text:
Question: Estimating cell size factors for single cell RNA-seq data
1
2.0 years ago by
gquon10
gquon10 wrote:
Hi all, I'm interested in calculating cell size factors for scRNA-seq data. The standard calculation for size factors (e.g. https://genomebiology.biomedcentral.com/articles/10.1186/s13059-014-0550-8) involves computing geometric means of each gene's expression level across all cells, but this isn't practical due to the large number of zeros in scRNA-seq data. I've seen suggestions to add 1 to all counts, but wonder if there is a more rigorous, unbiased calculation.
modified 2.0 years ago by Michael Love24k • written 2.0 years ago by gquon10
Answer: Estimating cell size factors for single cell RNA-seq data
2
2.0 years ago by
Aaron Lun24k
Cambridge, United Kingdom
Aaron Lun24k wrote:

Check out:

https://genomebiology.biomedcentral.com/articles/10.1186/s13059-016-0947-7

... implemented as the computeSumFactors function in scran. Make sure you read the documentation, though.

Answer: Estimating cell size factors for single cell RNA-seq data
2
2.0 years ago by
Andrew_McDavid190 wrote:

You might also try

Bacher R, Chu L, Leng N, Gasch AP, Thomson JA, Stewart RM, Newton MA and Kendziorski C (2017). “SCnorm: robust normalization of single-cell RNA-seq data.” Nature Methodshttps://www.nature.com/nmeth/journal/vaop/ncurrent/full/nmeth.4263.html.

Software is available in Bioconductor devel and github: https://github.com/rhondabacher/SCnorm

Answer: Estimating cell size factors for single cell RNA-seq data
2
2.0 years ago by
Michael Love24k
United States
Michael Love24k wrote:

These were the papers I was going to suggest :) Another one which looks at size factors and their relationship to zeros is this one:

http://www.biorxiv.org/content/early/2017/06/30/157982


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# Reference Request: Group C* Algebra

Currently I am finishing the reference called "C* Algebra By Example" written by Kenneth Davidson and looking for another reference related to Group C* Algebra. I tried to read the "C* Algebras and Operator Theory" written by Gerard Murray but found out that this book only focuses on representations. I used the lecture notes written by Lan Putnam before, which cover quite a number of topics in C* Algebra but does not contain that many details.

Could anyone share some of the reference you used or liked if you have ever studied Group C* Algebra? Ideally your reference will cover C* Algebra on a locally compact group or free group (e.g. $$\mathbb{F}_{2}$$).

The flavor of the continuous case is also much more classical, while for discrete groups there are many topics that are currently (or recently) active (approximation properties, Kazhdan property for $$C^\ast$$-algebras, $$C^\ast$$-simplicity, etc)
• Dixmier, Jacques, $$C^*$$-algebras. North-Holland Mathematical Library. Vol. 15. Amsterdam (1977). ZBL0372.46058. Dixmier book has a few chapters dedicated to group algebras.
• Brown, Nathanial P.; Ozawa, Narutaka, $$C^*$$-algebras and finite-dimensional approximations, Graduate Studies in Mathematics (2008). ZBL1160.46001. Chapters !2 and 15.

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## Wednesday, October 9, 2019

### The gas station problem: where to pump gas and how much

#### Problem

The problem (from [1]) is to determine where to pump gasoline (and how much) during a trip, where prices between gas stations fluctuate.

We consider some different objectives:

• Minimize Cost. This results in an LP model.
• Minimize Number of Stops. This makes the model a MIP.
• Minimize Number of Stops followed by Minimize Cost. This is essentially a multi-objective problem.
• As a bonus: Minimize Cost but always fill up the tank completely. This is a MIP model.

#### Data

I invented some data:

----     34 SET i  locations

start    ,    Station1 ,    Station2 ,    Station3 ,    Station4 ,    Station5 ,    Station6 ,    Station7
Station8 ,    Station9 ,    Station10,    Station11,    Station12,    Station13,    Station14,    Station15
Station16,    Station17,    Station18,    Station19,    Station20,    finish

----     34 SET g  gas stations

Station1 ,    Station2 ,    Station3 ,    Station4 ,    Station5 ,    Station6 ,    Station7 ,    Station8
Station9 ,    Station10,    Station11,    Station12,    Station13,    Station14,    Station15,    Station16
Station17,    Station18,    Station19,    Station20

----     34 PARAMETER efficiency           =       18.000  [miles/gallon]
PARAMETER capacity             =       50.000  tank-capacity [gallons]
PARAMETER initgas              =       25.000  initial amount of gasoline in tank [gallons]
PARAMETER finalgas             =       10.000  minimum final amount of gas in tank [gallons]
PARAMETER triplen              =     2000.000  length of trip [miles]

In the previous section we solved the minimize cost problem. This gave us 4 stops to refuel with total fuel cost of 219. Now, let's try to minimize the number of times we visit a gas station. Counting in general needs binary variables, and this is no exception. The model can look like: Min Number of Stops Model \begin{align} \min \> & \color{darkred}{\mathit{numstops}}\\ & \color{darkred}{\mathit{numstops}} = \sum_g \color{darkred} \delta_g \\ & \color{darkred}{\mathit{cost}} = \sum_g \color{darkred}f_{\mathit{pumped},g} \cdot \color{darkblue}{\mathit{price}}_g \\ & \color{darkred}f_{\mathit{before},i} = \color{darkred}f_{\mathit{after},i-1} - \color{darkblue}{\mathit{use}}_i && \forall i \ne \mathit{start} \\ & \color{darkred}f_{\mathit{after},g} = \color{darkred}f_{\mathit{before},g} + \color{darkred}f_{\mathit{pumped},g} && \forall g \\ & \color{darkred}f_{\mathit{after},\mathit{start}} = \color{darkblue}{\mathit{initgas}} \\ & \color{darkred}f_{\mathit{before},\mathit{finish}} \ge \color{darkblue}{\mathit{finalgas}} \\ & \color{darkred} f_{\mathit{pumped},g} \le \color{darkred} \delta_g \cdot \color{darkblue}{\mathit{capacity}} && \forall g \\ & \color{darkred}f_{k,i} \in [0,\color{darkblue}{\mathit{capacity}}] \\ & \color{darkred} \delta_g \in \{0,1\} \end{align} Because we have binary variables, this is now a MIP model. The constraint $$f_{\mathit{pumped},g} \le \delta_g \cdot \mathit{capacity}$$ implements the implication: $\delta_g=0 \Rightarrow f_{\mathit{pumped},g}=0$When we solve this we see: ---- 71 VARIABLE f.L amounts of fuel start Station1 Station2 Station3 Station4 Station5 Station6 Station7 Station8 before 20.107 10.428 10.247 1.488 1.385 41.954 32.712 pumped 6.406 46.358 after 25.000 20.107 10.428 10.247 1.488 7.791 46.358 41.954 32.712 + Station9 Station10 Station11 Station12 Station13 Station14 Station15 Station16 Station17 before 26.211 18.611 17.694 16.388 7.079 41.595 36.490 31.415 pumped 43.346 after 26.211 18.611 17.694 16.388 7.079 43.346 41.595 36.490 31.415 + Station18 Station19 Station20 finish before 27.270 19.004 17.955 10.000 after 27.270 19.004 17.955 ---- 71 VARIABLE delta.L Station5 1.000, Station6 1.000, Station14 1.000 ---- 71 VARIABLE cost.L = 314.254 VARIABLE numstops.L = 3.000 So instead of 4 stops, now we only need 3 stops. We ignored the cost in this model. This causes the fuel cost to skyrocket to314 (from $219 in the min cost model). I kept the cost constraint in the problem for two reasons. First, it functions as an accounting constraint. Such a constraint is just for informational purposes (it is not meant to change or restrict the solution). A second reason is that we use the cost variable in a second solve in order to minimize cost while keeping the number of stops optimal. This is explained in the next section. #### Problem 3: minimize number of stops followed by minimizing cost After solving the min number of stops problem (previous section), we can fix the number of stops variable $$\mathit{numstops}$$ to the optimal value and resolve minimizing the cost. This is essentially a lexicographic approach to solving the multi-objective problem min numstops, min cost. If we do this we get as solution: ---- 76 VARIABLE f.L amounts of fuel start Station1 Station2 Station3 Station4 Station5 Station6 Station7 Station8 before 20.107 21.238 21.058 12.298 12.196 4.404 40.758 pumped 10.811 50.000 after 25.000 30.918 21.238 21.058 12.298 12.196 4.404 50.000 40.758 + Station9 Station10 Station11 Station12 Station13 Station14 Station15 Station16 Station17 before 34.256 26.657 25.740 24.434 15.125 8.046 41.595 36.490 31.415 pumped 35.301 after 34.256 26.657 25.740 24.434 15.125 43.346 41.595 36.490 31.415 + Station18 Station19 Station20 finish before 27.270 19.004 17.955 10.000 after 27.270 19.004 17.955 ---- 76 VARIABLE delta.L Station1 1.000, Station7 1.000, Station14 1.000 ---- 76 VARIABLE cost.L = 239.188 VARIABLE numstops.L = 3.000 Now we have a solution with 3 stops and a fuel cost of$239. This is my proposal for a solution strategy for the problem stated in [1].

An alternative would be to create a single optimization problem with a weighted sum objective: $\min \> \mathit{numstops} + w \cdot \mathit{cost}$ with $$w$$ a small constant to make sure that $$\mathit{numstops}$$ is the most important variable. As the value of $$w$$ requires some thought, it may be better to use the lexicographic approach.

#### Filling up the gas tank

Suppose that when pumping gas we always fill up the tank completely. This alternative is not too difficult to handle. We need to add the implication: $\delta_g=1 \Rightarrow f_{\mathit{pumped},g}=\mathit{capacity}-f_{\mathit{before},g}$ This can be handled using the inequality: $f_{\mathit{pumped},g} \ge \delta_g \cdot \mathit{capacity}-f_{\mathit{before},g}$

If we add this constraint and solve the min cost model we see:

----     84 VARIABLE f.L  amounts of fuel

start    Station1    Station2    Station3    Station4    Station5    Station6    Station7    Station8

before                  20.107      40.321      40.140      31.381      31.278      23.487      19.082      40.758
pumped                  29.893                                                                  30.918
after       25.000      50.000      40.321      40.140      31.381      31.278      23.487      50.000      40.758

+    Station9   Station10   Station11   Station12   Station13   Station14   Station15   Station16   Station17

before      34.256      26.657      25.740      24.434      40.691      33.612      48.249      43.144      38.068
pumped                                          25.566                  16.388
after       34.256      26.657      25.740      50.000      40.691      50.000      48.249      43.144      38.068

+   Station18   Station19   Station20      finish

before      33.924      25.658      24.609      16.654
after       33.924      25.658      24.609

----     84 VARIABLE delta.L

Station1  1.000,    Station7  1.000,    Station12 1.000,    Station14 1.000

----     84 VARIABLE cost.L                =      261.709
VARIABLE numstops.L            =        4.000

In this case we have a little bit more gasoline left in the tank at the finish than strictly needed. Notice how in each case we pump gas, we end up with a full tank. This fill-up strategy is surprisingly expensive.

#### Conclusion

Here we see the advantages of using an optimization model compared to a tailored algorithm. We can adapt the optimization model to different situations. From the basic min cost model, we can quickly react to new questions.

#### References

1. Gas Station Problem - cheapest and least amount of stations, https://stackoverflow.com/questions/58289424/gas-station-problem-cheapest-and-least-amount-of-stations
2. Shamir Khuller, Azarakhsh Malekian, Julian Mestre, To Fill or not to Fill: The Gas Station Problem, ACM Transactions on Algorithms, Volume 7, Issue 3, July 2011.


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Why does Export not raise an error message? [closed]

Why does Export["str", str, "Table"] not evaluate to an error, where str is any expression?

• What happens if you evaluate Import[ "str", "Table"] immediately after? – Jason B. Feb 22 '19 at 19:26
• @Jason B {{"str"}} which, to me, is equally weird; – yosimitsu kodanuri Feb 22 '19 at 19:36
• This seems like expected behavior. The doc page says "The Wolfram Language automatically transforms arbitrary expressions to a list of lists when exporting to the "Table" format." - if you need to restrict this to only tabular data you could write a small wrapper function that checks that the input is the right form and then calls Export – Jason B. Feb 22 '19 at 19:40
• "str" is a perfectly good path relative to the current directory. – John Doty Feb 22 '19 at 20:04
• Export["str", ... , "Table"] exports to the file "str" (without file extension) in Directory[]. So the full file path is FileNameJoin[{Directory[], "str"}]. Notice also that a single symbol in the second argument will converted to a string and then written to file. Run Import["str", "Text"] in order to see the verbatim file content. Hence, it is Import that converts to a table, not export. – Henrik Schumacher Feb 22 '19 at 20:16


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# generate Keynote presentation from text or Markdown?

Is there a way to automatically generate a Keynote presentation from a source file written in text format, Markdown format, or org-mode?

I know that Pandoc and other tools can generate HTML-based slideshows from Markdown. But Keynote allows you to put all your speaker notes to yourself in "Presenter View," which allows you to have a detailed view of your slideshow + notes on your laptop, and project a clean presentation that is not cluttered up with all your speaker notes.

(Whereas with HTML presentations, since there's only one window, you either have to put your speaker notes in the presentation slide itself, or put your speaker notes elsewhere.)

So can I generate a Keynote presentation, or at least a barebones one with slide headlines, from another source?

# Example

# A headline

Some text here.

- bullet point
- bullet point

Some text.

> Speaker notes.

-
I don't have a specific answer, but Keynote can open PowerPoint presentations. It might be easier to generate one of those form your markdown files. –  jmk Mar 20 '13 at 9:06
We already have a longstanding request for a generic Automator input to keynote, so I will close this as a duplicate, but if you wanted to edit in even a short sample of a markdown file you need minimal support for, I could see reopening this to get a more limited or narrow answer. –  bmike Sep 15 '13 at 14:31

I don't know of any tools that convert from markdown to Keynote or Powerpoint.

If it is a simple presentation, that just consists of slides and bullet points, you can import it into Keynote by first converting it to an unordered list, with slide titles at the top level, e.g.,

-   First Slide
-   Point 1
-   Point 2
-   Second Slide
-   Point 1
-   Point 2

Then convert this to docx using pandoc. Open the docx file in Pages. Meanwhile, open a new slideshow in Keynote, and go to Outline View. Copy the list from Pages to your clipboard. Right click on the little blue square in the outline pane in Keynote, and "Paste and Match Style".

For a more detailed explanation of those last steps, with screenshots, see http://www.peterstagg.com/welcome/apple-inc/creating-outlines-for-keynote-in-pages-and-textedit/. For an explanation of how to do something similar with Powerpoint, see http://www.indezine.com/products/powerpoint/learn/interface/creating-outlines-in-word-2011-mac.html.

-

makeSlides is an iPad app that allows you to convert a markdown file to Powerpoint or Keynote.

-

You could use Org Beamer mode to create the presentation, and then show PDFs instead of Keynote, or run PDF2Keynote to generate a Keynote from the PDFs.

-


text:
Charity Cost-Effectiveness in an Uncertain World

First written: 28 Oct. 2013; last update: 4 Dec. 2015

Summary

Evaluating the effectiveness of our actions, or even just whether they're positive or negative by our values, is very difficult. One approach is to focus on clear, quantifiable metrics and assume that the larger, indirect considerations just kind of work out. Another way to deal with uncertainty is to focus on actions that seem likely to have generally positive effects across many scenarios, and often this approach amounts to meta-level activities like encouraging positive-sum institutions, philosophical inquiry, and effective altruism in general. When we consider flow-through effects of our actions, the seemingly vast gaps in cost-effectiveness among charities are humbled to more modest differences, and we begin to find more worth in the diversity of activities that different people are pursuing. Those who have abnormal values may be more wary of a general "promote wisdom" approach to shaping the future, but it seems plausible that all value systems will ultimately benefit in expectation from a more cooperative and reflective future populace.

Epigraphs

To teach how to live without certainty, and yet without being paralyzed by hesitation, is perhaps the chief thing that philosophy, in our age, can still do for those who study it. --Bertrand Russell, History of Western Philosophy

If something sounds too good to be true, it probably is. --proverb

Introductory dialogue

In fall 2005, I was talking with a friend about utilitarianism:

Friend: "I see where you're coming from, but utilitarianism doesn't work."

Me_2005: "Why not?"

Friend: "You have no way of assessing all the effects of your actions. Everything you do has a million consequences."

Me_2005: "We do the best we can to estimate them."

Friend: "The error bars are infinite in both directions."

Me_2005: "Hmm, yes, the error bars are infinite, but we can assume the unknowns cancel out. For example, consider building safer seat belts. In the short term, we know it prevents injuries, which is good. There may be spill-over longer-term effects, but those could equally be good or bad, so they cancel out in the calculations. Hence, the expected value is still positive."

If I were to continue the conversation now, talking with my past self, here's how it might go:

Me_2013: "Ok, let's consider the example of seat-belt safety. One effect is to prevent injuries and tragic deaths, which is good. But another effect is to increase the human population, which means more meat consumption. Since people eat over a thousand chickens and an order of magnitude more fish in their lifetimes, this seems net bad on balance."

Me_2005: "Hmm, ok. Then maybe seat belts are net negative.... Those two factors you enumerated are pretty concrete, and everything else is fuzzy, so we can assume everything else cancels out. Hence the overall balance is bad."

Me_2013: "Well, there might be other good side effects of seat belts. Better car safety means more people driving, which means more inclination to build parking lots. And parking lots are one very clear way to prevent vast amounts of suffering by wildlife that would have otherwise lived short lives and endured painful deaths on the land had it not been paved. Maybe there are more insects whose painful deaths are spared by parking lots than there are additional chickens and fish killed by the drivers who remain alive."

Me_2005: "Ah, good point. Parking lots are quite beneficial, so on balance, it may be that seat belts are net positive."

Me_2013: "On the other hand, more driving of cars means more greenhouse-gas emissions, which means more climate change, which means more global political instability, which may worsen prospects for compromise in the far future. The amount at stake there could swamp everything else."

Me_2005: "Oh, yes, you're right. So then seat belts may be net bad on balance."

Me_2013: "On the other hand, fewer premature deaths may allow people to feel less threatened and more far-sighted in their actions...."

[...and so on]

Nick Bostrom offers more examples of this type in his 2014 talk, "Crucial considerations and wise philanthropy".

Should we only use rigorous data?

This idea of focusing on the effects you can see and ignoring those you can't, hoping they all kind of cancel out, is tempting. It's one way to feel like "I'm actually making a difference" by doing a given action, rather than being paralyzed by uncertainty, which can sometimes be depressing.

Some in the effective-altruism movement adopt this kind of approach. Basically, "any cause that's uncertain, far off, and speculative isn't 'rigorous,' so we should ignore it. Instead, we should focus on clearly proven interventions with hard scientific evidence behind them, like malaria prevention or veg outreach, because at least here we know we're doing something good rather than floating off into space."

I think there's some value to this perspective, especially insofar as digging deep into scientific details can teach you important lessons about the world that are transferable elsewhere. However, where it falls down as a philosophical stance is with this question: How do you know malaria prevention or veg outreach is good on balance? How can you know the sign of the activity (much less the effectiveness) without considering the longer-range and speculative implications? You could try to assume that everything you can't see "just cancels out," but as we saw in the introductory dialogue, this approach can yield arbitrarily flip-flopping conclusions depending on where the boundary of "known facts" meets the boundary of "everything else we assume away." Ultimately we have no choice but to look at the whole picture and grapple with it as best we can.

Alternate approach: Cause robustness

Another way to pick a cause to work on is to look for actions that have broadly positive effects across a wide range of scenarios. For example, in general:

• More cooperation, democracy, and effective institutions for positive-sum compromise are better.
• More philosophical reflectiveness and discourse are better.
• Meta-level activities to support the above (like the effective-altruism movement, advising people on career choice for making a difference, and so on) are probably good.

Note that I didn't include on this list technology, economic growth, and other trends generally seen as positive, because both negative-leaning and positive-leaning utilitarians have concerns about whether faster technology is net good or bad. Of course, particular kinds of technologies, like those that advance wisdom faster than raw power, are safer and often clearly beneficial.

Punting to the future

Focusing on the very robust projects often amounts to punting the hard questions to future generations who will be better equipped to solve them. In general, we have basically no other choice. There are known puzzles and unknown future discoveries in physics, neuroscience, anthropics, infinity, general epistemology, human (and nonhuman) values, and many other areas of life that are likely to radically transform our views on ethics and how we should act in the world. Taking object-level actions based only on what we know now is sort of like Socrates trying to determine whether the Higgs boson exists. Socrates would have been at a complete loss to solve this question directly, but one thing he could have done would have been to encourage more thinking on intellectual topics in general, with eventual payoff in the future.

Gaverick on Felicifia proposed this basic idea to "get smarter" before we try to address object-level problems. The caution I would add is that we don't just need knowledge per se but specifically ethically reflective knowledge that can slowly, carefully, and circumspectly decide how to move ahead. We don't want a quick knowledge explosion in which one party runs roughshod over most things that most organisms care about in a winner-takes-all fashion. Thus, even though artificial general intelligence (AGI) would ultimately be needed to figure out these questions that are beyond human grasp, we need to develop AGI wisely, and fostering better social conditions within which that AGI development can proceed more prudently can make sense in the short term.

One aspect of preparing the ground for future generations to do good things is making sure our values are transferred, at least in broad outline. The biggest danger of the "punt to the future" strategy is not that the future won't be intelligent (selection pressure makes it likely that it will be) but that it may not care about what we care about. While we don't want to lock the future in to a moral view that would seem silly with greater understanding of the universe, we also don't want the future's values to float around arbitrarily. The space of possible values is huge, and the space of values that we might come to care about even upon further reflection is a tiny subset of the total. This is why our slogan shouldn't be just "more intelligence" but instead something like "more wisdom."

(I should mention in passing that it would probably be better from a suffering-focused perspective if humans don't develop AGI because of the extreme risks of future suffering that doing so entails. However, given that humanity will develop AGI whether I like it or not, my best prospects for making a difference seem to come from pushing it in more humane and positive-sum directions. I also recognize that other people care very much about the fruits that AGI could offer, and I give this some moral weight as well.)

Thinking meta doesn't always mean acting meta

It seems that the main way in which our actions make a difference is by how they prepare the ground for our successors to think more carefully about big questions in altruism and take good actions based on that thinking. However, this doesn't mean that the only way to affect the far future is to work directly on meta-level activities, like movement-building, career advising, or friendly AGI. Rather, all causes that we might work on have flow-through effects in other areas. For example, studying how to reduce wild-animal suffering in the near term can encourage people to recognize the importance of the issue more broadly, which might also make them think more cautiously before spreading wildlife to other planets or in simulations. Studying object-level crucial considerations in philosophy can motivate more people to follow suit, perhaps more effectively than by just preaching about the general importance of philosophical reflection without setting the example. In general, taking small, concrete steps alongside a bigger vision can potentially be more inspiring than just talking about the bigger vision, although exactly how to strike the balance between these two is up for debate.

An effective altruist in 1800

As one final example to drive home the point, imagine an effective altruist in the year 1800 trying to optimize his positive impact. He would not know most of modern economics, political science, game theory, physics, cosmology, biology, cognitive science, psychology, business, philosophy, probability theory, computation theory, or manifold other subjects that would have been crucial for him to consider. If he tried to place his bets on the most significant object-level issue that would be relevant centuries later, he'd almost certainly get it wrong. I doubt we would fare substantially better today at trying to guess a specific, concrete area of focus more than a few decades out. (Of course, if we can guess such an area with decent precision, we could achieve high leverage, as Nick Beckstead points out in the presentation discussed at the end of this essay.)

What this 1800s effective altruist might have guessed correctly would have been the importance of world peace, philosophical reflection, positive-sum social institutions, and wisdom. Promoting those in 1800 may have been close to the best thing this person could have done, and this suggests that these may remain among the best options for us today. We should of course be on the lookout for more specific, high-leverage options, but we ought also to remain humble about the extent of our abilities against the vast space of unknown unknowns as far as errors in our current beliefs and new domains of knowledge that we never even knew existed.

Nick Beckstead discusses a similar analogy in section 6.4.3 of On the Overwhelming Importance of Shaping the Far Future, giving the example of a person in the year 1500 who wanted to help humanity build telephones centuries later.

Against charity fanaticism

Treating other groups as competitors

In business, another company that performs a similar service to customers as yours is a competitor, and your goal is to steal as much market share as you can from that competitor. The only cost of marketing is the money that you spend on it, and if it draws away enough customers from the competitor, it's worth it.

Charities, both EA and otherwise, can adopt a similar mindset: They want more donors for their cause, without paying too much attention about what charities they're pulling donors away from. EAs are concerned with replaceability issues and recognize that pulling donors away from other issues might matter, but usually they feel that the charity they're promoting is vastly more effective than the one they're pulling people away from, so there's not much lost. It's possible this is true in some cases -- e.g., encouraging donors to fund HIV prevention instead of AIDS treatments, or recruiting donors who would have funded art galleries -- but in other cases it becomes much less clear. Especially in the realm of policy analysis and political advocacy, which arguably have some of the highest returns, it's more difficult to say that one charity is vastly more important than another, because the issues are complex and multifaceted.

So for altruists, the cost of marketing and fundraising is more than the time and money required to carry them out. Charity is not a competition.

After writing this piece, I came across a presentation that Nick Beckstead gave in July 2013. Nick explains several similar views to those expressed in this essay. For instance, his concluding slide (p. 39):

• There is an interesting question about where you want to be on the targeted vs. broad spectrum, and I think it is pretty unclear
• Lots of ordinary stuff done by people who aren't thinking about the far future at all may be valuable by far future standards
• Broad approaches (including general technological progress) look more robustly good, but some targeted approaches may lead to outsized returns if done properly
• There are many complicated questions, and putting it all together requires challenging big picture thinking. Studying targeted approaches stands out somewhat because it has the potential for outsized returns.

Nick proposes these as some robustly positive goals (p. 5):

• Coordination: How well-coordinated people are
• Capability: How capable individuals are at achieving their goals
• Motives: How well-motivated people are

I agree with Coordination and Motives. I'm less certain about Information, because this speeds up development of risks along with development of safety measures. The same is even more true for Capability. I would therefore favor differentially pushing on wisdom and compromise relatively more than economic and technological growth. Nick makes some recognition of this on p. 30:

• Broad approaches are more likely to enhance bad stuff as well as good stuff
• Increasing people's general capabilities/information makes people more able to do things that would be dangerous, offsetting some of the benefits of increased capabilities/information
• Improving coordination or motives may do this to a lesser extent

Nick himself argues that faster economic growth is very likely positive because it improves cooperation and tolerance. He quotes Benjamin Friedman's The Moral Consequences of Economic Growth: "Economic growth -- meaning a rising standard of living for the clear majority of citizens -- more often than not fosters greater opportunity, tolerance of diversity, social mobility, commitment to fairness, and dedication to democracy." I agree with this, but the question is not whether economic growth has good effects of this type but whether these effects can outpace the risks that it also accelerates. I feel that this question remains unresolved.

On pp. 18-19, Nick deflects the argument that faster technology is net bad by pointing out that it also means faster countermeasures, along with some other considerations that I think are minor. This point is relevant, but I maintain that it's not clear what the net balance is. In my view it's too early to say that faster technology is net good, much less sufficiently good that we should push on it compared with other things.

On p. 24, Nick echoes my point about deferring to the future on some questions:

• In some ways, trying to help future people navigate specific challenges better is like trying to help people from a different country solve their specific challenges, and to do so without intimate knowledge of the situation, and without the ability to travel to their country or talk to anyone who has been there at all recently.
• Sometimes, only we can work on the problem (this is true for climate change and people who will be alive in 100 years)
• It is less clearly true with risks from future technology

Nick concludes with some important research questions about historical examples of what interventions were most important and what current opportunities and funding/talent gaps look like.

Carl Shulman on flow-through effects

Carl Shulman has a piece, "What proxies to use for flow-through effects?," that suggests many possible metrics that are relevant for impacts on the far future, though he explains that not all of them are always obviously positive in sign. From Carl's list, these are some that I believe are pretty robustly positive:

• Education to increase "wisdom"
• International peace and cooperation, including all of Carl's sub-bullets there
• Institutional quality metrics

The sign of most other metrics is less clear to me, including economic growth, population, education in general, and especially technology. Carl cites the World Values Survey as an important demonstration of the impact of per-capita wealth on rationality and cosmopolitan perspective.

Within the "wisdom" category, I would include scientometrics that Carl mentions for natural sciences applied to social sciences and philosophy. For example, number of publications, number of web pages discussing those topics, number and length of Wikipedia articles on those topics, etc. Of course, the value of some of these domains is in the pudding -- insofar as they improve democracy, transparency, global cooperation, and so on.

In the comments, Nick Beckstead suggested inequality as another candidate metric. I haven't studied the literature extensively, but I have heard arguments about how it erodes many other relevant metrics, including trust, cooperation, mental health, and interpersonal kindness. For example, according to Richard Wilkinson: "Where there is more equality we use more cooperative social strategies, but where there is more inequality, people feel they have to fend for themselves and competition for status becomes more important."

Modeling unknown unknowns

It might seem as though we're helpless to respond to not-yet-discovered crucial considerations for how we should act. Is our only option to keep researching to find more crucial considerations and to move society toward a more cooperative and wise state in the meanwhile? Not necessarily. Maybe another possibility is to model the unknown crucial considerations.

Consider the following narrative. Andrew is a young boy who sees people going to a blood-donation drive. He doesn't know what they're doing, but he sees them being stuck with needles. He concludes that he wouldn't like to participate in a blood drive. Let's call this his "initial evaluation" (IE) and represent it by a number to indicate whether it favors or opposes the action. In this case, Andrew assumes he would not like to participate in the blood drive, so let's say IE = -1, where the negative number means "oppose".

A few years later, Andrew learns that blood drives are intended to save lives, which is a good thing. This crucial consideration is not something he anticipated earlier, which makes it an "unknown unknown" discovery. Since it's Andrew's first unknown-unknown insight, let's call it UU1. Since this consideration favors giving blood, and it does so more strongly than Andrew's initial evaluation opposed giving blood, let's say UU1 = 3. Since IE + UU1 = -1 + 3 > 0, Andrew now gives blood at drives.

However, one year later, Andrew becomes a deep ecologist. He feels that humans are ruining the Earth, and that nature preservation deserves more weight than human lives. Giving blood allows a person in a rich country to live perhaps an additional few years, during which time the person will ride in cars, eat farmed food, use electricity, and so on. Andrew judges that these environmental impacts are sufficiently bad they're not worth the benefit of saving the person's life. Let's say UU2 = -5, so that now IE + UU1 + UU2 = -1 + 3 + -5 = -3 < 0, and Andrew now stops giving blood again.

After another few months, Andrew reads Peter Singer and realizes that individual animals also matter. Since human activities like driving and farming food injure and kill lots of wild animals, Andrew concludes that this additional insight further argues against blood donation. Say UU3 = -2.

However, not long after, Andrew learns about wild-animal suffering and realizes that animals suffer immensely even when they aren't being harmed by humans. Because human activity seems to have on the whole reduced wild-animal populations, Andrew concludes that it's better if more humans exist, and this outweighs the harm they cause to wild animals and to the planet. Say UU4 = 10. Now IE + Σi=04 UUi = -1 + 3 + -5 + -2 + 10 = 5. Andrew donates blood once more.

Finally, Andrew realizes that donating blood takes time that he could otherwise spend on useful activities. This consideration is relevant but not dominating. UU5 = -1.

What about future crucial considerations that Andrew hasn't yet discovered? Can he make any statements about them? One way to do so would be to model unknown unknowns (UUs) as being sampled from some probability distribution P: UUi ~ P for all i. The distribution of UUs so far was {3, -5, -2, 10, -1}. The sample mean is 1, and the standard error is 2.6. The standard error is big enough that Andrew can't have much confidence about future UUs, though the sample mean very weakly suggests future UUs are more likely on average to be positive than negative.

If Andrew instead had 100 UU data points, the standard error would be much smaller, which would give more confidence. This illustrates one lesson when handling UUs: The more considerations you've already considered, the more confident you can be that the distribution of remaining UUs also has positive mean.

That we can anticipate something about UUs despite not knowing what they will be can be seen more clearly in a case where the current UUs are more lopsided. For example, suppose the action under consideration is "start fights with random people on the street". While this probably has a few considerations in its favor, almost all of the crucial considerations that one could think of argue against the idea, suggesting that most new UUs will point against it as well.

Modeling UUs in practice may be messier than what I've discussed here, because it's not clear how many UUs remain (although one could apply a prior probability distribution over the number remaining), nor is it clear that they all come from a fixed probability distribution. Perhaps future UUs tend to dominate past ones in size, leading to ever more unstable estimates; for example, if previous UUs tend to change the sign of lots of previous considerations at once, then the latest UU would have a bigger and bigger magnitude as time went on, since it would need to "undo" more and more past UUs. It's also not clear how to partition insights into UU buckets. For example, the insight that donating blood helps wild animals could be stated simply as a single UU with magnitude 10, or it could be broken down as "donating blood helps wild vertebrates" (magnitude 2) and "donating blood helps wild invertebrates" (magnitude 8). Different ways of partitioning UUs would lead to a different estimated probability distribution, although the sign of the sample mean would always remain the same.

There are problems with the approach I described. Magnus Vinding noted to me that

When it comes to UUs, a major problem is that pretty much our entire value system and worldview seem to be up for grabs, and, moreover, that the different UUs likely will be dependent in deep, complex ways that will make modelling of them very hard. Modelling the interrelations of the UUs in our sample and how they make each other change would also seem a necessary element to include in such an analysis.

Acknowledgments

My thoughts on these topics were influenced by many effective-altruist thinkers, including Holden Karnofsky, Jonah Sinick, and Nick Beckstead. See also Paul Christiano's "Beware brittle arguments."

Feedback

The discussion of this essay on Facebook's "Effective Altruists" forum includes a debate about whether flow-through effects are actually significant relative to first-order effects and how inevitable the future is likely to be.


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# 0.8 Reactions in aqueous solutions  (Page 3/10)

 Page 3 / 10

## Interesting fact

The simplest way to check whether water is hard or soft is to use the lather/froth test. If the water is very soft, soap will lather more easily when it is rubbed against the skin. With hard water this won't happen. Toothpaste will also not froth well in hard water.

A water softener works on the principle of ion exchange . Hard water passes through a media bed, usually made of resin beads that are supersaturated with sodium. As the water passes through the beads, the hardness minerals (e.g. calcium and magnesium) attach themselves to the beads. The sodium that was originally on the beads is released into the water. When the resin becomes saturated with calcium and magnesium, it must be recharged. A salt solution is passed through the resin. The sodium replaces the calcium and magnesium and these ions are released into the waste water and discharged.

## Acid rain

This section is not examinable and is included as an example of ions in aqueous solution.

The acidity of rainwater comes from the natural presence of three substances ( $\mathrm{CO}{}_{2}$ , $\mathrm{NO}$ , and $\mathrm{SO}{}_{2}$ ) in the lowest layer of the atmosphere. These gases are able to dissolve in water and therefore make rain more acidic than it would otherwise be. Of these gases, carbon dioxide ( $\mathrm{CO}{}_{2}$ ) has the highest concentration and therefore contributes the most to the natural acidity of rainwater. We will look at each of these gases in turn.

Acid rain

Acid rain refers to the deposition of acidic components in rain, snow and dew. Acid rain occurs when sulphur dioxide and nitrogen oxides are emitted into the atmosphere, undergo chemical transformations and are absorbed by water droplets in clouds. The droplets then fall to earth as rain, snow, mist, dry dust, hail, or sleet. This increases the acidity of the soil and affects the chemical balance of lakes and streams.

1. Carbon dioxide Carbon dioxide reacts with water in the atmosphere to form carbonic acid ( ${\mathrm{H}}_{2}{\mathrm{CO}}_{3}$ ).
${\mathrm{CO}}_{2}+\mathrm{H}{}_{2}\mathrm{O}\to {\mathrm{H}}_{2}{\mathrm{CO}}_{3}$
The carbonic acid dissociates to form hydrogen and hydrogen carbonate ions. It is the presence of hydrogen ions that lowers the pH of the solution making the rain acidic.
${\mathrm{H}}_{2}{\mathrm{CO}}_{3}\to {\mathrm{H}}^{+}+{\mathrm{HCO}}_{3}^{-}$
2. Nitric oxide Nitric oxide ( $\mathrm{NO}$ ) also contributes to the natural acidity of rainwater and is formed during lightning storms when nitrogen and oxygen react. In air, $\mathrm{NO}$ is oxidised to form nitrogen dioxide ( ${\mathrm{NO}}_{2}$ ). It is the nitrogen dioxide which then reacts with water in the atmosphere to form nitric acid ( ${\mathrm{HNO}}_{3}$ ).
$3\mathrm{NO}{}_{2}\left(\mathrm{g}\right)+\mathrm{H}{}_{2}\mathrm{O}\left(\mathrm{l}\right)\to 2\mathrm{HNO}{}_{3}\left(\mathrm{aq}\right)+\mathrm{NO}\left(\mathrm{g}\right)$
The nitric acid dissociates in water to produce hydrogen ions and nitrate ions. This again lowers the pH of the solution making it acidic.
$\mathrm{HNO}{}_{3}\to {\mathrm{H}}^{+}+{\mathrm{NO}}_{3}^{-}$
3. Sulphur dioxide Sulphur dioxide in the atmosphere first reacts with oxygen to form sulphur trioxide, before reacting with water to form sulphuric acid .
$2\mathrm{SO}{}_{2}+\mathrm{O}{}_{2}\to 2\mathrm{SO}{}_{3}$
$\mathrm{SO}{}_{3}+\mathrm{H}{}_{2}\mathrm{O}\to \mathrm{H}{}_{2}{\mathrm{SO}}_{4}$
Sulphuric acid dissociates in a similar way to the previous reactions.
$\mathrm{H}{}_{2}{\mathrm{SO}}_{4}\to \mathrm{H}{\mathrm{SO}}_{4}^{-}+{\mathrm{H}}^{+}$

Although these reactions do take place naturally, human activities can greatly increase the concentration of these gases in the atmosphere, so that rain becomes far more acidic than it would otherwise be. The burning of fossil fuels in industries, vehicles etc is one of the biggest culprits. If the acidity of the rain drops to below 5, it is referred to as acid rain .

#### Questions & Answers

If potatoes cost Jane $1 per kilogram and she has$5 that could possibly spend on potatoes or other items. If she feels that the first kilogram of potatoes is worth $1.50, the second kilogram is worth$1.14, the third is worth $1.05 and subsequent kilograms are worth$0.30, how many kilograms of potatoes will she purchase? What if she only had $2 to spend? Susan Reply cause of poverty in urban DAVY Reply QI: (A) Asume the following cost data are for a purely competitive producer: At a product price Of$56. will this firm produce in the short run? Why Why not? If it is preferable to produce, what will be the profit-maximizing Or loss-minimizing Output? Explain. What economic profit or loss will the
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# How do you use the Pythagorean Theorem to determine if the three sides are a right triangle: 10 cm, 49.5 cm, 50.5 cm?

${\left(50.5\right)}^{2} = {\left(10\right)}^{2} + {\left(49.5\right)}^{2}$
$2550.25 = 100 + 2450.25 = 2550.25$


text:
Reference : Analysis of SNOW 3G XOR Resynchronization Mechanism
 Document type : Scientific congresses, symposiums and conference proceedings : Paper published in a book Discipline(s) : Engineering, computing & technology : Computer science To cite this reference: http://hdl.handle.net/10993/17071
 Title : Analysis of SNOW 3G XOR Resynchronization Mechanism Language : English Author, co-author : Biryukov, Alex [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >] Priemuth-Schmid, Deike [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >] Zhang, Bin [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >] Publication date : 2010 Main document title : SECRYPT 2010 Pages : 327-333 Peer reviewed : Yes Audience : International ISBN : 978-989-8425-18-8 Event name : SECRYPT 2010 Event date : July 26-28, 2010 Event place (city) : Athens Event country : Greece Keywords : [en] stream cipher ; resynchronization attack ; SNOW 3G Abstract : [en] The stream cipher SNOW 3G designed in 2006 by ETSI/SA-GE is a base algorithm for the second set of 3GPP confidentiality and integrity algorithms. In this paper, we investigate the resynchronization security of a close variant of SNOW 3G, in which two modular additions are replaced by xors and which is called SNOW 3G$^{\oplus}$. It is shown that the feedback from the FSM to the LFSR is crucial for security. Given a pair of \textit{known} IVs, the cipher without such a feedback is extremely vulnerable to differential known IV attacks with practical complexities ($2^{57}$ time and $2^{33}$ keystream). With such a feedback, it is shown that $16$ out of $33$ initialization rounds can be broken by a differential \textit{chosen} IV attack. This is the first public evaluation result for this algorithm. Permalink : http://hdl.handle.net/10993/17071 Commentary : SECRYPT 2010

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# The Herschel galaxy reference survey

Abstract : In order to study the dust properties of different galaxies in the nearby Universe, the SPIRE extragalactic group selected a volume limited (15$<$ $D$ $<$25 Mpc), complete sample of 313 galaxies spanning the whole range in morphological type (from ellipticals to late-type spirals) and luminosity (8.5 $<$ log $L_H$ $<$ 12 L$_H\odot$, -22 $<$ $M_B$ $<$ -16) extracted from 2MASS, to be observed in guaranteed time with Herschel. The 250-360-520 $\mu$m SPIRE data, combined with those collected at other frequencies, will be used to trace the dust properties of normal galaxies and provide a reference sample for studies at high redshift.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-00129139
Contributor : Catherine Beaussier <>
Submitted on : Tuesday, February 6, 2007 - 9:54:53 AM
Last modification on : Friday, November 6, 2020 - 3:11:11 AM

### Citation

Alessandro Boselli, The Spire Extragalactic Group. The Herschel galaxy reference survey. 2006. ⟨hal-00129139⟩

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text:
# Why Are Cargo Ships Backed Up If The US Economy Is Struggling Due To The Pandemic?

Since the start of the present pandemic, the US Congress has authorized over \$5 trillion in various forms of economic aid (Business Insider), including the just-signed$1.9 trillion American Rescue Plan. So things are pretty bad, right?

Then why are cargo ships queuing up outside the ports of Los Angeles and Long Beach (Axios)? The articles I've read (such as CNBC and WSJ) say the backup is caused by the combination of surging consumer demand and COVID-19 disruptions. I'm looking for data to corroborate that interpretation, because a "surging customer demand" narrative seems to contradict the "the economy is in a bad way" narrative.

So is consumer spending surging? If I am reading these FRED graphs right, personal spending on durable and nondurable goods spending are roughly 10% above pre-pandemic levels. (I'm eyeballing these on a smartphone.) So yes, demand could be described as "surging."

So then why the need for \\$1.9 trillion in new government spending? My belief and understanding was that the economy is struggling right now, but then how are we all paying for so much more stuff that our ports are clogged? (I know the pandemic has disproportionately hurt service industries; is that the answer? Spending on goods is fine but the lack of spending on services is dragging the economy down?)

(The COVID-19 disruptions part of the explanation also confuses me but that's less important, and less relevant to this forum. But from that CNBC article, 800 of 15,000 longshoremen have been "out of work due to COVID;" so if 5% of Longshoremen call in sick, the ports grind to a halt? There's got to be more to the story that I'm missing.)

• Perhaps some people are spending more while other are able to spend less. If I get a new cellphone and you can't afford rent, it may cancel out in total numbers, but it doesn't mean there isn't a struggle. It would be better if you could afford rent and I didn't get a new cellphone. Mar 15 '21 at 12:14
• Yes, I suspect the uneven impacts of the pandemic are at the root of my question. So what I am looking for are: (1) data corroborate the two narratives I identified, and (2) data to illustrate why those narratives are not actually contradictory. Mar 15 '21 at 14:04


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# Synopsis: Fragile state

Optical measurements in electron gases at low temperatures and high magnetic fields show the electron spins are, as predicted, polarized, but that this state is surprisingly delicate.

In the presence of a magnetic field, the physics of a two-dimensional electron gas such as $\text{GaAs}$ at very low temperatures is often determined by electron-electron interactions rather than single-electron effects alone. In the lowest Landau level, i.e., for states with the least cyclotron energy, the physics is particularly interesting near the case where the number of electrons exactly equals the number of available states (often referred to as a “filling factor $\nu =1$”). Here the ground state is expected to form a so-called quantum Hall ferromagnet, with fully polarized spins, even for the small Zeeman coupling typical in $\text{GaAs}$.

Writing in Physical Review Letters, Paulina Plochocka and co-workers at the CNRS in Grenoble, France, and colleagues in Israel and the US report detailed optical absorption measurements, which are often more reliable than transport measurements near integral filling factors, confirming that a full spin alignment does occur at $\nu =1$ in a quantum Hall ferromagnet. Though predicted by theory, the polarized state could not be concluded from earlier experiments. More significantly, the authors find that the spin polarization is very fragile and the spins depolarize rapidly as either the filling factor or the temperature changes even slightly. This depolarization appears to be consistent with the presence of spin textures, known as skyrmions, that have been predicted in quantum Hall ferromagnets. – Sami Mitra

More Features »

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## derivation of the quotient rule

The quotient rule is used to take the derivative of a function with divided expressions:

It is possible to prove this rule by utilizing the definition of the derivative; however, this is not nearly as elegant as the following simple proofs which use other derivative properties instead.

## logarithmic proofs

As well as being used in the proof of the quotient rule, logarithms can also be used to prove a couple of other derivative rules.


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# Can you solve any induction problem with base case 0

A book I'm reading introduces a dummy principle called the "Weak Principle of Mathematical Induction", which is simply the Principle of Mathematical Induction, with the base case $$n_0$$ fixed at $$0$$. The book claims that any problem solvable by the Principle of Mathematical Induction is also solvable by the Weak Principle of Mathematical Induction. It provides the following question:

A lot of problems solved by induction are presented as:

For all $$n \geq x$$, show P(n)

Traditional induction would start at the base case $$n_0 = x$$, and only apply P to values $$n \geq x$$ to show that $$P(n) \rightarrow P(n + 1)$$ proves that $$P(n)$$ holds for all $$n \geq x$$.

However, this Weak Principle seems very general to me actually in that speaks in terms of all $$n$$, not limited to $$n > 0$$, which confuses me. At first, I thought the way to get around this was that if a given problem states that $$P$$ should only be applied to values $$n > 0$$, then maybe $$P(0)$$ is vacuously true, just as $$P(x) \rightarrow P(x + 1)$$ where $$x \leq 0$$ would be. But I don't think that's the correct approach.

The only thing I can think of is that the answer relies on the idea of re-indexing that this answer explains, to basically re-index any induction problem such that the base case is $$0$$. Then furthermore $$P(n) \rightarrow P(n + 1)$$ is:

• Is always true for $$n \geq 0$$, assuming the problem is solvable by traditional induction
• Is vacuously true for for $$P(n)$$ that is false, i.e., $$n$$ that $$P$$ is not meant to be applied to, given the problem statement

Does this approach make sense? I'd appreciate thoughts and perspectives on this. If this is the right approach, then I think I need to understand re-indexing a bit more. The example in the answer I linked to above makes sense because it is so simple...but it is hard to see that it always works with very complicated predicates, i.e., that involve summations etc.

• "For all $n\ge x$, show $P(n)$" is the same as "for all $n\ge0$, show $Q(n)$, where $Q(n)$ is defined to be $P(n+x)$" so it is just re-indexing. Jun 28 '20 at 6:18

First of all, there is an implicit assumption in your Weak Principle of Induction that $$P(n)$$ is a predicate defined on the natural numbers (integers $$n \ge 0$$). Likely if you carefully read the context where you found this, it will actually say somewhere that they are dealing with predicates defined on integers greater than or equal to the base case. So when it says "for all $$n$$" it actually means "for all integers $$n \ge 0$$".

Second, note that your Weak Principle explicitly states "$$P(0)$$ is true" as one of the hypotheses. So it is not a case that "$$P(0)$$ is vacuously true". That $$P(0)$$ is true is something you have to show explicitly for your predicate before you can apply this "Weak Principle".

As Gerry Myerson has pointed out, the equivalence is just a matter of re-indexing. If all you knew was the weak principle, and you have a predicate $$P(n)$$ defined on all integers $$n \ge x$$ where $$x$$ is some arbitrary integer. And if you can prove both that $$P(x)$$ is true, and that for all $$n \ge x, P(n) \implies P(n+1)$$, then you can show $$P(n)$$ is true for all $$n \ge x$$ as follows:

• Define the predicate $$Q(m) = P(m + x), m\ge 0$$
• $$Q(0) = P(x)$$. Since $$P(x)$$ is true, so is $$Q(0)$$.
• $$Q(m) \equiv P(m + x) \implies P((m + x) + 1) \equiv Q(m + 1)$$, so $$Q(m) \implies Q(m+1)$$ for all $$m \ge 0$$.
• By the weak principle, $$Q(m)$$ is true for all $$m\ge 0$$.
• That is, $$P(m + x)$$ is true for all $$m \ge 0$$.
• Setting $$n = m + x, P(n)$$ is true for all $$n \ge x$$.

There is a stronger version of induction. That version is probably where you got the idea of $$P(0)$$ being "vacuously true". That version (for natural numbers) is

If $$P(n)$$ is defined for $$n \in \Bbb N$$, and if $$\forall n\in \Bbb N, (\forall m < n, P(m)) \implies P(n)$$, then $$\forall n \in \Bbb N, P(n)$$.

This is stronger than the versions you have been discussing, since there are predicates $$P$$ for which just knowing $$P(n-1)$$ is not enough to show $$P(n)$$, but for which knowing $$P(m)$$ for every $$m < n$$ is enough to show $$P(n)$$. Such predicates can be proven always true from this version of induction, but not using the versions you gave.

You may note that there is no explicit mention of a base case in this version. But this version still has a base case. It is just that the induction case implies the base case, so it doesn't need to be mentioned separately. Since there is no $$m < 0$$ in $$\Bbb N$$, the statement $$\forall m < 0, P(m)$$ is "vacuously" true. And therefore if the induction case has been shown true, $$P(0)$$ must also be true.

Note that it is "$$\forall m < 0, P(m)$$" that is "vacuously true" (true because there is no $$m < 0$$ rather than any property of $$P$$), not $$P(0)$$, for which the phrase "vacuously true" has no definition. $$P(0)$$ is just a consequence of the vacuous truth.

• Thanks. I agree there is an implicit assumption, and oddly enough I cannot find written anywhere that we're explicitly dealing with $n \geq 0$. However, if we choose not to acknowledge that assumption (because it is not explicit anywhere), re-indexing still works right? Because $P(n) \implies P(n + 1)$ is still true where $P(n)$ is false (i.e., we're dealing with an $n$ that $P$ is not meant to be applied to). Does that make sense? Jun 28 '20 at 17:00
• One more question: I definitely understand the intent of re-indexing, but I'm still a little confused about why it is fair to apply it. $P(0)$ is either true or false. We can of course create a wrapper predicate $Q$ such that $Q(0) = P(x)$ as you did, but the Weak Principle doesn't say "If Q(0) is true [....] where Q is some wrapper predicate over P, then [..]". Instead, you're simply given a predicate $P$, which might not be true for $0$, and the Weak Principle directly applies $P$ to $0$. How is there room for re-indexing? Jun 28 '20 at 17:31
• First of all, induction requires a well-founded class to induct over, and without a lot of extra development, that means a subset of the integers bounded below. Second, "$P(n) \implies P(n+1)$" induction requires that no integers above the minimum can be skipped. Thirdly, the base case is $0$, so you cannot deduct anything about $n < 0$. And you don't need anything about $n < 0$ to induct for $n > 0$, So you cannot get $n < 0$ in the result and there is no point in requiring it in the induction step. Therefore, until you learn about well ordering, induction means "all integers $\ge x$". Jun 28 '20 at 18:55
• For your second comment. I did not apply induction to $P$ through $Q$. I applied induction to $Q$. Period. Once $\forall n\ge 0,Q(n)$ is proved, I then obtained $\forall n\ge x, P(n)$ by the equivalence $Q(n) \iff P(n+x)$, not by induction. You will note that there is no restriction in the induction principle placed on the nature of the predicate to which it is applied. There is nothing that says the predicate cannot be constructed from another predicate (particularly since such a restriction would make it practically useless). Jun 28 '20 at 19:05
• Thanks for the explanations Jun 29 '20 at 16:08


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One of my net core 5 web apps has just given me this runtime error when I try to run it from Visual Studio 2019 Community

Could not load type 'System.Runtime.CompilerServices.DefaultInterpolatedStringHandler' from assembly 'System.Runtime, Version=6.0.0.0

I can't see anything in my project that uses that assembly ? all was good until today Windows updates maybe ? I'm currently on the latest version of Win 10.

What I have tried:

Googled and all the usual stuff
If I build and run it from a Linux terminal there isn't a problem
Posted
BillWoodruff 2-Jan-22 12:01pm
Is there any way you can examine the project file, or other app settings, to see if there is a valid reference to 'System.Runtime, Version=6.0.0.0 ?
pkfox 3-Jan-22 3:54am
Hi Bill, thanks for replying - there is no reference to it in the .csproj file, but it is shown under Dependencies\Microsoft.NETCore.App which points to a physical file in C:\Program Files\dotnet\packs\Microsoft.NETCore.App.Ref\6.0.1\ref\net6.0\System.Runtime.dll - but that file is dated 23/11/2021
BillWoodruff 4-Jan-22 10:41am
Sorry, that's the only thing i can think of ... one way to check that might be to look for some other call to that librarys facilities and see if that, also, breaks ?
Maciej Los 12-Jan-22 15:29pm
I'd suggest to close VS, delete hidden folder .vs, open project and build project again.


text:
Outlook: BLUE ENERGY LIMITED. is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Sell
Time series to forecast n: 04 Feb 2023 for (n+8 weeks)
Methodology : Active Learning (ML)

## Abstract

BLUE ENERGY LIMITED. prediction model is evaluated with Active Learning (ML) and Independent T-Test1,2,3,4 and it is concluded that the BLU stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Sell

## Key Points

1. Fundemental Analysis with Algorithmic Trading
2. Game Theory
3. What is a prediction confidence?

## BLU Target Price Prediction Modeling Methodology

We consider BLUE ENERGY LIMITED. Decision Process with Active Learning (ML) where A is the set of discrete actions of BLU stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4

F(Independent T-Test)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Active Learning (ML)) X S(n):→ (n+8 weeks) $∑ i = 1 n a i$

n:Time series to forecast

p:Price signals of BLU stock

j:Nash equilibria (Neural Network)

k:Dominated move

a:Best response for target price

For further technical information as per how our model work we invite you to visit the article below:

How do AC Investment Research machine learning (predictive) algorithms actually work?

## BLU Stock Forecast (Buy or Sell) for (n+8 weeks)

Sample Set: Neural Network
Stock/Index: BLU BLUE ENERGY LIMITED.
Time series to forecast n: 04 Feb 2023 for (n+8 weeks)

According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Sell

X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)

Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)

Z axis (Grey to Black): *Technical Analysis%

## IFRS Reconciliation Adjustments for BLUE ENERGY LIMITED.

1. If items are hedged together as a group in a cash flow hedge, they might affect different line items in the statement of profit or loss and other comprehensive income. The presentation of hedging gains or losses in that statement depends on the group of items
2. An entity is not required to incorporate forecasts of future conditions over the entire expected life of a financial instrument. The degree of judgement that is required to estimate expected credit losses depends on the availability of detailed information. As the forecast horizon increases, the availability of detailed information decreases and the degree of judgement required to estimate expected credit losses increases. The estimate of expected credit losses does not require a detailed estimate for periods that are far in the future—for such periods, an entity may extrapolate projections from available, detailed information.
3. For the purpose of applying the requirement in paragraph 6.5.12 in order to determine whether the hedged future cash flows are expected to occur, an entity shall assume that the interest rate benchmark on which the hedged cash flows (contractually or non-contractually specified) are based is not altered as a result of interest rate benchmark reform.
4. At the date of initial application, an entity shall assess whether a financial asset meets the condition in paragraphs 4.1.2(a) or 4.1.2A(a) on the basis of the facts and circumstances that exist at that date. The resulting classification shall be applied retrospectively irrespective of the entity's business model in prior reporting periods.

*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.

## Conclusions

BLUE ENERGY LIMITED. is assigned short-term Ba1 & long-term Ba1 estimated rating. BLUE ENERGY LIMITED. prediction model is evaluated with Active Learning (ML) and Independent T-Test1,2,3,4 and it is concluded that the BLU stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Sell

### BLU BLUE ENERGY LIMITED. Financial Analysis*

Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementCaa2Baa2
Balance SheetBaa2Ba3
Leverage RatiosCBaa2
Cash FlowBa1Ba2
Rates of Return and ProfitabilityBa2Ba1

*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?

### Prediction Confidence Score

Trust metric by Neural Network: 84 out of 100 with 832 signals.

## References

1. Cortes C, Vapnik V. 1995. Support-vector networks. Mach. Learn. 20:273–97
2. Doudchenko N, Imbens GW. 2016. Balancing, regression, difference-in-differences and synthetic control methods: a synthesis. NBER Work. Pap. 22791
3. Bennett J, Lanning S. 2007. The Netflix prize. In Proceedings of KDD Cup and Workshop 2007, p. 35. New York: ACM
4. L. Prashanth and M. Ghavamzadeh. Actor-critic algorithms for risk-sensitive MDPs. In Proceedings of Advances in Neural Information Processing Systems 26, pages 252–260, 2013.
5. Mazumder R, Hastie T, Tibshirani R. 2010. Spectral regularization algorithms for learning large incomplete matrices. J. Mach. Learn. Res. 11:2287–322
6. Bewley, R. M. Yang (1998), "On the size and power of system tests for cointegration," Review of Economics and Statistics, 80, 675–679.
7. Abadie A, Diamond A, Hainmueller J. 2015. Comparative politics and the synthetic control method. Am. J. Political Sci. 59:495–510
Frequently Asked QuestionsQ: What is the prediction methodology for BLU stock?
A: BLU stock prediction methodology: We evaluate the prediction models Active Learning (ML) and Independent T-Test
Q: Is BLU stock a buy or sell?
A: The dominant strategy among neural network is to Sell BLU Stock.
Q: Is BLUE ENERGY LIMITED. stock a good investment?
A: The consensus rating for BLUE ENERGY LIMITED. is Sell and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of BLU stock?
A: The consensus rating for BLU is Sell.
Q: What is the prediction period for BLU stock?
A: The prediction period for BLU is (n+8 weeks)


text:
# Volatility in Credit Default Swaps

A credit default swap (CDS) is a financial derivative contract in which the seller agrees to compensate the buyer, who pays a fixed premium in advance for the contract, if an underlying security (usually a debt instrument such as a fixed-rate, fixed-term bond) defaults (fails to pay interest, return principal at maturity, delays payments, or makes partial payments). Given the complexity of the instruments and possible events over the term of the contract, these contracts are usually very complex and may be customised by the buyer and seller, but the general concept is simple: it amounts to the buyer purchasing insurance from a third party against the risk of default by the issuer of the underlying security. As with any form of insurance, the buyer must also weigh the risk of the seller failing to pay when the risk becomes reality—this is referred to as “counterparty risk” and can be substantial when things get spicy in otherwise staid financial markets.

Although credit default swaps are complicated and can be customised, to allow comparison across issuers, securities, maturities, and time, they are often quoted in terms of basis points of premium on a contract with an underlying nominal value of US$10 million. For example, at this writing, a five year credit default swap on the sovereign debt of the United States is quoted at 14.70 basis points. Since a basis point is a “percent of a percent” that means the buyer pays 14.70\times\frac{1}{100}\times\frac{1}{100}=0.00147 of the amount insured for the contract. For the standard principal of US$ 10 million, this would be US\$ 14,700 for the contract. (While credit default swaps are structured like insurance, you don’t need to own the underlying asset to buy a swap on it. A swap bought as a speculation on default of the asset is called a “naked swap”, and such swaps are estimated to account for around 80% of the total swap market.)

What’s interesting is comparing the swap rates, and implied risks, of the sovereign debt of various countries and the changes in these rates over time. U.S. Treasury debt is often said to be the safest investment in the world since it is denominated in the world’s reserve currency and the issuer has the ability to print new dollars at will to redeem its debt. And yet, given the political instability of that country and its history of brinksmanship and grandstanding over government shutdowns and increasing the statutory debt limit, credit default swaps on its bonds cost 40% more than those on the debt of the Netherlands, currently considered the least likely to default in the world. (If you really believe that climate change and rising oceans posed a real threat, why would a country more than one quarter of which is below sea level be the safest bond issuer in the world?)

Anyway, comparing risk, as assessed by traders in the market with their (or their clients’) money on the line, is interesting, as is the rate of change in that perceived risk. Other than dramatic recent changes due to geopolitical events (see Germany, Poland, Finland, and Russia), what is also obvious is that recent instability in the foundations of the financial system (in particular, freezing the foreign exchange reserves of Russia by the central banks which held it on their behalf) has caused a world-wide increase in the perceived risk of sovereign defaults with only a few exceptions, notably Netherlands, Japan, and Canada.

The “PD” column in the table gives the estimated probability of default implied by the CDS rates according to a complex formula assuming creditors recover 40% from an eventual default. While the probability for the U.S. is just 0.25% and China is 1.01%, Russia’s default probability now stands at 6.87% (although it is unlikely many new CDS contracts are being issued on Russian debt, and the number comes from a thin and volatile market).

This is an interesting indicator to watch, as it indicates confidence in the foundations of the international financial system that underlies world trade.

5 Likes

…and then…

2 Likes

What is not clear is just who will be hurt if Russia defaults on its debt? Russia got the money and spent it. Whoever now holds that debt and expects to get regular interest payments is the entity which will feel the pain first – or maybe the entity which has insured the loans to Russia – or maybe the entity which has speculated in CDS. It seems quite likely that the people closest to that financial Ground Zero will not be in Russia.

The immediate losers will be whoever sold the credit default contracts, as they’ll be on the hook to the buyers to make up the loss. Given the deterioration in Russia’s credit risk even before the recent collapse, it’s likely that the swap dealers have been putting on hedges (for example, buying put options on Russian sovereign debt, which will appreciate if it goes into default), but there’s no way to know until it’s time to start unwinding these contracts. Anybody who owns the debt and doesn’t have a CDS to insure against the loss is the next round of losers. In many cases holders in such a situation will sell the debt at a deep discount to a “vulture fund” which bets that more will be recovered from the in-default bonds than the market expects. (Some such funds have done well in past Latin American and Asian debt crises.)

Many banks who may hold this debt are subject to “mark to market” rules and may not be able to carry the debt at full value on their books hoping it will be eventually recover. Those banks will have to reserve for potential losses, which will hit their earnings.

A recent post on ZeroHedge, “Traders Concerned Russian CDS Won’t Pay Out In Event Of Default” discusses a Financial Times article (behind a paywall), on the various ways holders of credit default swaps may be left holding the bag due to sanctions, disruption of markets, and counterparty risk.

When things are moving this quickly, it’s nearly impossible to make predictions or forecast what might break.

2 Likes

If you’re curious about how the probability of default is computed from the quoted price of a credit default swap (CDS), here’s they do it, as described in this quant.stackexchange post. The price, usually called the “CDS spread”, is S and R is the expected recovery rate from a default event, expressed as a fraction or percent. In the case of a total default, R would be zero; in quoted probabilities of default R=40\%=0.4 is often used.

To compute probability P of default over time period t in years, use:

P=1-e^{\frac{-S t}{1-R}}

To compute the CDS spread S from default probability P recovery rate R and term t years, use:

S=\ln (1-P)\frac{R-1}{t}

The S value for CDS spread is expressed as a fraction, not in terms of “basis points” as usually quoted in the financial press. To convert basis points to fractional value, divide by 10,000. The term value t is also confusing in published data. The financial community is inordinately fond of curious units—in addtion to basis points, these are the people who quote U.S. Treasury securities prices in 1/32nds of a dollar. While credit default swaps are often quoted in terms of a five year swap, the CDS spread S and probability of default P are quoted as if the term was one year, so with such published data you should set t=1 in the above equations.

Let’s work an example from the table in the main post. Poland’s sovereign debt was quoted at 86.80 basis points for a 5 year CDS. To compute probability of default, we convert basis points to S=86.80/10000=0.00868, set t=1, R=0.4 and evaluate:

P=1-e^{\frac{-0.00868\times 1}{1-0.4}}\\ P=1-e^{\frac{-0.00868}{0.6}}\\ P=1-0.9856\\ P=0.01436=1.436%

Why does this not agree exactly with the 1.45% quoted in the table?—sloppiness.

Let’s do the inverse calculation just to be sure.

S=\ln (1-0.01436)\frac{0.4-1}{1}\\ S=\ln 0.98564\times -0.6\\ S=\ln -0.014464\times -0.6\\ S=0.0086784

Or, in finance-speak, 0.0086784\times 10000=86.784 basis points.

2 Likes

Got to love it! We see this kind of apparently sophisticated calculation in many industries. But right down at the bottom of the process are often some very arbitrary assumptions – in this case, that 40% of the loaned money will eventually be recovered in the event of default.

So the obvious question is – Where does the assumption of 40% come from? When I have asked related questions in other contexts, the people presenting the results usually shrug their shoulders and say – We always use 40%.

And if it is ever possible to find the person who originally blessed the 40% number, it turns out to be from a historical analysis of a large number of prior occurrences – with a range that goes from 0% to maybe 90%. And that person will clearly say that it is ok to use 40% provided (a) one is looking at the average outcome from a diversified portfolio of at least 20 independent entities, and (b) that there are good reasons for projecting past performance to predict future likely behavior.

But hiding arbitrary assumptions behind equations (the more complex the better!) makes it seem so much more credible.

2 Likes

There are also even more complicated models with forbiddingly arcane equations behind simplified calculations such as this one. See, for example, the Hull-White pricing model [PDF], which is one of the most commonly used in pricing these contracts. And behind that is the assumption, buried all over the place, that the distribution of the numbers they are aggregating into the ensemble values they employ are Gaussian and well-behaved, when there is abundant evidence that, like so many things, a power law is a better fit.

1 Like

This touches a hot issue with me. I was once a bystander at an enormous business catastrophe – lost a Billion Dollars. It turned out that the executive who placed the bet did not realize he was placing a bet. He expected the “Expectation Value” result from a Monte Carlo analysis, without realizing that the Expectation Value could be expected only as the average result if he had placed a large number of similar bets. Any single bet would have a result anywhere from total loss to an El Dorado-like gain. This executive’s failure to understand the assumptions involved in simple statistics ended his business.

2 Likes

This is very interesting. Thank you for sharing.

I think I am confused by the units. When we use the basis points for a five year swap, are we calculating the probability of a default over a one year period?

2 Likes

I don’t know. What’s odd is that the term of the swaps quoted is five years, so you’d expect the default figure would apply to that term, but the spreads and probabilities quoted are computed with a term of one year. I don’t know if that means the probability applies for one year or five. My guess would be for one year, since the five year term appears nowhere in the formula used to compute the probability.

2 Likes


text:
# How do you write 0.125 as a fraction?

Mar 4, 2017

$\frac{1}{8}$

#### Explanation:

Decimals can be written as fractions with the denominators as powers of 10.

3 decimal places indicates that the fraction is thousandths.

$0.125 = \frac{125}{1000}$

This can be simplified.

$\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}$


text:
## The Annals of Statistics

### Minimum $G_2$-aberration for nonregular fractional factorial designs

#### Abstract

Deng and Tang proposed generalized resolution and minimum aberration criteria for comparing and assessing nonregular fractional factorials, of which Plackett–Burman designs are special cases.A relaxed variant of generalized aberration is proposed and studied in this paper.We show that a best design according to this criterion minimizes the contamination of nonnegligible interactions on the estimation of main effects in the order of importance given by the hierarchical assumption.The new criterion is defined through a set of $B$ values, a generalization of word length pattern. We derive some theoretical results that relate the $B$ values of a nonregular fractional factorial and those of its complementary design. Application of this theory to the construction of the best designs according to the new aberration criterion is discussed. The results in this paper generalize those in Tang and Wu, which characterize a minimum aberration (regular) $2^{m-k}$ design through its complementary design.

#### Article information

Source
Ann. Statist., Volume 27, Number 6 (1999), 1914-1926.

Dates
First available in Project Euclid: 4 April 2002

https://projecteuclid.org/euclid.aos/1017939244

Digital Object Identifier
doi:10.1214/aos/1017939244

Mathematical Reviews number (MathSciNet)
MR1765622

Zentralblatt MATH identifier
0967.62055

Subjects
Primary: 62K15: Factorial designs
Secondary: 62K05: Optimal designs

#### Citation

Tang, Boxin; Deng, Lih-Yuan. Minimum $G_2$-aberration for nonregular fractional factorial designs. Ann. Statist. 27 (1999), no. 6, 1914--1926. doi:10.1214/aos/1017939244. https://projecteuclid.org/euclid.aos/1017939244

#### References

• Box, G. E. P. and Hunter, J. S. (1961). The 2k-p fractional factorial designs. Technometrics 3 311-351; 449-458.
• Box, G. E. P., Hunter, W. G. and Hunter, J. S. (1978). Statistics for Experimenters. Wiley, New York.
• Box, G. E. P. and Tyssedal, J. (1996). Projective properties ofcertain orthogonal arrays. Biometrika 84 950-955.
• Chen, H. and Hedayat, A. S. (1996). 2n-m fractional factorial designs with (weak) minimum aberration. Ann. Statist. 24 2536-2548.
• Chen, J. (1992). Some results on 2n-k fractional factorial designs and search for minimum aberration designs. Ann. Statist. 20 2124-2141.
• Chen, J. and Wu, C. F. J. (1991). Some results on sn-k fractional factorial designs with minimum aberration or optimal moments. Ann. Statist. 19 1028-1041.
• Cheng, C. S. (1995). Some projection properties oforthogonal arrays. Ann. Statist. 23 1223-1233.
• Cheng, C. S., Steinberg, D. M. and Sun, D. X. (1999). Minimum aberration and model robustness for two level fractional factorial designs. J. Roy. Statist. Soc. Ser. B 61 85-93.
• Deng, L. Y. and Tang, B. (1998). Design selection and classification for Hadamard matrices using generalized minimum aberration criterion. Unpublished manuscript.
• Deng, L. Y. and Tang, B. (1999). Generalized resolution and minimum aberration criteria for Plackett-Burman and other nonregular factorial designs. Statist. Sinica 9 1071-1082.
• Franklin, M. F. (1984). Constructing tables ofminimum aberration pn-m designs. Technometrics 26 225-232.
• Fries, A. and Hunter, W. G. (1980). Minimum aberration 2k-p designs. Technometrics 22 601- 608.
• Hall, M., Jr. (1961). Hadamard matrix oforder 16. Jet Propulsion Laboratory Research Summary 1 21-26.
• Hall, M., Jr. (1965). Hadamard matrix oforder 20. Jet Propulsion Laboratory Technical Report 1 32-76.
• Hamada, M. and Wu, C. F. J. (1992). Analysis ofdesigned experiments with complex aliasing. J. Quality Technology 24 130-137.
• Kimura, H. (1989). New Hadamard matrix oforder 24. Graphs Combin. 5 235-242.
• Lin, D. K. J. (1993). A new class ofsupersaturated designs. Technometrics 35 28-31.
• Lin, D. K. J. and Draper, N. R. (1992). Projection properties ofPlackett and Burman designs. Technometrics 34 423-428.
• Mukerjee, R. and Wu, C. F. J. (1997). Minimum aberration designs for mixed factorials in terms oftheir complementary sets. Preprint.
• Paley, R. E. A. C. (1933). On orthogonal matrices. J. Math. and Phys. 12 311-320.
• Plackett, R. L. and Burman, J. P. (1946). The design ofoptimum multi-factorial experiments. Biometrika 33 305-325.
• Spence, E. (1995). Classification ofHadamard matrices oforder 24 and 28. Discrete Math. 140 185-243.
• Suen, C-Y., Chen, H. and Wu, C. F. J. (1997). Some identities on qn-m designs with application to minimum aberrations. Ann. Statist. 25 1176-1188.
• Tang, B. and Wu, C. F. J. (1996). Characterization ofminimum aberration 2n-k designs in terms oftheir complementary designs. Ann. Statist. 24 2549-2559.
• Tang, B. and Wu, C. F. J. (1997). A method for constructing supersaturated designs and its E s2 optimality. Canad. J. Statist. 25 191-201.
• Vijayan, K. (1976). Hadamard matrices and submatrices. J. Austral. Math. Soc. Ser. 22 A 469- 475.
• Wang, J. C. and Wu, C. F. J. (1995). A hidden projection property ofPlackett-Burman and related designs. Statist. Sinica 5 235-250.
• Webb, S. R. (1964). Characterization ofnonorthogonal incomplete factorial designs. Appendix B ofARL 65-116, Part I. Areospace Research Laboratories, United States Air Force, Wright-Patterson Air Force Base.
• Williamson, J. (1944). Hadamard's determinant theorem and the sum offour squares. Duke Math. J. 11 65-81.
• Wu, C. F. J. (1993). Construction ofsupersaturated designs through partially aliased interactions. Biometrika 80 661-669.


text:
# Revision history [back]

### Using ros pluggin & catkin build

Hi,

I am trying to build and link my ros pluggin to Gazebo. I am building all my ros packages (and therefore the pluggin) using catkin build.

I am using this example from the tutorial as a base : http://gazebosim.org/tutorials?tut=ros_plugins

The main difference I see is that I am not using catkin_make but caktin build

In the tutorial, it is explained that you need to add the following lines to your package.xml : <gazebo_ros plugin_path="${prefix}/lib" gazebo_media_path="${prefix}"/>

Which if I understand correctly, will tell Gazebo where to search for my compiled plugin library (plugin.so).

What I am seeing, is that when building with catkin_make, my plugin.so is located @ catkin_ws/devel/lib/plugin.so So I suppose that the path ${prefix}/lib is correct (that is${prefix} somehow resolves to catkin_ws/devel/)

But if I build using catkin build, my plugin.so is located @ catkin_ws/build/package_name/plugin.so.

How should I adjust my package.xml such that Gazebo can find my plugin ?

Also, is there other variable, other then ${prefix} that I can use in package.xml, and to what does${prefix} resolve to ?

 2 None sloretz 496 ●3 ●14

### Using ros pluggin & catkin build

Hi,

I am trying to build and link my ros pluggin to Gazebo. I am building all my ros packages (and therefore the pluggin) using catkin build.

I am using this example from the tutorial as a base : http://gazebosim.org/tutorials?tut=ros_plugins

The main difference I see is that I am not using catkin_make but caktin build

In the tutorial, it is explained that you need to add the following lines to your package.xml :

<gazebo_ros plugin_path="${prefix}/lib" gazebo_media_path="${prefix}"/>gazebo_media_path="${prefix}" />  Which if I understand correctly, will tell Gazebo where to search for my compiled plugin library (plugin.so). What I am seeing, is that when building with catkin_make, my plugin.so is located @ catkin_ws/devel/lib/plugin.so catkin_ws/devel/lib/plugin.so So I suppose that the path ${prefix}/lib is is correct (that is ${prefix} ${prefix} somehow resolves to catkin_ws/devel/)catkin_ws/devel/)

But if I build using catkin build, my plugin.so is located @ catkin_ws/build/package_name/plugin.so.catkin_ws/build/package_name/plugin.so.

How should I adjust my package.xml such that Gazebo can find my plugin ?

Also, is there other variable, other then ${prefix} ${prefix}that I can use in package.xml, and to what does ${prefix} ${prefix} resolve to ?


text:
# Turn-around time

Turn-around time is defined as the amount of time an airplane requires after landing to prepare for take-off.


text:
Conference paper Open Access

# Generalized Multiple Correlation Coefficient as a Similarity Measurements between Trajectories

Urain, Julen; Peters, Jan

### Citation Style Language JSON Export

{
"publisher": "Zenodo",
"DOI": "10.5281/zenodo.3829179",
"author": [
{
"family": "Urain, Julen"
},
{
"family": "Peters, Jan"
}
],
"issued": {
"date-parts": [
[
2019,
6,
24
]
]
},
"abstract": "
A similarity distance measure between two trajectories is an essential tool to understand patterns in motion, for example, in Human-Robot Interaction or Imitation Learning. The problem has been faced in many fields, from Signal Processing, Probabilistic Theory field, Topology field, or Statistics field. Anyway, up to now, none of the trajectory similarity measurement metrics are invariant to all possible linear transformation of the trajectories (rotation, scaling, reflection, shear mapping, or squeeze mapping). Also, not all of them are robust in front of noisy signals or fast enough for real-time trajectory classification. To overcome this limitation this paper proposes a similarity distance metric that will remain invariant in front of any possible linear transformation. Based on Pearson Correlation Coefficient and the Coefficient of Determination, our similarity metric, the Generalized Multiple Correlation Coefficient (GMCC) is presented as the natural extension of the Multiple Correlation Coefficient. The motivation of this paper is two-fold. First, to introduce a new correlation metric that presents the best properties to compute similarities between trajectories invariant to linear transformations and compare it with some state of the art similarity distances. Second, to present a natural way of integrating the similarity metric in an Imitation Learning scenario for clustering robot trajectories
",
"title": "Generalized Multiple Correlation Coefficient as a Similarity Measurements between Trajectories",
"type": "paper-conference",
"id": "3829179"
}
71
46
views


text:
# Can I move $\lim$ into $\sin$?

In my maths lecture notes:

$$\lim_{x \to \infty} \sqrt{\sin{\frac{3}{\sqrt{x}}}} = \sqrt{\sin{3 \sqrt{ \lim_{x \to \infty} \frac{1}{x} }}}$$

When can I move the $\lim$ into a function like this?

-
You can do this whenever the function is known to be continuous. – student Feb 21 '12 at 13:21
It should be $$\lim_{x \to \infty} \sqrt{\sin{\frac{3}{\sqrt{x}}}} = \sqrt{\sin{3 \sqrt{ \lim_{x \to \infty} \frac{1}{x} }}}$$ – sdcvvc Feb 21 '12 at 13:23
@sdcvvc, where would the problem break down if the function was not continuous? – Inquest Feb 21 '12 at 13:33
@sdcvvc, updated the post – Jiew Meng Feb 21 '12 at 13:36
Oh. I see. Thanks! – Inquest Feb 21 '12 at 13:55
Let $\frac{1}{ x} = t$
As ${x \to \infty}, t \to 0$
$$\lim_{x \to \infty} \sqrt{\sin{\frac{3}{\sqrt{x}}}} = \lim_{t \to 0} \sqrt{\sin (3\sqrt{t})} = \sqrt{\sin(3 \times \lim_{t \to 0} \sqrt{t})}$$ (Owing to Continuity)