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# Nominated Posts for the 2019 Review

Posts need at least 2 nominations to continue into the Review Phase.
Nominate posts that you have personally found useful and important.
Sort by: fewest nominations

# 2019 Review Discussion

Paul Graham has a new essay out, The Lesson to Unlearn, on the desire to pass tests. It covers the basic points made in Hotel Concierge's The Stanford Marshmallow Prison Experiment. But something must be missing from the theory, because what Paul Graham did with his life was start Y Combinator, the apex predator of the real-life Stanford Marshmallow Prison Experiment. Or it's just false advertising.

As a matter of basic epistemic self-defense, the conscientious reader will want to read the main source texts for this essay before seeing what I do to them:

The first four are recommended on their own merits as well. For...

I did the first 20 from each column of your spreadsheet, and got a different result. I hid your answers before writing mine. My rubric was different; instead of focusing on social value, I focused on what type of business relations a company has. You can see my answers here. These are all very noisy, and I'm not entirely confident I didn't have rating-drift between when I did the YC ones and when I did the S&P ones, but I got a slightly higher score for S&P companies.

In my rubric, things that mean low scores:

• You have a Compliance department
• A signif

Based on a comment I made on this EA Forum Post on Burnout.

Related links: Sabbath hard and go home, Bring Back the Sabbath

That comment I made generated more positive feedback than usual (in that people seemed to find it helpful to read and found themselves thinking about it months after reading it), so I'm elevating it to a LW post of its own. Consider this an update to the original comment.

Like Ben Hoffman, I stumbled upon and rediscovered the Sabbath (although my implementation seems different from both Ben and Zvi). I was experiencing burnout at CFAR, and while I wasn't able to escape the effects entirely, I found some refuge in the following distinction between Rest Days and Recovery Days.

# Recovery Days

A Recovery Day is where...

"Free Day", while perhaps not the best option overall, has the merit that these days involving freeing the part of you that communicatess through your gut (and through what you feel like doing). During much of our working (and non-working) week, that part is overridden by our mind's sense of what we have to do.

By contrast, in OP's Recovery Days this part is either:

(a) doing the most basic recharging before it can do things it positively feels like and enjoys, or

(b) overridden or hijacked by addictive behaviours that it doesn't find as roundly rewarding as Free Day activities.

Addiction can also be seen as a lack of freedom.

1tog2dI agree about the names. 'Rest' days are particularly confusing, since recovery days involve a lot of rest. A main characteristic of 'rest' days instead seems to doing what you feel like and following your gut.

(This is a comment that has been turned into a post.)

From Chris_Leong’s post, “Making Exceptions to General Rules”:

Suppose you make a general rule, ie. “I won’t eat any cookies”. Then you encounter a situation that legitimately feels exceptional , “These are generally considered the best cookies in the entire state”. This tends to make people torn between two threads of reasoning:

1. Clearly the optimal strategy is to make an exception this one time and then follow the rule the rest of the time.

2. If you break the rule this one time, then you risk dismantling the rule and ending up not following it at all.

How can we resolve this? …

Consider even a single exception to totally undermine any rule. Consequently, only follow rules with no exceptions.[1].

...
4Unnamed2dReviewIt seems like the core thing that this post is doing is treating the concept of "rule" as fundamental. If you have a general rule plus some exceptions, then obviously that "general rule" isn't the real process that is determining the results. And noticing that (obvious once you look at it) fact can be a useful insight/reframing. The core claim that this post is putting forward, IMO, is that you should think of that "real process" as being a rule, and aim to give it the virtues of good rules such as being simple, explicit, stable, and legitimate (having legible justifications). An alternative approach is to step outside of the "rules" framework and get in touch with what the rule is for - what preferences/values/strategy/patterns/structures/relationships/etc. it serves. Once you're in touch with that purpose, then you can think about both the current case, and what will become of the "general rule", in that light. This could end up with an explicitly reformulated rule, or not. It seems like treating the "real process" as a rule is more fitting in some cases than others, a better fit for some people's style of thinking than for other people's, and also something that a person could choose to aim for more or less. I think I'd find it easier to think through this topic if there was a long, diverse list of brief examples.

This comment discusses a class of situations where what you say seems likely to be true.

In most other cases, I think the sort of attitude you describe is likely to be a way to avoid admitting (to yourself or others) what the “real rules” are. Once you start saying stuff like…

… treating the “real process” as a rule is more fitting in some cases than others, a better fit for some people’s style of thinking than for other people’s, and also something that a person could choose to aim for more or less.

… then the usefulness of the concept/approach described... (read more)

1Ericf3dIt sounds like the actual meta-meta-rule is not "Real rules have no exceptions," but rather "the full set of all rules, and their relative priorities, fully determines (compliant) behavior, without any specific case exceptions"

# Introduction

Internal Family Systems (IFS) is a psychotherapy school/technique/model which lends itself particularly well for being used alone or with a peer. For years, I had noticed that many of the kinds of people who put in a lot of work into developing their emotional and communication skills, some within the rationalist community and some outside it, kept mentioning IFS.

So I looked at the Wikipedia page about the IFS model, and bounced off, since it sounded like nonsense to me. Then someone brought it up again, and I thought that maybe I should reconsider. So I looked at the WP page again, thought “nah, still nonsense”, and continued to ignore it.

This continued until I participated in CFAR mentorship training last September, and we had a class on CFAR’s...

The back-and-forth (here and elsewhere) between Kaj & pjeby was an unusually good, rich, productive discussion, and it would be cool if the book could capture some of that. Not sure how feasible that is, given the sprawling nature of the discussion.

Related to: Asymmetric JusticePrivacyBlackmail

Previously (Paul Christiano): Epistemic Incentives and Sluggish Updating

The starting context here is the problem of what Paul calls sluggish updating. Bob is asked to predict the probability of a recession this summer. He said 75% in January, and how believes 50% in February. What to do? Paul sees Bob as thinking roughly this:

If I stick to my guns with 75%, then I still have a 50-50 chance of looking smarter than Alice when a recession occurs. If I waffle and say 50%, then I won’t get any credit even if my initial prediction was good. Of course if I stick with 75% now and only go down to 50% later then I’ll get dinged for making a bad prediction right now—but that’s little worse than what

...

This post seems to me to be misunderstanding a major piece of Paul's "sluggish updating" post, and clashing with Paul's post in ways that aren't explicit.

The core of Paul's post, as I understood it, is that incentive landscapes often reward people for changing their stated views too gradually in response to new arguments/evidence, and Paul thinks he has often observed this behavioral pattern which he called "sluggish updating." Paul illustrated this incentive landscape through a story involving Alice and Bob, where Bob is thinking through his optimal strat... (read more)

“I didn’t get much done last week because it was so hot.”

It wasn’t the first time a client said this to me, and I was curious. “Have you considered getting an air conditioner if it’s that bad?”

“No” He replied (let’s call him Philip), “An open window is usually enough. It’s just that the heatwave this week was particularly bad.” When we discussed it a bit more, Philip said it didn’t seem worth the hassle since the AC only really felt necessary for a few weeks during the summer.

So, was Philip right? Is it worth buying an AC as a productivity hack?

# How much is your time worth?

Most people don’t think about air conditioners when evaluating their productivity, because it’s not within the normal...

AC doesn't "completely" solve the problem, because they:

a) Have time-needs for the purchase, installation and maintenance, none of which are included here.
b) Make noise, at least some of us also work less efficiently while subject to noise.

Followup to: What Evidence Filtered Evidence?

In "What Evidence Filtered Evidence?", we are asked to consider a scenario involving a coin that is either biased to land Heads 2/3rds of the time, or Tails 2/3rds of the time. Observing Heads is 1 bit of evidence for the coin being Heads-biased (because the Heads-biased coin lands Heads with probability 2/3, the Tails-biased coin does so with probability 1/3, the likelihood ratio of these is , and ), and analogously and respectively for Tails.

If such a coin is flipped ten times by someone who doesn't make literally false statements, who then reports that the 4th, 6th, and 9th flips came up Heads, then the update to our beliefs about the coin depends on what algorithm the not-lying[1] reporter used to...

Crucial. I definitely remember reading this and thinking it was one of the most valuable posts I'd seen all year. Good logical structure.

But it's hard to read? It has jarring, erratic rhetoric flow; succinct where elaboration is predictably needed, and verbose where it is redundant. A mathematician's scratch notes, I think.

Imagine that tomorrow everyone on the planet forgets the concept of training basketball skill.

The next day everyone is as good at basketball as they were the previous day, but this talent is assumed to be fixed. No one expects their performance to change over time. No one teaches basketball, although many people continue to play the game for fun.

Geneticists explain that some people are born with better hand-eye coordination and are able to shoot a basketball accurately. Economists explain that highly-paid NBA players have a stronger incentive to hit shots, which explains their improved performance. Psychologists note that people who take more jump shots each day hit a higher percentage and theorize a principal factor of basketball affinity that influences both desire and skill at...

The fosbury flop is a good analogy. Where i think it comes short is that rationality is indeed a much more complex thing than jumping. You would need more than just the invention and application of a technique by one person for a paradigm shift - It would at least also require distilling the technique well, learning how to teach it well, and changing the rationality cannon in light of it.

I think a paradigm shift would happen when a new rationality cannon will be created and adopted that outperforms the current sequences (very likely also containing new tec... (read more)

Followup to: Where to Draw the Boundary?

Figuring where to cut reality in order to carve along the joints—figuring which things are similar to each other, which things are clustered together: this is the problem worthy of a rationalist. It is what people should be trying to do, when they set out in search of the floating essence of a word.

Once upon a time it was thought that the word "fish" included dolphins ...

The one comes to you and says:

The list: {salmon, guppies, sharks, dolphins, trout} is just a list—you can't say that a list is wrong. You draw category boundaries in specific ways to capture tradeoffs you care about: sailors in the ancient world wanted a word to describe the swimming finned creatures that they saw in

...

The point of the thought experiment is that, for the alien, all of that is totally mundane (ie scientific) knowledge. So why can’t that observation count as scientific for us?

The point is that the rule "if it is not in the territory it should not be in the map" does not apply in cases where we are constructing reality, not just reflecting it.

If you are drafting a law to introduce gay marriage, it isn't objection to say that it doesn't already exist.

IE, just because we have control over a thing doesn’t—in my ontology—indicate that the concept of map/t

2abramdemski6dIt seems like part of our persistent disagreement is: * I see this as one of very few pathways, and by far the dominant pathway, by which beliefs can be beneficial in a different way from useful-for-prediction * You see this as one of many many pathways, and very much a corner case I frankly admit that I think you're just wrong about this, and you seem quite mistaken in many of the other pathways you point out. The argument you quoted above was supposed to help establish my perspective, by showing that there would be no reason to use gerrymandered concepts unless there was some manipulation going on. Yet you casually brush this off as a very particular set of problems. As a general policy, I think that yes, frequently pointing out subtler inaccuracies in language helps practice specificity and gradually refines concepts. For example, if you keep pointing out that tomatoes are fruit, you might eventually be corrected by someone pointing out that "vegetable" is a culinary distinction rather than a biological one, and so there is no reason to object to the classification of a tomato as a vegetable. This could help you develop philosophically, by providing a vivid example of how we use multiple overlapping classification systems rather than one; and further, that scientific-sounding classification criteria don't always take precedence (IE culinary knowledge is just as valid as biology knowledge). In what you quoted, I was trying to point out the distinction between speaking a certain way vs thinking a certain way. My overall conversational strategy was to try to separate out the question of whether you should speak a specific way from the question of whether you should think a specific way. This was because I had hoped that we could more easily reach agreement about the "thinking" side of the question. More specifically, I was pointing out that if we restrict our attention to how to think, then (I claim) the cost of using concepts for non-epistemic reasons is
4Raemon6d(I say all of this largely agreeing with the thrust of what the post and your (Abram's) comments are pointing at, but feeling like something about the exact reasoning is off. And it feeling consistently off has been part of why I've taken awhile to come around to the reasoning)

In discussions of algorithm bias, the COMPAS scandal has been too often quoted out of context. This post gives the facts, and the interpretation, as quickly as possible. See this for details.

#### The fight

The COMPAS system is a statistical decision algorithm trained on past statistical data on American convicts. It takes as inputs features about the convict and outputs a "risk score" that indicates how likely the convict would reoffend if released.

In 2016, ProPublica organization claimed that COMPAS is clearly unfair for blacks in one way. Northpointe replied that it is approximately fair in another way. ProPublica rebukes with many statistical details that I didn't read.

The basic paradox at the heart of the contention is very simple and is not a simple "machines are biased because it learns

...

All evidence is "biased compared to our prior". That is what evidence is.

2IlyaShpitser5d90% of the work ought to go into figuring out what fairness measure you want and why. Not so easy. Also not really a "math problem." Most ML papers on fairness just solve math problems.
3BrianChristian7d>> False negative rate = (false negative)/(actual positive) >> False positive rate = (false positive)/(actual negative) Correct me if I’m mistaken, but isn’t it: False negative rate = (false negative)/(false negative + actual positive) False positive rate = (false positive)/(false positive + actual negative)

Cross posted from the EA Forum.

Epistemic Status: all numbers are made up and/or sketchily sourced. Post errs on the side of simplistic poetry – take seriously but not literally.

If you want to coordinate with one person on a thing about something nuanced, you can spend as much time as you want talking to them – answering questions in realtime, addressing confusions as you notice them. You can trust them to go off and attempt complex tasks without as much oversight, and you can decide to change your collective plans quickly and nimbly.

You probably speak at around 100 words per minute. That's 6,000 words per hour. If you talk for 3 hours a day, every workday for a year, you can communicate 4.3 million words worth...

Not about Gendlin, but following the trail of relating chunks to other things: I wonder if propaganda or cult indoctrination can be described as a malicious chunking process.

I've weighed in against taking the numbers literally elsewhere, but following this thread I suddenly wondered if the work that using few words was doing isn't delivering the chunk, but rather screening out any alternative chunk. If what we are interested in is common knowledge, it isn't getting people to develop a chunk per se that is the challenge; rather everyone has to agree on exac... (read more)

2ryan_b6dThis part points pretty directly at research debt and inferential distance, where the debt is how many of these chunks need to be named and communicated as chunks, and the distance is how many re-chunking steps need to be done.

Reply to: Decoupling vs Contextualising Norms

Chris Leong, following John Nerst, distinguishes between two alleged discursive norm-sets. Under "decoupling norms", it is understood that claims should be considered in isolation; under "contextualizing norms", it is understood that those making claims should also address potential implications of those claims in context.

I argue that, at best, this is a false dichotomy that fails to clarify the underlying issues—and at worst (through no fault of Leong or Nerst), the concept of "contextualizing norms" has the potential to legitimize derailing discussions for arbitrary political reasons by eliding the key question of which contextual concerns are genuinely relevant, thereby conflating legitimate and illegitimate bids for contextualization.

Real discussions adhere to what we might call "relevance norms": it is almost universally "eminently reasonable to expect

...
2Raemon8dHmm. I don't I want to commit to a huge discussion of it. I'm happy to continue doing async LW comments about it. I'm busier than usual this month. There might turn out to be a day I had a spare hour or two to chat in more detail but don't think I want to spend cognition planning around that. I think I've mostly said my main piece and am fairly happy with "LW members can read what Matt and Ray have said so far and vote accordingly." If you raise specific points on specific posts I (and others) might change their vote for those posts.
2Matt Goldenberg8dYeah so I think my thought on this is that it's often impossible to point at these sorts of missing frames or implicit assumptions in a single post. In my review of Liron's post I was able to pull out a bunch of quotes pointing to some specific frames, but that's because it was unusually dense with examples. In the case of this post, if I were to do the same thing, I think I'd have to pull out quotes from at least 3-4 of the posts in the sequence to point to this underlying straw man (in this case I didn't actually do that and just sort of hoped others could do it own their own through reading my review).
4Raemon8dThat seems true, but I think it still makes sense to concentrate the discussion on particular posts. (Zack specifically disavowed this post and the meta-honesty response, so I think it makes most sense to concentrate on Where To Draw The Boundaries and Heads I Win, Tails Never Heard Of Her) I think it's reasonable to bring up "this post seems rooted in a wrong frame" on both of those, linking to other examples. But my own voting algorithm for those posts will personally be asking "does this single post have a high overall mix of 'true' and 'important'?" I think most posts in the review, even the top posts, have something wrong with them, and in some cases I disagree with the author about which things are wrong-enough-to-warrant-fixing. I do feel that the overall review process isn't quite solid enough for me to really endorse the Best Of book as a statement of "The LessWrong Community fully endorses this post", and I think that's a major problem to be fixed for next year. But meanwhile I think it makes more sense to accept that some posts will have flaws.

Zack specifically disavowed this post and the meta-honesty response, so I think it makes most sense to concentrate on Where To Draw The Boundaries and Heads I Win, Tails Never Heard Of Her

Ahh, I didn't realize that, definitely would not have reviewed this post if I realized this was the case.

But my own voting algorithm for those posts will personally be asking "does this single post have a high overall mix of 'true' and 'important'?"

Yeah I think this is reasonable. I'm worried about thinks that are wrong is subtle non-obvious ways with certain frames or as... (read more)

Related and required reading in life (ANOIEAEIB): The Copenhagen Interpretation of Ethics

Epistemic Status: Trying to be minimally judgmental

Spoiler Alert: Contains minor mostly harmless spoiler for The Good Place, which is the best show currently on television.

The Copenhagen Interpretation of Ethics (in parallel with the similarly named one in physics) is as follows:

The Copenhagen Interpretation of Ethics says that when you observe or interact with a problem in any way, you can be blamed for it. At the very least, you are to blame for not doing more. Even if you don’t make the problem worse, even if you make it slightly better, the ethical burden of the problem falls on you as soon as you observe it. In particular, if you interact with a problem and benefit from it, you

...

I really like this post. I think it points out an important problem with intuitive credit-assignment algorithms which people often use. The incentive toward inaction is a real problem which is often encountered in practice. While I was somewhat aware of the problem before, this post explains it well.

I also think this post is wrong, in a significant way: asymmetric justice is not always a problem and is sometimes exactly what you want. in particular, it's how you want a justice system (in the sense of police, judges, etc) to work.

The book Law's Order explai... (read more)

A few years ago, the rationalsphere was small, and it was hard to get funding to run even one organization. Spinning up a second one with the same focus area might have risked killing the first one.

By now, I think we have the capacity (financial, coordinational and human-talent-wise) that that's less of a risk. Meanwhile, I think there are a number of benefits to having more, better, friendly competition.

## Reasons competition seems good

Diversity of worldviews is better.

Two research orgs might develop different schools of thought that lead to different insights. This can lead to more ideas as well as avoiding the tail risks of bias and groupthink.

Easier criticism.

When there's only one org doing A Thing, criticizing that org feels sort of like criticizing That Thing. And...

2Raemon7dI ended up chatting with Habryka (who had originally inspired this post, and now wasn't sure he agreed with it). One key additional point here is "gee, doing anything at all is really goddamn hard, and you might not want people to feel any additional disincentive from doing anything, including building monopolies." There's the frustrating "consider reversing all advice you hear [https://slatestarcodex.com/2014/03/24/should-you-reverse-any-advice-you-hear/], because you maybe filter yourself to hear advice that reinforces your own biases" thingy. I think I endorse the specific phrasings used in this post (which I think were properly caveated). But, I wouldn't want the takeaway to be people being too overly worried about ensuring they have competitors when they themselves haven't gotten off the ground. There's an additional confusing issue where... 1. it's really bad if a mediocre organization is a monopoly, or if organizations stretch beyond their capacity. 2. it... actually can be good if a highly competent organization does a lot of vertical integration. And the problem is that figuring out "am I competent or not?" is one off the hardest things you can try to figure out.

Note: I don't think objectively figuring out "am I competent or not?" is that hard of a question. It's just one that the people who are incompetent will very likely get wrong in a highly predictable direction, so building norms that start with "if you think you are competent do X, if you don't do Y" are hard to make work.

Followup/distillation/alternate-take on Duncan Sabien's Dragon Army Retrospective and Open Problems in Group Rationality.

There's a particular failure mode I've witnessed, and fallen into myself:

I see a problem. I see, what seems to me, to be an obvious solution to the problem. If only everyone Took Action X, we could Fix Problem Z. So I start X-ing, and maybe talking about how other people should start X-ing. Action X takes some effort on my part but it's obviously worth it.

And yet... nobody does. Or not enough people do. And a few months later, here I'm still taking Action X and feeling burned and frustrated.

Or –

– the problem is that everyone is taking Action Y, which directly causes Problem Z. If only everyone would stop Y-ing, Problem Z would go...

Self Review.

I still endorse the broad thrusts of this post. But I think it should change at least somewhat. I'm not sure how extensively, but here are some considerations

Clearer distinctions between Prisoner's Dilemma and Stag Hunts

I should be more clear about what the game theoretical distinctions I'm actually making between Prisoners Dilemma and Stag Hunt. I think Rob Bensinger rightly criticized the current wording, which equivocates between "stag hunting is meaningfully different" and "'hunting rabbit' has nicer aesthetic properties than 'defect'".&nbs... (read more)

This post grew out of a conversation with Laurent Orseau; we were initially going to write a paper for a consciousness/philosophy journal of some sort, but that now seems unlikely, so I thought I'd post the key ideas here.

A summary of this post can be found here - it even has some diagrams.

The central idea is that thinking in terms of AI or similar artificial agent, we can get some interesting solutions to old philosophical problems, such as the Mary's room/knowledge problem. In essence, simple agents exhibit similar features to Mary in the thought experiments, so (most) explanations of Mary's experience must also apply to simple artificial agents.

To summarise:

• Artificial agents can treat certain inputs as if the input were different from mere information.
• This analogises loosely to how
...
2Stuart_Armstrong9dAdded a summary post here: https://www.lesswrong.com/posts/rmBS5nTJh6pxERWEu/short-summary-of-mairy-s-room [https://www.lesswrong.com/posts/rmBS5nTJh6pxERWEu/short-summary-of-mairy-s-room]
4Chris_Leong9dReviewI've already written a comment with a suggestion that this post needs a summary so that you can benefit from it, even if you don't feel like wading through a bunch of technical material.
4Stuart_Armstrong9dAdded a summary post here: https://www.lesswrong.com/posts/rmBS5nTJh6pxERWEu/short-summary-of-mairy-s-room [https://www.lesswrong.com/posts/rmBS5nTJh6pxERWEu/short-summary-of-mairy-s-room]

Fantastic!

Summary: I think it’s important for surveys about the future of technology or society to check how people's predictions of the future depend on their beliefs about what actions or responsibilities they and others will take on. Moreover, surveys should also help people to calibrate their beliefs about those responsibilities by collecting feedback from the participants about their individual plans. Successive surveys could help improve the groups calibration as people update their responsibilities upon hearing from each other. Further down, I’ll argue that not doing this — i.e. surveying only for predictions but not responsibilities — might even be actively harmful.

### An example

Here's an example of the type of survey question combination I'm advocating for, in the case of a survey to AI researchers about...

I agree it would be good to add a note about push polling, but it's also good to note that the absence of information is itself a choice! The most spare possible survey is not necessarily the most informative. The question of what is a neutral framing is a tricky one, and a question about the future that deliberate does not draw attention to responsibilities is not necessarily less push-poll-y than one that does.

I’ve recently been spending some time thinking about the rationality mistakes I’ve made in the past. Here’s an interesting one: I think I have historically been too hasty to go from “other people seem very wrong on this topic” to “I am right on this topic”.

Throughout my life, I’ve often thought that other people had beliefs that were really repugnant and stupid. Now that I am older and wiser, I still think I was correct to think that these ideas were repugnant and stupid. Overall I was probably slightly insufficiently dismissive of things like the opinions of apparent domain experts and the opinions of people who seemed smart whose arguments I couldn’t really follow. I also overrated conventional wisdom about factual claims about how the world worked,

...

One good idea to take out of this is that other people's ability to articulate their reasons for their belief can be weak—weak enough that it can distract from the strength of evidence for the actual belief. (More people can catch a ball than explain why it follows the arc that it does).

This post covers the set-up and results from our exploration in amplifying generalist research using predictions, in detail. It is accompanied by a second post with a high-level description of the results, and more detailed models of impact and challenges. For an introduction to the project, see that post.

___

The rest of this post is structured as follows.

First, we cover the basic set-up of the exploration.

Second, we share some results, in particular focusing on the accuracy and cost-effectiveness of this method of doing research.

Third, we briefly go through some perspectives on what we were trying to accomplish and why that might be impactful, as well as challenges with this approach. These are covered more in-depth in a separate post.

Overall, we are very interested...

2Raemon11dIt's unclear to me whether I should think of the forecasters as more replaceable than Elizabeth. If they're all generalist researchers, having "a bunch of generalist researchers do generalist research for the same amount of time as the original researcher" doesn't seem obviously scalable. (That said, my current belief is that this work was pretty interesting and important overall)

The forecasters were only quite loosely selected for "some forecasting experience". Some of them I know are very able forecasters, others are people much less experienced, and who I don't think are affiliated that much with the rationality or effective altruism communities.

Previously: More Dakka

Epistemic Status: The Dakka Files

Smartphones are wonderful things.

Get a second one. And get a lot of chargers.

I did this a week ago. My phone (a Google Pixel 2) had some sort of ink leak onto its screen, so I purchased a second one (a Google Pixel 3a) while I attempted to repair the old one. When the repair attempt was successful, but I hadn’t finished transferring some features and data across, I tried carrying around both.

It was clear by the end of the day that the second phone was a huge improvement.

On reflection, this was a basic case of More Dakka. A substantial portion of the people one interacts with worry about running out of phone battery, or running out of phone storage space, or needing to...

Agreeing that just the final paragraph would be a good idea to include; otherwise, I don't think this passes my bar for "worth including as best-of."

6Gunnar_Zarncke9dI just saw this in the 2019 review and was surprised I didn't see it earlier. I'm using two phones for a while now and it just have been standard advice for executives for ages (2014?). Just google "executive two phones".
4Raemon9dThe first google result is called "most executives agree: one phone is enough" (but, has a list of testimonials where are least some do advocate two phones for the reasons Zvi describes) https://www.miamiherald.com/news/business/biz-monday/article34635054.html


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# Using Henderson-Hasselbalch equation, how do you find pH of a solution that is 11.5g HF and 22.5 g NaF in 125 ml of solution?

$p H$ $=$ $p {K}_{a} + {\log}_{10} \left(\frac{\left[{F}^{-}\right]}{\left[H F\right]}\right)$
You can easily work out the concentrations of hydrogen fluoride and its conjugate base with the info given. You will have to find the $p {K}_{a}$ of $H F$.

format: plain


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# Binomial-like summation

This is a bit embarrassing, but I'm struggling to evaluate this sum.

$$\sum_{m=0}^{2k} \frac{x^{m}}{(2k-m)!}$$

The coefficients are nearly the binomial coefficients, but with an $m!$ missing. (The $(2k)!$ could just be added by hand).

Any pointers?

• Have you tried summing backwards, i.e., changing the iterator from m to 2k - n ? – Lucian Oct 24 '16 at 5:02

Consider the series in the following way: \begin{align} \sum_{m=0}^{2k} \frac{x^{m}}{(2k-m)!} &= \frac{x^{0}}{(2k)!} + \cdots + \frac{x^{2k-1}}{1!} + \frac{x^{2k}}{0!} \\ &= \sum_{m=0}^{2k} \frac{x^{2k-m}}{m!} \\ &= x^{2k} \, e_{2k}\left(\frac{1}{x}\right), \end{align} where the $e_{n}(x)$ is the finite exponential functions given by $$e_{n}(x) = \sum_{k=0}^{n} \frac{x^{k}}{k!}.$$
$$\sum_{m=0}^{2k} \frac{x^{m}}{(2k-m)!}=\sum_{m=0}^{2k} \frac{x^{2k-m}}{m!}= e^{\frac{1}{x}} \frac{x^{2 k} }{(2 k)!}\,\Gamma \left(2 k+1,\frac{1}{x}\right)$$


text:
# Reducible and irreducible polynomials.

• Dec 22nd 2012, 03:33 PM
m112358
Reducible and irreducible polynomials.
Hey guys.

Alright. I have this three-part assignment, but im really stuck on the second question. So if you could give me some pointers, it would be nice.

Let $R = F_3 [X]$ (Where the F is the double-stroke F. Didnt know how to do this.)

(i) Show that $X^2+1, X^2+X+1 and X^2+2X+2$ are the only monic irreducible polynomials of degree 2 in R.

I have already solved this question. I just listed all monic polynomials of degree 2 in R, and made a table showing which functions had roots and which where irreducible.

(ii) Show that if a polynomial $f \in R$ of degree 4 or 5 with no roots is reducible, then there is a monic irreducible polynomial of degree 2 dividing $f$

This is the thing I dont know how to prove.
A section of my textbook says that a polynomial ring (in this case $R$) is a unique factorization domain, which means that if $f \in R$ isn't irreducible, there is a factorization $f = f_1 f_2$ such that $0 < deg(f_1) , deg(f_2) < deg(f)$ and $deg(f) = deg(f_1) + deg(f_2)$.
I also have a part that says that if $R$ is a domain (which I believe is the case here), we have that $V(fg) = V(f) \cup V(g)$ where $V(x)$ is defined as the set of roots of $x$.
So we can say, that there exists $f_1$ and $f_2$, where both have no roots.
I have a feeling, that's the way I'm supposed to go, but I can't quite figure out how to tie it all together. So if someone could give me a hint, or tell me if im going the wrong way?

/Morten
• Dec 22nd 2012, 04:05 PM
jakncoke
Re: Reducible and irreducible polynomials.

Now say we have a polynomial P(x) such that deg(P(x)) = 4.
Now if P(x) is reducible then there are f(x),g(x) $\in F[X]$ such P(x) = f(x)g(x).
Now i say that Deg(f(x)) = Deg(g(x)) = 2 (Why? I'll let you take a moment to think about this, do ask if you want to know why.)

So since a quadratic is reducible iff it has roots in the underlying field.
This would mean, if f(x) was reducible, then $\exists a \in F$ such that $f(a) = 0$, which would mean f(a)g(a) = P(a) = 0, since P has no roots in $F$, this cannot be and f(x) is irreducible. Same thing for g(x). So P(x) = f(x)g(x) where f,g are irreducible, f is deg 2 (The monic part is easy, just divide out by the leading coeff of f(x) or g(x).

Now for Deg(P(x)) = 5, It is the same, if P(x) = f(x)g(x) then Deg(f(x)) = 3 and Deg(g(x)) = 2, or Deg(f(x)) = 2 and Deg(g(x) = 3 (Again why?). For brevity Say Deg(f(x)) = 3, Deg(g(x))=2, Now, again using the same thing, g(x) reduces iff roots exist and if roots existed, then P(x) would also have roots, which cannot be so, g(x) is irreducible,
P(x) = f(x)g(x).
• Dec 22nd 2012, 04:15 PM
m112358
Re: Reducible and irreducible polynomials.
Thanks for the help.
Why do you say the monic part is simple?
If I say $a_2 X^2 + a_1 X + a_0 = a_2(X^2 + a_1/a_2 X + a_0/a_2)$ how can I be sure that $a_1/a_2 \in Z$ and $a_0/a_2 \in Z$?
Thats only valid if $a_2$ divides $a_1$ and $a_0$.
Or have a misunderstood what kind of elements are inside $F_3$?
• Dec 22nd 2012, 04:25 PM
ILikeSerena
Re: Reducible and irreducible polynomials.
Hi m112358! ;)

$F_3$ or $\mathbb{F}_3$ or $\mathbb{Z}/3 \mathbb{Z}$ is the field of the set {0,1,2} with the operations $+$ and $\times$ modulo 3.

Since the calculations are modulo 3, every division is well defined, except divisions by 0.

Btw, to get the black board F, use \mathbb{F}.
• Dec 22nd 2012, 04:30 PM
m112358
Re: Reducible and irreducible polynomials.
Arh... So $1/2 \equiv 1/(-1) = -1 \equiv 2$ because it's modulo.

Now I understand everything, thanks both of you :) Felt a bit stupid on the last bit there.

/Morten
• Dec 22nd 2012, 04:35 PM
jakncoke
Re: Reducible and irreducible polynomials.
Yes, Since the leading coefficient if its not 1, is certainly not 0, you divide by non zero element of $F$, since a field has units, division is possible.
• Dec 22nd 2012, 05:38 PM
m112358
Re: Reducible and irreducible polynomials.
Alright. I dont know if I should put this question in its own forum post, but now I just add it here, because it's related to the other questions.

As you might have noticed, I mentioned that it was a three-part problem.
I've been looking at the third part, but I'm getting stuck here as well.

(iii) Show that $X^5 - X + 1$ is an irreducible polynomial in $R$ and that $L = R/$ is a field with 243 elements. Let $\alpha = [X]$. Find an element $\gamma \in L$ such that $\alpha \gamma = 1$ in $L$.

Alright. I've looked at it a bit. First I'm looking at the irreducability of $X^5 - X + 1$. I have a proposition that says "The ideal $$ is a maximal ideal if and only if f is irreducible. In this case the quotient ring $F[X]/$ is a field.".
So I'm guessing that first point on the agenda is proving that $$ is a maximal idea. But when I look through the stuff on maximal ideals in my book, all I find that seems usefull is "An ideal $I \in R$ is maximal if and only if $R/I$ is a field." But I have absolutely no idea on how to prove that $R/I$ is a field.
I'm guessing that I have to show, that if we assume there is an ideal $J$ where $I = $ and $I \subset J$ implies that $J = R$. So if we imagine an ideal $J$ that contains $I$ and elements not part of $I$. Then we have to prove that $J = R$. The only way I can think of, is by proving that $1 \in J$.
I just dont know how to do that. Any tips?
• Dec 22nd 2012, 06:04 PM
m112358
Re: Reducible and irreducible polynomials.
I've read some proofs where they do something like this:

Let $I = $. Then we define $J$ as an ideal containing $I$. Choose $m \in J \backslash I$, where $deg(m) = 1$. Then we have that $m$ is not in $I$, so $X^5-X+1$ doesn't divide m, and since $X^5-X+1$ doesnt have any roots, $m$ doesnt divide $X^5-X+1$ and therefore gcd(m, X^5 - X + 1) = 1.
Then according to Euclid there exists $s, t \in \mathbb{Z}, 1 = sm + t(X^5-X+1)$ and then we have that $m \in J \Rightarrow sm \in J$ and $X^5-X+1 \in I \subset J \Rightarrow t(X^5-X+1) \in J$ which together gives us that $1 \in J \Rightarrow J = R$.

Now I'm just thinking, couldn't this be done with every I? Is this really a proper proof that $$ is maximal?
• Dec 22nd 2012, 06:21 PM
m112358
Re: Reducible and irreducible polynomials.
God I'm an idiot. I can use (ii) to show that $X^5 - X + 1$ is irreducible. I guess I'm getting a bit too tired for this. Thanks for the help guys :)

/Morten
• Dec 22nd 2012, 06:33 PM
jakncoke
Re: Reducible and irreducible polynomials.
Quote:

Originally Posted by m112358
God I'm an idiot. I can use (ii) to show that $X^5 - X + 1$ is irreducible. I guess I'm getting a bit too tired for this. Thanks for the help guys :)

/Morten

Not only you, me 2, i just proved that and i compleltely forget about it. t.t
• Dec 23rd 2012, 05:11 AM
Deveno
Re: Reducible and irreducible polynomials.
Quote:

Originally Posted by m112358
Alright. I dont know if I should put this question in its own forum post, but now I just add it here, because it's related to the other questions.

As you might have noticed, I mentioned that it was a three-part problem.
I've been looking at the third part, but I'm getting stuck here as well.

(iii) Show that $X^5 - X + 1$ is an irreducible polynomial in $R$ and that $L = R/$ is a field with 243 elements. Let $\alpha = [X]$. Find an element $\gamma \in L$ such that $\alpha \gamma = 1$ in $L$.

Alright. I've looked at it a bit. First I'm looking at the irreducability of $X^5 - X + 1$. I have a proposition that says "The ideal $$ is a maximal ideal if and only if f is irreducible. In this case the quotient ring $F[X]/$ is a field.".
So I'm guessing that first point on the agenda is proving that $$ is a maximal idea. But when I look through the stuff on maximal ideals in my book, all I find that seems usefull is "An ideal $I \in R$ is maximal if and only if $R/I$ is a field." But I have absolutely no idea on how to prove that $R/I$ is a field.
I'm guessing that I have to show, that if we assume there is an ideal $J$ where $I = $ and $I \subset J$ implies that $J = R$. So if we imagine an ideal $J$ that contains $I$ and elements not part of $I$. Then we have to prove that $J = R$. The only way I can think of, is by proving that $1 \in J$.
I just dont know how to do that. Any tips?

no, the first thing to do is show that f(x) is irreducible. then <f(x)> is maximal. why? because F[x] for any field F is a principal ideal domain (why? because it is a euclidean domain with d(p(x)) = degree of p(x), and all euclidean domains are PIDs).

that is, in F[x], for two ideals I and J, we have I = <p(x)> and J = <q(x)> for some polynomials p and q, so that I is contained in J only if q(x) divides p(x). but if f(x) is irreducible, the only proper factors it has are units, and for any unit u of any ring R, <u> = R, the entire ring. that is irreducible polynomials generate maximal ideals in F[x]. that's why you did parts (i) and (ii) first.

and then, since <f(x)> is maximal, F[x]/<f(x)> is a field. we can just count the cosets to find out out big it is. since deg(x5+x+1) = 5, every coset can be written in the form:

ax4+bx3+cx2+dx+e + <x5+x+1>, and since the difference of any 2 polynomials of degree 4 or less is also a polynomial of degree 4 or less, no two of these cosets can coincide (every element of the ideal generated by f is at least of degree 5). that gives us 3 choices for a, 3 choices for b, 3 choices for c, 3 choices for d, and 3 choices for e, for a total of 35 = 243 elements of F[x]/<f(x)> (243 distinct cosets).

it is common to write the elements of F[x]/<f(x)> by writing x + <f(x)> = a, and considering the evaluation map F[x]-->F(a) (f(x)-->f(a)). this lets us write the elements of F[x]/<f(x)> as "polynomials in a", where we multiply "almost like normal", except for using:

a5 = -a - 1, to keep all our expressions of degree 4 or less.

note that -a5 - a = 1, that is: a(-a4 - 1) = 1, so the inverse of a is evidently -a4 - 1 (or 2a4 + 2, if you prefer, since (mod 3) -1 = 2).
• Dec 10th 2014, 12:40 PM
Yellow1
Re: Reducible and irreducible polynomials.
Hello. Sorry, but I was just wondering… How do you use (ii) to show that X^5-X+1 is irreducible?


text:
Please wait a minute...
 Chin. Phys. B, 2010, Vol. 19(6): 066101    DOI: 10.1088/1674-1056/19/6/066101
 CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next

# Direct transition of potential of water droplets to electric energy using aligned single-walled carbon nanotubes

Zheng Kai-Honga, Hu Li-Juna, Sun Lian-Fenga, Liu Jib, Liu Zhengb
a National Center for Nanoscience and Technology, Beijing 100190, China; b National Center for Nanoscience and Technology, Beijing 100190, China;Graduate School of the Chinese Academy of Sciences, Beijing 100049, China
Abstract  In this paper, we report that an electromotive force (EMF) can be induced in a rope of aligned single-walled carbon nanotubes (SWNTs) when water droplets fall on this rope. The magnitude of this EMF depends sensitively on the slant angle of the SWNTs. Most interestingly, both the magnitude and the direction of the induced EFM can be modulated by applying a current to the SWNTs. The concepts of electrical slip and no-slip are proposed and can be quantitatively described by electrical slip resistance''. This kind of generator does not need any magnet, rotor, {etc} and shows quite a different operating mechanism and design compared with a conventional large scale hydroelectric power generator.
Received:  19 October 2009      Published:  15 June 2010
 PACS: 85.35.Kt (Nanotube devices) 61.48.-c (Structure of fullerenes and related hollow and planar molecular structures) 84.60.-h (Direct energy conversion and storage)
Fund: Project supported by the National Basic Research Program of China (Grant No.~2006CB932402) and the National Natural Science Foundation of China (Grant Nos.~50702015, 10574034, and 10774032).


text:
LATEX-L@LISTSERV.UNI-HEIDELBERG.DE

 Options: Use Forum View Use Monospaced Font Show Text Part by Default Condense Mail Headers Message: [<< First] [< Prev] [Next >] [Last >>] Topic: [<< First] [< Prev] [Next >] [Last >>] Author: [<< First] [< Prev] [Next >] [Last >>]

```Le 29/09/14 à 23h36, Joseph Wright
a écrit :

> Sean has pointed to a similarity to dealing with mandatory arguments at
> a design level. This request seems a little different as l3keys isn't
> meant to be targeting that area. However, there is clearly overlap.

OK.

> At present, key properties mainly apply to individual keys in a 'stand
> alone' sense. This request is different as it's actually about an entire
> set of keys.

No, maybe I was unclear: my question concerned the "requireness" of
a single (or maybe several but treated separately) key property.

> To me, that seems a bit odd: it's pretty rare that buried inside a set
> of optional settings is one or more mandatory ones. There is also the
> question of what 'required' might mean, as
>
>     key = \empty
>
> or similar might well be equally invalid in the real use case but would
> presumably pass such a test.

In the use case I have in mind, `key' would be required and expect an
integer. Would it be missing, an error message would be emitted; would
its value be anything but an integer, an(other) error message would be
emitted.

> What I think we need before we can really comment is some solid proposed
> use cases, showing why the property is needed as opposed to other
> approaches as you outline.

Here is an outline of my use case. I'm working on a class for
a quarterly mathematical journal and I'd like to provide an \issuesetup
document command that lets the secretary specify, for each issue, at
least the (mandatory) number. The issue's month and year are computed
from the number but I'd like to let them be (optionally) specified if,
for any reason, a given issue is not published at time.

OK, this \issuesetup command could (and I started like this) be designed
to have a mandatory argument for the number and an optional argument for
specifying the month and the year in a key-value fashion:

┌────
│ \issuesetup{143}
└────
or:
┌────
│ \issuesetup[month=3]{143}
└────
or:
┌────
│ \issuesetup[month=3,year=2016]{143}
└────

but it is less explicit than:

┌────
│ \issuesetup{number=143}
└────
or:
┌────
│ \issuesetup{month=3,number=143}
└────
or:
┌────
│ \issuesetup{month=3,year=2016,number=143}
└────

OK, I could give a more explicit name: \issuenumber rather than
\issuesetup but:

1. \issuenumber[month=3,year=2016]{143} would look rather strange (has
a "number" an optional "month"?)
2. other properties than just the number (and related month and year)
could be added in the issue setup, hence \issuesetup is a more
appropriate name than \issuenumber.

Thanks.
--
Denis
```


text:
Astronomy Answers: From the Astronomical Dictionary

# Astronomy AnswersFrom the Astronomical Dictionary

$$\def\|{&}$$

The description of the word you requested from the astronomical dictionary is given below.

Tucana

Tucana (Toucan) is a southern constellation, close to the ecliptic, close to the Milky Way. The official abbreviation is Tuc.


text:
# [LON-CAPA-cvs] cvs: doc /help domain.manual.texxml loncom/html/adm/help/tex Domain_Configuration_User_Sessions.tex

raeburn raeburn at source.lon-capa.org
Tue Apr 7 17:16:24 EDT 2015

raeburn		Tue Apr  7 21:16:24 2015 EDT

Modified files:
/loncom/html/adm/help/tex	Domain_Configuration_User_Sessions.tex
/doc/help	domain.manual.texxml
Log:
- Update Domain Coordinator documentation for session hosting/offloading.

Index: loncom/html/adm/help/tex/Domain_Configuration_User_Sessions.tex
diff -u loncom/html/adm/help/tex/Domain_Configuration_User_Sessions.tex:1.2 loncom/html/adm/help/tex/Domain_Configuration_User_Sessions.tex:1.3
--- loncom/html/adm/help/tex/Domain_Configuration_User_Sessions.tex:1.2	Fri Jan 14 00:56:11 2011
+++ loncom/html/adm/help/tex/Domain_Configuration_User_Sessions.tex	Tue Apr  7 21:16:20 2015
@@ -1,4 +1,78 @@
\label{Domain_Configuration_User_Sessions}
+Default domain configurations can be assigned for:
+
+\begin{itemize}
+
+\item Offloading sessions when busy, or prior to maintenance
+
+Starting with LON-CAPA 2.11, as Domain Coordinator you can use the web GUI to
+configure where your servers will offload user sessions (for new log-ins)
+when they are busy, if your server is a member of a cluster of servers.
+
+If you have not yet configured offloading then the least busy of the servers
+listed in /home/httpd/lonTabs/spare.tab on each server will be used, if your server
+is found to be at over 100\% user load or 100\% server load.
+
+The default spare.tab file included with a LON-CAPA release includes four access
+servers in the msu domain, and one access server in the csm domain.
+If your LON-CAPA domain is part of the LON-CAPA network then one of the five servers
+will host offloaded sessions from busy servers in your domain.
+Once offloading has been configured using the GUI, the spare.tab files on your servers
+will no longer be consulted, since offload settings for your domain will now be
+stored centrally in the configuration.db file for your domain.  Changes
+made via the web GUI are propagated immediately to all servers in your domain.
+
+The load limits which are used to compute percentage load are currently set on each
+server when you run UPDATE to install LON-CAPA (or update to a new release).
+The defaults are: Server Load: 2.00; User Load: 0.
+
+These values can also be set by editing the /etc/httpd/conf/loncapa.conf file
+(CentOS, Scientific Linux, RHEL, Fedora) or the /etc/apache2/loncapa.conf file
+(SuSE, SLES, Ubuntu), and setting values for lonLoadLim and/or lonUserLoadLim.
+(Web server reload required after making changes to loncapa.conf).
+
+The percent server load is computed from: 100 * loadavg/lonLoadLim, and
+percent user load is computed from 100 * activeusers/lonUserLoadLim.
+
+If you do not wish to restrict the number of active user sessions on your server
+set the User Load (i.e., lonUserLoadLim) to 0.
+
+The loadavg comes from the one minute average for CPU utiization, i.e., the
+first number in the output from cat /proc/loadavg.
+
+The activeusers total is the number of user session files in
+/home/httpd/lonIDs which have modification times within the last 30 minutes.
+
+The User session hosting/offloading'' option in the domain configuration GUI
+allows you to set where user sessions will be offloaded, separately for each
+server in your domain.  You can designate offload servers as either primary or default.
+Primary servers are considered first when seeking to offload a user session.
+
+Ordinarily, session offloading only occurs when a user first logs in.  However,
+you can also choose to offload all active users from a particular server by
+checking the Switch active users on next access'' checkbox for that server.
+You might use this feature if you wanted to take an access server out of the
+pool of servers in your domain for maintenance (all sessions are switched
+regardless of current load values, with the exception of Domain Coordinators).
+
+Notes:
+\begin{enumerate}
+
+\item
+As this type of offload happens on page load, it requires the user to be
+actively interacting with the system (i.e., the web browser needs to request
+a page).
+
+\item
+Any transactions resulting from the original page request (e.g.,
+grading of a homework submission) will be completed on the server
+before the output containing the server switch function is returned to
+the client.
+
+\end{enumerate}
+
+\item Session Hosting
+
Starting with LON-CAPA 2.10, as Domain Coordinator you can configure a domain
to include constraints on where sessions for users from your domain may be
hosted, and also which other domains may have their users hosted on your
@@ -9,13 +83,13 @@
then options to control user session hosting are unavailable, as they
do not make sense in this context.

-Default domain configurations can be assigned for:
-
\begin{itemize}
\item Hosting of users from other domains.

-  There are two types of setting: Allow all, but exclude specific domains'' or Deny all, but include specific domains''.  In both cases the options are (a) for the setting to be in use, or (b) not be in use (the default).  If in use, then checkboxes can be checked for any internet domains'' for which the constraint is to apply. Internet domains encompass all servers at a particular institution, and also any aliases used on a multiple domain server.  For example, there is a single internet domain for educog.com.  Constraints for that internet domain will apply to all *.educog.com servers, as well as all domains on the multi-domain educog server.  On a multiple domain server, session hosting constraints are defined in a single domain - the default domain included in the loncapa.conf file (e.g., the author'' domain for educog.com'').
+There are two types of setting: Allow all, but exclude specific domains'' or Deny all, but include specific domains''.  In both cases the options are (a) for the setting to be in use, or (b) not be in use (the default).  If in use, then checkboxes can be checked for any internet domains'' for which the constraint is to apply. Internet domains encompass all servers at a particular institution, and also any aliases used on a multiple domain server.  For example, there is a single internet domain for educog.com.  Constraints for that internet domain will apply to all *.educog.com servers, as well as all domains on the multi-domain educog server.  On a multiple domain server, session hosting constraints are defined in a single domain - the default domain included in the loncapa.conf file (e.g., the author'' domain for educog.com'').
\item Hosting domain's own users elsewhere.

-  Again the same two types of setting are available: (a) Allow all, but exclude specific domains'' or (b) Deny all, but include specific domains''.  There is a third type of setting: LON-CAPA version requirement'', which, in common with the other two can be set to be:  in use'', or not in use'' (the default).  This setting can be used to require that sessions for users in your domain are not hosted on LON-CAPA versions which predate a particular selected version.
+Again the same two types of setting are available: (a) Allow all, but exclude specific domains'' or (b) Deny all, but include specific domains''.  There is a third type of setting: LON-CAPA version requirement'', which, in common with the other two can be set to be:  in use'', or not in use'' (the default).  This setting can be used to require that sessions for users in your domain are not hosted on LON-CAPA versions which predate a particular selected version.
+\end{itemize}
+
\end{itemize}
Index: doc/help/domain.manual.texxml
diff -u doc/help/domain.manual.texxml:1.17 doc/help/domain.manual.texxml:1.18
--- doc/help/domain.manual.texxml:1.17	Thu Mar 26 16:05:28 2015
+++ doc/help/domain.manual.texxml	Tue Apr  7 21:16:24 2015
@@ -62,7 +62,7 @@
<subsection name="Access to Server Status Pages">
<file name="Domain_Configuration_Server_Status.tex" />
</subsection>
-        <subsection name="User Session Hosting">
+        <subsection name="User Session Hosting/Offloading">
<file name="Domain_Configuration_User_Sessions.tex" />
</subsection>
<subsection name="Load Balancing with Dedicated LON-CAPA Server">

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text:
# What is BioShell¶

BioShell is a general bioinformatics toolkit, focused on biomolecular structures. It provides:

Command line applications
that have been distributed since the original 1.0 version of the package. Some of them have changed their names (e.g. HCPM has been renamed to clust)
Many (currently over a hundred) small applications
that also serve as integration tests. They come with example input data and expected output
Python library
majority of BioShell classes may be directly used in Python
C++ library
which offers highly optimized implementations of oftenly used BioInformatics algorithms and protocols.

## BioShell functionality¶

BioShell functionality covers file processing such as data filtering and file formats convertion. It handle protein sequences, sequence profiles and alignments. Structures calculations capabilities include superimpositions, crmsd calculations, alignments, Phi/Psi angles and many more.

Since its first publication, BioShell has been providing a small set of command-line programs for easy data manipulation from a UNIX-like terminal or a shell script. The newest release extends this set by over a hundred simple command-line utilities. See examples page to see which program can help you in solving a particular problem.

## BioShell command-line utilities¶

The original BioShell command line utilities are still maintained, although their functionality is a bit redundant with applications released with BioShell 3.0 version. See Programs page for details.

## BioShell tests & examples¶

Since the most recently published version 3.0, BioShell package comes with extensive set of example applications, which have been created to simultaneously reach tree goals:

• to extend the set of BioShell command line tools. Programs with names starting with ap_ are in fact yet another applications. The difference between these test and standard apps is that the latter perform only a single action and their command line is simplified. These programs are integration tests at the same time.
• to provide high quality code snippets that help BioShell users write their own programs. Small programs, that show how to use a particular class or a function, are named ex_*. At the same time they serve as unit tests
• to test the code. Both ex_* and ap_* tests are automatically executed by a test server to ensure the quality and integrity of the package. Input data as well as curated output of these tests is versioned in git repository along the source code.

All the examples are included in respective API documentation pages. Since the test are continuously tested, the serve as a source of validated snippets for creating future programs.

## BioShell library for Python (aka PyBioShell)¶

BioShell distribution provides also bindings to Python scripting language; that is, BioShell is also a versatile library for python scripting. BioShell objects can be imported as any other python modules. Example scripts are also included in the repository.

Precompiled library (a single .so file) for Unix distribitions can be downloaded for the following Python versions. Click on an appropriate link below:

or type this command in your terminal:

curl -O http://bioshell.pl/downloads/bioshell/Python37/pybioshell.so

Remember to add path with pybioshell.so to your PyBioShell script eg.

sys.path.append('/home/username/src.git/bioshell/bin/')

If you really need to compile your own version follow the instructions here

## Previous versions¶

### BioShell versions 1.x¶

The original BioShell package was designed as a suite of programs designed for pre- and post-processing in protein structure modeling protocols. The package has been providing a convenient set of tools for in conversion between various sequence and structure formats. It has been also possible to calculate simple properties of protein conformations. The very first commands (e.g. HCPM for clustering protein structures) were implemented in C, later on the development switched to C++.

### BioShell versions 2.x¶

Around 2006/07 BioShell has been reimplemented in JAVA, designed as a library for scripting languages running on Java Virtual Machine, most notably Python, but also Scala, Ruby, Groovy and many others. Currently the most recent stable release is 2.2. API docs as well as example scripts may be found in documentation. All program from 1.x versions were also ported to JAVA.

## Citations¶

• BioShell - the third version:
Joanna M. Macnar, Natalia A. Szulc, Justyna D. Kryś, Aleksandra E. Badaczewska-Dawid and Dominik Gront “BioShell 3.0: Library for processing structural biology data.” submitted to MDPI Biomolecules


text:
# Is Daryl Jr.'s Birthday Card Hiding Something?

Disclaimer: This puzzle stands alone. No knowledge is needed of or from the linked puzzle below. The link is included only because it is the same character in a similar situation.

Daryl the convict was recently caught trying to send his wife a Valentine's Day card with a hidden message about his planned escape. The lead mail inspector discovered the message, shut down the plan, and returned the card to Daryl.

Although Daryl's latest mail, a birthday card to Daryl Jr., underwent heavy scrutiny by the same mail inspectors, it actually made it through the gauntlet and went out.

Did they miss something? Is Daryl Jr's birthday card hiding something?

On the front of the card was just "Happy 10th Birthday, Son".

And inside of the card:

Daryl Jr.,

I hope you have the best birthday ever. I wish I could be there. I made you a word search because I know you love doing those. Remember the strategy I taught you: left to right, top to bottom. Also, looking for an entire word is difficult, so focus on the first part of each word, and you'll find it!

Love,

ACE
ACRE
AEON
AIM
ANGEL
EACH
EASY
EITHER
ESCORT
ESSAY
IMAGE
JEANS
OCEAN
PEANUT
SEEK
SEIZE
TEACH
TEAM
TEETH
TOOTH
WONDER

Text version of word search above:

R   O   J   S   L   I   F   T   N   B   T   W
O   C   E   F   S   U   A   E   R   D   O   H
D   E   S   S   A   Y   E   A   I   N   S   C
K   A   I   M   E   O   O   M   D   P   E   A
U   N   L   E   C   T   N   E   E   T   I   E
O   I   Z   R   A   E   R   A   I   H   Z   T
B   C   N   J   S   C   N   H   T   A   E   I
H   T   S   C   E   U   H   O   H   N   D   T
I   E   O   W   T   A   O   D   E   G   E   E
D   R   R   H   I   T   N   Y   R   E   L   A
T   L   O   C   V   N   O   S   T   L   F   S
U   T   E   G   A   M   I   H   G   R   P   Y

EDIT: 9-11-2022
Just now realizing that EACH is contained in TEACH, I am adding in a restriction for the word search: A word cannot be fully contained in another word. Therefore, the EACH that is not in TEACH is the correct EACH.

The grid is not a ruse. It is needed. The front of the card and 1st 3 sentences on the inside are just flavor text/fluff. Once you find the word property, it will lead to the answer. It is a simple and cool property which I do not remember ever having seen used, but I'm sure it has been used by someone, somewhere.

• Please leave feedback in the comments. What is the issue with this puzzle? Can I make it more enjoyable or interesting? Is it difficult to know where to start?
– JLee
Sep 10 at 13:45
• It's not that the puzzle isn't interesting or intriguing. (Unless the headline follows Betteridge's law, but then it wouldn't be much of a puzzle.) But I'm stuck and no conspirative messages about files in bread loaves have turned up. Sep 11 at 7:32
• rot13(Pyrneyl, gur uvag va gur yrggre nobhg tbvat sebz yrsg gb evtug naq gbc gb obggbz naq nobhg sbphfvat ba gur jbeqf' ortvaavatf vf vzcbegnag, ohg V qba'g frr ubj. (Gur ntr bs zl fba, gra, zvtug or vzcbegnag, gbb.) Gur jbeqf va gur tevq ner va nyy rvtug qverpgvbaf naq gurer vfa'g nalguvat arne gurve urnqf va gur tevq. Gur urnqf naq gur yrsgbire yrggref qba'g fcryy nalguvat.) ... Sep 11 at 7:33
• ... rot13(V gubhtug nobhg ybbxvat ng gur yrggref orsber gur jbeqf, ohg fbzr bs gur jbeqf fgneg ng gur znetva. V unira'g sbhaq n pbzzba cebcregl bs gur jbeqf, rvgure. Creuncf bar pna rkgraq be punatr gur "urnqf" gb trg bgure jbeqf, ohg lbh pna'g qb gung jvgu BPRNA be VZNTR. Gur pubvpr bs jbeqf vf n ovg fgenatr: GRNPU pbagnvaf RNPU, naq GRRGU/GBBGU naq NPR/NPER ner gbb fvzvyne. V'z abg fher gur tevq vf arrqrq ng nyy; vg zvtug whfg or n ehfr sbe gur jneqraf.) Sep 11 at 7:33
• @MOehm Thx for the feedback. All your ideas are good and generally on the right track. Definitely not Betteridge's Law, lest I be booed off stage! In considering your comments, I just now realized that "each" is also in "teach", meaning that there are 2 instances of each, which was not intended. I will add this fact into the puzzle by adding the restriction that a word cannot be fully contained in another word. The grid is not a ruse. It is needed. The front of the card and 1st 3 sentences on the inside are just flavor text/fluff. I will add all this into the puzzle also.
– JLee
Sep 11 at 9:07

Following from Stiv's solved wordsearch...

The beginning sound of each word is either the name of a letter or a number. For example, "OCEAN" begins with an "OH" sound, giving O, "ESSAY" begins with an "ESS" sound, giving S, and "TOOTH" begins with a "TWO" sound, giving 2.

We can then order by the position of the first letter of each word within the grid, in reading order per the letter, to get the message OCT 1 ESCAPE EAST GATE 2 AM.

• Ah, now it all makes sense :) Well spotted...
– Stiv
Sep 11 at 15:29
• Is there somewhere that M is pronounced Im or was that to make it harder? That made me rule out the mechanism. Nice puzzle!
– Amoz
Sep 11 at 16:30
• It's all rather obvious now. I wondered why so many words begin with a vowel and had similar beginnings, but couldn't see why. Sep 11 at 16:45
• @Amoz I ruled this out too, because of 'WONDER' and 'TOOTH', totally failing to see that they had their own slightly different significance...
– Stiv
Sep 11 at 21:09

A community wiki answer to share the solution of the wordsearch, initial letters circled:

Shared in the hope this might help others spot the word property and next steps...

• thx @Stiv. The word property exists apart from the word search, but both are needed to find the solution.
– JLee
Sep 11 at 14:56
• @JLee Having posted this, I've suddenly had an idea myself that I'm now working through to see if it goes anywhere! EDIT: Yeah, that didn't work either...
– Stiv
Sep 11 at 14:57
• To save you time, if it is not simple, it's probably not it.
– JLee
Sep 11 at 14:58


text:
### Even Prime Fallacy

The simplest possible Even Prime Fallacy is shown below:
Salviati: Most prime numbers are odd.
Simplicio: Two is even! Your argument completely falls apart.
We may express this idea more formally:
Salviati: p is sometimes true.
Simplicio: Yes, but p is sometimes false! Your argument completely falls apart.
Simplicio has failed to disprove Salviati, not because Simplicio's rebuttal is illogical or irrelevant, but because it is literally the exact same argument as the one Salviati made! "p is sometimes false" is an inevitable logical consequence of "p is sometimes true."
Someone who invokes an even prime fallacy probably thinks of an argument as "words you say in response to words someone else says," rather than as an exercise in logic.


text:
# Determinant from eigenvalues [duplicate]

Is it always true that product of eigenvalues is determinant of a matrix ? what if one of the eigenvalues are same and matrix is not diagonalizable ? Is this statement is still true ?

• Yes, if you count each eigenvalue with suitable multiplicity. – Angina Seng Aug 31 '17 at 8:32
• Do you know what a Jordan form is? – 5xum Aug 31 '17 at 8:37
• More precisely, determinant is the product of all zeroes of the characteristic polynomial, multiplicity included. These are not necessarily eigenvalues, as the underlying field does not have to be algebraically closed. The proof in general uses Vieta's formulas on the zeroes of the characteristic polynomial, not diagonalizing the matrix and then using the fact that the determinant is a similarity invariant (although that proof works for diagonalizable matrices). – mechanodroid Aug 31 '17 at 9:16

$\DeclareMathOperator{\Tr}{Tr}$ The determinant is the product of the zeroes of the characteristic polynomial (counting with their multiplicity), and the trace is their sum, regardless of diagonalizability of the matrix. If the underlying field is algebraically closed (such as $\mathbb{C}$), then those zeroes will exactly be the eigenvalues.

Proof:

Let $k_A$ be the characteristic polynomial $k_A(\lambda)=\det(A-\lambda I)$ of the $n\times n$ matrix $A$. It's expanded form is $k_A(\lambda)=a_n\lambda^n + a_{n-1}\lambda^{n-1} + \cdots + a_1\lambda + a_0$, noting that the degree of the polynomial is $n$ because the determinant is a sum of products of $n$ matrix entries (each entry having at most one $\lambda$).

Observe that $k_A(0) = \det(A)$, so $a_0 = \det(A)$.

Notice that the only way to get the power $\lambda^n$ as a product of $n$ matrix entries, taking exactly one from every row and column, is to choose the entries on the main diagonal: $(a_{11} - \lambda)(a_{22} - \lambda)\cdots (a_{nn} - \lambda)$. This yields $(-1)^n\lambda^n$ when expanded, so $a_n = (-1)^n$.

Now, let's calculate $a_{n-1}$: the power $\lambda^{n-1}$ is yielded also only from the product of main diagonal entries $(a_{11} - \lambda)(a_{22} - \lambda)\cdots (a_{nn} - \lambda)$, when multiplying $n-1$ terms with $-\lambda$, and one $a_{ii}$ term. This is multiplied to $a_{ii}(-1)^{n-1}\lambda^{n-1}$. Doing this for every $i \in \{1, 2, \ldots, n\}$ and summing the results, we get $(a_{11} + a_{22} + \cdots + a_{nn})(-1)^{n-1}\lambda^{n-1} = \Tr(A)(-1)^{n-1}\lambda^{n-1}$, so $a_{n-1} = \Tr(A)(-1)^{n-1}$

So, $k_A(\lambda)=(-1)^n\lambda^n + \Tr(A)(-1)^{n-1}\lambda^{n-1} + \cdots + a_1\lambda + \det(A)$. Let's denote the roots of $k_A$ with $\lambda_1, \ldots, \lambda_n$ (not necessarily distinct).

Now, using Vieta's formulas we have:

$$\lambda_1\lambda_2\cdots\lambda_n = (-1)^n\frac{a_0}{a_n} = \det(A)$$

$$\lambda_1 + \lambda_2 + \cdots + \lambda_n = -\frac{a_{n-1}}{a_n} = \Tr(A)$$

As you probably know, if $A$ is diagonalizable, then we can write:

$$A = P^{-1}\begin{bmatrix} \lambda_1 & 0 & 0 & \ldots & 0 \\ 0 & \lambda_2 & 0 & \ldots & 0 \\ \vdots & \vdots & \vdots & & \vdots \\ 0 & 0 & 0 & \ldots & \lambda_n \\ \end{bmatrix}P$$

for an invertible matrix $P$. Then, using the fact that $\det$ and $\Tr$ are similarity invariants, we get the desired identities.


text:
# +0/1 polnts TanApCalcBr10 6.5.0291FInd the area of the reglon under the graph of fon [a, b]: Kx) - x2 Gx

###### Question:

+0/1 polnts TanApCalcBr10 6.5.0291 FInd the area of the reglon under the graph of fon [a, b]: Kx) - x2 Gx + 11; [-1, 2] 0/1 points Prevlous Answers TanApCalcBr10 6.5.036. Find the average value of the function f over the Interval [5, 8]. f(x) Submit Answer

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# Vol. 19 (2013), no. 2

### The inner structure of the Jacobi-Laurent matrix related to the strong Hamburger moment problem

Mykola E. Dudkin

Methods Funct. Anal. Topology 19 (2013), no. 2, 97-107

The form of the Jacobi type matrix related to the strong Hamburger moment problem is known \cite{N5,BD}, i.e., there are known the zero elements of corresponding matrix. We describe the relations between of non-zero elements of such matrices, i.e., we describe ''the inner structure'' of the Jacobi-Laurent matrices related to the strong Hamburger moment problem.

### An operator approach to Vlasov scaling for some models of spatial ecology

Methods Funct. Anal. Topology 19 (2013), no. 2, 108-126

We consider Vlasov-type scaling for Markov evolution of birth-and-death type in continuum, which is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. The existence of rescaled and limiting evolutions of correlation functions and convergence to the limiting evolution are shown. The obtained results enable us to derive a non-linear Vlasov-type equation for the density of the limiting system.

### Tachyon generalization for Lorentz transforms

Ya. I. Grushka

Methods Funct. Anal. Topology 19 (2013), no. 2, 127-145

In the present paper we construct an expansion of the set of Lorentz transforms, which allows for the velocity of the reference frame to be greater than the speed of light. For maximum generality we investigate this tachyon expansion in the case of Minkowski space time over any real Hilbert space.

### Parabolic problems and interpolation with a function parameter

Methods Funct. Anal. Topology 19 (2013), no. 2, 146-160

We give an application of interpolation with a function parameter to parabolic differential operators. We introduce a refined anisotropic Sobolev scale that consists of some Hilbert function spaces of generalized smoothness. The latter is characterized by a real number and a function varying slowly at infinity in Karamata's sense. This scale is connected with anisotropic Sobolev spaces by means of interpolation with a function parameter. We investigate a general initial--boundary value parabolic problem in the refined Sobolev scale. We prove that the operator corresponding to this problem sets isomorphisms between appropriate spaces pertaining to this scale.

### Remarks on Schrödinger operators with singular matrix potentials

Methods Funct. Anal. Topology 19 (2013), no. 2, 161-167

In this paper, an asymmetric generalization of the Glazman-Povzner-Wienholtz theorem is proved for one-dimensional Schrödinger operators with strongly singular matrix potentials from the space $H_{loc}^{-1}(\mathbb{R}, \mathbb{C}^{m\times m})$. This result is new in the scalar case as well.

### Indefinite moment problem as an abstract interpolation problem

Evgen Neiman

Methods Funct. Anal. Topology 19 (2013), no. 2, 168-186

Indefinite moment problem was considered by M. G. Krein and H. Langer in 1979. In the present paper the general indefinite moment problem is associated with an abstract interpolation problem in generalized Nevanlinna classes. To prove the equivalence of these two problems we investigate the structure of de Branges space $H(m)$ associated with a generalized Nevanlinna function $m$. A general formula for description of the set of solutions of indefinite moment problem is found. It is shown that the Kein-Langer description can be derived from this formula by a special choice of biorthogonal system of polynomials.

### $\ell^{1}$-Munn ideal amenability of certain semigroup algebras

Methods Funct. Anal. Topology 19 (2013), no. 2, 187-190

In this paper we investigate ideal amenability of $\ell^{1}(G_{p})$, where $G_{p}$ is a maximal subgroup of inverse semigroup $S$ with uniformly locally finite idempotent. Also we find some conditions for ideal amenability of Rees matrix semigroup.

### Decomposition of a unitary scalar operator into a product of roots of the identity

D. Yu. Yakymenko

Methods Funct. Anal. Topology 19 (2013), no. 2, 191-196

We prove that for all $m_1,m_2,m_3 \in \mathbb{N},~ \frac{1}{m_1}+\frac{1}{m_2}+\frac{1}{m_3} \leq 1$, every unitary scalar operator $\gamma I$ on a complex infinite-dimensional Hilbert space is a product $\gamma I = U_1 U_2 U_3$ where $U_i$ is a unitary operator such that $U_i^{m_i} = I$.


text:
Geometry: Common Core (15th Edition)

The Pythagorean Theorem says that $(leg_{1}) ^{2}$+$(leg_{2})^{2}$=$hypotenuse^{2}$. This formula is more commonly referred to as $a^{2}$+$b^{2}$=$c^{2}$ The walkway forms the hypotenuse of a right triangle, which is given as 24m. The playground is square, so each side of the right triangle can be represented by x. Substitute x in for a and b and 24 in for c. $a^{2}$+$b^{2}$=$c^{2}$ $x^{2}$+$x^{2}$=$24^{2}$ 2$x^{2}$=576 Divide both sides by 2. $b^{2}$=288 Take the square root of both sides to find the length of the sides of the playground. b=16.970 Round to the nearest meter 17m


text:
# How to simplify and evaluate Integral with lots of DiracDelta dists

I have a question about an Integrals which I can do by hand but I want to implement this Integral in Mathematica. Actually it is the definition of a 2 Particle Phase Space. The Expression is the following:

$$\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\theta (\text{E1}) \theta (\text{E2}) \delta \left(\text{E1}^2-\text{k1}^2-\text{m1}^2\right) \delta \left(\text{E2}^2-\text{k2}^2-\text{m2}^2\right) \delta (-\text{E1}-\text{E2}+\text{Ea}+\text{Eb}) \delta (-\text{k1}-\text{k2}+\text{ka}+\text{kb}) T(\text{E2},\text{k2},\text{E1},\text{k1})d\text{k2}d\text{E2}d\text{k1}d\text{E1}$$

When I try to integrate this with Mathematica it does nothing. (BTW T here is just a function e.g. the matrix element squared).I mean, when I do it by hand I treat e.g. the last delta dist. as a "function" of k1 and replace all the k1s in the other distributions and functions. So I kill step by step most of the deltas, at least two of them. But Mathematica does nothing. Can't Mathematica handle expressions like that? Or do I have to use some tricks? I would be very happy for some help:)

I mean, I know that it could be tricky for Mathematica to treat a specific delta as only a dist dependent on one specific argument for the specific integration.

Cheers,

Marcel

• $\theta$ is HeavisideTheta[]? Jun 18 '15 at 8:58
• yep, sorry. Just copied from mathematica as LaTeX output:) Jun 18 '15 at 9:04
• I have run into this before and decided that the best way was not to use Integrate but my own Head, that behaves like Integrate when the integrand contains no DiracDeltas but does something smarter when it does exist. I think it's just a few simple replacement rules. Sep 16 '15 at 21:37

Delta functions are equivalent to a system of equations. They have several solutions. I am not quite sure, but it seems that it is this that is the reason for Mma doubts.

sl = Solve[{-k1 - k2 + ka + kb == 0, e1^2 - k1^2 - m1^2 == 0,
e2^2 - k2^2 - m2^2 == 0, -e1 - e2 + ea + eb == 0} , {k1, k2, e1,
e2}];

You could help Mma as follows substituting the first and then the second solution:

HeavisideTheta[e1]*HeavisideTheta[e2]*T[e2, k2, e1, k1] /. sl[[1]]

I cannot imagine, however, what you can do with the answer. Have fun!

• This is partly true, but it omits the transformation that needs to be done in order to get rid of the squared integration variables inside the delta functions, which introduces additional denominators.
– Jens
Jul 18 '15 at 17:03

I am sure there are more elegant ways to solve this, but one possibility might be the following module. As noted by Alexei Boulbitch it is necessary to transform the arguments of the delta functions as equations to be solved by Solve. The following implementation includes the necessary jacobian factors and allows in principle to start from the complete integrand. All integrations (which are evaluated through delta functions) are assumed to run from minus to plus infinity. Integration bounds can in principle included through corresponding HeavisideTheta-functions. The current implementation only applies to a scalar integrand (an extension to vector integrals shouldn't be too hard). The result must be then used as further input for Integrate or NIntegrate to evaluate the remaining integrations. Note that the module makes use of the function removeTimes defined at Convert head Times to List

deltaevalv[expr_, intlist_] :=
Module[{tmp, deltaprod, arglist, arglisteq0, jac, resS},
tmp = expr /. delta[a_] :> 1; deltaprod = expr/tmp;
arglist = removeTimes[deltaprod] /. delta[a_] :> a;
jac = Abs[
Det[Table[
D[arglist[[i]], intlist[[j]]], {i, 1,
Dimensions[intlist][[1]]}, {j, 1,
Dimensions[intlist][[1]]}]]]^-1;
arglisteq0 =
Table[arglist[[i]] == 0, {i, 1, Dimensions[intlist][[1]]}];
resS = Solve[arglisteq0, intlist];
Sum[jac *tmp /. resS[[j]], {j, 1, Dimensions[resS][[1]]}]]

The arguments are defined as follows: expr_ denotes the complete integrand which includes delta functions \delta(a) as delta[a] and intlist_ are the variables which should be evaluated through the delta functions. It is implicitly assumed that the number of intlist agrees with the number of delta functions. An example would be

deltaevalv[f[x1] g[x2] h[x3] delta[x1^2 - m12] delta[x2^2 - m22] delta[
x2 + x1 - x3 - 4], {x1, x2, x3}]

which yields the result

(f[-Sqrt[m12]]*g[-Sqrt[m22]]*h[-4 - Sqrt[m12] - Sqrt[m22]])/
(4*Abs[Sqrt[m12]*Sqrt[m22]]) +
(f[Sqrt[m12]]*g[-Sqrt[m22]]*h[-4 + Sqrt[m12] - Sqrt[m22]])/
(4*Abs[Sqrt[m12]*Sqrt[m22]]) +
(f[-Sqrt[m12]]*g[Sqrt[m22]]*h[-4 - Sqrt[m12] + Sqrt[m22]])/
(4*Abs[Sqrt[m12]*Sqrt[m22]]) +
(f[Sqrt[m12]]*g[Sqrt[m22]]*h[-4 + Sqrt[m12] + Sqrt[m22]])/
(4*Abs[Sqrt[m12]*Sqrt[m22]])


text:
## CryptoDB

### Apoorvaa Deshpande

#### Publications

Year
Venue
Title
2019
TCC
In this work, we define and construct fully homomorphic non-interactive zero knowledge (FH-NIZK) and non-interactive witness-indistinguishable (FH-NIWI) proof systems.     We focus on the NP complete language L, where, for a boolean circuit C and a bit b, the pair $(C,b)\in L$ if there exists an input $\mathbf {w}$ such that $C(\mathbf {w})=b$. For this language, we call a non-interactive proof system fully homomorphic if, given instances $(C_i,b_i)\in L$ along with their proofs $\varPi _i$, for $i\in \{1,\ldots ,k\}$, and given any circuit $D:\{0,1\}^k\rightarrow \{0,1\}$, one can efficiently compute a proof $\varPi$ for $(C^*,b)\in L$, where $C^*(\mathbf {w}^{(1)},\ldots ,\mathbf {w}^{(k)})=D(C_1(\mathbf {w}^{(1)}),\ldots ,C_k(\mathbf {w}^{(k)}))$ and $D(b_1,\ldots ,b_k)=b$. The key security property is unlinkability: the resulting proof $\varPi$ is indistinguishable from a fresh proof of the same statement.     Our first result, under the Decision Linear Assumption (DLIN), is an FH-NIZK proof system for L in the common random string model. Our more surprising second result (under a new decisional assumption on groups with bilinear maps) is an FH-NIWI proof system that requires no setup.
2016
EUROCRYPT

#### Coauthors

Prabhanjan Ananth (1)
Yael Tauman Kalai (1)
Venkata Koppula (1)
Anna Lysyanskaya (1)
Brent Waters (1)


text:
# Difference between direct sum and direct product

• I
Hello! I am reading something about applications of group theory in quantum mechanics and I got confused about the difference between direct sum and direct product. In many places I found that they mean the same thing. However, the ways I found them defined in the book I read from, seem to be different, even if they use the same mathematical symbol to represent the 2 of them. I attached the 2 ways they are defined in the book. So according to these definitions, if I understand it right, If A is 2x2 and B is 3x3, the direct sum will be 5x5 and the direct product will be 6x6, which are obviously not the same thing. So, can anyone explain this to me please? Thank you!

#### Attachments

• DirectSum.png
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• DirectProduct.png
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fresh_42
Mentor
What is called a direct product here is misleading. It should better be named what it is: a tensor product.
A direct product and a direct sum are really often the same and are used to emphasize on the underlying structure. With additive structures like vector spaces, rings, algebras and here mappings one usually uses direct sum. On multiplicative structures like groups one may use direct product. The direct product can also be the cartesian product of sets. E.g.: Addition in a vector space ##V## is a function from the direct product ##V \times V## - here the cartesian product of pairs - onto ##V##. And the direct sum ##V \oplus V## is the set of all pairs added: ##V \oplus V = \{ u + v \, | \, u,v \in V\}##

Normally it is clear by the context it is used in.
However, the term direct product for a tensor product - only to distinguish between the direct sum of mappings and the tensor product - is rather unfortunate.

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