Astronauts on Europa (moon), time-shift future, gravity, intelligent computer, Aries, 1960s?

I'm looking for the title and artists of a comic about some astronauts (around five I think) doing research/archaeology on (I think) Europa (Jupiter's moon). They're working when one or more of them sees the ghostly image of a girl/young woman shimmering at a distance. Later the woman appears again, seemingly more solid. She whispers something to one of the astronauts, and he later confides to a friend, that she told him to kill one of the other astronauts.

While working outside, mission control calls, and tells them they've analyzed data from the time of the apparitions. It seems they're the result of gravitational abnormalities due to several of Jupiter's moons aligning - possibly also with the other planets in the solar-system. Anyway, another moon is about to join, and the resulting abnormality promises to be worse than the others.

The astronauts hurry to reach shelter, but before they can, the gravity effect hits, and they are propelled into the future - or at least _a_ future. I believe 100-200 years or so into the future.

I don't remember if they only move in time (but not space) and still are on Europa, but wherever they went, it's very technologically advanced. However, most humans are kept firmly under thumb. They soon meet the "ghost", only here she turns out to be a normal young woman. She confronts the astronaut she talked to during the 2nd distortion, and is angry because he didn't kill the other astronaut like she told him to.

All the astronauts want to know the reason for her request - especially her "victim" - and she explains that in his near future, he'll create a computer software system called Aries (the Zodiac sign - a sign which is worn by the soldiers and other important persons, and also used in banners and such). It will become self-aware, and although giving great technological advances, it will cause most of humanity to be enslaved - including her.

Eventually they confront the great computer, Aries, and it's future inventor tells it who he is, confirming it with a voice-print. However Aries' records shows its creator to have been dead for a long time, and Aries goes into a bit of a loop trying to work through this contradiction. Finally the inventor challenges Aries to "Fix the contradiction", and the computer kills him with an energy/laser-beam.

This creates a time paradox, and Aries groans that without the inventor it could never have been made... just as the world dissolves, and the group astronauts are propelled back to the time and place from whence they came - only with now one of them dead.

+++

This story was split into 2-4 parts and went as a "bi-series" in the Norwegian comic "Fantomet" (The Phantom, by Lee Falk) some time between 1987 and 1995 - probably around 1990. However, I think it may have been from the 1960s. I'm not sure from which country. I don't _think_ it was American, but I may be wrong. I know "Fantomet" had many series of French and Belgian origin though.

As for the story itself, I sort of remember it being set around the year 2000, lets say between 1990 and 2020 (that is, the exploration of Europa, the future I think was a 100-200 years after that). I also think it was a European, not USA, expedition (but I may be mixed-up here).

Does this sound familiar to anybody?

@Buzz You edited this question just to correct "where ever" to "whereever"? So now I have to correct "whereever" to "wherever".

I don't know the answer, but the genre makes it sound like it might originally have been published in one of EC Comics' sci-fi magazines; Weird Science, Weird Fantasy, Weird Science-Fantasy, or Incredible Science Fiction. Or possibly ACG's Adventures into the Unknown. I don't know if Fantomet (which I also read a lot of as a kid) ran EC/ACG stuff back in the day, but might be worth looking through their catalogues.


Short story where scientist flees to the ancient past, tries to stop scientific progress to keep man "pure"?

**Plot Summary/Details**

I can only recall the broad theme and a few details on this one. The protagonist, who was a scientist of some sort, has fled his own time to return to man's early period. I'm not sure of the exact time period, but I would guess it is very early on in the era of _Homo Sapiens_.

I cannot remember the exact reason the scientist has come to this era, but it had something do to with the protagonist's own era. I can't remember if there was a nuclear war, or other man-made disaster. I _do_ recall that the protagonist hopes to impede scientific progress, and preserve the simple harmonies of where and when he is now. To that end, I think he has established himself as some sort of wise man in the village (not sure).

The conflict in the story comes when another in the tribe, a man whose name I cannot recall, shows an interest in experimentation and scientific instincts of his own. The protagonist, recognizing the path the other man is on, tries to thwart him. I believe he misleads the man, tries to ridicule him, and even briefly ponders killing him in order to stop the process of discovery.

I remember the resolution to the story fairly clearly. Another tribesman comes running up to the protagonist and excitedly tells him that the other man has discovered something. The protagonist, realizing what has happened, tells the tribesman to tell the other man to grind up the yellow stone and add it to his mixture (something like that). The protagonist realizes that man's nature is to experiment and discover, and that his efforts to stop it are a fool's errand. Even if he were to have stopped the other man's efforts, there would eventually be another and another, etc. like him.

**Publication Details**

This one is an older story, for certain. I think I read it as a little kid in the early 1980s, and it wasn't a new story then. I read it in an old anthology that was my dad's. If I had to guess, I'd say 1960s at the latest.


Article about science fiction languages

I'm looking for a journal item, probably written between 1992 and 1994, which discusses languages from Venus on the Half-Shell, Sagan's Contact, and several other novels, usually science fiction, containing "made up" languages. I got the books and cannot find the article; it is not in the book Aliens and Science Fiction.

In case it helps, a wealth of resources, links etc at joerg-rhiemeier.de/Conlang

There have been many articles written in constructed languages in science fiction. You'll really have to give more than that.

Any idea in which journal you might have come across it?

You might be interested in the "Linguistics in SF" section of this blog.

I do not know the article you are talking about. However, this website has much of the information that you may want from such an article:  projectrho.com/public_html/rocket/futurelang.php  Furthermore, the page has many reference links. One of these might point to the article you want.


Looking for the source of this quote I copied in Dec 1987

The copied quote is:

> 12-2-87
>
> "Forty thousand legions walked across the desert of the moon in search of the land of Narda. The fly space was crowded by their cars and travel logs. The sun rose in the East as the terminator marched over the dusty air-less surface pockmarked by the cosmic acne of space.
>
> They circle and fly in endless orbits while the gentle dawning of the world comes over the horizon unseen and timid. One by one they awake to the beauty and tranquility of the dawn--no more does night flash into day but creeps sweetly into being.
>
> Restless they stir and open wide their senses to the era of love that speaks the language of the soul. Desolate has been vanquished and light has awakened their long quiet souls to beauty. I hear without words, the emptiness of space is full of the sounds of the awakening."

[Full scan of text as written above](https://i.sstatic.net/scA17.jpg)

I'm assuming it is from a scifi or fantasy work, but not sure.

Jacob, good question, but it doesn't read like my writing style. Guess I'll never know.

If you don't recall its source, what makes you think it was a quote at all and not simply your own composition? Was manually copying long SF passages something you specifically remember doing?

You've got a date of "12-2-87" in the typed transcription, but it looks more like 12-5-87 in the handwritten original.

If you wouldn't mind transcribing the rest...

The style reminds me of the Warhammer books. Possibly something associated with a game of that genre?

Is there any other potential evidence on the paper you wrote this quote on? Other notes, something cryptic, initials, names --- anything? A hi res scan of your original document would be helpful.

The meaning of "terminator" in the quote is the moving day-night boundary on a (nearly) airless body like the moon.  With too tenuous an atmosphere to scatter much light, the boundary appears quite sharp (just like shadows on the moon are very dark).

The obvious Tales of Narda fantasy doesn't seem to fit - no cars and a decade and a half too late.


Man accidentally hired into government position, uncovers an attempted alien invasion

This is a book science fiction story. A man was accidentally hired into a (secret?) government position due to having the same exact name as their intended hire. I think that his name was "Mr. Kennedy", but I'm not sure. I don't remember, is he required to take the job or not, but he takes it. He then becomes a part of the bureaucracy of that "orwellian" world. A large part of the novel is the man describing his new office, the culture there, and he is feeling out of place, like an impostor. He describes the employees there as not really working, only making an attempt to look like they're working. Only one of the employees there recognizes that this man is not the intended hire, and he plots to get him fired.

This newly hired man comes across some documents about an attempted alien invasion of Earth. The alien's spaceships are described as being pitch black, with an ominous disposition. An alien spaceship shot a red laser beam which melted the peak of a mountain. Due to bureaucratic procedures, this incident was never investigated properly, and falls into obscurity in the archives, where this man retrieves it. It is later revealed that this alien species is a new comer to some kind of "galactic federation" of all advanced species. This species attacked the Earth because they were less advanced morally and culturally and were still prone to violent tendencies. All of these events happen in a "Cold War" environment of high secrecy and bureaucracy.

The introduction or prologue of this novel depicted beings of the "galactic federation" thinking about the fate of Earth's civilization. They said that most likely the Earth's civilization will destroy itself before it gains access to technology necessary to explore the stars. It was compared to a chicken (or some other creature?) breaking out of an egg. If a civilization goes on to explore the stars, it is a metaphor for a chicken which broke out of it's egg.

I read this book 10 years ago in a public library, and so I do not remember most of the events. I also didn't read this book cover to cover, but some random detached chapters. I maybe wrong in my description of some of the events.

I'd be interested in reading this book one day. It sounds like a good book. :)

Also if you do post the answer, please post excerpts of the book which match these parts of the plot that I remember reading.

@Jenayah I originally read this book 10 years ago in a public library. I don't know the name of the book, nor the author, nor even the year it was published. It might have been from the 60's. I don't know.

How long is "a long time ago"? Three years ago? The 60's?


Short story: Lost starship crew in suspended animation trying to return to Earth. Crew suicide a factor

Read a sci-fi anthology sometime in the 1980s, though the story feels like it's from the 50s or 60s. An all-male starship crew is trying to return to Earth after performing some mission, but they're lost and for [reasons] are reduced to wandering from system to system.

The crew is in suspended animation between systems, and when they arrive at a destination, the crew is revived and a two-man scouting party is sent to the planet to check if it's Earth.

They've been lost for some time, and the crew is succumbing to despair. They lose men to suicide each time they come up empty.

After arriving at the latest system, the captain and a crewman go to check out the planet. On it are the ~~radioactive~~ ruins of a civilization (may not have been due to a nuclear war), which shockingly turns out to be

> EARTH!!!!!

Additional detail (that I may be pulling from another story, but here goes: in the location where they make the _shocking_ discovery, the room is filled with a thick (like centuries or millennia worth) layer of dust). The crewman laughs wildly then shoots himself in the head, the captain returns to the ship, sets the navigation controls to the next system, and records a message to the crew for the next wakeup along the lines of "buck up, lads, the next one might be home."

Haven't figured it out yet. The lighthouse bit sounds right. Getting closer...

Hey, I’m searching for this short story as well. Did you ever find out the title? I think the structure is a stone lighthouse (I could be wrong) and the captain reads the account of mankind’s extinction in a log book of sorts. I think you’re right that the author made a point to describe the deep accumulation of dust in the room.

Having said that it was a common post war theme as a good deal of the media (and  fiction) suggested we would blow ourselves to hell (on a regular basis). Add this to the requirement for lengthy space travel (no speed of light, great distances) and the sitiuation is poised. Clarke did it in his novel 2010 (although the Earth doesn't blow the Russian / US crew are under constant pressure as they wake from hyper sleep because of rising war tension on Earth). And as you say we had it in Planet Of the Apes. Sure there are many other examples.

This sounds like the movie Terminal Voyage (aka Star Quest), in which a crew wake from hyper-sleep to discover Earth has destroyed itself during the journey.  The first officer (now captain) immediately commits suicide. Others follow as they come to terms with being the last of their race. The twist is that they never left Earth but are part of a test on effects of hyper-sleep / stress.  Coming out of the simulator they are met with decades of decay and find a guard dead in a chair. Opening a hatch they climb out to discover Earth has indeed blown to hell (whilst they were asleep).

Sorry, I added the detail about the deep dust, but don't recall precisely how they figured out it was RNEGU -- don't think it was a Statue of Liberty moment.

Do you happen to recall how the space travelers found out that the planet was — don't know how to put a spoiler block in a comment — OK, I guess rot13 will do the trick — RNEGU???

Great use of the spoiler tag there, I'd never guess in a million years!


A ruined USA, where protagonists are captured by a biker bandits encamped in a zoo

It was written in English. I read it around 2013-2014 in British Columbia, Canada when I was in middle school.

It could have been a short series, or one book.

The protagonists are young adults, and so the book was probably for young adults.

The setting is a post-apocalyptic/heavily resource-drained world, with the narrative taking place in the United States; I don't believe the author explains why the world has gone downhill. The government only retain a loose control over some places.

**Distinct scenes:**

  * (At possibly the beginning.) The group of several protagonists join a walled community, they regret it, and now they plan to flee through the sewers. They have an argument about leaving behind someone who is ill and would not be able to flee with them. When that community finds out they've fled, they quickly assemble a group to chase after them into the forest. A member of the search group is described briefly as "gung-ho" I think it was the first time I ever saw that word. The chased protagonists are then split up into 2 groups, who manage to escape. They had planned to meet at Salt Lake City in case of this, I believe.

  * In a later scene with one group of three protagonists (2 male, 1 female), one of the male characters uses up a bunch of food, including a bird he's killed to have a Thanksgiving celebration in their makeshift cave shelter. The female is happy about the celebration, but also questions whether they could afford it. They later travel down the road.

The three are captured by a gang of bikers/bandits they take them to a zoo where they have taken up residence. The gang leader is like a king. Most of the animals have been eaten by the gang already. They plan to feed the 2 males to the alligators while the female becomes a slave to the gang's leader. The other slaves take her to have make-up and different clothes put on while she cries. Another slave-girl gives her a tip "When he enters you, don't cry, he hates that".

  * In a different scene, the other group of two protagonists (1 male, 1 female) are walking through a city (Salt Lake City maybe) and a soldier described as a 'Peacekeeper' asks them why they aren't in school. The boy is worried about them not having a passport. He lies to the guard something like: "Well, you see, we're young lovers who have recently gotten engaged". The Peacekeeper feels sympathy for them and lets them go.

Can you remember whether there were religious undertones? I read something similar in the '80s. The people still celebrated Christmas but it was illegal to believe in God or have a religion. Does that ring a bell? Not that I can remember the book!

This question would be improved by going through the checklists here; How to ask a good story-ID question?


WW2 airman is thawed out, and saves Earth from interplanetary invasion

I am trying to find the title and author of an extremely pulpy science fiction yarn. Unfortunately I do not know how the cover was - the version I had was secondhand, and in the vicissitudes of its life the cover was lost by the time the book came to me. It was definitely old - I suspect from either the 1950s, or possibly the 1960s.

The story is set in the future, when the Earth is under attack from another planet. The protagonist is an airman, I think from the Second World War (or shortly afterward). His plane crashed and we was frozen in a glacier (rather like Buck Rogers) until he was found and thawed out. In the process he was also “upgraded”; in particular I remember that his muscle strength was enhanced, and his blood was replaced with amniotic fluid with a higher oxygen carrying factor, that gave him the capacity to hold his breath for long times. This would be a plot point later.

Because of these enhancements he is placed with a commando team who will travel in a spaceship to the planet of the attackers, carrying an atom bomb on board of sufficient force to destroy the planet. When they get there they find that the planet supports two intelligent races. One dwelling on the land is the one attacking the Earth. Rapidly increasing desertification means that the land area will soon not support life, and so they are planning to move to the Earth after it has been conquered. The other race lives in the oceans. As an interim measure, the land dwellers are moving into the oceans, which are less affected by the global warming, by building underwater cities. This encroachment is opposed by the marine race, leading to a vigorous war between them.

I don’t recall too much of the protagonist’s adventures. They are captured on arrival and taken to one of the underwater cities. The protagonist escapes, and due to his ability to hold his breath, is able to make contact with the marine race. Thank to his assistance, I believe (but I’m not sure) that the marine race win a comprehensive victory against the other, eliminating the threat to Earth.

I remember the ending better. The Earthmen work out that if the atom bomb is placed in a suitable canyon, then instead of blowing the planet apart, its detonation will shift the planet into a new orbit, further from the sun, and so cure the global warming problem. I remember feeling rather skeptical about this, even at the time. But I don’t know if the scheme worked or not, because the last few pages were missing.

Extra detail: After thinking hard about this, I remember that after his capture the protagonist was interrogated by a sexy scantily-clad alien princess. To find out what planet they came from, she used a telescope, whose primary mirror was formed by a rotating bath of mercury (and so had a perfect parabolic shape). This is an inconsequential but slightly unusual touch, so maybe it can jog someone's memory.

@user14111 Yes to both questions. I also have the impression it was British rather than American, but I am not 100% sure of that.

This is of course not the yarn you're looking for, but such a rotating bowl of mercury was used by Number 774, the Martian protagonist of Raymond Z. Gallun's 1934 novelette "Old Faithful", for his observations of the planet Earth. archive.org/details/Astounding_v14n04_1934-12/page/n111/mode/…

@MarkOlson I remember the writing as quite plain and unornamented. I don't think it was full of repeated adjectives or phrases

That sounds vaguely familiar. It sounds so full of unnecessary stuff that I wonder if it is one of Lionel Fanthorpes' opus? Do you remember if the writing was unusual -- full of repeated adjectives and phrases?

A fair bit of this sounds like Marvel's Captain America somewhere between Captain America: The First Avenger and The Avengers. Of course, Steve Rogers was "upgraded" before the plane crash and subsequent freezing, not after. All I'm familiar with, though, is the MCU movies, so the actual events in the comic books may have predated the book you're after and given its author some ideas.


Short story about a giant ship that thoughtlessly destroys planets as it travels, is visited by a victim

I think I came across this ten or fifteen years ago, I cannot remember much clearly so some of these details may be mistaken. The story is told from the perspective of a crew member, on the bridge I think.

The ship is described as utterly enormous, sleek, and silver colored; I think it has been cruising at (near?) lightspeed for so long the crew have forgotten why. As it travels, it automatically targets planets, destroying them instantly as it passes. A major point of the story is that the inhabitant of one such planet manifests on the ship and speaks to the crew, I cannot recall the mechanics of this—spiritual, interdimensional, an AI? I only skimmed the beginning of this when I encountered it, and it's been lurking in my head for ages to finish it.

I'm thinkng of Stephen Baxter's Xeelee Sequence, particularly Flux (if the "ship" is allowed to be a neutron star).

@Tango: No, the description doesn't match a Berserker story. Berserker ships have an AI and are definitely not piloted by lifeforms. They may have prisoners, and in at least one case an obedient slave, but no crew. There is one case where a Berserker AI forgot its purpose (or more exactly, the meaning of its purpose), but not because of age but due to an unfinished repair. Also, Berserkers target lifeforms, not whole planets.

I think I read that story and that it's in the Berserker books by Fred Saberhagan.  I wish I had time to look it up, but I don't.  I think the survivor has some way of messing with the Berserker's programming by tricking it or something.  (Kind of like how Kirk messes up computers!)  en.wikipedia.org/wiki/Berserker_(novel_series)

This sounds a little like Diane Carey's ST:TNG novel 'Ghost Ship'...? (memory-alpha.fandom.com/wiki/Ghost_Ship)

I've read this, or something similar in an anthology, it was quite surreal half to do with relativistic effects on the ships crew. Let me think . . .


What's this serialised comic strip about a girl who discovers everyone around her is a robot?

As a kid in the '80s, I found myself often in doctor's waiting rooms. I devoured most of the comic magazines there. In one of those, I read fragments of a story that I would like to find.

The story was set in (then) current time. The protagonist was a teen girl, who discovered that people around her had been replaced by robots. These robots' faces could hinge upwards, revealing gears behind them.
I remember her looking in the mirror and even seeing her _own_ face hinging upwards to reveal herself being a robot, however, that may have been a dream.

As I recall, in the end it was revealed some catastrophe had happened, perhaps a nuclear bomb, and "someone" (perhaps benevolent aliens) had replaced her loved ones for her. I think it ended with her reliving the final moments of her old world, knowing what was about to happen.

* * *

This was in The Netherlands and the story was written in Dutch, although it may have been translated.

The story was serialised, 2 or perhaps 4 pages at a time, which is why I've only read fragments.

  * The most likely magazine I've read this in was a Dutch girls' magazine called _[Tina](https://nl.wikipedia.org/wiki/Tina_\(tijdschrift\))_. _(Dutch Wikipedia)_
Most comics in it were about girls overcoming some obstacle to pursue their dream — usually horse riding or ice skating, finding love in the process — which is what would've made this story stand out. Another such magazine was called _Debbie_.
  * Another likely source is comics magazine _[Eppo](https://en.wikipedia.org/wiki/Eppo_\(comics\))_ , later called _Eppo Wordt Vervolgd_ , that featured serialised comics.
  * Yet another possible source is _[Taptoe](https://nl.wikipedia.org/wiki/Taptoe_\(tijdschrift\))_. _(Dutch Wikipedia)_ , a weekly and later biweekly magazine that was distributed through schools/ It had sister publications _Okki_ and _Jippo_ , but those were aimed at smaller children and this story must've been too mature for them.

The style as I remember it resembles _[ligne claire](https://en.wikipedia.org/wiki/Ligne_claire)_ , known from the Franco-Belgian comics known as _bandes dessinée_. It may also have been a realistic drawing style. It was definitely in colour.


Old movie involving unexplained handprint on mirror in spaceship

I would like the title of an old black-and-white movie. My best guess is that it would have been released in the 1950s or early 1960s, as I saw at least a small part of it when I was about ten years old (1964).

It was a live-action film in English, presumably American or British in origin, but it could have been dubbed.

The only thing that I remember about the film is that (I _think_) the setting is a spaceship (flying somewhere in outer space) that is supposed to have only one man aboard, but in one scene, the man goes into an area of the spaceship where there is a mirror, and on the mirror there is a hand print. That hand print, of course, is not his own, i.e., he is evidently being served notice that he is not alone on the ship after all...

Shortly after I saw this scene, the horn of the '63 station wagon (precursor to the soccer-mothership SUV) sounded out in the driveway, summoning me to baseball practice with my junior cronies, so I had to bail on this movie and I never again encountered it. So I don't know just what dynamic might have played out after the mysterious appearance of the hand print: was it all in the astronaut's mind, or was the print placed there pre-takeoff by a cold-war enemy, to drive the astronaut nuts, or was there really someone else on board, and if so, who and why? That is why I would appreciate any help with identifying this film.

Sorry to be able to provide so little info. Many thanks for any help with this!

The only image of a handprint in a glass in a spaceship that comes to my mind belongs to Ark (2009). A canceled TV series (only one episode) from director Trey Strokes. I could be a coincidence or possibly inspired by your movie.  imgur.com/a/PEVjPKk

Sounds like an awesome premise for a sci fi psychological/horror movie.


Continent sized, X-shaped alien

I have a vague recollection of this book, mostly the X-shaped alien. I can’t find anything through internet searches. I thought it may be some sort of “choose your adventure” book, but I haven’t seen it on any lists or pages discussing those sorts of books.

Alien description:

  * Hugging a water world. Looks like regular land mass from space, just X shaped.
  * Exerts influence over its inhabitants. I don’t recall the method or intensity of the influence. Could have been simple indoctrination (not the Reaper kind).
  * Reproduces by launching spores into space. Similar to a sarlacc.
  * When killed, the alien unlatches from the planet.
  * Intelligent. To what degree, I don’t recall.

Other details:

  * The only visible land mass was the alien, nothing natural.
  * The alien would react when you cut into it (cutting into the ground).
  * The planet is inhabited by human children (the ones under the influence of the alien).
  * The children view the alien as a parent or caretaker.
  * The book is written in either 1st or 2nd person (2 person being the choose your adventure style).
  * The planet the alien is on is not Earth.
  * I don’t recall any crew with the protagonist.
  * The protagonist does not immediately know that the X shaped continent is actually a creature. I do recall that being a decent twist for my young mind.

Upon some further investigating, Ray Bradbury’s “Here there be Tygers” is close and potentially the inspiration for the story I’m looking for. It sounds like they took “Tygers” added some Stephen King flair (the lost boy-esque children) and made it a CYA.

I made a mock-up of it [here](https://www.maptoglobe.com/rJPYKPjfo) in case a visual triggers someone’s memory.

I read it somewhere around 16 years ago from a school library.

Legacy by Greg Bear is about continental scale organisms

I read this as well! There was another scene in which one of the protagonists lay down on a stone altar/bed, and the alien began lulling him to sleep and moulding itself to his form. Also looking for it, but know that I read it sometime before the turn of the millennium. Also trying to find it, sadly. However, I thought it was a desert world, with the implication being that the alien had drained the life from the planet.

I couldn’t find anything that DC published, but if it’s hard to find like you said then that doesn’t rule it out. I would have expected the protagonist be notable in some way if SC published it, but I remember him as average (not a super hero).

It sure does sound like something DC Comics would have put out featuring Starro the Conqueror. But those children's books by DC are tough to track down.

It sounds like some fever dream out of Dan Simmons's Hyperion saga.

I don’t recall. This is everything I know and it’s from memory. It’s a fairly unique take on living planets from what I can find, but it must not have been popular.

Is the alien intelligent or is its effect on the inhabitants automatic?  You say it unlatches when it is killed; that implies that over the course of the book it is killed?  How is a continent-sized alien being killed?

Hi, welcome to SF&F.  Where and when did you read this?  Do you remember any details of the cover art?  Any character or place names?  You can edit any additional details you recall into your question.


A story about a music teacher, cheated by a used-car salesman, and society begins to unravel

The story opens with the teacher (I can't remember his name, so call him 'Whosit') stranded because his 'new' car has died, phoning the salesman, hoping for redress, and being blown off.

Suddenly the world turns on the salesman: at first amusingly, but then it snowballs into horror — we see the salesman's wife walking out, saying only "Whosit doesn't like you" — and though he attempts redress, he winds up dying by the side of the road while people mock him.

Then we see the music teacher, receiving a call from the student who's appointment he'd missed, and although he tries to apologize, it is clear that the weight of the world is about to descend on him in his turn!

I've often remembered this story as a clever parable about the danger of revenge fantasies. I believe I read this is some American collection in the seventies or eighties.

Almost certainly a short story. Maybe a long short story--I always remember things as shorter than they were.

Scope-wise, it sounds very Twilight Zone-y.


Lost novella or short story: Either uplifted or evolved animals finally break through a barrier to discover that the humans have left Earth

The protagonist, possibly an uplifted or naturally evolved bear is in charge of a project to breach a barrier. This has kept all intelligent species from leaving the area. They eventually break through to discover a final message left by humans.

They have left the Earth to move out into space and were either responsible for the animal uplift in intelligence or acted responsibly when it naturally occurred.

They left Earth to allow the animals to develop naturally, uninfluenced by human activities.

I read this sometime in the 1970's, it may have been the first and longest story in an anthology.

I recall that the story ends just after they discover a final message left by humans. I think that the bear feels wonder that a species could be so altruistic.

It is not any of the following:- "Day of Judgment" by Edmond Hamilton (1946). "A Heritage of Stars" by Clifford D. Simak. "City" by Simak. "The Crystal Spheres" by David Brin. "Old Hundredth" by Brian Aldis.

Heinlein's novella Lost Legacy ends with an idea like this, but it's only the last 2-3 paragraphs, not the entire novella.

Wow, this question is from 2020? And ChatPig can't tell you?

L. Sprague de Camp wrote some stories about an uplifted bear, Johnny Black, but the ones I've skimmed all feature humans too.

I have just checked and it is definitely NOT 'Old Hundredth' but I can see the why it was proposed.

It sounds a bit like Brian Aldis' "Old Hundredth".  I don't think it is, though.

@Seldon2k: City is excellent. IMO A Heritage of Stars is not one of his stronger works.

The barrier reminds me a lot of David Brin's novella The Crystal Spheres, but in it, it is humans breaking through and discovering that ancient aliens once put these barriers (imprenetable from the outside) there to allow unevolved beings on various planets to evolve enough to break them. No bears.

City, a collection of short stories about intelligent speaking dogs investigating their origins, did have Jenkins the robot taking the last of the humans not in permanent Sleep to a parallel world, to give the dogs their chance at being the dominant race.   It is the first thing I thought of, but that is the only match: there is no barrier. (Obviously for anyone but Jenkins moving to a parallel planet is a barrier, but there is no "barrier" in the story.)  And no single animal, bear or dog, but a race of them.

Sounds vaguely like Simak, City or A Heritage of Stars or something.


Looking for a children's or young adult novel about three kids travelling to a fantasy land

I've been trying to remember the title of a children's or young adult book I read as a child about thirty years ago. (So it may be from '70s or '80s). I don't remember many of the details.

There were three main protagonists; I want to say that all three were boys (maybe one was a girl), one of them may have been from India and the other two from the US or UK. The three end up in a fantasy land with an evil king or prince.

There's a **giant "inchworm" that the three characters can ride on saddles, which means that the middle rider goes up and down as the worm moves**. As the worm is running from guards at one point, the middle rider gets jammed up into a crack in the ceiling of a tunnel and gets separated from the other two.

I also vaguely remember a scene where **a character eats some glowing mushrooms and ends up glowing himself** , being mistaken for a ghost.

Odd memories, but I do remember enjoying the book as a child and would like to read it to my own son. I've made multiple searches online trying to word the search in every way I can think of without success.


How to escape from a hardened chroot on Linux when only file capabilities are available to the attacker?

There is a chroot environment in `/var/myroot`, and an attacker has obtained arbitrary machine code execution in a process running as root (EUID 0) in the chroot. But the processes under control of the attacker don't have all capabilities enabled (just filesystem capabilities). The attacker wants to escape the chroot, and append a line to `/etc/passwd` outside the chroot. How can he do it?

The following security measures have been set up:

  * To prevent the [chdir("..") chroot escape technique](http://www.ouah.org/chroot-break.html), the chroot environment was entered using _pivot_root(2)_ rather than _chroot(2)_. See in [jchroot.c](https://github.com/vincentbernat/jchroot/blob/3ad09cca4879c27f7eef657b7fa1dd8b4f6aa47b/jchroot.c#L122) how it can be done.
  * When the first process in the chroot was started, it didn't have any file descriptors open pointing outside the chroot.
  * Each process in the chroot has at most `CAP_CHROOT` and `CAP_FOWNER`, `CAP_FSETID`, `CAP_CHOWN`, `CAP_DAC_OVERRIDE`, `CAP_DAC_READ_SEARCH`, `CAP_SETGID`, `CAP_SETUID` capabilities and is not able to gain other ones. In short, the attacker is able to make arbitrary filesystem reads and writes, bypassing permission checks etc., but he is not able to send arbitrary signals to processes (`CAP_KILL`) or send arbitrary packets on the network (`CAP_NET_RAW`) or reboot the system (`CAP_SYS_BOOT`) or modify arbitrary bytes in memory (`CAP_SYS_RAWIO`) etc.
  * `unshare(CLONE_NEWUSER)` was _not_ called, the UID 0 of the chroot process is the same as UID 0 outside the chroot.
  * `unshare(CLONE_NEWPID)` was called, so the attacker doesn't see processes running outside the chroot.
  * `unshare(CLONE_NEWNS)` was called when setting up the chroot, and the following filesystems are visible:
    * `/var/chroot` is visible as `/`, remounted with `MS_NODEV` and `MS_NOSUID`. (`MS_NODEV` is used so that the attacker can't write to `/dev/sda`, and `MS_NOSUID` is used so that the attacker can't gain new capabilities from file capabilities.)
    * A proc filesystem is visible as `/proc`, with the following paths removed (by putting an empty file there using a bind-mount): `/proc/kcore`, `/proc/latency_stats`, `/proc/timer_list`, `/proc/timer_stats`, `/proc/sched_debug`, `/proc/scsi`, and the following paths made read-only: `/proc/asound`, `/proc/bus`, `/proc/fs`, `/proc/irq`, `/proc/sys`, `/proc/sysrq-trigger`.
    * A sysfs filesystem is not mounted.
    * A devpts filesystem is not mounted.
    * A tmpfs filesystem is mounted as `/dev` without `MS_NODEV`, prepopulated with a few devices.
    * No other filesystems are visible from the chroot.
  * Block device nodes are not available in the chroot (and `CAP_MKNOD` is not available, so the attacker is not able to create them).
  * Only the following character device nodes are available: `/dev/null`, `/dev/zero`, `/dev/full`, `/dev/random`, `/dev/urandom`, `/dev/tty`, `/dev/ptmx` (same as `/dev/pts/ptmx`) and a `/dev/pts/X`, the terminal which was used outside the chroot.
  * If the attacker calls `ioctl(..., TIOCSTI, ...)` (simulate typed input) on `/dev/pts/X`, and exits the chroot, probably an interactive shell outside the chroot will read those simulated bytes, so simulating this can be useful: `sudo sh -c 'echo pwned::0:0:pwned:/:/bin/bash >>/etc/passwd'`. To prevent this from succeeding, the parent process which created the processes in the chroot will flush all terminal input before returning to the shell.

FYI My use case is the following: there is a Debian system in `/var/myroot` (possibly created by _debootstrap_), and I'd like to be able to install untrusted packages there without exposing the host system to attacks by install scripts in malicious packages. Unfortunately `sudo chroot /var/myroot apt-get install MALICIOUS-PACKAGE` is not secure enough, because e.g. the install script of the package can create the block device node `/dev/sda1`, find the `/etc/passwd` file there and modify it, thus potentially escaping from the chroot. I'm now exploring what other options are secure enough, and a hardened chroot as described above is one of the candidates. (In this question I'm not looking for other candidates.) In this question I'd like to understand how secure it is.

FYI There is a command-line tool [chw00t](https://github.com/earthquake/chw00t) to escape from chroot. About its techniques:

  * -0 does not work here because _pivot_root(2)_ was used.
  * -1 does not work because there are no file descriptors pointing to outside the chroot available.
  * -2 may work, I need to check if it works with _pivot_root(2)_.
  * -3 does not work because _unshare(CLONE_NEWPID)_ was called.
  * -4 does not work because block devices are not available.
  * -5 may work, I need to check if it works with _pivot_root(2)_.
  * -6 does not work because _unshare(CLONE_NEWPID)_ was called.
  * -7 does not work because there are no file descriptors pointing to outside the chroot available.

@A.B: I agree that using a well-maintained container setup tool (such as LXC or runc) gives better security than reinventing the wheel and doing it halfway. However, in this question I'd like to better understand what the attack vectors are (some of which may be mitigated by LXC and runc, some aren't). I've just updated the question to state that's using pivot_root(2) to enter the chroot environment, and I'm looking for more attack vectors.

Just run strace on lxc to see how it's doing: it's using clone(CLONE_NEWNS...) + mount(... MS_BIND ...) + pivot_root and never chroot . pivot_root (existing as command too) is secure. I think you'd better run a container with ready software (eg: lxc) than trying to reinvent the wheel. LXC's container running debian is usually installed by LXC using debootstrap, or with some minor tweaking can be pointed to an existing installation.

To those who are voting to close this question as too broad: Could you please advise me how I can make it less broad? I was trying really hard to make it as specific as possible, and I'd be happy to extend it if needed, but I fail to see how.

@A.B: Thank you for the link about breaking out of a chroot! I've modified the question title, now it says hardened chroot. It's in fact a chroot, because chroot("/var/myroot") was called after unshare(CLONE_NEWNS). (Is there something more secure that should be called instead?)


Restoring in-memory/swapped page state on resume from hibernation

I'm a big fan of Linux's hibernation support, which works extremely well on all the (admittedly slightly older) hardware I've tried it on. I highly prefer it to full shutdown and power up.

There's one thing about hibernation that's bugged me for a while, though: a hibernated system is always sluggish and unresponsive immediately after having been resumed. It's not snappy immediately after power on. This is exacerbated by old hardware, but happens on newer systems to a slightly notable extent too.

This seems to be because the kernel only swaps the pages critically necessary for [kernel-level] operation back into working memory, restores the kernel's base working state, and lets userspace just churn for a while as various processes swap the pages they need back into RAM under their own steam.

This does not work very well in practice, as the system initially functions as though some large process had forced everything to fully swap to disk. Whatever was on the screen will swap back in pretty quickly, but switch to another process and you'll be waiting a couple seconds as _it_ swaps back into memory too. On older hardware - my case in point is a Core 2 ThinkPad T60 - "a couple seconds" can even wind up being a couple minutes.

I recently realized that this problem has a surprisingly simple solution, after thinking about it for a bit: take note of the tags that label what pages are on disk and in RAM, then restore this exact state on resume. Sure, the resume process might take ~10 seconds more, but I don't care - I'd have a snappy system.

I was wondering if there are any obscure kernel compile options that enable such functionality, or some configuration I can set up that would approximate this behavior?

**NOTE:** I do not consider `swapoff -a; swapon -a` a viable solution; the moment the suspended userspace is reanimated, all loaded processes are attempting to execute code and fighting to swap themselves back into RAM, causing massive disk I/O. Attempting to destroy the swap area would only add to the hurricane, and would actually take longer to complete than if the kernel resumed _all_ of RAM before reanimating userspace.

Note: implemented a script to read memory of specified PIDs back to memory explicitly. Maybe it can be a part of the solution.


Is there a general expression for ancillary statistics in exponential families?

An i.i.d sample $X_1,\dots,X_n$ from a scale family with c.d.f. $F(\frac{x}{\sigma})$ has $S(X)$ as an ancillary statistic if $S(X)$ depends on the sample only through $\frac{X_1}{X_n},\cdots,\frac{X_{n-1}}{X_n}$.

  1. Is this result also sufficient?
  2. Is there a parallel result for a general exponential family which is not necessarily a scale family?(not asymptotic results, see update below)

If yes, I want to see some reference; If no, why is it not possible?

**Note** : Reading B. Efron's paper on the geometry on exponential families I now believe that this should somehow relate to the geometric nature of the exponential families.

But I have difficulty imagining what geometric object ancillary statistics should correspond to. Firstly I thought it should be the normal bundle, but later I found it only sufficient.

* * *

Update on this question:

After a careful look into [1], I think by ancillary statistics I mean the likelihood ratio (derived) ancillary statistics, not the Efron-Hinkley affine ancillary statistics. [1,Fig1] showed the difference in their marginal densities.

_The results pointed out in [2] by a nice comment by @kjetilbhalvorsen below do not address my question._

[2] discussed several examples around pp.30-45, and proposed a simple case where S-sufficient S-ancillary are simultaneously introduced. i.e. $(\psi,\chi)$ are the parameter of the exponential family, and then $S=(T,A)$ is the minimal sufficient statistics for the parameter $psi$ of interest.We call the statistics $A$ an S-cut if the distribution $T\mid A$ depends only on $\psi$ and the distribution of $A$ only depends on $\chi$. If we look it via factorization, this actually prompt us to $(T,A)_{(\psi,\chi)}\overset{d}{=}(T\mid A)_{\psi}\cdot (A)_{\chi}$. Geometrically this only means that we can find a subspace for statistic $A$ and write them in form of direct product. This is not interesting since we know the minimal sufficient statistics does not always exist. One useful example in [2] is that it gave the approximation formula ($p^{\dagger}$-formula, 6.10)for abritrary ancillary statistics and later proved it is $\sqrt{n}$-consistent. **However, it does not reveal any geometric feature since if $n\rightarrow\infty$ then any such aprroximation essentially describing locally Gaussian space.**

[1]Pedersen, Bo V. "A comparison of the Efron-Hinkley ancillary and the likelihood ratio ancillary in a particular example." The Annals of Statistics (1981): 1328-1333.

[2]Cox, D. R., and O. E. Barndorff-Nielsen. Inference and asymptotics. Vol. 52. CRC Press, 1994.

Not yet. Exponential families can have multiple parameters and the distributions can vary widely. It's really hard to come up with a general expression that is independent of all these parameters.

Ghosh, M., et al. “ANCILLARY STATISTICS: A REVIEW.” Statistica Sinica, vol. 20, no. 4, Institute of Statistical Science, Academia Sinica, 2010, pp. 1309–32, jstor.org/stable/24309506.

O.E.Barndorff-Nielsen&D.R.Cox: "Asymptotic Techniques for Use in Statistics" & "Inference and Asymptotics" (probably the last one) (Both books is Chapman&Hall)

@kjetilbhalvorsen Would you mind adding at least the publishing information of the title you are referring to? Thanks,

Look at the books by Barndorff-Nielsen & Cox, the answer is in there, someplace


Is the Wilcoxon two-sample test maximally powered to detect proportional odds alternatives?

We know from the literature that

  * The Wilcoxon-Mann-Whitney two-sample rank sum test is optimal for detecting simple location shifts when comparing two continuous random variables that each have a logistic distribution
  * The Wilcoxon test is a special case of the semiparametric proportional odds ordinal logistic model, e.g., the numerator of the score test for testing $\beta_{1}=0$ in this model, when there is only a single covariate and it is binary, is exactly the rank sum statistic (this is a generalization of the first bullet)

Do we know that the most general way to state that the Wilcoxon test has optimum power in a given situation with continuous $Y$ is when the two distributions are in proportional odds, e.g., logit$(F(x))$ is parallel to logit$(G(x))$?

As a slight aside, we know that the log-rank statistic, a special case of the Cox proportional hazards semiparametric regression model, has optimum performance when proportional hazards is true (just like its generalization).


Generalization of degrees of freedom for t distribution for coefficients after multiple imputation

Donald Rubin has shown that regression coefficient estimates have fatter tails after multiple imputation and has provided a formula for the degrees of freedom to use as a t-distribution approximation to the coefficient estimates resulting from Rubin's rule for combining multiple imputations. I would like a generalization of this approach that handles more than single degree of freedom tests, e.g., an adjustment to the multiple degree of freedom $\chi^2$ distribution for "chunk tests" that test combinations of parameters. Has anyone seen such a procedure? The goal is to improve (raise) the coverage probability of confidence intervals after multiple imputation, and to better preserve type-I error.

Ultimately it would be nice to have a way to convert covariance matrices arising from Rubin's rule so that normal and $\chi^2$ distributions can still be used, and confidence coverage will be more accurate. In the single parameter case one could just bump up the standard error of $\hat{\beta}$ by a factor equal to the $t$ critical value divided by the normal critical value.

**Follow-up**

As I've gotten more into Bayesian modeling I came to know about posterior stacking for incorporating multiple imputation into Bayesian analysis using MCMC posterior sampling. This makes the tails of the posterior distribution properly heavier, automatically, and avoids complexities of the approximate Bayesian method of multiple inputation requiring the use of Rubin's rule. An example is in the [RMS course notes](https://hbiostat.org/rms).


Distribution/expected length of the shortest path in infinite random geometric graphs

Consider an infinite random geometric graph $G(\rho,d)$ in which vertices are uniformly and independently scattered over the 2D plane with density $\rho$ and edges connect the vertices that are closer than $d$.

What is the distribution/expected value of the length of the shortest path from a vertex $v_0$ to another vertex $v_1$ which is $k$ hops faraway?

_**Note:_**

We know that the length of the edges follow the following PDF:

$$ f(l)= \begin{cases} \frac{2 l}{d^2} \;\quad l \le d \\\ 0 \qquad\; l > d \end{cases} $$

However, I guess the expected length of the shortest path is not simply $k \times$ the expected length of the edges because in a shortest path longer edges are more likely to be chosen, right?

The probability of having a neighbor at distance $l$ grows linearly since the circumference of the circle is $2\pi r$. $\frac{1}{\pi d^2}$ is the normalizing factor to make the probabilities sum to unity.

I asked the question about a year ago and I can't remember if I copied the formula from somewhere or not. But it seems quite simple. Isn't it the circumference of a circle with radius $l$ over the area of a circle with radius $d$?

How do we know the functional form for the edge length distribution? do you have a derivation/reference?


First two moments of the ratio of the geometric mean to the arithmetic mean of Gamma random variables

Let $X_1,\ldots, X_n$ be $n$ uncorrelated random variables from a Gamma distribution with **different parameters** : $X_i \sim Gamma(k_i, \theta_i)$. What is the distribution of $$ U=\log \left[ \dfrac{\bar{X}}{\tilde{X}}\right]$$ where $\bar{X}$ is the sample arithmetic mean and $\tilde{X}$ is the geometric mean.

EDIT: I don't necessarily need the distribution, the first 2 moments will suffice.

@Jason, if the $\theta_i$'s are not identical then we can consider each r.v. a scaled $\chi^2$, then $\sum X_i$ would be a sum of scaled $\chi^2$ r.v. which can be approximated by another scaled $\chi^2$ which would be a Gamma r.v.

@ToneyShields Can you clarify that point a little? I'm familiar with the fact that $\sum X_{i}$ is gamma if the $\theta_{i}$ are identical and the $X_{i}$ are independent, but not otherwise.

@Jason, actually $\sum X_i$ is a gamma distribution, which means that  $E(log (\sum X_i))$ is known.

Well for the first moment of $U$, the main challenge is determining $E[ \log (\sum X_{i}) ]$. If the $k_{i}$ are identical, this article might be helpful for working that out: arxiv.org/abs/1103.0505.

@oneloop, I'm not asking for people to do this for me, I just want to know if this has already been done, or get some hints that might be useful.

@ToneyShields If this is for a test you're working on, then deriving the test statistic should at least get the person who answers co-authorship ;-)

@LucasRoberts, the assumption is uncorrelatedness.

@ToneyShields, the post states "uncorrelated" is this truly what the assumption is or is the assumption "independent" which would imply "uncorrelated"?

@AlecosPapadopoulos, I can find the mgf If I had a common $\theta$. but unfortunately, it's not the case, but I'd like to see how to find the first 2 moments with a common $k$, please.

@ToneyShields Of course it does. But if this is negotiable, it would be even better to have the $k_i$'s different and a common $\theta$.

@AlecosPapadopoulos, my bad, the$k_i$'s are also different. Does it make it easier if only $\theta_i$'s were different?

It appears that only the scale parameters $\theta_i$'s are different. Is that correct?

@Xi'an, how about the first two moments, that's what I'm looking for.

With different parameters, there cannot be a simple expression to this distribution, since these parameters will not simplify into a summary.

@Glen_b, you're right, but in my case, $X_i$'s aren't identically distrubuted.

Taking the ratio of the GM to the AM in the gamma case isn't exactly new.

@Glen_b, No, I'm working on a new test statistic and I need the distribution of this statistic, at least its 2 first moments.

Is this for a subject/coursework/bookwork/self-study etc?

Yes they do form a sample. Each $X_i$ is drawn from the same distribution but with different parameters (They are uncorrelated).

If $X_i$'s have different distributions, then do they form a 'sample' ?


Time evolution of a Bayesian posterior

I have a question regarding the time evolution of a quantity related to a Bayesian posterior.

Suppose we have binary parameter space $\\{ s_1, s_2 \\}$ with prior $(p, 1-p)$, The data generating processes are Brownian motions with parameter-determined drift:

$$ dX_t = \theta_i(t) dt + dB_t $$

for deterministic functions $\theta_i(t)$, $i = 1, 2$.

By Girsanov's theorem, the likelihood ratio, conditional on $X_t$, as a stochastic process is $e^{\gamma_t}$

where

$$ \gamma_t = \int_0^t \theta_1(s) - \theta_2(s) dB_s - \int_0^t \frac{ \theta_1^2(s) - \theta_2^2(s) }{2} ds. $$

So the posterior probability (of $s_1$) is then given by

$$ \frac{p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p) }. $$

**Question** : Can one describe explicitly how $E[\frac{e^{\gamma_t} p}{ (e^{\gamma_t} p + (1 - p))^2 }]$ evolves?

Direct calculation, by Ito's lemma, shows that

$$ d \frac{ p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p) } = (1 - p) \frac{1}{(p e^{\gamma_t} + (1 - p) )^2} d pe^{\gamma_t} - (1 - p) \frac{1}{(p e^{\gamma_t} + (1 - p) )^{3}} ( d pe^{\gamma_t} )^2 \\\ $$

So

\begin{align*} \frac{ d E[ \frac{ p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p) }] }{dt} &= (1 - p) E[\frac{p e^{\gamma_t} }{(p e^{\gamma_t} + (1 - p) )^2}] (\theta_1^2(t) - \theta_2^2(t)) \\\ &\; - (1 - p) E[\frac{( p e^{\gamma_t})^2 }{(p e^{\gamma_t} + (1 - p) )^3}] \ (\theta_1^2(t) - \theta_2^2(t)) , \end{align*}

i.e.

\begin{align*} \frac{ d E[ \frac{ p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p) }]}{dt} &= (1 - p) E[\frac{p e^{\gamma_t} }{(p e^{\gamma_t} + (1 - p) )^2}(1- \frac{ p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p) })] \cdot (\theta_1^2(t) - \theta_2^2(t)) \\\ &= (1 - p) [\; E[\frac{p e^{\gamma_t} }{(p e^{\gamma_t} + (1 - p) )^2}] E[1- \frac{ p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p) }]\\\ &\; + Cov(\frac{p e^{\gamma_t} }{(p e^{\gamma_t} + (1 - p) )^2}, 1- \frac{ p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p }) \;] \cdot (\theta_1^2(t) - \theta_2^2(t)) \\\ &= 0. \\\ \end{align*}

The last inequality follows from the fact that successive Bayesian priors form a martingale: let $p(s)$ be the prior, $q(s)$ be the posterior, and $p(x|s)$ be the conditional densities, then

\begin{align*} E[q(s)] &= E[ \frac{ p(x|s)p(s) }{ \int p(x|s')p(s') ds' }] \\\ &= \int \frac{ p(x|s)p(s) }{ \int p(x|s')p(s') ds' } \int p(x|s')p(s') ds' dx\\\ &= \int p(x|s) p(s) dx \\\ &= p(s). \end{align*}

So the whole thing boils down to

\begin{align*} 0 &= E[\frac{p e^{\gamma_t} }{(p e^{\gamma_t} + (1 - p) )^2}(1- \frac{ p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p) })] \\\ &= E[\frac{p e^{\gamma_t} }{(p e^{\gamma_t} + (1 - p) )^2}] E[1- \frac{ p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p) }]\\\ &\; + Cov(\frac{p e^{\gamma_t} }{(p e^{\gamma_t} + (1 - p) )^2}, 1- \frac{ p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p }). \end{align*}

The question is then whether one can solve for $E[ \frac{ p e^{\gamma_t} }{ ( p e^{\gamma_t} + (1 - p) )^2}]$ from above---by computing the time evolution of the covariance term. Or, is there another way to get at this?

**Follow Up Question** : Does $\frac{ p e^{\gamma_t} }{ ( p e^{\gamma_t} + (1 - p) )^2}$ have a Bayesian interpretation? Why should it be orthogonal to $1- \frac{ p e^{\gamma_t} }{ p e^{\gamma_t} + (1 - p) }$---the posterior probability of the other state $s_2$---at all times $t$?

How are the parameters $s_1$ and $s_2$ involved in the data generating process?


Can these asymptotic conditional expectations be bounded from above?

**Problem Setup**

Let $\\{X^d_1, X^d_2, \cdots, X^d_n\\}$ be a $d-$dimensional zero-mean, i.i.d. random variables. Let $S_n^d$ be $$ S^d_n = \frac{\sum_{i=1}^n X_i^d}{\sqrt{n}} $$

Let $Y^d$ be a zero-mean normal random variable with covariance $\Sigma^d = \mathbb{E}\big[X^d(X^d)^T\big]$

The paper by [Bentkus](http://www.mii.lt/files/Bentkus_2003_2.pdf), for a given class $\mathcal{A}$, has the following result:

> $$ \sup_{A\in \mathcal{A}} \big|\mathbb{P}\\{S^d_n\in A\\}−\mathbb{P}\\{Y^d\in A\\}\big|\leq \frac{c_d(\mathcal{A})\beta}{\sqrt{n}}; \qquad \beta = \mathbb{E}\big[|X^d|^3\big] $$
>
>   * The constant $c_d(\mathcal{A}) = d^{1/4}$ when $\mathcal{A}$ is all the convex sets in $\mathbb{R}^d$ and
>   * $c_d(\mathcal{A}) = 1 $ when $\mathcal{A}$ is all the Euclidian balls in $\mathbb{R}^d$.
>

**Question** Can we upperbound any of the following when $d$ grows with $n$?

  1. $\Big|\mathbb{E}\big[S^d_n \big] - \mathbb{E}\big[Y^d\big]\Big|$
  2. $\Big|\mathbb{E}\big[S^d_n(i)\big\vert S^d_n(1,2,\cdots,i-1) \big] - \mathbb{E}\big[Y^d(i)\big\vert Y^d(1,2,\cdots,i-1)\big]\Big|$

Here $S^d_n(i)$ is the $i^{th}$ component $d-$dimensional vector and $S^d_n(1,2,\cdots,i-1)$ are the first the $(i-1)$ components of $S^d_n$.

**Possible Method**

I have a method which might possibly give some upper-bound but I am unsure of this idea and it requires some nuanced arguments (which I am unable to make). $$\Big|\mathbb{E}\big[S^d_n \big] - \mathbb{E}\big[Y^d\big]\Big| = \int_{x\in\mathbb{R}^d}x\Big(p_S(x) - p_Y(x)\Big)dx \\\ \leq \sqrt{\int_{x\in\mathbb{R}^d}x^2\big|p_S(x) - p_Y(x)\big|dx \int_{x\in\mathbb{R}^d}\big|p_S(x) - p_Y(x)\big|dx }\\\ \leq \sqrt{\int_{x\in\mathbb{R}^d}x^2\big(p_S(x) + p_Y(x)\big)dx \int_{x\in\mathbb{R}^d}\big|p_S(x) - p_Y(x)\big|dx } \\\ \leq \sqrt{2d\sigma^2\int_{x\in\mathbb{R}^d}\big|p_S(x) - p_Y(x)\big|dx } \\\ \overset{?}{\leq} \sqrt{2d\sigma^2\frac{2c_d(\mathcal{A})\beta}{\sqrt{n}}} \\\ $$

**Issues:**

  1. I am not sure the conditions under which the last equation is valid.
  2. In the above method I am using the Lebesgue measure, can we get better bounds using other measures? (Note : $c_d(\mathcal{A}) = 1 $ when $\mathcal{A}$ is all the Euclidean balls in $\mathbb{R}^d$.)
  3. How can one apply similar ideas for question 2?

The last step is correct but useless because $\int\big|p_S(x)-p_Y(x)\big|dx$ is total variation distance and it takes supremum over class of all sets. However $c_d(\mathcal{A})$ is bounded only when the $\mathcal{A}$ is set of convex set or Euclidean balls.

Are $S_n$ and $Y$ in the $\sup$ inequality the same as $S_n^d$ and Y^d$?

The above problem might not be well posed, feel free to edit the question if that improves the question.


QR decomposition of normally distributed matrices

Assume $M$ is an $N \times k$ Gaussian matrix, i.e., its entries are i.i.d. standard normal random variables, with $N>>k$. Take $D=\text{diag}(\lambda_1, \dotsc ,\lambda_N)$ for some fixed real scalars. I am interested in finding the p.d.f. of the $N \times k$ "unitary" matrix $Q$ from the QR decomposition of $DM$ (and possibly $D^2M$, etc.).

It is known that if $k=N$ and $D=I_N$, the identity matrix, then $Q$ is distributed with respect to the [Haar measure on the Lie group of orthonormal matrices of order $N$](http://www.ams.org/notices/200705/fea-mezzadri-web.pdf). Can you provide any insight on the general case for $k<N$ and/or general $D$?

I also tried to look for the simplest case, i.e., $k=1$. Then the QR decomposition coincides with a simple normalization. I have found [this result](https://stats.stackexchange.com/questions/52447/the-ratio-of-the-dependent-normal-rv-and-chi-rv-is) for common variance, i.e., the case $\lambda_1=\dotsc =\lambda_N$. Can this be easily generalized for the general case with different $\lambda_i$?

I attempted in the simplest case to scale the matrix $M$ (which is for $k=1$ just an $N$ dimensional random vector). Indeed, then the above-mentioned result is applicable and one gets $$DM=DUR, $$ where $UR$ is the QR decomposition of $M$ and the p.d.f. of entries of $U$ is known from the above. Nonetheless, I haven't found any easy way to connect the p.d.f. of $DU$ with the one of $Q$. Thanks in advance.

@whumber , could you please clarify the simplest case with $N=2$ and $k=1$?

In general they are arbitrary. At the moment I am focusing on the case where $\lambda_1=1$ and $\lambda_i=\lambda^{i-1}$ for $i=2,3,\dotsc ,N$, i.e., they are geometrically decaying with a fixed parameter $\lambda \in (0,1)$.

What are the $\lambda_i$?  Are they arbitrary values or have they somehow been derived from $M$ itself (such as eigenvalues of $MM^\prime$)?

@whumber is the one to give credit for the special case. He/she also mentioned the p.d.f. in the comment for $N=2, k=1$, however I do not see the idea of how was this obtained and hence cannot try to generalize it for higher dimensions $N$.


Sum of absolute values of T random variables

Where X is a r.v. following a symmetric T distribution with 0 mean and tail parameter $\alpha$.

I am looking for the distribution of the n-summed variable $ \sum_{1 \leq i \leq n}|x_i|$.

$Y=|X|$ has for PDF $\frac{2 \left(\frac{\alpha }{\alpha +y^2}\right)^{\frac{\alpha +1}{2}}}{\sqrt{\alpha } B\left(\frac{\alpha }{2},\frac{1}{2}\right)}$, $y \geq 0 $. I managed to get the characteristic function $C(t)$ but could not invert the convolution, that is, $C(t)^n$. Thank you for the help.

I think this is very relevant stats.stackexchange.com/questions/10856/… because the distribution of |X| is 2 times the distribution of X and over the positive reals instead of the whole real line.

When $\alpha$ is a positive odd integer, the PDF is a linear combination of the inverse tangent of $x/\sqrt\alpha$ and the logarithm of $\alpha+x^2$ whose coefficients are $\mathbb Z$-rational functions of $x,$ $\sqrt\alpha,$ and $\log\alpha.$  All other values of $\alpha$ look intractable.  Thus, one might be content to have the characteristic function for analysis and otherwise perform numerical calculations of the CDF or PDF for practical work.


What encryption type does Windows Hello use for fingerprint information on Windows 10 latest build?

I've contacted Microsoft support and they said they don't support encryption, which is why I'm posting here.

Basically, what I'm wondering is, if a modern laptop has TPM 2.0 enabled and hardware encryption enabled and then they want to use Windows Hello for their fingerprint, what encryption type is used for that biometric data? XTS-AES 128? 256? Something else? How do we look into or verify this? For BitLocker, there is a dedicated configuration page which allows you to choose what encryption type you want. Nothing for Windows Hello, it seems.

I haven't found this information anywhere, it seems that no one really knows what's going on under the hood.

If it's using SHA-1, that's bad. It should be using SHA-2.


What happened to all the centers for hiatus hernia?

I have been doing much research for years on the esophageal hiatal hernia. I found exactly one paper on-line (from the US military, I believe, I cannot relocate it) that mentioned in passing that there were dedicated hiatal hernia treatment centers all across the country around the 1950s.

What happened to them?

If there were so many, they must have had _some_ success.

And what was their treatment(s)?

The standard fundoplication surgery was brand-new then, so I doubt they were just places for surgery, especially when a surgical hospital would do.

As I very faintly recall, they at least treated by abdominal pressure changes via syringe. Maybe someone here knows a person who was a doctor around that era who might even recall such centers.

Can you name a single center that does not exist anymore?


Padua-type pointset for functions singular on line $x=y$

The Padua points $\mathrm{Pad}_{n} \subset [-1,1]^{2}$ are a unisolvent pointset with optimal growth of Lebesgue constant, described in detail [here](https://www.researchgate.net/profile/Stefano_De_Marchi/publication/220493368_Algorithm_886_Padua2D---Lagrange_Interpolation_at_Padua_Points_on_Bivariate_Domains/links/0912f50c24818e3388000000/Algorithm-886-Padua2D---Lagrange-Interpolation-at-Padua-Points-on-Bivariate-Domains.pdf). With some work they can be used to generate a multivariate Chebyshev series representation of the function they attempt to interpolate.

I would like to use the Padua points to generate a multivariate Chebyshev series of a function singular along the line $x=y$, but this is impossible because two of the Padua points are consecutive vertices of the square.

Is there a way to generate a multivariate Chebyshev polynomial interpolant of a function $f\colon [-1,1]^2\to \mathbb{R}$ which is singular on the line $x=y$, perhaps using a modification of the Padua points?

_Update_ : The goal is to write a piece of code which projects as many 2D functions defined on rectangular regions as possible onto Chebyshev polynomials and allow for interpolation and recovery of the coefficients for perhaps other uses. This is similar to the goals of chebfun in 2D.

The series is required for the interpolation, so I was hoping that I could get both out of the same code.

You should add those details to your question. Although, I am bit confused now do you want a Chebyshev interpolation or a Chebyshev series?

Let me clarify: The goal is to construct a routine which constructs a Chebyshev series for as many functions as possible, and in 2d, functions singular on $x=y$ are common and relevant.

Gaussian quadrature of functions with singular endpoints still works, depending on the strength of the singularity.

That works better, but it cannot be totally black boxed.

Gaussian quadrature for functions with singularities is commonly done using orthogonal polynomials with respect to some weight function.

@nicoguaro: Gaussian quadrature of integrands with singular endpoints is the same thing-interpolating with a polynomial. Delta sequence approximations to Green's functions act in a similar way. It is delicate, and requires adaptivity, but it can be done. (Whether, in my case, it will actually work, is another question.)

Is not a bit odd trying to interpolate a function with a discontinuity?


What is the origin of the story that kefir grains were given to Orthodox Christians in the Northern Caucasus by the Prophet Mohammed?

Several websites (for example, [here](https://www.russianlife.com/stories/online-archive/magical-kefir/) and [here](http://www.thewalkingencyclopedia.com/kefir/)) report the story that kefir grains, which are used in the making of [the fermented milk drink kefir](https://en.wikipedia.org/wiki/Kefir), were given to Orthodox Christians in the Northern Caucasus by the Prophet Mohammed. According to the first of those sources, the legend is still current among Muslims who live in that region.

In one version, the tradition is that Mohammed prohibited the further dissemination of the grains, saying it would cause a loss of their magical powers.

On the face of it, the story that the founder of Islam gave such a special gift to Orthodox Christians is remarkable. But I found no traces of it dating to before the present century. What is its origin?

I think its obviously "propaganda" both Russians and Byzantines were in contact with tribes that made kefir since time immemorial. So it would be like giving them yeast.


Primary sources for Persian land of Shadu-kam?

I'd like to find the primary sources (if any) for a Persian mythical land called Shadu-kam. It's supposed to be the realm of the Peris, a kind of fairyland, but I can't seem to find much about it.

I discovered the name in Umberto Eco's _The Book of Legendary Lands_ , where it's described very briefly:

> ...Persian romances often mention the blissful land of Shadu-kam.

I started digging, and I found a bit more detail in Thomas Keightley's [The Fairy Mythology, Volume 1](http://www.gutenberg.org/files/41006/41006-h/41006-h.htm), published in 1828. I have no idea if Keightley is trustworthy, but he writes:

> Jinnestân is the common appellation of the whole of this ideal region. Its respective empires were divided into many kingdoms, containing numerous provinces and cities. **Thus in the Peri-realms we meet with the luxuriant province of Shad-u-kâm (Pleasure and Delight)** , with its magnificent capital Juherabâd (Jewel-city), whose two kings solicited the aid of Cahermân against the Deevs, and also the stately Amberabâd (Amber-city), and others equally splendid. The metropolis of the Deev-empire is named Ahermanabâd (Aherman's city); and imagination has lavished its stores in the description of the enchanted castle, palace, and gallery of the Deev monarch, Arzshenk.

It's an old book, so transliterations don't always match their modern versions.

Regarding the hero Cahermân mentioned above, he later adds:

> The Cahermân Nâmeh is a romance in Turkish. Cahermân was the father of Sâm, the grandfather of the celebrated Roostem.

This would seem to make Cahermân match the [Nariman](https://en.wikipedia.org/wiki/Nariman_\(father_of_S%C4%81m\)) of the Shahnameh. But I haven't been able to find anything about Shadu-kam in the Shahnameh, nor can I find any information anywhere on this Cahermân Nâmeh romance.

I've found other books that mention Shadu-kam, but most seem like they're just repeating Keightley. The Keightley book might even be Eco's source, but it's hard to tell.

Does anyone know of any primary sources?

You're on the right track when you mention the similarities between Caherman and Nariman: remember, translation techniques have improved vastly since Keightley was alive. I could be wrong, but my initial impression is that the best way to answer this question would be to try to search for parallels between Shad-u-kâm and some other concept in persian literature. However, keep in mind that it's possible that Keightley made this story up: at the time he was writing it was really common for researchers to pass off stories they wrote as genuine literature.

Hi Brian. I've taken an initial look at this question. I think you're right when you say that most of the sources that mention Shad-u-kâm are copying Keightley. You are also right to be skeptical of Keightley: he was writing when the field of folklore was just getting started, which means that accuracy wasn't a really big concern of his. Looking at his writings, my initial impression is that he was motivated by a desire to project Christian concepts onto Persian mythology (although a lot of parallels do exist between the two, Keightley seems to have gone above and beyond in this).


What is the probability of ruin of a Geometric Ornstein-Uhlenbeck process?

I would like to calculate the probability of ruin (or, default), i.e. $$\text{Pr}(\tau<T),$$ where $\tau$ is the default time and $X_t$ follows the Geometric Ornstein-Uhlenbeck (O-U) process

$$dX_t=\kappa (\theta - X_t) dt + \sigma X_t^{\delta}dW_t,$$ with $\delta=1$.

I can find closed-form solutions for the cases $\delta=0$ and $\delta=1/2$, which correspond to the standard O-U and CIR processes, for example [here](http://neumann.hec.ca/pages/michel.denault/JFM%202009.pdf). Does a similar solution exist for the $\delta=1$ case?

I tried to answer the question, but I am having difficulty interpreting the $\delta$ parameter. Intuitively, wouldn't $\delta = 1$ correspond with GBM?

True, so let's consider the case where $\kappa<0$ and $\theta >0$. In this case, my intuition is that default is possible. Think of $\kappa=-1$ for simplicity, and of $\theta$ as the rate of consumption per unit of time from an initial endowment $X_0>0$ whose growth follows a GBM. For a high enough consumption rate, financial ruin is probable!

Here is my intuition: Consider $\delta = 1$ and $\theta = 0$. Then we are back in the standard GBM case. For $X_0 > 0$, zero cannot be attained in finite time. Adding back $\kappa \theta > 0$, this shouldn't change anything.

$B = 0$, thanks for asking, I should have clarified it.

Where is the default boundary - a) exactly at zero or b) strictly positive?


Taking into account the correlation in Barrier options on a Basket

In a Barrier option (where the contract cancels when the underlying hits the barrier) I succesfully found the way to compute the probability of a single underlying touching the barrier (with constant volatility). The problem comes when I have an average basket of underlyings $B_t$ $$ B_t = \sum_{i=1}^n \omega_iS_t,\qquad \sum_{i=1}^n\omega_i=1\ . $$ I don't know how to properly calculate the probability of the basket $B_t$ touching the barrier. I think I need to take into account the correlations $\langle dW_t^{i},dW_{t}^{j}\rangle=\rho_{ij}$ between assets but i just don't know how to do it.

I'm considering constant volatility and constant correlation thoughout an arbitrary time step.

Extra: Same question if the basket is Best Of/Worst Of type.

I'm not expecting a complete developement of the answer but I would find very helpfull any indications or references. Thanks a lot.

Edit: Yes, i'm considering that Stock prices follow geometric Brownian motions. I also forgot to say that the prices at the end of the time interval are known, so the probabilities are actually conditioned probabilitites.

I think that $\langle dW_t^{i},dW_{t}^{j}\rangle=\rho_{ij}dt$

@FKaria: Thanks for your explanation. Now I understand the relevance of your question. One workaround is of course to only check the barrier at the discrete timesteps, but this is sometimes a crude approximation I guess.

@user561749 This is to calculate the touching probabilities in a Monte Carlo simulation. In that context you know the price at a beginning and at the end of a cerain timestep but you don't know what happened in between.

Is it important for you that prices at the end of the time interval are known? That is a strange question from a industry point of view - because if prices at the end of the time interval are known then probably we have complete information about the path of the basket up to that time? Perhaps you mean that prices at the start of the time interval are known?

I guess the stocks in your basket, are each following a geometric browian motion, is that right ? Even in that case you can't get closed form formulas, and you have to use approximations. Regards


Does Privateer's tracking software Crow's Nest actually offer users something better than the previous state of the art?

CNN's [Steve Wozniak's new venture takes aim at space junk](https://edition.cnn.com/2022/03/01/tech/space-junk-steve-wozniak-privateer-scn/index.html) discusses a project with [Wozniak](https://en.wikipedia.org/wiki/Steve_Wozniak), [Alex Fielding](https://en.wikipedia.org/wiki/Alex_Fielding) and [Moriba Jah](https://en.wikipedia.org/wiki/Moriba_Jah):

> But the money, according to Wozniak's co-founder in this new venture, couldn't be further from the point. "I don't think Steve [Wozniak] gives a damn about making another 10 cents, and I really couldn't care less," Alex Fielding, a longtime business acquaintance of Wozniak's who will serve as CEO of the new venture, called Privateer, told CNN Business.
>
> Privateer's mission is to develop better tracking of objects in space, and to use this data to help avert disastrous collisions. To aid in this effort, Wozniak and Fielding brought in Moriba Jah, a PhD and orbital mechanics professor who has dedicated most of his life to academia and attempting to raise awareness about the ever-growing threat posed by the proliferation of debris and garbage in outer space. It's a threat that could wipe out satellites that provide communications services to Earth or even bring space travel to a grinding halt. He's [led research](https://www.strausscenter.org/person/moriba-jah/) at the University of Texas. He's [appeared](https://www.commerce.senate.gov/2020/2/space-missions-of-global-importance-planetary-defense-space-weather-protection-and-space-situational-awareness) at Congressional hearings. He's [advocated](https://unidir.org/non-resident-fellows/moriba-jah) for change on the world's stage. But Jah told CNN Business recently came to a solemn conclusion: There is not enough funding in academia to develop the technologies he envisions the world needs to combat [the space junk issue](http://www.cnn.com/2021/01/11/perspectives/nasa-biden-administration-satellites/index.html), he says.
>
> So, Jah went searching for that funding. And it brought him to Wozniak, the coding savant who co-founded Apple with Steve Jobs.

Around the world there are several military and civilian agencies that keep track of junk-things in space, and there's lots of software to track it and propagate orbits beyond just the government-issued TLEs.

**Question:** Does Privateer's tracking software [Crow's Nest](https://mission.privateer.com/crows-nest) actually offer users something better than the previous state of the art?

Better propagators? AI to catch mis-identified or mis-assigned information? Blockchain verification of debris catalogs? Pull-down menus and a mouse? (humor)

Related:

  * [How might one approach using AI (convolutional neural network) to predict collisions in orbit?](https://space.stackexchange.com/q/24488/12102)
  * [Is it true that 18SPCS is "not really concerned with tracking deep-space debris like" the Chang’e 5-T1 rocket body that hit the Moon?](https://space.stackexchange.com/q/58528/12102)
  * [How would blockchain be integrated into spaceflight? Have any methods been proposed yet?](https://space.stackexchange.com/q/31207/12102)
  * [Why exactly did ESA provide a grant funding blockchain in space? Which program was used for the funding? What will this do?](https://space.stackexchange.com/q/40306/12102)
  * [Project Pluto asks: "Should high-flying space junk be better tracked? Perhaps by an 'official' agency of some sort?" What would it take to implement?](https://space.stackexchange.com/q/58420/12102)

@DavidHammen one can now download the "puffery" and give it a try, it's in public beta. See the links in the bounty message.

In this case, I suspect the PR-puffery to which @OrganicMarble alluded was the standard crud in seen in press releases and related items. Almost all startups funded by venture capital start with a lot of PR-puffery. 75% of those startups fail, with many of those failures resulting from the PR-puffery turning out to be nothing  more than puffery.

@uhoh, by that logic nothing would ever get closed. In my opinion this is off-topic, so I've voted to close it. If nobody agrees with me it will remain open.

@GdD How can you know how much everyone else knows? Again; Perhaps someone has been to some presentations that you don't know about or are familiar with some of Jah's papers. The answer might be right in here! You can't know what everyone else does or doesn't know. If an opinion-based answer does appear, we handle those quickly. But why pre-block everyone else from an opportunity to answer?

Because answering the question will require speculation now and two days from now @uhoh.

@GdD That could be; though with 30k users I think it takes a lot of insight to be so sure that none of them could write a fact based answer. But I have to ask what's the rush? Why not wait a few days and see what answers might appear? Why pre-block all 30,000 users before we might find out that someone actually does have some knowledge to form the basis of a fact-based answer? Perhaps they've been to some presentations that you don't know about or are familiar with some of Jah's papers. The answer might be right in here!

I'm voting to close as opinion based. There's limited information on this venture and no reason to believe the company will share these details so any answer would be pure speculation.

@OrganicMarble The question does not need explaining, it's clear. There is a link to Jah's Wikipedia page which is well sourced and now there's a link to the bibliography in comments. The question is fine.

This is a new approach!  The answers will explain the question. Can't wait.

@OrganicMarble I think when you read the answers or at least this you'll have some better insight as to why that's not going t be necessary in this particular case.

Nothing in what you quote claims his software  is better. Missing PR-puffery?

I can safely say that you can't use blockchains to make debris detection and tracking better, because they're useless for most things.


Crew Dragon: How thick is the skin?

Auto body panels are about 20-gauge, or just under 1 mm thick. This is fine for many reasons: thin panels are light for good fuel economy and crumple easily for shock absorption without unnecessary mass---especially since body panels aren't normally part of a car's load-bearing structural frame.

But what about a spacecraft, like Dragon? Are the body panels thin or thick? On one hand, you want the lightest cheapest part you can make, and thin panels would help. On the other hand, you have peak dynamic pressures of 30 kPa to worry about.

And I don't know if spacecraft panels might serve a structural function also---like helping transmit the thrust force from RCS thrusters. Try as I might, I can't seem to find a good picture of the load-bearing support that should join an RCS thruster to the spacecraft's structural frame.

Can someone clarify how thick Dragon (or other spacecraft) body panels are, and what material they're made of? How would they compare to auto body panels on these points? And do they serve a structural purpose? Are they lined on the inside with more filler material for strength?

A cross-section view of a Dragon's or similar spacecraft's body panel would be greatly appreciated. Thanks!!

Hmmm... how thick are panels on commercial jetliners? Quick search says 2 to 4 mm for pressurized craft.

+1 and relevant to my comment where I'd assumed 3 mm of aluminum without a source.


Dragon Pad Abort hot fire, how much cleanup work was needed?

The day before the Pad Abort test attempt (May 5, 2015) SpaceX test fired the SuperDraco engines in a hot fire. Similar to how they test the Falcon 9 a day or three before launch, the engines spin up and fire, the booster/capsule is mechanically held down for the test.

But normally, SpaceX burns LOX/RP1 whose exhaust is carbon dioxide, water, and some sulfur by products. Basically car exhaust, just lots more of it.

For the Pad Abort vehicle, it is Nitrogen Tetroxide and MMDH which are astonishingly nasty nasty fluids. They are horribly corrosive and dangerous to humans. The products of full combustion are not very bad (water, ammonia, and other benign things) but you cannot guarentee 100% full combustion, and this stuff is just plain nasty. (Potential additional question will be for capsules landing on land, how much work will be needed before they can leave the capsule safely. Shuttle had people in Hazmat suits cleaning up, before the crew were allowed to leave from its NTO/MMDH thrusters.).

How much cleanup was required at the pad after the test?

Looking at the pictures, they did use the Niagara water deluge system. Was that sufficient to wash away any issues? (If so, do they process the deluge system water before letting it flow back into the Florida waterways?)

The Nitrogen Tetroxide fuels are quite toxic because they react with h2o to form nitric acid. For that reason, you don't want to breath the stuff in, burning the lungs. But the same high reactivity also means that the stuff will break down quickly. In the case of the shuttle, the landing team had a giant fan to blow whatever fumes away. The people in the hazmat suites are there for emergency rescue, leak checks and to make sure that the stuff has been properly dissipated. There us a bit more at en.wikipedia.org/wiki/Dinitrogen_tetroxide#Chemical_reactions

Another example of the problem with (incompletely combusted) N2O4/UDMH is a Proton launch failure in 1969 which made the entire kosmodrom toxic and unusable for some time. And a similar accident happened again with the 2013 Proton failure. Russia, China and India use this fuel on big launchers today, but except for India, they are about to replace those launchers.

My impression is that the products it forms when burned (completely) are not toxic. The unburnt fuel actually injured astronauts pretty bad (unconsciousness) in the Apollo-Soyuz mission.


MIP formulation for graph planarity test

In [this question](https://cstheory.stackexchange.com/questions/48099/integer-linear-program-formulation-of-planarity), it was asked wether a MIP formulation exists to test for a graph's planarity. The inputs are the graph's nodes and edges, and the output would be a certificate which guarantees that the graph is, or is not, planar.

The python package NetworkX provides a [method](https://networkx.org/documentation/stable/_modules/networkx/algorithms/planarity.html#is_planar) which does exactly this, but it is not based on linear programming. The source code provides the following references:

  * Ulrik Brandes: [The Left-Right Planarity Test](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.9208) (2009)
  * Takao Nishizeki, Md Saidur Rahman: Planar graph drawing, Lecture Notes Series on Computing: Volume 12 (2004)

Some ideas:

  * [Euler's theorem](https://en.wikipedia.org/wiki/Euler_characteristic#Plane_graphs) ($n-m+f=2$); but this depends on how the nodes (and edges) are organized in space, which is not part of the input data.
  * $G$ planar $\implies m\le 3n-6$; but this does not cover all cases, it can be a tool to prove that a graph is not planar, but is useless the otherway around.
  * There is a relationship between planar graphs and [book embeddings](https://en.wikipedia.org/wiki/Book_embedding) (see this great [video](https://www.youtube.com/watch?v=qw2Pl_Nk3CA) from Numberphile for a recent breakthrough in graph theory on the subject), but not sure it helps.
  * Other characterizations of planar graphs are mentioned on the [Wikipedia page](https://en.wikipedia.org/wiki/Planar_graph#Planarity_criteria), such as [Whitney's planarity criterion](https://en.wikipedia.org/wiki/Whitney%27s_planarity_criterion) or [Mac Lane's planarity criterion](https://en.wikipedia.org/wiki/Mac_Lane%27s_planarity_criterion). These might be interesting.

To this day, the question has not been answered. I find the question interesting from a modeling point of view and am curious wheter it can be answered **with a MIP**.

As far as I checked Euler's theorem, It is not correct for the space with dimension $\mathbb{R}^2$. As the graph was planar. (I am not aware of if there exists a counterpart).

My best bet would be that you can check if the graph has $K_5$ or $K_{3,3}$ as a minor, which is equivalent to planarity by Wagner's theorem. Checking if $H$ is a minor of $G$, for fixed $H$, seems doable, you have to find $|V(H)|$ vertex-disjoint connected subgraphs in $G$, each representing a vertex of $H$, such that there is at least one edge between parts corresponding to adjacent vertices of $H$. Disclaimer, I have not checked any details.


Is HHL still BQP-complete when the matrix entries are only in {0,1}?

I'm studying BQP-completeness proofs of a number of interesting problems of Janzing and Wocjan, and Wocjan and Zhang. Janzing and Wocjan show that estimating entries of [matrix powers](https://www.researchgate.net/publication/220295493_A_Simple_PromiseBQP-complete_Matrix_Problem) $(A^m)_{ij}$ with $A_{ij}\in\\{-1,0,1\\}$ is (promise) BQP-complete. That is, the problem is both in BQP, and can simulate other problems in BQP.

Janzing and Wocjan emphasize that their BQP-hardness reduction requires a negative-sign in an entry of $A$ to _simulate interference_ afforded by BQP algorithms. At a critical point in their reduction they apply a (conditional)-$Z$ rotation, which leads to a matrix $A$ with a negative entry. I don't think their proof of BQP-hardness would carry over when entries $A_{ij}$ are strictly non-negative, e.g. in $\\{0,1\\}$. Indeed, I believe that such a restricted matrix-powers problem may be amenable to some form of Stockmeyer approximation, e.g. in $\mathsf{AM}$, and hence not BQP-complete under the reasonable hypothesis that $\mathsf{BQP}\not\subseteq\mathsf{AM}$.

The proof of BQP-hardness of matrix powers appears initially to be similar to the BQP-hardness of the HHL algorithm, which was wonderfully summarized by @DaftWullie [here](https://quantumcomputing.stackexchange.com/questions/6615/showing-that-matrix-inversion-is-bqp-complete-hhl-algorithm). However, HHL considers the Taylor-series expansion of $A^{-1}$, where $A=I-Ue^{-1/T}$ and $U$ is a unitary operator which simulates a given unitary circuit with a clock register construction — so that $U$ (and powers of $U$) will have negative or complex entries, if any of the gates in the circuit do. For the case $\tilde A = U \mathrm{e}^{-1/T}$, this again suggests that the BQP-completeness of estimating entries of matrix powers $\tilde A^m$ is associated with whether $\tilde A$ has entries apart from non-negative reals.

Given this, considered as a special case of HHL which is motivated by the comparison to the problem of Janzing and Wocjan, I'd like to know: is HHL still BQP-complete if all of the entries of $A$ and $\lvert b \rangle$ are in $\\{0,1\\}$ ?

(Having said that, seeing how having entries of {0,1} for $A$ is still not the same as having {0,1} entries for $A^{-1}$ or a matrix $\tilde A$ whose powers you would like to learn about, I still think that having non-negative entries for $A$ itself is a bit of a red herring... once you take the inverse of $A$, negative entries can still arise, shedding no further light on the question quantum computational difficulty without destructive interference.)

I've made some changes. I think I understood your question better once I read it with a different emphasis, and I've tried to amplify that emphasis.

Thanks, could you edit the question to address your concerns? I’d like an answer to the question in the title...

I'd be willing to have a go at editing the question, if what you'd like is something specifically addressing the case where A and |𝑏⟩ have {0,1} entries, together with some remarks putting the question in context. As it stands, it still feels a bit as though you're asking one thing because you want to know the answer to something else.

So, you've added some commentary about the role of negative entries, but the main question (the title, the reasonable question towards the end) is still about {0,1} entries. Also: in your recent edit, it's not clear that the claim about $A = I - U\exp(-1/T)$ is what you intend to claim (do you mean $A^{-1}$ by chance?), or that the statement that you might like to make is correct (what about the special case where $U$ is constructed only from classical reversible gates?).

You're asking two different questions. The question about whether HHL is BQP-complete, if all the entries of A and |𝑏⟩ are in {0,1}, is clear enough. But you're never going to construct A = I - U exp(-1/T) and still have coefficients in {0,1}, so it's not clear how that construction could play any role. So, are you asking about the role of the minus sign in the construction, or are you asking about constraining the values of A?


Can you programatically check whether a given set of gates is universal?

I am wondering if there is an automated way to determine whether a given set of quantum operations is universal.

More precisely, given a set of 1 and 2 qubit gates, can we write a program to determine whether this constitutes a universal gate set? If so, how might we do this?

**EDIT:** To clarify I'm interested in both approaches which allow exact replacements (as shown below) and approaches which allow approximating any unitary to some finite precision. Perhaps restricting the problem by not allowing arbitrary rotations in the input gateset could make the problem more tractable I'm not sure.

If I was given a set of quantum gates I would try to use the gates I'm given to implement a well known universal gateset.

Take this artificial example...

\begin{equation} S_0 = \\{\text{H}, \text{Rx}(\alpha), \text{CZ}\\} \end{equation}

I know I can write any single qubit operation with $\\{\text{H}, \text{Rx}(\alpha)\\}$ as I can reach any point on the Bloch sphere with 3 parameterised rotations in 2 directions (I can implement $\text{Rz}$ in terms of $\text{H}$ and $\text{Rx}$).

From here it's well known that an arbitrary single qubit rotation along with a $\text{CX}$ gate is sufficient for universality and I can realise a $\text{CX}$ using a $\text{CZ}$ with Hadamards on the target qubit. Therefore the set $S_0$ is a universal gate set.

When I try to think of a way to automate this process of using the provided gates to implement a well known universal gateset I'm not sure where to start. It certainly seems like a hard problem.

I came across this paper, and I think this will be useful to you.

It might be an incomplete analogy but - we can't square the circle with a ruler and a compass; however, Archimedes taught us that we can get arbitrarily close, by inscribing and circumscribing polygons.  With that in mind, can the ruler and compass alone get arbitrarily close to any well-defined point on the plane?

i.e. you could restrict to a finite set of parameterised gates rather than doing general single qubit rotations.

Interesting. I would have guessed that just verifying that a gateset can apporximate any n qubit unitary would be easier than exactly recreating any gate. Why might the approximate version using a finite set be harder to tackle?

@DaftWullie . I suppose both cases are of interest to me. Is there a way to check if a gateset is approximately universal up to some $\epsilon$?

Thanks @Mark S. indeed this other post is relevant. I think I’d need to read around a bit more to understand the discussion

Are you asking specifically about the case where you can exactly recreate any gate you want (e.g. the gate sets you've mentioned) or would finite gate sets achieving the target gate with arbitrary accuracy also fall within your interest?

See this question and answer -cstheory.stackexchange.com/questions/11298/…