be really hard to read. I was hopping to find a clean solution that allow me to maintain both documents readable. The main idea is to be able to quote parts of the first document into the second one, and do not re-write the quotes when the first one change. –  adn Aug 31 '11 at 12:03
@adn: This approach won't be so hard to read, you can give the fragments proper names. What you want (like xr) can be implemented, but needs one more compilation. –  Leo Liu Aug 31 '11 at 12:23

You could put any code that wanted to re-use into your own package, and name it something like mypackage.sty, and then include it in the relevant documents using \usepackage{mypackage.sty}.

Below is a sample MWE:

mypackage.sty

\def\myfigure{\begin{figure}[!h]%
\centering%
\rule{30pt}{20pt}%
\end{figure}%
}
\def\myparagraph{%
}

document.tex

 \documentclass{article}
\usepackage{mypackage}

\begin{document}

hello world

\myfigure

\myparagraph
\end{document}

Note that if you plan to use the mypackage.sty in documents that reside in different directories, you will have to put it in a place where TeX will know to look for it.

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Is there a way to use this definitions within the .tex file? So I can define it in the normal document and then just referencing it in the other document? Or should I stick with the .sty files? –  adn Aug 31 '11 at 13:33
If you put definitions in one .tex file, then in order to access these commands in another .tex file you would need to use \input or \include which might lead to undesired results. –  cmhughes Aug 31 '11 at 13:40


text:
Institute: MPI für Physik     Collection: YB 2016     Display Documents

ID: 716310.0, MPI für Physik / YB 2016
Long-range Pseudorapidity Dihadron Correlations in d+Au Collisions at sqrt{s_NN}=200 GeV
Authors:
Date of Publication (YYYY-MM-DD):2015
Title of Journal:Physics Letters B
Journal Abbrev.:Phys.Lett.B
Issue / Number:747
Start Page:265
End Page:271
Audience:Not Specified
Intended Educational Use:No
Abstract / Description:Dihadron angular correlations in $d$+Au collisions at sqrt{s_NN}=200 GeV are reported as a function of the measured zero-degree calorimeter neutral energy and the forward charged hadron multiplicity in the Au-beam direction. A finite correlated yield is observed at large relative pseudorapidity (\\Delta\\eta) on the near side (i.e. relative azimuth \\Delta\\phi\\sim0). This correlated yield as a function of \\Delta\\eta$appears to scale with the dominant, primarily jet-related, away-side ($\\Delta\\phi\\sim\\pi) yield. The Fourier coefficients of the \\Delta\\phi correlation, V_n=\\langle\\cos n\\Delta\\phi\\rangle, have a strong \\Delta\\eta dependence. In addition, it is found that V_1 is approximately inversely proportional to the mid-rapidity event multiplicity, while V_2 is independent of it with similar magnitude in the forward ($d$-going) and backward (Au-going) directions.
Classification / Thesaurus:STAR
Comment of the Author/Creator:8 pages, 4 figures
External Publication Status:published
Document Type:Article
Communicated by:MPI für Physik
Affiliations:
Identifiers:
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text:
CarlShulman

Sorted by New

# Wiki Contributions

What Multipolar Failure Looks Like, and Robust Agent-Agnostic Processes (RAAPs)

Mainly such complete (and irreversible!) delegation to such incompetent systems being necessary or executed. If AI is so powerful that the nuclear weapons are launched on hair-trigger without direction from human leadership I expect it to not be awful at forecasting that risk.

You could tell a story where bargaining problems lead to mutual destruction, but the outcome shouldn't be very surprising on average, i.e. the AI should be telling you about it happening with calibrated forecasts.

What Multipolar Failure Looks Like, and Robust Agent-Agnostic Processes (RAAPs)

The US and China might well wreck the world  by knowingly taking gargantuan risks even if both had aligned AI advisors, although I think they likely wouldn't.

But what I'm saying is really hard to do is to make the scenarios in the OP (with competition among individual corporate boards and the like) occur without extreme failure of 1-to-1 alignment (for both companies and governments). Competitive pressures are the main reason why AI systems with inadequate 1-to-1 alignment would be given long enough leashes to bring catastrophe. I would cosign Vanessa and Paul's comments about these scenarios being hard to fit with the idea that technical 1-to-1 alignment work is much less impactful than cooperative RL or the like.

In more detail, I assign a ≥10% chance to a scenario where two or more cultures each progressively diminish the degree of control they exercise over their tech, and the safety of the economic activities of that tech to human existence, until an involuntary human extinction event.  (By comparison, I assign at most around a ~3% chance of a unipolar "world takeover" event, i.e., I'd sell at 3%.)

If this means that a 'robot rebellion' would include software produced by more than one company or country, I think that that is a substantial possibility, as well as the alternative, since competitive dynamics in a world with a few giant countries and a few giant AI companies (and only a couple leading chip firms) can mean that the way safety tradeoffs work is by one party introducing rogue AI systems that outcompete by not paying an alignment tax (and intrinsically embodying in themselves astronomically valuable and expensive IP), or cascading alignment failure in software traceable to a leading company/consortium or country/alliance.

But either way reasonably effective 1-to-1 alignment methods (of the 'trying to help you and not lie to you and murder you with human-level abilities' variety) seem to eliminate a supermajority of the risk.

[I am separately skeptical that technical work on multi-agent RL is particularly helpful, since it can be done by 1-to-1 aligned systems when they are smart, and the more important coordination problems seem to be earlier between humans in the development phase.]

What Multipolar Failure Looks Like, and Robust Agent-Agnostic Processes (RAAPs)

I think I disagree with you on the tininess of the advantage conferred by ignoring human values early on during a multi-polar take-off.  I agree the long-run cost of supporting humans is tiny, but I'm trying to highlight a dynamic where fairly myopic/nihilistic power-maximizing entities end up quickly out-competing entities with other values, due to, as you say, bargaining failure on the part of the creators of the power-maximizing entities.

Right now the United States has a GDP of >$20T, US plus its NATO allies and Japan >$40T, the PRC >$14T, with a world economy of >$130T. For AI and computing industries the concentration is even greater.

These leading powers are willing to regulate companies and invade small countries based on reasons much less serious than imminent human extinction. They have also avoided destroying one another with nuclear weapons.

If one-to-one intent alignment works well enough that one's own AI will not blatantly lie about upcoming AI extermination of humanity, then superintelligent locally-aligned AI advisors will tell the governments of these major powers (and many corporate and other actors with the capacity to activate governmental action) about the likely downside of conflict or unregulated AI havens (meaning specifically the deaths of the top leadership and everyone else in all countries).

All Boards wish other Boards would stop doing this, but neither they nor their CEOs manage to strike up a bargain with the rest of the world stop it.

Within a country, one-to-one intent alignment for government officials or actors who support the government means superintelligent advisors identify and assist in suppressing attempts by an individual AI company or its products to overthrow the government.

Internationally, with the current balance of power (and with fairly substantial deviations from it) a handful of actors have the capacity to force a slowdown or other measures to stop an outcome that will otherwise destroy them.  They (and the corporations that they have legal authority over, as well as physical power to coerce) are few enough to make bargaining feasible, and powerful enough to pay a large 'tax' while still being ahead of smaller actors. And I think they are well enough motivated to stop their imminent annihilation, in a way that is more like avoiding mutual nuclear destruction than cosmopolitan altruistic optimal climate mitigation timing.

That situation could change if AI enables tiny firms and countries to match the superpowers in AI capabilities or WMD before leading powers can block it.

So I agree with others in this thread that good one-to-one alignment basically blocks the scenarios above.

Another (outer) alignment failure story

I think they are fighting each other all the time, though mostly in very prosaic ways (e.g. McDonald's and Burger King's marketing AIs are directly competing for customers). Are there some particular conflicts you imagine that are suppressed in the story?

I think the one that stands out the most is 'why isn't it possible for some security/inspector AIs to get a ton of marginal reward by whistleblowing against the efforts required for a flawless global camera grab?' I understand the scenario says it isn't because the demonstrations are incomprehensible, but why/how?

2019 AI Alignment Literature Review and Charity Comparison
MIRI researchers contributed to the following research led by other organisations
MacAskill & Demski's A Critique of Functional Decision Theory

This seems like a pretty weird description of Demski replying to MacAskill's draft.

What failure looks like

OK, thanks for the clarification!

My own sense is that the intermediate scenarios are unstable: if we have fairly aligned AI we immediately use it to make more aligned AI and collectively largely reverse things like Facebook click-maximization manipulation. If we have lost the power to reverse things then they go all the way to near-total loss of control over the future. So i would tend to think we wind up in the extremes.

I could imagine a scenario where there is a close balance among multiple centers of AI+human power, and some but not all of those centers have local AI takeovers before the remainder solve AI alignment, and then you get a world that is a patchwork of human-controlled and autonomous states, both types automated. E.g. the United States and China are taken over by their AI systems (inlcuding robot armies), but the Japanese AI assistants and robot army remain under human control and the future geopolitical system keeps both types of states intact thereafter.

What failure looks like
Failure would presumably occur before we get to the stage of "robot army can defeat unified humanity"---failure should happen soon after it becomes possible, and there are easier ways to fail than to win a clean war. Emphasizing this may give people the wrong idea, since it makes unity and stability seem like a solution rather than a stopgap. But emphasizing the robot army seems to have a similar problem---it doesn't really matter whether there is a literal robot army, you are in trouble anyway.

I agree other powerful tools can achieve the same outcome, and since in practice humanity isn't unified rogue AI could act earlier, but either way you get to AI controlling the means of coercive force, which helps people to understand the end-state reached.

It's good to both understand the events by which one is shifted into the bad trajectory, and to be clear on what the trajectory is. It sounds like your focus on the former may have interfered with the latter.

What failure looks like
I think we can probably build systems that really do avoid killing people, e.g. by using straightforward versions of "do things that are predicted to lead to videos that people rate as acceptable," and that at the point when things have gone off the rails those videos still look fine (and to understand that there is a deep problem at that point you need to engage with complicated facts about the situation that are beyond human comprehension, not things like "are the robots killing people?"). I'm not visualizing the case where no one does anything to try to make their AI safe, I'm imagining the most probable cases where people fail.

Haven't you yourself written about the failure modes of 'do things predicted to lead to videos that people rate as acceptable' where the attack involves surreptitiously reprogramming the camera to get optimal videos (including weird engineered videos designed to optimize on infelicities in the learned objective? E.g. in your discussion of an unaligned benchmark here:

We train an autoregressive generative model, to maximize the log probability assigned to the actual sequence of actions and observations produced by the AI (with each observation conditioned on the past actions). This isn’t actually a good way to train the generative model, but it’s not really central to the discussion.
We train the reward function by showing humans sequences of actions and predicted observations, asking them to assign scores, then predicting those scores with supervised learning. We show humans the sequences of actions that look most promising to the system...
I am quite confident that “world which looks appealing on screen” is not the same as “world which is good;” the gap is already large today, and it will grow much larger over time.
Maintaining a fiction. Ultimately the goal of this AI is to make the sensors look like good things are happening in the world. This can be done either by making the world good or by carefully controlling what gets fed to the sensors. In general, there are many fewer constraints on “what gets fed to the sensors” than “what the world is actually like,” and so it’s going to be possible to produce much more desirable-looking outcomes, much more easily, by controlling the sensors.
If the humans understand what the AI is doing in detail then they can observe the sequence of actions to notice any actions that might corrupt the sensors. But as soon as the AI is engaging in complicated plans this appears to be totally intractable. Even if the AI was human-level, there are many extremely hard-to-detect plans: for example, the AI could collaborate with an external attacker, who will surreptitiously corrupt the sensor. Or the AI could create a copy of itself on an external server who then helped orchestrate a hard-to-detect corruption.

Are you now very confident that no AI company would implement something with this vulnerability? Or does the paragraph below just mean that the part where the AI gets control of the camera has to happen before the robot armies (or even robot armies identified as traceable to the AI in question), which then happen?

Part I has this focus because (i) that's where I think the action is---by the time you have robot armies killing everyone the ship is so sailed, I think a reasonable common-sense viewpoint would acknowledge this by reacting with incredulity to the "robots kill everyone" scenario, and would correctly place the "blame" on the point where everything got completely out of control even though there weren't actually robot armies yet (ii) the alternative visualization leads people to seriously underestimate the difficulty of the alignment problem, (iii) I was trying to describe the part of the picture which is reasonably accurate regardless of my views on the singularity.

Because it definitely seems that Vox got the impression from it that there is never a robot army takeover in the scenario, not that it's slightly preceded by camera hacking.

Is the idea that the AI systems develops goals over the external world (rather than the sense inputs/video pixels) so that they are really pursuing the appearance of prosperity, or corporate profits, and so don't just wirehead their sense inputs as in your benchmark post?

What failure looks like

I think the kind of phrasing you use in this post and others like it systematically misleads readers into thinking that in your scenarios there are no robot armies seizing control of the world (or rather, that all armies worth anything at that point are robotic, and so AIs in conflict with humanity means military force that humanity cannot overcome). I.e. AI systems pursuing badly aligned proxy goals or influence-seeking tendencies wind up controlling or creating that military power and expropriating humanity (which eventually couldn't fight back thereafter even if unified).

E.g. Dylan Matthews' Vox writeup of the OP seems to think that your scenarios don't involve robot armies taking control of the means of production and using the universe for their ends against human objections or killing off existing humans (perhaps destructively scanning their brains for information but not giving good living conditions to the scanned data):

Even so, Christiano’s first scenario doesn’t precisely envision human extinction. It envisions human irrelevance, as we become agents of machines we created.
Human reliance on these systems, combined with the systems failing, leads to a massive societal breakdown. And in the wake of the breakdown, there are still machines that are great at persuading and influencing people to do what they want, machines that got everyone into this catastrophe and yet are still giving advice that some of us will listen to.

The Vox article also mistakes the source of influence-seeking patterns to be about social influence rather than systems that try to increase in power and numbers tend to do so, so are selected for if we accidentally or intentionally produce them and don't effectively weed them out; this is why living things are adapted to survive and expand; such desires motivate conflict with humans when power and reproduction can be obtained by conflict with humans, which can look like robot armies taking control.takes the point about influence-seeking patterns to be about. That seems to me just a mistake about the meaning of influence you had in mind here:

Often, he notes, the best way to achieve a given goal is to obtain influence over other people who can help you achieve that goal. If you are trying to launch a startup, you need to influence investors to give you money and engineers to come work for you. If you’re trying to pass a law, you need to influence advocacy groups and members of Congress.
That means that machine-learning algorithms will probably, over time, produce programs that are extremely good at influencing people. And it’s dangerous to have machines that are extremely good at influencing people.

Two Neglected Problems in Human-AI Safety

I think this is under-discussed, but also that I have seen many discussions in this area. E.g. I have seen it come up and brought it up in the context of Paul's research agenda, where success relies on humans being able to play their part safely in the amplification system. Many people say they are more worried about misuse than accident on the basis of the corruption issues (and much discussion about CEV and idealization, superstimuli, etc addresses the kind of path-dependence and adversarial search you mention).

However, those varied problems mostly aren't formulated as 'ML safety problems in humans' (I have seen robustness and distributional shift discussion for Paul's amplification, and daemons/wireheading/safe-self-modification for humans and human organizations), and that seems like a productive framing for systematic exploration, going through the known inventories and trying to see how they cross-apply.


text:
• ### KiDS-i-800: Comparing weak gravitational lensing measurements in same-sky surveys(1707.04105)

Oct. 25, 2018 astro-ph.CO
We present a weak gravitational lensing analysis of 815 square degree of $i$-band imaging from the Kilo-Degree Survey (KiDS-$i$-800). In contrast to the deep $r$-band observations, which take priority during excellent seeing conditions and form the primary KiDS dataset (KiDS-$r$-450), the complementary yet shallower KiDS-$i$-800 spans a wide range of observing conditions. The overlapping KiDS-$i$-800 and KiDS-$r$-450 imaging therefore provides a unique opportunity to assess the robustness of weak lensing measurements. In our analysis, we introduce two new null' tests. The nulled' two-point shear correlation function uses a matched catalogue to show that the calibrated KiDS-$i$-800 and KiDS-$r$-450 shear measurements agree at the level of $1 \pm 4$\%. We use five galaxy lens samples to determine a nulled' galaxy-galaxy lensing signal from the full KiDS-$i$-800 and KiDS-$r$-450 surveys and find that the measurements agree to $7 \pm 5$\% when the KiDS-$i$-800 source redshift distribution is calibrated using either spectroscopic redshifts, or the 30-band photometric redshifts from the COSMOS survey.
• ### KiDS-450: The tomographic weak lensing power spectrum and constraints on cosmological parameters(1706.02892)

Aug. 7, 2017 astro-ph.CO
We present measurements of the weak gravitational lensing shear power spectrum based on $450$ sq. deg. of imaging data from the Kilo Degree Survey. We employ a quadratic estimator in two and three redshift bins and extract band powers of redshift auto-correlation and cross-correlation spectra in the multipole range $76 \leq \ell \leq 1310$. The cosmological interpretation of the measured shear power spectra is performed in a Bayesian framework assuming a $\Lambda$CDM model with spatially flat geometry, while accounting for small residual uncertainties in the shear calibration and redshift distributions as well as marginalising over intrinsic alignments, baryon feedback and an excess-noise power model. Moreover, massive neutrinos are included in the modelling. The cosmological main result is expressed in terms of the parameter combination $S_8 \equiv \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$ yielding $S_8 = \ 0.651 \pm 0.058$ (3 z-bins), confirming the recently reported tension in this parameter with constraints from Planck at $3.2\sigma$ (3 z-bins). We cross-check the results of the 3 z-bin analysis with the weaker constraints from the 2 z-bin analysis and find them to be consistent. The high-level data products of this analysis, such as the band power measurements, covariance matrices, redshift distributions, and likelihood evaluation chains are available at http://kids.strw.leidenuniv.nl/
• ### KiDS-450: Cosmological parameter constraints from tomographic weak gravitational lensing(1606.05338)

Oct. 28, 2016 astro-ph.CO
We present cosmological parameter constraints from a tomographic weak gravitational lensing analysis of ~450deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). For a flat $\Lambda$CDM cosmology with a prior on $H_0$ that encompasses the most recent direct measurements, we find $S_8\equiv\sigma_8\sqrt{\Omega_{\rm m}/0.3}=0.745\pm0.039$. This result is in good agreement with other low redshift probes of large scale structure, including recent cosmic shear results, along with pre-Planck cosmic microwave background constraints. A $2.3$-$\sigma$ tension in $S_8$ and substantial discordance' in the full parameter space is found with respect to the Planck 2015 results. We use shear measurements for nearly 15 million galaxies, determined with a new improved `self-calibrating' version of $lens$fit validated using an extensive suite of image simulations. Four-band $ugri$ photometric redshifts are calibrated directly with deep spectroscopic surveys. The redshift calibration is confirmed using two independent techniques based on angular cross-correlations and the properties of the photometric redshift probability distributions. Our covariance matrix is determined using an analytical approach, verified numerically with large mock galaxy catalogues. We account for uncertainties in the modelling of intrinsic galaxy alignments and the impact of baryon feedback on the shape of the non-linear matter power spectrum, in addition to the small residual uncertainties in the shear and redshift calibration. The cosmology analysis was performed blind. Our high-level data products, including shear correlation functions, covariance matrices, redshift distributions, and Monte Carlo Markov Chains are available at http://kids.strw.leidenuniv.nl.
• ### RCSLenS: Cosmic Distances from Weak Lensing(1512.03627)

Dec. 11, 2015 astro-ph.CO
In this paper we present results of applying the shear-ratio method to the RCSLenS data. The method takes the ratio of the mean of the weak lensing tangential shear signal about galaxy clusters, averaged over all clusters of the same redshift, in multiple background redshift bins. In taking a ratio the mass-dependency of the shear signal is cancelled-out leaving a statistic that is dependent on the geometric part of the lensing kernel only. We apply this method to 535 clusters and measure a cosmology-independent distance-redshift relation to redshifts z~1. In combination with Planck data the method lifts the degeneracies in the CMB measurements, resulting in cosmological parameter constraints of OmegaM=0.31 +/- 0.10 and w0 = -1.02 +/- 0.37, for a flat wCDM cosmology.
• ### Dark matter halo properties of GAMA galaxy groups from 100 square degrees of KiDS weak lensing data(1507.00735)

July 10, 2015 astro-ph.CO, astro-ph.GA
The Kilo-Degree Survey (KiDS) is an optical wide-field survey designed to map the matter distribution in the Universe using weak gravitational lensing. In this paper, we use these data to measure the density profiles and masses of a sample of $\sim \mathrm{1400}$ spectroscopically identified galaxy groups and clusters from the Galaxy And Mass Assembly (GAMA) survey. We detect a highly significant signal (signal-to-noise-ratio $\sim$ 120), allowing us to study the properties of dark matter haloes over one and a half order of magnitude in mass, from $M \sim 10^{13}-10^{14.5} h^{-1}\mathrm{M_{\odot}}$. We interpret the results for various subsamples of groups using a halo model framework which accounts for the mis-centring of the Brightest Cluster Galaxy (used as the tracer of the group centre) with respect to the centre of the group's dark matter halo. We find that the density profiles of the haloes are well described by an NFW profile with concentrations that agree with predictions from numerical simulations. In addition, we constrain scaling relations between the mass and a number of observable group properties. We find that the mass scales with the total r-band luminosity as a power-law with slope $1.16 \pm 0.13$ (1-sigma) and with the group velocity dispersion as a power-law with slope $1.89 \pm 0.27$ (1-sigma). Finally, we demonstrate the potential of weak lensing studies of groups to discriminate between models of baryonic feedback at group scales by comparing our results with the predictions from the Cosmo-OverWhelmingly Large Simulations (Cosmo-OWLS) project, ruling out models without AGN feedback.
• ### CFHTLenS: Weak lensing calibrated scaling relations for low mass clusters of galaxies(1410.8769)

April 9, 2015 astro-ph.CO
We present weak lensing and X-ray analysis of 12 low mass clusters from the CFHTLenS and XMM-CFHTLS surveys. We combine these systems with high-mass systems from CCCP and low-mass systems from COSMOS to obtain a sample of 70 systems, spanning over two orders of magnitude in mass. We measure core-excised Lx-Tx, M-Lx and M-Tx scaling relations and include corrections for observational biases. By providing fully bias corrected relations, we give the current limitations for Lx and Tx as cluster mass proxies. We demonstrate that Tx benefits from a significantly lower intrinsic scatter at fixed mass than Lx. By studying the residuals of the bias corrected relations, we show for the first time using weak lensing masses that galaxy groups seem more luminous and warmer for their mass than clusters. This implies a steepening of the M-Lx and M-Tx relations at low masses. We verify the inferred steepening using a different high mass sample from the literature and show that variance between samples is the dominant effect leading to discrepant scaling relations. We divide our sample into subsamples of merging and relaxed systems, and find that mergers may have enhanced scatter in lensing measurements, most likely due to stronger triaxiality and more substructure. For the Lx-Tx relation, which is unaffected by lensing measurements, we find the opposite trend in scatter. We also explore the effects of X-ray cross-calibration and find that Chandra calibration leads to flatter Lx-Tx and M-Tx relations than XMM-Newton.
• ### The galaxy-halo connection from a joint lensing, clustering and abundance analysis in the CFHTLenS/VIPERS field(1502.02867)

Feb. 10, 2015 astro-ph.CO
We present new constraints on the relationship between galaxies and their host dark matter halos, measured from the location of the peak of the stellar-to-halo mass ratio (SHMR), up to the most massive galaxy clusters at redshift $z\sim0.8$ and over a volume of nearly 0.1~Gpc$^3$. We use a unique combination of deep observations in the CFHTLenS/VIPERS field from the near-UV to the near-IR, supplemented by $\sim60\,000$ secure spectroscopic redshifts, analysing galaxy clustering, galaxy-galaxy lensing and the stellar mass function. We interpret our measurements within the halo occupation distribution (HOD) framework, separating the contributions from central and satellite galaxies. We find that the SHMR for the central galaxies peaks at $M_{\rm h, peak} = 1.9^{+0.2}_{-0.1}\times10^{12} M_{\odot}$ with an amplitude of $0.025$, which decreases to $\sim0.001$ for massive halos ($M_{\rm h} > 10^{14} M_{\odot}$). Compared to central galaxies only, the total SHMR (including satellites) is boosted by a factor 10 in the high-mass regime (cluster-size halos), a result consistent with cluster analyses from the literature based on fully independent methods. After properly accounting for differences in modelling, we have compared our results with a large number of results from the literature up to $z=1$: we find good general agreement, independently of the method used, within the typical stellar-mass systematic errors at low to intermediate mass (${M}_{\star} < 10^{11} M_{\odot}$) and the statistical errors above. We have also compared our SHMR results to semi-analytic simulations and found that the SHMR is tilted compared to our measurements in such a way that they over- (under-) predict star formation efficiency in central (satellite) galaxies.
• ### CFHTLenS: The Canada-France-Hawaii Telescope Lensing Survey - Imaging Data and Catalogue Products(1210.8156)

Oct. 30, 2012 astro-ph.CO
We present data products from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). CFHTLenS is based on the Wide component of the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). It encompasses 154 deg^2 of deep, optical, high-quality, sub-arcsecond imaging data in the five optical filters u^*g'r'i'z'. The article presents our data processing of the complete CFHTLenS data set. We were able to obtain a data set with very good image quality and high-quality astrometric and photometric calibration. Our external astrometric accuracy is between 60-70 mas with respect to SDSS data and the internal alignment in all filters is around 30 mas. Our average photometric calibration shows a dispersion on the order of 0.01 to 0.03 mag for g'r'i'z' and about 0.04 mag for u^* with respect to SDSS sources down to i <= 21. In the spirit of the CFHTLS all our data products are released to the astronomical community via the Canadian Astronomy Data Centre. We give a description and how-to manuals of the public products which include image pixel data, source catalogues with photometric redshift estimates and all relevant quantities to perform weak lensing studies.


text:
Home > Matrix Algebra calculators > is Orothogonal Matrix calculator

 Solve any problem (step by step solutions) Input table (Matrix, Statistics)
Mode :
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Solution
Find Is Orothogonal matrix [[0,1],[1,0]] [ Calculator, Method and examples ]

Solution:
Your problem -> Is Orothogonal matrix [[0,1],[1,0]]

A square matrix A, such that A xx A^T = I, is called an orothogonal matrix, where I is an identity matrix and A^T is the transpose of matrix A.

A =
 0 1 1 0

A^T =
 0 1 1 0
T
=
 0 1 1 0

A×(A^T)=
 0 1 1 0
×
 0 1 1 0

=
 0×0+1×1 0×1+1×0 1×0+0×1 1×1+0×0

=
 0+1 0+0 0+0 1+0

=
 1 0 0 1

A xx A^T = I, So A is an orothogonal matrix

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text:
# List the assumptions necessary for each of the following inferential techniques: a. Large-sample inferences about the difference (mu_1 - mu_2) between

List the assumptions necessary for each of the following inferential techniques: a. Large-sample inferences about the difference $$\displaystyle{\left(\mu_{{1}}-\mu_{{2}}\right)}$$ between population means using a two-sample z-statistic b. Small-sample inferences about $$\displaystyle{\left(\mu_{{1}}-\mu_{{2}}\right)}$$ using an independent samples design and a two-sample t-statistic c. Small-sample inferences about $$\displaystyle{\left(\mu_{{1}}-\mu_{{2}}\right)}$$ using a paired difference design and a single-sample t-statistic to analyze the differences d. Large-sample inferences about the differences $$\displaystyle{\left(\mu_{{1}}-\mu_{{2}}\right)}$$ between binomial proportions using a two sample z-statistic e. Inferences about the ratio $$\displaystyle{\frac{{{\sigma_{{{1}}}^{{{2}}}}}}{{{\sigma_{{{2}}}^{{{2}}}}}}}$$ of two population variances using an F-test.

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a) Assumptions large sample inferences about the population difference between population means using two sample z-tests. We have three conditions as follows:

1) The two samples are independent.

2) Two samples are large samples that is $$\displaystyle{n}_{{1}}\ne{q}{30},{n}_{{2}}\ne{q}{30}$$ Here, $$\displaystyle{n}_{{1}},{\quad\text{and}\quad}{n}_{{2}}$$ are the sizes of the two samples.

b) Assumptions small sample inferences about the population difference between populations means using independent sample design We have three conditions as follows

1) Independent random samples

2) Both populations are normal

3) Both populations are having equal variances, that is $$\displaystyle{\sigma_{{{1}}}^{{{2}}}}={\sigma_{{{2}}}^{{{2}}}}$$ Assumptions small sample inferences about the population difference between population means using two sample t-tests.

c) Assumptions required to small sample inferences about $$\displaystyle{\left(\mu_{{1}}-\mu_{{2}}\right)}$$ using a paired difference design as follows:

1) Random sample of paired differences

2) Populations of difference are normal Here, $$\displaystyle{n}_{{d}}$$ is the number of paired differences considered.

d) Assumptions required to large sample inferences about the differences $$(p_1 - p_2)$$ using two sample z-tests as follows:

1) Independent random samples

2) $$n_{1}p_{1}\Uparrow\neq 15$$, and $$n_{1}q_{1}\Uparrow\neq 15$$

3) $$n_{2}p_{2}\Uparrow\neq 15$$, and $$n_{2}q_{2}\Uparrow\neq 15\Uparrow$$

e) Assumptions required to inferences about the ratio $$\displaystyle{\frac{{{\sigma_{{{1}}}^{{{2}}}}}}{{{\sigma_{{{2}}}^{{{2}}}}}}}$$ of two population variances using F test. The assumptions are same for either small or large samples.

1) Independent samples.

2) Both populations normal


text:
## Non linear constraints in Mixture DOE

Hello, I need to add constraints in my Mixture DOE that are not linear. Is it possible ? Typically I would add these constraints : X1/X2<0.5 and X1/X2

thanks a lot,
dp

Super User

Joined:

Jun 23, 2011

## Re: Non linear constraints in Mixture DOE

Can't tell what your second constraint is but the first can be rewritten as

X1 - 0.5*X2 < 0

which is linear. If you have a constraint that cannot be reframed as a linear constraint then you can use the Disallowed Combinations option, but that is not the preferred way to go.


text:
# Why does into_iter() not return type T?

From this topic, I guess `Vec<i32>.into_iter()` would return `i32` type.
https://doc.rust-lang.org/std/iter/index.html#the-three-forms-of-iteration

• `iter()` , which iterates over `&T` .
• `iter_mut()` , which iterates over `&mut T` .
• `into_iter()` , which iterates over `T` .

But as following, I find that `into_iter()` depend on the context , and `iter()`, `iter_mut()` work fine.
https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=a0ae390e8dca9d5b8183842c82194210

``````fn into_iter_mut(v: &mut Vec<i32>) {
for i in v.into_iter(){
// expected `i32`, found `&mut i32`
let a:i32 = i;
}

for i in v.iter(){
// expected `i32`, found `&i32`
let a:i32 = i;
}

for i in v.iter_mut(){
// expected `i32`, found `&mut i32`
let a:i32 = i;
}
}

fn into_iter_ref(v: &Vec<i32>) {
for i in v.into_iter(){
// expected `i32`, found `&i32`
let a:i32 = i;
}

for i in v.iter(){
// expected `i32`, found `&i32`
let a:i32 = i;
}

for i in v.iter_mut(){
// expected `i32`, found `&mut i32`
let a:i32 = i;
}
}

fn into_iter(v: Vec<i32>) {
for i in v.into_iter(){
// expected `i32`, found `i32`
let a:i32 = i;
}

for i in v.iter(){
// expected `i32`, found `&i32`
let a:i32 = i;
}

for i in v.iter_mut(){
// expected `i32`, found `&mut i32`
let a:i32 = i;
}
}

fn main() {}
``````
1 Like

Each of `Vec<T>`, `&Vec<T>`, and `&mut Vec<T>` has its own `IntoIterator` implementation, returning `T`, `&T`, and `&mut T` respectively.

6 Likes

And indeed you couldn't call `Vec`'s own `IntoIterator` through a reference even by manually dereferencing it, because you cannot consume (move) what you're only borrowing. And consuming `self` is the true defining semantic of `IntoIterator`; if you just want copies or clones of the elements, that can be done for any iterator using the `copied()` and `cloned()` adapters respectively.

2 Likes

Well, it is possible to move out of something behind a mutably reference, you just also have to move something else in at the same time using `mem::swap` or `mem::replace` or `mem::take`. E.g.

``````fn into_iter_mut(v: &mut Vec<i32>) {
for i in std::mem::take(v).into_iter() {
// compiles fine
let a: i32 = i;
}
}
``````

@z-Wind
In this case, there’s also the alternative of using `Vec::drain` (so: “`for i in v.drain(..)` {”) that keeps the allocation in place, or in the specific case of `i32`, you can use `for i in v.iter().copied()` even with the immutable reference. Also note that having functions with `&Vec<i32>`-arguments, i.e. shared reference to `Vec`, is an antipattern in general, you’d usually want to change that to `&[i32]` instead. Finally note that `into_iter()` is often redundant when `for` loops are used, since

``````for i in 𝑒𝑥𝑝𝑟 {…}
``````

desugars to something similar to

``````let iterator = 𝑒𝑥𝑝𝑟.into_iter();
while let Some(i) = iterator.next() {…}
``````

This – together with the `IntoIter` implementations that @2e71828 mentioned – allows for nice `for` loops without any need for explicit `iter` or `iter_mut` calls like this:

``````let v = vec![1,2,3];
for i in &v {
// i: &i32
}
for i in &mut v {
// i: &mut i32
}
for i in v { // <- consumes / moves out of `v`
// i: i32
}``````
7 Likes


text:
## Program Semantics and Classical Logic

### Abstract

In the tradition of Denotational Semantics one usually lets program constructs take their denotations in reflexive domains, i.e. in domains where self-application is possible. For the bulk of programming constructs, however, working with reflexive domains is an unnecessary complication. In this paper we shall use the domains of ordinary classical type logic to provide the semantics of a simple programming language containing choice and recursion. We prove that the rule of {\em Scott Induction\/} holds in this new setting, prove soundness of a Hoare calculus relative to our semantics, give a direct calculus ${\cal C}$ on programs, and prove that the denotation of any program $P$ in our semantics is equal to the union of the denotations of all those programs $L$ such that $P$ follows from $L$ in our calculus and $L$ does not contain recursion or choice

Topics: Language, Logic
Year: 1997
OAI identifier: oai:cogprints.org:5044

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.

### Citations

1. (1940). A Formulation of the Simple Theory of Types.
2. (1969). A Theory of Programs,
3. (1963). A Theory of Propositional Types.
4. (1975). An Introduction to Mathematical Logic and Type Theory: to Truth through Proof.
5. (1991). Anaphora and the Logic of Change.
6. (1996). Combining Montague Semantics and Discourse Representation. Linguistics and Philosophy,
7. (1950). Completeness in the Theory of Types.
8. (1990). Denotational Semantics.
9. Domains for Denotational Semantics.
10. (1984). Dynamic Logic.
11. (1990). Dynamic Montague Grammar.
12. (1996). Exploring Logical Dynamics.
13. (1986). Foundations and Applications of Montague Grammar.
14. (1983). Higher-Order Logic.
15. (1975). Intensional and Higher-Order Modal Logic.
16. (1987). Logics of Time and Computation.
17. (1980). Mathematical Theory of Program Correctness.
18. (1994). Modal State Semantics,
19. (1976). Semantical Considerations on Floyd-Hoare Logic.
20. (1995). Tense and the Logic of Change. In
21. (1973). The Proper Treatment of Quantification in Ordinary English.
22. Toward a Mathematical Semantics for Computer Languages. In
23. (1997). Typed Logics with States.
24. (1970). Universal Grammar. In Formal Philosophy,


text:
Now showing items 1-20 of 42

• #### ALICE measurement of the $J/\psi$ nuclear modification factor at mid-rapidity in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV

(Peer reviewed; Journal article, 2017-11)
ALICE at the LHC provides unique capabilities to study charmonium production at low transverse momenta ( p T ). At central rapidity, ( |y|<0.8 ), ALICE can reconstruct J/ ψ via their decay into two electrons down to zero ...
• #### Anisotropic flow of charged particles in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV

(Peer reviewed; Journal article, 2016-04)
We report the first results of elliptic $v_2$ , triangular $v_3$ and quadrangular flow $v_4$ of charged particles in Pb--Pb collisions at $\sqrt{s_{_{\rm NN}}}=$ 5.02 TeV with the ALICE detector at the CERN ...
• #### Anomalous evolution of the near-side jet peak shape in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV

(Peer reviewed; Journal article, 2017-09-08)
The measurement of two-particle angular correlations is a powerful tool to study jet quenching in a $p_{\mathrm{T}}$ region inaccessible by direct jet identification. In these measurements pseudorapidity $\Delta\eta$ ...
• #### Azimuthal anisotropy of charged jet production in $\sqrt{s_{\rm NN}}=2.76$ TeV Pb–Pb collisions

(Peer reviewed; Journal article, 2016-02)
This paper presents measurements of the azimuthal dependence of charged jet production in central and semi-central $\sqrt{s_{\rm NN}}=2.76$ TeV Pb–Pb collisions with respect to the second harmonic event plane, quantified ...
• #### Beauty production in pp collisions at √s=2.76 TeV measured via semi-electronic decays

(Peer reviewed; Journal article, 2014-11)
The ALICE Collaboration at the LHC reports measurement of the inclusive production cross section of electrons from semi-leptonic decays of beauty hadrons with rapidity |y|<0.8 and transverse momentum 1<pT<10 GeV/c, in pp ...
• #### Centrality dependence of the pseudorapidity density distribution for charged particles in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV

(Peer reviewed; Journal article, 2017-09)
We present the charged-particle pseudorapidity density in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\,\mathrm{Te\kern-.25exV}$ in centrality classes measured by ALICE. The measurement covers a wide pseudorapidity ...
• #### Centrality, rapidity and transverse momentum dependence of the J/$psi$ suppression in Pb-Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV

(Peer reviewed; Journal article, 2014-06)
The inclusive J/\).psi\) nuclear modification factor $R_{AA}$ in Pb-Pb collisions at $\sqrt{s_{NN}}$.2.76TeV has been measured by ALICE as a function of centrality in the $e^+e^-$ decay channel at mid-rapidity |y| ...
• #### Charge-dependent flow and the search for the chiral magnetic wave in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

(Peer reviewed; Journal article, 2016-04)
We report on measurements of a charge-dependent flow using a novel three-particle correlator with ALICE in Pb–Pb collisions at the LHC, and discuss the implications for observation of local parity violation and the Chiral ...
• #### Charmonium and $e^+e^-$ pair photoproduction at mid-rapidity in ultra-peripheral Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

(Peer reviewed; Journal article, 2013-11)
The ALICE Collaboration at the LHC has measured the $J/\psi$ and $\psi$' photoproduction at mid-rapidity in ultra-peripheral Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV. The charmonium is identified via its leptonic ...
• #### Charmonium production in Pb–Pb and p–Pb collisions at forward rapidity measured with ALICE

(Peer reviewed; Journal article, 2017-11)
The ALICE collaboration has measured the inclusive charmonium production at forward rapidity in Pb–Pb and p–Pb collisions at sNN=5.02TeV and sNN=8.16TeV , respectively. In Pb–Pb collisions, the J/ ψ and ψ (2S) nuclear ...
• #### Correlated event-by-event fluctuations of flow harmonics in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV

(Peer reviewed; Journal article, 2016-10)
We report the measurements of correlations between event-by-event fluctuations of amplitudes of anisotropic flow harmonics in nucleus–nucleus collisions, obtained for the first time using a new analysis method based on ...
• #### D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC

(Peer reviewed; Journal article, 2017-11)
ALICE measured the nuclear modification factor $R_{AA}$ and elliptic flow $\nu_{2}$ of D mesons $D^{0}$. $D^{+}$. $D^{⁎+}$ and $D^{s+}$ in semi-central Pb–Pb collisions at $\sqrt{s_{NN}} =5.02$ TeV. The ...
• #### D-meson production in $p$–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and in $pp$ collisions at $\sqrt{s}=7$ TeV

(Peer reviewed; Journal article, 2016-11)
• #### Energy dependence of the transverse momentum distributions of charged particles in pp collisions measured by ALICE

(Peer reviewed; Journal article, 2013-12)
Differential cross sections of charged particles in inelastic pp collisions as a function of $p_T$ have been measured at $\sqrt{s}$ = 0.9, 2.76 and 7 TeV at the LHC. The $p_T$ spectra are compared to NLO-pQCD ...
• #### Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions

(Peer reviewed; Journal article, 2017)
At sufficiently high temperature and energy density, nuclear matter undergoes a transition to a phase in which quarks and gluons are not confined: the quark–gluon plasma (QGP)1. Such an exotic state of strongly interacting ...
• #### Evolution of the longitudinal and azimuthal structure of the near-side peak in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV

(Peer reviewed; Journal article, 2017-09-08)
In two-particle angular correlation measurements, jets give rise to a near-side peak, formed by particles associated to a higher $p_{\mathrm{T}}$ trigger particle. Measurements of these correlations as a function of ...


text:
# Find the differential equations of the following family of curves.

14 posts / 0 new
Find the differential equations of the following family of curves.

Differential Equations
Find the differential equations of the following family of curves.

1. Parabolas with axis parallel to the y – axis with distance vertex to focus fixed as a.
2. Parabolas with axis parallel to the x – axis with distance vertex to focus fixed as a.
3. All ellipses with center at the origin and axes on the coordinate axes.
4. Family of cardioids.
5. Family of 3 – leaf roses.

## Tags:

(1) Upwards and downwards parabolas with latus rectum equal to 4a.
$y - k = \pm 4a(x - h)^2$

$y' = \pm 8a(x - h)$

$y'' = \pm 8a$

y−k=±4a(x−h)2 is this the equation for parabolas?
isn't it 4a(y-k)=(x-h)2 ?

I made a mistake in there, it should be (x - h)2 = ±4a(y - k). The solution for (1) should go this way:
$(x - h)^2 = \pm 4a(y - k)$

$2(x - h) = \pm 4ay'$

$2 = \pm 4ay''$

$y'' = \pm \frac{1}{2a}$

y−k=±4a(x−h)2 is this the equation for parabolas?
isn't it 4a(y-k)=(x-h)2 ?

Yes you are right, please refer to my reply above

so for number 2,
x-h=±4a(y-k)2
x'=±8a(y-k)
x''=±8a
am i wrong?

It is better to express your answer in terms of y' rather than x'. Although x' will do and simpler.
$(y − k)^2 = \pm 4a(x − h)$

$2(y − k)y' = \pm 4a$

$y' = \dfrac{\pm 2a}{y - k}$

Note: $y - k = \dfrac{y'}{\pm 2a}$

$y'' = \dfrac{\mp 2a \, y'}{(y - k)^2}$

$y'' = \dfrac{\mp 2a \, y'}{\left( \dfrac{y'}{\pm 2a} \right)^2}$

$y'' = \dfrac{\mp 8a}{y'}$

$y'' \, y' = \pm 8a$

our prof. gave the same question but the ans. he gave is different from your ans. in no 2, his answer is (y')^3 + 2ay"=0 are they the same with your answer sir ?

They are different. I made a mistake in $y - k$ of the above solution.
$(y − k)^2 = \pm 4a(x − h)$

$2(y - k) \, y' = \pm 4a$

$y' = \dfrac{\pm 2a}{y - k}$

$y - k = \dfrac{\pm 2a}{y'}$

$y'' = \dfrac{\mp 2a \, y'}{(y - k)^2}$

$y'' = \dfrac{\mp 2a \, y'}{\left( \dfrac{\pm 2a}{y'} \right)^2}$

$y'' = \dfrac{\mp 2a \, y'}{\dfrac{4a^2}{(y')^2}}$

$y'' = \dfrac{\mp (y')^3}{2a}$

$2a \, y'' = \mp (y')^3$

$\pm (y')^3 + 2a \, y'' = 0$

Thank You so much sir.

sir, do you know the standard or general equations for the last 3 problems?
what equations should i use?

I think you are from ADZU haha


text:
Summary

The Rank Structured Cholesky (RSC) solver was developed by Jeff Chadwick (Ph.D. 2013) in joint work with me; it is based on Tim Davis’s CHOLMOD, a widely-used standard sparse Cholesky solver. Unlike CHOLMOD, the RSC solver takes advantage of low-rank block structure that appears naturally in many large linear systems that arise in elliptic PDE discretizations, and so has good scaling properties in both time and memory complexity. Unlike some other solvers based on similar ideas, the RSC solver also has good performance in practice, as it is engineered from the ground up to make good use of fast level-3 BLAS routines.

Papers

J. Chadwick and D. Bindel, “An Efficient Solver for Sparse Linear Systems Based on Rank-Structured Cholesky Factorization,” Jul. 2015.
@techreport{2015-rsc,
author = {Chadwick, Jeffrey and Bindel, David},
title = {An Efficient Solver for Sparse Linear Systems Based on
Rank-Structured {Cholesky} Factorization},
month = jul,
year = {2015},
arxiv = {1507.05593},
status = {unrefereed}
}

Abstract:

Direct factorization methods for the solution of large, sparse linear systems that arise from PDE discretizations are robust, but typically show poor time and memory scalability for large systems. In this paper, we describe an efficient sparse, rank-structured Cholesky algorithm for solution of the positive definite linear system Ax=b when A comes from a discretized partial-differential equation. Our approach combines the efficient memory access patterns of conventional supernodal Cholesky algorithms with the memory efficiency of rank-structured direct solvers. For several test problems arising from PDE discretizations, our method takes less memory than standard sparse Cholesky solvers and less wall-clock time than standard preconditioned iterations.

Talks

An Efficient Solver for Sparse Linear Systems based on Rank-Structured Cholesky Factorization

TSIMF Workshop on Structured Matrix Computations with Applications
rscmeeting external invited

An Efficient Solver for Sparse Linear Systems based on Rank-Structured Cholesky Factorization

SIAM LA 2015
rscminisymposium external invited

An Efficient Solver for Sparse Linear Systems based on Rank-Structured Cholesky Factorization

Workshop on Forty Years of Nested Dissection, University of Waterloo
rscmeeting external


text:
# The Equivalency of Newton's Second Law, Hamilton's Principle and Lagrange Equations [closed]

Consider the following question in classical mechanics

Are Newton's Second Law, Hamilton's Principle and Lagrange Equations equivalent for particles and system of particles?

• If Yes, where can I find a complete proof?
Are there certain conditions for this equivalence?

• If No, which one is the most general one?

I couldn't find the answer of my question in the books since there are lots of sentences and no clear conclusion! Or at least I couldn't get it from the books! Maybe the reason is that physical books are not written axiomatically (like mathematics books). The book which I had my focus on was Classical Mechanics of Herbert Goldstein.

where $N$ is the number of particles and $M$ is the number of generalized coordinates $q_j$. Interested readers may also read this post.

## closed as too broad by AccidentalFourierTransform, Jon Custer, Gert, Cosmas Zachos, user36790 Nov 15 '16 at 3:27

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• – Qmechanic Nov 14 '16 at 21:07
• @AccidentalFourierTransform: It would be much nicer if you made some comments or edits on how to narrow the question instead of closing it! :) I don't know the answer of the question and so I don't know how to narrow it down since I am not a physicits! :( – H. R. Nov 15 '16 at 8:07
• Without even touching on whether Hamilton's principle and the Euler-Lagrange equations are equivalent, it's easy to answer your question with "No" because Newton's II law is obviously not equivalent to either. Newton II only covers the change of momentum over time being equal to the force applied. Nothing about this law give you the true equations of motion for exotic systems, it doesn't include energy, it doesn't give a mechanism for application to other physics problems. Sure you can get Newton II from Hamilton, but saying they're equivalent is like saying sums are equivalent to integrals. – Jim Nov 15 '16 at 13:40
• @Jim: See this link – H. R. Nov 15 '16 at 20:04
• I don't understand how this question got closed. It is definitly not broad. Since the question is closed I cannot answer.. but the answer is simple: No. And in overall physics, there isn't a "general" either. There are systems only Hamilton can do. There are systems only newton can do. And so on. If you restrict only to classical mechanics (not relativity, not EM), then it is possible to prove that $P(H)\subset P(L)\subset P(N)$, where $P(N)$ is the set of all problems newton can solve, and so on. – Physicist137 Dec 2 '16 at 14:37

The earlier formulations of this question was quite broad. This answer is constructed as as a broad response within classical$^{\dagger}$ theories with some hopefully helpful navigation points:

1. On one hand, the stationary action principle (= Hamilton's principle) and the Euler-Lagrange equations make sense far beyond the realm of Newtonian mechanics, e.g. in field theory or relativistic point mechanics.

2. On the other hand, there are dissipative systems in Newtonian mechanics that have no action formulation, see e.g. this Phys.SE post.

3. One may show that broad classes of Newtonian systems satisfy D'Alemberts principle, such as, e.g. rigid bodies, see this Phys.SE post.

4. For the validity of D'Alembert's principle, see this & this Phys.SE post.

5. One may show that D'Alembert's principle leads to Lagrange equations, cf. e.g. this Phys.SE post.

6. Note that Lagrange equations are more general than Euler-Lagrange equations, cf. e.g. this Phys.SE post.

Within Newtonian mechanics, a comparison of various formulations is also discussed in this Phys.SE post.

--

$^{\dagger}$ By the word classical we will mean $\hbar=0$.

• Broad? Why broad? It is either equivalent, or it is not. Which the answer is obviously no. And to nicely answer it, a single counter example would suffice as formal proof. – Physicist137 Dec 2 '16 at 14:17
• @Physicist137 - This is a pretty good answer to the equivalence conditions! Equivalences can depend on conditions. Thus your stipulation "It is equivalent, or not." is not correct. – freecharly Dec 2 '16 at 19:54
• @freecharly Well.. When I've read the question, I think I got the impression OP was asking mathematically. Ie, is set of equation $A$ equivalent to set of equations $B$, in the sense that $A\Longleftrightarrow B$? From math logic, either this sentence is true, or false. So..... And OP's comments seems to confirm it. I mean.. what other interpretation that is? – Physicist137 Dec 2 '16 at 19:59
• The equivalence is not true in general. It seems like a hopeless task to try and formulate precise sufficient & necessary conditions for equivalence. The above answer only points out one-way implication arrows, not bi-implications. – Qmechanic Aug 8 '17 at 17:02

The equivalence of Newtons 2nd law with Hamilton's principle and Lagrange's equations means that you can (mathematically) derive Hamilton's principle and Lagrange's equations from Newtons law, and conversely that you can derive Newtons law from Hamilton's principle and Lagrange's equations.

First, the variational Hamilton's principle of stationary action is equivalent to the Euler-Lagrange equations (Lagrange equations of second kind)Hamilton's Principle, i.e., each follows from the other. Second, from Newtons laws follow the Lagrange equations. On the other hand, it can be easily seen that Newtons law follows from the Lagrange equations for cartesian coordinates.See e.g.Equivalence Newton and Lagrange

Thus Newtons law, Hamilton's principle and Lagrange's equations are equivalent, because they can mutually can be derived from each other. However, these equivalences might be restricted to certain conditions, like, e.g., assumption of conservative forces derived from a potential while the validity of the Lagrange equations or Hamilton's principle might be more general.

• (+1) Thanks for your clear answer, but I am interested in the details under which the equivalence is valid. Can you kindly add some details. – H. R. Nov 15 '16 at 7:59
• @H.R. - I don't know a monograph where the most general conditions are given. For the validity of Lagrange's equations sometimes a monogenic potential is stated, i.e., that all forces are derived from a potential that depends on generalized coordinates, velocitities, and time, and that constraints are holonomic, constraint forces do no work and thus friction is excluded. See these Harvard lectures (starting with 3) for a derivation of equivalences starting from Newton's law. users.physics.harvard.edu/~morii/phys151/lectures/Lecture03.pdf – freecharly Nov 15 '16 at 14:18
• @H.R. Not sure if it would totally answer your questions but you should consider spending time in the book "Mathematical Methods of Classical Mechanics" by V. I. Arnold. It delves more deeply into the mathematical arguments of classical mechanics than many other books on the subject. At least give it some time and then you may be able to more suitably ask the particular detailed question that helps you gain the understanding you want. – K7PEH Nov 16 '16 at 16:17
• @K7PEH: Thanks for the advice. :) My question is put on hold for a ridiculous reason! :( – H. R. Nov 16 '16 at 17:02
• I disagree. They are not equivalent. When you move from newton to lagrange, you make restrictions, thus newton remains more general. That is, there are systems only newton can solve. – Physicist137 Dec 2 '16 at 14:47


text:
# Fungrim entry: bac745

Symbol: CarlsonRJ $R_J\!\left(x, y, z, w\right)$ Carlson symmetric elliptic integral of the third kind
Definitions:
Fungrim symbol Notation Short description
CarlsonRJ$R_J\!\left(x, y, z, w\right)$ Carlson symmetric elliptic integral of the third kind
Source code for this entry:
Entry(ID("bac745"),
SymbolDefinition(CarlsonRJ, CarlsonRJ(x, y, z, w), "Carlson symmetric elliptic integral of the third kind"))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC


text:
Stable homotopy category and the moduli space of formal groups

The usual disclaimer applies: I'm new to all this stuff, so be gentle.

It seems like the spectrum, as defined by Balmer, of the stable homotopy category of finite complexes is something like $M_{FG}$, the stack of formal groups (that is, $Spec L/ G$ where $L$ is the Lazard ring and $G$ acts by coordinate changes). I'm not actually sure if that's true, I don't think I've seen it written quite like that, but the picture of the spectrum in Balmer's paper looks an awful lot like how I'd imagine $M_{FG}$ looking.

If the above is right, then there's another tensor triangulated category with the same spectrum, namely the derived category of perfect complexes on $M_{FG}$ (whatever that means for stacks...).

So my question is:

Just how far away is the stable homotopy category from actually being equivalent to this derived category? Is there a theorem to the effect that it can't be equivalent to such a thing? Do we even know that it's not equivalent?

I've heard that chromatic homotopy theory is about setting up a rough dictionary between algebro-geometric terminology regarding $M_{FG}$ and the stable homotopy category, so I guess the question is about whether or not we can make the dictionary into a proper functor.

-
Uh oh... I'm realizing that this $M_{FG}$ doesn't make much sense unless I pick a field... should I rephrase the question by localizing the stable homotopy category at a prime and picking a field of characteristic $p$? Or am I being paranoid? – Dylan Wilson Aug 19 '11 at 7:13
Section 2.4.2 of Morava's Complex cobordism and algebraic topology says something about this and provides references for sub-questions. Here's an arXiv link: arxiv.org/abs/0707.3216 . – Eric Peterson Aug 19 '11 at 8:18
The Hopf map is an obstruction for the existence of an algebraic model for the stable homotopy category – Fernando Muro Aug 19 '11 at 9:16
(You don't need to pick a field, the moduli of formal groups makes sense over any base.) – Tyler Lawson Aug 19 '11 at 13:05
@Fernando: I was thinking about this... I know there are no Hopf maps in things like $D^{perf}(X)$ when $X$ is a scheme, but I wasn't sure if this still held for stacks – Dylan Wilson Aug 19 '11 at 15:54

One useful thing to keep in mind is that the cohomological functor from the stable homotopy category to the category of quasi-coherent sheaves on the moduli stack $\mathcal{M}$ is not essentially surjective. For example, if you fix a prime $p$ and a height $n \geq 1$, then there is a closed substack $\mathcal{M}^{\geq n}$ consisting of formal groups over $\mathbb{F}_p$ having height $\geq n$. A standard problem in stable homotopy theory is to try to cook up finite spectra which map to the structure sheaf of $\mathcal{M}^{\geq n}$. You can generally only do this when $p$ is large compared with $n$. For small values of $p$ you generally have to make do with finite spectra whose image is the structure sheaf of some nilpotent thickening of $\mathcal{M}^{\geq n}$. These can always be found (a deep result of Devinatz-Hopkins-Smith) and this is what gives you such a strong connection between the topology of $\mathcal{M}$ and the "spectrum" of the stable homotopy category. But you have to work hard for it, and the connection is much weaker (closed subsets of $\mathcal{M}$ have an interpretation in the stable homotopy category, rather than closed substacks) than what you would expect if Adams-Novikov spectral sequences were to degenerate.

-
Ah, thank you! Just to make sure I know what you're talking about: The finite spectra mapping to the structure sheaf of $\mathcal{M}^{\ge n}$ would be these $V(n)$-type spectra, yeah? And a finite spectrum with image the structure sheaf of a nilpotent thickening of $\mathcal{M}^{\ge n}$ would be the ones constructed in the proof of the periodicity theorem? This language is wonderful, conceptually! – Dylan Wilson Aug 19 '11 at 16:01

The relationship between the derived category of $M_{FG}$ and the stable homotopy category $\mathcal{S}$ is somewhat like the relationship between $D(gr_I(R))$ and $D(R)$, where $R$ is a commutative ring, and $I$ is an ideal in $R$, and $gr_I(R)=\bigoplus_nI^n/I^{n+1}$ is the associated graded ring. Complex cobordism gives a homological functor from $\mathcal{S}$ to the abelian category of quasicoherent sheaves on $M_{FG}$, but there is no useful functor from $\mathcal{S}$ to the associated derived category $D(M_{FG})$. Computationally, the morphism groups in $\mathcal{S}$ are the target of an Adams-Novikov spectral sequence whose $E^2$ page can be described as morphism groups in $D(M_{FG})$.

-
This answer is great! I was torn between all of them... so I went with the popular vote. – Dylan Wilson Aug 19 '11 at 16:05

It's definitely known that the derived category of ${\cal M}_{FG}$ and the stable homotopy category are not equivalent. This is an instance of

The Mahowald Uncertainty Principle: Any spectral sequence converging to the homotopy groups of spheres with an $E_2$-term that can be named using homological algebra will be infinitely far from the actual answer.

(The naming is due to Ravenel; this quote is from Paul Goerss' "The Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres".) There is often a feeling that stable homotopy theory always deviates from algebra as soon as is possible.

As Neil said, the Adams-Novikov spectral sequence starts with morphisms in the derived category and computes stable homotopy groups of spheres. Every place where this spectral sequence does not degenerate indicates a point where the stable homotopy category deviates from the algebraic approximation. This includes the following phenomena.

• Hidden additive extensions, such as the hidden additive extension making $\pi_3^s$ into $\mathbb{Z}/24$ rather than $\mathbb{Z}/12 \times \mathbb{Z}/2$.

• Hidden multiplicative extensions. In the (2-local) stable homotopy groups there are elements $\eta \in \pi_1^s$, $\nu \in \pi_3^s$, and $\sigma \in \pi_7^s$. My recollection is that such that $\eta^2 \sigma = \nu^3$ on the $E_2$-term, but Toda showed that this relationship doesn't hold on-the-nose in stable homotopy groups of spheres.

• Differentials. For any prime $p$, there is always a nontrivial differential in the Adams-Novikov spectral sequence, and the first differential is called the Toda differential.

-


text:
# $i^{-1} F$ a sheaf if and only if $\varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U) \to F_x \times F_y$ is an isomorphism [duplicate]

Let $X$ be a topological space containing two closed points $x,y$ and let $i : \{x,y\} \to X$ denote the inclusion map. Notice that $\{x,y\}$ carries the discrete topology. Let $F$ be a sheaf on $X$. Then $i^{-1} F$ is a presheaf on $\{x,y\}$ which is given by $(i^{-1} F)(\emptyset)=1$ (the terminal set), $(i^{-1} F)(\{x\}) = F_x$ (the stalk at $x$), $(i^{-1} F)(\{y\})=F_y$ (the stalk at $y$) and $$(i^{-1} F)(\{x,y\}) = \varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U).$$ Why is, $i^{-1} F$ a sheaf if and only if the canonical map $$\varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U) \to F_x \times F_y.$$ is an isomorphism ?.

Thanks a lot to all of you.


text:
# Can adiabatic quantum computing be faster than Grover's algorithm?

It has been proven that adiabatic quantum computing is equivalent to "standard", or gate-model quantum computing. Adiabatic computing, however, shows promises for optimisation problems, where the objective is to minimise (or maximise) a function which is in some way related to the problem – that is, finding the instance that minimises (or maximises) this function immediately solves the problem.

Now, it seems to me that Grover's algorithm can essentially do the same: by searching over the solution space, it will find one solution (possibly out of many solutions) that satisfies the oracle criterion, which in this case equates to the optimality condition, in time $O(\sqrt N)$, where $N$ is the size of the solution space.

This algorithm has been shown to be optimal: as Bennett et al. (1997) put it, "the class $\rm NP$ cannot be solved on a quantum Turing machine in time $o(2^{n/2})$". In my understanding, this means there is no way to construct any quantum algorithm that finds a solution by searching through the space faster than $O(\sqrt N)$, where $N$ scales with the problem size.

So my question is: while adiabatic quantum computing is often presented as being superior when it comes to optimisation problems, can it really be faster than $O(\sqrt N)$? If yes, this seems to contradict the optimality of Grover's algorithm, since any adiabatic algorithm can be simulated by a quantum circuit. If not, what is the point of developing adiabatic algorithms, if they are never going to be faster than something we can systematically construct with circuits? Or is there something wrong with my understanding?

• This may be more suitable on quantumcomputing.stackexchange.com – user191954 Jun 15 '18 at 2:46
• Grover's algorithm is optimal for a specific kind of search problems, and adiabatic computing cannot do better for that kind of search problem. But Grover's algorithm isn't known to be optimal for all optimization problems. – Peter Shor Jun 16 '18 at 1:47
• Grover's algorithm is the 'most universal' optimization algorithm since it uses the minimal structural information. In fact for general optimization problem, we posses more information, which can be explored to accelerate the optimization. As a kind of universal QC, adiabatic QC can do better on those optimization problems than Grover's algorithm. – XXDD Sep 28 '18 at 15:13


text:
# Find RAB.

Free Practice With Testbook Mock Tests

## Options:

1. 6 Ω

2. 1 Ω

3. 5 Ω

4. 3 Ω

### Correct Answer: Option 4 (Solution Below)

This question was previously asked in

UPPCL AE EE Previous Paper 3 (Held On: 4 November 2019 Shift 1)

## Solution:

Concept:

• When resistors are connected in series, the total resistance is the sum of the individual resistances.

(Req )series = R1 + R2 + ………… + Rn

Where, n = 1,2,3 …….

• When resistors are connected in parallel, the total resistance is less than the least resistance connected in series.

$$\frac{1}{{{{\left( {{R_{eq}}} \right)}_{parallel}}}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}} + \; \ldots \ldots .. + \frac{1}{{{R_n}}}$$

Calculation:

By re-drawing given circuit diagram, we get

RAB = 1 + 0.8 + 1.2

RAB = 3 Ω


text:
The Lumber Room

"Consign them to dust and damp by way of preserving them"

A “Möbius” inversion formula

[Not the Möbius inversion formula, but something similar.]
As usual, define the Möbius function μ on the natural numbers as
$\mu(n) = \begin{cases}0 \text{ if n is not square free,}\\ -1\text{ if n is squarefree with an odd number of prime factors,}\\ 1\text{ if n is squarefree with an even number of prime factors.}\\\end{cases}$
Let $f$ be any function defined on the natural numbers, and let $F$ be the function defined as $\displaystyle F(n) = \sum_{j=1}^{n}{f(\left\lfloor{n/j}\right\rfloor)}$.
Then it is true that $\displaystyle f(n) = \sum_{k=1}^{n}{\mu(k)F(\left\lfloor{n/k}\right\rfloor)}$.

Note that f need not be multiplicative; it can be any arbitrarily defined function. I have no idea why it is true. Help?

Written by S

Fri, 2008-11-28 at 18:55:44

Posted in Uncategorized

Tagged with , ,

Asimov on ‘The Last Question’

I like tracking down quotes, but find it terribly hard to track down quotes by Asimov about his writing: there are so many anthologies, and so many comments he has made about a single story in different places. Here, for example, are two comments I remember having read about what is definitely one of his two most famous stories, The Last Question:

• The first was easier to track down; it’s on Wikipedia with a date. In The Best of Isaac Asimov, published in 1973, he says:

‘The Last Question’ is my personal favorite, the one story I made sure would not be omitted from this collection.
Why is it my favorite? For one thing I got the idea all at once and didn’t have to fiddle with it; and I wrote it in white-heat and scarcely had to change a word. This sort of thing endears any story to any writer.
Then, too, it has had the strangest effect on my readers. Frequently someone writes to ask me if I can write them the name of a story, which they think I may have written, and tell them where to find it. They don’t remember the title but when they describe the story it is invariably ‘The Last Question’. This has reached the point where I recently received a long-distance phone call from a desperate man who began, ‘Dr. Asimov, there’s a story I think you wrote, whose title I can’t remember–‘ at which point I interrupted to tell him it was ‘The Last Question’ and when I described the plot it proved to be indeed the story he was after. I left him convinced I could read minds at a distance of a thousand miles.
No other story I have written has anything like this effect on my readers—producing at once an unshakeable memory of the plot and an unshakeable forgettery of the title and even author. I think it may be that the story fills them so frighteningly full, that they can retain none of the side-issues.

Written by S

Fri, 2008-11-28 at 06:47:42

Posted in Uncategorized


text:
# Why is this code does not work

261
9
07-31-2018 07:54 AM
New Contributor II

I am tring to warb many rasters to others using python in ArcMap, But I field, I need help.

I have two workspaces, because first contain many rasters with correct coordinate , and second workspace contain rasters with incorrect coordinate .

I need to warb rasters in socand worksapce to rasters in first workspace.

import arcpy

i = 0

while i <= 1:

inRasterworkspace = r'C:\Users\AgmnDesk\Desktop\GooleImage\GI_R'
#inRasterworkspace = arcpy.GetParameterAsText(0)
arcpy.env.workspace = inRasterworkspace
inRasters = arcpy.ListRasters()
inRaster = inRasters

SoTop=arcpy.GetRasterProperties_management(inRaster , "TOP")
SoLeft=arcpy.GetRasterProperties_management(inRaster , "LEFT")
SoRight=arcpy.GetRasterProperties_management(inRaster , "RIGHT")
SoBottom=arcpy.GetRasterProperties_management(inRaster , "BOTTOM")
Source_pnt = '\''+ str(SoLeft) + ' ' + str(SoTop) + '\' ;' + str(SoRight) + ' ' + str(SoTop) + '\' ;' + str(SoLeft) + ' ' + str(SoBottom)+'\''

# ========================
taRasterworkspace = r'C:\Users\AgmnDesk\Desktop\GooleImage\GI2018'
#taRasterworkspace = arcpy.GetParameterAsText(1)
arcpy.env.workspace = taRasterworkspace
taRasters = arcpy.ListRasters('*', 'jpg')
taRaster = taRasters

TaTop=arcpy.GetRasterProperties_management(taRaster , "TOP")
TaLeft=arcpy.GetRasterProperties_management(taRaster , "LEFT")
TaRight=arcpy.GetRasterProperties_management(taRaster , "RIGHT")
TaBottom=arcpy.GetRasterProperties_management(taRaster , "BOTTOM")
Target_pnt = '\''+ str(TaLeft) + ' ' + str(TaTop) + '\' ;' + str(TaRight) + ' ' + str(TaTop) + '\' ;' + str(TaLeft) + ' ' + str(TaBottom)+'\''

# ========================
arcpy.env.workspace = r'C:\Users\AgmnDesk\Desktop\GooleImage\GI2018'
arcpy.env.overwriteOutput = True
arcpy.Warp_management(str(taRaster), Source_pnt, Target_pnt, str(taRaster[:-4])+'tif', "POLYORDER2", "BILINEAR")

# ========================
i = i + 1

9 Replies
Esri Esteemed Contributor

Please place your code in the body of the question. Many will not download and unzip documents for computer security reasons, so you're shutting yourself out from assistance.  Be sure to specify what you are attempting to accomplish and what your actual result is, especially any errors (as text, not as an image)

- V

New Contributor II

!The problem is in the varibales, the take the same value

inRaster

taRaster

Source_pnt

Target_pnt

MVP Esteemed Contributor

As Vince mentions, you may want to articulate the objective.  My question is why are you using a while loop and why do you change workspace environments so many times?

can't wait to retire....
New Contributor II

I have two workspaces, because first contain many rasters with correct coordinate , and second workspace contain rasters with incorrect coordinate .

I need to warb rasters in socand worksapce to rasters in first workspace.

MVP Esteemed Contributor

Now I see the while loop, but you are limiting yourself to just 2 input rasters, right?  ( 0,1)

Even still, changing up your workspace environments can get confusing; it does for me anyway.  What if you  set variables instead of workspaces like :

in_ws = r'C:\path\to\in\rasters'out_ws = r'C:\path\to\out\rasters'

You might also reconsider the while loop in favor of a for loop like this:

in_raster_list = arcpy.ListRasters()for r in in_raster_list:  #do what you need to do  #to all of the rasters by using r  #as the iterator....

As a matter of personal style, I try to avoid counters, opting rather to step through a list until it's exhausted.

can't wait to retire....
New Contributor II

You do one rasterlist, while I have two rasterlist. first one to raster with correct coordinate , and second raster list for rasters with incorrect doordinate.

in other way :

I have 500 rasters had georeferenced  , and others (500 rasters) need to georeference .

How I can do georeference second group to first group without using georeference toolbar? because they need long time to use toolbar?

MVP Esteemed Contributor

I don't know of a way to georeference rasters/images to ground truthing locations in an automated fashion.  Unless each of them are of the exact same area, and even then I'm thinking you'd only be able to reference the corners or extents; that's only 4 points of reference which is borderline at best for for you least mean squares errors...

can't wait to retire....
New Contributor II

There are a tool with name (warp) in arctoolbox, it let us to referance image to correct xy data, I try to use this tool in python to referance many rasters, I use the top code. But there is small problem.

By the way, thank you for your tring to help me. And I will try maybe I will get the solution .

MVP Esteemed Contributor

Looking at the tool online help, if I understand it correctly you'd need the same number of reference points and control points and then they need to be ordered in such a fashion that RasterPoint1 is 'warped' to ControlPoint1 etc etc.  With as many rasters as you have to reference, I don't see how this is possible to automate.

Best of luck.

can't wait to retire....


text:
# 2D Collision Box Clipping

There is this strange issue with the collision in a game I am making. When the player is slightly lower than a block it is colliding with from the side, the player ends up clipping to the top of the block rather than sliding along the side of it down. Do you have an idea how to fix it?

If that description didn't help you at all you can reproduce it here (goes to the website with the game on it). (Use WASD/Space/Arrow Keys to move) To reproduce, stand on the single block and hold the right move button. You will fall off the edge, hit the side of the block, and get clipped to the top of it. You are meant to fall onto the block below instead. (The words and colors are debug info)

The code below is what handles the collision detection. If you need the rest of the code, you can view the source of the page linked above.

this.doCollision = function() {
var tx = Math.floor(this.x),
ty = Math.floor(this.y),
nx = this.x % 1,
ny = this.y % 1,
cell = this.cell = levelStorage.currentLevel.getTileAtPosition(tx, ty),
cellRight = this.cellRight = levelStorage.currentLevel.getTileAtPosition(tx + 1, ty),
cellDown = this.cellDown = levelStorage.currentLevel.getTileAtPosition(tx, ty + 1),
cellDiag = this.cellDiag = levelStorage.currentLevel.getTileAtPosition(tx + 1, ty + 1);

if(this.vy > 0) { // Ground collision
// The !cell checks return if the cell exists or not (null)
if((cellDown && !cell) || (!cellRight && cellDiag && nx)) {
this.y = ty;
this.vy = 0;
this.falling = false;
this.jumping = false;
ny = 0
}
}else
if(this.vy < 0) { // Ceiling collision
if((!cellDown && cell) || (cellRight && !cellDiag && nx)) {
this.y = ty + 1;
this.vy = 0;
cell = this.cell = cellDown;
cellRight = this.cellRight = cellDiag;
ny = 0;
}
}
if(this.vx > 0) { // Right collision
if((cellRight && !cell) || (!cellDown && cellDiag && ny)) {
this.x = tx;
this.vx = 0;
nx = 0;
}
}else
if(this.vx < 0) { // Left collision
if((!cellRight && cell) || (cellDown && !cellDiag && ny)) {
this.x = tx + 1;
this.vx = 0;
cell = this.cell = cellRight;
cellDown = this.cellDown = cellDiag;
nx = 0;
}
}
this.falling = !(cellDown || (nx && cellDiag)); // If player isn't on ground
}
}

Thanks for the help!

EDIT: I should note this also happens with the bottom of blocks as well. The same principles apply as clipping to the top, except you clip to the bottom instead.

I'm guessing that vx and vy are velocities...

Since you check for vy floor and ceiling first, then any down-and-right collision gets corrected vertically first, then horizontally, so you end up running rooftop-to-rooftop.

In this particular case, maybe checking for vx left and right first might just fix it. Or handle it as an else clause, since once you correct horizontally (hitting the wall) it shouldn't continue to also handle it vertically.

Other strategies that apply for this kind of collision checking include:

• Look at x- and y-penetration, and fix the smaller of the two
• Never "correct" a motion more than you've moved in that tick
• Handle x- and y-penetrations sequentially

None of these is always the right thing to do, each has their place depending what kind of a world you're trying to simulate or present.

P.S. Having the demo live was very useful to understand what you were describing. ++.

• I have tried all the suggestions you mentioned but none of them seem to be working out. By checking horizontal collisions before vertical the player ends up phasing through walls on the vertical axis. By handling it as an else statement the player ends up falling through the ground or phasing through walls due to only one type of collision being detected. By checking which axis penetrates the wall least and only checking that, the player ends up going inside blocks. Thank you for the suggestions though. – Esophose Oct 19 '15 at 15:22
• Also, to consider, for every motion, if the player is smaller than a block, you may have to resolve as many as 3 collisions. – david van brink Oct 19 '15 at 18:27

You cannot determine the collision response by the velocity in this case.

You must separate the collision between the player and a block using the minimum translation distance. This is how you perform real collision: http://gamedevelopment.tutsplus.com/tutorials/collision-detection-using-the-separating-axis-theorem--gamedev-169


text:
calyne Group Title Find an equation of the tangent line to the hyperbola: x^2/a^2 - y^2/b^2 = 1 at the point (x0,x1) 2 years ago 2 years ago

1. satellite73

implicit diff for this one

2. satellite73

$\frac{2x}{a^2}-\frac{2y}{b^2}y'=0$ $y'=\frac{x}{a^2}\times \frac{b^2}{y}=\frac{b^2x}{a^2y}$

3. calyne

yeah i got that but so what's the equation of the tangent line i don't get the textbook's answer

4. exraven

$\frac{2x}{a^{2}}-\frac{2y}{b^{2}}y'=0$$y'=\frac{b^{2}x}{a^{2}y}$$m=\frac{b^{2}x_{0}}{a^{2}x_{1}}$the equation of the tangent line is$y-x_{1}=\frac{b^{2}x_{0}}{a^{2}x_{1}}\left( x-x_{0} \right)$

5. calyne

yeah well the textbook says x0x/a^2 - y0y/b^2 = 1 so what's that about

6. exraven

algebra..$y-x_{1}=\frac{b^{2}x_{0}}{a^{2}x_{1}}\left( x-x_{0} \right)$$a^{2}x_{1}y-a^{2}x_{1}^{2}=b^{2}x_{0}x-b^{2}x_{0}^{2}$$b^{2}x_{0}^{2}-a^{2}x_{1}^{2}=b^{2}x_{0}x-a^{2}x_{1}y$look back at the hyperbola equation, plug the point (x0,x1)$\frac{x_{0}^{2}}{a^{2}}-\frac{x_{1}^{2}}{b^{2}}=1$$b^{2}x_{0}^{2}-a^{2}x_{1}^{2}=a^{2}b^{2}$substitute to the tangent line equation

7. exraven

$a^{2}b^{2}=b^{2}x_{0}x-a^{2}x_{1}y$$\frac{x_{0}x}{a^{2}}-\frac{x_{1}y}{b^{2}}=1$same as what the textbook said :)


text:
• CN：11-2187/TH
• ISSN：0577-6686

›› 2007, Vol. 43 ›› Issue (2): 132-135.

• 论文 •

### 塑料优化分选设备风选运动特性分析和试验

1. 山东理工大学机械工程学院
• 发布日期:2007-02-15

### KINEMATIC PROPERTIES AND TEST OF PLASTICS’ OPTIMAL SEPARATION EQUIPMENT

YANG Xianhai; Lü Chuanyi

1. School of Machinery Engineering, Shangdong Uni-versity of Technology
• Published:2007-02-15

Abstract: A new process of plastics’ optimal separation from domestic waste is presented, and principle and mechanism for separating plastics are analyzed. A mathematical model of the separating process is established, and the effect of some parameters such as density, wind speed, sloping angle of airflow and height of separating zone on the separating rate is studied, then range of these parameters is determined. The test-beds for plastics separating are developed and a lot of tests are conducted. The rationality of this new study result is validated through tests, and the structure and kinematics parameters of plastic separating equipments are established, with an optimal 13~17 m/s wind-speed horizontally and 14o blowing angle, thus presenting certain theoretical basis for developing plastics separation equipment, so that the rate of separating plastic is over 85%


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# Figure 2

 < p>a)~$\rpp$ for $\pz$ and $\eta$ mesons in \pPb\ collisions at $\sU$ together with NLO~, CGC~ and FCEL~ predictions b)~$\rpp$ for $\pz$ at $\sU$ compared with $\pz$~ and charged hadron measurements~ at $\snn=5.02$ TeV c)~Ratio of the $\pz$ $\rpp$ at $\sU$ to that at $\snn=5.02$ TeV together with corresponding CGC and FCEL model predictions Statistical uncertainties are shown as vertical bars; the systematic uncertainties as boxes. The overall normalization uncertainties are indicated as solid boxes around unity and amount to 3.4\% in a) and b), and to 6.2\% in c).< /p>


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I'm trying to get a quadratic equation in general form from this word question:

"A grower has 100 tonnes of potatoes that she can sell now for a profit of $500 per tonne. For each week that she delays shipment, she can produce an additional 10 tonnes of potatoes. However, for each week she delays, the profit decreases$25 a tonne."

So I figured that if I could write all the information so that they are all related to the number of weeks (or as it relates to tonnes?) I could get a quadratic equation. There are questions like:

a) when should she ship to maximize her profit, and what is the maximum profit?

but if I just have the quadratic equation I can do the questions.. what I'm getting isn't working.

Help would be much appreciated! Thanks!

2. Originally Posted by greatsheelephant
I'm trying to get a quadratic equation in general form from this word question:

"A grower has 100 tonnes of potatoes that she can sell now for a profit of $500 per tonne. For each week that she delays shipment, she can produce an additional 10 tonnes of potatoes. However, for each week she delays, the profit decreases$25 a tonne."

So I figured that if I could write all the information so that they are all related to the number of weeks (or as it relates to tonnes?) I could get a quadratic equation. There are questions like:

a) when should she ship to maximize her profit, and what is the maximum profit?

but if I just have the quadratic equation I can do the questions.. what I'm getting isn't working.

Help would be much appreciated! Thanks!
So the numbers look like this:

Wait 0 weeks: 100 * 500 = 50000
Wait 1 week: 110 * 475 = 52250
Wait 2 weeks: 120 * 450 = 54000

You can actually just calculate them all out and get to the maximum pretty quickly, but as for equation, let $t$ be the number of weeks the grower waits, and let $p$ be profit. So the equation is

$p = (100+10t) \cdot (500-25t)$

This is quadratic; from your post it seems that you know where to go from here.


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2016
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, Wurtzite silicon as a potential absorber in photovoltaics: Tailoring the optical absorption by applying strain, Phys. Rev. B, vol. 92. American Physical Society, p. 045207, 2015.
2014
, Cumulant expansion of the retarded one-electron Green function, Phys. Rev. B, vol. 90. American Physical Society, p. 085112, 2014.
, Defects and strain enhancements of second-harmonic generation in Si/Ge superlattices, The Journal of Chemical Physics, vol. 140. p. -, 2014.
, Effect of material properties on the accuracy of antiresonant approximation: Linear and second-order optical responses, Phys. Rev. B, vol. 90. American Physical Society, p. 035212, 2014.
, Erratum: Solution to the many-body problem in one point, New Journal of Physics, vol. 16. p. 119601, 2014.